El Niño Southern Oscillation diversity in a changing climate

Transcription

1 El Niño Southern Oscillation diversity in a changing climate Chen Chen Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 26

2 c 26 Chen Chen All Rights Reserved

3 ABSTRACT El Niño Southern Oscillation diversity in a changing climate Chen Chen This thesis aims to improve the understanding of El Niño Southern Oscillation (ENSO) diversity, in its future change, modeling and predictability. How might ENSO change in the warming climate? To reach a comprehensive understanding, a set of empirical probabilistic diagnoses (EPD) is introduced to measure the ENSO behaviors as to tropical Pacific sea surface temperature (SST) climatology, annual cycle, ENSO amplitude, seasonal phase locking, diversity in peak location and propagation direction, as well as the El Niño-La Niña asymmetry in amplitude, duration and transition. This diagnosis is applied to the observations, and consistency with previous studies indicates it is valid. Analysis of 37 CMIP5 model simulations for the 2th century and the 2st century shows that, other than the projected increase in SST climatology, changes in other aspects are largely model dependent and generally within the range of natural variation. The change favoring eastward propagating El Niños is the most robust seen in the SST anomaly field. To what extent can we trust the future projection? CMIP5 models show large spreads in terms of 2th century ENSO performance. So a data-driven approach called Empirical Model Reduction (EMR) is carried out, by fitting a low-dimensional nonlinear model from the observation with a representation of memory effect and seasonality. The stochastic simulation of EMR is able to reproduce a realistic ENSO diversity statistics and a reasonable range of natural variation, thus provides an additional benchmark to evaluate the CMIP5 model biases. What are the key model components leading to a good performance to simulate and

4 predict ENSO? Using a suite of models under the aforementioned framework of EMR, control experiments are conducted to advance the understanding of ENSO diversity, nonlinearity, seasonality and the memory effects. Nonlinearity is found necessary to reproduce the ENSO diversity features by simulating the extreme El Niños. Nonlinear models reconstruct the skewed distribution of SST anomalies and improve the prediction of the El Niño-La Niña transition. Models with periodic terms reproduce the SST seasonal phase locking but do not improve the prediction appreciably. Models representing the ENSO memory effect, based on either the recharge oscillator (multivariate model with tropical Pacific subsurface information) or the time-delayed oscillator (multilevel model with SST history information), both improve the prediction skill dramatically. Models with multiple ingredients capture several ENSO characteristics simultaneously and exhibit overall better prediction skill. In particular, models with a memory effect show an alleviated skill drop during the spring barrier and a reduced prediction timing delay. One new ENSO prediction target is to predict not only the occurrence and amplitude of El Niño (EN) but also the peak location is at the central Pacific (CP) or the eastern Pacific (EP). Many prediction models have difficulty with it, which motivates the investigation on whether such ENSO diversity has intrinsically limited predictability. Here three aspects are addressed including the source/limit of predictability, time range and uncertainty. Approaches are combined including linear inverse modeling, singular vector analysis and probabilistic measure. The results show that two similar initial conditions with western Pacific SST warming anomalies may finally develop to either CPEN or EPEN. The equatorial Pacific subsurface evolution is important to tell the final outcome. Restricted by the chaotic property, the prediction horizon appears to be 4 months before CPEN and 7 months before EPEN. A flavor prediction model using data s transition probabilities is introduced as a new benchmark for probabilistic prediction.

5 TABLE OF CONTENTS List of Tables List of Figures Acknowledgments Dedication v vii xix xx Introduction Assessing ENSO behavior variations in a changing climate 7. Introduction Data Observations, GFDL CM2., EMR CMIP Methods: empirical probabilistic diagnosis Definition of ENSO states Seasonal occurrence probabilities State transition probabilities A set of indices for ENSO behaviors Natural variation of ENSO behaviors in EMR ENSO behavior performance in GFDL CM2. PI Results: future projections using 37 CMIP5 models SST climatology and anomaly SST annual cycle and seasonality ENSO diversity in peak location ENSO diversity in propagation direction i

6 .4.5 ENSO asymmetry in amplitude, duration and transition Case study using GFDL ESMs Discussion CMIP5 model rating on ENSO performance Uncertainty of projected changes Conclusion Diversity, nonlinearity, seasonality and memory effect in ENSO simulation and prediction 4 2. Introduction Data GFDL CM2. PI Comparison with observations Methods: empirical model reduction Baseline model Model with nonlinearity Model with seasonality Model with memory effect Modeling experiments Model goodness of fit Results of ENSO simulation Nonlinearity: El Niño-La Niña asymmetry Diversity: moderate and extreme El Niño Seasonality: phase locking Seasonal memory: lagged correlation Results of ENSO prediction Performance for El Niño (PC) and El Niño-La Niña transition (PC2) Skill drop due to spring barrier and autumn barrier ii

7 2.6.3 Timing delay: target month slippage ENSO Diversity performance measured in PC-PC Summary Discussion Nonlinearity: pros, cons, future direction Seasonality: not directly indicating predictability Memory effect: recharge oscillator vs time-delayed oscillator Seasonal barrier: memory refill, noises Target month slippage: lack of growth from recharge mechanism ENSO diversity: nonlinearity, future direction Transferring from GFDL CM2. to nature Conclusion Predictability of ENSO flavors: prediction horizon, optimal precursors and probabilistic measures Introduction Data Observed records Simulated records El Niño evolutions in observation and simulation Pinpointing the prediction horizon Questions Projecting patterns onto EOF basis Categorizing ENSO states Distinguishing EPEN/CPEN evolution Identifying optimal precursors for EPEN and CPEN Questions Linear inverse modeling (LIM) Singular vector analysis iii

8 3.4.4 SST amplification and sensitivity to data length Optimal initial pattens for EP/CP flavors Assigning a likelihood for flavor prediction Questions A probabilistic benchmark using state transition probabilities Transition diagram Likelihood map Discussion Implications for ENSO prediction in nature ENSO predictability and underlying dynamics Conclusion Conclusions 97 Bibliography iv

9 LIST OF TABLES. List of 37 CMIP5 models analyzed in this study. Due to the lack of availability in certain models for temperature of ocean surface tos, we instead analyzed monthly surface temperature ts in each model s rip run. st column is the official model name. 2nd column is the length of pre-industrial control run (year). 3rd to 5th columns are the model rank as shown in each individual figure and panel, e.g., f8b indicating Fig..8 panel b. According ENSO aspect is labelled in 2nd and 3rd rows. Note that for individual ENSO behavior models with * are models with smallest error between each model s 2th century run (orange o) and the 2th century observation value (black line in the panel). The last column is the total number of * for each model. There are best models with 5 and above *, which are indicated with + at the end the model name in st column. Note that these relative better models are only restricted to ENSO behavior aspects analyzed in this study, therefore, it is not generally applicable to model performances on other phenomena. Model center information and experiment designs see Taylor et al. (22) and CMIP5 website ( 27 v

10 2. List of ENSO empirical models with different model settings. L(m) is a linear model in the form of Eq. 2. without quadratic terms, constructed from a state vector of the leading m PCs of tropical Pacific SSTA; m=3 and 8 are presented. M(k) is the linear model constructed from a multivariate state vector of the leading 3 PCs of tropical Pacific SSTA and the leading n PCs of tropical Pacific 2 o C isotherm depth (Z2) anomalies; k=3+n with n=5 and presented here. 2L/5L is a multilevel linear model with 2/5 time levels and 3 SST PCs. NL denote the nonlinear models with quadratic terms. 2L+NL is a combined model with quadratic nonlinearity in the main level and linear terms in the one additional time level. S is the seasonal model with additional periodic terms. S+NL, 2L+S, and 2L+S+NL are combined models including seasonality. 2L+S+NL is the most comprehensive model of the 2 models studied here. Coeff# denotes the total number of coefficients in the design matrix. Coefficients in the noise covariance matrix are not included. Condition # denotes the condition number of design matrix for each level. See appendix of Kravtsov et al. (25) for more details vi

11 LIST OF FIGURES. The first three normalized EOF patterns of Tropical Pacific SSTA in OBS (87-present monthly HadISST v.) (a, c, e) and GCM (4- year monthly GFDL CM2. pre-industrial control run) (b, d, f). Positive/negative values are shown in solid/dashed contours. The zero value is highlighted in the thick solid contour Simulation evaluation: yearly running averaged time series of tropical Pacific SSTA PC in OBS (a), year -4 of 4 year EMR simulation fit from OBS (b and c) and year -4 of 4 year GFDL CM2. GCM simulation (d and e). All PCs are normalized to have standard deviation equal to one. Decimal logarithm of the bivariate probability density function (2dPDF) in PC-PC2 space in OBS (f), 4 year EMR (g) and 4-year GCM (h) Definition of 3 ENSO states (a) (El Niño/La Niña and neutral patterns, denoted as EN/LN/NEU) and 5 ENSO states (b) (Eastern/Central Pacific El Niño/La Niña and neutral patterns, denoted as EPEN/ CPEN/ EPLN/ CPLN/ NEU) are shown using smoothed monthly PCs from 87- present HadiSST v.. ±.7 s.d. (PC), where s.d. is one standard deviation, is used to distinguish EN/LN from NEU. Zero line of PC2 is used to distinguish EP/CP states. Averaged patterns for each ENSO flavor CPLN (c)/epln (e)/cpen(d)/epen(f) are shown. Each state is assigned a color code for further analysis vii

12 .4 Monthly occurrence probabilities for 3 ENSO states (a,b,c) and 5 ENSO state (d,e,f) in OBS (a,d), EMR (b,e) and GFDL CM2. GCM (c,f) are shown. Stacked bars along the vertical coordinate are the occurrence probabilities of each color-coded state. The horizontal coordinate is the calendar month from Jan to Dec. Full year data is used thus the sample size for each calendar month is equal. In panel a, higher probability of EN/LN in winter months than summer months indicates observed ENSO s winter phase locking. In panel d, higher probability of EPEN over CPEN indicates El Niño favor peaking in EP, and higher probability of CPLN over EPLN indicates LN favor peaking in CP State transition probabilities for LN (st row), NEU (2nd row) and EN (3rd row) in OBS (first column), EMR (2nd column) and GFDL CM2. GCM (3rd column) are shown. The horizontal coordinate represents the transition from the past (-3 years) to the future (+3 years) in monthly intervals, with zero indicating the current state. Taking GCM EN transition (panel i) for example, bars along the vertical coordinate at + year (+2 months) represent: the self-transition probability P EN EN (upper bar), the P EN NEU (middle bar) and the opposite-sign transition P EN LN (lower bar). The decaying of P EN EN as function of lead time indicates EN s duration. The discrepancy between P EN LN (lead< side) and P EN LN (lead> side) indicates the EN-LN asymmetry in transition. The transition probabilities generally converge to the climatology, i.e., the nonseasonal occurrence probability of each state (dotted line in each panel) viii

13 .6 Same as Fig..5, but for transition probabilities of 5 ENSO states. Taking GFDL CM2. GCM CPEN transition (panel l) for example, bars along the vertical coordinate at +6 months represent: st is P CP EN EP EN, 2nd is P CP EN CP EN, 3rd is P CP EN NEU, 4th is P CP EN EP LN, 5th is P CP EN CP LN. The discrepancy between P CP EN EP EN (lead< side) and P CP EN EP EN (lead> side) indicates the zonal propagation asymmetry. Note that zonal propagation asymmetry is best measured between -6 months while the EN-LN transition asymmetry is best measured between -2 years Variation of ENSO behaviors in 4-year EMR and GFDL CM2. GCM simulation. Each index (see text for definitions) is calculated in - year overlapping epochs years apart. The probability density function (PDF) is shown in the blue curve. Index values in epochs of OBS are shown in magenta lines (five in total). ENSO diversity indices, including I sea, I cp/ep, I e/w, are shown in the top rows for El Niño and La Niña. EN- LN asymmetry indices, including I amp, I dur, I tra are shown in the bottom row. For each panel, the percentage of epochs in the EMR satisfying the specified index range is shown. Taking panel b for example, OBS have more EPEN than CPEN (I cp/ep < ). Among 39 -year epochs in EMR, 9% of epochs have more EPEN than CPEN ix

14 .8 Niño-3.4 SST climatology and anomaly in the 2th century (2C, historical run, 9-999) and the 2st century (2C, RCP8.5 scenario, 2-299) in 37 CMIP5 models that participated in IPCC AR5. (a) The 2-year running average Niño-3.4 SST with OBS in black, CMIP5 models in gray, GFDL ESM2G in red, GFDL ESM2M in green. (b) The mean SST in the 2C and 2C for each CMIP5 model. The models are sorted according to the -year averaged Niño-3.4 SST in the 2C runs. The black vertical line marks the 2C OBS value. Multi-model mean (MMM) is shown at the top, 2C in orange and 2C in blue. Pre-industrial control simulations of each model are divided into -year sliding epochs to calculate the -year averaged SST and the percentile of the distribution are shown as gray horizontal lines. The number of models with decreased/ increased change is indicated in a number with < / >. (c) Niño 3.4 SST anomaly time series from 9 to 299. (d) The standard deviation of SSTA in pre-industrial, 2C and 2C runs. In addition here the 2C results with an increased change are shown filled and those with decreased values are unfilled. Meanwhile, the 2.5, 5, 97.5 percentile range estimated from the distribution in the EMR simulation is shown in brown line at the bottom x

15 .9 Annual cycle and ENSO seasonality change from 2th century (2C) to 2st century (2C) in 37 CMIP5 models: (a) The 2C seasonal cycle of Niño-3.4 SST, with OBS in black, CMIP5 models in gray, GFDL ESM2G in red, GFDL ESM2M in green. The horizontal axis shows the calendar month. (b) The Niño- 3.4 SST difference between the March-August (summer half year) average and the September-February (winter half year) average. The models are sorted according to the 2C value of this difference. (c) 2C occurrence probability of El Niño P EN, (e) 2C occurrence probability of La Niña P LN. (d) seasonality index of El Niño (I season EN ) defined using summer half year averaged P EN divided by winter half year averaged P EN, thus I season EN < indicates El Niño in a given -year epoch prefers winter phase locking. (f) I season LN, defined the same way, but for La Niña event ENSO peaking location and propagation direction in the 2th century (2C) and 2st century (2C) in 37 CMIP5 models. (a) The location diversity index I cp/ep for EN, defined as P CP EN divided by P EP EN. (c) I cp/ep for LN. I cp/ep > indicates El Niños or La Niñas preferentially peak in CP. (b) The propagation diversity index I e/w for EN defined as P CP EN EP EN minus P CP EN EP EN. (d) I e/w for La Niña. I e/w > indicates El Niños or La Niñas prefer eastward propagation EN-LN asymmetry in the 2th century (2C) and 2st century (2C) in 37 CMIP5 models. (a) the skewness of Niño-3.4 SSTA. (b) The amplitude asymmetry index (I amp ) defined as EN amplitude divided by LN amplitude. I amp > indicates El Niños have larger amplitude than La Niñas in a given -year epoch. (c) the duration asymmetry index (I dur ) defined as P EN EN divided by P LN LN. I dur < indicates La Niñas are more persistent than El Niños. (d) the transition asymmetry index (I tra ) defined as P EN LN minus P EN LN. I tra > indicates El Niños are quickly followed by La Niñas but not vice versa xi

16 .2 Summary of ENSO behaviors in the 2th century and the 2st century using all 37 CMIP5 models (a37, blue), overall best models (b, yellow) and best models for individual aspect of behavior (c, red). The 2th century observation (obs, black) results are shown as a reference. A 4-year stochastically forced simulation of EMR model fit from the observation provides the natural variation range (the percentile range is shown). In each panel, a pair of numbers indicate the degree of model agreement. The left one is the number of models showing a decrease from the 2th century to the 2st century while the right one is the number of models showing an increase xii

17 2. Comparison of ENSO statistics in SST observations (87-23) and GFDL CM2.. In the st and 4th row only HadiSSTv. results are shown. In 2nd and 3rd rows, four observation datasets are color-coded: HadiS- STv. (black), COBEv2 (green), ERSSTv3b (blue) and Kaplan (red). The 4-year pre-industrial run of GFDL CM2. is divided into 2 mutually exclusive 2-year segments for calculations in the 2nd and 3rd rows. Each segment is in gray and averaged result is in black. st row: Empirical Orthogonal Functions EOF and EOF2 of tropical Pacific SST anomalies. Shading is regression coefficient of tropical Pacific SST anomalies on principal component PC and PC2. Contour is the percentage of explained variance of PC and PC2. 2nd row: ENSO asymmetry and nonlinearity represented in the probability density functions (PDF) of PC and PC2. The skewness averaged among four observation datasets (SKm) is shown. For GFDL CM2. 2-segment averaged skewness is shown. 3rd row: ENSO seasonality is represented in standard deviation (STD) varying as to each calendar month. 4th row: ENSO memory and seasonal break of persistence are represented in lagged correlation coefficient (Corrcoeff). The x-axis is the initial calendar month, y-axis is the lag month Goodness of fit measures are shown for all models in Table 2.. a) and b) are the residual standard deviation (STD) of the two leading PCs of tropical Pacific SSTA. c) and d) are the residual skewness. Models are displayed in three groups: models without memory effect, models with multivariate (SST and Z2) memory, and models with multilevel memory. The total number of model coefficients is given at the bottom. Each model carries its own color code. Error bars (one standard deviation) indicate the spread of the fit among 2-year training segments. Small residual STD and residual skewness close to zero indicate a good fit xiii

18 2.3 a) log of the 2-dimensional PDF [log (2dPDF)] of the two leading SSTA PCs in OBS. The grid cell size is.267x.267. b) as in a) but for GCM, the training data. c)-j) as in a) but for eight models in Table 2., based on -year stochastically forced simulations in each case. Linear models are grouped in the first column and nonlinear models in second column. A good simulation of ENSO nonlinearity is indicated by resemblance to the curved pattern and the PDF value distribution of the GCM data in panel b) Lagged autocorrelation coefficients for each calendar month. a) and h) are the average of 2 2-year segments from the GCM data (GFDL CM2.). The other panels show model results calculated by averaging over 2 2- year stochastically forced simulations. The 6 models shown are described in Table 2.. Every second calendar month is labelled Prediction performance: correlation coefficients for PC and PC2 of SSTA. For each model in Table 2., 2-member ensemble forecasts are carried out for 2 years that are out-of-sample (i.e distinct from the data used to construct the models). Correlations are between the data and the ensemble average. a), b) Forecast correlations at leads of to 2 months. Persistence (black line) is given as a reference. c), d) Correlations of 2- month lead forecasts. Error bars are created by dividing the forecasts into non-overlapping segments of 2 years each and showing the standard deviation. For PC, models with or without memory effect are grouped separately, while for PC2, linear and nonlinear models are grouped separately. The dashed line is the correlation coefficient for the benchmark model, L(3) xiv

19 2.6 Prediction performance: seasonal variations and the boreal spring and autumn barriers. a), c) For all models in Table 2., the correlation coefficient between the GCM target time series and 6-month predictions initialized at each calendar month. Persistence is shown in black. Note that seasonal barrier exists for PC when initialized from boreal spring (e.g., March) and for PC2 when initialized from boreal autumn (e.g., September). c) PC 6-month lead prediction initialized in March. Models with or without a memory effect are grouped separately. d) PC2 6-month lead prediction initialized in September. Linear and nonlinear models are grouped separately. See Fig. 2.5 for additional descriptions Prediction performance for PC and PC2 of each target calendar month, for six models in Table 2.. Correlation coefficient (Corrcoeff) between - 2 month lead predicted time series and the target time series according to each calendar month. The result shown is averaged among 2- year prediction segments. Calendar months are labelled as F(February), A(April), J(June), A(August) and O(October). Good prediction skill is indicated by retaining large Corrcoeff toward 2-month lead prediction as well as having a small seasonal skill drop Prediction performance: slippage, measured by the correlation coefficients between -2 month lead predictions and -2 to 2 month lagged target GCM data. Panels c) to n) show results for 6 of the models in Table 2.. Persistence, shown in the top panels as a reference, necessarily has an τ-month lag to the target month for an τ-month lead prediction. Good prediction performance is indicated by large correlation coefficients for the target month; i.e. along the vertical line at zero lag. Less slippage is indicated by reduced tilt with time of the maximum correlation coefficient. See Fig. 2.5 for additional descriptions of prediction methodology xv

20 2.9 Prediction performance: slippage, defined as the lag which has the maximum correlation coefficient. Good prediction performance is indicated by fewer month of slippage. a), b) The slippage for -2 month lead predictions for each model in Table 2.. Persistence, shown as reference, necessarily has a slippage of τ months for an τ-month lead prediction. c), d) Slippage for 6-month lead predictions. See Fig. 2.5 for additional descriptions of prediction methodology Prediction performance: ENSO diversity. Prediction skill is measured here by the Euclidean distance D 2 between the predicted and GCM target PC-PC2 pairs. The space is divided into grid cells and D 2 is averaged according to the target PC-PC2 grid cell. The grid cell size is.33 for PC and.3 for PC2. Persistence is shown on the first row as a reference. Prediction results are shown for 3, 6 and 2 -month leads. Good predictions of ENSO diversity are indicated by small D 2 in a greater number of grid cells and for longer leads. See Fig. 2.5 for additional descriptions of prediction methodology Influence of an energy conserving constraint on the four nonlinear models in Table 2.. Models without a constraint are grouped in column 2-4 and models with the constraint are grouped in the last four columns. The constrained models carry the same color code as the unconstrained versions, but with a c subscript. The quality of the model simulations is measured by skewness in a) and b); the GCM data skewness to be simulated is shown in the first column. Skewness is chosen because it depends on nonlinearity. Prediction performance, as measured by the correlation coefficient for 2 month forecasts is shown in panels c) and d). See Fig. 2.5 for additional descriptions of prediction methodology xvi

21 3. Panels (a,c,e,g) show 2-month SSTA evolution during CPEN event using the HadISST V. record. Panels (b,d,f,h) show SSTA evolution during EPEN event. Though these two events show similar initial warming their later evolutions are different Panels (a,c,e,g) show 2-month of SSTA evolution during a CPEN event in GFDL CM2. control simulation. Panels (b,d,f,h) show SSTA evolution during a EPEN event. Though these two events show similar initial warming but their later evolutions are different Panels (a,b) are the leading two EOFs of tropical Pacific SST. Panel c shows the definition of the 5 ENSO states in PC, PC2 space. Each state carries the same color code throughout this study year CM2. data is divided into epochs 5-years long. Precursors of EPEN and CPEN are tracked to 5 months before to illustrate when the tracks become distinguishable, suggesting a prediction horizon For 5-year long epochs, two growing modes contribute to SST amplification. The two modes allow for ENSO diversity Signal to noise ratio of leading growing mode is analyzed to measure the model robustness among epochs. 2mG indicates G(2), the transition across a 2 month interval (a, b) optimal initial pattern in SST for EPEN and CPEN, respectively. (b,d) are for the associated Tsub. Magenta curve is the 28 o C isotherm, and the red curve is the 2 o C isotherm. Units are o C The EPEN and CPEN are distinguishable at 6 month leads, with different surface and subsurface patterns Variation of the diagnosed OIP for SST in five different epochs. -epoch averaged OIPs are shown in a/b panel similar to Fig. 3.7, but for 2 month lead. OIPs look similar for EPEN and CPEN at 2 month lead Transition probability based on the definition of 5 ENSO states in Fig xvii

22 3. a,b,c show the most-likely state to come. Associated probability measures are shown in the same column xviii

23 ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor Prof. Mark A. Cane, who introduced me into the field of El Niño and spent vast amount of time and effort to provide extraordinary guidance and strong support throughout these years. Great thanks also go to my committee members Dr. Dake Chen, Prof. Mingfang Ting, Prof. Arnold L. Gordon as well as many other faculty and scientists at LDEO, who unselfishly shared with me their great insights and are exemplary role models. I am very grateful to Dr. Andrew T. Wittenberg from NOAA/GFDL, who is a wonderful collaborator/mentor providing me with valuable suggestions during our collaboration and giving me much academic advice. I also acknowledge the MURI project and especially thank Dr. Michael K. Tippett from IRI for leading the LDEO team on this project and providing continued support for my research. I greatly appreciate the collaboration with Dr. Dmitri Kondrashov and Dr. Mickaël D. Chekroun from UCLA, who introduced the new modeling approach to us and provided many useful suggestions. I have enjoyed working together with Dr. Naomi Henderson, Dr. Dong Eun Lee and Dr. David Chapman; I sincerely thank all the help and support they have given me. I also thank administrative assistant Ms Virginia DiBlasi for her kind assistance. I would like to thank many peer friends at LDEO, with whom the interesting conversations add a lot of fun and laughter to my everyday life. Last but not least I would like to convey my deepest gratitude to my parents and my husband for their unconditional love and encouragement. Thank everyone, without you this dissertation would not have been possible. xix

24 To my family xx

25 INTRODUCTION This introduction serves the purpose to overview the background of the thesis and summarize main questions and approaches for each chapter. Background El Niño-Southern Oscillation (ENSO), often depicted as the inter-annual sea surface temperature (SST) warming anomalies at the tropical Pacific, has significant impacts on the global hydrological cycle. Therefore, ENSO has been extensively investigated for over 3 years. Numerous studies have contributed to the advancement of ENSO research. Working groups and initiatives have played important roles to orientate and integrate the research efforts to important and urgent questions in this field. e.g., 2 international workshop on New strategies for evaluating ENSO processes in climate models, 23 US CLIVAR working group on ENSO diversity, 25 workshop on ENSO extremes and diversity, and a new international CLIVAR research focus initiative on ENSO in a changing climate. This thesis is aimed to join the ENSO community to tackle new challenges. It combines the data analysis, diagnosis, modeling and prediction experiments, with the main theme of ENSO diversity in a changing climate. Main topics This thesis focuses to improve the understanding of ENSO diversity, advance modeling and prediction, as well as to better assess ENSO s future change. Chapter assesses the ENSO behavior change in a warming climate via a new set of empirical probabilistic diagnosis. Chapter 2 focuses on understanding ENSO diversity, nonlinearity, seasonality and

26 memory effect in ENSO simulation and prediction. Chapter 3 investigates the predictability of different El Niño flavors, as to prediction horizon, optimal precursors and probabilistic forecasts. Motivations Chapter : Future change One main direction of ENSO research is its future change (Collins et al. 2; Cai et al. 25). The earth system could be viewed as a dissipative natural heat engine forced by various radiative forcings. The processes of heat absorption and dissipation are efficiently carried out via global scale atmospheric and oceanic circulation. Besides this, a series of regional modulators, commonly known as climate variabilities (e.g., ENSO), form naturally and largely dominate the interannual to decadal variation of SST, precipitation, etc. In the global warming scenario, responses of the earth system could be reflected by changes in varying temporal and spatial scales (Xie et al. 25). ENSO, as an important modulator to redistribute the heat anomaly, may experience changes along with the changing mean state of the climate. The change may be not just in its amplitude but also in various aspects of ENSO behavior and characteristics. Therefore, it is necessary to investigate how ENSO may adapt in the changing climate. This question motivates chapter of the thesis. Chapter 2: Modeling Models have developed from simplified analytical model, low-dimensional empirical model, to fully coupled global circulation model, even the all-in-one earth system model. Varying construction details make it difficult to pinpoint the biases in model dynamics. In ENSO modeling the aim is to mimic the dynamics of the ENSO system. So a feasible common ground to understand various model dynamics is to characterize them according to components of ENSO dynamics, including the recharge oscillation mechanism (i.e. memory effect), nonlinearity and seasonality. When comparing ENSO 2

27 prediction skills of varying models, we may then attribute the difference in skill to the difference in model s ability to reproduce three aspects of ENSO dynamics. This motivates chapter 2 of the thesis. Chapter 3: Predictability After three decades since the experimental ENSO forecast by Cane et al. (986), current ENSO prediction is expanding in two directions. First one is extending to decadal prediction, which is not optimistic due to the intrinsic limit of ENSO modulation (Wittenberg et al. 24). The other direction is to predict ENSO diversity. One important diversity feature is that El Niños (EN) show two flavors peaking at the central Pacific (CP) or the eastern Pacific (EP) with different global impacts (Larkin and Harrison 25; Ashok et al.27; Weng et al. 27). Therefore one new target is to predict not only the amplitude of the ENSO variability but also its correct peak location. However, the real-time predictions still show some difficulties. Along with more CPEN appearing in the last decade (Lee and McPhaden 2), the prediction skills of most models drop (Barnston et al. 22), and dynamical models with advanced data assimilation like CFSv2 and NMME have the systematic tendency to predict a CPEN as an EPEN (Xue et al. 23; Kirtman et al. 24). To find out the key to the problem, it is necessary to investigate the predictability, i.e., to what degree EP/CP El Niño flavors are intrinsically predictable? This question motivates chapter 3 of the thesis. Main questions Chapter We introduce a new set of diagnostics to investigate the projected changes as to the following ENSO characteristics and behaviors: Whether ENSO amplitude may increase along with the warming SST climatology? Whether the SST annual cycle and seasonal phase locking (e.g., Tziperman et al. 995) features may shift into other seasons? El Niños peak at central Pacific or eastern Pacific (e.g., Kao and Yu 29). Whether CPEN may become more frequent than EPEN, as suggested by Yeh et al. (29) or not? El Niños propagate eastward or westward (e.g., McPhaden and Zhang 29). Whether El 3

28 Niños may favor one propagation direction in the future? ENSO asymmetry exists in amplitude, duration and transition. El Niños often have larger amplitude than La Niñas, La Niñas are more durable than El Niños and La Niñas often tightly follow extreme El Niños but not vice versa (e.g., Choi et al. 23). Whether these asymmetry features may change? Are the CMIP5 models able to represent realistic ENSO behaviors in the 2th century (2C) and thus reliable to project for 2C? How to measure the model performance and pick out a subset of good models? Which aspects of ENSO behaviors are the most prone to change in the future? Do most model projections agree on these aspects? For each ENSO behavior, what is the possibility that the projected change may be part of the natural variability? Chapter 2 Recharge oscillation mechanism (i.e. memory effect), nonlinearity and seasonality are generally viewed as main components of ENSO dynamics. How to implement each component into a model? Here we use a data-driven modeling procedure, empirical model reduction (Kondrashov et al. 25) as an example. How to understand the relation between two different ways to represent a memory effect of the ENSO dynamics in the model? What is the most important component of the model to reproduce the El Niño-La Niña asymmetry feature (e.g., Choi et al. 23) as well as the ENSO diversity feature, e.g., ENSO flavors with moderate/extreme amplitude (Takahashi et al. 2)? Does a linear model such as Newman et al. (2b) work, or is nonlinearity necessary? What is the role of each component in the model to provide the predictability? i.e., could the prediction skill be improved once that component be implemented? How to maximize the model performance to predict the ENSO diversity? How to measure the skill? Which component in the model is important to cope with the prediction issues, e.g., seasonal skill drop during boreal spring and prediction timing delay (e.g., Tippett et al. 22; Barnston et al. 22; 23; Xue et al. 23)? 4

29 Chapter 3 CPEN and EPEN flavors may both originate from similar initial patterns with SST warming anomaly at the equatorial western Pacific. How far in advance can EPEN and CPEN flavors become distinguishable? What constrains the long-term predictability of different El Niño flavors? Which El Niño flavor is more difficult to predict? What are the main physical processes contributing to the development of El Niño flavors? What is the role of the equatorial subsurface process as to the final outcome of the flavor? What do the optimal precursors for EPEN and CPEN look like? To what degree does the short length of data influence diagnosing the optimal patterns? ENSO flavor prediction is intrinsically a probabilistic question, so a probabilistic forecast is necessary. Since systematic biases in ensemble dynamical prediction may give a biased distribution for probabilistic forecasts, does a benchmark using the data s transition probabilities work? Main approaches Chapter Definition of ENSO diversity categorize 5 ENSO states using tropical Pacific SST PC-PC2 space, including EPEN, CPEN, neutral state, EPLN, CPLN. Empirical probabilistic diagnostics introduce a new set of diagnosis to measure the statistics for SST mean climatology, annual cycle, amplitude of ENSO, the seasonal phase locking, diversity in peak location and propagation direction, as well as the El Niño-La Niña asymmetry in amplitude, duration and transition. CMIP5 Model projection analyze ENSO behaviors using 37 models in Climate Model Intercomparison Project phase 5 (CMIP5) (Taylor et al. 22): historical simulations from 85 to at least 25 using realistic natural and anthropogenic forcing, and representative concentrating pathway 8.5 simulations from the end of the historical runs to 2 when the radiative forcing reaches 8.5W m 2. Estimate the natural variation of ENSO behaviors two approaches are used. One is using long simulations of coupled models with fixed external forcing (e.g., pre- 5

30 industrial control simulation of GFDL CM2. and other CMIP5 models). The other one is using long stochastically forced simulations from a data-driven model (Empirical Model Reduction, Kondrashov et al. 25). Chapter 2 A data-driven modeling framework Empirical Model Reduction (EMR) (Kravtsov et al. 25; Kondrashov et al. 25; Kondrashov et al. 25) is among the competitive forecast models. This EMR framework allows model settings to include additional nonlinear (quadratic) terms, periodic terms and multilevel predictors. Simulation experiment A series of models are constructed in control groups, e.g., with/without nonlinearity, with/without seasonality, with/without memory, multivariate or multilevel approach. Stochastic simulations of individual model are compared to evaluate each model s ability to reproduce ENSO characteristics, in which process we could identify the role of nonlinearity, seasonality and memory effect. Prediction experiment ensemble prediction experiments are conducted to evaluate the overall prediction performance, as well as the ability to cope with spring barrier, reduce timing delay, and predict ENSO diversity. Chapter 3 Predictability diagnostics Linear inverse modeling and singular vector analysis (e.g., Blumenthal 99; Penland and Sardeshmukh 995; Xue et al. 997; Newman et al. 2b) are carried out to reconstruct the SSTA amplification process and identify the optimal initial patterns for EPEN and CPEN. Sensitivity tests on data length are also conducted. A prediction horizon is also estimated. Probabilistic forecast Introduce a new probability benchmark using the data s transition probabilities. An experimental forecast for ENSO flavor is also carried out. 6

31 CHAPTER Assessing ENSO behavior variations in a changing climate. Introduction ENSO behaviors in observations and models have shown rich diversity and asymmetry. The phase locking of ENSO peaks with the end of the calendar year has been found to be the outcome of several feedbacks and is subject to change when these competing influences change (e.g., Tziperman et al. 995, 997, 998; Neelin et al. 2; An and Wang 2; Xiao and Mechoso 29). El Niños can peak at both the eastern Pacific (EP) and the central Pacific (CP) (e.g., Larkin and Harrison 25; Ashok et al. 27; Weng et al. 27; Kao and Yu 29; Kug et al. 29; Taschetto and England 29; Newman et al. 2; Takahashi et al. 2; Karnauskas 23; Capotondi et al. 25). Extreme El Niños propagate eastward while moderate El Niños and La Niñas tend to propagate westward (Fedorov and Philander 2; McPhaden and Zhang 29; Lengaigne and Vecchi 2; Santoso et al. 23; Kim and Cai 24). Asymmetries between El Niño and La Niña have also been documented, e.g., El Niños often have larger amplitude than La Niñas, La Niñas are more durable than El Niños and La Niñas often tightly follow extreme El Niños but not vice versa (Kang and Kug 22; Larkin et al. 22; An and Jin 24; Schopf and Burgman 26; Ohba and Ueda 29; Frauen and Dommenget 2; Okumura et al. 2; Choi et al. 23; Dommenget et al. 23). ENSO diversity and asymmetry call for an analysis framework with comprehensive metrics. In this study, we introduce a set of empirical diagnostics for ENSO behavior with two considerations. The first is to make the dia=gnostics efficient by carrying out calculations under one framework. The second is to provide a probabilistic view on the ENSO behaviors by defining probability-based metrics. These diagnostics are first applied to observed SST data. That the results are consistent with previous studies indicate this new diagnostic framework is valid and reliable. We then present applications using these 7

32 diagnostics. ENSO varies from century to century, not only in amplitude and frequency but also in its diversity and asymmetry characteristics. Wittenberg (29) showed that, in a 2-year pre-industrial control simulation of the GFDL CM2. model, ENSO amplitude (e.g., the Niño 3 SST anomaly) could change dramatically in different epochs. Lee and McPhaden (2) suggested Central Pacific El Niño (CPEN) is more frequent after 2 and Yeh et al. (29) suggested CPENs are potentially more likely to dominate in a warming climate. However, Yeh et al. s (2) analysis of a 42 year control simulation of the Kiel Climate model illustrated that the increase in CPEN during recent decades could be due to natural variability rather than a forced response. A similar conclusion was reached in Newman et al. (2b) by analyzing a long stochastic-forced simulation of a linear inverse model (LIM). Nature only provides one realization, thus the limited record of SST observations is an obstacle to investigate the variation of ENSO behavior on a century scale. Therefore, long simulations of coupled intermediate models like the Zebiak-Cane model (ZC; Zebiak and Cane 987) and fully coupled general circulation models (GCM) with fixed external forcing were often used to investigate the natural variation of ENSO (e.g., Cane et al. 995; Wittenberg 29; Yeh et al. 2). However, since every coupled model has its own ENSO behavior that is to some extent biased away from the current climate, the natural variation of ENSO estimated by an individual GCM may be model-dependent. Long stochastically forced simulations from a data-driven model offer an alternative approach. The model dynamics are fit from the observations thus assuring that at least some of the statistics and features of the simulated ENSO resemble the observed ENSO closely. In this study, we investigate ENSO seasonality, diversity and nonlinear features like El Niño-La Niña (EN-LN) asymmetry. We apply a relatively new data-driven model, empirical model reduction (EMR) (e.g, Kravtsov et al. 25; Kondrashov et al. 25, 25; Chen et al. 25), which allows for ENSO nonlinearity, seasonality and a memory effect for prior times, and is competitive among empirical models for ENSO real-time 8

33 prediction (Barnston et al. 22). After generating a 4-year stochastically-forced simulation with an EMR model fit from the observed SST anomaly field, we apply the empirical probability diagnostics to assess a broad set of ENSO behaviors. The results will show that EMR provides a reasonably realistic simulated ENSO variation. State-of-the-art coupled GCMs are the main advanced tools to project future climate change (e.g., Capotondi et al. 26; Guilyardi et al. 23, 29, 22; Yu and Kim 2; Stevenson et al. 22; Ham and Kug 22, 24; Kim and Yu 22; Bellenger et al. 23; Taschetto et al. 24). In this study, we analyze a 4-year pre-industrial simulation from the GFDL CM2. coupled GCM (Delworth et al. 26) as one example. We seek to better assess model performance by using the aforementioned 4-year data-driven model simulation as an extension of the observed record and a benchmark to evaluate GCMs. We further analyze 37 Climate Model Intercomparison Project phase 5 (CMIP5) models in order to see if the models suggest that ENSO behavior will change significantly in the 2st century. We will also address several evaluation questions: Are the CMIP5 models able to represent realistic ENSO behavior in the 2th century (2C) and thus reliable to project 2C? Which aspects of the 2C projections do models agree on?.2 Data.2. Observations, GFDL CM2., EMR The 87-present monthly HadISST v. (Rayner et al. 23) and 85-present monthly COBE v2 (Hirahara et al. 24) datasets have relatively high spatial resolution ( ) and capture the diversity of ENSO behaviors. The results using COBE are overall consistent with HadISST, so only the HadISST results, referred to as OBS, are shown hereafter. We analyze a 4-year monthly control simulation from the GFDL CM2. coupled GCM (Delworth et al. 26) with the forcings, including solar irradiance, land cover and atmospheric composition fixed at pre-industrial (86) values. This simulation has been analyzed in various ENSO studies (e.g., Wittenberg et al. 26, Wittenberg 29; Kug 9

34 et al. 2; Xie et al. 2; Choi et al. 23; Karamperidou et al. 24; Wittenberg et al. 24) and is shown to have reasonable ENSO performance though with a too strong amplitude and too little seasonal synchronization. This simulation is referred to as GCM hereafter. Tropical Pacific (8E-72W, 3S-3N) SST anomalies (SSTA) are calculated by removing the monthly climatology based on the commonly-used 95-2 period in OBS and based on the full length of record in GCM. A linear detrending is applied on the SSTA at each grid point to remove the global warming trend in OBS or the model drift in GCM. Then a 3-month running average is applied to SSTA to smooth the temporal noise. Empirical Orthogonal Function (EOF) analysis is then performed (Fig..). The leading EOF shows the classic El Niño pattern, which is the dominant variability explaining 5% (52%) of total variance in OBS (GCM). The second EOF shows a zonal dipole pattern with positive loading in the western Pacific and negative loading in the eastern Pacific, which adds CP or EP flavor to the main El Niño pattern and explains 8% (%) of total variance in OBS (GCM). The third EOF depicts equatorial cooling and extra-tropic warming which explains 7% (6%) of total variance in OBS (GCM). It is similar to the equatorial ocean dynamic thermostat pattern (Clement et al. 996; Cane et al. 997; Solomon and Newman 22). The EOF patterns from GCM are overall consistent with OBS. Further analyses are mainly carried out using the leading Principal Components (PC). We next apply the empirical model reduction (EMR) (e.g, Kravtsov et al. 25; Kondrashov et al. 25, 25).The model is fit from the observed SST anomaly field and allows for ENSO nonlinearity, seasonality and memory effect for prior times. Note that the real climate is subjected to changing forcing, so the detrended data is used to fit the model in order to produce a stationary simulation without a trend in the forcing. Detailed settings are given in Chapter 2. A 4-year stochastic-forced EMR simulation is generated. For simplicity, this simulation is referred to as EMR hereafter. In later sections, we will show that a EMR fit from the SSTA observation is well-behaved and

35 reproduces reasonably realistic ENSO statistics. EMR also has limitations, which will be discussed in the results section. We make a crude first check of the EMR and GCM simulations by comparing to the tropical Pacific SST PC ( Niño 3.4) time series from observations (Fig..2a-e). Both the EMR and GCM time series appear reasonably realistic. The long EMR time series has epochs with energetic ENSO events and epochs with very weak anomalies, as has been seen in the GFDL CM2. run (Wittenberg 29). The model s ability to reproduce the observed nonlinear statistics is evaluated by comparing the 2-dimensional probability density function (2dPDF) of two leading principal components (PC-PC2) (Fig..2f-h). Both EMR and GCM simulations resemble the curved 2dPDF seen in OBS. The intermediate coupled model ZC also shows this curved feature in PC-PC2, as shown in Takahashi et al. (2)..2.2 CMIP5 Assessing potential ENSO behavior changes in the 2st century is carried out by analyzing the projection in 37 CMIP5 models that participated in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report (AR5) (Table.). Model descriptions and experiment designs are given in Taylor et al. (22). We analyzed three sets of simulation experiments: (i) pre-industrial control simulation (PI). (ii) the historical simulations which are integrations from around 85 to at least 25 using realistic natural and anthropogenic forcing. (iii) representative concentrating pathway 8.5 (RCP8.5) simulations from the end of the historical runs to 2 when the radiative forcing reaches 8.5W m 2. We concatenate on historical runs and RCP8.5 runs and then divide them into 2th century runs (9-999, denoted as 2C) and 2st century runs (2-299, 2C). For PI, 2C and 2C runs, monthly anomalies are calculated by linearly detrending and subtracting the monthly climatology for the whole period of each run. We also choose two models from the 37 CMIP5 models for examples. These two models are Geophysical Fluid Dynamics Laboratory (GFDL) Earth System Model (ESM): ESM2M and ESM2G (Dunne et al, 22, 23). They differ exclusively in the physical

36 ocean component; ESM2M uses Modular Ocean Model version 4p with vertical pressure layers. ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. These models illustrate the impact of the ocean configuration on ENSO behavior performance..3 Methods: empirical probabilistic diagnosis The diagnostics are carried out in three steps. We first define ENSO states. We next calculate the occurrence probability of each ENSO state for each calendar month and present the results in a seasonality diagram. We then present the transition probability between each ENSO state as well as the ENSO duration, zonal propagation and EN-LN asymmetry in a transition diagram. After that, we derive a set of probability-based indices for ENSO seasonality (I season ), diversity (I cp/ep, I e/w ) and EN-LN asymmetry (I amp, I dur, I tra )..3. Definition of ENSO states We define a set of mutually exclusive ENSO states and then categorize each monthly time step into one of these ENSO states. Later we calculate probabilities for state transitions and derive other indices. The states are determined using the full length of data in order to investigate ENSO behavior in shorter epochs without changing the definitions of states. We start from the usual 3 states: El Niño (EN), Neutral (NEU) and La Niña (LN). Since the absolute value of Niño indices vary in different simulations, we define the 3- state categories as follows: EN is P C >.7s.d.(P C), where s.d. denotes one standard deviation. This threshold is generally consistent with the Niño 3.4>.5 C criterion used by the NOAA Climate Prediction Center. Similarly, La Niña is P C <.7s.d.(P C); the remainder are defined as NEU (see Fig..3a). When ENSO flavors are considered, the 3-state category is expanded to 5 states in the space of PC-PC2. This phase space has been shown to characterize ENSO diversity (Takahashi et al. 2). We keep the same thresholds for El Niño/ Neutral/ La Niña using PC, and add negative or positive PC2 as another threshold to divide into the 2

37 EP/CP flavors (see Fig..3b). The typical patterns of the EP/CP flavors of El Niño and La Niña categories (Fig..3c, 3d, 3e, 3f) are consistent with the patterns defined in earlier literature using Niño indices (Kao and Yu 29) or C/E indices (Takahashi et al. 2). Any attempt to classify ENSO, including the PC-based classification presented here, is to some extent subjective and needs to be verified by its consistency with our understanding of ENSO dynamics (Chen et al. 25). Previous ENSO diversity studies have shown that CPEN are often moderate El Niños while EPEN could be either moderate or extreme El Niños. Thus the statistics of the EPEN behaviors may be dependent on the relative occurrence of moderate or extreme El Niños. In this study, we do not have a special category of extreme ENSO since only a few extreme El Niños occurred in the historical records. Thus the overall ENSO statistics for OBS are dominated by the moderate events. However in GFDL CM2. there are many extreme El Niños so the overall statistics may be shifted by these extreme El Niños..3.2 Seasonal occurrence probabilities Based on the above state definition, we measure the occurrence probability of each ENSO state for each calendar month. In OBS, the 3-state result (Fig..4a) shows El Niños and La Niñas both have higher occurrence probabilities of peaking in winter, which agrees with the observed winter phase locking diagnosed in much prior work (e.g., Tziperman et al. 995, 997, 998). The 5-state result (Fig..4d) shows that, in winter El Niños prefer to peak at EP while La Niñas prefer CP, in agreement with earlier studies on the EN-LN asymmetry (Kang and Kug 22; Schopf and Burgman 26; Frauen and Dommenget 2; Dommenget et al. 23). Turning now to the two simulations, EMR reproduces the observed seasonal statistics for both 3 and 5 categories (Fig..4b and 3.4e). In GCM, La Niñas prefer winter, which agrees with OBS, but El Niños show no clear seasonal preference (Fig..4c). Expansion to 5 states (Fig..4f) shows CPENs prefer to peak in winter while EPENs prefer summer, the latter out of keeping with the winter phase locking of El Niño. 3

38 .3.3 State transition probabilities We calculate the transition probability between each ENSO state by tracking precursors and successors. Given k El Niños for example, among the precursors τ months ago there are m El Niños, m 2 La Niñas and m 3 Neutral states (m + m 2 + m 3 = k). Among successors τ months later, there are n El Niños, n 2 La Niñas and n 3 Neutral states (n +n 2 +n 3 = k). Then the transition probability from La Niña to El Niño at a τ month interval P EN LN (τ) is calculated as the conditional probability P LN(t τ) EN(t) = m 2 /k, where t is the time. The transition probability from El Niño to La Niña at a τ month interval P EN LN (τ) is calculated as P LN(t+τ) EN(t) = n 2 /k. The 3-state transition probabilities are shown in Fig..5. In OBS, El Niño persists for several months and migrates to La Niña or neutral in about one year, then converges toward climatology (i.e. the annual mean occurrence probability of each state) at about three years. P EN LN is generally equal to P EN LN, which indicates the transition between El Niño and La Niña is generally symmetric. In EMR, the transition characteristics agree well with OBS; note that transition characteristics are not explicitly fit when the EMR model is constructed. In GCM, the EN-LN transition asymmetry is much greater than OBS with large discrepancy between P EN LN and P EN LN at τ -2 year. This is one indication of GCM s strong nonlinearity. The 5-state transition result, shown in Fig..6 enables us to identify the favored zonal propagation direction from the CPEN and EPLN panels. In OBS, El Niños favor westward propagation from EPEN to CPEN with P CP EN EP EN > P CP EN EP EN (Fig..6j). La Niñas also favor westward propagation from EPLN to CPLN (Fig..6d). In EMR, the zonal transition of El Niños and La Niñas both agree well with OBS (Fig..6k and 6e). In GCM, La Niñas favor westward propagation (Fig..6f) but El Niños differ from OBS by favoring eastward propagation (Fig..6l)..3.4 A set of indices for ENSO behaviors Since the probability results show that the data-driven EMR produces realistic ENSO behaviors, we use it to evaluate ENSO behavior variations under stochastic noise. We 4

39 divide the 4-year simulation into 39 overlapping -year epochs starting -years apart. We next define a set of indices to measure different aspects of ENSO behavior. A seasonality index I sea is defined to identify the favored peak season for a given epoch. For El Niños, I sea is the total occurrence of El Niño in the summer half year (March-August) divided by the total occurrence of El Niño in the winter half year (Sep.- Feb.). I sea < (> ) indicates El Niño preferentially peaks in winter (summer). The results (Fig..7a and 7d) show that both El Niño and La Niña of OBS prefer winter. In EMR, El Niños and La Niñas also prefer the winter half year in all epochs. A diversity index I cp/ep is defined for El Niños to diagnose the dominant peak location in a given epoch, calculated as the total occurrence of CPEN divided by the total occurrence of EPEN. I cp/ep < (> ) indicates El Niño prefers to peak at EP (CP). There is a similar definition for La Niña. The results (Fig..7b and 7e) show that, EPENs and CPLNs dominate in OBS. In EMR, 9% of epochs are dominated by EPEN and 97% of epochs are dominated by CPLN. Another diversity index I e/w is defined to diagnose the dominant zonal propagation in a given epoch. For El Niños, I e/w is the mean of the eastward transition probability P CP EN EP EN within a 6-month interval minus the mean of the westward transition probability P CP EN EP EN within a 6-month interval. I e/w < (> ) indicates El Niño prefers westward (eastward) propagation. Fig..7c and.7f show that OBS has more westward moving El Niños and La Niñas. In EMR, El Niños favor westward propagation in 74% of epochs while La Niñas favor westward propagation in all epochs. The asymmetry index I amp, which diagnoses the relative amplitude of El Niño and La Niña in a given epoch, is calculated as the mean of PC value for El Niños divided by the mean of PC value for La Niñas; I amp > indicates that the overall amplitude of El Niño is larger than La Niña. Fig..7g shows that El Niños have larger amplitude than La Niñas in OBS: I amp > in all cases. In EMR, 82% of epochs have I amp >. Another asymmetry index I dur diagnoses the relative duration of El Niño and La Niña in a given epoch. It is calculated as the mean of El Niño self-transition probabilities P EN EN within a 36-month interval divided by the mean of La Niña self-transition 5

40 probabilities P LN LN within a 36-month interval. I dur < indicates La Niña is more durable. Fig..7h shows that La Niña is more durable in OBS, while in EMR 6% of epochs have more durable La Niñas. A third asymmetry index I tra, which diagnoses the transition asymmetry between El Niño and La Niña, is calculated as the mean of El Niño to La Niña transition probabilities P EN LN within a 8-month interval minus the mean of La Niña to El Niño transition probability P EN LN within a 8-month interval. I tra > indicates La Niñas tightly follow El Niños more than vice versa. Fig..7i shows that in OBS there is no substantial asymmetry in transition. In EMR, 55% of epochs have I tra >. This EN-LN asymmetry index is similar to Choi et al. (23), in which the transition is defined based on individual events with the time range set to one year. In this study, we analyze the state-based transitions rather than the event-based transition and use different time ranges. Our results indicate that, under stochastic noise, epochs with characteristics different from OBS could also occur. This occurs even though the EMR model is built from the OBS data. We thus provide additional evidence that the recent change in EP/CP diversity may be a natural variation as in Newman et al. (2b) and Yeh et al. (2) and show that the changes in other ENSO behaviors may also be results of natural variation. So one needs to be cautious when attributing ENSO variations as a response to the global warming trend..3.5 Natural variation of ENSO behaviors in EMR In nature, each -year period may have different ENSO behaviors. Thus it is understandable that the ENSO statistics in the 4-year EMR may be slightly different from the past centurial historical records in Fig The EMR is built to best capture the transition from one month to the next. It includes some nonlinear dynamics, memory effects from a single prior time step, and annual periodic terms. One might therefore expect that EMR will agree with OBS with respect to the overall nonlinear measure 2dPDF in Fig..2g and for the seasonal phase locking in Fig..4b and 4e. EMR does not explicitly build in different peak locations, 6

41 different propagation direction, or the EN-LN asymmetry. The ability of EMR to capture these aspects is an implicit and non-obvious consequence of the model construction. What are the advantage and limitation of EMR? As a data-driven model, EMR produces simulation generally more realistic than GCM. As a low order empirical model, an EMR simulation is numerically efficient. Therefore, the ENSO behavior range estimated by EMR could be used as a diagnostic tool to evaluate ENSO performance in GCMs. In particular, EMR could be used to help tune the model nonlinearity toward the real climate. EMR could be wrong, but it does agree with data in ways not obvious from its construction and its extended behaviors in the long runs are at least as plausible as the GCM..3.6 ENSO behavior performance in GFDL CM2. PI As with the EMR simulation, the 4 year GFDL CM2. GCM simulation is divided into year overlapping epochs year apart and OBS is also divided into year overlapping epochs. In the GCM simulation, El Niños in all epochs favor eastward propagation (Fig..7c) and all epochs show a strong transition asymmetry with La Niñas tightly following El Niños (Fig..7i). These aspects of the GCM simulation are the most easily distinguishable from OBS and might be the only robust biases if only centennial-long simulations are available. On the other hand, GFDL CM2. is consistent with EMR in the ratio of CP/EP ENSO (Fig..7b,e), El Niño-La Niña asymmetry in amplitude (Fig..7g) and duration (Fig..7h). Why do EPENs in GFDL CM2. tend to peak in summer rather than in winter? Previous studies have shown that the SST anomaly peaks when the collective positive feedbacks become weakest and are balanced by negative feedbacks and dissipation (Tziperman et al. 995, 997, 998; Neelin et al. 2; An and Wang 2; Xiao and Mechoso 29). In the strongly nonlinear GCM, positive and negative feedbacks may both change altering the peak timing and location. Wittenberg et al. (26) showed that GFDL CM2. simulated events tend to peak either in summer or winter and such semiannual locking is likely tied to the semiannual cycle of the background convection and currents, which is associated with double ITCZ and the seasonal reversal of the 7

42 meridional SST gradient and winds in the eastern Pacific. Why does El Niño in GFDL CM2. tends to propagate eastward rather than westward? Previous studies have shown extreme El Niños propagate eastward and moderate El Niños propagate westward (Santoso et al. 23; Kim and Cai 24). This simulation has many extreme El Niños, which makes eastward propagation dominant. GFDL CM2. does better with SSTAs associated with La Niña than El Niño. Since the coupling only becomes nonlinear above a certain temperature threshold (Takahashi et al. 25), good performance on El Niño demands that the strength of the model s nonlinearity resemble that in the real climate. Since La Niñas are less sensitive to nonlinearity, they do not show as greater a diversity as El Niños (Kug and Ham 2). Even for a model where the nonlinearity is too strong, La Niñas may still be simulated realistically..4 Results: future projections using 37 CMIP5 models The PC-based definition works well for the models with correct representations of EOF and EOF2, but this definition may not be optimal for the models with poor performance on ENSO diversity. So we will use a similar Niño-based definition for CMIP5 model evaluation. Normalized Niño-3.4 replaces normalized PC; the time series are almost identical with correlation r =.97 in the observations. The second dimension is normalized Niño-4 minus normalized Niño-3, replacing the normalized PC2, correlation r =.88. All are normalized to have standard deviation equal to one. Overall, this Niño-based definition works, though in some models SST anomaly averaged at standard Niño regions may not exactly capture the westward shifted maximum variability. We first carry out a coarse evaluation of SST climatology and anomalies in the CMIP5 models and then present detailed ENSO behaviors. The results from each model are sorted in an ascending order for each aspect of ENSO behavior. Table. gives the rank of each model for each aspect. We will compare the 2C to 2C change with its own control run range to interpret the attribution of the change. 8

43 .4. SST climatology and anomaly ENSO is an anomaly on top of the climatology, so we first investigate whether these CMIP5 models reproduce a realistic tropical Pacific climatology. The time series of Niño-3.4 SST from 9 to 2 are shown in Fig..8a and averaged Niño-3.4 SST in the 2th century (2C) and 2st century (2C) are shown in Fig..8b. The multi-model mean (MMM) is also calculated. The averaged Niño-3.4 SST in sliding -year epochs for the pre-industrial control run (PI) is also provided as reference. Though there is a considerable spread compared to observations in 2th century runs, all 37 models project a warming future for the RCP8.5 scenario with MMM showing a 2 o C temperature increase. The Niño-3.4 SST anomalies in 2C and 2C are obtained by linearly detrending and removing monthly climatology in each year segment (Fig..8c) and the s.d. of Niño-3.4 are shown in Fig..8d. The natural variation range is provided by PI control runs of each model and the 4-year stochastic-forced EMR simulation fit from OBS. The results show that there is large spread of 2C runs ranging from half the amplitude of OBS to nearly twice OBS, similar to Bellenger et al. (23). We also see that those large changes are outside of the range due to stochastic noise in the EMR simulation. Twenty models project decreases in Niño-3.4 s.d. and 7 models project increase. Among these 7 models, models show changes beyond the range of its PI control run and the MMM of 37 models also project an increase. Cai et al. (25b) suggested more extreme La Niñas in the 2C projections..4.2 SST annual cycle and seasonality The annual cycle of Niño-3.4 SST in 2C of all CMIP5 models are presented in Fig..9a and the structure of the annual cycle is measured using the averaged SST during winter half year (Sept.-Feb.) minus that during summer half year (Mar.-Aug.). Most models produce a reasonable annual cycle by this measure. The future change in 2C shows no apparent change in the MMM. 8 models project a decreased index value while 9 models project an increase. 9

44 The seasonal phase locking for El Niño and La Niña is shown using occurrence probability for each calendar month (Fig..9c and 9e). I sea results also show that most models produce winter phase locking as in 2C OBS, consistent with Taschetto et al. (24). For 2C, there is not much projected change for El Niño and only a slight change for La Niña (strengthened winter half year peaking). The variation in each model from 2C to 2C is largely within the range of natural variation of the control run. Some models produce summer phase-locking, as in Ham and Kug (24). Guilyardi et al. (23) and Ham and Kug (24) suggested that the biased models tend to also have biases in climatology and oceanic mean state..4.3 ENSO diversity in peak location The existence of ENSO diversity sets a high bar for the CMIP5 models. The results of I cp/ep (Fig..a and c) show that more than half of the models resemble the 2C observation that El Niños favor the eastern Pacific and La Niñas favor the central Pacific. Similarly, Taschetto et al. (24) showed most models realistically simulate the observed intensity and location of maximum SST anomalies during ENSO events. As to the future change of the peaking location, Yeh et al. (29) suggested increased frequency of CPEN compared to EPEN using 2 CMIP3 models and related this change to flattening of the thermocline in the equatorial Pacific. Kim and Yu (22) suggested a increased ratio of warm pool El Niño to cold tongue El Niño from the historical run to the RCP4.5 scenario using 6 CMIP5 models. Taschetto et al. (24) suggested no enhancement of the ratio of warm pool to cold tongue ENSO from historical to RCP8.5 using 27 CMIP5 models. The discrepancy among above studies suggests the uncertainties are dependent on the selected models and the performance of these models in the historical run. We use 37 models to measure the change from 2C to 2C using the probability shift in relative occurrence (I cp/ep ). We find no significant change of ENSO peaking in central Pacific or eastern Pacific given that the MMM showing no notable change and there is no consistent change among models. I cp/ep in 2C and 2C are both within the natural variation range of the control run thus the projected change of CP/EP diversity is more likely to be natural variation, consistent with the conclusion 2

45 in Yeh et al. (2) and Newman et al. (2b)..4.4 ENSO diversity in propagation direction I e/w results (Fig..b and d) show that in 2C most models favor westward propagating El Niños and all models favor westward propagating La Niñas as the observations. This agrees with Santoso et al. (23). Two third of 37 models (24 models) project a shift toward eastward propagating El Niños in 2C and MMM shows the same shift. For La Niña, two third of 37 models (25 models) project a shift toward eastward propagation in 2C, consistent with the MMM. The change in most models are beyond the range of natural variation of the control runs. Santoso et al. (23) have shown the westward mean equatorial currents weaken under global warming and thus there may be more occurrences of El Niño events that feature prominent eastward propagation characteristics in a warmer world..4.5 ENSO asymmetry in amplitude, duration and transition The El Niño-La Niña asymmetry could be coarsely measured using the skewness of the Niño-3.4 SST anomaly (Fig..a). More than half of the 37 models show a positive skewness in agreement with OBS, though MMM underestimates the skewness. For 2C, MMM shows a slight decrease of skewness as do almost 2/3rds of the models. The 2C skewness value of each model is generally within the range of its PI control run so this weakened skewness may be natural variation rather than a forced response. The El Niño-La Niña asymmetry is further decomposed into three aspects (Fig..b, c,d). The amplitude asymmetry I amp results show that more than half the models agree with OBS in 2C with larger amplitude in El Niño. MMM projects a decrease in the asymmetry for 2C but only 2 of the 37 models support the same shift. As to the duration, I dur shows that only half the models agree with 2C OBS in showing a more persistent La Niña. MMM does not show much change for 2C and models do not agree on the shift. As to the transition, I tra, most models show much larger transition asymmetry than OBS in 2C. MMM does not show much change for 2C and there is no agreement among models. The projected values for the 2C in most 2

46 models are within the natural variation range of the control run thus the change may be largely due to natural variation. Zhang and Sun (24) and Cai et al. (25a) pointed out that most CMIP5 models underestimate ENSO asymmetry. Our diagnostics show that most models underestimate the EN-LN asymmetry in amplitude and duration, but overestimate the EN-LN asymmetry in transition..4.6 Case study using GFDL ESMs GFDL ESM2M and GFDL ESM2G are two new models which incorporate carbon dynamics. In the former the atmosphere is coupled to a z-level ocean model and in the latter the ocean model is isopycnal. The overall assessment (e.g., Dunne et al. 22, 23) illustrates that neither model is fundamentally better than the other. Dunne et al. (22) also show that the thermocline depth are relatively deeper in ESM2M and shallower in ESM2G compared to the observations. The role of ocean dynamics on climate variability is highlighted in ENSO being too strong in ESM2M and too weak in ESM2G relative to observations. Comparing these two models shows how different ocean representations may influence model performance on climate variability like ENSO. ESM2G has less bias for the annual cycle, SSTA standard deviation, SSTA skewness, I sea, I e/w EN and I tra while ESM2M shows less bias for I cp/ep, I e/w LN, I amp, I dur and SST mean climatology. Overall, ESM2G shows more realistic ENSO behaviors. The 2C projections of these two models seldom agree with each other..5 Discussion.5. CMIP5 model rating on ENSO performance Using only more reliable models might better predict for the future. Kim and Yu (22) identified 7 CMIP5 models with best ENSO characteristics, including CNRM- CM5, GFDL-ESM2G, GFDL-ESM2M, HadGEM2-CC, HadGEM2-ES, MPI-ESM-LR, NorESM-M. Bellenger et al. (23) also found 7 best models including GFDL- ESM2G, HadGEM2-ES, HadGEM2-CC, MPI-ESM-LR, MPI-ESM-P, NorESM-M, NorESM- ME. 22

47 Table. summarizes 37 CMIP5 model performances based on 3 ENSO behavior metrics. The ten models with the smallest errors on each aspect are tagged with an asterisk. We then use the total number of asterisk to identify the best models overall, including ACCESS., ACCESS.3, BNU-ESM, CMCC-CMS, GFDL-ESM2G, HadGEM2-ES, IPSL-CM5B-LR, MPI-ESM-LR, MRI-CGCM3, NorESM-M. The models here and in the two cited studies are GFDL ESM2G, HadGEM2-ES, MPI-ESM-LR, NorESM-M. We have weighted all aspects equally in this study, and future studies may provide a better rationale to rank and rate all the models. Once subsets of good models are identified, one may make quantitative judgements on how to use the information from a collection of models for a particular application (Gleckler et al. 28). One may further weight models differently based on their performance or eliminate some poor models from a multi-model ensemble for a given aspect. Since even the best models have a large spread in the variable-by-variable performance, one need to be cautious when extracting subsets of models for a given aspect of ENSO behavior..5.2 Uncertainty of projected changes Projections for the future based on CMIP models often involve considerable uncertainty (Vecchi and Wittenberg 2). Changes in ENSO are difficult to detect given the natural variability present in each model (e.g., Wittenberg 29) as well as the lack of model agreement (e.g., Guilyardi 26; Collins et al. 2; Stevenson 22; Taschetto et al. 24). In this study, we summarize the future change using the MMM of all 37 models, the overall best models and the best models for individual aspect (Fig..2). Skewness is not shown in this summary since it is closely correlated with EN-LN asymmetry in amplitude. Among all aspects, only the mean SST climatology increase is consistently predicted by all models. For other aspects, the varying ability of models on 2C ENSO behaviors and the lack of agreement in the future leaves little to confidently predict about the future of ENSO. Only a shift toward eastward propagation of El Niño is both supported by MMM and nearly 2/3rds of the models. To address whether the projected future change is mainly due to natural variation or 23

48 is a forced response, we use the natural variation range of century-long epochs based on the EMR simulation and the range of control run from each model to provide references. Clearly the change in mean SST climatology is mainly due to the external forcing. Changes in propagation are likely due to changing external forcing. Santoso et al. (23) have shown that the westward mean current is the main reason for ENSO s westward propagation. If the westward mean current becomes weak in 2C, it would shift ENSO toward eastward propagation. For other aspects, it is possible that all the model changes are due to internal variability rather than greenhouse gas forcing. By basing our metrics on SSTA we follow the practice in the vast majority of prior ENSO literature. However, based on observations (Karl et al. 995), CMIP modeling results and theory (Allen and Ingram 22), it is expected that with global warming the atmospheric water vapor content will increase faster than overall precipitation, with the consequence that convective events will become more intense. Thus we expect that even if ENSO amplitude as measured by SSTA variations remains unchanged the rainfall associated with ENSO events will increase, as has been found by Power et al. (23) and Cai et al (24)..6 Conclusion We introduced a set of probabilistic measures for a broad set of ENSO behaviors, including variations in season, location and propagation direction as well as El Niño-La Niña asymmetries. We applied it to SST observations and the diagnostics show that, El Niños and La Niñas are phase-locked to boreal winter. They both favor westward propagation. El Niños mainly occur at the eastern Pacific and La Niñas prefer the central Pacific. These results agree with current understanding and thus provide support for the validity and reliability of our new diagnostics. The diagnostics were applied to a 4-year pre-industrial control simulation of the GFDL CM2. coupled GCM. The strong nonlinearity of this model is indicated by an exaggerated El Niño-La Niña asymmetry. Although modeled La Niñas generally behave like the observations, El Niños behave quite differently. Because there are many extreme 24

49 El Niños eastward propagation become dominant. EPEN prefer peaking in summer and CPENs prefer winter. Thus the winter phase-locking feature is largely missed in GCM due to this summer-time compensation. Overall the statistics of EPEN in GFDL CM2. is largely dominated by extreme El Niños instead of moderate El Niños. The diagnostics were also applied to a 4-year stochastic-forced simulation of a nonlinear empirical model reduction (EMR) fit using SST observations. This simulation is realistic in broad aspects of ENSO behavior and thus may be considered as an extension to observations to help us assess the potential range of ENSO variation. Most epochs in a 4-year simulation agree well with observations. But epochs with more CP El Niños or epochs with more eastward El Niños do exist when stochastic noise is the only forcing. No forcing trend such as that due to greenhouse gases is required. The change of ENSO behaviors in a warming climate are assessed using 37 CMIP5 models that participated in IPCC AR5. Beyond the analyses of tropical Pacific SST seasonal climatology and SST anomaly standard deviation and skewness, we apply a set of empirical probabilistic diagnostics. Evaluation of model performance used preindustrial control runs (PI) and 2th century runs (2C, historical, 9-999). Each model shows pros and cons for varying aspects of ENSO behavior. As to the projected changes from the 2th century to 2st century (2C, RCP8.5 scenario, 2-299), except for a consensus in tropical Pacific SST increase due to the forcing, changes in other aspects are all model dependent. Overall the multi-model mean (MMM) suggests that ENSO behavior measured in SSTA may not undergo significant changes. The degree of model agreement, measured by numbers of model with decreased/ increased change from 2C to 2C, is low for all aspects. A shift favoring eastward propagating El Niño and La Niña shows slightly more robustness. The ENSO statistics generally remain unchanged for the annual cycle and seasonal phase locking, diversity peaking in eastern Pacific /central Pacific and El Niño-La Niña asymmetries. Except for the mean warming, the 2C change is within the bounds of the natural variation range produced by the PI control run and a stochastically-forced run of data-driven model EMR fit using SST observation. 25

50 We compare GFDL ESM2M and GFDL ESM2G, two earth system models differing only in their physical ocean component. ESM2G, as one of the best models, shows more realistic ENSO behaviors, though ESM2M shows a better SST climatology. The two models rarely agree in their projection for 2C. 26

51 Table.: List of 37 CMIP5 models analyzed in this study. Due to the lack of availability in certain models for temperature of ocean surface tos, we instead analyzed monthly surface temperature ts in each model s rip run. st column is the official model name. 2nd column is the length of preindustrial control run (year). 3rd to 5th columns are the model rank as shown in each individual figure and panel, e.g., f8b indicating Fig..8 panel b. According ENSO aspect is labelled in 2nd and 3rd rows. Note that for individual ENSO behavior models with * are models with smallest error between each model s 2th century run (orange o) and the 2th century observation value (black line in the panel). The last column is the total number of * for each model. There are best models with 5 and above *, which are indicated with + at the end the model name in st column. Note that these relative better models are only restricted to ENSO behavior aspects analyzed in this study, therefore, it is not generally applicable to model performances on other phenomena. Model center information and experiment designs see Taylor et al. (22) and CMIP5 website ( name PI f8b f9b f8d fa f9d f9f fa fc fb fd fb fc fd num clim anncli s.d. s.k. I sea I sea I cp/ep I cp/ep I e/w I e/w I amp I dur I tra EN LN EN LN EN LN ACCESS * 24* * * 2 33 * 5 ACCESS * * 6 6* 3 26* 2 7* 5 BCC-CSM. 5 22* * 3 3 3* 3 BCC-CSM.(m) 4 29* * 9* * 27 4 BNU-ESM * 36 9 * 8* 5* 3* * 25 6 CanESM * * 7* 9 5 5* CCSM4 5 27* 23* * * 35 4 CESM(BGC) 5 28* * 34* CESM(CAM5) * * 2 3* CMCC-CESM * 22* * CMCC-CM * 9 28* * * CMCC-CMS + 5 3* 29* 23* * * 5* CNRM-CM * 27 26* CSIRO-Mk * * 9* FGOALS-g * * * 3 FIO-ESM * 4* GFDL-CM GFDL-ESM2G * 4* 23* 32 * 35 26* 4* GFDL-ESM2M * 36 2* 36 4* 37 3 GISS-E2-H * 2* GISS-E2-H-CC * 2 3 3* GISS-E2-R * * * 3 GISS-E2-R-CC * 7* HadGEM2-CC * HadGEM2-ES * 6 2* * 22 7* * 5 INM-CM * IPSL-CM5A-LR 7 9 5* * 6* 3 IPSL-CM5A-MR 3 6 2* 25* * 2* 5 4 IPSL-CM5B-LR + 3 3* 2 2 6* 28 28* 3* 23* 29* 9* 7 MIROC-ESM * * 32 2* 3 MIROC-ESM-CHEM * * 4 5* 3 MIROC * * MPI-ESM-LR * 3* * 2 8* 8* 27* MPI-ESM-MR * 6 MRI-CGCM * 22 * 8 9* 24* 9 7* 8* 6 NorESM-M * 5* 9* 33* 2* 3 8* 33 6 NorESM-ME * 26 27* * *

52 EOF a) 3N OBS (HadISSTV.) b) 3N GCM (GFDL CM2.) EOF3 EOF2 3S 5% 8E 8 72W c) 3N 2 2 3S 8% 8E 8 72W e) 3N S 7% 8E 8 72W S 52% 8E 8 72W d) 3N S % 8E 8 72W f) 3N - 3S 6% 8E 8 72W Figure.: The first three normalized EOF patterns of Tropical Pacific SSTA in OBS (87-present monthly HadISST v.) (a, c, e) and GCM (4-year monthly GFDL CM2. pre-industrial control run) (b, d, f). Positive/negative values are shown in solid/dashed contours. The zero value is highlighted in the thick solid contour. 28

53 SSTA PCs in obervation and simulation (EMR & GCM) PC EMR GCM PC f) OBS 2 g) EMR PC PC 2 4 h) GCM log (2dPDF) OBS 4 2 a) b) c) d) e) PC Figure.2: Simulation evaluation: yearly running averaged time series of tropical Pacific SSTA PC in OBS (a), year -4 of 4 year EMR simulation fit from OBS (b and c) and year -4 of 4 year GFDL CM2. GCM simulation (d and e). All PCs are normalized to have standard deviation equal to one. Decimal logarithm of the bivariate probability density function (2dPDF) in PC-PC2 space in OBS (f), 4 year EMR (g) and 4-year GCM (h). 29-2

54 PC2 3 a) LN NEU EN PC c) 3N 3--states -.5 Definition of ENSO states in OBS PC2 3 b) NEU EPLN CPLN 5--states PC d) 3N CPEN EPEN CPLN -.5 3S 8E 8 72W e) 3N CPEN 3S 8E 8 72W f) 3N EPLN EPEN S 8E 8 72W 3S 8E 8 72W Figure.3: Definition of 3 ENSO states (a) (El Niño/La Niña and neutral patterns, denoted as EN/LN/NEU) and 5 ENSO states (b) (Eastern/Central Pacific El Niño/La Niña and neutral patterns, denoted as EPEN/ CPEN/ EPLN/ CPLN/ NEU) are shown using smoothed monthly PCs from 87-present HadiSST v.. ±.7 s.d. (PC), where s.d. is one standard deviation, is used to distinguish EN/LN from NEU. Zero line of PC2 is used to distinguish EP/CP states. Averaged patterns for each ENSO flavor CPLN (c)/epln (e)/cpen(d)/epen(f) are shown. Each state is assigned a color code for further analysis. 3

55 Occurrence Probability a) OBS b) EMR c) GCM EN.6 3-state NEU LN J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D d) state.4.2 J F M A M J J A S O N D e) J F M A M J J A S O N D Calendar month f) J F M A M J J A S O N D EPEN CPEN NEU EPLN CPLN Figure.4: Monthly occurrence probabilities for 3 ENSO states (a,b,c) and 5 ENSO state (d,e,f) in OBS (a,d), EMR (b,e) and GFDL CM2. GCM (c,f) are shown. Stacked bars along the vertical coordinate are the occurrence probabilities of each color-coded state. The horizontal coordinate is the calendar month from Jan to Dec. Full year data is used thus the sample size for each calendar month is equal. In panel a, higher probability of EN/LN in winter months than summer months indicates observed ENSO s winter phase locking. In panel d, higher probability of EPEN over CPEN indicates El Niño favor peaking in EP, and higher probability of CPLN over EPLN indicates LN favor peaking in CP. 3

56 a) OBS 3- state transition probability b) EMR c) GCM LN d) e) f) EN NEU NEU g) h) i) LN EN Lead time (yr) Figure.5: State transition probabilities for LN (st row), NEU (2nd row) and EN (3rd row) in OBS (first column), EMR (2nd column) and GFDL CM2. GCM (3rd column) are shown. The horizontal coordinate represents the transition from the past (-3 years) to the future (+3 years) in monthly intervals, with zero indicating the current state. Taking GCM EN transition (panel i) for example, bars along the vertical coordinate at + year (+2 months) represent: the self-transition probability P EN EN (upper bar), the P EN NEU (middle bar) and the opposite-sign transition P EN LN (lower bar). The decaying of P EN EN as function of lead time indicates EN s duration. The discrepancy between P EN LN (lead< side) and P EN LN (lead> side) indicates the EN-LN asymmetry in transition. The transition probabilities generally converge to the climatology, i.e., the nonseasonal occurrence probability of each state (dotted line in each panel). 32

57 5- state transition probability a) OBS b) EMR c) GCM CPLN d) e) f) EPEN EPLN g) h) i) CPEN NEU NEU j) k) l) EPLN CPEN CPLN m) n) o) EPEN Lead time (yr) Figure.6: Same as Fig..5, but for transition probabilities of 5 ENSO states. Taking GFDL CM2. GCM CPEN transition (panel l) for example, bars along the vertical coordinate at +6 months represent: st is P CP EN EP EN, 2nd is P CP EN CP EN, 3rd is P CP EN NEU, 4th is P CP EN EP LN, 5th is P CP EN CP LN. The discrepancy between P CP EN EP EN (lead< side) and P CP EN EP EN (lead> side) indicates the zonal propagation asymmetry. Note that zonal propagation asymmetry is best measured between -6 months while the EN-LN transition asymmetry is best measured between -2 years. 33

58 EN vs LN LN EN a).2 prefer winter.5 % prefer summer % Natural variation of ENSO behaviors in histogram (pdf).2.5 b) prefer EP prefer CP c).2 pref. westward 9% 9%.5 74% pref. eastward 26% I-season d).2 prefer winter prefer summer % % I-cp/ep e).2 prefer EP 3% prefer CP 97% I-e/w f).2 pref. westward pref. eastward. % %.5.5 I-season I-cp/ep I-e/w g).2.5 EN<LN 8% EN>LN 82% h).2 EN<LN.5 6% EN>LN 39% i).2 EN follow LN.5 45% LN follow EN 55% I-amplitude I-duration I-transition obs emr gfdl cm2. Figure.7: Variation of ENSO behaviors in 4-year EMR and GFDL CM2. GCM simulation. Each index (see text for definitions) is calculated in -year overlapping epochs years apart. The probability density function (PDF) is shown in the blue curve. Index values in epochs of OBS are shown in magenta lines (five in total). ENSO diversity indices, including I sea, I cp/ep, I e/w, are shown in the top rows for El Niño and La Niña. EN-LN asymmetry indices, including I amp, I dur, I tra are shown in the bottom row. For each panel, the percentage of epochs in the EMR satisfying the specified index range is shown. Taking panel b for example, OBS have more EPEN than CPEN (I cp/ep < ). Among 39 -year epochs in EMR, 9% of epochs have more EPEN than CPEN. 34

59 Tropical Pacific SST (N3.4) climatology and anomaly change from 2C to 2C in CMIP5 a) 2C mmm b) 35 2C SST ( oc) obs cmip5 gfdl esm2g gfdl esm2m models after sorting 32 < > C.obs 2C.hist 2C.rcp85 ctrl.pi gfdl esm2g gfdl esm2m c) 2C cmip5 gfdl esm2g gfdl esm2m time (yr) mmm d) 35 2C 2 models after sorting SSTA ( oc) 5 3 SST ( oc) time (yr) 3 < 2 25 > emr.5.5 SSTA s.d. (oc) 2 Figure.8: Nin o-3.4 SST climatology and anomaly in the 2th century (2C, historical run, 9-999) and the 2st century (2C, RCP8.5 scenario, 2-299) in 37 CMIP5 models that participated in IPCC AR5. (a) The 2-year running average Nin o-3.4 SST with OBS in black, CMIP5 models in gray, GFDL ESM2G in red, GFDL ESM2M in green. (b) The mean SST in the 2C and 2C for each CMIP5 model. The models are sorted according to the -year averaged Nin o-3.4 SST in the 2C runs. The black vertical line marks the 2C OBS value. Multi-model mean (MMM) is shown at the top, 2C in orange and 2C in blue. Pre-industrial control simulations of each model are divided into -year sliding epochs to calculate the year averaged SST and the percentile of the distribution are shown as gray horizontal lines. The number of models with decreased/ increased change is indicated in a number with < / >. (c) Nin o 3.4 SST anomaly time series from 9 to 299. (d) The standard deviation of SSTA in pre-industrial, 2C and 2C runs. In addition here the 2C results with an increased change are shown filled and those with decreased values are unfilled. Meanwhile, the 2.5, 5, 97.5 percentile range estimated from the distribution in the EMR simulation is shown in brown 35 line at the bottom.

60 models after sorting models after sorting seasonal SST ( o C) models after sorting a) SST (N3.4) annual cycle and anomaly seasonality change from 2C to 2C in CMIP5 2C 24 2C.obs 22 cmip5 gfdl esm2g gfdl esm2m 2 J F M A M J J A S O N D calendar month mmm b) < 8 > 9 2 2C.obs 5 2C.hist 2C.rcp85 ctrl.pi 5 gfdl esm2g gfdl esm2m SST summer-winter diff ( o C) p EN p LN c) EN 2C J F M A M J J A S O N D calendar month e) LN 2C J F M A M J J A S O N D calendar month mmm emr mmm emr d) f) prefer winter <- -> prefer summer < 2 > I-season-EN prefer winter <- -> prefer summer < 22 > I-season-LN Figure.9: Annual cycle and ENSO seasonality change from 2th century (2C) to 2st century (2C) in 37 CMIP5 models: (a) The 2C seasonal cycle of Niño-3.4 SST, with OBS in black, CMIP5 models in gray, GFDL ESM2G in red, GFDL ESM2M in green. The horizontal axis shows the calendar month. (b) The Niño-3.4 SST difference between the March-August (summer half year) average and the September-February (winter half year) average. The models are sorted according to the 2C value of this difference. (c) 2C occurrence probability of El Niño P EN, (e) 2C occurrence probability of La Niña P LN. (d) seasonality index of El Niño (I season EN ) defined using summer half year averaged P EN divided by winter half year averaged P EN, thus I season EN < indicates El Niño in a given -year epoch prefers winter phase locking. (f) I season LN, defined the same way, but for La Niña event. 36

61 models after sorting models after sorting models after sorting models after sorting prefer EP <- -> prefer CP mmm a) emr ENSO location and propagation direction change from 2C to 2C in CMIP5 < 2 > 7 2C.obs 2C.hist 2C.rcp85 ctrl.pi gfdl esm2g gfdl esm2m 2 3 I-cp/ep-EN pref.westward<- -> pref.eastward mmm b) 35 < 3 > emr I-e/w-EN.4.6 prefer EP<- -> prefer CP mmm c) < 5 > 22 emr 2 3 I-cp/ep-LN mmm emr pref.westward d) <- -> pref.eastward < 2 > I-e/w-LN Figure.: ENSO peaking location and propagation direction in the 2th century (2C) and 2st century (2C) in 37 CMIP5 models. (a) The location diversity index I cp/ep for EN, defined as P CP EN divided by P EP EN. (c) I cp/ep for LN. I cp/ep > indicates El Niños or La Niñas preferentially peak in CP. (b) The propagation diversity index I e/w for EN defined as P CP EN EP EN minus P CP EN EP EN. (d) I e/w for La Niña. I e/w > indicates El Niños or La Niñas prefer eastward propagation. 37

62 models after sorting models after sorting models after sorting models after sorting mmm emr a) ENSO asymmetry change from 2C to 2C in CMIP5 < 24 > 3 2C.obs 2C.hist 2C.rcp85 ctrl.pi gfdl esm2g gfdl esm2m SSTA skewness mmm b) < 24 > 3 EN<LN <- -> EN>LN < 2 > 6 emr.5.5 I-amplitude mmm c) EN<LN <- -> EN>LN < 6 > 2 EN follows LN<- -> LN follows EN mmm d) < 9 > emr.5.5 I-duration 5 emr I-transition.2.3 Figure.: EN-LN asymmetry in the 2th century (2C) and 2st century (2C) in 37 CMIP5 models. (a) the skewness of Niño-3.4 SSTA. (b) The amplitude asymmetry index (I amp ) defined as EN amplitude divided by LN amplitude. I amp > indicates El Niños have larger amplitude than La Niñas in a given -year epoch. (c) the duration asymmetry index (I dur ) defined as P EN EN divided by P LN LN. I dur < indicates La Niñas are more persistent than El Niños. (d) the transition asymmetry index (I tra ) defined as P EN LN minus P EN LN. I tra > indicates El Niños are quickly followed by La Niñas but not vice versa. 38

63 2C and 2C ENSO behaviors in CMIP5 models a37 b c obs a) /37 / / 2c 2c 8/9 2/8 6/4 b) 2/7 3/7 7/3 c) cli ( o C) ann-cli s-w diff ( o C) s.d.( o C) 2/6 3/7 6/4 d) 2/7 3/7 3/7 e) 3/24 2/8 2/8 f).6.8 I-season-EN.5.5 I-cp/ep-EN I-e/w-EN 22/5 5/5 7/3 g) 5/22 4/6 4/6 h) 2/25 5/5 3/7 i).6.8 I-season-LN 2 3 I-cp/ep-LN I-e/w-LN 2/6 3/7 9/ j) 6/2 6/4 2/8 k) 9/8 3/7 4/6 l) I-amp I-dur -.. I-tra Figure.2: Summary of ENSO behaviors in the 2th century and the 2st century using all 37 CMIP5 models (a37, blue), overall best models (b, yellow) and best models for individual aspect of behavior (c, red). The 2th century observation (obs, black) results are shown as a reference. A 4-year stochastically forced simulation of EMR model fit from the observation provides the natural variation range (the percentile range is shown). In each panel, a pair of numbers indicate the degree of model agreement. The left one is the number of models showing a decrease from the 2th century to the 2st century while the right one is the number of models showing an increase. 39

64 CHAPTER 2 Diversity, nonlinearity, seasonality and memory effect in ENSO simulation and prediction 2. Introduction In the modeling hierarchy ranging from simplified conceptual models, empirical/statistical models, intermediate coupled models, hybrid coupled models to the fully coupled general circulation models, empirical models not only assist in investigating ENSO behavior but are also skillful as prediction models. As data-based methods, they were popular before the arrival of fully coupled numerical model predictions and are still useful in the new era of big data. Advancing ENSO modeling depends on the understanding of ENSO behavior as well as the behavior of the models themselves. In this study, we carry out a series of empirical model experiments to study the important ENSO characteristics of diversity, nonlinearity, seasonality and memory effect. We also address prediction problems including the well-known spring barrier and the less known slippage, i.e., tendency for predictions to incorporate too much persistence and thus lag behind the actual target month observations (Barnston et al. 22). We conduct the analysis using the Empirical Model Reduction (EMR) framework (Kravtsov et al. 25; Kondrashov et al. 25; Kondrashov et al. 25), which allows model settings to include additional quadratic terms, periodic terms and multilevel predictors. The operational prediction version of EMR (UCLA-TCD) participates in the real-time ENSO prediction plume of the International Research Institute for Climate and Society (IRI). Among eight empirical models in the plume, the UCLA-TCD model is very competitive as measured by a 9-year (22-2) real-time prediction and a 3-yr (98-2) hindcast, exceeded by only a few dynamical models. It also better copes with the spring barrier and target month slippage (Barnston et al. 22). 4

65 The first task of this study is to decompose EMR in order to identify which ingredients contribute most to its good simulation and prediction skill. To do so, we construct a series of models with various settings including adding additional quadratic terms, periodic terms, and multilevel and multivariate predictors. We then evaluate them in control groups, e.g., with/without nonlinearity, with/without seasonality, with/without memory, multivariate or multilevel approach. Through panel comparison of each model s ability to reproduce ENSO characteristics and its predictive ability, we show that deficiencies of the baseline settings are largely remedied in more complex models. Not surprisingly, we find that even our most advanced model has limitations. Along with the general evaluation, we hope to contribute to the following aspects of ENSO or empirical modeling research. The first is to better understand the differences between two representations of the memory effect. The intrinsic predictability of ENSO largely comes from memory stored in the subsurface ocean, which may be described as a recharge oscillator (Cane et al. 986; Zebiak and Cane 987; Jin 997a,b) or as a time-delayed oscillator (Suarez and Schopf 988; Battisti and Hirst 989). The approach of adding subsurface information (e.g., the 2 o C isotherm depth, denoted as Z2) as an additional variable is a natural extension of the Linear Inverse Model (LIM) framework (e.g., Blumenthal 99; Xue et al. 994, 997, 2; Johnson et al. 2a; Thompson and Battisti 2; Newman et al. 2a, b), while the approach of EMR fitting multiple levels in an SST time-delayed model is less common. We construct models of each type to illustrate their relation and make a comparison. Considering these two approaches together offers more choices to embed the memory in the model setting. A second aspect of our work is to evaluate model performance on ENSO diversity (Capotondi et al. 25). El Niños occur not only in the eastern Pacific but also in the central Pacific (Larkin and Harrison 25; Ashok et al. 27; Kao and Yu 29; Kug et al. 29; Di Lorenzo et al. 2; Lee and McPhaden 2; Karnauskas 23; Vimont et al. 24; Chen et al. 25; Takahashi et al. 25; Fedorov et al. 25). Most model evaluations use one-dimensional (d) measures, e.g., Niño 3.4 or the leading principal component (PC) of tropical Pacific SST anomalies (SSTA), but a two-dimensional 4

66 (2d) framework is necessary to describe ENSO s spatial variation. Takahashi et al. (2) showed measures of ENSO diversity in the literature could be viewed as linear combinations of tropical Pacific SSTA PC and PC2. Following Takahashi et al. (2) and Vimont et al. (24), we introduce a measure using the PC-PC2 pair for overall ENSO diversity performance. Takahashi et al. (2) suggested that the curved shape in PC-PC2 space implies that the two flavors of El Niño may not describe different phenomena but rather the nonlinear evolution of ENSO. The EMR framework does not explicitly specify coefficients to characterize ENSO flavors, so model performance on ENSO diversity is implicitly determined by model dynamics. We conduct stochastically forced simulations of various model combinations and find that nonlinearity is necessary to reproduce the curved shape in PC-PC2 space, supporting Takahashi et al. (2) s suggestion that ENSO diversity may emerge from nonlinear evolution. ENSO nonlinearity is reflected in the El Niño-La Niña (EN-LN) asymmetry (e.g., Hoerling et al. 997; Kang and Kug 22; Larkin and Harrison 22; An and Jin 24; Okumura and Deser 2; Choi et al. 23). Given these nonlinear features of ENSO, one would expect that including nonlinearity in the empirical model will improve simulation and prediction. Here we find that the nonlinear model does not improve simulation and prediction of Niño 3.4 but it does improve the skewed amplitude and the transition patterns from El Niño to La Niña. We also investigate the spring barrier in ENSO prediction. Prediction skill in Niño 3.4 ( SST PC) drops if initialized from the boreal spring but recovers after spring in both dynamic and statistical ENSO forecasts (Barnston et al. 22; Barnston et al. 23; Xue et al. 23). There is also an autumn barrier in the prediction of warm water volume ( Z2 PC2 or SST PC2) (McPhaden 23). One would expect a model with seasonal-varying dynamics to improve ENSO prediction across the common spring barrier. We find that the seasonal setting does not contribute much to reducing the seasonal barrier until combined with the memory effect. Another goal of our work is to gain more knowledge of the slippage problem in prediction. Recent studies (e.g., Tippett et al. 22; Barnston et al. 22; 23) found 42

67 that both dynamic and statistical ENSO prediction models characteristically produce a delay to the target month. It is as if the model has too much persistence. UCLA-TCD model is among the models with little slippage and here we investigate which model ingredients contribute most to reducing the slippage and find that the memory effect is the most important factor. Limited observational data often bring in large uncertainties in model training and performance evaluation. In order to construct robust models and reduce evaluation uncertainty, we use a long record (4 year) of simulated data and conduct ensemble experiments to estimate uncertainty in training and verifying periods. 2.2 Data 2.2. GFDL CM2. PI This study uses monthly data from a 4 year pre-industrial simulation of the GFDL CM2. coupled GCM ( [.33 ] ) (Delworth et al. 26). This simulation has been shown to have a reasonably realistic ENSO (e.g., Wittenberg et al. 26; Kug et al. 2; Choi et al. 23; Wittenberg et al. 24), though its amplitude is too large (Wittenberg 29) and it may be less predictable than the real ENSO (Karamperidou et al. 24). To justify using a model simulation as a substitute for observations, we present comparisons of several main ENSO characteristics between the GFDL CM2. simulation and the observational dataset of HadISST V. 87-present monthly ( ) SSTs (Rayner et al. 23). We also compared with 3 other observational SST datasets: COBE V2 (Hirahara et al. 24), Kaplan (Kaplan et al. 998) and ERSST V3b (Smith et al. 28). Results with these 3 are nearly identical to those with HadISST. For simplicity, the observations are referred as OBS and the simulation is referred as GCM hereafter. All data are pre-processed as follows. SST data are restricted to the tropical Pacific domain (8E-72W, 3S-3N). SSTA in OBS are calculated by removing a monthly climatology based on the 95-2 period, while SSTAs in GCM are calculated by removing a monthly climatology based on the entire 4-year record. To remove the 43

68 influence of the global warming trend in OBS and model drift in GCM, linear detrending is applied to the SSTA at each grid point. Then a 3-month running average is applied to smooth the temporal noise. In addition to SST, we also use the 2 o C isotherm depth (Z2) in the tropical Pacific (8E-72W, 2S-2N), as a proxy for thermocline depth, to incorporate subsurface information. The processing of Z2 is similar to SST. SST and Z2 variability are then decomposed using Empirical Orthogonal Function (EOF) analysis Comparison with observations Fig. 2. top row shows the leading two EOF patterns of SSTA. In both OBS and GCM, the leading EOF (EOF) is the familiar El Niño pattern. The second EOF (EOF2), which adds flavor to the main El Niño pattern, has a zonal dipole pattern with positive loading in the western Pacific when the loading in the eastern Pacific is negative. The first and second mode explain 5 % and 8 % of the total variance in OBS, and 52 % and % in GCM. EOF patterns from GCM are reasonably realistic and are generally consistent with observations, although slightly shifted west and narrower in the meridional direction, as noted by Wittenberg et al. (26). Besides the EOF patterns (Fig. 2.), the results show good consistency between observation and simulation in the sign of the skewed distribution, seasonal standard deviation and lagged autocorrelation. The joint probability distribution of (PC, PC2) is also reasonably consistent between OBS and GCM (Fig. 2.3a and 3b). Additional discussion is given in section 5. These comparisons suggest that ENSO characteristics in GFDL CM2. are reasonable realistic so the understanding from the modeling study based on the GFDL CM2. may be applicable to nature. An important caveat is that nonlinearity in the GFDL CM2. is much stronger than in nature so the nonlinear setting may not be as helpful in modeling nature. 44

69 2.3 Methods: empirical model reduction 2.3. Baseline model Linear inverse models are widely used empirical modeling techniques for ENSO, in which the full dynamics of the tropical Pacific SST variability from seasonal to inter-annual time scales is approximated as a linear system of ordinary differential equations (e.g., Penland 989; Blumenthal 99; Penland and Magorian 993; Penland and Sardeshmukh 995; Penland 996; Xue et al. 994, 997, 2; Johnson et al. 2a; Thompson and Battisti 2; Compo and Sardeshmukh 2; Newman et al. 2a, b). LIMs have been shown successful in predicting ENSO (e.g., Penland and Sardeshmukh 995) and tropical Atlantic variability (Penland and Matrosova 998) as well as extratropical variability (Alexander et al. 28). In the LIM family, features like seasonality and memory effect may be implemented in many possible ways. In the EMR framework, we construct linear and nonlinear models, nonseasonal and seasonal models, models with and without memory effects. In this study a nonseasonal SST linear model without memory effect is considered as the baseline model. By construction the baseline model lacks nonlinearity and seasonality and assumes the next step SSTA only depends on the current state of SSTA, ignoring memory effects from subsurface processes or from the past history of SSTA Model with nonlinearity Nonlinear features of ENSO include the asymmetry between El Niño and La Niña in amplitude (El Niño is often stronger than La Niña), duration (La Niña is often more persistent), transition (an extreme El Niño is more often followed by a La Niña than vice versa), and in teleconnections (e.g., Hoerling et al. 997; Kang and Kug 22; Larkin and Harrison 22; An and Jin 24; Okumura and Deser 2; Choi et al. 23). There are many possible ways to construct a nonlinear model, e.g., multiple nonparametric regression (Timmermann et al. 2) or neural-networks (Tangang et al. 998). In the polynomial modeling framework of EMR, one straightforward way is to add a quadratic term, which has been shown to successfully reproduce the skewed probability 45

70 density function (PDF) characteristics of the observed ENSO (Kravtsov et al. 25; Kondrashov et al. 25). Taking this approach, the empirical model is constructed in a reduced phase space of K EOFs. For the main level, dx i = (x T A i x + b i x + c i )dt + dr i ; i =,..., K (2.) where x = {x i } is the K dimensional state vector (i.e. the time coefficients of the EOFs, the PCs). The quadratic terms on the right-hand side are dropped for linear models. The model coefficients in the matrices A i, the vectors b i of matrix B, the components c i of vector c and the components r i of the residual r are determined by multiple polynomial regression (MPR) (McCullagh and Nelder 989), which is the generalized version of multiple linear regression (MLR) (Wetherrill 986). The noise in the climate system usually have spatial dependence, as addressed in Penland and Sardeshmukh (995). Therefore the noise covariance matrix, implicitly embeding the spatial coherent information, is estimated along with other deterministic coefficients and further used to generate spatially coherent white noise for the stochastically forced simulations. For the nonlinear EMR models non-zero c accounts for the mean nonlinear drift (Kondrashov et al. 2). For consistency the c coefficients are retained in linear model as well, but their estimated values are negligible, as expected for a dataset of anomalies around a zero time mean and without a trend Model with seasonality Another notable feature of ENSO is seasonal phase locking, the tendency of El Niño and La Niña to peak toward the end of the calendar year, which is the result of competing coupling feedbacks (Tziperman et al. 995, 997, 998; Neelin et al. 2; An and Wang 2). There are several possible ways to introduce seasonality in a model. One way is to fit a varying linear propagator for each calendar month (e.g., Blumenthal 99; Xue et al. 2). Another is to treat seasonality as periodic terms as in EMR (Kravtsov et al. 25; Kondrashov et al. 25) with consideration of the interaction between the annual cycle and variability as in Tziperman et al. (995). 46

71 Following the EMR framework, we include seasonality by adding additional coefficients into the main level of the model: B = B n + B s sin(2πt/t ) + B c cos(2πt/t ) (2.2) c = c n + c s sin(2πt/t ) + c c cos(2πt/t ) (2.3) where the matrix B n and vector c n are the original nonseasonal terms as in Eq. 2., matrices B s, B c, vectors c s and c c are seasonal terms, and the period T =2 month. All these coefficients are determined simultaneously with the other coefficients in the main level. Note that the seasonal dependence is allowed for the linear part of the model on the main level, but not for the noise Model with memory effect ENSO is often viewed as a recharge oscillator where the system memory is stored in the subsurface ocean that re-emerges through the thermocline feedback in the eastern Pacific SST variability (Cane et al. 986; Zebiak and Cane 987; Jin 997a,b). It could be also viewed as a time-delayed oscillator where the subsurface ocean memory is embedded in the SST history (Suarez and Schopf 988; Battisti and Hirst 989). These theories suggest two alternative approaches that could be used to add memory to the models. A natural extension directly based on the recharge oscillator viewpoint is to extend the SST-only state vector to a multivariate state vector by adding the leading PCs of ocean heat content, 2 o C isotherm depth, or sea level variation in the tropical Pacific (e.g., Blumenthal 99; Xue et al. 994, 997, 2; Johnson et al. 2a; Thompson and Battisti 2; Newman et al. 2a, b). A direct representation from the time-delayed oscillator viewpoint is to use only SST PCs but fit a multiple time level model using previous time steps rather than just the current time step. The multilevel fit could be executed at once (Chapman et al. 25; Lee et al. 25) or conducted recursively (Kondrashov et al. 25; Kravtsov et al. 25). In this study, we construct models in both multilevel and multivariate settings to compare these two approaches. Following Kondrashov et al. (25), we add the memory 47

72 effect via multilevels but confine nonlinearity and seasonality to the main (first) level. Adding an additional level, the temporal increment of the residual at the main level dr is further modeled as a linear function of an extended state vector [x, r ] (x T, (r ) T ) T. More levels are added in the same way, until the Lth level s residual r L+ becomes uncorrelated in time with a lag- correlation matrix that converges to a constant matrix (details are given in Appendix A of Kondrashov et al. 25), where the b j i and rj i dx i = (x T A i x + b i x + c i )dt + dr i dr i = b 2 i [x, r ]dt + dr 2 i dr 2 i = b 3 i [x, r, r 2 ]dt + dr 3 i (2.4)... dr L i = b L+ i [x, r, r 2,..., r L ]dt + dr L+ i i =,..., K for level j are determined recursively. In addition to SST-only multilevel models, we also construct multivariate models, in which the state vector x is in K = m + n dimensions with the leading m normalized SST PCs and the leading n normalized Z2 PCs given equal weighting. Sensitivity tests show that slight weighting changes do not change the conclusion Modeling experiments In this modeling framework, there are many possible model settings and coefficient choices: m SST PCs, n Z2 PCs, j levels, linear or nonlinear, nonseasonal or seasonal. Since we can not include all possible settings in this study, we offer 2 typical model settings to conceptually compare simulation and prediction performance. The 2 models are specified in Table 2.. There is evidence that ENSO is a low-dimensional system with only a few degree of freedom (Tziperman et al. 994). Rather than simply increasing the size of the state vector, here we assess how adding other ingredients may improve the skill. For 48

73 the baseline model, we choose a linear model with 3 SST PCs, L(3). Models with a large state vector often encounter overfitting problems given insufficient data; thus fewer coefficients is a desired property. Nonlinear models are especially prone to the problem of an ill-conditioned matrix and numerical instability (Kondrashov et al. 25). In order to avoid this, all the empirical models here have K 3 PC predictors. Consequently, all the models included in this study behave well and are numerically stable without any constraint or regularization. Besides the baseline model L(3), we include a linear model L(8) with 8 SST PCs for comparison. Nonlinear models, all with quadratic terms, are denoted as NL, S+NL, 2L+NL, 2L+S+NL. Seasonal models, all with periodic terms, are denoted as S, 2L+S, S+NL, 2L+S+NL. Both the nonlinear and seasonal models have 3 SST PCs, as for L(3). Memory effects are represented either in multivariate models with 3 SST PCs and 5 or Z2 PCs (M(8), M(3)), or in SST models with multiple time levels (2L, 5L, 2L+NL, 2L+S, 2L+S+NL). The sensitivity test shows the qualitative conclusions still hold when using a linear model with more than 3 SST PC as the baseline model, though the quantitative improvement given by additional model complexity is less. SST and Z2 PCs for all 4 years are obtained once and then the data are divided into two parts for model training and evaluation as follows.. Model training and evaluation for goodness of fit are carried out in the first 2 years using non-overlapping segments of 2 years. The model used for further simulation and prediction is obtained by averaging the models from all segments. 2. Evaluation of simulation performance is made by conducting 2 -year stochastically forced simulations and then comparing simulated statistics with the GCM data statistics for the training period month lead out-of-sample predictions are carried out in the last 2 years using segments of 2 years. 2-member stochastic ensemble forecasts are carried out and the predicted value for each initial condition is the ensemble averaged result. An ensemble size of 2 is generally enough to sample the model spread. 49

74 2.4 Model goodness of fit Though goodness of fit does not guarantee good out-of-sample prediction skill (in section 6), it does indicate in-sample theoretical skill. We measure the model fit by applying the model on the training period and examining the residual statistics, including residual standard deviation (STD) and residual skewness. A good model fit is characterized by small residual STD and near zero residual skewness. Results for all the models in Table 2. are shown in Fig The total number of coefficients is shown for each model. This count does not include elements of the noise covariance matrix. Although the constant c is kept in the count, it is negligible for linear models. Error bars indicate the spread of residual STD in mutually exclusive training segments. L(3) is the baseline model with its residual STD as the benchmark. For PC, adding seasonality (S) or quadratic terms (NL) or the combination of both (S+NL) does not reduce residual STD much. Extending the SST state vector to 8 PCs, L(8), reduces residual STD by 2%, while extending the state vector to include Z2 PCs (M(8), M(3)) reduces residual STD by 3%. The other way to add memory effect, by fitting more time levels of the residual (2L) and its variations (2L+NL, 2L+S, 2L+S+NL) all show reductions of 5%. More levels (5L) reduce residual STD by 6%. For PC2, adding memory through Z2 or adding levels gives a better fit than adding seasonality and nonlinearity. Adding 2 levels (2L) reduces residual STD by 35% for PC2, less than the 5% reduction for PC. Note that including memory effect also reduces residual skewness to near zero (Fig. 2.2c,d). Compared to the baseline model L(3), models adding seasonality (S), nonlinearity (NL) or extending the state vector (L(8), M(8), M(3)) require more coefficients and do show a better fit. However, the multilevel model (2L), with fewer coefficients than multivariate model M(3), does fit better. The comparison shows that the multilevel approach successfully captures the effects of ocean memory in terms of SST itself, a better observed quantity than subsurface variables. These results show that the memory effect is the most important addition to the 5

75 baseline model. Nonlinearity and seasonality do not help much unless combined with the memory effect. Since from the physical perspective a large fraction of the total variance of the tropical Pacific SST anomalies is associated with the recharge oscillation, representing this memory effect in a data-drive model is essential. 2.5 Results of ENSO simulation We will first present ENSO characteristics in OBS and GCM and then compare them with the modeled statistics Nonlinearity: El Niño-La Niña asymmetry In both OBS and GCM, asymmetries about zero and the curved shape of the 2-dimensional probability density function (PDF) in PC-PC2 space indicate ENSO nonlinearity (Fig. 2.3a and 3b). The other plots in Fig. 2.3 show that various linear models (L(3), 2L, M(8), S) are not able to reproduce this curved shape but have an ellipsoid shape centered at (,). On the contrary, the various nonlinear models (NL, 2L+NL, S+NL, 2L+S+NL) show a curved shape in PC-PC2 space in approximate agreement with the data. The first three models (NL, 2L+NL, S+NL) show a small deficiency with a spike towards negative PC and negative PC2, but agreement is improved in the comprehensive model (2L+S+NL). In both OBS and GCM (Fig. 2.), the PC skewness (.39 and.35, respectively) is positive, meaning warm states occur less often than cold states but with stronger amplitude in El Niño than La Niña. PC2 skewness is negative and GCM has stronger nonlinearity than OBS with a more strongly skewed PDF in PC2 (-.23 vs -.4). This is associated with the fact that GCM has more extreme El Niños. For all the models trained using GCM data, the linear models show skewness close to zero, while the four nonlinear models approximately match the skewness in GCM and resemble its d PDF for PC and PC2 (not shown). 5

76 2.5.2 Diversity: moderate and extreme El Niño Both OBS and GCM show ENSO diversity in PC-PC2 space, represented by the curved shape of the 2-dimensional PDF (Fig. 2.3a and 3b). Takahashi et al. (2) inspired us to distinguish various SSTA patterns using the PC-PC2 space. The central region in PC-PC2 space (Fig. 2.3) is associated with neutral patterns with small variability. The upper right quadrant are the warming anomaly patterns occurring at the central Pacific. The lower right quadrant are the warming anomaly patterns peaking at the eastern Pacific and far end points are where extreme El Niños locate. The upper left quadrant are the cooling anomaly patterns occurring at the eastern Pacific. The lower left quadrant are the cooling anomaly patterns peaking at the central Pacific and far end points are where extreme La Niñas locate. The negative PC2 region is usually the transition patterns from the extreme El Niños to the following La Niñas. In order to reproduce the ENSO diversity, the model needs to not only generate anomaly patterns with realistic amplitude but also the correct location of the variability. Among the 8 models in Fig. 2.3 the linear models do generate SSTA patterns with large variabilities but their extreme El Niños are not in the far eastern Pacific (lower right region) and their extreme La Niñas are not toward the central Pacific (lower left region). The ENSO patterns produced by the nonlinear models more closely resemble the diversity characteristics of the data Seasonality: phase locking Both OBS and GCM exhibit seasonal phase locking in monthly standard deviations (STD), with PC showing larger variability in boreal winter and PC2 showing larger variability in boreal summer (Fig. 2.). The correlation coefficient (Corrcoeff) between the monthly STD of GCM and that from a stochastically forced simulation is used as a skill measure for seasonality. Nonseasonal models produce nearly constant monthly STD and thus a Corrcoeff near zero. Seasonal models have seasonal variations that are similar to the training data, which is consistent with Kondrashov et al. (25). For the simplest seasonality-only model Corrcoeff is close to one, but adding nonlinearity or 52

77 levels reduces this skill measure slightly Seasonal memory: lagged correlation In both OBS and GCM (Fig. 2.), PC is not autocorrelated across boreal spring but retains a substantial correlation after spring almost until the next spring. PC2 autocorrelation (Fig. 2.4h) shows a similar break, but in late autumn instead of spring. The modeling comparison (Column 2-7 in Fig. 2.4) shows that both seasonality and memory effects are needed to mimic the lagged autocorrelation. For models without the memory effect (L(3), NL, S), autocorrelation slowly decays as a function of lag. Models with the memory effect (M(8), 2L) better resemble the data. Nonseasonal models (L(3), M(8), 2L, NL) all show a uniform autocorrelation across all calendar months. Adding seasonality alone (S) produces seasonally varying lagged autocorrelations, but without the memory effect it does not resemble the GCM autocorrelation decay as function of lag. Thus the model with seasonality and memory effect (2L+S) shows the best overall resemblance to the data. 2.6 Results of ENSO prediction In this section, the evaluation aims to identify each model ingredient s contribution to prediction skill Performance for El Niño (PC) and El Niño-La Niña transition (PC2) Our principal measures of skill are the correlation coefficient (Corrcoeff) and root mean square error (RMSE) between target PC time series and predicted PC time series at given lead time τ. PC represents main variability thus is more important than PC2, so a model with poor skill for PC but good skill for PC2 is not viewed as a good model. Fig. 2.5 shows the improvement of the 2-month forecasts as measured using the Corrcoeff for different model settings compared to persistence and the baseline model L(3). For PC (Fig. 2.5c), the seasonal model (S) does not help much. The models with more SST PCs L(8) and with nonlinearity (NL) show slight improvement. Models with memory effect (both Z2 and levels) improve the most. For PC2 (Fig. 2.5d), the 2-53

78 month forecast Corrcoeff for persistence and L(3) are relatively high, thus improvement using other settings is not as remarkable as for PC. The models adding seasonality (S), more SST PCs or the memory effect do not help. Models with nonlinearity show better skill. Note that even though seasonal models do not show much improvement compared to the baseline model L(3), the model with both memory effect and seasonality (2L+S) does show slightly better skill than the memory model (2L) itself. The RMSE results (not shown) are consistent with Corrcoeff results, showing that the memory effect efficiently reduces PC RMSE and nonlinearity works best to reduce the PC2 RMSE. Models with both memory and nonlinearity have overall good performance on the PC-PC2 pair. Among all the models, the skill difference for PC is mainly between models with and without memory effect, rather than between linear and nonlinear models. The seasonal linear model with memory (2L+S) and the seasonal nonlinear model with memory (2L+S+NL) give overall the same performance for PC. For different evaluation periods with fewer or more extreme ENSO events, 2L+S may have higher/lower skill than 2L+S+NL though within the range of the error bar. Linear and nonlinear models have generally the same skill for PC once they include the memory effect, which is consistent with Kondrashov et al. (25). To see this, note that in their Fig. 2.2c -L is the same as S+NL in this study and 2-L is 2L+S+NL. In their Fig. 2.6a Linear is 2L+S in this study and Nonlinear is 2L+S+NL. The Corrcoeff difference between Linear and Nonlinear is.5, much smaller than the difference between -L and 2-L (.2) Skill drop due to spring barrier and autumn barrier The spring barrier in PC and autumn barrier in PC2 we saw in the SSTA seasonal lagged autocorrelations (Fig. 2.4a and 4h) are reflected in model predictions (Fig. 2.6). All model settings inherit this barrier problem to differing degrees. The prediction skill of persistence is the benchmark for comparison. Its skill for PC quickly drops if initiated from spring and its skill for PC2 drops quickly if initiated from autumn. The 6-month lead forecast from each calendar month (Fig. 2.6) shows that models with memory effect 54

79 (M(8), M(3), 2L, 5L, 2L+NL, 2L+S, 2L+S+NL) significantly reduce the problem for PC. For the PC2 autumn barrier, nonlinear models (NL, 2L+NL, S+NL, 2L+S+NL) have better skill than other models. The seasonal model (S) itself does not show much ability until combined with memory effect and nonlinearity. In Barnston et al. (22), both dynamical and statistical models with various data assimilation and advanced features all show some drop in skill around spring. Following the same layout as the Fig. 2.5 in Barnston et al. (22), the influence of the spring barrier is shown for each target calendar month (Fig. 2.7). The results show adding more features to the base model reduces the seasonal barrier but even the most complex models in this study still show signs of seasonal barrier, similar as shown in Kondrashov et al. (25). Also note that while the spring barrier in PC is the main problem in SST prediction, reducing the autumn barrier in PC2 improves the transition between El Niño and La Niña thus increasing the total prediction skill for SST Timing delay: target month slippage Slippage denotes the tendency of forecasts to retain initial conditions for too long; i.e. to overdo persistence. Thus, for example, a forecast intended to verify 6 months ahead may actually verify best at 4 months ahead: the prediction slipped by 2 months. Following Barnston et al. (22), we present the slippage performance by showing the lagged correlation coefficient between the target time series and the predicted time series (Fig. 2.8). Persistence is shown as a reference, and large slippage is indicated by the region with high Corrcoeff (>.8) pointed to the right rather than being vertical. The comparison among all models indicates that the memory effect (M(8), 2L, 2L+S+NL) substantially corrects the tilt for PC, while memory and nonlinearity (NL, 2L, 2L+S+NL) slightly correct the tilt for PC2. We then identify the degree of slippage using the lag which gives the maximum Corrcoeff and plot this slippage at each lead time (Fig. 2.9). Persistence, which is used as a benchmark, necessarily slips τ months for a τ month prediction. For PC, the slippage of each model slowly increases as the lead time increases. For a 6-month prediction, L(3) slips 5 months for PC and 6 months for PC2. Models with the memory 55

80 effect reduce the PC slippage to 2 months. Nonlinear models reduce the PC2 slippage to 3 months ENSO Diversity performance measured in PC-PC2 Model ability to predict ENSO diversity is evaluated in PC-PC2 space (Fig. 2.). We introduce a measure D 2 defined as the Euclidean distance between the target PC-PC2 pair (x, x 2 ) and the predicted PC-PC2 pair (y (τ), y 2 (τ)) at a τ month lead: D 2 (τ) = ((x y (τ)) 2 + (x 2 y 2 (τ)) 2 ) /2 We show the D 2 values at leads of 3, 6 and 2 months in Fig. 2.. The value in a given grid cell represents the model skill for the target SSTA patterns that projected to this given grid cell. The central points of PC-PC2 are associated with neutral patterns with small variability. The lower right corner are the patterns of strong El Niño and the lower left corner are the patterns of strong La Niñas. Given D 2 measuring the absolute errors rather than the errors normalized by the amplitude of the variability, large errors are associated with large variability. Comparison of different models show that persistence loses skill quickly. Baseline model L(3) gives a slight improvement over persistence. Models with memory effect show better skill than L(3) with the primary improvement occurring for strong La Niña patterns (negative PC). Nonlinear models account for ENSO skewness and mainly improve the skill in the negative PC2 region. The comprehensive model (2L+S+NL) has the best skill overall and shows improvement for a diverse target patterns. Note that at long lead (2 month) prediction, the comprehensive model settings do not show much improvement in predicting the extreme El Niños but somewhat improve the skill for the transition patterns from extreme El Niño to La Niña (negative PC2 region) as well as the extreme La Niñas (negative PC region). Many studies (e.g., Vecchi et al. 26; Chen et al. 25) have shown that the amplitude of extreme El Niño is largely a result of anomaly growth driven by the state-dependent noise such as the westerly wind bursts and is thus less predictable. Our current 2 models do not consider such state-dependent noise, which is proposed for future study. 56

81 2.6.5 Summary From the preceding results, some general conclusions emerge. The memory effect contributes most to PC prediction and nonlinearity contributes most to PC2 prediction. They both contribute to overcoming the seasonal barriers and reducing target month slippage. Adding seasonality does not help much for prediction until combined with memory effect and nonlinearity. Much room for improvement remains, especially for extreme El Niño patterns. 2.7 Discussion 2.7. Nonlinearity: pros, cons, future direction Nonlinear models are theoretically superior to linear models in terms of mimicking ENSO behavior, in particular, reproducing the skewed d and 2d PDFs. Linear models do not produce the skewed amplitude of ENSO while quadratic terms correct this deficiency. Nonlinearity does not contribute much to prediction of the slightly skewed PC but does matter for PC2. Thus its advantage may be overlooked if using PC (or Niño3.4) as the only metric, as seen in Kondrashov et al. (25). On the other hand, we may not be able to obtain robust nonlinear coefficients if the training data lacks sufficient extreme events, in which case a linear model may be the more practical choice. For the low-dimension state vectors and long training dataset used in this study, nonlinear models behave well without imposing energy conservation constraints. However, given a large state vector or insufficient training data, numerical instability may make constraints necessary (Appendix C of Kondrashov et al. 25). Therefore we examined the change in model performance after applying the energy conserving constraint. The results (Fig. 2.) show that the advantageous feature of nonlinear models to reproduce data skewness almost disappears thus the energy conserving nonlinear model performance ends up close to that of the linear model. The predictive skill for PC2 also slightly decreases. Nonlinear empirical models have many possible variations in format and algorithm beyond the quadratic terms. In addition to embedding nonlinearity explicitly in the for- 57

82 mulation, the skewed nonlinear effect could also be represented in state-dependent noise. Studies suggest that atmospheric noise like westerly wind bursts (WWB) may play a role in developing extreme El Niño events (Vecchi et al. 26) but WWBs are in-turn modulated by SST variation (Gebbie et al. 27). Chen et al. (25) added SST-modulated WWB-like perturbations to an intermediate ocean-atmosphere coupled model (Zebiak- Cane model) and successfully reproduced ENSO diversity, asymmetry and extremes. Chekroun et al. (2) introduced a past noise forecast (PNF) methodology by embedding the state-dependent noise into empirical prediction models and showed it can improve the ENSO prediction skill up to 6 months lead. Penland and Sardeshmukh (22) showed the multiplicative and additive noise forcing in a linear Markov model could also produce skewed distribution. Thus, a study of state-dependent noise may be a promising direction for further investigation Seasonality: not directly indicating predictability The seasonal model with periodic noise is able to reproduce seasonal phase locking for both PC and PC2. In contrast, a nonseasonal model even with a large SST state vector can not reproduce ENSO seasonality, although notable seasonal variations are present in these training PCs. It was expected that the seasonal model may improve the ENSO prediction and in particular help overcome the seasonal barrier, but it turned out the seasonal models did not improve prediction skill very much. A similar conclusion is also reached in Flügel and Chang (998) and Johnson et al. (2b). On the other hand, our results do show that adding seasonality to a model with memory (2L+S) has slightly better skill than the memory model itself (2L). This is similar to Xue et al. (2), who found that considering seasonality improved a multivariate LIM. Therefore it is fair to say that seasonality could improve the ENSO prediction if combined with a memory effect. Penland and Sardeshmukh (995) and Newman et al. (23) take an alternative approach of embedding seasonality into the noise forcing rather than in the dynamics. Further studies may explore other possible approaches to represent the seasonality in empirical modeling. 58

83 2.7.3 Memory effect: recharge oscillator vs time-delayed oscillator We incorporated the memory effect by adding Z2 in a multivariate model or adding more time levels. We confirmed that these approaches indeed improve the ENSO prediction skill, as shown in many previous studies using multivariate approach (e.g., Xue et al. 997; Newman et al. 2a) or multilevel approach (e.g., Kondrashov et al. 25). We also found that adding time levels of SST adds fewer coefficients than adding Z2 for similar skill improvement. If subsurface information is not available, one could construct an SST-only time-delayed model without loss of skill. We also showed that the memory effect is the most important factor for improving prediction skill, especially to reduce the seasonal barrier and target month slippage. Further study may explore more effective ways to implement and maximize the memory effect Seasonal barrier: memory refill, noises In addition to the well-known spring barrier in SST PC (Niño 3.4), we investigated an autumn barrier in SST PC2. It is consistent with the autumn barrier seen in Z2 PC2 (warm water volume mode) in McPhaden (23), given the strong linear relation between SST PC2 and Z2 PC2. The decorrelation across spring for PC and across autumn for PC2 strongly influence the models that rely heavily on SSTA persistence, but models with memory and nonlinearity can largely retain skill across all four seasons. The seasonal barrier appears not only in statistical models but also in dynamic models (Barnston et al. 22). Our results from empirical models may help us better understand the seasonal barrier in dynamic model prediction. In spring, the increase of atmospheric noises triggers large anomaly growth (e.g., Larson and Kirtman 25) and the SSTA field becomes noisy with a less distinguishable pattern (Xue et al. 994; Wu et al. 29). Models that initialize with additional subsurface state information work better (e.g., Chen et al. 995; 24). Usually, the SST variability of El Niño starts at the eastern Pacific when it emerges from the subsurface through the upwelling around autumn. Thus monitoring SST on the surface in the spring season does not offer much clue for whether the El Niño would occur in the following winter. So adding a memory 59

84 effect using the subsurface variable or SST history compensates the seasonal memory loss in the SST state alone Target month slippage: lack of growth from recharge mechanism Slippage, a measure of forecast mis-timing, occurs when models retain too much persistence. Barnston et al. (22) evaluated forecast models available at IRI and showed this slippage problem is common in both statistical and dynamical models. Tippett et al. (22) introduced a statistical post processing of model output to correct the slippage. Barnston and Tippet (23) also showed that Climate Forecast System Version 2 (CFSv2) (Saha et al. 24) greatly improves on slippage as compared to CFSv (Saha et al. 26). Adding multivariate or multilevel substantially reduces slippage suggests that the slippage is a consequence of insufficient representation of the memory effect ENSO diversity: nonlinearity, future direction ENSO diversity studies reveal the rich behaviors of the tropical coupled climate system. They also raise new challenges for ENSO modeling and prediction. In this study, we identified summer phase locking and an autumn barrier in PC2, in addition to the better known spring barrier seen in PC. The results suggest that if the modeling goal is merely the main ENSO signal (i.e. PC), then memory effect and seasonality may be sufficient. If the goal is to capture the skewed amplitude and have the ability to predict two flavors of El Niño, then also adding nonlinearity is useful. The new ENSO diversity measure D 2 reveals that the comprehensive model (2L+S+NL) is able to predict a wider range of SSTA patterns than the baseline model. Usually the extreme La Niñas tightly follow the extreme El Niños (Cai et al. 25a). Among all the model ingredients, adding nonlinearity most improves the skill for the transition patterns connecting extreme El Niños to La Niñas, thus strengthening the model s ability to simulate and predict diverse target SSTA patterns. This provides evidence supporting that ENSO diversity emerges from the nonlinear evolution of ENSO cycle as in Takahashi et al. (2). 6

85 2.7.7 Transferring from GFDL CM2. to nature Though there are discrepancies between GFDL CM2. and observations in the upper ocean stratification (Wittenberg et al. 26), the general understanding, that the memory effect is the most important factor to improve the model skill which is also supported by previous EMR and LIM studies conducted using observation, is applicable to nature. Here we also show that the memory effect largely reduce the seasonal barrier and slippage problems, though the improvement may be smaller in the real world with more stochasticity. For a strongly nonlinear system like GFDL CM2., nonlinear settings should by construction fit data better than linear settings and should show better skill to simulate and predict the given data. But in the real climate, though nonlinear features do show in extreme El Niño events, the majority of ENSO events are moderate. The overall degree of nonlinearity is much weaker in the observation; the observed SSTA PC2 skewness (-.4) is much less than that in GFDL CM2. (-.23). So the advantage of the nonlinear model compared with the linear setting may not be that notable in the real world, as in Kondrashov et al. (25). 2.8 Conclusion We use a 4-year GFDL CM2. pre-industrial simulation to help us gain better understanding of four important features in ENSO simulation and prediction: ENSO seasonality, diversity, nonlinearity and the memory effect. First we compare the ENSO statistics in simulation with observation and we find that the GFDL CM2. produces reasonably realistic ENSO statistics. It resembles the ENSO diversity feature embedded in the curved shape in the two leading principal components of tropical Pacific SSTA. It also agrees with observations as to the El Niño-La Niña asymmetry in the skewed probability density function of PC ( Niño 3.4) and in the winter phase locking. Thus the model experiments based on GFDL CM2. may inform us about nature. But we also note that GFDL CM2. has much greater nonlinearity than observed. In this study, a series of modeling experiments are carried out using empirical mod- 6

86 els ranging from a simple SSTA linear model to more refined models with additional model coefficients and terms. The conclusions are as follows: The memory effect, either by adding additional tropical Pacific subsurface information (e.g., a multivariate model with SST and 2 o C isotherm depth, as in the recharge oscillator viewpoint) or by adding additional SST history information (e.g., an SST-only model with multiple time levels, following the time-delayed oscillator viewpoint), improves the SSTA prediction significantly, though it is more efficient in a multilevel setting with fewer required model coefficients. The nonlinear models with quadratic terms reconstruct the skewed probability density function of SSTA and improve the prediction of the skewed amplitude. The memory effect and nonlinearity enhance the model s ability to retain prediction skill across the so-called spring/autumn prediction barriers and to substantially correct the prediction slippage (i.e., predicted value lags the target month value). The periodic terms enable the model to reproduce the seasonal phase locking of SSTA, even though they do not improve prediction by much. The comprehensive models with combined coefficients have the ability to capture several ENSO characteristics simultaneously and exhibit overall better prediction skill, in agreement with Kondrashov et al. (25), though they still have difficulty with the prediction of ENSO diversity, especially in predicting extreme El Niño patterns. In summary, this study contributes to our understanding of ENSO diversity, nonlinearity, seasonality and the memory effect in ENSO simulation and prediction. 62

87 Table 2.: List of ENSO empirical models with different model settings. L(m) is a linear model in the form of Eq. 2. without quadratic terms, constructed from a state vector of the leading m PCs of tropical Pacific SSTA; m=3 and 8 are presented. M(k) is the linear model constructed from a multivariate state vector of the leading 3 PCs of tropical Pacific SSTA and the leading n PCs of tropical Pacific 2 o C isotherm depth (Z2) anomalies; k=3+n with n=5 and presented here. 2L/5L is a multilevel linear model with 2/5 time levels and 3 SST PCs. NL denote the nonlinear models with quadratic terms. 2L+NL is a combined model with quadratic nonlinearity in the main level and linear terms in the one additional time level. S is the seasonal model with additional periodic terms. S+NL, 2L+S, and 2L+S+NL are combined models including seasonality. 2L+S+NL is the most comprehensive model of the 2 models studied here. Coeff# denotes the total number of coefficients in the design matrix. Coefficients in the noise covariance matrix are not included. Condition # denotes the condition number of design matrix for each level. See appendix of Kravtsov et al. (25) for more details. num. label SST Z2 Level NL seasonal coeff # condition # L(3) L(8) M(8) M(3) L ; L ;6.8;4.6;6.3;6.3 7 NL L+NL ; S S+NL L+S ; L+S+NL ;

88 3N EOF OBS 3N GFDL CM2. EOF2 3N EOF 3N EOF a) b) c) d) 3S 3S 3S 3S 8E 8 72W 8E 8 72W 8E 8 72W 8E 8 72W PC PC2 PC PC SKm=.39.2 SKm= SKm=.35.2 SKm= -.23 PDF.... e) f) g) h) STD.8 i).6 JFMAMJJASOND.8 j).6 JFMAMJJASOND.8 k).6 JFMAMJJASOND.8 l).6 JFMAMJJASOND Lagged Corrcoeff m) JFMAMJJASOND n) JFMAMJJASOND o) JFMAMJJASOND p) JFMAMJJASOND.5 Figure 2.: Comparison of ENSO statistics in SST observations (87-23) and GFDL CM2.. In the st and 4th row only HadiSSTv. results are shown. In 2nd and 3rd rows, four observation datasets are color-coded: HadiSSTv. (black), COBEv2 (green), ERSSTv3b (blue) and Kaplan (red). The 4-year pre-industrial run of GFDL CM2. is divided into 2 mutually exclusive 2-year segments for calculations in the 2nd and 3rd rows. Each segment is in gray and averaged result is in black. st row: Empirical Orthogonal Functions EOF and EOF2 of tropical Pacific SST anomalies. Shading is regression coefficient of tropical Pacific SST anomalies on principal component PC and PC2. Contour is the percentage of explained variance of PC and PC2. 2nd row: ENSO asymmetry and nonlinearity represented in the probability density functions (PDF) of PC and PC2. The skewness averaged among four observation datasets (SKm) is shown. For GFDL CM2. 2-segment averaged skewness is shown. 3rd row: ENSO seasonality is represented in standard deviation (STD) varying as to each calendar month. 4th row: ENSO memory and seasonal break of persistence are represented in lagged correlation coefficient (Corrcoeff). The x-axis is the initial calendar month, y-axis is the lag month. 64

89 Residual Skewness Residual Skewness Residual STD Residual STD.2 a) PC Goodness of fit Model w/o Memory w Memory w Memory + multivariate + multilevel. L(3) S NL S+NL L(8) M(8) M(3) 2L 2L+NL 2L+S 2L+S+NL 5L b) PC2.2. L(3) S NL S+NL L(8) M(8) M(3) 2L 2L+NL 2L+S 2L+S+NL 5L c) PC L(3) S NL S+NL L(8) M(8) M(3) 2L 2L+NL 2L+S 2L+S+NL 5L d) PC L(3) S NL S+NL L(8) M(8) M(3) 2L 2L+NL 2L+S 2L+S+NL 5L # of coeffs Figure 2.2: Goodness of fit measures are shown for all models in Table 2.. a) and b) are the residual standard deviation (STD) of the two leading PCs of tropical Pacific SSTA. c) and d) are the residual skewness. Models are displayed in three groups: models without memory effect, models with multivariate (SST and Z2) memory, and models with multilevel memory. The total number of model coefficients is given at the bottom. Each model carries its own color code. Error bars (one standard deviation) indicate the spread of the fit among 2-year training segments. Small residual STD and residual skewness close to zero indicate a good fit. 65

90 Figure 2.3: a) log of the 2-dimensional PDF [log (2dPDF)] of the two leading SSTA PCs in OBS. The grid cell size is.267x.267. b) as in a) but for GCM, the training data. c)-j) as in a) but for eight models in Table 2., based on -year stochastically forced simulations in each case. Linear models are grouped in the first column and nonlinear models in second column. A good simulation of ENSO nonlinearity is indicated by resemblance to the curved pattern and the PDF value distribution of the GCM data in panel b). 66

91 Lag (month).6 8 PC a) Data F A J A O b) L(3) F A J A O Simulation performance: ENSO lagged autocorrcoeff c) M(8) d) 2L e) NL f) S F A J A O F A J A O F A J A O F A J A O g) 2L+S F A J A O h) 2 8 PC i) j) k) l) m) n) F A J A O F A J A O F A J A O F A J A O F A J A O F A J A O F A J A O Initial calendar month Figure 2.4: Lagged autocorrelation coefficients for each calendar month. a) and h) are the average of 2 2-year segments from the GCM data (GFDL CM2.). The other panels show model results calculated by averaging over 2 2-year stochastically forced simulations. The 6 models shown are described in Table 2.. Every second calendar month is labelled. 67

92 Corrcoeff Corrcoeff Corrcoeff Corrcoeff Prediction performance: Corrcoeff PC fcst a) black--persistence Prediction lead (month) c) PC 2m lead fcst PC2 fcst b) Prediction lead (month) d) Model w/o Memory Model w Memory Per L(3) S S+NL NL L(8) M(8) M(3) 2L 5L 2L+NL 2L+S 2L+S+NL PC2 2m lead fcst.8 Linear Model Nonlinear Model Per L(3) S 2L+S L(8) M(8) M(3) 2L 5L NL 2L+NL S+NL 2L+S+NL Model construction Figure 2.5: Prediction performance: correlation coefficients for PC and PC2 of SSTA. For each model in Table 2., 2-member ensemble forecasts are carried out for 2 years that are out-of-sample (i.e distinct from the data used to construct the models). Correlations are between the data and the ensemble average. a), b) Forecast correlations at leads of to 2 months. Persistence (black line) is given as a reference. c), d) Correlations of 2-month lead forecasts. Error bars are created by dividing the forecasts into non-overlapping segments of 2 years each and showing the standard deviation. For PC, models with or without memory effect are grouped separately, while for PC2, linear and nonlinear models are grouped separately. The dashed line is the correlation coefficient for the benchmark model, L(3). 68

93 Corrcoeff Corrcoeff Corrcoeff Corrcoeff a) PC 6m lead fcst black--persistence J F M A M J J A S O N D Initial calendar month c) PC 6m lead fcst from March Model w/o Memory Prediction performance: seasonal barrier b) PC2 6m lead fcst J F M A M J J A S O N D Initial calendar month Model w Memory Per L(3) S S+NL NL L(8) M(8) M(3) 2L 5L 2L+NL 2L+S 2L+S+NL d).8 PC2 6m lead fcst from September Linear Model Nonlinear Model Per L(3) S 2L+S L(8) M(8) M(3) 2L 5L NL 2L+NL S+NL 2L+S+NL Model construction Figure 2.6: Prediction performance: seasonal variations and the boreal spring and autumn barriers. a), c) For all models in Table 2., the correlation coefficient between the GCM target time series and 6-month predictions initialized at each calendar month. Persistence is shown in black. Note that seasonal barrier exists for PC when initialized from boreal spring (e.g., March) and for PC2 when initialized from boreal autumn (e.g., September). c) PC 6-month lead prediction initialized in March. Models with or without a memory effect are grouped separately. d) PC2 6-month lead prediction initialized in September. Linear and nonlinear models are grouped separately. See Fig. 2.5 for additional descriptions. 69

94 PC2 Prediction lead (month) PC a) Per Prediction performance: Corrcoeff as to each target calendar month b) L(3) c) M(8) d) 2L e) NL f) S g)2l+s+nl F A J A O F A J A O F A J A O F A J A O F A J A O F A J A O F A J A O h) i) 2 8 j) k) l) m) n) F A J A O F A J A O F A J A O F A J A O F A J A O Target calendar month F A J A O F A J A O Figure 2.7: Prediction performance for PC and PC2 of each target calendar month, for six models in Table 2.. Correlation coefficient (Corrcoeff) between -2 month lead predicted time series and the target time series according to each calendar month. The result shown is averaged among 2-year prediction segments. Calendar months are labelled as F(February), A(April), J(June), A(August) and O(October). Good prediction skill is indicated by retaining large Corrcoeff toward 2-month lead prediction as well as having a small seasonal skill drop. 7

95 Prediction lead (months).6 Per Prediction performance: Corrcoeff as to lagged target a) PC b) PC L(3) c) d) M(8) e) f) L g) h) NL i) j) S k) l) m) 2L+S+NL Lag of target month n) Lag of target month Figure 2.8: Prediction performance: slippage, measured by the correlation coefficients between -2 month lead predictions and -2 to 2 month lagged target GCM data. Panels c) to n) show results for 6 of the models in Table 2.. Persistence, shown in the top panels as a reference, necessarily has an τ-month lag to the target month for an τ-month lead prediction. Good prediction performance is indicated by large correlation coefficients for the target month; i.e. along the vertical line at zero lag. Less slippage is indicated by reduced tilt with time of the maximum correlation coefficient. See Fig. 2.5 for additional descriptions of prediction methodology. 7

96 Slippage (month) Slippage (month) Slippage (month) Slippage (month) a) PC fcst black--persistence Prediction lead (month) Prediction performance: target month slippage b) PC2 fcst Prediction lead (month) c) PC 6m lead fcst 8 Model w/o Memory 6 Model w Memory 4 2 Per L(3) S S+NL NL L(8) M(8) M(3) 2L 5L 2L+NL 2L+S 2L+S+NL d) PC2 6m lead fcst Linear Model Nonlinear Model Per L(3) S 2L+S L(8) M(8) M(3) 2L 5L NL 2L+NL S+NL 2L+S+NL Model construction Figure 2.9: Prediction performance: slippage, defined as the lag which has the maximum correlation coefficient. Good prediction performance is indicated by fewer month of slippage. a), b) The slippage for -2 month lead predictions for each model in Table 2.. Persistence, shown as reference, necessarily has a slippage of τ months for an τ- month lead prediction. c), d) Slippage for 6-month lead predictions. See Fig. 2.5 for additional descriptions of prediction methodology. 72

97 Figure 2.: Prediction performance: ENSO diversity. Prediction skill is measured here by the Euclidean distance D2 between the predicted and GCM target PC-PC2 pairs. The space is divided into grid cells and D2 is averaged according to the target PC-PC2 grid cell. The grid cell size is.33 for PC and.3 for PC2. Persistence is shown on the first row as a reference. Prediction results are shown for 3, 6 and 2 -month leads. Good predictions of ENSO diversity are indicated by small D2 in a greater number of grid cells and for longer leads. See Fig. 2.5 for additional descriptions of prediction methodology. 73

98 Corrcoeff Corrcoeff Skewness Skewness Model performance after energy conserving constraint a) PC simulation w/o constraint w energy constraint.5 Data NL 2L+NL S+NL 2L+S+NL NL 2L+NL S+NL 2L+S+NL c c c c.5 b) PC2 simulation Data NL 2L+NL S+NL 2L+S+NL NL c 2L+NL c S+NL c 2L+S+NL c c) PC 2m lead fcst L(3) NL 2L+NL S+NL 2L+S+NL NL 2L+NL S+NL 2L+S+NL c c c c d) PC2 2m lead fcst L(3) NL 2L+NL S+NL 2L+S+NL NL 2L+NL S+NL 2L+S+NL c c c c Model construction Figure 2.: Influence of an energy conserving constraint on the four nonlinear models in Table 2.. Models without a constraint are grouped in column 2-4 and models with the constraint are grouped in the last four columns. The constrained models carry the same color code as the unconstrained versions, but with a c subscript. The quality of the model simulations is measured by skewness in a) and b); the GCM data skewness to be simulated is shown in the first column. Skewness is chosen because it depends on nonlinearity. Prediction performance, as measured by the correlation coefficient for 2 month forecasts is shown in panels c) and d). See Fig. 2.5 for additional descriptions of prediction methodology. 74

99 CHAPTER 3 Predictability of ENSO flavors: prediction horizon, optimal precursors and probabilistic measures 3. Introduction ENSO prediction has been improving (Goddard et al. 2; Chen et al. 24; Chen and Cane 28; Barnston et al. 22). Predictability questions have also been extensively investigated from various angles, such as whether El Niño is intrinsically predictable (Fedorov et al. 23) or whether the prediction uncertainty due to chaos or stochastic forcing is dominant (Palmer and Zanna 23). Optimal growing pattern for ENSO has been diagnosed (Penland and Sardeshmukh 995; Xue et al. 997) and the prediction horizon has been estimated, e.g., from a local Lyapunov exponents (Karampeidou et al. 24). Three decades after the dynamical ENSO forecast of Cane et al. (986), current ENSO prediction is heading in two directions. One is extending to decadal predictions, which is not optimistic due to the intrinsic limit of ENSO predictability (Wittenberg et al. 24). The other direction is to predict ENSO diversity. An important diversity feature is that El Niños (EN) show two flavors peaking either in the central Pacific (CP) or the eastern Pacific (EP). These CP and EPEN have different global impacts (e.g., Larkin and Harrison 25; Ashok et al.27; Weng et al. 27). Therefore the new target is to predict not only the amplitude of the ENSO variability (e.g., sea surface temperature anomaly) but also the correct location where it peaks. Real-time predictions show some difficulties. More CPEN appeared in the last decade (Lee and McPhaden 2) and the prediction skill of most models dropped (Barnston et al. 22). Dynamical models with advanced data assimilation like CFSv2 and NMME somehow have the systematical tendency to predict a CPEN as a EPEN (Xue et al. 75

100 23; Kirtman et al. 24). Why is it difficult to distinguish CPEN/EPEN flavors? Is the difficulty more dependent on model shortcomings or more in the intrinsic predictability of ENSO diversity itself? Figure 5 in Barnston et al. (22) showed that, for a certain period almost all models have good performance but for some other periods they all show a substantial drop in skill, which suggests the difficulty may be due to the phenomenon itself. Many previous studies indicate that ENSO system is chaotic (e.g., Tziperman et al. 994). The predictability is sensitive to initial conditions (Karamperidou et al. 24). Why are certain initial conditions difficult to specify adequately? What do they look like? We analyzed past observed El Niño events and found that the initial warming of SSTA at the western Pacific (WP) is often the precursor for both CPEN and strong EPEN events (Fig. 3., 2; details are in the data section). When such initial condition appears, the system may evolve to either CPEN or EPEN, so the long-term prediction is largely uncertain. In this study we will investigate whether the EPEN and CPEN have intrinsically limited predictability. Previous predictability studies identified some precursors for each El Niño flavor (e.g., Newman et al. 2; Vimont et al. 24; Capotondi and Sardeshmukh 25). We will revisit the precursors but will focus on predictability limits and uncertainty. Here we address the source and limits of predictability, the prediction horizon, and uncertainty. A robust evaluation requires sufficient ENSO events but the historical record is limited so we then turn to model simulations, in particular a 4 year GFDL CM2. pre-industrial control simulation that reproduces reasonably realistic El Niño flavors (e.g., Wittenberg et al. 26; Kug et al. 2). 3.2 Data 3.2. Observed records The observed sea surface temperature (SST) and subsurface temperature (Tsub) are examined. We analyzed the 43-year (87-22) monthly tropical Pacific (8E-72W, 3S-3N) SST in HadISST V. (Rayner et al. 23) is analyzed, which has been 76

101 investigated extensively in many climate studies (e.g., Deser et al. 2; Takahashi et al. 2). The 4-year (87-2) monthly equatorial (2S-2N averaged) Tsub (5m- 32m) from Simple Ocean Data Assimilation (SODA) version (Carton and Giese 28; Giese and Ray 2) is analyzed, which is also widely used (e.g, Newman et al. 2b; Santoso et al. 23; Vimont et al. 24). SST and Tsub anomalies are calculated relative to a 98-2 climatology. Linear detrending and a 3-month running average are applied Simulated records 4-year monthly tropical Pacific (8E-72W, 3S-3N) SST and equatorial Pacific (2S- 2N averaged) Tsub (5m-3m) in the GFDL CM2. pre-industrial control simulation (Delworth et al. 26) are analyzed. GFDL CM2. has been shown to successfully reproduce many characteristics of observed tropical climate variability (Wittenberg et al. 26) and it is widely used to investigate ENSO dynamics and diversity (e.g., Wittenberg 29; Kug et al. 2; Karamperidou et al. 24; Choi et al. 23). SST and Tsub anomalies are calculated relative to whole-length data climatology. Linear detrending and a 3-month running average are applied El Niño evolutions in observation and simulation We present 2-month observed SST evolution patterns of the CPEN event and the EPEN event (Fig. 3.). The results show that two similar initial conditions with equatorial western/central Pacific SST warming anomalies may develop to either CPEN or EPEN. In the simulation, we present the 2-month evolution patterns of one CPEN event and one EPEN event in the SST field (Fig. 3.2). The results again show that CPEN and EPEN flavors both originate from the equatorial western Pacific. The simulated process appear to be very similar to the observation, though the actual location of the warming anomaly at the western Pacific is slightly shifted westward, which is commonly seen in GCMs (Wittenberg et al. 26). Later analysis will show this simulation is useful to help understand the ENSO predictability. We will also discuss what understandings may be transferred to nature in the discussion section. 77

102 3.3 Pinpointing the prediction horizon 3.3. Questions When a tropical Pacific SST warming anomaly develops to near the mature stage, telling the El Niño flavor is obvious. But when it is unsure whether a small warming anomaly could develop to an El Niño, it is not plausible to predict the EP/CP flavor. So pinpointing a prediction horizon is necessary. Then we further investigate what determines this time range Projecting patterns onto EOF basis Principal Component (PC) analysis is carried out to decompose the GFDL CM2. tropical Pacific SSTA variability into Empirical Orthogonal Function (EOF) modes. Fig. 3.3 shows the leading two SST EOFs. The classic El Niño-like SSTA pattern of EOF represent the dominant variability (52%), while the west-east dipole pattern of EOF2 (%) with positive anomaly loading in western- central Pacific and negative loading in the eastern Pacific adds flavor to the main ENSO pattern. Then Tsub anomalies are regressed on the first SST PCs to obtain the associated Tsub patterns. A subsurface zonal dipole along the thermocline is associated with SST EOF, while a central Pacific subsurface anomaly is associated with SST EOF2 (Fig.3 c,d) Categorizing ENSO states SSTA patterns of EPEN and CPEN occupy different regions in the phase space of PC- PC2 (e.g, Takahashi et al. 2). So the definition of ENSO states could be based on SST PC-PC2 space, which has been shown feasible in our study on ENSO behavior variation in Chapter 2. In the present study, we will Follow the same categorization. We first categorize the usual El Niño (EN), Neutral (NEU) and La Niña (LN) states using PC. EN is P C >.7s.d.(P C), where s.d. denotes one standard deviation. Similarly, La Niña is P C <.7s.d.(P C); the remainder are defined as NEU. We then use negative or positive PC2 as another threshold to divide EN and LN into the EP/CP flavors (see Fig. 3.3). The typical patterns of the EPEN and CPEN categories 78

103 are consistent with the patterns defined in earlier literature using Niño indices (Kao and Yu 29) or C/E indices (Takahashi et al. 2). After we define these 5 mutually exclusive ENSO states, we then categorize each monthly time step into one of these ENSO states. The states are determined using the full length of the data in order to keep the same definition of states when 4-year record is divided into shorter epochs Distinguishing EPEN/CPEN evolution The target is to assess how far in advance the difference between EPEN and CPEN precursor patterns become distinguishable. We collect EPEN and CPEN patterns and their precursors back to 5 months in advance and then project the averaged precursor patterns onto the SST EOF basis and present their evolutions in PC-PC2 phase space. We divide the 4 year data record into sliding epochs with 35 years apart and 5- yr length, and present the variations in the evolution of precursors among epochs in Fig The tracks of EPEN and CPEN precursors since 5 months ago in PC-PC2 space indicate EPEN and CPEN come from very close initial patterns and then gradually depart from each other. The prediction horizon is 4 months for the CPEN peak and 7 months for the EPEN peak. The shorter time range for CPEN suggests that it is more difficult to predict. 3.4 Identifying optimal precursors for EPEN and CPEN 3.4. Questions ENSO predictability studies mainly focus on analyzing how a small scale anomaly in a system can amplify to a recognizable large scale pattern, and identifying the optimal initial pattern for the leading growing mode (e.g., Xue et al. 994; Penland and Sardeshmukh 995). Along with extending the context from ENSO to ENSO diversity, the argument of predictability is also extended. We may view the diversity in SSTA patterns as coming from two leading growing modes, as in Newman et al. (2). So the question turns into when can we can distinguish the optimal initial patterns of each 79

104 mode? Linear inverse modeling (LIM) LIM is a type of empirical model that is often used for diagnostics and prediction. It is a widely applied technique not only for ENSO (e.g., Blumenthal 99; Xue et al. 994; Penland and Sardeshmukh 995; Johnson et al. 2; Newman et al. 2) but also for other climate variability like the Pacific Decadal Oscillation (Alexander et al. 27) and Atlantic Multi-decadal Oscillation (Tziperman et al. 28; Hawkins and Sutton 29). In this study the full dynamics of the tropical Pacific SST variability from seasonal to interannual time scales is approximated by a set of linear ordinary differential equations as in Penland and Sardeshmukh (995), dt/dt = LT + F where T is the state vector of tropical Pacific SST anomaly in a reduced space, usually the leading n PCs. L is the linear operator to be determined. F is the forcing term, and t is time. As in most fluid dynamics equations, the linear operator L usually yield LL L L, where denotes the transpose of the matrix. This nonnormal property enables small anomalies in the linearized system to display transient amplification before decaying away. In practice, the linear propagator G across a τ-month interval is obtained from a least square fit of T(t + τ) = G(τ)T(t) + r where r is the residual. We chose 2 SST PCs as the state vector T, which explains 85% of the total variance of tropical Pacific SSTA. We obtain G() first and then obtain G(τ) = G() τ, where time is in units of months Singular vector analysis The amplification dynamics of G(τ) over τ months could be diagnosed via a singular value decomposition with a L2 norm G(τ)V(τ) = U(τ)S(τ). S(τ) is a diagonal matrix of singular values indicating the amount of amplification over the time interval τ. The 8

105 right singular vector V(τ) multiplying the EOF basis yield the optimal initial patterns (OIP), which evolve to the resulting optimal evolved patterns (OEP) when multiplied by the propagator G(τ). Then we analyze how the leading growing modes develop from OIP to OEP. In each of the 5-year long epochs we diagnose the leading two growing modes of G and identify pairs of OIPs and OEPs SST amplification and sensitivity to data length The amplification curve in Fig. 3.5 shows that the leading growing mode (denoted as SV) can accumulate growth for months, while secondary growing mode (SV2) can only amplify for 5 months. Later Fig. 3.7 shows that SV is associated with EPEN and SV2 is associated with CPEN. SST amplification varies among epochs. We measure the robustness of growth using a signal to noise ratio (SNR) defined as the all-epoch averaged SV growth divided by the standard deviation of the SV growth rate over all epochs. We test the SNR of SV as function of lead time (, 3, 6, 9 months) and also as function of record length (2, 5,, 2, 5, 7, year). The results in Fig. 3.6 show that the robustness of the SNR increases with the slength of the data sample and decreases with lead time. A short data length(3-5 yr) may be acceptable for estimating the -3 month dynamical operator. But for long lead (6-2 months) forecasts, over years is needed to build a robust model, using SNR = as a threshold for 2-month prediction Optimal initial pattens for EP/CP flavors Using SST alone, the prediction horizon for CPEN is 4 month and that for EPEN is 7 months. We use a 6-month interval to identify the OIP difference between EPEN and CPEN. Fig. 3.7 shows that SSTA at the western Pacific dominates the optimal initial condition for CPEN while SSTA at the far eastern Pacific is optimal for EPEN. The recognizable difference in OIP suggests a possible short-term predictability. These two OIP are consistent with OIP Newman et al. (2) found using the observation data. One important feature for the OIPs is to find the sensitive regions where the SST 8

106 anomalies are prone to atmospheric noise. Taking advantage of the 4 year record, we do a sensitivity test on how diagnosed OIP vary in each individual epoch and whether using a longer data makes the diagnosed OIP more stable among different epochs. The results show, for a 6-month lead OIPs, 5-yr epochs have much less spread compared to the 5-yr epochs. Among different 5-yr epochs in Fig. 3.8, the most robust regions are the equatorial western Pacific for CPEN and equatorial eastern Pacific for EPEN. We also note that sensitive regions diagnosed in one 5-yr epoch may not be identified as sensitive in another 5 yr. So a long record helps to ensure a robust diagnosed pattern. Fig. 3.9 shows a 2-month OIPs of EP/CPEN mode. The OIPs for EPEN and CPEN flavors have similar patterns, consisting equatorial western and eastern Pacific warming, as well as a meridional anomaly north and south. Overall, the close initial conditions indicates that long-term prediction of ENSO flavors is difficult. The evolutions of the OIPs diagnosed using LIM generally tell a similar story as the evolutions in Fig. and Assigning a likelihood for flavor prediction 3.5. Questions Given the target is to predict El Niño flavor, a probabilistic forecast is necessary. If we categorize 5 ENSO states as in Fig. 3.3, then we may calculate a climatology probability distribution from the occurrence probability of each state D cli = (P EP EN, P CP EN, P NEU, P EP LN, P CP LN ). Given a SST anomaly pattern categorized in CPEN state, the initial probability distribution is D() = (,,,, ). For this specified initial condition, how should we predict the ENSO state that is most likely to happen? Since some dynamical models are systematically biased to predict a CPEN as a EPEN, the probabilistic forecast based on such dynamical models may be also biased. Here we seek to create a new benchmark for probabilistic forecast of ENSO 82

107 flavor using the state transition probability fit from the data. Note that we assume a stationary statistics for a certain period of time A probabilistic benchmark using state transition probabilities If we don t have any information about the system, then the simplest prediction is persistence (assuming the state will stay the same), so the distribution after a small τ month could be approximated the same as the initial distribution, i.e., when τ, D(τ) D(). For a long lead time, we expect the distribution will converge to the climatology distribution, i.e., when τ, D(τ) D cli. These two benchmarks are not functions of the lead time, and they only work at the limits of small or large lead time. So we present a new benchmark using the state transition probabilities which can vary with the lead time. We fit from data the probabilities in the transition matrix M(τ), M(τ) ij = P (X(t + τ) = j X(t) = i), i, j =,..., 5. Then we apply the transition matrix as a new benchmark, i.e., when < τ <, D(τ) = M(τ)D() Transition diagram The result of transition matrix can be visualized in a transition probability diagram (Fig. 3.). For a given state like CPEN (Fig. 3.e), the evolution for the next 36 months includes 5 possible outcomes. Here we highlight three relationships. The first is the local persistence of CPEN itself. The second is zonal propagation, i.e., migration from CPEN state to EPEN state. The third is the EN-LN transition, i.e., CPEN may change phase to become LN. From the short lead to long lead, the distribution gradually converges to the climatology distribution as expected. 83

108 The transition matrix may be used to evaluate probabilistic prediction reliability. For a same set of initial conditions, if the dynamical model is reliable and stationary, then the model-created transition diagram should look similar to the data-based diagram. If the model is biased, then the model-based diagram will have a skewed distribution favoring a certain ENSO state Likelihood map For prediction purpose, we further divide the PC-PC2 space into grid cells (c) to collect similar SSTA patterns and create a transition matrix for each grid cell M(τ, c). We first gather the initial patterns projected in a given grid cell and then count its destinations τ months later to calculate the likelihood to become one of five ENSO states. The likelihood maps for lead time at, 3 and 6 months are shown in Fig. 3.. When a new initial condition of SST anomaly is given, we can project it into PC-PC2 space and estimate the probability of each of the 5 states based on its location, i.e., for a grid cell c, D(τ, c) = M(τ, c)d(). Note that we can do this in practice if we have sufficient data to define the transition matrix and assume the system is stationary for a certain period. 3.6 Discussion 3.6. Implications for ENSO prediction in nature In this study, we analyzed the predictability using a 4-year simulated SST and Tsub from the GFDL CM2. control run. Our general conclusions are transferrable to nature, though the detailed geographic location may be slightly shifted in the modeled world. Equatorial western Pacific is a sensitive region. One feature of chaotic systems is the sensitivity to initial conditions, as shown in Karamperidou et al. (24). In this study, we find the initial pattern with SSTA warming at western Pacific is sensitive, thus it is difficult to predict the outcome from it. It is understandable that the western Pacific is prone to convective instability and Gill-type atmospheric and oceanic coupling. Long-term flavor prediction is limited. Many previous studies indicate ENSO system is chaotic (e.g., Tziperman et al. 994). Therefore besides the environmental noise, the chaotic dynamics also restricts the predictability. In this study we find that the long- 84

109 term predictability for ENSO diversity is limited, so we pinpoint a prediction horizon for CPEN and EPEN. We also find that short-term predictability of ENSO diversity is feasible. Equatorial Pacific subsurface process is the key to tell the final outcome. Comparison of the evolution in Figs. 7 and 8 shows how CPEN and EPEN s development involve surface and subsurface branches. For CPEN the accumulated subsurface heat anomaly does not upwell at the eastern Pacific as it does for EPEN. Therefore, monitoring the subsurface heat anomaly and especially the upwelling at the eastern Pacific may give us more evidence to predict the final outcome. Once the SSTA anomaly is upwelled at EP, the predictability for EPEN increases. CPEN is less predictable than EPEN. Our analysis shows that CPEN has 4 months prediction range while EPEN has 7 months. Therefore, it is difficult to tell CPEN until it approaches the mature stage. The uncertainty also comes from the possibility that CPEN may finally become EPEN through a subsurface detour. As to the source of predictability, recharged subsurface heat anomaly is a potential indicator for EPEN. But for CPEN the subsurface process is the outcome instead of the precursor. For CPEN warming, an advective feedback may contribute to the SSTA amplification locally (e.g. An et al. 999; An and Jin 2;Kug et al. 29; Kim and Jin 2 a,b). In addition, the extra-tropical atmospheric forcing (Yu and Kim 2) may also play a role through the North Pacific Meridional Mode (Vimont et al. 24). Probabilistic forecast is necessary. The nature of ENSO flavor prediction, to predict the outcome from 5 ENSO states, is intrinsically a probabilistic question. In this study, we introduce a new benchmark using a state transition probability approach. We remind the reader that the transition diagram and likelihood map are based on GFDL CM2. s statistics instead of the statistics of the natural ENSO system. Here we use the long simulated records to demonstrate how the transition probability approach works. For practical use, one could fit the transition diagram from the observations and apply it as a metric for model comparison. In addition to the common probabilistic forecast for ENSO amplitude, studies are needed on ENSO flavor probabilistic forecasts. 85

110 3.6.2 ENSO predictability and underlying dynamics Predictability studies not only assess how predictable the system is, but also aim to understand why it is predictable or not. Here we combine our study on predictability with previous studies on ENSO diversity mechanisms to try to reach a better understanding of the system. Besides the linear inverse modeling we have applied, the SSTA amplification from collective effects could be also addressed via a heat budget analysis of the ocean mixed layer using the Bjerknes instability index I BJ (Jin et al. 26). The thermocline feedback and zonal advective feedback are shown to be the leading positive feedbacks (Picaut et al. 997; An et al. 999; Jin and An 999; An and Jin 2), which are considered as the main players for ENSO diversity (Kug et al. 29, 2; Kim and Jin 2 a,b). In this study, we reconstruct the evolution of EPEN and CPEN, and find that the thermocline feedback working at eastern Pacific upwelling region can amplify SSTA for 9 months (Fig. 3.5). Advective feedback working at western Pacific wave source region can sustain the SST warming at CP for 5 months. 3.7 Conclusion Recent ENSO diversity study showed EP/CP El Niño flavors are associated with different climate impacts, so one new ENSO prediction target is to predict not only the occurrence and amplitude of El Niño (EN) but also the peak location. Many prediction models have difficulties to predict CPEN, which motivates the investigation on whether such ENSO diversity has intrinsically limited predictability. We address the question through three aspects: pinpointing a prediction horizon to distinguish the flavor, identifying the sensitive regions and optimal initial patterns, as well as measuring the prediction uncertainty. We combine approaches including case study, linear inverse modeling, singular vector analysis and introduce a new benchmark for probabilistic forecast. We analyze a 4 year GFDL CM2. pre-industrial control simulation. The results and sensitivity tests show that the long record is very useful and important to 86

111 ensure a robust evaluation, especially when fitting a long-term lead operator. The SSTA evolutions show that two similar initial conditions with western Pacific SST warming anomalies may finally develop to either CPEN or EPEN. Equatorial Pacific subsurface evolution is important to tell the final outcome. Restricted by the chaotic property, the prediction horizon appears to be 4 months before CPEN and 7 months based on SSTA. Since predicting El Niño flavor is by nature a probabilistic question, operational prediction models need to check how reliably they can reproduce a realistic transition probability. This research direction, as in the observational data, needs further investigation. 87

112 a) 2-month evolution of obs SSTA CPEN EPEN b) m c) d) e) f) g) h) 4m 8m 2m -2-2 Figure 3.: Panels (a,c,e,g) show 2-month SSTA evolution during CPEN event using the HadISST V. record. Panels (b,d,f,h) show SSTA evolution during EPEN event. Though these two events show similar initial warming their later evolutions are different. 88

113 2-month evolution of GCM SSTA a) CPEN b) EPEN m c) d) e) f) g) h) 4m 8m 2m -5 5 Figure 3.2: Panels (a,c,e,g) show 2-month of SSTA evolution during a CPEN event in GFDL CM2. control simulation. Panels (b,d,f,h) show SSTA evolution during a EPEN event. Though these two events show similar initial warming but their later evolutions are different. 89

114 3N a) Tropical Pacific SST EOF in GCM 5 ENSO state category c) 3 NEU 2 EOF EPLN CPEN CPLN EPEN 3N W 4 b) PC2 3S 8E EOF S 8E 8 72W PC Figure 3.3: Panels (a,b) are the leading two EOFs of tropical Pacific SST. Panel c shows the definition of the 5 ENSO states in PC, PC2 space. Each state carries the same color code throughout this study. Prediction horizon.2-5m Neutral PC2 m CPEN -.2 m EP avg CP avg -.4 EPEN.5.5 PC Figure 3.4: 4 year CM2. data is divided into epochs 5-years long. Precursors of EPEN and CPEN are tracked to 5 months before to illustrate when the tracks become distinguishable, suggesting a prediction horizon. 9

115 SNR of SV Growth 4 SSTA amplification SV 2.5 SV Lead time (month) Figure 3.5: For 5-year long epochs, two growing modes contribute to SST amplification. The two modes allow for ENSO diversity Robustness of diagnostics 5 m G 3m G 6m G 5 2m G Datalength (Year) Figure 3.6: Signal to noise ratio of leading growing mode is analyzed to measure the model robustness among epochs. 2mG indicates G(2), the transition across a 2 month interval. 9

116 a) 3N 6-mth lead optimal initial patterns for CPEN and EPEN CPEN b) EPEN 3N SST Tsub 3S 8E 8 72W c) 5m m 2m 3S 8E 8 72W d) 5m m 2m m 8E 8 72W 3m 8E 8 72W Figure 3.7: (a, b) optimal initial pattern in SST for EPEN and CPEN, respectively. (b,d) are for the associated Tsub. Magenta curve is the 28 o C isotherm, and the red curve is the 2 o C isotherm. Units are o C The EPEN and CPEN are distinguishable at 6 month leads, with different surface and subsurface patterns. 92

117 Figure 3.8: Variation of the diagnosed OIP for SST in five different epochs. -epoch averaged OIPs are shown in a/b panel. 93

118 a) 3N 2-mth lead optimal initial patterns for CPEN and EPEN CPEN b) EPEN 3N SST Tsub 3S 8E 8 72W c) 5m m 2m 3S 8E 8 72W d) 5m m 2m m 8E 8 72W 3m 8E 8 72W Figure 3.9: similar to Fig. 3.7, but for 2 month lead. OIPs look similar for EPEN and CPEN at 2 month lead. 94

119 Prob. a) EPEN 5-state transition probabilities b) CPEN c) NEU d) EPLN e) CPLN Lead time (yr) CPLN EPLN NEU CPEN EPEN Figure 3.: Transition probability based on the definition of 5 ENSO states in Fig

120 Figure 3.: a,b,c show the most-likely state to come. Associated probability measures are shown in the same column. 96