Modeling ENSO Teleconnections Using a Markov/GLM Framework

Transcription

1 Modeling ENSO Teleconnections Using a Markov/GLM Framework Samantha Stevenson CVEN 6833 term paper: due 12/17/09 1 Abstract A new method is applied to ENSO simulation, to understand the role of remote teleconnections in ENSO activity at a variety of frequencies. A lag-1 Markov chain is used to predict the state of the system (El Niño vs. La Niña), and a generalized linear model is then fit to the thermocline depth and zonal wind stress at a variety of locations and lag times. The model accurately reproduces the PDF of El Niño/La Niña persistence during the historical record ( ), and suggests that return times for long El Niño events might be relatively short. In contrast, few of the 50-year epochs within the 1200-year CCSM control run used yield long-persistence El Niño events, suggesting either that some model bias remains in CCSM or that the period is unusual relative to long-term ENSO variability. Changes to the best predictor set for various model epochs are then examined, and inclusion of wind stress variables found to be essential for accurate reproduction of the El Niño PDF. Additionally, off-equatorial thermocline/zonal wind stress conditions found to contribute more strongly to ENSO prediction at low frequencies. Finally, the potential of this method for ENSO prediction is examined, and found to be comparable to present, more complex forecasting systems. 2 Introduction Drought and flooding events worldwide are associated with the phase of ENSO (Nicholls et al., 1996; Ropelewski and Halpert, 1987), especially in regions with strong teleconnections to the equatorial Pacific, such as the southwestern United States. ENSO dynamics must be considered when discussing water management issues in arid regions, which rely heavily on predicting streamflow years into the future (Dettinger et al., 2000). Understanding ENSO s impact on water management may become even more important in the 21st century, as climate change is expected to decrease streamflow in the Colorado River by a significant percentage (McCabe and Wolock, 2007). However, the precise extent of the risk to the Southwestern US water supply from climate change is not well known at the moment, and most likely will depend strongly on the management choices made in response to the changing climate (Rajagopalan et al., 2009). Accurate prediction of ENSO allows for better knowledge of the future state of the system, simplifying water managers decision processes. However, predicting El Niño and La Niña events is extremely difficult, since the dynamics involved are highly nonlinear (Timmermann et al., 2003). Even for state-of-the-art dynamical models such as those used in the creation of the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), predictive accuracy is currently very limited at lead times longer than a year (Mason and Goddard, 2001). Interestingly, the overall performance of statistical ENSO forecasting models is currently comparable to that of dynamical models, which will be the subject of this paper. Since neither type of model performs particularly well, especially for strong El Niño/La Niña events (Lima et al., 2009), incorporating ENSO forecasts into operational guidelines for water management is not practical, given that timelines for such guidelines are typically on the order of 24 months. Modulations to ENSO dynamics often take place accompanied by large changes to teleconnections to other parts of the world (Alexander et al., 2002); for example, Ashok et al. (2007) have identified a distinct type of ENSO, the ENSO-Modoki, which exhibits dramatically different correlations with the central Pacific than do the more typically observed ENSO patterns. Also interesting are the results of (Kao and Yu., 2009), who point out that ENSO may be thought of in terms of two types of events having centers of action in either the eastern or central Pacific. It is therefore logical to assume that improving forecast accuracy will be easier if changes to such teleconnections is taken into account. Understanding the relative contribution of distinct types of ENSO event is unfortunately not possible using solely the instrumental record, since only a few decades of observations are available (McPhaden et al., 1998). Both observational (McPhaden, 1999) and modeling (Wittenberg, 2009) studies suggest that 1

2 this timescale is much shorter than the typical timescales on which ENSO dynamics shift. For instance, Wittenberg (2009) was able to identify multiple time periods within a 2,000 year integration of the GFDL CM2.1 which bore a qualitative resemblance to distinct portions of the 20th century NINO3.4 record; if this is indeed the case, then many centuries indeed are needed to truly pin down the statistical behavior of ENSO. Long coupled model integrations are therefore the best available option for building up robust statistics on the relation between variability in different parts of the world and ENSO activity. This work uses NCAR s Community Climate System Model (CCSM3.5), which has one of the best representations of ENSO of any IPCC-class model to date (Neale et al., 2008). A pre-industrial control simulation is currently available of length 1200 years, which should be sufficient to sample the majority of ENSO variability present in the system. The major variables thought to be related to changes in ENSO activity are the zonal wind stress and the depth of the thermocline, here assumed equivalent to the depth of the 15 C isotherm. Changes in the thermocline depth are related to changes in the total heat content of the Pacific basin (Jin, 1997; Liu and Philander, 1995), while changes to zonal wind stress can lead to shifting patterns of advective heat transport (Picaut et al., 1997). Wave activity related to both variables may also be quite important to ENSO dynamics (Capotondi et al., 2006). This paper seeks to parameterize several popular theoretical ENSO models and evaluate their importance throughout the 1200 year CCSM run used. A nonparametric approach is taken to the problem, combining both a generalized linear model and a lag-1 Markov chain incorporating the state of the system at the previous timestep; hereafter the approach is known as the Markov GLM. The Markov/GLM framework used to simulate ENSO activity, and its performance at reproducing the historical ENSO record, is described in Section 3. 3 Modeling Framework This project aims to use long integrations of a dynamical model (in this case, the NCAR CCSM3.5) to understand long-term ENSO statistics. The idea is that using coupled climate model output can provide a complete set of dynamical information, which should be more or less representative of the true behavior of the system in the real world. Since more than 1,000 years of data are currently available, a wide variety of dynamical behaviors should be present, changes to which can provide insight into the types of changes one might expect to see in the real ENSO in the future. These dynamical behaviors can then be input into a statistical model, which can quickly generate many time series having the same statistical properties as any arbitrary subset of the dynamical model output at a tiny fraction of the computational cost. The statistical framework for these simulations is built on the stochastic weather generation model of Kim et al. (2009). In that work, the authors found that including the binary system state, lagged by one timestep, as a predictor within a GLM for predicting precipitation occurrence makes the system equivalent to a 2-state lag-1 Markov chain. Doing so makes it possible to take advantage of the potential of the Markov chain formulation to predict the system state, while still allowing the inclusion of potentially important covariates. Kim et al. (2009) showed that the combined Markov chain/glm setup was quite effective at producing stochastic weather information consistent with larger-scale climate forecasts from coupled climate models. My goal is to adapt the Kim et al. (2009) model to work for the NINO3.4 index. NINO3.4 is a good proxy for the state of ENSO, and computing a single time series for the NINO3.4 region is straightforward. Here, dependencies of the NINO3.4 index upon both independent variables believed to hold dynamical importance to the system are considered, in combination with potential autocorrelative effects (i.e. lag-1 Markov chain). The strength of the GLM is that an arbitrarily large number of covariates may be considered simultaneously, and the best predictor set obtained (see below). All variables are seasonally averaged, to reduce the contribution from monthly variations. The mathematical formulation of the model is p ln( 1 p ) = µ + α 1J t 1 + Σ n 1 β n x n (1) where p is the probability of the system being in a positive anomaly (in this case, the El Niño state), J t 1 is the state of the system at lag 1, and β n x n represents the regression against additional covariates. 2

3 This setup differs slightly from that of Kim et al. (2009) in that I have removed the seasonal cycle from the NINO3.4 time series before beginning the fit. Additionally, the method of calculating the magnitude of the NINO3.4 index differs from Kim et al. (2009) s calculation of weather variables. Instead of adopting a parametric gamma distribution from which to generate the NINO3.4 index, I use the nonparametric K- nearest neighbor approach of Prairie et al. (2008). This allows for better estimation of small-scale features in the time series. Table 1: Averaging regions for NINO3.4 covariates. Region Lat (degrees N) Lon (degrees E) NINO3.4-5 : : 240 Mean z -5 : : 240 Central z -5 : : 220 Northern z 15 : : 220 Southern z -25 : : 220 Mean τ x -5 : : 240 Central τ x -5 : : 180 Southern τ x -15 : : 180 I have chosen the covariates for NINO3.4 such that they may shed some light on the relative contributions of previously discovered dynamical modes to CCSM3.5 ENSO dynamics. The primary drivers for ENSO activity are generally thought to be the depth of the thermocline and the zonal wind stress (Zebiak and Cane, 1987; Jin, 1997). For example, the classical delayed oscillator model of Zebiak and Cane (1987) presumes that communication between parts of the Pacific takes place via Kelvin wave reflection off the eastern boundary of the basin. In contrast, the recharge oscillator model of (Jin, 1997) concentrates more strongly on the role of warm water buildup before the peak of an El Niño event. As proxies for both of these oscillator types, I have chosen to look at the mean depth of the thermocline in the equatorial Pacific and in two regions off the equator as well. Zonal wind stress is examined in several places. Many previous papers (Lengaigne et al., 2004; Vecchi and Harrison, 2000) have demonstrated the importance of westerly wind bursts (WWBs) in driving ENSO dynamics; in particular, Vecchi and Harrison (2000) have created a catalog of distinct types of WWB activity and the regions over which these types are active. I have chosen to look at two of these types, the C and S regions (Figure 1); this choice is somewhat arbitrary, and is meant to allow my model to serve as a preliminary look at changes to wind dynamics. z th z th NINO3.4 z th C S Figure 1: Regions of interest in creating predictor time series for the Markov/GLM. Left: regions for SST and thermocline depth. Right: regions for zonal wind stress. Although there has been some previous work on the lag-correlations between the variables described above and the NINO3.4 index, I did not want to make a priori assumptions about which lags should be the most important. Accordingly, for each of the variables in Table 1 I have included lags 0-3: each variable may be lagged relative to the peak El Niño by up to nine months. This should be sufficient to capture the majority of the relevant wind/thermocline dynamics. When the model is fit to the CCSM3.5 output, the best-fit set of predictors is selected using the AIC criterion of (Akaike, 1974). This is done using a stepwise algorithm within the R statistical package: the algorithm is called stepaic. Results for the best predictor set as a function of model time are discussed in 3

4 Section 6. Since each lag is stored separately for each predictor variable, this allows the persistence properties associated with each active region to be captured. As a test of the effectiveness of the model, I first examine its ability to reproduce the properties of the historical NINO3.4 record. I am using an ocean hindcast covering the time period from , forced with the so-called Interannually Varying Forcing (IAF) generated for the Common Ocean-Ice Reference Experiments (COREs) described by Large and Yeager (2004). I have used this SST product rather than one covering a longer time period since the hindcast has the advantage of providing concurrent global thermocline depth and zonal wind stress information, on the same CCSM grid as SST. Throughout this paper, the data product will be referred to as the CORE hindcast. There are a great number of variables that may be examined to determine the accuracy of the modeling framework; there are many more which may be of interest to planners and other people impacted by ENSO. Here, I have restricted my analysis to the following quantities: The accuracy of simulated NINO3.4 spectra The variance of NINO3.4 over the time period of interest The length of maximum persistence of the El Niño and La Niña phases of the oscillation The probability distribution function (PDF) of these phases The return period of long-persistence El Niño events Cross-validated forecast accuracy In Sections 3-5, the forecast accuracy will be evaluated at zero lead time; in other words, cross-validation is performed using all predictors up to and including those concurrent with the event being simulated. Changes to cross-validated accuracy at larger lead times is discussed in Section 7. Results for the CORE hindcast are shown in Figures 2 and 5. Boxplots represent the simulated values for the NINO3.4 variance, maximum event persistence and the PDF of El Niño and La Niña lengths. As can be seen from Figure 2a, there is an underestimation of NINO3.4 variance by the Markov/GLM simulations. This seems to hold true across the board; not only is the variance underestimated for the CORE hindcast, but for every model epoch examined (see Section 5). This seems to be associated with the inability of the model to reproduce the largest El Niño and La Niña events (Figure 3). (a) (b) Figure 2: Basic statistics for minimum-aic Markov/GLM fit to the CORE hindcast. (a) NINO3.4 variance; (b) length (in seasons) of the maximum El Niño and La Niña event. One interesting feature that should be pointed out is the effect of changing the predictor set used in the model fit for the CORE hindcast. This effect is most pronounced on the PDF of El Niño/La Niña, as seen in Figure 4. At first, the fit was performed using stepwise regression on the thermocline depth variables alone; Figure 4a indicates that this leads to a dramatic overestimate in the number of short-period El Niño/La Niña events, and an underestimate of the long-period events. Most remarkably, when zonal wind stress 4

5 Figure 3: Cross-validated prediction of NINO3.4 at zero lag, generated using the CORE hindcast. information is incorporated into the GLM fit, the majority of these estimation errors disappear (Figure 4b). Now the simulations follow the observed PDF closely, even down to small features such as the hump near 25 seasons. This leads to a small return period for long-persistence El Niño events. This effect will be discussed more in Section 5, but the return periods calculated using the hindcast is only about 30 years! More verification statistics for the CORE hindcast are seen in Figure 5. In the right-hand panel, the spectra of the simulated NINO3.4 time series have been boxplotted over the observed values. In general, agreement is fairly good at low frequencies but becomes degraded at higher frequencies. This is somewhat intuitive; since the data has a sampling frequency of 4/yr, one should probably not trust frequencies beyond about 2/yr. The probability of being in the El Niño state, generated using the GLM framework, is shown in Figure 5a. The strength of the GLM approach here is that no smoothing is necessary to estimate the transition probability as a function of time, as is needed in the kernel density approach of Rajagopalan et al. (1997). Instead, this quantity may be calculated directly for each point in time considered; this leads to a much higher probability of being in an El Niño when one is in fact observed in the data. The overall success of the Markov/GLM approach at reproducing many of the observed behaviors of the CORE hindcast gives credence to its use in modeling ENSO teleconnections throughout the CCSM integration. This is discussed in the next section. 4 Epoch Identification One of the primary goals of this project is to isolate changes to ENSO teleconnections with model time; this requires that subsets of the model be isolated and fit separately. These subsets are hereafter referred to as epochs; epochs are identified using the wavelet spectrum of NINO3.4 index. This spectrum is shown in Figure 6, which demonstrates the large spectral variability present in the run and the fact that variability occurs at a wide variety of oscillation periods (i.e. 3-5 year wavelet power is not always associated with

6 Figure 4: PDFs of El Niño and La Niña events for the CORE hindcast. Left-hand panel: fit using only thermocline depth variables. Right-hand panel: fit using thermocline depth and zonal wind stress. (a) (b)(a) Figure 5: Simulation accuracy for the CORE hindcast. (a) Probability of being in the positive anomaly state as a function of time; (b) simulated vs. measured NINO3.4 spectrum; (c) cross-validated NINO3.4 index predictions. 6

7 year wavelet power). The large excursions of the model run from the observed ENSO are also depicted in Figure 6, in the spectral RMS distances shown in the right-hand panel. Large spikes in the RMS distance are seen, indicating that there are indeed epochs within the model run bearing little resemblance to the instrumental record. From Figure 6, it is clear that spectral activity comes and goes at both short and long wavelet periods. Accordingly, epochs of length 50 years are chosen, which are active in one of four distinct period bands (Table 2). An active epoch, in this case, is defined by having mean spectral activity above the 75th percentile for the entire model run; epochs are chosen to be active in only one band at a time, to isolate particular patterns of variability which may be associated with ENSO at that particular period. Figure 6: Left: Wavelet spectrum of NINO3.4 index, for the control CCSM simulation. Right: RMS spectral distance between 50-year epochs and the ocean hindcast. The complete list of all active epochs in each of the four spectral bands is somewhat larger than that shown in Table 2; however, the list has been shortened to minimize temporal overlap within and between spectral bands. Epochs are fairly evenly distributed throughout the 1200-year length of the CCSM run, which gives some confidence that shorter-term effects (trends etc.) are not dominating the results. Table 2: Spectrally selected epoch locations within the CCSM3.5 model run. Band Period (yrs) Epoch start (yrs) , 490, 614, 818, , 367, 741, , 298, 424, 735, , 194, 681, 760, Event Statistics The accuracy of the Markov/GLM framework at reproducing the statistics of ENSO behavior during various model epochs is examined here, and compared with the results from the historical record. As was noted in previous sections, there is a tendency for the model to underpredict the observed variance during any given epoch; this effect is visually demonstrated in Figure 7. The PDF for the lengths of El Niño and La Niña events is computed; not all results are shown, but examples are pictured in Figure 8 for model years and These two epochs show distinctly nonnormal distributions of event lengths, but the observed distributions from CCSM output are reproduced 7

8 (a) (b) (c) (d) Figure 7: Epoch variances and simulated values for each spectrally selected group. (a): epochs in group 1 (periods 2-3 years); (b) epochs in group 2 (periods 3-5 years); (c) epochs in group 3 (periods 5-7 years); (d) epochs in group 4 (periods 7-12 years). fairly accurately by the Markov/GLM framework. This is not unlike the behavior observed in Section 3 for the CORE hindcast, and indicates that the Markov/GLM code is performing with the same degree of accuracy for the hindcast as for the CCSM data. (a) (b) Figure 8: PDF for persistence of El Niño and La Niña events, for two selected model epochs. (a): Model years (b): Model years Event persistence is given in seasons; red points indicate the input PDF, while boxplots show simulation results. The simulated spectra of the CCSM data are reproduced with comparable accuracy as the CORE hindcast fit as well. This is demonstrated for a single epoch, years , below (Figure 9). For comparison, I have performed 50 simulations using both the Markov/GLM formulation and an ARMA (2,2) model, to illustrate the advantages of using the Markov/GLM approach to simulate the CCSM output. The ARMA model fits the overall shape of the spectrum, but fails to reproduce the smaller-scale features such as the spectral dips at 0.25 and 0.75 cycles/yr. The Markov/GLM simulations are able to bracket the observed spectrum throughout both of these features, as well as providing relatively accurate spectral estimates out to nearly 1.25 cycles/yr. I have calculated the return periods associated with persistent El Niño events of length 20 seasons (5 years), analogous to the event, for all model epochs. The results are shown in Table 3. As was noted in previous sections, the PDF of event length appears to be well captured for most epochs, indicating that these return periods are representative of the true statistics of each epoch. Extremely few model epochs show return periods less than 10,000 years; in fact for many epochs, the return periods are much longer than that, since the probability of a 5-year El Niño is essentially negligible. 8

9 (a) (b) Figure 9: Comparison of simulated spectral properties for model years , using (a) an ARMA (2,2) model and (b) the Markov/GLM framework. Table 3: Return periods for El Niño events of 20 seasons. Band 1 epochs Period Band 2 epochs Period Band 3 epochs Period Band 4 epochs Period There is a marked tendency for the epochs selected at longer periods (bands 3 and 4) to exhibit smaller return periods than those selected at shorter periods, but this is in some sense a result that comes about by definition; epochs dominated by lower-frequency variability should be required to exhibit longer-persistence El Niño and La Niña events. The interesting thing about these epochs is not that their return times are shorter than the epochs selected at 2-3 year periods; it is that even the shortest return times documented in the CCSM simulations are much longer than the return time simulated for the CORE hindcast. This leads me to believe that there is something fundamentally different about the observational record and the CCSM model epochs. It is possible that some aspect of ENSO representation in CCSM remains inaccurately simulated, such that persistent El Niño events are difficult to obtain. It is also possible that the epoch in the real world is itself unusual compared to the long-term statistics of ENSO activity. Trenberth and Hoar (1996) used their derived long return periods for 5-year ENSO to suggest that anthropogenically induced global warming was responsible for changing ENSO dynamics. My results could possibly support that conclusion, but are not strong enough evidence on their own to make a decision either way. 6 Changes to ENSO Teleconnections The approach of Section 3 has been applied to each of the epochs identified in Table 2. For most epochs, the Markov/GLM simulation performs relatively well; RPSS values are in the range of much of the time, indicating that the model is predicting ENSO state significantly better than would a climatological forecast. An example is shown for model years in Figure 10, showing the zero-lag cross-validated NINO3.4 prediction; as was seen for the CORE hindcast, agreement is generally good but the most extreme events are systematically underpredicted. In order to summarize the changes to ENSO teleconnections with model time, I have displayed the best predictors for NINO3.4 index in Table 4. As discussed above, the possible lags for each predictor variable range from 0-3 seasons, and the NINO3.4 state in the previous two seasons is also taken into account. 9

10 Figure 10: Cross-validated fits for the epoch from model years , fit with best predictor set from AIC. Table 4: Lags, RPSS and correlation coefficient associated with predictors used in minimum-aic model for all epochs considered. Last row: predictors from fit to ocean hindcast, RPSS and correlation coefficients have been calculated at a lead time of 0 (concurrent with simulated data). Start year Band NINO3.4 z mn τ x,mn z N z S τ x,s τ x,c RPSS Corr ,1, ,1,3 0,2 0, ,1 0,1 2,3 2 1, ,1,2 1 0,1 0,1, ,1, ,1, ,3 0, ,1,2,3 2,3 0,1,3 1,2 1,2, ,3 0,1 0, ,2,3 0,1, ,1, ,2,3 0,1,2 2 0, ,1,3 0,1,3 1 0,1,2, ,1,3 0,1,2 3 1,2 3 1,2, ,3 0,1,2 1 0, ,3 0,1,2, ,1, ,1,3 0,1,2 0,2 0,1,2 0,1 0,1, ,1,2, ,3 1, ,2,3 0,1,2 2, , ,3 0,1 1,2 0,3 1, ,2,3 0,2 0,1,2 2 1, N/A 1 1,3 0, ,2 0,

11 It was my hope at the start of this project that there would be a coherent pattern to the best-fit predictors which show up in each spectral band, which might explain the occurrence of a high degree of spectral power in some epochs but not in others. This does not appear to be the case at first glance, but one may still identify some differences between the spectral groups. Epochs are labeled according to their selection band (Table 4, second column from left); the occurrence of lag-1 NINO3.4 as a predictor variable appears to become less common in the bands having longer periods. In particular, bands 3 and 4 (5-7 and 7-12 year ENSO) do not include the system state in previous seasons for a majority of epochs. Capotondi et al. (2006) did a detailed analysis of ENSO in current-generation coupled climate models, and found that longer-period oscillations appeared to be associated with wind activity at progressively higher latitudes. Those authors hypothesized that longer-period Rossby waves were excited farther from the equator, and therefore required more time to reflect off the western boundary of the Pacific basin and create El Niño-like conditions, leading to longer-period ENSO. Some hints of this behavior may be seen in Table 4; the northern and southern thermocline depth regions are included in the minimum-aic model for more of the epochs selected at long periods than epochs selected at shorter periods. Some recharge oscillator-like behavior appears to be present in the epochs selected at longer periods. Jin (1997) constructed this model to de-emphasize wave activity and to emphasize longer-period flushing of heat in and out of the basin. One would expect that a recharge oscillator ENSO mode would be well predicted by the mean thermocline depth and wind stress conditions during the previous months, and this does seem to be the case for epochs in bands 3 and 4. Mean thermocline and wind conditions are part of the minimum-aic predictor set during these epochs more frequently than during those selected in bands 1 and 2. Interestingly, none of the model epochs use the same set of predictor variables as was needed for the CORE hindcast. For the hindcast, nearly all input variables turn up in the minimum-aic model, including the system state at both lags 1 and 2. This is consistent with the dramatic differences in 5-year El Niño return periods between the CCSM epochs and the CORE hindcast; if a different physical mechanism is driving ENSO then one would expect to see different persistence statistics. I hope in the future to spend more time understanding exactly what that different mechanism might be. 7 Forecasting Framework The final aspect of this project is to evaluate the effectiveness of the Markov/GLM framework at predicting future ENSO activity. This model is conceptually simpler than statistical models based on multivariate decompositions; for example, the method of Lima et al. (2009) relies upon a nonlinear dimensional reduction in order to predict the future state of leading modes of variability. I therefore need to evaluate its performance relative to such statistical models. The Markov/GLM is adapted to serve as a forecasting model by simply using values of the predictor variables at times previous to the desired forecast lead time. I have tried to keep similar numbers of variables in the prediction model as appeared in the zero-lag cross-validations of Section 6; what I have done is to include all values of the predictors at lags up to 3 seasons previous to the forecast lead time. This allows similar physical processes to play a role in determining the regression relationships in the model. Likewise, the NINO3.4 system state remains a lag-1 Markov chain, but the input states are now lagged by 1 season relative to the forecast lead time instead of the time of interest. Pictured below, in Figure 11, is the forecast at 18 months lead. It should be noted that for less intense El Niño/La Niña events, the forecast model does much better than for larger events. As positive and negative anomalies become more intense, the forecast becomes degraded, consistent with the model s behavior at zero lead; the 1982 and 1998 El Niño events, two of the strongest on record, are underpredicted by approximately a factor of 2. I hope to extend this analysis to all of the model epochs as well, to understand the role that varying the most important predictor variables might play in potential forecast accuracy. However, the poor performance of the forecast configuration on the CORE hindcast means that this must be seriously considered before embarking on a more detailed study. I suspect that some of this poor performance could be rectified by changing the way the K-NN resampling is performed. Currently, the intensity of the El Niño/La Niña is calculated by resampling the K nearest neighbors of the estimated state from the previous timestep, having 11

12 Figure 11: Cross-validated forecast estimates for NINO3.4 at a lead time of 18 months, using the CORE hindcast. 12

13 the correct transition state according to the Markov chain (El Niño-El Niño, El Niño-La Niña, etc.). But a more representative way to do this in the forecasting framework would be to choose from the K nearest neighbors at the forecast lead time; this would preserve the lag-lead relationships between ENSO intensities at various times in a way that the current approach does not. Due to time constraints, I was not able to implement this next step as of the current writing, but hope to extend the analysis in the future. 8 Summary and Conclusions This project has presented a new way of modeling ENSO activity as a function of time. The combination of a lag-1 Markov chain with a GLM allows the state of the system to be predicted based upon the values of an arbitrary number of covariates, at any given time. Here the NINO3.4 index is used as a proxy for ENSO state, since this is the operational definition used by NOAA and other agencies. The nonparametric K-nearest neighbor resampling algorithm is then used to generate the magnitude of the NINO3.4 index at any given time. This particular model uses as input the values of thermocline depth and zonal wind stress averaged over several regions believed to be important to ENSO dynamics, at lag times ranging from 0 to 3 seasons. The set of predictors most effective at providing estimates of NINO3.4 index are chosen via stepwise regression, and the set minimizing the value of AIC chosen to do all simulations for the epoch under consideration. Use of the Markov/GLM approach for ENSO modeling is justified through testing on an ocean hindcast covering the period from Several interesting results come out of this analysis; first, that the overall fit is relatively accurate, and that return times for long-persistence El Niño events are comparable to those calculated by Rajagopalan et al. (1997). Also interesting is the fact that without wind stress predictors, the model is unable to reproduce the observed PDF of El Niño/La Niña lengths, suggesting that these are essential ingredients to any ENSO forecast model. The Markov/GLM is then applied to spectrally selected epochs of length 50 years, taken from a year CCSM3.5 integration. When multiple simulations of a given epoch are performed, the results are found to reproduce the PDF of the El Niño/La Niña length quite well. There is a systematic underestimate of NINO3.4 variance, possibly associated with the underperformance of the model at reproducing the most intense El Niño and La Niña events; however on the whole the model does relatively well. Minimum-AIC fits give the best predictor variable sets for all model epochs. There is no single coherent pattern to the predictors belonging to the minimum-aic variable set for a give epoch; however, in general there appears to be a greater importance attaching to off-equatorial wind stress for epochs having larger spectral power at long periods. This may prove to be consistent with the picture painted by Capotondi et al. (2006), who theorized that Rossby wave excitation was of key importance to the dominant period of ENSO. The return period of long-persistence El Niño events is calculated for the CORE hindcast as well as for all model epochs; the hindcast is found to be unusual relative to all model epochs, in that its return period is much lower than for any period within the CCSM run. This may have some potential importance as it relates to the contribution of anthropogenic influence on ENSO activity. Finally, the usefulness of this framework as a forecast model for ENSO is evaluated through application to the CORE hindcast. At lead times longer than a few months, the model does not appear to do very well at reproducing more intense El Niño or La Niña events, which is consistent with its behavior at zero lead time. This may be related to the setup of the K-nearest neighbor resampling used to generate the magnitude of the event, and should be investigated in future work. References Akaike, H., A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19 (6), , Alexander, M. A., I. Bladé, M. Newman, J. R. Lanzante, N.-C. Lau, and J. D. Scott, The atmospheric bridge: The influence of ENSO teleconnections on air sea interaction over the global oceans, Journal of Climate, 15, , Ashok, K., S. Behera, S. Rao, and H. Weng, El Niño-Modoki and its possible teleconnection, Journal of Geophysical Research, 112, C11,007,

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