Assessing ENSO Simulations and Predictions Using Adjoint Ocean State Estimation

Transcription

1 VOL. 17, NO. 22 JOURNAL OF CLIMATE 15 NOVEMBER 2004 Assessing ENSO Simulations and Predictions Using Adjoint Ocean State Estimation DIETMAR DOMMENGET * AND DETLEF STAMMER Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California (Manuscript received 17 April 2003, in final form 18 April 2004) ABSTRACT Simulations and seasonal forecasts of tropical Pacific SST and subsurface fields that are based on the global Consortium for Estimating the Circulation and Climate of the Ocean (ECCO) ocean-state estimation procedure are investigated. As compared to similar results from a traditional ENSO simulation and forecast procedure, the hindcast of the constrained ocean state is significantly closer to observed surface and subsurface conditions. The skill of the 12-month lead SST forecast in the equatorial Pacific is comparable in both approaches. The optimization appears to have better skill in the SST anomaly correlations, suggesting that the initial ocean conditions and forcing corrections calculated by the ocean-state estimation do have a positive impact on the predictive skill. However, the optimized forecast skill is currently limited by the low quality of the statistical atmosphere. Progress is expected from optimizing a coupled model over a longer time interval with the coupling statistics being part of the control vector. 1. Introduction Key to improving forecasts of ENSO and related sea surface temperature (SST) anomalies over the tropical Pacific Ocean is a proper choice of the initial condition and coupling parameters of the ocean atmosphere system that reflect the actual state of the ocean and the overlying atmosphere. To obtain initial conditions for a forecast run of a coupled model, ocean observations are traditionally ingested into its ocean component. The simplest of such an approach would be to force an ocean model by surface wind stress, heat flux, and freshwater fluxes available from a numerical weather prediction model and at the same time strongly relax its surface temperature toward observed SST fields. This approach has the limitation that only SST observations are being used in the assimilation approach, while subsurface observations are not. Furthermore, the skill of the ocean simulation is limited by uncertainties in the atmospheric forcing fields that usually result in systematic errors (biases). A better approach therefore also uses subsurface ocean observations against which the ocean component is be- * Current affiliation: Leibniz-Institut für Meereswissenschaften (IFM-GEOMAR), Kiel, Germany. Current affiliation: Institut für Meereskunde, Zentrum für Meeres- und Klimaforschung, Universität Hamburg, Hamburg, Germany. Corresponding author address: Dietmar Dommenget, Leibniz-Institut für Meereswissenschaften (IFM-GEOMAR), Düsternbrooker Weg 20, Kiel, Germay. ddommenget@ifm.uni-kiel.de ing relaxed ( nudged ). While leading to improved ocean conditions, this procedure is associated with significant sources of heat, salt, and momentum that correct locally (in space and time) errors in surface forcing fields and internal model errors. Those extra terms can dominate over dynamics and therefore upset a dynamical evolution of the model ocean; moreover, their absence in the forecast mode can lead to abrupt dynamical adjustments and thus a degradation during the first few months of the forecast. A summary of state-of-the-art operational forecast activities is given by Ji et al. (1995) and Ji and Leetmaa (1997) who describe the National Centers for Environmental Prediction (NCEP) forecasting approach and by Segschneider et al. (2000) who describe the work at the European Centre for Medium- Range Weather Forecasts (ECMWF). To improve existing forecast attempts, one requires in principle an assimilation procedure that in a mathematically and dynamically rigorous way estimates the ocean and atmosphere initial conditions and coupling parameters so as to assure a dynamically balanced coupled forecast system. Several recent ENSO-related assimilation and prediction efforts therefore attempted to generate dynamically balanced initial states by assimilating ocean observations into regional hybrid coupled ocean atmosphere models (e.g., Lee et al. 2000; Galanti et al. 2003). Today we are not yet in the position to run global coupled ocean atmosphere models in an assimilation mode so as to improve climate forecasts. However, mathematically rigorous ocean-only state estimates are pursued routinely by the ECCO ( Estimating the Cir American Meteorological Society 4301

2 4302 JOURNAL OF CLIMATE VOLUME 17 culation and Climate of the Ocean ; see Stammer et al. 2002a) consortium and have resulted in estimates of the changing ocean that are consistent with ocean observations, the underlying ocean model, and with atmospheric forcing fields that are estimated as part of the procedure. One goal of the ECCO approach is to improve our understanding of the ocean s role in climate. It is hoped that eventually those estimates will also be used for improving climate forecasts. Before this goal can be reached, however, much has to be learned regarding data assimilation in support of coupled models and climate predictions. It is therefore important to gain experience with existing suboptimal configurations to assure sufficient progress toward the common goal of improving our climate model s predictive skill. Here we present a feasibility study, in which we investigate the use of an existing ECCO ocean-state estimation experiment for improving seasonal ENSO predictions by providing dynamically balanced initial ocean conditions. The underlying ECCO estimation procedure and solution is described in detail by Stammer et al. (2002b). It represents a first extensive attempt to produce a full, nearly rigorous, state estimation of the ocean from 1992 through 2000, using much of the World Ocean Circulation Experiment (WOCE) data and surface fluxes from the NCEP National Center for Atmospheric Research (NCAR) reanalysis. Stammer et al. (2003) computed the quantities that appear to be most important in understanding the climate system, such as ocean transports of volume, heat, and freshwater and their divergences and respective air sea fluxes. A significant feature of the ECCO optimization approach is that the model s equations are not being altered during the assimilation procedure. Results are therefore dynamically self-consistent and consistent with the surface forcing that is being modified during the estimation so as to bring the model into consistency with observations. This is in contrast to many other assimilation approaches, which, instead, add artificial forcing terms to the model equations either at the surface or subsurface (e.g., Segschneider et al. 2000). The ECCO results should therefore be superior for initializing forecast models and should, in principle, result in improved forecast skills. While the skill of any predictive procedure inevitably has to be tested against the future evolution of the climate system itself, we use here more modest measures of success: Any improvement in ENSO prediction through ocean-state estimation has to emerge as an improvement above existing routine and computationally less demanding systems. For that purpose we will compare the results from the optimized setup with those obtained from a routine ENSO prediction effort that has state-of-the-art forecast skill (Barnett et al. 1993; see also online at html). The two setups differ not only in the assimilation approach but also in the data constraints they use. Methods that assimilate data similar to those used in the ECCO ocean-state estimation procedure are presented, for example, by Segschneider et al. (2000). Because their published forecast skills are not better than the Barnett et al. method and given our limitation in resources, we will therefore use here the Barnett et al. method as a typical reference for state-of-the-art forecast skill. Beyond using SST as the traditional metric for success, we will also investigate the skill of both approaches in simulating the dynamical evolution of the tropical Pacific on ENSO time scales. As will be seen below, the simulated evolution of the tropical Pacific is significantly different in the two approaches, as are the dynamics that led to it. This paper is organized as follows. In the next section we will describe the control experiment, the estimation procedure, and the forecast setup. The skill of the control and the optimized run in simulating the evolution of the observed ocean over the past decade (hindcast) will be discussed in section 3, with specific focus on the tropical Pacific. Limitations in the forecast skill that arise from uncertainties in the statistical atmosphere model that is being used in forecast mode will then be discussed in section 4. In section 5 the skill of the optimized forecasts will be compared to the control run, and we will conclude with a more general discussion of the limitations in our understanding of the use of assimilation for the initialization of coupled models. 2. Experimental setup The basis for our study is the Massachusetts Institute of Technology (MIT) Ocean General Circulation Model (Marshall et al. 1997a,b), which is based on the primitive equations on a sphere under the Boussinesq approximation. The model consists of prognostic equations for horizontal velocity, heat, and salt integrated forward in time on a staggered C grid (Arakawa and Lamb 1977). A full surface mixed layer model is used (called KPP; Large et al. 1994) as is convective adjustment to remove occasional gravitational instabilities underneath the planetary boundary layer. The model was configured globally with 2 horizontal resolution over 80 latitude with 22 levels in the vertical. See Stammer et al. (2002b) for details. We used the MIT model in two distinct settings for ENSO simulation and prediction studies that will be described in more detail below. The first setup serves as a control run and is a traditional but simple approach to assimilate SST and wind stress fields into a model, which will be used subsequently for seasonal ENSO forecasts (Barnett et al. 1993). Results from this simple control run will be compared to similar results that we obtained in a second approach by using a full oceanstate estimation procedure. This procedure uses the MIT adjoint model (Marotzke et al. 1999) to obtain a solution of the time-varying ocean over the period 1992 through 2000 that is consistent with WOCE and remote-sensing datasets. A prerequisite for quantitative forecast studies is a test of the model s skill in simulating observed ocean

3 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4303 TABLE 1. List of observations, by which the optimization model is constrained. Cost term Time base Levels Reference NCEP forcing TOPEX/Poseidon SSH Reynolds SST Levitus temperature Levitus salt Daily About every 10 days 10-day mean Monthly Monthly Surface Surface Surface All levels All levels Kalnay et al. (1996) Reynolds and Smith (1994) Levitus and Bayer (1994) Levitus et al. (1994) conditions. Those simulations are often called hindcasts and we will use this terminology here as well to distinguish them from forecasts. Both setups will be compared first in a hindcast mode to test their ability to simulate observed tropical Pacific fluctuations during the past decade. They will be run subsequently in forecast mode to test their relative predictive skill against each other. Computationally, the control run is much less demanding than the adjointoptimization procedure; the latter is solved iteratively and requires about 100 times more computational resources. a. Control run The design of the control setup is described in detail by Barnett et al. (1993). The approach essentially consists of two stages: 1) a hindcast simulation over the period 1970 through 2000, which is forced by NCEP NCAR reanalysis (Kalnay et al. 1996) and Reynolds and Smith (1994) SST fields, and 2) a subsequent forecast with a statistical atmosphere coupled to the ocean model. We implemented this concept into the MIT ocean model configuration. Because our model has a lower resolution than the Barnett et al. (1993) study, the skill of our simulations may therefore be somewhat reduced. In hindcast mode, the model is being forced globally by a climatological monthly mean NCEP NCAR reanalysis forcing (momentum, net heat, and net freshwater fluxes) that represents the period from 1970 to Superimposed onto those fields are global monthly mean wind stress anomaly fields based on a statistical relation between the monthly mean NCEP wind stress anomalies and observed Reynolds and Smith (1994) SST anomalies over the tropical regions (20 S 20 N) from 1970 to The statistical atmosphere anomaly model is based on the first 10 leading SST EOF modes, estimated separately for four different seasons. Although resulting wind stress anomaly fields are global, they show significant amplitude only over the tropical oceans between 20 S and 20 N, where the SST EOF modes are defined. In hindcast mode, the control run is therefore forced without any feedback from the model to the wind stress, as it is being used in forecast mode. However, the model SST field is relaxed toward Reynolds and Smith (1994) SST fields with a Newtonian damping time scale of 90 days [equivalent to 5 W m 2 K] globally. The control hindcast run started from an initial state that was close to the Levitus and Boyer (1994) and Levitus et al. (1994) January temperature and salinity climatology. During the first six years, the model adjusted to the surface forcing but remained statistically stable subsequently. In forecast mode, the statistical atmosphere model is coupled to the ocean component. That is to say, that the simulated SST of the ocean model is used to calculate the wind stress anomalies of the statistical atmosphere, which in turn feeds back to the ocean model. Over the tropical oceans, the statistical atmosphere and the ocean model can then be considered a coupled system, with feedback mechanisms present in both directions. We note that, while this method of assimilating SST and wind stress leads to seasonal forecasts with reasonable skill over the tropical Pacific, it cannot be applied to the higher latitudes where a simple relation between the SST fields and wind stress does not exist (e.g., see Frankignoul 1999). b. Optimized run In a second approach, a full ocean-state estimation procedure is used, which provides a dynamically consistent estimate of the evolving ocean during the 9-yr period A detailed description of the optimization approach is provided by Stammer et al. (2002b). Observations, by which the model is constrained, include the daily TOPEX/Poseidon (T/P) and European Remote Sensing Satellite (ERS) altimetric sea surface height (SSH) anomalies, the mean SSH, monthly mean SST, monthly mean temperature and salinity climatologies over the entire water column, as well as surface flux fields of momentum, heat, and freshwater (see Table 1). Control parameters that are being adjusted to bring the model into consistency with the observations include initial conditions of temperature and salinity, as well as the surface forcing over the full time interval. The model uncertainties are thus assumed to reside entirely in the initial conditions and surface forcing fields. We note that an adjoint assimilation approach is a whole-domain approach that uses information from the past and the future to estimate the present ocean state. To test the capabilities of a coupled forecast system, its initial conditions must not contain information from the future. Because we aim at producing several forecasts during the period , this requires a change in the assimilation strategy used by Stammer et al. (2004) to make the optimized initial conditions causal: In con-

4 4304 JOURNAL OF CLIMATE VOLUME 17 trast to the previous 9-yr-long optimization (and to keep the problem tractable) the estimate of the ocean was performed here over 24 consecutive but shorter segments, each extending over only four months in time. This was accomplished by optimizing the initial state of the model and the surface forcing during the very first 6-month time segment. Each of the consecutive optimizations then started from the final condition of the previous optimization while adjusting only the surface forcing as control variables. (The computational requirements of the optimization precluded us from performing 24 individual optimizations of increasing length and each starting from the beginning of 1992, as would have been ideal.) Other changes include a stronger constraint to the 10-day mean Reynolds and Smith SST fields by reducing the prior SST error (from 0.5 to 0.05 K) and by increasing the Levitus temperature error in the upper five levels (i.e., the top 75 m) to 1 C. Both changes lead to an improved estimation of observed SST variations. The first guess for the optimization was taken from the 9 years of global optimization described in Stammer et al. (2002b). During the hindcast simulation, the model was run forward one last time after the optimization converged, starting from the estimated initial conditions and using the estimated surface forcing fields over the period from 1993 to The final state of each of the 24 optimizations was used as the initial conditions for a forecast experiment. Moreover, we use a statistical atmosphere model to describe the low-latitude wind stress forcing during the forecast runs. The concept of the statistical atmosphere model is identical to the control method. However, a new statistical relation is required that accounts for the changes in the estimated wind stress forcing and SST fields. Of primary importance for this study are changes in the low-latitude wind forcing, where the estimated changes in the wind stress fields are significant. Stammer et al. (2004) provide a detailed discussion of estimated changes in surface flux fields and demonstrate the improved quality of wind stress fields, globally as well as over the tropical Pacific. 3. Testing the model s skill We will start the discussion with a comparison of the control and optimization hindcasts with ocean observations on a global scale. Because the focus of this paper is on forecasting tropical Pacific SST anomalies, most of the model data comparison in the subsequent subsection will focus on the tropical Pacific region. a. Global comparison In Fig. 1 we show the standard deviation of the observed SST variability as it results from the Reynolds and Smith (1994) SST dataset during the period ; also shown is the root-mean-square (rms) error of the control and optimized hindcast over the same time period. The observed SST variability is strongest in the eastern tropical Pacific and along the western boundaries of the midlatitude oceans. All ocean models, if left alone, will deviate from observed SST and subsurface conditions in terms of their time-mean values and their simulated variability. A goal of data assimilation is, in turn, to correct respective deficiencies so as to improve the simulated state as well as the predictive skill of the model. A visual inspection of the figure reveals that the rms error of the optimized simulation is significantly smaller than that obtained from the control run: Although both runs were constrained by the same SST data, the optimized simulation leads to SST variations with significantly more realism. This is especially obvious over the equatorial Pacific where the rms SST error in the control simulation is actually maximum and exceeds the observed variability in amplitude. We note that the rms error of the control hindcast exceeds the Reynold SST variances in several places along the tropocal Pacific. This is not the case for the optimized hindcast (Figs. 1d,e). The anomaly correlation between the observed SST anomalies and the two hindcasts is shown in Fig. 2. Anomalies are defined here and in the following as the deviation from the seasonal cycle of the individual dataset, estimated over the time period The relatively large anomaly correlations in both hindcasts indicate that much of the rms error of the control run shown in Fig. 1 can be attributed to SST errors in the seasonal cycle, which is to some extent related to uncertainties in surface heat fluxes. In the optimized run this was improved; it shows maximum correlation with observed SST fields in the central tropical Pacific and generally a high correlation over the entire model domain. In contrast, the control hindcast shows high correlations with observed SST fields only in the tropical Pacific. However, this is not surprising since the control run was forced with only monthly mean climatological forcing outside the tropical regions (20 S 20 N). We note that in the central tropical Pacific the anomaly correlation amplitudes of the control hindcast actually agree with results shown by Barnett et al. (1993), suggesting that despite our relatively low model resolution of 2, our simulations are of comparable quality. Barnett et al. used output from the Hamburg Ocean with Primitive Equations (HOPE) ocean model with a zonal resolution of about 3 and a variable meridional resolution of 0.3 at the equator to 3 poleward of 30 latitude in their study. b. Equatorial Pacific To provide a more detailed evaluation of the quality of each model simulation over the tropical Pacific, we compare in Fig. 3 time series of simulated temperatures with respective observations obtained from the Tropical Ocean Global Atmosphere (TOGA) Tropical Atmosphere Ocean (TAO) (McPhaden et al. 1998) moorings.

5 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4305 FIG. 1. (top) Standard deviation of the observed monthly mean SST over the time period of (middle) Rms error of the control (right) and the optimization hindcast (left). (bottom) Normalized rms errors, which is the rms error (middle) divided by the standard deviation of the observations (top). The unit for the upper three plots in kelvin and the lower two plots are nondimensional. The frame on top of all panels indicates the EQ-2 region (5 S 5 N, W). Time series are shown separately for absolute values and anomalies, with the latter defined as the deviations from the seasonal cycle of each dataset. In all cases, temperatue values represent averages over the region 5 S 5 N, N (henceforth referred to as EQ-2 region). We recall that the TAO observations were not assimilated and are therefore independent from both simulations. The EQ-2 region is considered the most predictable in the seasonal SST (Barnett et al. 1993) and it has also been central in the predictability study of Segschneider et al. (2000) (see also Ji and Leetmaa 1997). The control run has a bias in the mean subsurface temperature that increases with depth. The mean temperatures of the optimized hindcast are closer to observed values over the displayed depth range because in this approach the model is being constrained by Levitus subsurface fields as well as surface Reynolds and Smith (1994) SST and T/P SSH data. Focusing on the temperature anomalies only (right column of the figure), the TAO observations indicate that the subsurface temperature variability along the equator is strongest at the level of the thermocline (Fig. 4). This is partly reproduced in the optimized simulations, although the variability in the subsurface is too weak. However, the control simulation shows little resemblance to the observed subsurface temperature variability amplitudes along the equator, with the surface variability being too strong and the subsurface variability being too weak. Segschneider et al. (2000) provides a similar comparison using a simple and a more sophisticated assimilation approach. Their comparison shows a similar bias in the subsurface mean temperature for the simpler method. This suggests that, if just driven by surface fluxes, mod-

6 4306 JOURNAL OF CLIMATE VOLUME 17 FIG. 2. (top) The anomaly correlation between the observed SST anomalies and the control and (bottom) the optimization hindcast. The frame on top of all panels indicates the EQ-2 region. els are not realistic, even on the equator. The ECCO assimilation of subsurface observations is essential to produce the initial conditions and forcing fields required to keep the model consistent with the surface and subsurface observations. (The remaining reduced skill in the ECCO results may in part be attributed to the limited resolution of our ocean model.) The evolution of the anomalous sea surface height (SSH) (relative to 9-yr mean) along the equator in the Pacific is shown in Fig. 5 and allows us to test the dynamical quality of model simulations. Optimized SSH fields compare reasonably well with T/P observations both in terms of space and time scales and in terms of amplitude. There seems to be a tendency in the optimized run, however, to move the maximum anomalies closer to the eastern side of the basin as compared to the observations. The control run lacks the observed SSH variability on short space and time scales because the applied statistical atmosphere model does not simulate the high-frequency wind stress variations that are required to force observed SSH anomalies. Furthermore, the long-period variations of the SSH appear to be significantly weaker in the control hindcast as compared to the observed or optimized SSH fields. Shown in Fig. 6 are the mean velocity fields as they result from hindcasts at 120-m depth. The mean subsurface currents appear similar in their amplitude and in their spatial pattern. However, a detailed comparison reveals that maximum amplitudes are shifted eastward in the optimized run, where it shows a clear convergence that is absent in the control run. Note also the asymmetry around the equator in the ridge trough system in the optimized run that appears more symmetrical in the control run. Also shown in the figure are seasonal anomalies of the flow field, representing spring (AMJ) and fall (OND). The seasonal cycle of the flow field is more pronounced in the optimized run. 4. Statistical limitations of the forecasts In forecast mode, both the control setup and the optimization setup are coupled to a statistical atmosphere model. As mentioned in section 2b, the statistical atmospheric model for the optimized forecast has to be calculated on the basis of the estimated wind forcing and SST fields, which both differ substantially from the observed conditions (cf. Figs. 1 and 2). However, those estimated forcing and SST fields exist only over a 9-yr period. For quantitatively useful results, the statistical atmosphere model should be determined over a time interval of years. Our results are therefore affected by the artificial (due to the short period) degradation of the atmospheric statistics in the optimized forecast. Moreover, given the limited length of the training period for the statistical atmosphere model for the optimized run, we have to overlap the training period and the forecast time intervals, which potentially leads to artificial skill in the forecasts.

7 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4307 FIG. 3. Time series of (left) the temperature and (right) temperature anomalies at different depth levels in the EQ-2 region for the TAO observations, the control, and optimization simulation. FIG. 4. Standard deviation of the monthly mean of the vertical temperature anomalies profiles averaged from 5 S 5 N shown for (left) the control hindcast, (middle) the TAO array observations, and (right) for the optimization hindcast.

8 4308 JOURNAL OF CLIMATE VOLUME 17 FIG. 5. Evolutions of the anomalous SSH along the equator in the Pacific in (left) the control hindcast, (middle) in the TOPEX/Poseidon observations, and (right) in the optimization hindcast (right). Units are cm. The SST fields simulated in the control run also differ significantly from observed conditions, as can be seen from Figs. 1 and 2. Applying the same statistical atmosphere in the forecast mode that was used in the hindcast runs would inevitably lead to erroneous wind stress forcing and thus incorrect forecasts. To cope with this problem, we evaluated here a new statistical relation between SST and wind stress, but now using the SST fields from the control hindcast. Those new statistics account for model biases on seasonal and longer time scales. They are in turn equivalent to a statistical correction that is sometimes applied to the statistical atmosphere in traditional seasonal forecasts, called model output statistics correction (MOS; e.g., see Barnett et al. (1993)]. Those corrections also account for a model bias in forecast mode, which makes a direct comparison with observed SST possible. To analyze the sensitivity of the forecast skill to the quality of the atmospheric model we compare in Fig. 7 the forecasts obtained using three different statistical atmospheric models, each differing from the other in the length of the training period. The lengths of the training period of the statistical atmosphere covered 1) the full period from 1976 to 2000, 2) the intermediate ranged from 1976 to 1995 (excluding the strong ENSO event of ), and 3) a very short period range from 1993 to We note that 1) and 3) overlap entirely with the forecasting period, while 2) does not. Each set of statistics is based on 21 forecasts, equally distributed over the time interval from 1993 to Each forecast is compared against the hindcasts obtained from the control run over the entire period. The forecasts resulting from the statistical atmosphere based on the period 1970 through 2000 capture basically all SST variability over the EQ-2 region and simulate the onset and decay of even the last ENSO rather well. As was to be expected, the forecasts based on the shorter intervals 2) and 3) show increasingly less skill. The skill of each forecast setup is quantified in Fig. 8 in terms of the rms error and the anomaly correlation of SST in the EQ-2 region. It is clear from the figure that 3) especially shows a significant degradation, de-

9 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4309 FIG. 6. Mean and seasonal anomalies of the horizontal velocity in the control and optimization hindcasts at 120-m depth. Units arems 1. spite the fact that the forecast period overlaps entirely with the training period. The results clearly indicate that feedbacks between the wind stress and the SST fields are poorly represented in this statistical atmospheric model. We conclude that we are limited in our evaluation of the impact of the optimized model for improving seasonal forecasts through the fairly short estimation period of around 10 years and that the success of the optimized forecasts presented here inevitably has to be rather pessimistic. We also note that the skill of our control forecast system based on the longer atmospheric statistics (as compared to the hindcast of the control) is comparable to the skill of state-of-the-art forecast systems, e.g., as published by Ji and Leetmaa (1997) and Segschneider et al. (2000). Our results agree especially well with Barnett et al. (1993), who used a similar method as we do here. 5. The optimized forecasts We have seen in section 3 that the optimized run simulates the observed ocean significantly better than the control run. This is to be expected given the differences in the assimilation approach and the data used as constraints. A good agreement between the simulated model state and ocean observation is a necessary condition for using the model s simulations for studies of the ocean and climate. However, it does not guarantee a better forecast skill of the optimized model since the forecast skill depends to a large extent on the quality of the atmosphere and the coupling coefficients. In the previous section we have already drawn the conclusion that the true skill of the optimized forecast can not yet be determined, given the reduced quality of the available statistical atmospheric model. However, the optimized forecast can be compared with the control forecast based

10 4310 JOURNAL OF CLIMATE VOLUME 17 FIG. 7. The time series of several control forecasts and the control hindcast in the EQ-2 region are shown for different statistical atmosphere models. (top) The statistics from 1976 to 2000 are used, (middle) from 1976 to 1995, and (bottom) from 1993 to Units are C. on a similarly limited statistical atmosphere model. From such a comparison one can obtain a qualitative indication of the potential of the optimized forecast relative to the control forecast. So to answer the question, To what extent can results, obtained from ocean-state estimation, be used to improve seasonal forecasts in the future, we will evaluate in the following the forecast skill of the optimized solution and compare it with the respective results from the control simulation on a seasonal time scale. The control and optimized forecasts are based on a limited statistical atmosphere trained during In Fig. 9 the time series of the SST simulation in the EQ-2 region is shown together with 21 forecasts, each FIG. 8. Skills of 21 control forecasts in the EQ-2 region for three different statistical atmosphere models: (left) rms error and (right) the anomaly correlation. Both skill values are relative to the hindcast. The shaded area in the left panel indicates the statistical uncertainty (90% confidence interval) of the SST peristence rms error, estimated by a 2 test. The shaded area in the right panel incidates the statistical uncertainty (one standard deviation) of the observed SST persistence anomaly correlation, estimated by a Fisher z transform. Both uncertainty measures are based on 21 degrees of freedom.

11 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4311 FIG. 9. Time series of SST in the EQ-2 region for 21 forecasts and the optimization hindcast. Each forecast is 12 months long and the values are C. of which started from the final condition of the previous optimization. The results agree largely with those from the respective control forecasts shown in the lower panel of Fig. 7. However, all predictions are now biased low as compared to the optimized hindcast, while the control forecasts were biased high. Figure 10a shows the rms EQ-2 SST errors of the optimized forecasts. Also shown are similar results but obtained from the control forecasts. As before, we measure the skill of the forecasts by comparing their EQ-2 SST values with similar fields from the respective hindcasts. To compare the rms errors from those two independent forecasts, we normalized each by its respective hindcast persistence error (Fig. 10b). Although both normalized curves follow each other, one significant difference between them can be seen in the enhanced rms error of the optimized forecast during the first three months. This difference is due to small-scale structures in the optimized (estimated) wind stress forcing that cannot be simulated by the statistical atmosphere model in forecast mode and can be interpreted as an initial adjustment and as such, an artifact of the statistical atmosphere. In the control run such short time and space scale wind stress fluctuations do not exist. (We note that these enhanced rms errors during the first three months of the optimized forecasts disappear when the run is started from initial conditions obtained from a run driven by temporarily smoothed wind stress fields. We also

12 4312 JOURNAL OF CLIMATE VOLUME 17 FIG. 10. Skills of 21 forecasts in the EQ-2 region for the optimization schema. The skill values for the control with the limited statistical atmosphere are shown for comparison: (upper left) the rms error, (upper right) the rms error normalized by the rms error of the hindcast persistence, (lower left) the anomaly correlation, and (lower right) the anomaly correlation normalized by subtracting the persistences anomaly correlation. All skill values are relative to the hindcast. Shaded areas are uncertainty estimates as given in Fig. 8. note that a similar or larger shock would be present when using more sophisticated nudging assimilation methods in the control runs.) Anomaly correlations of the control and optimization forecast are shown in Fig. 10c. To be compatible with each other, the anomaly correlation from each run needs to be measured against its respective persistence correlation from the respective hindcast runs. We therefore show in Fig. 10d the difference between the forecast and persistence anomaly correlation. It appears that the improvement of the forecast relative to persistence is significantly larger in the optimization than in the control simulation for lead times between 3 and 10 months. However, it appears from Figs. 9 and 10 that the optimized and control forecasts have compatible skills with none standing out against the other in terms of its EQ- 2 SST forecast skill. While in the last figure we used the hindcast SST as a measure of success, the real test of a forecast is against observed SST values. As can be seen from Fig. 9 the simulated EQ-2 temperature differs only somewhat from the observed values for the optimized runs. This does not hold for the control hindcast, however. For a detailed comparison of the forecast results with observed SST values we show in in Fig. 11 the skill of the anomaly correlation of various SST forecasts, but now as measured against observed Reynolds and Smith SST in the EQ-2 region. As before, each set of statistics is based on 21 forecasts, equally distributed over the time interval from 1993 to The control forecast based on an atmosphere trained during shows relatively high skill scores over the entire forecast lead time of 12 months when a MOS correction was applied (red curve). Without applying the MOS correction (light

13 15 NOVEMBER 2004 DOMMENGET AND STAMMER 4313 FIG. 11. SST anomaly correlation of 21 control forecasts in the EQ-2 region relative to the observed SST for four different models with up to 12-month lead time. The shaded area incidates the statistical uncertainty (one std dev) of the observed SST peristence anomaly correlation, estimated by a Fisher z transform based on 21 degrees of freedom. blue line), the forecast skill of the observed SST is significantly degraded, especially during short lead times. Using the shorter periods from 1993 to 1999 to train the atmosphere does degrade the quality of the forecast even further, as was discussed before. In contrast, the optimized forecast (green line) has, during the first few months lead time, skills about as high as the control forecast with MOS correction applied. For longer lead times its skill declines but approaches the levels of the control forecast only after about 12-months lead time. Figure 11 illustrates in a quantitative way that when measured not against the hindcast SST but against actually observed values, the optimized forecast is superior to the control forecast for which no MOS correction was applied. The best estimate of the control forecast (with MOS correction applied, red line) has high skill compared to observations, which is very similar to the skill relative to the hindcast (Fig. 8). This indicates that the forecast skill measured relative to the hindcast are very similar to the skill relative to observation, which justifies our previous skill measure. The reduced skill of the control runs now with the MOS correction applied is due to the bad mean state as can be seen from Figs. 1 and 2. A fair comparison of the control and optimized forecasts is therefore difficult when measured against real SST observations. Nevertheless, when measured against the hindcasts, skill results should still reveal the relative performance of the optimized approach relative to the control approach. 6. Summary and discussion Our goal was to evaluate the feasibility of using results from an existing ocean-state estimation procedure as initial conditions for coupled forecast systems so as to improve the skill of seasonal ENSO forecasts through the improved ocean dynamics in the coupled systems and the synthesis of ocean data. For that purpose we used results from the ECCO ocean-state estimate with 2 horizontal resolution that adjusted initial temperature and salinity conditions as well as time-varying surface forcing fields to bring the model into consistency with various large-scale ocean datasets, such as Reynolds and Smith (1994) SST fields, altimetry, and Levitus and Boyer (1994) and Levitus et al. (1994) hydrography. Because we built our forecast system on a statistical atmospheric model and because the surface forcing fields were adjusted during the optimization, it was necessary to infer atmospheric statistics from the estimation results over only a relatively short period that also overlapped with the forecast period. All of these limitations led to an artificial degradation of the forecast skill and precluded a clear demonstration that ocean-state estimation can indeed improve the predictive skill of coupled models. Because those problems are not unique to our solution, but will affect many (if not most) attempts to use ocean-state estimation results for initializing coupled models, it is necessary to further discuss implications and remedies. Summarizing our findings, it is noteworthy that, despite the difficulties that we encountered in demonstrating improved predictability using the optimized state estimation results to initialize coupled seasonal forecast runs, we can see in Figs. 8 and 10 a clear improvement in the predictive skill of the optimized and dynamically balanced run through higher anomaly correlations with the actually observed SST in the EQ-2 region than can be found from the control approach. It is also important to recall that the ECCO estimation effort is global in emphasis and is intended to ultimately improve global forecasts of SST and other quantities on time scales beyond seasonal. The emphasis thus is on the entire ocean, its transports, and its interaction with the entire climate system. Although the system was never intended or tuned for producing forecasts, in terms of SST the results from the ocean-state estimation led to forecasts with skill comparable to traditional state-of-the-art and tuned procedures. But in contrast to those other procedures, the state estimation approach provides a synthesis of various different observations into a dynamically consistent initial state of the ocean model and especially leads to improved subsurface conditions both in the hindcast and forecast mode. One could argue that part of the missing success here is related to our low model resolution. However, we recall that the skill of the control hind/forecast system with a suitable quality of the statistical atmosphere is comparable to state-of-the-art published results (e.g., Ji and Leetmaa 1997; Segschneider et al. 2000; Barnett et al. 1993). This indicates that our model setup with a global 2 spatial resolution and the coupled statistical atmosphere model is, in principle, capable of simulating

14 4314 JOURNAL OF CLIMATE VOLUME 17 skillfull seasonal forecasts and that it is indeed the low quality of the statistical atmospheric model that is the major limiting factor. How can we improve the present situation? Two advances are required: First, it will be necessary to improve and constrain a coupled model that consists of the ocean component and at least a simple atmospheric boundary layer comparable to what was done previously for Tropics-only attempts (e.g., Lee et al. 2000). This step will eliminate the estimate of atmospheric statistics and any extra MOS corrections. Instead the atmospheric state will be estimated directly and surface fluxes will follow from bulk formula, given the ocean and atmospheric near-surface conditions. Instead of correcting the observed forcing during the hindcast and performing an anomaly coupling to the atmosphere model during the forecast, one would do the hindcast and forecast with the anomaly coupled atmosphere model, in which the anomaly coupling would be estimated itself during the optimization. Galanti et al. (2003) provided a recent attempt to improve seasonal forecasts through constraining a coupled adjoint model. However, in their effort, only initial ocean model conditions were modified, thus creating discontinuities in the ocean evolution. In contrast, it will be essential to estimate the coupling parameters over the entire estimation period, thus correcting the atmospheric model. At the same time it will be essential to extend the estimation period to several decades. Respective efforts are being pursued now, with the goal of providing ocean estimates over the last 50 years. It can be anticipated that both improvements together will significantly advance our ability in initializing coupled ocean atmosphere models for forecast purposes. Ultimately a fully, complex, coupled ocean atmosphere model needs to be constrained by ocean data such that the ocean and atmosphere components are in equilibrium with each other before it is run in forecast mode. However, much has to be learned before we can reach that goal. Constraining fully coupled ocean atmosphere models in a rigorous way requires dealing with model biases in the coupled system that are not compatible with ocean observations. Such biases can encompass errors in cloud formulation, problems in the model s moisture transport, or simply resolution-dependent deficiencies, among many other candidates. An error seen in coupled simulations is the amplification of meridional heat flux errors: In a coupled model, the midlatitude atmosphere tends to react to erroneous oceanic heat fluxes by changing its storm tracks. This modifies wind-stress patterns and ocean gyre boundaries, which is likely to further accentuate the heat flux error. In a normal atmospheric reanalysis or forecast mode, such internal biases of the atmospheric model are being adjusted through local sources or sinks of heat, moisture, or momentum. But in a fully coupled and predictive mode, such corrections are no longer possible. Short predictive time scales and nonlinearities in the coupled system might pose additional problems that have to be dealt with. A goal is to use the ocean-state estimate first to understand and remedy those shortcomings; then, in a later step, fully coupled models can be initialized through ocean data in estimation to ultimately leading to better climate simulations and predictions. Acknowledgments. Stimulating discussions with David Pierce, Tim Barnett, Bruce Cornuelle, Nicklas Schneider, and Mojib Latif are gratefully acknowledged. We would also like to thank Katja Lorbacher for handling the TAO data. We thank two anonymous reviewers for their helpful comments, which led to an improved presentation of our analysis. Computational support was provided through the Los Alamos National Laboratory and through an NRAC grant from the National Partnership for Computational Infrastructure (NPACI). Reanalysis surface forcing fields from the National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP NCAR) were obtained through NCAR. Support was provided in part through ONR (NOPP) ECCO Grant N , through NASA Grant NAG5-7857, and through a contract with the Jet Propulsion Laboratory ( ). 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