Retrospective Forecasts of Interannual Sea Surface Temperature ...

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MONTHLY WEATHER REVIEW

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Retrospective Forecasts of Interannual Sea Surface Temperature Anomalies from 1982 to Present Using a Directly Coupled Atmosphere–Ocean General Circulation Model DAVID G. DEWITT International Research Institute for Climate Prediction, Palisades, New York (Manuscript received 11 August 2004, in final form 7 March 2005) ABSTRACT A large number of ensemble hindcasts (or retrospective forecasts) of tropical Pacific sea surface temperature (SST) have been made with a coupled atmosphere–ocean general circulation model (CGCM) that does not employ flux correction in order to evaluate the potential skill of the model as a seasonal forecasting tool. Oceanic initial conditions are provided by an ocean data assimilation system. Ensembles of seven forecasts of 6-month length are made starting each month in the 1982 to 2002 period. Skill of the coupled model is evaluated from both a deterministic and a probabilistic perspective. The skill metrics are calculated using both the bulk method, which includes all initial condition months together, and as a function of initial condition month. The latter method allows a more objective evaluation of how the model has performed in the context in which forecasts are actually made and applied. The deterministic metrics used are the anomaly correlation and the root-mean-square error. The coupled model deterministic skill metrics are compared with those from persistence and damped persistence reference forecasts. Despite the fact that the coupled model has a large cold bias in the central and eastern equatorial Pacific this coupled model is shown to have forecast skill that is competitive with other state-of-the-art forecasting techniques. Potential skill from probabilistic forecasts made using the coupled model ensemble members are evaluated using the relative operating characteristics method. This analysis indicates that for most initial condition months this coupled model has more skill at forecasting cold events than warm or neutral events in the central Pacific. In common with other forecasting systems, the coupled model forecast skill is found to be lowest for forecasts passing through the Northern Hemisphere (NH) spring. Diagnostics of this so-called spring predictability barrier in the context of this coupled model indicate that two factors likely contribute to this predictability barrier. First, the coupled model shows a too-weak coupling of the surface and subsurface temperature anomalies during NH spring. Second, the coupled-model-simulated signal-to-noise ratio for SST anomalies is much lower during NH spring than at other times of the year, indicating that the model’s potential predictability is low at this time.

1. Introduction Prediction of sea surface temperature (SST) anomalies on seasonal time scales in the central and eastern Pacific is important because of associated global-scale climate anomalies of precipitation and near-surface air temperature (Ropelewski and Halpert 1987; Trenberth et al. 1998; Mason and Goddard 2001). Inspired by the first successful forecast of warming in the eastern tropical Pacific associated with the El Niño–Southern Oscillation (ENSO) phenomenon by Cane et al. (1986)

Corresponding author address: David G. DeWitt, International Research Institute for Climate Prediction, 223 Monell Building, 61 Route 9W, Palisades, NY 10964-8000. E-mail: [email protected]

© 2005 American Meteorological Society

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many prediction systems have been developed and refined. These forecasting systems vary in complexity and include both statistical and dynamical approaches. A recent review article (Kirtman et al. 2002) summarizes the forecast skill from many of the state-of-the-art forecasting models. This paper reports on the forecast skill for a large ensemble of hindcasts from a new coupled forecasting system consisting of a coupled atmosphere– ocean general circulation model (GCM) that does not use flux correction, anomaly coupling, or other statistical corrections and is initialized from an ocean data assimilation (ODA) system. The noteworthy aspects of this study are the large number of hindcasts (1764) used to evaluate the model skill, use of oceanic initial conditions (ICs) produced from an ODA system with different resolution than the coupled model ocean GCM

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(OGCM) component model, comparison of model forecast skill calculated using bulk indices with the same metrics calculated as a function of IC month and comparison in both contexts with persistence forecasts, an evaluation of the model’s forecast skill in a probabilistic sense following Kirtman (2003), and a diagnosis of the causes of the coupled model’s spring predictability barrier. The results presented here document an update of one of the coupled GCMs described in Schneider et al. (2003). Differences from that paper include extension of the forecasts to the 2002 period, making forecasts for all IC months instead of just January and July ICs, and use of ensembles of forecasts from the same IC date instead of single realizations. Coupled atmosphere–ocean GCMS (CGCMs) are at the top of the modeling hierarchy in terms of complexity and computational expense. In theory, a CGCM should be the most accurate approximation to the actual coupled system and hence should be able to produce the most accurate forecasts. In practical application, CGCMs do not always model all of the relevant physical processes more realistically than simpler models, and not infrequently the CGCM representation of some relevant phenomenon is worse than that from simpler models. The dominant pathology of concern when applying a CGCM to the SST forecasting problem is the presence of climate drift away from the observed climate to the model’s own climate. Previous work (Stockdale 1997; Schneider et al. 1999, 2003; Wang et al. 2002; Alves et al. 2004) has shown that despite drift in uncorrected CGCM SST forecasts on the same order as that found in interannual variability these forecasts are competitive with other methods that do not suffer from such errors. Where possible the forecast skill from this model will be compared with forecast skill from these other methods as well as to other CGCMs. This work adds to the list of CGCMs initialized with an ODA product that are being used to forecast tropical Pacific SST. Previous successful efforts of this type include both uncorrected models (Rosati et al. 1997; Schneider et al. 1999, 2003; Wang et al. 2002; Alves et al. 2004) and corrected models (Ji et al. 1998; Kirtman 2003). The ODA product used for the forecasts made with this model is the same as was used in the studies of Kirtman (2003) and Schneider et al. (2003). This paper is outlined as follows. Section 2 describes the coupled model component models and coupling software. The hindcast experiments and initial condition information including details of how the ensemble members are generated is described in section 3. The model SST bias is also documented in this section. Forecast skill assessments from both a deterministic

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and a probabilistic perspective are given in section 4. These skill assessments are made using the bulk method including all months together and by calculating skill metrics as a function of IC month. Section 5 gives a diagnosis of the spring predictability barrier in this coupled model. Concluding remarks and a summary are given in section 6. One aim of this paper is to document the forecast skill from a new uncorrected coupled atmosphere–ocean general circulation model that is being used as one tool to forecast tropical Pacific SST at the International Research Institute for Climate Prediction (IRI).

2. Coupled model description The coupled GCM combines the Max Planck Institute for Meteorology (MPI) ECHAM4.5 atmospheric GCM (AGCM) (Roeckner et al. 1996) and the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 3 (MOM3) (Pacanowski and Griffes 1998) using the Ocean Atmosphere Sea Ice Soil (OASIS) coupling software (Terray et al. 1999) produced by the European Centre for Research and Advanced Training in Scientific Computation (CERFACS). These models are described below along with the coupling procedure.

a. Atmospheric model The ECHAM4.5 AGCM is a spectral model with triangular truncation at wavenumber 42 (T42). The model is discretized in the vertical on 19 unevenly spaced hybrid sigma-pressure layers. The vertical coordinate system used is from Simmons and Burridge (1981). Longwave radiative transfer is modeled following Morcrette et al. (1986), while shortwave radiation uses the scheme of Fouquart and Bonnel (1980). Cloud water is a prognostic quantity, and cloud properties are specified as in Rockel et al. (1991) and Roeckner (1995). Cumulus convection is parameterized using the mass flux scheme of Tiedtke (1989) as modified by Nordeng (1994). The turbulent surface fluxes are calculated from Monin–Obukhov similarity theory (Louis 1979), and a higher-order closure scheme (Brinkop and Roeckner 1995) is used to compute the vertical diffusion of heat, momentum, moisture, and cloud water. The drag associated with orographic gravity waves is simulated following Miller et al. (1989). A complete description of the model can be found in Roeckner et al. (1996).

b. Ocean model MOM3 is a finite-difference treatment of the primitive equations of motion using the Boussinesq and hy-

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drostatic approximations in spherical coordinates. The domain is that of the global ocean between 74°S and 65°N. The coastline and bottom topography are realistic except that ocean depths less than 100 m are set to 100 m and the maximum depth is set to 6000 m. The artificial high-latitude meridional boundaries are impermeable and insulating. The zonal resolution is 1.5° everywhere. The meridional grid spacing is 0.5° between 10°S and 10°N, gradually increasing to 1.5° at 30°S and 30°N and fixed at 1.5° in the extratropics. There are 25 layers in the vertical with 17 layers in the upper 450 m. The vertical mixing scheme is the nonlocal K-profile parameterization (KPP) scheme of Large et al. (1994). The horizontal mixing of tracers and momentum is Laplacian. The momentum mixing uses the space–time-dependent scheme of Smagorinsky (1963) and the tracer mixing uses Redi (1982) diffusion along with Gent and McWilliams (1990) quasi-adiabatic stirring.

c. Coupling methodology In the coupled model, the AGCM provides heat, momentum, freshwater, and surface solar flux to the OGCM. The OGCM provides SST to the AGCM. Information is exchanged between the AGCM and the OGCM once per simulated day. No empirical corrections are applied to either the fluxes or the SST, that is, the models are directly coupled. The models are coupled together using the OASIS coupling software from CERFACS.

3. Hindcast experimental design To estimate the predictive skill of the coupled model, a large number of hindcast experiments have been made and compared to observations. Hindcasts of 6-month length are initialized on the first of each month in the January 1982 to December 2002 period. For each initial month, an ensemble of 7 hindcasts is made, giving a total of 1764 hindcasts. In the remainder of this section, the method for generating the oceanic and atmospheric initial states is described, and the forecast postprocessing and definition of forecast lead time are described.

a. Initial condition generation The ocean initial conditions are taken from an ocean data assimilation system produced at GFDL using a variational optimal interpolation scheme (Derber and Rosati 1989). The ODA uses expendable bathythermograph (XBT) data for the subsurface and relaxes the SST to observed values with a 5-day time scale. The

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ODA was run with a higher-resolution version of the ocean model described above [and as discussed in Schneider et al. (2003)] but with identical physics and parameter settings. To use the ODA product in our coupled forecasts, it must be interpolated to the ocean grid described above. This is accomplished in two steps. First, the data are interpolated bilinearly on each vertical level from the higher-horizontal-resolution ODA grid to the coupled model coarser horizontal resolution. These data are then interpolated linearly in the vertical from the ODA vertical levels to the coupled model vertical levels. Based on the results shown in Schneider et al. (2003) and Kirtman (2003), which also use this linearly interpolated ODA product, and those presented here, this procedure leads to a reasonably balanced ocean initial state for use in making SST forecasts. The atmospheric initial conditions are taken from simulations made with the AGCM forced by the temperature from the uppermost layer of the ODA product, which is equivalent to the OGCM SST. This is done in order to bring the low-level atmospheric model winds into approximate equilibrium with the forecast initial condition SST. Following this procedure helps to reduce imbalances between the near-equatorial upperocean mass field and wind stress. Such imbalances can lead to quickly propagating, eastward moving Kelvin waves that are deleterious to SST forecasts in the Pacific (Schneider et al. 1999). Hindcasts of 6-month length are initialized on the first of each month in the January 1982 to December 2002 period. Ensembles of seven forecasts are made for each initial month. The ensemble members use the same ocean initial state but different atmospheric initial states. Initial atmospheric states for the different ensemble members are generated by adding different numerical noise perturbations to the wind field. This method of generating ensemble members is ad hoc and was chosen for convenience as the ODA product is produced elsewhere. On the other hand, questions remain regarding the best way to initialize ensemble seasonal coupled forecasts. A similar method for initializing coupled forecasts was followed by Kirtman (2003).

b. Postprocessing As shown later, the coupled model experiences a systematic drift or bias from observations over the course of the forecasts. To be useful in a forecasting context, this bias must be estimated and removed before comparing the model with observations. The bias in the mean annual cycle is removed by estimating the anomalies for the model about its own drifted climatology over all years as a function of initial condition month and forecast lead time. Observed anomalies are ob-

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tained by treating the observations in the same manner and using the same years as for the forecasts. A similar procedure for removing the model bias from coupled model forecasts was followed by Stockdale (1997), Wang et al. (2002), and Schneider et al. (2003). The mean model hindcast and observed SST are shown for two equatorial Pacific regions in Fig. 1 as a function of IC month and forecast lead time. The equatorial eastern Pacific is represented by the Niño-3 SST index (SST averaged over 5°S to 5°N and 150° to 90°W) while the equatorial central Pacific is represented by the Niño-3.4 SST index (SST averaged over 5°S to 5°N and 170° to 120°W). Both the central and eastern Pacific SST forecasts are seen to have a mostly cold bias that grows with forecast lead time. Despite the cold bias, the model simulates an annual cycle of SST in the eastern Pacific (Niño-3) that is similar to observed; that is, January (July) IC forecasts get warmer (colder) going into Northern Hemisphere (NH) spring (fall), while April (October) IC forecasts get colder (warmer) heading into NH summer (winter). The amplitude of the annual cycle in the eastern Pacific as measured by the difference between the warmest and coldest points is about 2.5°C for observations and about 3.0°C for the coupled model. In the central Pacific (Niño-3.4), the model also correctly simulates the annual cycle but the amplitude of the annual cycle is much too large for the model (3.0°C) compared to the observations (1.5°C). The mean annual cycles of SST shown in Fig. 1 are the fields that are removed from the forecasts and observations respectively to form the interannual anomalies. The observed SST data shown in Fig. 1 are from the Reynolds et al. (2002) Optimum Interpolation SST Version 2, which is also the dataset used to evaluate the model interannual anomalies.

4. Hindcast results In this section, the SST hindcasts are analyzed and their skill is assessed from both a deterministic and a probabilistic perspective. The probabilistic forecast evaluation is motivated by that performed in Kirtman (2003). All performance metrics are evaluated using all initial condition months together (referred to as the bulk method in the rest of the paper) as well as a function of initial condition month. This is done because forecast skills calculated using the bulk method are much more pervasive in the literature and this allows the reader to compare the present model’s forecast skill with previously published work. On the other hand, in reality, forecasts are most generally made and used as a function of initial condition month so they should be evaluated in this context as well.

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For the results discussed in this paper, forecast lead time is defined as follows: Forecasts initialized in January, also called January IC forecasts, are started from 1 January 0000 UTC data for that year. The first monthly mean—that is, the January mean—is defined as the 1-month-lead forecast. For the January IC forecast of a particular year, the 6-month-lead forecast corresponds to the June monthly mean of that year. Other IC months and leads are similarly defined.

a. Deterministic forecast evaluation In evaluating the model’s deterministic forecast skill, the seven ensemble members with the same IC month and year are combined to form an arithmetic mean. The two most commonly used metrics of tropical Pacific SST forecast skill are the anomaly correlation coefficient (ACC) and root-mean-square error (rmse) for the Niño-3 and Niño-3.4 regions computed using the bulk method. A commonly used, but perhaps not stringent enough, comparison forecast for evaluating the skill of coupled model forecasts is that of persistence of the observed anomaly on the IC date. In this paper all skill scores are computed using a non-cross-validated approach; that is, all years are used in the calculation including the year of the forecast. The bulk method ACC and rmse for Niño-3 and Niño-3.4 for the coupled model forecasts, persistence, and damped persistence using a 3-month e-folding time are shown in Fig. 2. For the ACC, the damped persistence skill is not given since it is identical to the persistence skill. By these measures the model can be considered to be skillful at all lead times in both the central and eastern Pacific because the model ACC is always higher than that of persistence and the model rmse is always lower than that of persistence or damped persistence. Another way to evaluate the skillfulness of the model is by comparing these skill measures against some predetermined criteria for skill. An ACC of 0.5 to 0.6 has been considered as skillful for forecasts of equatorial Pacific SST in the forecasting literature. By that metric, this model is seen to produce skillful forecasts in the equatorial central and eastern Pacific as the ACC for Niño-3.4 and Niño-3 is greater than or equal to 0.8 throughout the forecast period. A final measure of the skill of the forecasting system in terms of these SST indices is by comparison with other models. Unfortunately, such comparisons are not as objective as they could be due to the fact that each model generally has a slightly different period of forecasts and uses different verification data. That being said, this model does have competitive forecast skill for the bulk ACC and rmse for 1- to 6-month lead compared with other forecasting systems evaluated for simi-

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FIG. 1. Mean annual cycle of SST for the retrospective forecasts and the observations for the period Jan 1982 to May 2003. The black curve is the observational data while the red, green, and blue curves represent the 6-month evolution for the different initial conditions from the coupled forecast system. The multicolor curves are used to help distinguish between different start months for the forecasts. (a) Niño-3 SST and (b) Niño-3.4 SST.

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FIG. 2. Skill scores for the SST forecasts in the Niño-3 and Niño-3.4 regions as a function of lead time for all months’ initial conditions. (a) ACC for the retrospective forecasts and persistence. (b) Rmse for the retrospective forecasts, persistence, and damped persistence (see text for explanation). Coupled model forecasts are denoted as “Cpld.,” persistence forecasts are denoted as “Pers.,” and damped persistence forecasts are denoted as “Damp. Pers.”

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FIG. 3. Global ACC for all initial condition months for retrospective coupled forecasts and persistence at 3- and 6-month leads. (a) Persistence ACC at 3-month lead, (b) coupled model forecast ACC at 3-month lead, (c) persistence ACC at 6-month lead, (d) coupled model forecasts ACC at 6-month lead.

lar periods as found in the literature (Ji et al. 1998; Chen et al. 2000; Syu and Neelin 2000; Xue et al. 2000; Landman and Mason 2001; Kirtman et al. 2002; Wang et al. 2002; Tang and Kleeman 2002; Tang and Hsieh 2002; Dewitte et al. 2002; Kirtman 2003; Schneider et al. 2003; Alves et al. 2004). A more objective intermodel comparison can be made with the eight forecast models documented in the Climate Variability and Predictability (CLIVAR) Numerical Experimentation Group (NEG) report on ENSO forecast skill by Kirtman et al. (2002) for which the ACC was calculated for the common years of 1982, 1983, 1984, 1986, 1987, 1988, 1989, and 1991. The Niño-3 ACC at 6-months lead computed using those years for the models in that report ranges from 0.66 to 0.79. The model described in Wang et al. (2002) had an ACC of 0.77 for forecasts initialized during a subset of IC months in the common period. This coupled model has an ACC of 0.76 for that same set of years for forecasts from all of the IC months, indicating that this model has comparable skill to the models documented in that report which were considered state of the art. The global distribution of forecast skill computed using the bulk method for the coupled model and for

persistence at lead times of 3 and 6 months is shown in Fig. 3. As can be seen for both the coupled forecasts and for persistence, the only large-scale region of fairly high skill is in the central and eastern Pacific. When forecasts are broken down by IC month there are actually some leads and ICs where either persistence or the coupled model has fairly large regions of ACC greater than 0.6. Those results are outside the scope of this study and will be reported elsewhere. At both the 3- and 6-month leads, the model ACC is seen to be higher than that for persistence in the central and eastern Pacific within 10° of the equator. The region where the model has fairly high skill at these leads is comparable with the results from other previously published results (Schneider et al. 1999, 2003; Landman and Mason 2001; Wang et al. 2002; Tang and Hsieh 2002; Kirtman 2003). As discussed earlier, skill scores calculated using the bulk method are deficient in that it is hard to evaluate the potential predictive skill of a model in the context in which the forecasts will actually be used; that is, SST forecasts should be evaluated for a particular IC month and lead instead of combining all IC months together as done in the bulk method. If model forecast skill did not

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vary much as a function of IC month then this would not be an issue. However, as summarized in Balmaseda et al. (1995) model forecast skill can be a strong function of IC month. These authors also found that forecasts made using persistence exhibited a similar skill dependence on IC month. That study utilized a hybrid coupled model to make SST forecasts but more recent studies have shown that this seasonal dependence of forecast skill on IC month is a ubiquitous feature of the current state-of-the-art statistical and dynamical prediction models irrespective of the model’s complexity (Xue et al. 1994; Latif et al. 1998; Xue et al. 2000; Kirtman et al. 2002). The model forecast skill for the ACC and rmse for the Niño-3.4 region as a function of IC month is compared with that from persistence (and damped persistence for rmse) in Figs. 4 and 5, respectively. As found in previous studies, both the model and persistence have a strong annual cycle of forecast skill for the ACC such that forecasts begun in the NH winter and spring show a much more rapid decay in skill with lead time than those forecasts begun in NH summer and fall. It should be noted that the decay in skill for forecasts begun in NH winter and spring is much larger for persistence forecasts than for the coupled model forecasts. Because of this rather rapid decay of skill for the persistence forecasts with NH winter and spring ICs the annual cycle of forecast skill as a function of IC is much larger for persistence forecasts than for the coupled model forecasts. The coupled model is seen to not have a higher ACC than persistence for some leads and ICs. In particular, the model only has a higher ACC than persistence in the Niño-3.4 region for 1-month-lead forecasts with IC months of March, April, and May. The 1-month-lead model forecasts have about the same or slightly lower ACC values compared to persistence for the remaining IC months. It is important to note that at this lead both the model and persistence forecasts have quite high skill with almost all ACC being at the 0.85 level or higher. The model ACC values tend to be much higher than those for persistence at leads of 3 months and longer for forecasts begun during NH winter and spring. For forecasts begun in NH summer the coupled forecasts have higher ACC than those made using persistence for leads of 4 months and longer. However, the ACC values for the coupled model are much closer to persistence than for the forecasts begun in NH winter and spring. The ACC for forecasts from the coupled model are generally equivalent to those from persistence for NH fall ICs for the first 4 months but noticeably better than persistence for leads of 5 and 6 months. Few previous studies in the literature have compared

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FIG. 4. Niño-3.4 ACC for retrospective forecasts from the coupled model and persistence as a function of initial condition month ( y axis) and the forecast lead time (x axis). (a) Persistence forecasts and (b) coupled model forecasts.

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FIG. 5. Niño-3.4 rmse for retrospective forecasts from the coupled model, persistence, and damped persistence as a function of initial condition month ( y axis) and the forecast lead time (x axis). (a) Persistence forecasts, (b) coupled model forecasts, and (c) damped persistence forecasts.

the monthly IC breakdown of ACC forecast skill for a prediction scheme and persistence. An exception to this is Xue et al. (2000), whose results for their 1–6-monthlead forecasts seem quite consistent with the behavior

just documented for this model in terms of both relative skill compared to persistence as a function of IC month and also in terms of the overall skill level of the coupled model forecasts. The coupled model ACC skill scores

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as a function of IC month presented here are also comparable with those from the large sampling of models in the CLIVAR NEG report (Kirtman et al. 2002). Unfortunately, the CLIVAR NEG report does not include similar period persistence forecast ACC values for each of the coupled models so no general conclusions can be drawn. Based on the figures that are shown in that report those models exhibit similar relative skill compared to persistence as the coupled model described here. It is important to point out that both the Xue et al. (2000) and Kirtman et al. (2002) studies use different periods and verification data than the present study so a fully objective comparison is not possible As was found for the ACC, the rmse is a much stronger function of IC month for persistence and damped persistence (damped with a 3-month e-folding time) forecasts than for the coupled model forecasts. This is most dramatically seen for leads longer than 2 months (Fig. 5). The rmse for persistence (damped persistence) forecasts has largest values and fastest growth rates for forecasts initialized using NH winter and spring (NH summer and fall) ICs. In comparative terms, the 1-month- and 2-month-lead coupled model forecasts and the persistence and damped persistence forecasts have equivalent values of rmse while for the longerlead forecasts the coupled model has lower values of rmse. For forecasts begun in NH winter and spring, the coupled model rmse values can be 30%–50% lower than those from persistence and damped persistence forecasts at leads of 4 months and longer. No previous studies with rmse broken out as a function of IC month with which to compare these results have been found. Although the Niño-3.4 ACC and rmse calculated as a function of IC month give a compact way of evaluating the model forecast skill and comparing that skill with persistence in the central and eastern Pacific, it is also important to look at the actual latitude and longitude distribution of skill. This is particularly important for this coupled model as this SST forecast system will be used in combination with other SST forecast products by the IRI as the boundary condition for AGCM models in the second tier of a two-tier real-time forecasting system. Presumably, the tropical Pacific precipitation response of these AGCMs, which drives global climate anomalies (Ropelewski and Halpert 1987; Trenberth et al. 1998; Mason and Goddard 2001), is a function of the SST spatial distribution and not just its area mean. To give some idea of this horizontal distribution of SST forecast skill, the ACC and rmse from two IC months (January and July) for leads of 3 to 6 months are shown. It is at these longer leads that the coupled model can be expected to have a significant advantage in forecast skill over persistence forecasts. To keep the analysis

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here to a reasonable length, the damped persistence rmse is not shown. Based on the results from Fig. 5 we can infer that the damped persistence rmse at these leads will be smaller (larger) than for persistence for the January (July) IC. The ACC and rmse for January are shown in Figs. 6 and 7, respectively. The coupled model is seen to have a more coherent region of high ACC than persistence in the near-equatorial (defined here as 10°S to 5°N) central and eastern Pacific for leads of 4 to 6 months. The coupled model skill level in this region is fairly constant over the 3–5-month-lead forecasts. In contrast, the persistence forecast skill level drops rather dramatically between months 3 and 4 and even more dramatically from months 4 to 5, reaching a level of no skill in the near-equatorial central and eastern Pacific. Between months 5 and 6 the coupled model forecast skill drops enough in the central Pacific that the dominant region of forecast skill by this time is in the eastern Pacific. In terms of the rmse for January, the nearequatorial rmse grows much more slowly with increasing lead for the coupled model than it does for persistence. The magnitude of the rmse for all these leads is much smaller for the coupled model than for persistence. The other IC for which the horizontal distribution of forecast skill is examined is July, for which the ACC and rmse are shown in Figs. 8 and 9, respectively. For this IC, we see that the model has higher ACC than persistence in the central and eastern Pacific for all leads shown. The region of model skill does not decay in the central Pacific toward the later part of the forecast as was seen for the January forecasts. The decay in skill for persistence is also much slower than was seen for January. For the July IC persistence forecasts, the ACC in the equatorial central Pacific stays above the 0.7 level for all leads. But the persistence forecasts do have some decay of forecast skill in the far eastern Pacific from months 4 to 6. The region of maximum rmse for July persistence forecasts is seen to be significantly farther to the east than for the January persistence forecasts as can be seen by comparing Figs. 7 and 9. Persistence forecasts from July also have a significantly lower rmse maximum at long lead than for January. Coupled model forecasts have a similar level of rmse for January and July IC forecasts and the maximum values are found farther west in July than for January, exactly opposite to what was found for persistence forecasts. A final aspect of the deterministic forecasts to evaluate is the actual evolution of the forecasts themselves (Fig. 10). For compactness, the area mean SST fore-

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FIG. 6. ACC for Jan initial condition retrospective forecasts from coupled model and persistence for different lead times. Coupled model forecasts at leads of (a) 3, (b) 4, (c) 5, and (d) 6 months. Persistence forecasts at leads of (e) 3, (f) 4, (g) 5, and (h) 6 months. A single black contour denotes an ACC level of 0.8.

casts for Niño-3.4 are shown for four IC months: January, April, July, and October. This allows us to sample the annual cycle of ICs without the figures becoming too noisy to follow the evolution of the forecasts. The

forecasts are, for the most part, fairly accurate but certainly not perfect. Notable problems include the inability to forecast the onset of the 1986–87 warm event from the April and August 1986 IC. Also, the October

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FIG. 7. Rmse for Jan initial condition retrospective forecasts from coupled model and persistence for different lead times. Coupled model forecasts at leads of (a) 3, (b) 4, (c) 5, and (d) 6 months. Persistence forecasts at leads of (e) 3, (f) 4, (g) 5, and (h) 6 months. Units are degrees Celsius. A single black contour is drawn at 0.9°C.

1986 and April 1987 forecasts call for decreasing warm anomalies, while, in reality, the warm anomalies intensified at those times. This model like most is not able to capture all of the warm spikes during the 1991 to 1995

period. Finally, the January and April 2002 forecasts do not predict the warm event that occurred that year. Overall, the model forecasts seem comparable in skill with other results presented in the literature (Ji et al.

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FIG. 8. ACC for Jul initial condition retrospective forecasts from coupled model and persistence for different lead times. Coupled model forecasts at leads of (a) 3, (b) 4, (c) 5, and (d) 6 months. Persistence forecasts at leads of (e) 3, (f) 4, (g) 5, and (h) 6 months. A single black contour denotes an ACC level of 0.8.

1998; Wang et al. 2002) in terms of the ability of the model forecasts to track observations. In particular, both of those models seem to have similar problems to this model with respect to the 1986–87 event and the 1991 to 1995 period.

b. Probabilistic assessment of forecast skill Despite the fact that the most common use for tropical Pacific SST forecasts is in a deterministic framework, evaluating the probabilistic forecasts produced

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FIG. 9. Rmse for Jul initial condition retrospective forecasts from coupled model and persistence for different lead times. Coupled model forecasts at leads of (a) 3, (b) 4, (c) 5, and (d) 6 months. Persistence forecasts at leads of (e) 3, (f) 4, (g) 5, and (h) 6 months (°C). A single black contour is drawn at 0.9°C.

by a particular system can be useful supplemental information to help potential users to evaluate when the deterministic forecasts might be more or less skillful. To have some other forecast data with which to compare these results, the relative operating characteristic

(ROC) (Mason and Graham 1999) curves are computed as has been done by Kirtman (2003). A brief description of how the ROC is calculated is given here following that contained in Kirtman (2003). The ROC is calculated by determining hit rates and

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FIG. 10. Observed and predicted Niño-3.4 SST anomalies (°C). Coupled model forecasts starting from initial conditions of (a) Jan, (b) Apr, (c) Aug, and (d) Oct. Observed data are the continuous blue line while the coupled model forecasts are the discontinuous red lines.

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FIG. 11. ROC curves for lead times of 6 months for the Niño-3.4 region. Warm events are defined as the upper tercile, near-normal events are the middle tercile, and cold events are the lower tercile.

false alarm rates based on a contingency table. The hit rate is the number of times a categorical forecast is correct (a hit) divided by the total number of times that category actually occurred. A hit rate of one (zero) indicates that all (no) occurrences of an event were correctly predicted. The false alarm rate is the number of forecasts made for an event that did not actually occur (false alarm) divided by the number of times that event did not occur in observations. A false alarm rate of zero indicates that no false alarms were issued while a false alarm rate of one indicates that none of the forecasts issued actually occurred. The ROC curve is displayed as the intersection of the hit rate and the false alarm rate for different probabilities of occurrence, cumulative from the highest probability forecast down to the given forecast probability. The probabilities from an ensemble prediction system are the fraction of ensemble members that are forecasting a particular event. So, for the ensemble forecast system considered here, there are seven discrete probabilities representing the number of ensemble members out of seven forecasting a particular event. As was done for the deterministic forecasts, the ROC curves are calculated both using all months considered together (bulk method) and for separate initial condition months. The first method is done to be able to compare these results with those previously published while the second method gives more detailed information regarding the model’s skill from the perspective in which the model will actually be used. It should be

pointed out that due to an insufficient number of years the ROC curves for the separate IC months are actually computed for each of the consecutive three month IC seasons—that is, January–March (JFM), February– April (FMA), etc.—instead of for individual monthly ICs. The ROC curves for the Niño-3.4 region were calculated for three different events: warm events (upper tercile), near-normal events (middle tercile), and cold events (lower tercile). The ROC curves computed for the Niño-3.4 region for 6-month-lead forecasts using all IC months together are shown in Fig. 11. The symbols on the curves for the different types of events represent results for differing numbers of ensemble members forecasting a particular event. Starting from the lowerleft corner, the first symbol represents seven out of seven ensemble members forecasting this event. Moving to the right along the curve, the second symbol shows results for both seven out of seven and six out of seven members forecasting the event. Each successive symbol to the right along a particular curve shows results for one fewer ensemble member forecasting that event, cumulatively from seven out of seven down to the given number. The diagonal line drawn on the graph represents the situation where there is no relationship between the forecast probability and the frequency of outcome, that is, no skill. The farther above and to the left of the diagonal line, the more skillful the forecast is considered. Based on these curves the coupled model can be seen to have some skill, as indi-

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FIG. 12. ROC curves for the Niño-3.4 region for lead time of 6 months for different seasons. Each panel contains three consecutive running 3-month seasons. Warm events are defined as the upper tercile, near-normal events are the middle tercile, and cold events are the lower tercile. (a) Seasons JFM, FMA, and MAM. (b) Seasons AMJ, MJJ, and JJA. (c) Seasons JAS, ASO, and SON. (d) Seasons OND, NDJ, and DJF.

cated by the fact that the ROC curves are clustered toward the upper left-hand corner of the diagram, indicating relatively high hit rates and relatively low false alarm rates. In the Niño-3.4 region, the cold events are seen to be most skillfully forecast, followed by the warm events and then by the neutral events. This result is similar to that found by Kirtman (2003) for his anomaly coupled model ensemble forecasting system. Along each curve the fourth symbol from the lower left-hand corner represents the 57% probability level, indicating that at least four out of seven ensemble members forecast the event. From this level of forecast certainty up to 100%, the coupled model forecasts have a hit rate of 0.71 and a false alarm rate of 0.14 for cold events in Niño-3.4. Choosing the same certainty level for warm (neutral) events in Niño-3.4 the hit rate is 0.67 (0.55) and the false alarm rate is 0.17 (0.23). The level of skill of probabilistic SST forecasts for the Niño-3.4 region at 6-months lead from this ensemble forecasting system as indicated by the ROC curves computed using all months together

is comparable to that for the ensemble forecasting system documented in Kirtman (2003). That forecasting system is presently the only one for which such a comparison can be made based on published results. The skill of the coupled model probabilistic forecasts for Niño-3.4 is now shown as a function of each consecutive 3-month season (Fig. 12) so that the model can be evaluated in a context closer to that used in actual forecasting. In Figs. 12a–d, ROC curves are shown for three consecutive 3-month seasons of ICs as denoted by the different symbols on the curves. For example, in Fig. 12a results for the JFM, FMA, and March–May (MAM) seasons are shown, denoted by symbols of an open circle, a plus sign, and a closed square, respectively. The different types of events have color-coded curves so that warm events use red curves, neutral events use green curves, and cold events use blue curves. The finer temporal resolution of these ROC curves shows that model forecast of neutral events with a probability of at least a 57% level (the first four points on each green curve from the lower left-hand corner)

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for the JFM, FMA, MAM, April–June (AMJ), November–January (NDJ), and December–February (DJF) IC periods have little or no skill. Conversely, neutral event forecasts with ICs from the July–September (JAS), August–October (ASO), and September– October–November (SON) seasons are skillful. These curves also show that for the AMJ, MJJ, JJA, JAS, and ASO seasons (Figs. 12b and 12c) high probability forecasts of cold events can be made with quite high confidence levels (first or second symbol on each curve) with associated expected hit rates of greater than 50% and expected false alarm rate of significantly less than 10%. As was found in calculating the deterministic measures using a higher temporal frequency, the ROC curves calculated for each season of IC give a different impression of the model forecast skill than when using the bulk method taking all months together for the calculation. Compared to the bulk calculation the higherfrequency calculation gives a more pessimistic impression of the utility of the model for forecasting neutral events for some ICs. On the other hand, the higherfrequency calculation allows one to issue forecasts with higher probabilities for cold events with an even higher expected skill level than is possible from interpreting the ROC curves made using the bulk method.

5. Diagnosing the coupled model’s spring predictability barrier As shown earlier, this coupled model exhibits the typical NH spring prediction barrier in central and eastern Pacific SST, which has been found to exist in varying degrees for all forecasting systems developed to date (Latif et al. 1998; Kirtman et al. 2002). Currently, there are two dominant hypotheses for the underlying cause of this breakdown in skill. The first hypothesis is that during NH spring the coupling between the atmosphere and the ocean (or the coupled instability strength) is weaker than at other times of the year (Zebiak and Cane 1987). The second hypothesis is that during NH spring the SST variability is weakest and hence most sensitive to contamination by noise (perhaps better characterized as stochastic effects) and subsequent growth of errors (Webster and Yang 1992; Xue et al. 1994). In an intermediate coupled model framework, Kleeman (1993) showed that model forecast skill was very sensitive to which term is dominant in the SST equation. Model configurations that had SST anomalies strongly dependent on thermocline depth anomalies were found to give the highest forecast skill. This result is consistent with the fact that outside the tropical Pacific, where thermocline variations are small on the seasonal time scale, SST forecast skill is fairly low. This can

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be seen, for example, in Fig. 3 as well as numerous other studies. Recent observational work suggests that the magnitude of eastern and central Pacific SST anomalies are highly correlated at a lag of 3 to 6 months with the equatorial basin mean upper-ocean heat content (McPhaden 2003; Hasegawa and Hanawa 2003). The near-equatorial SST anomalies in the Pacific have also been found to be highly correlated with the local heat content anomalies at different lags, with almost no lag in the far-eastern Pacific and a lag approaching 1 yr in the central Pacific (Zelle et al. 2004). An important caveat on the Zelle et al. (2004) results is that the data were not stratified by the annual cycle so that the local relationship between SST and heat content might include effects due to the seasonal cycle. Indeed, using an adjoint of a hybrid coupled model Galanti et al. (2002) find that the seasonal dependence of the coupled atmosphere–ocean instability in the equatorial Pacific is largely due to how strongly the thermocline and surface waters are connected. It would seem then that a potential source of the spring predictability barrier might be this decoupling of the surface and subsurface anomalies. The correlation between upper-ocean heat content (HC) anomalies and SST anomalies averaged between 2°S and 2°N in the Pacific is shown for the National Centers for Environmental Prediction (NCEP) ODA product (Behringer et al. 1998) and the coupled model in Figs. 13 and 14. For the purpose of this analysis the NCEP ODA will be treated as observations. The HC as defined here is simply the temperature averaged over the upper 200 m of the ocean. Figure 13 compares the evolution of the observed correlation of anomalous HC and SST with that from the February IC forecasts. This shows the strength of the SST coupling with HC passing through the spring predictability barrier. Figure 14 is the same as Fig. 13 except that the period chosen (August IC forecasts) does not pass through the spring predictability barrier. Comparing the correlation for the observations during these two time periods shows that starting in late NH fall the region of strong correlation between the surface and subsurface temperature contracts to the east. The eastward contraction stops around March to April and from April until the fall the region of strong correlation expands westward again. This tendency for the SST to have a seasonally dependent coupling strength with the subsurface could certainly give rise to a variation in seasonal predictability. In particular, based on the results of Kleeman (1993), during periods when the SST is not strongly correlated with the upper-ocean HC variations predictive skill could be expected to be lower than during periods

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FIG. 13. Correlation coefficient between SST anomalies and upper-ocean heat content anomalies averaged between 2°S and 2°N as a function of month. (a) NCEP ODA product. (b) Coupled model Feb IC forecasts.

when it is strongly correlated. Presumably, during these periods of relatively low correlation between HC and SST anomalies other processes such as horizontal temperature advection and heat fluxes are dominant in determining the SST anomalies. The correlation between HC and SST anomalies for the coupled model is seen to have an exaggeration of

the observed behavior for the two periods. In particular, the region of high correlation contracts farther eastward for the model compared to observations during NH spring and results in a lower coupling of the SST and HC than found for observations during spring and early summer in the eastern Pacific (Fig. 13). Conversely, for the forecast starting in midsummer (Au-

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FIG. 14. Correlation coefficient between SST anomalies and upper-ocean heat content anomalies averaged between 2°S and 2°N as a function of month. (a) NCEP ODA product. (b) Coupled model Aug IC forecasts.

gust; Fig. 14) the region of strong correlation for the coupled model expands farther westward than for observations and starts contracting eastward later in the year. Also, the region with very strong correlation (correlation exceeding 0.9) is more extensive for the coupled model than for observations. These results taken together with the modeling study of Kleeman

(1993) tend to indicate that the observed system has a spring predictability barrier due to the annual cycle in the strength of coupling between HC and SST. Furthermore, the model has lower predictability, or equivalently, a stronger predictability barrier compared to the real system during this period due to a weaker HC and SST coupling compared to reality.

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As discussed earlier, another hypothesis for the presence of the spring predictability barrier is that the weak variability during this period makes the system more susceptible to error growth induced by stochastic processes. The possibility that this applies to the coupled model is tested using a method commonly employed in potential predictability studies of the atmosphere. In this method, the variance of a field (SST here) is divided into a signal component and a noise component. The ratio of these two components of the variance is known as the signal-to-noise ratio. Higher values of the signal-to-noise ratio indicate less contamination of the signal by presumably unpredictable random effects. Here the signal and noise variance of the SST are estimated using the ensemble mean and deviation about the ensemble mean following Rowell et al. (1995) and as applied by Straus and Shukla (2000), for example. The signal-to-noise ratio at leads of 3 to 6 months is shown for February and August IC forecasts in Fig. 15. The magnitude of the signal-to-noise ratio is seen to exceed 0.5 only in the central and eastern nearequatorial Pacific. Comparing the two different ICs shows that the signal-to-noise ratio is much higher (approaching an order of magnitude in the central Pacific at 6-months lead) for the August forecast. Thus, for this coupled model the spring is indeed a time when stochastic effects can be expected to more easily degrade forecast skill. It should be noted that the reason for this might not be distinct from the HC and SST coupling discussed earlier; that is, during spring the reason that the signal-to-noise ratio is lower is that the SST is controlled less by HC variations and more by other more stochastic processes such as horizontal temperature advection and heat fluxes.

6. Summary and concluding remarks This paper analyzes the results from a large number of hindcasts of central and eastern tropical Pacific SST for the period 1982 to 2002 made using a coupled atmosphere–ocean GCM. These hindcasts were evaluated using both deterministic and probabilistic metrics. Skill measures have been calculated using bulk methods in which all months are considered together and as a function of initial condition month. The former calculations allow more direct comparison with other results in the literature while the latter calculations are arguably more relevant for evaluating the utility of the forecast model in the context in which it will actually be applied, that is, to produce forecasts from a particular month. The forecasts made using this model are found to have competitive skill with those documented in the literature both for the bulk index metrics and for the

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metrics calculated as a function of initial condition month. When forecast skill is considered as a function of initial condition month there is a clear loss of skill in NH spring. This applies both to forecasts initiated at this time as well as forecasts extending into this period. This behavior has been found for most other forecast systems (Balmaseda et al. 1995; Latif et al. 1998; Kirtman et al. 2002). Diagnostics of this so-called spring predictability barrier in the context of this coupled model indicate that two factors likely contribute to the predictability barrier. First, the coupled model shows a too-weak coupling of the surface and subsurface temperature anomalies during NH spring. Second, the coupled-model-simulated signal-to-noise ratio for SST anomalies is much lower during NH spring than at other times of the year, indicating that the model is more susceptible to stochastic effects at this time. Model forecast skill considered as a function of initial condition month does not always exceed that of a reference persistence forecast for lead times of 1 to 2 months and even 3 months for some seasons. This behavior is consistent with what has been reported for other forecast systems (Goddard et al. 2001). Even though only tropical Pacific SST forecast skill has been discussed here this model is actually producing forecasts for each of the tropical ocean basins. A detailed analysis of the forecast skill for the tropical Atlantic and Indian Oceans is now being conducted, and those results will be reported in due course. Despite the fact that the model forecasts presented here are competitive with other state-of-the-art systems there is still plenty of room for improvement in forecast skill. The coupled forecast system documented here has a rather large cold bias similar to that documented in Alves et al. (2004). It is not known how this bias affects forecast skill. However, it is reasonable to expect that reducing the bias could lead to improved forecast skill. Previous work by Chen et al. (2000) and Yang and Anderson (2000) has shown significant improvement in forecast skill when empirical methods are used to reduce coupled model biases. Currently, work is being conducted to empirically reduce the SST and other biases in this coupled model, which will hopefully lead to an improvement in forecast skill. Two other potential improvements to the forecast system are a more rigorous method for generating the different ensemble members, including potentially perturbing the ocean initial state, and use of an ODA system and OGCM component model at the same horizontal resolution. Despite the fact that this study and those of Kirtman (2003) and Schneider et al. (2003) do

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FIG. 15. Signal-to-noise ratio for coupled model SST forecasts at different leads (see text for details). (a)–(d) Feb IC forecasts at leads of (a) 3, (b) 4, (c) 5, and (d) 6 months. (e)–(h) Aug IC forecasts at leads of (e) 3, (f) 4, (g) 5, and (h) 6 months.

not show any noticeable deleterious effect from this interpolation of the ODA to the OGCM grid it surely cannot be optimal and some imbalance near the equator must result from this procedure even if it is not perceptible.

A final note regarding this forecasting system is that it is skillful but imperfect like other forecasting systems. Hence this coupled model will be used as one component of a multiple-source SST forecast product that will be used as boundary conditions for AGCMs in the sec-

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ond tier of the International Research Institute for Climate Prediction (IRI) operational forecast suite. Acknowledgments. The forecasts described in this paper were made possible due to help from several institutions. Matt Harrison and Tony Rosati of GFDL developed the ODA system and produced the ODA product until December 1999. Ben Kirtman and Duhong Min of COLA have ported the GFDL ODA system to their own computer hardware and produced the ODA product from January 2000 to present. Bohua Huang of COLA implemented the version of the OGCM used here. Lennart Bengsston of the MaxPlanck-Institut für Meteorologie (MPI) has kindly provided the ECHAM4.5 AGCM code. Uwe Schulzweida and Luis Kornblueh of MPI graciously gave assistance in the initial setting up the ECHAM4.5 code to run at IRI. CERFACS kindly provided the OASIS coupler to us for use in our experiments. Simon Mason provided sample code for computing the ROC scores. This work was partially completed using computing time provided under the NCAR CSL program. David DeWitt’s time was supported by a grant/cooperative agreement from the National Oceanic and Atmospheric Administration (NA07-GP0213). The views expressed herein are those of the authors and do no necessarily reflect the view of NOAA or any of its subagencies. REFERENCES Alves, O., M. A. Balmaseda, D. Anderson, and T. Stockdale, 2004: Sensitivity of dynamical seasonal forecasts to ocean initial conditions. Quart. J. Roy. Meteor. Soc., 130, 647–667. Balmaseda, M. A., M. K. Davey, and D. L. T. Anderson, 1995: Decadal and seasonal dependence of ENSO prediction skill. J. Climate, 8, 2705–2715. Behringer, D. W., M. Ji, and A. Leetma, 1998: An improved coupled model for ENSO prediction and implications for ocean initialization. Part I: The ocean data assimilation system. Mon. Wea. Rev., 126, 1013–1021. Brinkop, S., and E. Roeckner, 1995: Sensitivity of a general circulation model to parameterization of cloud-turbulence interactions in the atmospheric boundary layer. Tellus, 47A, 197–220. Cane, M. A., S. E. Zebiak, and S. C. Dolan, 1986: Experimental forecasts of El Nino. Nature, 321, 827–832. Chen, D., M. A. Cane, S. E. Zebiak, R. Canizares, and A. Kaplan, 2000: Bias correction of an ocean–atmosphere coupled model. Geophys. Res. Lett., 27, 2585–2588. Derber, J., and A. Rosati, 1989: A global oceanic data assimilation system. J. Phys. Oceanogr., 19, 1333–1347. Dewitte, B., D. Gushchina, Y. duPenhoat, and S. Lakeev, 2002: On the importance of subsurface variability for ENSO simulation and prediction with intermediate coupled model of the tropical Pacific: A case study for the 1997–1998 El Nino. Geophys. Res. Lett., 29, 1666, doi:10.1029/2001GL014452. Fouquart, Y., and B. Bonnel, 1980: Computations of solar heating

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