The El Niño/Southern Oscillation (ENSO) in the tropical Pacific is one of the most important seasonal-to-interannual climate signals. Although it originates and develops primarily in the tropical Pacific, it can affect season-to-interannual climate variability globally. Over the past decades the ability by the dynamical models to predict ENSO has been significantly improved (Cane et al., 1986; Chen et al., 1995; Latif et al., 1998; Barnston et al., 1999; Kirtman et al., 2002; Zhang et al., 2003; Zheng et al., 2006; Jin et al., 2008; Zhu et al.2011). However, ENSO simulation and prediction are still far from perfect due to systematic biases in various components of a coupled ocean-atmosphere model.
On the oceanic side, systematic biases are still a major challenge in simulations of both mean climatology and interannual variability when using ocean general circulation models (OGCMs). Generally, the thermocline represented in OGCMs is too diffuse, leading to the simulated vertical gradient of temperature that is much weaker than that which is observed (e.g. Delecluse et al., 1998). The simulated SST variability is also significantly underestimated in the eastern equatorial Pacific (e.g. Zhang and Zebiak, 2004; Zhang et al., 2006). Furthermore, OGCM-based coupled systems commonly simulate ENSO cycles with a 2–3 year oscillation period, which is shorter than that observed (e.g. referred to as the SST-mode; Guilyardi, 2006). As suggested by a number of modelling studies (e.g. Syu et al., 1995; Rosati and Miyakoda, 1998; Zhang and Zebiak, 2004; Zhang et al., 2006), these biases and systematic errors can be partially ascribed to the parameterisations of the entrainment and vertical mixing in ocean models. In particular, vertical mixing schemes currently used in OGCMs likely underestimate the connection between surface and sub-surface layers, which leads to an underestimation of the thermocline feedback in coupled simulations. As a result, some coupled models are predominated by the so-called SST-mode (Guilyardi, 2006), favouring a relatively short oscillation period. Therefore, there is a clear need to improve representations of the thermocline feedback in OGCM-based coupled climate models for better ENSO simulations and, thus, predictions.
As schematically shown in Figure 1, the thermal structure of the ocean can be characterized by a well-mixed layer at the surface and a thermocline below where temperature drops rapidly with depth. It has been known that subsurface processes at the base of the mixed layer (i.e. entrainment and mixing) are important in controlling SST variability in the central and eastern equatorial Pacific, where the thermocline is shallow and the mean upwelling is strong (Zebiak and Cane, 1987). Previously, in order to improve simulations of upper-ocean temperature variability, numerous studies have focused on better determinations of entrainment velocity in OGCMs layers (e.g. Schopf and Loughe, 1995; Wallcraft et al., 2003) and/or the coefficients of vertical diffusivity in level OGCMs (e.g. Pacanowski and Philander, 1981; Large and Gent, 1999).
As the effects of both entrainment and vertical mixing processes on SST also depend on the temperature of subsurface entrainment water at the base of the mixed layer (Te), it is conceivable that one can seek a better estimate of Te for improving SST anomaly simulations and predictions in numerical models (e.g. Kang and Kug, 2000). In particular, an empirical procedure to optimize Te has been developed by taking into account observational data and model simulations (Zhang et al., 2005a). This procedure acts to produce a balanced representation of the subsurface effects on SST variability relative to other SST budget terms, including the entrainment and vertical mixing. In the context of intermediate ocean models, it has been demonstrated that SST anomaly simulations and predictions can be significantly improved (Zhang et al., 2003, 2005a,b). To take advantage of the empirical Te parameterisation for improving SST anomaly simulations in the context of OGCMs, an embedding approach has been developed by explicitly embedding a separate SST anomaly submodel into OGCMs. It has been demonstrated that ENSO simulations can be improved effectively in OGCM-based HCMs (Zhang et al., 2006; Zhu et al., 2006, 2009). It remains to be seen if the embedded approach can improve ENSO predictions in OGCM-based HCMs.
In this work, retrospective forecasts for ENSO are performed by using two types of HCMs, one with a standard coupling, and the other with the embedded approach. The paper is arranged as follows. Section 2 describes two OGCM-based HCMs. Coupled interannual variability in the two HCMs is briefly compared in Section 3. The hindcast results are examined for dependent (Section 4) and independent (Section 5) periods using the derived empirical Te parameterisations. Conclusions are given in Section 6.
2. Descriptions of model components
As illustrated in Figure 2(a), we developed an OGCM-based standard HCM (Zhu et al., 2009), consisting of an OGCM and an empirical model for wind stress anomaly. The OGCM used here was first developed by Zhang and Endoh (1992), and has been used for ENSO prediction at the Institute of Atmospheric Physics, the Chinese Academy of Sciences (IAP/CAS) (Zhou and Zeng, 2001). The dynamics of the model are governed by primitive equations under hydrostatics, and the Boussinesq approximation in σ-coordinates with a free surface. The model domain is confined within the tropical Pacific region (30°S–30°N, 121°E–69°W), with realistic land–sea boundaries and flat bottom. There are 14 vertical levels with a resolution of 20 m in the upper 60 m, and a 30-m resolution between 60 and 240 m depth. The model's horizontal resolution was increased from 1° × 2° in Zhang and Endoh (1992) to 0.5° × 0.5° in the present study (Fu et al., 2005; hereafter IAP-TPOGCM), allowing for a proper depiction of equatorial waves. Detailed descriptions of IAP-TPOGCM can be found in Zhang and Endoh (1992) and Fu et al. (2005).
The atmospheric model is a statistical one constructed from a singular value decomposition (SVD) of the covariance matrix from the time series of monthly mean SST and wind stress (τ) anomaly fields (Zhang et al., 2003; Zhu et al., 2011). Observed SSTAs are from Reynolds et al. (2002). Wind stress data are the ensemble mean of a 24-member ECHAM 4.5 simulation forced by observed SST anomalies. Since seasonality in the atmosphere can have an important effect on the onset and evolution of El Niño (e.g. Barnett et al., 1993), we use seasonally varying SVD analyses to construct the τ model during the period 1963–1996 (the training period). In this study, the first five SVD modes are included in estimating wind stress fields from SST anomalies. The atmospheric τ model does not take into account the stochastic wind effect. As shown in Figure 2(a), SST anomalies from the OGCM (relative to its uncoupled mean climatology) are directly used to calculate the τ anomalies, which are added onto observed mean seasonal climatology of τ to drive the OGCM. This is a standard method in coupling the atmosphere and the ocean, referred to as a standard coupling (HCMstd; e.g. Barnett et al., 1993; Syu et al., 1995)
In addition, we have developed an embedded HCM (Figure 2(b), referred to as HCMembed). In this embedded coupling, a separate SST anomaly submodel is embedded into the OGCM, whose governing equation can be written as.
where T′ and Te′ are anomalies of SST and the temperature of the subsurface water entrained into the mixed layer, respectively; T̄ and T̄e are the prescribed seasonally varying mean SST and Te, which are obtained from the observations and the OGCM run; ū and v̄ are the prescribed seasonally varying mean zonal and meridional currents in the mixed layer, and w̄ is the prescribed seasonally varying mean entrainment velocity at the base of a mixed layer, all of which are obtained from the OGCM run forced by prescribed forcings from ERA40 (Uppala et al., 2005); u′, v′ and w′ are the corresponding anomaly fields; H is the depth of the mixed layer; H + H2 is a constant (125 m); M(δ) is the Heaviside step function (i.e. M(δ) = δ if δ is positive and M(δ) = 0 if δ is negative); κh and κv are the horizontal (respectively taken as 2.5 × 103 m2 s−1 meridionally and 2.5 × 104 m2 s−1 zonally) and vertical (taken as 10−3 m2s−1) diffusion coefficients, respectively; α is the thermal damping coefficient (taken as (100 days)−1); and the other variables are conventional.
An empirical parameterisation for T′e is implemented in the HCM, which is developed in two steps. First, an inverse modelling approach is adopted to estimate Te anomalies using the SST anomaly equation (Equation (1)), with monthly SST fields observed (Reynolds et al., 2002) and monthly upper ocean currents simulated from the IAP-TPOGCM. Second, a relationship between the T′e fields estimated from the inverse modelling and monthly sea level (SL) anomalies simulated from the IAP-TPOGCM is then established using an empirical orthogonal function (EOF) analysis. More detailed descriptions about the method can be found in Barnett et al. (1993); its application to the empirical T′e model is presented by Zhang et al. (2005a) and Zhu et al. (2006). In this study, the EOF analysis is preformed on all time series of T′e and SL anomalies during 1963–1996 irrespective of seasons; the first 10 EOF modes are retained to construct the Te model, which account for 82.6 and 62.9% of the variance for SL anomalies and T′e fields, respectively. Thus, given an SL anomaly, an Te anomaly can be calculated from the empirical T′e model for use in the SST anomaly submodel. In doing so, the empirical T′e parameterisation optimally yields a better balanced representation of the subsurface effect on SST variability associated with the mean upwelling of anomalous subsurface temperature and vertical mixing in the equatorial Pacific, leading to an improved SST simulation.
The embedded coupling is implemented in the HCM as follows. At each time step, the OGCM calculates SL and currents in the surface mixed layer, the anomalies of which are obtained relative to their mean climatological fields that are predetermined from the OGCM-only run forced by observed atmospheric fields. Te anomalies, used for the embedded SST anomaly submodel, are calculated from the empirical T′e model in terms of the SL anomalies simulated from the OGCM. These interannual anomalies, together with prescribed mean climatological fields, are passed to the embedded SST anomaly submodel to calculate its own space-time evolution. These components exchange anomaly information every day.
Note that in the HCMembed, two SST anomaly fields are available: one from the embedded SST anomaly submodel and the other from the OGCM (calculated as departures from its uncoupled mean climatology). Since SST anomalies from the former have more reasonable structure and amplitude in the central and eastern equatorial Pacific, they are used to determine τ anomalies via the statistical atmospheric τ model.
In addition, coupled behaviours in the HCMs depend on the so-called relative coupling coefficient (ατ), i.e. the wind stress anomalies calculated from the statistical atmospheric model can be multiplied by a scalar parameter before being used to drive ocean models (Barnett et al., 1993). Different values have been tested to get a sustainable oscillation for each HCM (HCMstd and HCMembed). It can be shown that in both HCMs, the value of ατ does not significantly change the coupled oscillation period and space structure of interannual variability. In the prediction experiments shown below, ατ has been chosen for each HCM to produce a self-sustaining ENSO oscillation: ατ = 2.0 for HCMstd and ατ = 1.05 for HCMembed, respectively.
3. Coupled interannual variability
Both HCMstd and HCMembed have been integrated for 45 years, started from an ocean spin-up run forced by atmospheric climatological fields. The simulated interannual variability from HCMstd and HCMembed are shown in Figures 3 and 4, respectively. In HCMstd (Figure 3), several unrealistic features are evident. For example, the interannual oscillation tends to have a shorter period, characterized by quasi-biennial cycle (green curves in Figure 5). Also, the zonal distributions of SST variability are not simulated well, with the amplitudes of SST anomalies being too weak in the eastern equatorial Pacific. These systematic biases can also be found in other coupled models (e.g. Barnett et al., 1993; Syu et al., 1995; Guilyardi, 2006; Zhang et al., 2006). As studied in Zhang et al. (2006), these biases may be associated with weak anomalies of Te in the uncoupled OGCM simulation. It can be speculated that the coupled system with a weak thermocline feedback among SST, thermocline, and wind stress will be dominated by the SST-mode, acting to have short-lived interannual oscillations with weak SST variability (Guilyardi, 2006).
In HCMembed (Figure 4) in which an additional SST anomaly submodel is embedded into the OGCM with optimized Te parameterisation, an improved ENSO cycle is strikingly evident: a pronounced interannual oscillation with a major 4-year period (red curves in Figure 5) and a significantly enhanced SST variability in the central and eastern Pacific. The time scale of the interannual variability, its structure and the coherent phase relationships among these anomalies of SST, surface wind and SL are consistent with observations (e.g. Zhang and Levitus, 1997). More detailed analyses about the coupled interannual oscillations in HCMstd and HCMembed can be found in Zhu et al. (2009).
4. Hindcast results
Now we compare the hindcast results from two experiments using HCMstd and HCMembed. In both cases, the OGCM is initialized from a 3D-Var ocean data assimilation system (Zhu et al., 2006). Additionally, the SST anomaly submodel in HCMembed is initialized by directly inserting observed SST anomalies (This insertion may introduce a shock in the coupled model, which is detrimental to a predictive system, and thus, the prediction skill in HCMembed may be affected). A total of 252 retrospective forecasts are made for a 12-month duration, starting at the beginning of each month from January 1982 to December 2002. The observed SSTs used for validation are taken from the OI SST dataset (Reynolds et al., 2002).
Figure 6 shows the predicted and observed Niño-3.4 SST anomalies at 3-, 6-, and 9-month lead times. At a 3-month lead time (Figure 6(a)), the predicted SST anomalies by both HCMstd and HCMembed closely follow the corresponding observations. At a 6-month lead time (Figure 6(b)), the differences in the predicted SST variability in HCMstd and HCMembed become obvious. While the forecast in HCMembed can generally follow the observations closely, that in HCMstd exhibits large deviations. For example, in HCMstd forecast, there are a few false alarms, such as a cold event in early 1984 and warm events in 1989/1990 and during the period from 2000 to 2002. At a 9-month lead time (Figure 6(c)), the differences between observations and forecasts become larger, but HCMembed can still predict major events with a reasonable degree of accuracy, like the 1984/1985, 1988 and 1999 La Niña and the 1997/1998 El Niño. In contrast, the HCMstd forecast has completely missed these events. The false alarms are also more frequently seen in HCMstd than in HCMembed.
To be more quantitative, their overall prediction skills are compared in Figure 7 by anomaly correlation and RMS errors between observed and predicted Niño-3.4 SST anomalies as a function of lead times. In addition, as has been commonly used for a reference, persistence forecast can be made from observed SST fields (note that a damped persistence forecast may be more suitable for being taken as a benchmark). Comparisons among these forecasts (Figure 7) clearly indicate that the HCM forecasts generally show a higher skill than persistence forecast, except for the lead times of the first 1–3 months in HCMstd. It is also clearly evident that the skill of HCMembed beats both persistence and HCMstd forecasts at all lead times. The anomaly correlation skill also decreases more slowly in HCMembed than in persistence and the HCMstd forecast. At most lead times, the anomaly correlation is 0.1–0.2 higher in HCMembed than in HCMstd, and the corresponding RMS error is 0.1–0.2 °C lower. If a valuable prediction is defined as the correlation being higher than 0.5, it can be found that HCMembed can provide valuable predictions for about 9 months, but only for 6 months in HCMstd. The better performance of HCMembed, especially on the longer lead times, indicates that the embedded model is able to capture ENSO time scales associated with coupled ocean-atmosphere interactions, which should be attributed to more realistic simulations of interannual oscillations (Section 3).
The horizontal distributions of the anomaly correlations at lead times of 3, 6 and 9 months are further presented in Figures 8, 9 and 10, respectively. At a 3-month lead time (Figure 8), all persistence, HCMstd and HCMembed forecasts display useful predictions (anomaly correlation higher than 0.5) over the equatorial region. However, similar to previous standard HCMs (e.g. Barnett et al., 1993; Syu et al., 1995), higher prediction skill in HCMstd is confined to a narrow region with 10°N/S (Figure 8(b)). In HCMembed forecast, it is striking that high anomaly correlation (more than 0.8) covers the most regions of the central and eastern equatorial Pacific. At a 6-month lead time, the skill drops fastest in persistence forecast (Figure 9(a)), with the correlation below 0.4 in the equatorial eastern Pacific. The skill in HCMstd forecast is slightly higher than persistence forecast in the narrow equatorial eastern Pacific. Strikingly, HCMembed forecast presents a much higher skill (Figure 9(c)), with the correlation greater than 0.5 in a large area of the tropical Pacific, and even 0.7 in the central and eastern equatorial Pacific. At a 9-month lead time (Figure 10), the persistence and HCMstd forecasts offer no predictable information in the equatorial Pacific, but HCMembed forecast (Figure 10(c)) can still be in the central and eastern equatorial Pacific to some degree.
In addition, from Figures 8(b) and 9(b), the HCMstd forecast exhibits a clear trend that the far eastern Pacific Ocean (east of 110°W) is much less predictable than the central basin, with its performance being even worse than in the persistence forecast. This problem is consistent with the biases in its simulated coupled interannual variability, which tends to underestimate SST variability significantly in the far eastern equatorial Pacific (Zhu et al., 2009; Figure 3). As has been argued by Zhang et al. (2006), these biases can be associated with weak anomalies of Te in the uncoupled OGCM simulation. As configured in HCMembed, an empirical Te parameterisation is employed to optimize the Te fields, which acts to balance the mixing/upwelling-related subsurface effects on SST with other SST budget terms. As demonstrated in Section 3 for coupled experiments, simulated interannual SST variability in the equatorial Pacific Ocean in HCMembed can be improved significantly through the embedded approach (Zhu et al.2009; Figure 4). Forecast experiments presented here further demonstrate that the embedded approach is able to improve the prediction skill as well.
The zonal distributions of the prediction skill are further displayed in Figure 11, exhibiting the anomaly correlation along the equator as a function of lead months. The low skill problem over the far eastern Pacific Ocean in HCMstd is clearly shown in Figure 11(b): the prediction skill decreases most rapidly in the far eastern equatorial Pacific in HCMstd (Figure 11(b)), compared with persistence (Figure 11(a)) and HCMembed (Figure 11(c)) forecasts. In addition, it can also be seen that the most predictable areas reside in the central and eastern Pacific, but the prediction skill decreases dramatically west of 160°E, which is due to the relatively low variability signal in the region. The comparison among the three forecasts indicates that the prediction skill in HCMembed is much higher than that in persistence and HCMstd forecasts. In particular, the predictable period in the central and eastern Pacific can reach about 9 months in HCMembed, but only 5–6 months in the persistence and HCMstd forecasts, respectively.
To compare the seasonality of prediction skill among persistence, HCMstd and HCMembed forecasts, the correlations are calculated as a function of initiation month and lead times. Such an analysis for the Niño-3.4 SST anomalies is shown in Figure 12. A striking feature is that the prediction skill in persistence and HCMembed forecasts highly depend on the seasons, similar to previous results (e.g. Chen et al., 1995). For example, correlation skill is relatively low for predictions starting in the earlier part of the year (Jan–Apr), and significantly higher for predictions starting thereafter. The boreal spring predictability barrier is also evident: the most rapid decrease of skill occurs when the hindcasts pass through the northern spring. For both persistence and HCMembed cases, the most rapid drop in skill occurs for forecasts started in April/May and in the first month; but for forecasts starting between July and November, skill is maintained significantly higher. In contrast, there is less seasonality of the prediction skill in HCMstd forecast. The correlation skill drops to 0.5 after 6 months for hindcasts starting in most months.
In summary, the HCMstd shows large biases in the predicted SST anomalies, which can be attributed to those in the simulated coupled interannual variability. By embedding an SST anomaly submodel with optimized Te into the coupled system, the HCMembed can not only depict coupled interannual oscillations more realistically, but also achieve a higher skill in predicting ENSO. As similar biases also exist in other standard HCM-based prediction systems, the embedded approach we developed here can be easily and effectively applied to other models for better ENSO prediction.
5. Forecasts during the period 1997–2002: an independent application
In the above analysis, there is an overlap between the hindcast period (1982–2002) and the training period (1963–1996) for constructing the empirical atmospheric and Te models. Here, we briefly present the prediction skills estimated during the period 1997–2002, which is independent from the training period 1963–1996 in constructing the Te model. As such, this can be a strict test of the embedded approach in terms of ENSO prediction. Figure 13 shows the anomaly correlation and RMS errors between observed and predicted Niño-3.4 index calculated during the period 1997–2002 (72 members). It seems that compared to the period 1982–2002, both HCMstd and HCMembed show higher prediction ability during this independent period, which may be due to their good performance in predicting the strong 1997/1998 El Niño and 1999/2000 La Niño events. Moreover, the improvement in the prediction skill using HCMembed against using HCMstd, is even more striking for the period 1997–2002 as compared with the total period 1982–2002, with above 0.2 in anomaly correlation appearing at lead time of 7–11 months (Figure 13). The horizontal distribution of the anomaly correlations at a 6-month lead time is further shown in Figure 14 for the period 1997–2002. Compared with those from the period 1982–2002 shown above (e.g. Figure 9), the patterns are generally the same for persistence, HCMembed and HCMstd forecasts. Moreover, the prediction skill for this independent period is even slightly superior to that for the period 1982–2002 (e.g. Figure 9). Comparing HCMembed with HCMstd improvement is in the horizontal maps, with anomaly correlations above 0.7 appearing over large areas in HCMembed, but mostly below 0.5 in HCMstd.
These analyses are very encouraging and clearly indicate that the prediction skill of the coupled system is not particularly dependent on the data periods selected for constructing the empirical atmospheric and Te models. Although the periods selected for these forecast tests may be too short to produce stable statistics for prediction skills in these coupled prediction experiments, an improvement is clearly demonstrated through embedding an SST anomaly submodel with optimized Te parameterisation in the coupled system, being insensitive to the training period and application period taken for the statistical Te modelling.
6. Concluding remarks
An embedded HCM has been developed in which a separate SST anomaly submodel is explicitly added to an OGCM. The purpose of such an embedded modelling exercise is to improve SST anomaly simulations through the embedded SST anomaly submodel, which can be accomplished by optimizing Te parameterisation. Previously, the empirical parameterisation for Te was implemented in OGCMs to show improvements in SST variability simulation in the tropical Pacific (Zhang et al., 2006; Zhu et al., 2006; Zhu et al., 2009). In this work, two retrospective forecasts are performed using HCMs to demonstrate the benefit in terms of ENSO prediction: a standard HCM, and an embedded HCM in which the empirical Te parameterisation is incorporated in an optimized way. The results indicate that ENSO predictions can be effectively improved in the HCMembed. As compared with the HCMstd, the anomaly correlation in the Niño-3.4 region is higher by 0.1–0.2 at a 12-month lead time in the HCMembed; the corresponding RMS error is decreased by 0.1–0.2 °C; in the far eastern equatorial Pacific, the prediction skill is also improved significantly.
These experiments have clearly demonstrated the robustness and effectiveness of an optimized Te parameterisation for reducing model errors in SST anomaly simulations and predictions. This embedding method can be easily applied to other ocean models for better ENSO prediction since this embedding scheme does not modify an ocean model itself. Furthermore, as discussed in Zhang et al. (2006), considering that the embedded SST anomaly submodel is just one equation with its various terms diagnostically estimated from OGCMs, it can be implemented in any ocean model with little computational cost. Particularly, the computer CPU time is increased only by about 1% in the embedded HCM as compared to the standard HCM. Note that the approach taken with embedded coupling in the HCMembed for improving SST simulations is different from model output statistics (MOS) corrections (e.g. Barnett et al., 1993), a post-processing analysis to reduce systematic SST model errors that have already been produced. In our embedding approach, the major source of error for SST simulations, the subsurface effects as represented in Te, is corrected in a way that good SST anomaly simulations can be achieved through an empirical Te parameterisation that optimally balances various processes affecting SST variability. These preliminary results presented in this paper are very encouraging and further experiments are worthy of being performed, such as the effects of the scheme on reducing spring predictability barrier, and the applications to real-time ENSO forecasts.
We would like to thank SE Zebiak and AJ Busalacchi for their comments. We are also grateful to two anonymous reviewers and the editor Prof. Andrew Comrie for their suggestions and comments. This research is supported by the National Basic Research Program of China (973 Program: 2010CB951901), the CAS Strategic Priority Research Program Grant No. XDA05110203, and the National High Technology R&D Program of China (Project No. 2010AA012401). Zhang is supported in part by an NSF Grant (ATM-0727668 and AGS 1061998) and NOAA Grant (NA08OAR4310885).