An Intermediate Model of the Tropical Pacific Ocean

Bin Wang and Tianming Li
Department of Meteorology, School of Ocean and Earth Science and
Technology, University of Hawaii
Ping Chang
Department of Oceanography, Texas A&M University

J. Phys. Oceanogr., 25, 1599-1616

Abstract | Introduction | Summary


An intermediate tropical Pacific ocean model is developed to bridge the gap between anomaly models of El Nino and ocean general circulation models. The model contains essential physics for reproducing both the annual and interannual variations of sea surface temperature (SST). A new parameterization scheme for entrained water temperature is shown to work satisfactorily in both the cold tongues and warm pools. This scheme combines Cane-Zebiak (CZ) model's dynamic framework and mixed layer physics, giving a more realistic description of the active tropical ocean.

Incorporation of the Niiler-Kraus scheme for turbulent entrainment enables the model to better simulate El Nino-Southern Oscillation (ENSO) in the central equatorial Pacific where the CZ model considerably underestimates observed SST variations. It also improves the model's performance on the seasonal cycle, especially in the central-eastern equatorial Pacific and the intertropical convergence zone (ITCZ). The potential energy generation induced by penetrative solar radiation tends to reduce entrainment in the central equatorial Pacific but to enhance mixing in the far eastern equatorial Pacific. Without this process the model central (eastern) Pacific would be excessively cold (warm).

In response to an idealized sequential westerly burst located in the western equatorial Pacific, the CZ model produces SST oscillations in the eastern equatorial Pacific due to the thermocline oscillation associated with passages of Kelvin waves. In the present model, however, SST variation in the eastern Pacific is insignificant because local entrainment transcends the influence of thermocline oscillation; on the other hand, positive SST anomalies slowly amplify near the dateline due to the reduction in wind-induced mixing and surface evaporation.

The annual variations of the oceanic momentum and heat transports associated with the annual march of the ITCZ are shown to have significant impacts on the annual mean state. On the other hand, including an annual mean heat flux correction in the present model does not strongly influence the amplitudes of annual and interannual SST variations. However, it does improve the phase structure of the annual cycle by providing a more accurate annual mean state.


Sea surface temperature (SST) is a key variable in modeling Earth's climate systems. In the last decade, a considerable number of upper ocean models with a hierarchy of physical complexity have been developed to model tropical SST. Of those, models with an intermediate degree of complexity (termed intermediate models by McCreary and Anderson (1991)) have proven to be valuable for testing hypotheses such as Bjerknes' (1969) and for understanding the physics of the El Nino-Southern Oscillation (ENSO). They have even been used to predict El Nino with skill at lead times of several seasons (Cane et al. 1986).

The existing intermediate models of tropical ocean may be classified into two categories: Kraus-Turner (KT hereafter) model and Cane-Zebiak (CZ hereafter) model. The KT model is a one-dimensional bulk model of oceanic mixed layer (ML) first formulated by Kraus and Turner (1967) and successively implemented by many investigators (e.g., Niiler and Kraus 1977; Garwood 1977). It describes the vertical entrainment generated by wind stirring, convection, and other subgrid-scale processes. Turbulence is assumed to mix all the physical properties uniformly within the layer, and the integral properties of the ML (temperature, velocity, depth, etc.) evolve with time. Various versions of the KT model have been used to investigate El Nino (e.g., Anderson and McCreary 1985; Yamagata and Masumoto 1989), annual cycle (Chang 1994), and midlatitude ocean-atmosphere interaction (e.g., Alexander 1992). Hirst (1986) employed a linearized KT model to estimate entrainment rate in the thermodynamic equation. He examined the stability of the coupled ocean-atmosphere and obtained a comprehensive picture of various coupled unstable modes including those found by Philander et al. (1984). The KT model, however, could not determine entrained water temperature without invoking a proper dynamic framework or a multi-layer model.

The CZ model originally designed by Cane (1979) for the study of wind-driven equatorial ocean circulation, is a 1-1/2 layer, linear, reduced gravity ocean coupled with a constant-depth surface layer. The model provides a simple yet extremely pertinent dynamic framework for modeling interannual variation of SST. The change in the model thermocline depth in response to a wind forcing captures an essential process of SST variation in the eastern equatorial Pacific during ENSO. The physics of the CZ model have been carefully analyzed (e.g., Cane and Zebiak 1985; Zebiak and Cane 1987; Battisti 1988; Neelin 1991; Jin and Neelin 1993). The model was also shown to be capable of reproducing reasonable SST seasonal variation (Seager et al. 1988, hereafter SZC model). In the western and central Pacific, however, the CZ model tends to underestimate SST anomalies (Cane 1993). The model also exhibits relatively large SST error along the eastern boundary of the Pacific Ocean in simulating SST climatology (Seager et al. 1988, Chang 1994), implying that coastal upwelling may not be handled properly. These shortcomings may be attributed to the neglect of entrainment: a fixed-depth surface layer does not allow a realistic specification of eastern boundary conditions and a reliable assessment of SST in the regions where the thermocline is deep.

Chang (1994) assessed the performance of both models in simulating the annual cycle of SST in the tropical Pacific Ocean and found that both models have considerable skills in reproducing SST variability. However, he also noted that the CZ model has a bias towards dynamical responses to surface winds whereas the KT model has a bias towards thermodynamic responses to surface heat fluxes.

Apparently, an integration of the complementary virtues of the two models is desirable. It is important for the CZ model to incorporate ML physics in the regions outside the equatorial cold SST tongues, where the effect of surface heat fluxes dominates that of oceanic advective processes. This motivates the development of the present model which combines the dynamics of the CZ model with the ML physics of the KT model in a consistent and rudimentary manner and without a sizable increase in numerical computation. The present model differs from Schopf and Cane's (1983) 2-1/2 layer model primarily in the treatment of the layer between the ML and the deep inert layer and in the parameterization of entrained water temperature as well as interfacial Reynolds stress. These are critical elements for integrating the virtues of the two models.

The goal of such a model development is, upon coupling an intermediate atmospheric model, to investigate the processes which govern the interaction between the annual and interannual variations and to explore the possibility of predicting ENSO without specifying annual cycle. For this purpose, the model must be capable of simulating both the annual cycle and interannual variation of the upper ocean. This is a challenge task for intermediate as well as general circulation model (GCM), because certain physical processes on seasonal time scale differ considerably from those on ENSO time scale. Mitchell and Wallace (1992) first emphasized the important contribution of the positive feedback between meridional wind component and SST gradient to the annual variation of the cold tongue-ITCZ complexes in the Pacific and Atlantic oceans. This process may not be critical to ENSO cycle, but is certainly relevant to the annual cycle in the Pacific. Wang (1994) showed that the annual cycle in the tropical eastern-central Pacific is alternatively dominated by a quasi-symmetric (with respect to the equator) equatorial-coastal mode, which primarily results from dynamic coupling of ocean and atmosphere, and an anti-symmetric monsoonal mode, which is driven by the contrast in surface heat fluxes between the southern and northern hemispheres. The annual variation involves an interaction between the two modes. Chang and Philander's (1994) theoretical analysis of coupled ocean-atmosphere instability produced a family of anti-symmetric and symmetric coupled ocean-atmosphere modes. They suggested that the anti-symmetric mode may be instrumental in rapidly reestablishing the cold tongues during northern summer, whereas the symmetric mode contributes to the annual westward propagation of the near-equatorial zonal wind and SST.

In next section we describe physical and numerical aspects of the model. Particular attention is given to the closure of the mixed layer equations, including parameterizations of entrained water temperature and interfacial momentum exchange. Section 3 presents a steady solution under the annual mean atmospheric forcing. To understand the model's response to atmospheric forcing, sensitivities of the steady solution to various processes are examined in section 4. Models with reduced physics are investigated and the linkage of the present model with the SZC model is discussed in section 5. Section 6 further elaborates differences between the SZC model and the present model in the processes that determine SST variation. The model's ability in reproducing annual cycle and interannual variations is demonstrated in section 7. The last section summarizes major results and discusses possible future improvements.


An intermediate tropical Pacific Ocean model is developed in an attempt to bridge the gap between simple anomaly models of El Nino (for example, Zebiak and Cane 1987) and more sophisticated GCMs. A precise definition of an intermediate model is not a simple matter. For the purpose of modeling SST, complete thermodynamics in the oceanic ML are necessary. Numerical simulations demonstrate that the present model contains essential elements for reproducing seasonal to interannual variability of SST. The model is computationally effective so that a large number of experiment can be performed to better understand important physical processes. The model thus provides a valuable tool for understanding results derived from more complicated GCMs or observations.

The present model has two active upper ocean layers overlaying a deep inert layer: a ML and a thermocline layer, both with a variable thickness. It is capable of modeling total, rather than anomalous, SST. In an anomalous intermediate model of El Nino (e.g., Zebiak and Cane 1987, Anderson and McCreary 1985), surface wind forcing and ocean dynamics are of prime importance. For modeling climatological seasonal cycle, however, the local surface buoyancy fluxes and turbulent mixing processes across the ML base are also essential. For this reason, we implemented Seager-Zebiak-Cane (1988) model with Niiler-Kraus' (1977) ML physics. The model is more sophisticated than SZC in that the present model dynamics includes the Yoshida Jet component and a variable depth ML.

The entrainment is one of the most important processes governing SST variation. Determination of the entrained water temperature is a key for the closure of entrainment parameterization schemes. In the previous intermediate models, it was determined using observed subsurface temperature or empirical relations derived from observations (Seager et al. 1988, Chang 1994). Our approach is self-contained. It assumes that the temperature difference between the ML water and entrained water is proportional to the mean vertical temperature gradient in the thermocline layer, or inversely proportional to the thickness of the thermocline layer. The thermocline is treated as an immiscible layer so that not only the displacement of the thermocline layer base, but also the change of ML depth affects the thickness of the thermocline. This allows for combining the virtues of the SZC model's dynamics and ML physics. The surface winds affect thermocline layer thickness by changing thermocline depth via Sverdrup balance and by changing ML depth via turbulent mixing. The entrained water temperature, therefore, depends highly nonlinearly on the surface wind forcing. The proposed scheme works reasonably well in the tropical region, both the warm pools and cold tongues.

Surface evaporation is another prominent process acting in the annual and interannual variation of SST. An accurate estimation of surface latent heat flux is also a key to model annual cycle of SST. The errors may arise from two major sources when the bulk formula (2.16) and monthly mean winds are used. One is the effect of the transients. A modification of wind speed, such as (2.20) used in this work, is necessary. This supports the finding of the previous studies (e.g., Philander et al. 1987, Seager et al. 1988). Another error comes from inaccurate measurement or computation of the surface air humidity. Philander and Pacanowski (1986a,b) and Seager et al. (1988) simply assumed a constant relative humidity in their computation of surface latent heat flux. A more accurate linear empirical relation was previously proposed to estimate surface air specific humidity from SST (Wang 1988, Wang and Li 1993). In the present model, this empirical relation was refined using more comprehensive data sets that cover the entire tropical Pacific and Indian Ocean (30oS-30oN, 40oE-80oW). We have found that the latent and sensible heat fluxes computed using (2.18) and (2.19) are close enough to those obtained using observed air humidity and temperature so that the resultant ML temperature fields are almost the same. This approach will avoid errors possibly arising from the use of atmospheric model-computed air humidity and temperature when coupling the ocean model with an atmospheric model.

The solution in the present model, thus, depends upon only two atmospheric variables: surface winds and cloud cover for given insulation. The surface winds affect ML temperature indirectly by changing entrained water temperature as discussed early in this section. More importantly, the surface winds can affect ML temperature by directly changing the turbulent entrainment, the surface evaporation and sensible heat flux, and the temperature advection by wind-induced currents. The cloudiness influences ML temperature via directly changing shortwave and longwave radiation fluxes and indirectly changing the entrainment rate associated with mixing process.

The change in ML temperature is thus a result of subtle balance and complex interaction among above-mentioned processes. As such, the response of SST to a transient wind forcing in the present model differs considerably from the SZC model in which the turbulent mixing is absent. For a given stationary wind forcing of intraseasonal oscillation located in the western equatorial Pacific, for instance, the SZC model shows a decaying oscillation in SST that is most prominent in the remote eastern Pacific, whereas the present model exhibits a slow amplification of positive SST anomalies just to the east of the forcing. Observations have shown considerable intraseasonal variations in the sea-level height and the thermocline depth which are remotely forced by the counterpart variations in surface winds over the western equatorial Pacific (e.g., Ericksen et al. 1983; Enfield 1987). The SST, however, does not seem to have significant response in the eastern Pacific. In the ocean GCM experiment (Latif et al. 1988) westerly bursts in the western Pacific (130-180oE) induced an anomalous warming primarily in the central Pacific which is not due to thermocline variation associated with the Kelvin wave passage. The present model result resembles that of Latif et al. (1988). The model ocean response to high frequency wind variability certainly depends upon the model's representation of the ML physics.

Inclusion of the Niiler-Kraus (1977) scheme for ML entrainment in the CZ model improves the model's performance on the annual cycle, especially in the equatorial Pacific cold tongue and ITCZ regions. Penetrated solar radiation was found to play a significant role in the SST variation in the eastern-central equatorial Pacific. It enhances (reduces) entrainment in the far eastern (central) equatorial Pacific where the ML is relatively shallow (deep). Without this process the central equatorial Pacific would be excessively cold whereas the far eastern equatorial Pacific would be excessively warm. Inclusion of the ML physics also significantly improves the model's ability in simulating ENSO variability in the central equatorial Pacific where the CZ model substantially underestimates SST anomalies.

Numerical experiments demonstrated that the momentum and heat transports during the annual cycle can significantly modify the annual mean ML temperature and the depths of thermocline and ML. The transient effect tends to lower the annual mean SST in the tropical Pacific Ocean by 0.5-1.5oC. It is most significant in the vicinity of the ITCZ which migrates annually back and forth between 4o N and 12oN.

The most serious problem with modeling annual cycle of SST is the phase delay. This problem is likely related to the uncertainty in the surface heat flux forcing (in particular the cloud effects on solar radiation) and model errors in representing ML processes. At this stage, an effective way to leverage the problem is to introduce a correction to the long-term mean heat flux. This approach was previously used in GCM simulations (e.g., Meehl et al. 1982; Han 1984; Gordon and Corry 1991) and intermediate models (e.g., Chang 1994). We have shown that the inclusion of a mean heat flux correction in the present model does not significantly influence amplitudes of the annual and interannual variations of ML temperature. It, however, significantly improves the simulation of the annual cycle by providing a more accurate mean state.

The tests of the present model in reproducing SST variabilities on various time scales are preliminary. Further analyses are needed to diagnose the causes of the model's major deficiencies. Inclusion of the effects of stratocumulus cloud on solar radiation appears to be desirable for further improvement. The mechanisms of ML temperature variability need to be better understood before coupling atmospheric models.

Back to top | Back to menu