This study investigates biases of the climatological mean state of the northern Arabian Sea (NAS) in 31 coupled ocean–atmosphere models. The focus is to understand the cause of the large biases in the depth of the 20°C isotherm that occur in many of them. Other prominent biases are the depth and temperature of Persian Gulf water (PGW) and the wintertime mixed-layer thickness (MLT) along the northern boundary.
For models that lack a Persian Gulf (group 1), is determined by the wintertime MLT bias through the formation of an Arabian Sea high-salinity water mass (ASHSW) that is too deep. For models with a Persian Gulf (group 2), if > MLT (group 2B), PGW remains mostly trapped to the western boundary and, again, directly controls . If MLT (group 2A), PGW spreads into the NAS and impacts because > 20°C; nevertheless still influences indirectly through its impact on .
The thick wintertime mixed layer is driven primarily by surface cooling during the fall. Nevertheless, variations in ΔMLT among the models are more strongly linked to biases in the density stratification (jump) across the bottom of the mixed layer than to biases. The jump is in turn determined primarily by sea surface salinity biases (ΔSSS) advected into the NAS by the West India Coastal Current, and the source of ΔSSS is the rainfall deficit associated with the models’ weak summer monsoon. Ultimately, then, ΔD20 is linked to this deficit.
Collectively, the current suite of coupled general circulation models (CGCMs) is not able to simulate the Asian monsoon mean state (climatological annual cycle) realistically. Biases include weak monsoonal winds, a rainfall deficit in the Bay of Bengal, excess rainfall in the western equatorial Indian Ocean (WEIO), and an easterly bias along the equator (Annamalai et al. 2017). Despite considerable effort, the causes of these errors are still not known. Some researchers have sought to relate them to biases in the atmospheric component of the coupled models (e.g., Martin et al. 2010; Ma et al. 2014). Others have focused on the ocean component, considering the causes and impacts of surface (e.g., Han et al. 2012; Levine et al. 2013; Sandeep and Ajayamohan 2014) and subsurface (e.g., Chowdary et al. 2016) temperature biases and of Bay of Bengal salinity biases (e.g., Seo et al. 2009). Recently, Annamalai et al. (2017) argued that the cause of poor monsoon simulations is the models’ near-equatorial coupled processes (Bjerknes feedback) being too strong, thereby suggesting that both oceanic and atmospheric errors are involved.
In this study, we investigate the causes of errors in the depth of the 20°C isotherm (D20), a measure of thermocline depth in tropical oceans. Its misrepresentation can lead to SST errors in upwelling regions where it rises near to the surface. Moreover, its accurate simulation has been shown to be essential for the successful prediction of climate modes, such as for El Niño (e.g., Ji and Leetmaa 1997) and the Indian Ocean dipole (e.g., Luo et al. 2007).
Figure 1 provides maps of biases in annual-mean D20 (ΔD20; Fig. 1a) and the mixed-layer thickness (MLT) in January (ΔMLT; Fig. 1b). In both panels, errors are defined by differences between observations and the multimodel-mean (MMM) fields from a suite of coupled ocean–atmosphere models (see section 2 for details). We show ΔMLT during January because that is when the mixed layer is thickest in response to wintertime cooling and, hence, impacts the upper-ocean stratification most strongly (see below). The most striking biases occur in the northern Arabian Sea (NAS), where ΔD20 and ΔMLT attain maxima of 182 and 126 m, respectively, in the northwest corner of the basin.
A possible cause of ΔD20, suggested by the property that it is largest in the northwest corner, is error in the models’ formation of Persian Gulf water (PGW). In the annual mean, Arabian Sea water enters the Gulf near the surface, and PGW exits near the bottom, with an overall exchange of 0.1–0.3 Sv (1 Sv ≡ 106 m3 s−1; e.g., Schott and McCreary 2001; Kämpf and Sadrinasab 2006; Yao 2008; Yao and Johns 2010). When PGW enters the Arabian Sea its core salinity and temperature are 36.5 psu and 18°–19°C owing to high evaporation and cooling within the Gulf, and it sinks to depths of 200–300 m. From there, it spreads either southward along the Omani coast during winter or first eastward along the northern boundary and then southward into the interior of the NAS during summer (Premchand et al. 1986; Shenoi et al. 1993; Morrison 1997; Prasad et al. 2001). Errors in the depth and water mass properties of PGW could be passed into the interior of the Arabian Sea via the latter pathway to impact and generate .
Another possible cause of , suggested by the large wintertime ΔMLT, is error in the formation of Arabian Sea High Salinity Water (ASHSW). ASHSW is generated near the northern boundary within the thick mixed layer that develops there during winter (Kumar and Prasad 1999; Prasad and Ikeda 2002a). When the mixed layer thins during the spring, the now subsurface (subducted) water spreads into the interior of the Arabian Sea at a depth of about 75 m (Rochford 1964; Shenoi et al. 1993; Morrison 1997; Prasad and Ikeda 2002b). The large MLT bias in Fig. 1b could result in the models’ ASHSW being too extensive and too deep, thereby generating ΔD20. We note that the linkage between wintertime MLT in one region and subsurface water-mass properties elsewhere is a specific example of ventilated thermocline theory, which has been shown to explain thermocline structure (upper-ocean stratification) in many parts of the subtropical ocean (e.g., Stommel 1979; Talley 1985; de Szoeke 1987; Pedlosky 1996a,b).
A number of processes might force . Local processes include surface wind stirring and buoyancy (heat Q and evaporative E − P) fluxes, which generate turbulence that leads to entrainment across the bottom of the mixed layer; further, the entrainment rate is related to the stratification just beneath the mixed layer (measured by ), with weaker stratification leading to stronger entrainment and vice versa [e.g., Kraus and Turner 1967; see Eq. (3) below]. Mixed-layer thickness can also be impacted by isopycnal processes (e.g., wind-driven upwelling and downwelling, and the radiation of baroclinic waves). In the NAS, cooling by during winter, which results from the outflow of cool, dry continental air, is known to be an important factor in generating the thick mixed layer there (e.g., Prasad and Ikeda 2002a). So, a plausible cause for is bias in , but could result from errors in any of the other processes.
Near-surface salinity is another variable with a large bias in the NAS. The Arabian Sea is a region of net evaporation. As such, the local production of salty water must be balanced by the advection of freshwater into the basin. There are two freshwater pathways into the NAS: the West India Coastal Current (WICC) and summertime Somali Current, with the former bringing freshwater into the Arabian Sea from the Bay of Bengal and the latter from the south Indian Ocean (Shetye et al. 1994; Prasad and Ikeda 2002b; Rao and Sivakumar 2003). Shankar et al. (2016) explicitly demonstrated the strong impact of salinity advection by the WICC on upper-ocean stratification in the NAS, tending to lower near-surface density there. Thus, errors in these freshwater sources could also impact through their influence on .
b. Present research
In this study, we seek to understand the causes of the NAS mean-state biases that occur in the ocean components of a suite of 31 coupled ocean–atmosphere models. For this purpose, we describe the biases that occur in their MMM fields and, to illustrate differences among the solutions, also in four model subgroups (defined in section 3a) and for several individual models. To identify the processes that cause the biases, we then report a series of scatterplots of data points from pairs of model variables. In some of the plots, the points are highly correlated, an indication that variations in biases among the models occur systematically, despite large differences in process parameterizations across the models. Of course, high correlations between variables x and y do not necessarily indicate causality: could cause , could cause , or some other process could account for the link. So, for each scatterplot we also discuss the physics that supports one of these interpretations.
Key results are the following. Large D20 biases result from the wintertime MLT near the northern boundary of the NAS being too thick, which generates ASHSW that is too deep. For the models in which PGW spreads into the NAS, is impacted by the depth of PGW because the temperature of PGW at its core is greater than 20°C; however, for these models MLT in the northwest corner of the NAS is thick enough to entrain PGW and impact , so indirectly controls through its impact on . Thus, ΔMLT is the overall cause of ΔD20. The NAS mixed layer is seasonally thickened by surface cooling during the fall; nevertheless, bias at the bottom of the mixed layer is the primary cause of ΔMLT, because its magnitude is so large that it overwhelms the impact of bias. In turn, is determined primarily by salinity inflow into the NAS by the WICC. Ultimately, then, the NAS stratification errors are linked to the rainfall deficit associated with the models’ weak summer monsoon.
The paper is organized as follows. Section 2 summarizes our data sources and analysis techniques. Section 3 describes the model biases, and section 4 identifies the processes that determine them. Section 5 provides a summary and discussion of our results, the latter including their implications for the improvement of climate models.
2. Data and analyses
a. Observational and model data
The observational data we use include oceanic variables from the World Ocean Atlas 2013 (WOA13; Locarnini et al. 2013; Zweng et al. 2013), rainfall from the Global Precipitation Climatology Project (GPCP; Huffman et al. 1997), and surface heat and evaporative fluxes from OAFlux (Yu et al. 2008). Surface winds are obtained from the European Centre for Medium-Range Weather Forecast (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011). Horizontal grid intervals are 1° × 1° for WOA13 and OAFlux, 2.5° × 2.5° for GPCP rain, and 1.5° × 1.5° for the ERA-Interim reanalysis. The time series we use for each dataset extend from 1979 to 2015 for GPCP rainfall and the ERA-Interim reanalysis, 1984 to 2009 for OAFlux surface heat flux, and 1985 to 2014 for OAFlux evaporative flux. All the datasets are provided as monthly averages.
The coupled models we analyze are listed alphabetically in appendix A. The suite consists of solutions from 31 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5); see Sperber et al. (2013) and Nagura et al. (2013) for details. It also includes a solution from the Coupled Model For the Earth Simulator (CFES) developed at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). In our analyses, we use output from the models’ historical runs, that is, from their solutions forced by observed atmospheric composition changes and solar radiation. Table 1 and Fig. 2 (below) list each model’s acronym, symbol, and basic properties relevant to the present study.
The CGCMs are all global in extent. In their ocean components, the number of vertical levels varies from 30 to 50 and their horizontal resolution is typically 1°. Given their low horizontal resolution, almost all the models cannot resolve mesoscale eddies. With regard to the NAS, misrepresentation of eddy activity is potentially serious, as eddies are known to be vigorous in the Gulf of Oman and to contribute to the spreading of PGW (L’Hégaret et al. 2013, 2015, 2016; Vic et al. 2015). On the other hand, PGW does spread throughout the NAS in many of the CGCMs, and so must occur by a large-scale process rather than by eddies [see section 3b(1)(iv)].
Not surprisingly, the models specify the flow of PGW into the Arabian Sea differently. The PG column in Table 1 separates the models into four general categories: models without any Persian Gulf (N); with a Persian Gulf that freely exchanges water with the Arabian Sea (D); and with an isolated Persian Gulf region in which the exchange is either prescribed (P) or parameterized by enhanced cross-land mixing (C; Griffies et al. 2004). To our knowledge, none of the models without a Persian Gulf prescribed the impact of PGW within the NAS (e.g., by restoring temperature and salinity toward observed values in the northwest corner of the basin); rather, the NAS stratification was entirely determined by processes within the basin. The strait that connects the Persian Gulf to the NAS is only about 50 km wide, too narrow to be resolved in most of the models; in the models that have a Persian Gulf, then, the strait is unrealistically wide. A result of these model differences is that the depth, salinity, and temperature of PGW vary considerably among the models (see the discussion of Fig. 2 below).
The models also differ in their mixed-layer parameterizations, using six different types (see the ML column of Table 1): 1) K-profile parameterization (Large et al. 1994; KPP) or its updated version (Danabasoglu et al. 2006); 2) the Kraus-Turner (1967) scheme (KT); 3) the Noh and Kim (1999) method (NK) or its updated version (Noh et al. 2005); 4) the Blanke and Delecluse (1993) method (BD) or its updated version (Madec et al. 2008); 5) the Pacanowski and Philander (1981) scheme (PP); and 6) Oberhuber’s (1993) parameterization (OB).
Monthly climatologies are computed for the observations using the complete time series for each dataset and for the models using the last 50 years of model output. We define MLT, which is not included in the model datasets, to be the depth where density increases by = 1.25 × 10−4 g cm−3 with respect to the overlying surface density. We calculate observed MLT from WOA13 climatological data using the same criterion. The use of monthly averages to estimate MLT can underestimate its value by 10–20 m (de Boyer Montégut et al. 2004; Toyoda et al. 2017). In addition, the WOA13 dataset is heavily smoothed in space, which can lead to further underestimation of MLT (see sections 3a and 4b). These potential errors are acceptable for our purposes, since we only seek a qualitative comparison between models and observations.
For a particular variable , model biases are then computed by subtracting the observed field from the corresponding model field . Biases are also defined when is an average over groups of models, either for all the models (MMM fields) or for one of the four model subgroups defined in section 3a.
To help determine the processes that cause biases to differ among the models, we obtain scatterplots between data points, and , taken from individual models, where is a model index, and N is the number of models included in a particular plot . In many plots, points tend to lie along a sloping straight line, indicating that the same processes link the two variables in all the models. A measure of the goodness of fit is the correlation coefficient
where and are the mean values of and . With this definition, the linear fit is better for values of closer to one.
Assuming the data points are scattered with a Gaussian distribution, there is a correlation value above which we can say that the correlation exists (i.e., ) with a confidence level of n%. Throughout the text, we use n = 95%, in which case the 95% confidence level for the entire dataset (N = 31) is C = 0.30. In some scatterplots, we report correlations for subsets of the models (the groups defined in section 3a), labeling them with a subscript indicating the group , , , and . Their 95% significance levels are 0.62 for group 1 (N = 8), 0.35 for group 2 (N = 23), 0.50 for group 2A (N = 12), and 0.52 for group 2B (N = 11).
In each scatterplot, we also plot lines, , that best fit either all of the data points or the group 1 and group 2 points separately, with a and b determined in the usual way by minimizing the quantity , that is, by setting and . We are also interested in determining whether the slopes of the group 1 and group 2 lines are significantly different. Assuming the data points are scattered about the best-fit line with a Gaussian distribution, there is an n% confidence interval such that the true slope lies within . Let and be the slopes of the two lines, and assume that . Then, we can say that the two lines have different slopes with a confidence level of % provided that . Similarly, we can say that the slope of a line differs from zero at the % confidence level provided that . In this study, values correspond to the 95% confidence level.
3. Model biases
In this section, we discuss the stratification biases that occur in the coupled models. We first note that their magnitude varies considerably and that they divide into four distinct groups (section 3a). Then, we describe the horizontal, temporal, and vertical structures for the complete set of models [section 3b(1)] and for four subgroups and several individual models [section 3b(2)].
Throughout the text, we define to be the area average of a variable in a limited region of the NAS; the averaging region is almost always the box in Fig. 3f, the exceptions being for the curves in Figs. 3g and 3h and in Fig. 2a (and in Fig. 12a), which are averaged over the region in Figs. 3d and 3e. In most cases, is also averaged in time (either a season or year), the exceptions being for the curves in the bottom panels of Fig. 3. Variables and denote evaluated at the bottom of the mixed layer and in the northwest corner of the basin, respectively. Variables designate introduced into the NAS from the Persian Gulf: They are evaluated in the northwest corner of the basin, either at the depth of the PGW salinity maximum or, for solutions that lack a salinity maximum, at the bottom of the mixed layer. Finally, and are the values of SSS at 15°N, just offshore from the coasts of India and Somalia, respectively.
a. Bias differences and model groups
There is a large variation in magnitude of the NAS biases among the models. To illustrate, for all the models Fig. 2 lists from left to right , /, /, /, and . The / bars show both Persian Gulf variables (, darker bars) and related variables in the NAS (, lighter bars). Values of and are their annual averages, whereas for the other variables are values during January, the time when the mixed layer is thickest and its temperature and salinity are close to their values of the subducted water mass.
For our analyses, we found it useful to divide the models into four groups, indicated by the different colored bars in Fig. 2. Two major groups are defined by whether the model lacks (group 1; black and gray bars) or includes a Persian Gulf (group 2; blue and red bars). Within these two groups, D20 values either increase to unrealistic values larger than 200 m (groups 1A and 2A; black and blue bars) or remain smaller than 200 m (groups 1B and 2B; gray and red bars). For convenience, throughout the text we shorten the group names to Gn, GX, and GnX, where n = 1, 2 and X = A, B (e.g., group 2a is G2A).
There are obvious model–observation differences for all the variables. Most notably, observed is smaller than almost all but two of the modeled values, and observed is smaller than all modeled values (Figs. 2a,b). Regarding observed , its low value (50 m) may result (likely results) from smoothing in WOA13 that smears out the bottom of the ML; assuming that the models with the smallest are accurate (100 m), the magnitude of this observational error is 50 m. Alternately, the difference might be real, a result of the models’ surface heat flux and/or stratification bias in the NAS [sections 3b(1)(iii) and 4c)]. Another notable difference is that in the observations the temperature of PGW, , is considerably cooler than wintertime mixed-layer temperature, (green bars in Fig. 2d), whereas in all but three of the models > 20°C (dashed line) and close to (blue and red bars in Fig. 2d). Thus, D20 is located above the PGW in observations but below the PGW in the models, a difference that tends to increase D20 in the G2A models (section 4b).
It is visually apparent that variations between some pairs of variables are correlated. The models are arranged in Fig. 2 in order of increasing . With this ordering, there is a tendency for to increase similarly (black, light blue, and light red bars in Fig. 2b), pointing toward a dynamical link between the two variables (see section 4b). Variations in , , and are similar (Figs. 2c,e), an indication of the strong impact of on the other two variables (see section 4e). Likewise, variations in closely follow those of (Fig. 2d), except for two G1B models (INM-CM4 and NorESM1-ME), suggesting that temperatures of PGW and the mixed layer in the NAS are determined by the same processes. Finally, although less apparent, and vary similarly for the G2A models (blue bars in Fig. 2b), suggesting that the two variables are dynamically linked for that group (see section 4b).
b. Bias structures
Although biases vary considerably among the models, many of them tend to have a common structure. To illustrate these commonalities, we first describe basic features of the MMM stratification and forcing fields [section 3b(1)]. We then discuss differences that occur within the four groups [section 3b(2)] and for a few individual models [section 3b(2)(iii)].
1) Common features
(i) D20, S, and MLT biases
Figure 3 shows the horizontal structure of the stratification errors, providing maps of annual-mean D20 (left column), annual-mean salinity S at a depth of 200 m (, middle column), and the January MLT (right column) from observations (top row), and differences between the MMM and observed fields (middle row). The largest biases occur in the northwest corner of the Arabian Sea (Figs. 3d–f), where ΔD20, , and ΔMLT attain maxima of 181 m, 0.51 psu, and 126 m, respectively. The northwestern intensification of ΔD20 suggests that biases in the properties of PGW may be part of its cause. At the same time, the structures of and are similar along the northern boundary, despite their being very different offshore; this similarity supports the idea that the cause of is the large and positive wintertime , which leads to excessive subduction and spreading of ASHSW (Prasad and Ikeda 2002b). We consider both hypotheses in later sections.
The curves in the bottom panels of Fig. 3 illustrate the time dependence of the biases, plotting areal averages of D20, , and MLT in the boxes shown in the middle panels for the observations (green curve) and MMM fields (thick black curve). The magnitudes of and for all the curves are relatively constant throughout the year. In contrast, is largest during winter in response to strong cooling by surface heat flux at that time (Fig. 5 below). Note also that the magnitudes of , , and (differences between the thick black and green curves) are all positive, consistent with the positive (red-to-yellow shading) maps of those quantities in the middle row of Fig. 3.
Figure 4 illustrates the vertical structure of the stratification errors, showing sections along 65°E of (left to right) annual-mean, temperature T, salinity S, and density from (top) observations, and (bottom) differences between the MMM and observed fields. Below 125 m, and are salty and warm and have their largest amplitudes near 100–300 m (Figs. 4b,d).
The stratification within the wintertime mixed layer (above the black curves in Fig. 4) is influenced by surface buoyancy fluxes. The negative there results from an annual-mean cooling bias in the surface heat flux, (Figs. 5a,d; Marathayil et al. 2013; Sandeep and Ajayamohan 2014; Fathrio et al. 2017) and, particularly near the northern boundary, from excessive entrainment of cool subsurface water during the fall. On the other hand, the source of the near-surface negative cannot be error in the surface freshwater flux, , which is weak throughout most of the year and positive during winter (Figs. 5b,e). Rather, its source is erroneously fresh near-equatorial water generated by the large precipitation bias there (Fig. 5b; see also Figs. 10e–h below): Our interpretation is that during the summer, this erroneously freshwater is advected first northward along the western boundary by the Somali and Omani Currents and then eastward into the interior of Arabian Sea (Fig. 6e). Farther north, the fresh anomaly weakens in response to wintertime entrainment of the subsurface salt bias and to advection of less-freshwater into the NAS by the WICC (Fig. 6f).
(ii) Density bias
Because the and fields tend to have the same sign (Figs. 4b,d), they compensate in their effect on , but the compensation is not complete. Throughout most of the section, is negative (Fig. 4f). The subsurface bias extends to depths of 1000 m and into the Southern Hemisphere (figure not shown), suggesting that its cause lies outside the Arabian Sea. (Determining the cause of this deep bias is beyond the scope of this paper. It is possibly linked to errors in the Southern Hemisphere processes that determine thermocline and intermediate waters.) In the upper ocean, the negative density bias south of 10°N results from excessive rainfall in the western equatorial Indian Ocean (Figs. 10e–h below). North of about 10°N, becomes positive in a wedge-shaped region in the upper ocean where near-surface is lower and is less negative (bottom panels of Fig. 4). The region extends to the depth of the MLT (black curves in the bottom panels of Fig. 4), suggesting that it is related to the mixed layer being too thick. Consistent with this idea, note that in the region (Fig. 4f), so that the magnitude of the vertical density gradient is weakened.
Figure 5 illustrates the horizontal structure and time dependence of the MMM surface forcings in the NAS. The top panels show and averaged from October through December (OND) during the time when the mixed layer thickens, and the annual-mean, Ekman pumping velocity , where and are the zonal and meridional components of the wind stress, respectively, is the Coriolis parameter, and is a typical density of seawater. The bottom panels plot temporal curves of the observed (solid) and modeled (dashed) forcings averaged over the box in Fig. 3d or 3f.
The map shows intensified cooling in the NAS (Fig. 5a), which reaches a minimum value of −158 W m−2 near the northern boundary due to cool, dry air blowing off the continent. There is a cooling bias throughout most of the year in the NAS (difference between curves in Fig. 5d), with modeled being less positive from April to July and negative from September to December and a minimum of −80 W m−2 in October. The negative is one of the causes of the MMM cool bias in the upper NAS (Fig. 4b; Marathayil et al. 2013; Sandeep and Ajayamohan 2014; Sayantani et al. 2016; Fathrio et al. 2017), with cooling by entrainment during the fall being the other. Curiously, though, is not the primary driver of variations in wintertime among the models, as might be expected (section 4c).
The E − P map shows strong evaporation during OND in the NAS (Fig. 5b), with a maximum of 7 mm day−1 near the northern boundary due to the influence of dry continental air. The E − P bias in the NAS (difference between curves in Fig. 5e) is weak throughout most of the year, being negative only during March–May and positive during November–December.
The map has negative values over the interior of the Arabian Sea, with positive values confined near coasts (Fig. 5c), a pattern that reflects the dominance of the southwest monsoon winds in the annual cycle. The bias is largest during the summer (Fig. 5f), because the low-level (Findlater) jet in the models is weaker than observed.
The NAS circulation is complex, with a prominent annual cycle driven by the annually reversing monsoon winds. Given this complexity, a thorough discussion of the circulation and dynamics of the region is beyond the scope of our study (see, e.g., Prasad and Ikeda 2002a,b). Here, then, we note two aspects of the flow field relevant to our results: the existence of mean, subsurface, southward flow away from the northern boundary of the basin; and of seasonal, northward, near-surface currents into the boundary.
(a) Annual mean southward flow
Because the intense winds of the southwest monsoon dominate the annual cycle, the NAS has a significant mean circulation. Figures 6a and 6b illustrate its horizontal structure, showing annual-mean, depth-integrated current vectors and pressure anomalies, both for the MMM, and (Fig. 6a), and for the Sverdrup (1947) circulation driven by the annual-mean wind field of Fig. 5c, and (Fig. 6b). We define the plotted variables precisely in the next two paragraphs.
The integrations to determine and extend from 500 m to the surface. Given that the annual-mean circulation is highly concentrated in the upper ocean (Figs. 6c,d), this depth range is sufficient to capture nearly all of the annual-mean transport. (To confirm this property, we obtained versions of Fig. 6a with , 1000, and 1500 m; all the plots were very similar, for example, with only slight shifts in isolines.) To calculate , we first define the dynamic height at any depth by , where and is the density of seawater when °C and psu. Then, , that is, is equal to times the depth integral of dynamic height relative to its value at a depth of 500 m (Tomczak and Godfrey 1994).
Variables and are Sverdrup’s (1947) solution for a flat-bottom ocean,
where , is the eastern boundary of the domain (either the west coast of India/Sri Lanka north of = 6°N or of Sumatra south of ), and
In (2b), and are unit vectors pointing north and directed parallel to , respectively, , are points at the tip of India/Sri Lanka (+) and at the coast of Sumatra at 6°N (−). Variable is the field that balances the alongshore wind stress along the eastern boundary, thereby cancelling any Ekman drift that might otherwise flow across it; owing to Rossby wave propagation, spreads uniformly across the basin. Constant , the value of at the tip of Sri Lanka, ensures there is no flow into the Bay of Bengal; it follows from an integration of the zonal momentum equation across the Bay at 6°N. Since for in (2b), is the depth-integrated pressure anomaly relative to its value off Sumatra. In Fig. 6b, we used ERA-Interim winds to evaluate (2).
Sverdrup (1947) derived solution (2) from depth-integrated equations, and in so doing lost all information about the vertical structure of the flow. In a model that allows for vertical structure, baroclinic adjustments (namely, the radiation of baroclinic Rossby waves across the basin) tend to trap the Sverdrup flow in the upper ocean (e.g., Anderson and Gill 1975; McCreary 1981a,b). It is reasonable, then, to compare the surface-trapped, annual-mean circulations in the coupled models to that of a Sverdrup flow. Indeed, the striking similarity of the interior circulations in Figs. 6a and 6b indicates that Sverdrup theory does capture the basic dynamics of the models’ annual-mean circulation. One prominent difference in the two flow fields is the presence of a western boundary current in the MMM, a flow that is not included in (2). Another obvious difference is the jump in near 6°N, a consequence of the abrupt change in from the tip of Sri Lanka to Sumatra at that latitude.
Figures 6c and 6d illustrate the vertical structure of the annual-mean MMM flow, showing meridional and zonal sections of across-section (color shading) and along-section (contours) currents, respectively. Although the strongest flows are surface trapped, the flow field is not confined above the wintertime MLT (green line); moreover, currents are not unidirectional but can reverse vertically. These properties are evident in the structure of the υ field (contours) in Fig. 6c: Near the northern boundary, υ is southward very near the surface and below 175 m, and is positive in between; farther to the south, it is southward well below the mixed layer. We interpret these features to result from the overturning circulations associated with PGW and ASHSW, which introduce baroclinicity and deepen the overall Sverdrup response. The southward current below the mixed layer likely contributes to the southward spreading of the saline warm bias shown in Fig. 4.
(b) Seasonal northward currents
Figures 6e and 6f provide maps of the average currents in the upper 100 m during summer (JJA) and fall (OND), respectively. Meridional and zonal sections like those in Figs. 6c and 6d show that both circulations are generally confined above 200 m (not shown). During the fall, there is northward flow in the WICC that extends from the southern tip of India into the NAS (Fig. 6f). During the summer, there is northward flow in the western Arabian Sea via the Somali and Omani Currents, but it does not extend to the northern boundary (Fig. 6e). We checked the summertime flow in each of the models, and in almost all of them the Omani Current separates from the coast before reaching the northern boundary. These results demonstrate that the WICC and the summertime Somali and Omani Currents are realistically simulated in the coupled models, and that they are capable of advecting freshwater into the NAS.
2) Group and individual differences
(i) D20, S, and MLT biases
Figures 7 and 8 plot annual-mean stratification biases for the four groups, showing maps of annual-mean ΔD20 and (top panels) and sections of annual-mean and along 65°E (bottom panels). Large subsurface biases occur in the G1A (panels a and e) and G2A models (panels c and g), and they closely resemble their counterparts in Figs. 3 and 4. The property that the biases are similar in both groups, and that the G1A models lack PGW, suggests PGW plays a secondary role in generating them (see sections 4b and 4d for discussions of PGW impacts). Rather, they occur because the mixed layer is unrealistically thick in most of them (black curves in panels e and g; black and light blue bars in Fig. 2), so that warm and erroneously salty, near-surface water is mixed downward. Note that the maxima of and lie above the wintertime MLT near the northern boundary but below it farther to the south (black curves), consistent with the idea that the biases are generated near the northern boundary and then advected southward in the interior ocean in a similar manner to ASHSW (Prasad and Ikeda 2002b).
The G1B (panels b and f) and G2B (panels d and h) biases differ most strikingly from the MMM fields in that they have no subsurface-intensified biases, a consequence of their wintertime mixed layers being relatively (realistically) thin (Fig. 9). Note also that is more negative for the G1B and G2B models than for the other two groups (Fig. 8), particularly near the surface 125 m): The deep error likely originates in the Southern Hemisphere; the near-surface bias results from excessive freshwater being advected into the NAS from the WEIO and, for the G1B models, from the WICC [section 3b(2)(ii)].
Figure 9 plots maps of January ΔMLT for each group. As for ΔD20 and , the spatial structures of ΔMLT for the G1A and G2A models are similar to that of the overall MMM (Fig. 3f), whereas for the G1B and G2B models is much thinner along the northern boundary. Interestingly, has about the same magnitude along the southwest coast of India in all of the models. The reason for this similarity is not clear: its pattern resembles that of the Rossby wave packet that propagates off the coast during the fall, so its cause may be ocean dynamics rather than mixed-layer physics.
The above properties are also apparent in the MLT temporal curves in the bottom panels of Fig. 3. For and (Figs. 3g,h), the G1A and G2A biases (distances of the thin black and blue curves to the green curve) are large. In contrast, the G1B and G2B biases (distances of the gray and red curves to the green curve) are almost all small; the sole exception is for G1B, which is significantly negative consistent with Figs. 8b and 8f. Similarly, for MLT (Fig. 3i), the wintertime bias is largest for the G1A and G2A models (thin-black and blue curves relative to the green curve) and much weaker for the G1B and G2B models (gray and red curves relative to the green curve).
To investigate possible circulation differences among the groups, we obtained figures similar to Fig. 6 for each of them (not shown). The horizontal structures of the annual-mean and seasonal circulations are very similar to those for the MMM (panels a, b, e, and f), a consequence of the wind forcing being similar in each of the groups. The circulations, however, differ considerably in their depth, extending to greater depths in the GA models but remaining shallow in the GB models. The deep southward flow likely advects S and T bias to the south in the GA models (Figs. 7e,g and 8e,g).
(ii) SSS biases
As discussed in section 4e, an important influence on the NAS biases is SSS biases that are advected into the region. Figure 10 presents maps of (top) annual-mean ΔSSS and (bottom) rainfall bias for the four groups. Significant biases are present in the NAS for all the models, with SSS in the NAS being salty for the G1A and G2A models (panels a and c) and fresh for the G1B and G2B models (panels b and d). Further, the biases are part of large-scale patterns that extend into the Bay of Bengal (salty bias) or the equatorial ocean (fresh bias). The primary sources of freshwater bias are 1) weak summer-monsoon rainfall over South Asia, the Bay of Bengal, and along the west coast of India south of about 15°N (called bias 1 below), and 2) erroneously strong rainfall in the WEIO centered near 5°S (bias 2).
We attribute the various ΔSSS patterns in Fig. 10 to the relative strengths of these two sources. In G2B, bias 1 is smaller and bias 2 is larger in magnitude compared to G2A; as a result, the NAS is erroneously fresh (salty) in the G2B (G2A) models. Similar differences exist for the G1A and G1B models, except that for G1B is completely negative, a consequence of the expansion of bias 1 into the southwestern Bay and eastern Arabian Sea. (It is worth noting that these biases occur in two of the three G1B models, namely, MIROC-ESM and MIROC-ESM-CHEM. In the third, MIROC5, is positive in the WEIO and bias 2 is weak, a very different response than in any other model.) Note that for G1B is most strongly negative in the far northern Bay of Bengal (Fig. 10b) despite there being a rainfall deficit there (Fig. 10f); it must result from the existence of a large positive bias in river outflow. Unfortunately, river runoff is not provided in the CMIP5 archive for almost all the models, so it is not possible to examine explicitly the impact of river outflow.
There are two pathways by which remotely generated salinity biases reach the NAS. During the fall and winter, anomalously salty water due to bias 1 flows southward along the east coast of India, around Sri Lanka, and northward along the west coast of India within the WICC (Fig. 6f; Han et al. 2001; Shankar et al. 2016). The impact of this pathway is evident by the tongues of salty water that extend into the NAS (Figs. 10a,c,d). During the summer, freshwater generated in the WEIO due to bias 2 flows northward in the western Arabian Sea in all the models (Fig. 6e), but only appears to reach the NAS in the G2B models for which bias 1 is weak (Fig. 10d). In the G1B models, salinity is less fresh in the WEIO than elsewhere, due to the excessive rainfall outside the WEIO and river runoff into the northern Bay; thus, the freshest water appears to be carried into the NAS by the WICC rather than by western Arabian Sea currents.
(iii) PGW biases
PGW spreads into the interior of the NAS in some, but not all, of the models. To illustrate, Fig. 11 plots sections of (shading) and (contours) during January along latitudes close to the northern boundary for three of the G2A (left column) and G2B (right column) models. Sections for individual models are shown because the spreading is blurred by group averaging. The models cover the range of behaviors within each group.
For all the G2B models, the mixed layer is thin and PGW appears as a distinct salinity maximum within the upper pycnocline. For most of them (9 of the 11), PGW is trapped near the western boundary, and the / structure along isopycnals (spiciness) changes abruptly away from the western boundary in the depth range of PGW, as indicated by the 20°C isotherm (green curve) crossing density lines (Figs. 11d,f); the two exceptions are the MIROC4h and GFDL-ESM2G (Fig. 11e) models, which lie near the G2A/G2B boundary (between the red and blue points in Fig. 2) and for which PGW to some extent spreads away from the western boundary. In addition, away from the western boundary D20 lies close to MLT.
In contrast, for most of the G2A models the / structures change more gradually in the depth range of PGW (11 of the 12) and D20 is more than 100 m deeper than MLT over the entire section (9 of the 12; Figs. 11b,c). For most of the models (8 of the 12), PGW is deep enough so that it spreads into the NAS within the pycnocline (as in Fig. 11b); however, for the other four models the wintertime MLT in the northwest corner of the basin is large enough to entrain most of the PGW (as in Figs. 11a,c; CFES-mini; GISS-E2-H).
The above properties suggest that PGW spreads weakly or not at all into the NAS for the G2B models but spreads efficiently for the G2A models. The dynamical cause of this difference is not clear. One possibility is that PGW is deeper than the NAS MLT for the G2B models ( > MLT), but is shallower than the MLT for the G2A models ( MLT); as a result, PGW is impacted by the strong, near-surface, wind-driven currents only for the G2A models. Unfortunately, our analyses are unable to confirm or refute this idea.
In section 3, we identified key properties of the model biases in the NAS. Here, we organize those properties into an interrelated chain of processes. We begin with an overview of our analysis approach (section 4a). In the rest of the section, we fill out the chain, discussing one bias and process at a time (sections 4b to 4e).
The discussion in sections 4b to 4e is centered on analyses of a series of scatterplots between model variables. Figure 12 shows six members from the series, ordered so that the identification of one process leads logically to another. Model data points in Fig. 12 are colored by their group as in Table 1: G1A (black), G1B (gray), G2A (blue), and G2B (red). The straight lines are best-fit lines either for all the models (solid black) or separately for the G1 (black dashed) and G2 (blue dashed) models (section 2b). The G1 and G2 lines are plotted (Figs. 12a,e) if the difference in their slopes is significant at the 95% level (section 2b); otherwise, the data points do not tend to separate for the two groups, so a single best-fit line is included (Figs. 12b,c,d,f). Given that PGW is present in the G2 but not in the G1 models, the existence of slope differences in Figs. 12a and 12e suggests that only those linkages are impacted by PGW.
As noted in section 1b, an issue is that high correlation between two variables, and , does not necessarily indicate causality. Conversely, a weak correlation between and does not necessarily mean that they are not physically linked: it is possible that the linkage is blurred because some other variable influences or more strongly. (An example of this latter case is the weak correlation between and noted in section 4c, which is low because the impact of on is considerably stronger.) Therefore, for each scatterplot we only draw conclusions after a careful consideration of known ocean dynamics. Generally, this approach allows us to conclude that a single process is dominant.
Note that, although significant correlations indicate that a systematic process causes biases to vary among the models, they provide no information about why models differ from observations [since Eq. (1) does not involve observations at all]. The green dots in each panel of Fig. 12 indicate observational values. In all but one of the plots (Fig. 12b), some data points lie near the dot, indicating that their models represent the observations better than the others. We infer that the process that causes biases to vary among the models is also represented “better” in those models.
b. D20 bias
Existing knowledge of the formation of ASHSW and ventilated thermocline theory (section 1), as well as results from section 3, suggests that the wintertime MLT along the NAS northern boundary determines D20. Specifically, the thick wintertime mixed layer there generates a warm and saline water mass that subducts during spring and spreads southward (Figs. 7 and 8), leading to a deeper D20. In this view, as MLT increases, the warm bias extends deeper and D20 should increase.
Figure 12a provides a scatterplot of annual-mean versus January . Consistent with the ideas in the previous paragraph, D20 and MLT are highly correlated both for the G1 and G2 models (C1 = 0.99; C2 = 0.90). Data points for the G1 models (black and gray points) all lie near a best-fit line with a slope close to unity and a small, positive y intercept ( = 0.95 ± 0.11, = 52 m). In contrast, points for the G2 models (blue and red points) lie near a best-fit line that has a slope greater than unity ( = 0.30, = −29 m), so that is deeper than . The line slopes for the G1 and G2 models differ significantly at the 95% level, which indicates that PGW contributes to the linkage in the G2 models (discussed below). Finally, note that the green dot lies at the low edge of the spread of data points, consistent with and being too large for almost all the models (Fig. 2). Recall that the observed MLT may be underestimated due to smoothing (sections 2b and 3a), so its value may be closer to 100 m, in which case the green dot in Fig. 12a lies very close to the best-fit lines, assuring that the reduction of leads to that of .
For the G1 models (black and gray points), the nearly one-to-one linkage between the two variables exists because it involves only basic properties of the stratification: 20°C for all the G1 models (black bars in Fig. 2d), and hence must be greater than (i.e., it lies above the main diagonal of Fig. 12a); moreover, given the strong, upper-ocean stratification in the NAS, must be close to . For the G2B models (red points), PGW flows weakly or not at all into the NAS [section 3b(2)(iii)], which makes the G2B models essentially the same as the G1 models in terms of their – relationship; as a consequence, is also close to .
For the G2A models, the correlation between and apparent in Fig. 12a is also high (C2A = 0.67), suggesting that is impacted by . On the other hand, one expects for the G2A models to be determined by the depth of the PGW, , since PGW spreads into the NAS for this group [section 3b(2)(iii)]. Therefore, because PGW in the models is erroneously warmer than 20°C (Fig. 2d), must lie below PGW. The resolution of this apparent contradiction is that is significantly correlated with MLT in the northwest corner of the basin, (C2A = 0.72): There, is thick enough to entrain the PGW salinity maximum completely for most of the G2A models (8 out of 12; left panels of Fig. 11); since increases as increases (C = 0.85), increases with , thereby accounting for the correlation between them. We conclude that, although is directly linked physically to , it is indirectly determined by through the impact of on .
In the above discussion, we have assumed that causes , a reasonable assumption given known ocean dynamics. For completeness, we also tested the possibility that determines . In this scenario, wind forcing by Ekman pumping pushes down (or pulls up) the thermocline via Ekman pumping, leading to a thick (thin) mixed layer. Consider the response of a steady-state (annual mean), linear, inviscid, reduced-gravity, 1.5-layer model. Upper-layer thickness (a proxy for ) satisfies the equation , where is the Rossby wave speed ( = 5 cm s−1 at 20°N). Setting with = 1000 km (roughly the width of the NAS) and = 10−6 m s−1 (a typical magnitude of the bias in Figs. 5c,f), we obtain = 20 m, which is an order of magnitude smaller than the range of (~100–400 m). Thus, we rule out the reverse causality that determines
c. MLT bias
What processes, then, cause to increase to unrealistically large values near the NAS northern boundary in the G1A and G2A models? Since the summertime mixed layer is not biased (Fig. 3i), the cause involves misrepresentation of the entrainment rate into the mixed layer, , during the fall.
The models’ entrainment rate is determined by their mixed-layer scheme (section 2a). Here, we base our analysis on the KT model, but similar processes are also active in other mixed-layer models. There are several versions of the KT model, but in all of them is determined by an equation like
where is the mixed-layer thickness, is the gravitational acceleration, is the density jump across bottom of the layer, and
parameterizes the production of turbulent kinetic energy that drives the entrainment. In (3b), and are coefficients of salinity and thermal expansion, respectively, m and n are constants with values typically between 0 and 1, and is mixed-layer salinity.1
According to Eqs. (3a) and (3b), results from turbulence generated by surface fluxes (wind stirring , surface cooling , and net evaporation ) and is inversely proportional to the density jump across the bottom of the mixed layer (Kraus and Turner 1967; Niiler and Kraus 1977). To explore these relationships, we obtained scatterplots between (a measure of the time integral of ), , , , and the inverse of just beneath the mixed layer (a measure of 1/), where , denotes mixed-layer density, , , and 100 m. Variable is evaluated during January, whereas the other four are averaged during October–December, the season when the mixed layer thickens. Positive (negative) indicates surface heating (cooling).
The correlations of with the surface fluxes, (C = −0.28), (C = −0.34; Fig. 12b), and (C = 0.23), are weak, either insignificant or barely significant. In contrast, the correlation with is very high (C = 0.99; Fig. 12c), and, consistent with the KT relationship, it is positive so that increases with a weaker stratification. As in Fig. 12a, the observed point lies at the low end of the model points, so that is too small for almost all the models. Considering that observed MLT might be underestimated by about 50 m (section 3a), the best-fit lines in Figs. 12b and 12c lie close to the observed points, indicating that improvements in the models’ ability to simulate and can lead to a better representation of MLT. Indeed, after shifting the observed point upward by 50 m, the G1B and G2B (gray and red) data points in Fig. 12c lie close to the observational one. In contrast, even with the shift, no data points in Fig. 12b lie close to the observational one, a consequence of being biased negative in all the models.
The weak correlations with the surface fluxes are surprising, particularly for since surface cooling is believed to be the primary driver of the wintertime in the NAS [section 3b(1)(iii)]; moreover, Eqs. (3a) and (3b) state that surface fluxes are required for any turbulence and, hence, entrainment to exist at all . The negative correlation with is not physically sensible, since stronger wind stirring should lead to larger , indicating that has little or no impact on . On the other hand, the negative correlation between and and the positive correlation between and are physically sensible, and so they likely do impact . The low values of their correlations with , then, must indicate that some process other than surface fluxes impacts variations of among the models much more strongly (see the second paragraph of section 4a). Since the versus correlation is so high, it must capture that process. Without the strong influence of , the correlations of with and particularly would surely be much higher.
With the aid of Eqs. (3a) and (3b), it is possible to quantify the relative impacts of and on . For convenience, drop the and terms, define , and split and into mean and perturbation parts. Assuming the perturbations are small, it follows from (3) that
Then, we estimate the average of over the NAS box (Fig. 3f) by
replacing each variable with its own average. We estimate and from their standard deviations in the 31 coupled models, finding that = 0.22 and = 0.63. It follows that the correlation between and is larger than that with by the factor 0.63/0.22 3. Thus, has much greater control on the generation of MLT biases, even though it is cooling by that drives the seasonal thickening of the mixed layer.
The above results suggest that controls bias but the opposite causality, in which leads to MLT variations and then to variations, is also possible. Suppose that stronger cooling strengthens entrainment and so increases MLT. As MLT increases, so does the mixed-layer density due to the entrainment of deeper, heavier water. Therefore, the difference between the mixed-layer and deep-ocean densities decreases and hence increases with MLT. Part of the high correlation between and may happen in this way. On the other hand, for this causality to hold we expect both and to be strongly linked to variations in , which—as demonstrated by their low correlations, C = −0.34 and C = −0.24, respectively—is not the case. So, we rule out the causality that drives .
What processes determine ? As defined, is proportional to the difference between mixed-layer density and the density = 100 m below the mixed layer . In a first step, we assess the relative importance of and in setting . In scatterplots of versus (Fig. 12d) and (not shown), the correlations with (C = −0.87) and (C = −0.32) are both significant. The negative correlation with is sensible, since should increase as decreases. On the other hand, the negative correlation with is not, since should increase with . From these properties, we conclude that is controlled by . Further, the correlation between and does not result from an independent process, but rather likely from the link of to (C = 0.74). Finally, note in Fig. 12d that is denser than observed in most of the models, so that models with lower simulate more realistically.
In a second step, we determine whether temperature or salinity affects . For the G2 models, the correlation of with is high (C2 = 0.87; Fig. 12e) but is insignificant with (C2 = −0.04), indicating that controls . For the G1 models, the correlations of with (C1 = 0.99) and (C1 = −0.81) are both high. Nevertheless, as discussed next, the impact of on is still much smaller than that of because the range of temperature values is relatively small.
Neglecting the influence of pressure, the equation of state implies that changes in salinity and temperature, and , cause a density change according to
where is a background density. In the G1 models, the ranges of salinity and temperature values among the models are 4 psu (Fig. 12e) and 2.0°C. According to (5) with = 1 gm cm−3, = 7.5 × 10−4 (psu)−1, and = −2.5 × 10−4 °C−1, the density ranges caused by salinity and temperature variations are 3.0 mg cm−3 and 0.5 mg cm−3, respectively. Since is close to the range of (3 mg cm−3) but is much smaller, we conclude that, even for the G1 models, provides the primary control for and, hence, for .
Similar to Fig. 12a, the slopes of the best-fit lines between versus differ significantly for the G1 and G2 models (Fig. 12e; = 0.94 ± 0.12 mg cm−3 psu−1; = 0.61 ± 0.14 mg cm−3 psu−1). This property suggests that, due to the presence of PGW in the G2A models, there is a systematic difference in the mixed-layer water mass (/) structures between the two groups. To confirm this idea, we obtained a scatterplot between and during January, finding that data points are significantly and oppositely correlated for the G1 and G2 models (C1 = −0.67; C2 = 0.37) and that the slopes of their best-fit lines also have opposite signs ( = −0.41 psu °C−1; = 0.46 psu °C−1).
For both groups, wintertime mixed-layer water in the NAS is a mixture of water advected primarily from the WICC [section 3b(2)(ii); Prasad and Ikeda 2002b; Shankar et al. 2016] and entrained from below. The temperature of the entrained water, however, differs between them: For the G1 and G2B models, it is colder because warmer PGW does not spread into the interior of the NAS, whereas for the G2A models it is warmer because it does. In confirmation of this difference, water 100 m below the mixed layer is colder than that in the mixed layer by 3.5°C for the G1 and G2B models but by only 1.6°C for the G2A models.
The different temperatures of entrained water lead to the opposite signs in the – correlations among the groups. In the G1 and G2B models, when is erroneously high, the mixed layer is thick, cooler water is entrained into the mixed layer, and the correlation is negative. In contrast, in the G2A models high leads to the entrainment of warmer PGW, and the correlation is positive. We therefore attribute the positive – correlation in the G2A models to the entrainment of PGW into the winter mixed layer; in support of this idea, the correlation is positive only near the northern boundary where the wintertime mixed layer is thick, and it is almost zero elsewhere where the mixed layer is relatively thin.
To summarize, for a given , is lower and is higher in the G1 and G2B models relative to the G2A models owing to PGW in the latter, and hence in Fig. 12e. The difference in the two slopes is not large, however, because the impact of on is secondary compared to that of .
What processes determine ? Consider the annual-mean salinity budget in the NAS box (Fig. 3f) with its bottom equal to MLT. In this box, evaporation (Fig. 5e) and entrainment of PGW (for the G2A models) are sources of salinity that must be balanced by freshwater input. A possible freshwater source is coastal upwelling of freshwater from below ASHSW; however, upwelling is weak in the NAS where the dominant process is rather the downwelling (subduction) that forms ASHSW. The required freshwater input, then, has to be advection from the south, namely, from the western Arabian Sea or WICC [sections 3b(1)(iv) and 3b(2)(ii)].
To investigate the above processes, we obtained scatterplots of January with OND (C = 0.17), January (C2 = 0.87), annual-mean SSS off Somalia, (C = 0.80), and annual-mean SSS off India, (C = 0.86; Fig. 12f). The correlation between and is weak and insignificant, indicating that the other processes are responsible for errors. The correlations with the other three variables are high and significant, so that advection from the Persian Gulf, western Arabian Sea, and WICC could all be important for determining . From the correlations alone, then, it is impossible to argue for the relative importance of the three advective sources.
For the G2 models, SSS in the Persian Gulf, and hence , is determined by a balance between evaporation and freshwater advection into the Gulf. Similar to the NAS, the correlations of annual-mean with January SSS averaged over the Persian Gulf (; C2 = 0.08) and January (C2 = 0.22) are insignificant, which suggests that and are more strongly influenced by a factor other than local . Consistent with this result, is significantly correlated with the salinity of inflow water, and (C2 = 0.71 / and 0.79 for /). From these properties, we eliminate as an independent process, and consider and to be the determining factors of .
It remains to assess the sources and impacts of the and biases. Regarding impacts, affects wintertime strongly since it is directly connected to the NAS at that time by the northward-flowing WICC (Fig. 6f); in contrast, is advected into the NAS during the summer, and so its impact on wintertime must be relatively weak (Fig. 6e). Concerning sources, and are linked, respectively, to regions of weak summer monsoon rainfall in the Bay of Bengal and off the west coast of India and of high precipitation in the WEIO [section 3b(2)(ii)]. Figure 13 illustrates these linkages in another way, plotting correlation maps of and (indicated by ’s) with SSS at every point in the basin. Tongues of high correlation extend northward from the ’s into the NAS, confirming the impacts of both and on in the NAS. Regions of high correlations also extend southward to the WEIO (Fig. 13a) and to the Bay of Bengal (Fig. 13b), indicating their source regions.
Note also in Fig. 13 the correlations are positive everywhere (red and blue colors show strong and weak positive correlation, respectively). This property appears to contradict the fact that the deficit in rainfall in the Bay of Bengal (excess rainfall in the WEIO) generates a saline (fresh) bias (Fig. 10). The resolution of the contradiction is that, although WEIO salinity and certainly are impacted by the WEIO rainfall, they are even more strongly impacted by the advection of salty water into the region generated by the weak-monsoon, dry biases elsewhere in the basin: Without the strong influence of this remotely generated salty water, would be positively correlated with local rainfall and, hence, negatively correlated with .
f. G1B and G2B models
The most striking difference between the GB models (G1B + G2B models; gray and red points) and the GA models (G1A + G2A models; black and blue points) is that remains realistically thin in the GB models (100–140 m), thereby allowing for the shallowness of (125–85 m) as well (Fig. 12a). Why does remain thin for the GB models?
One possible reason is suggested by the separation of GA and GB data points in the other panels of Fig. 12: Although there is some overlap, their mean values are clearly different. In particular, in Fig. 12d note that data points for GA lie below those for GB, the sole exception being the dark-blue circle. As a result, the mean value of for GA (0.7 × 10−4 s−2) is nearly halved compared to the mean for GB (1.2 × 10−4 s−2), suggesting that the entrainment rate is weaker and, hence, should be thinner by a factor of 0.7/1.2 = 0.6. There is more overlap between GA and GB data points in the other fields; however, consistent with the difference, their mean values are still distinctly separate and they all act to decrease (increase) for the GA (GB) models.
Another possibility is that different mixed-layer schemes are used in the GA and GB models: The KPP and BD mixing schemes are used in 12 of the 17 GA models, but not at all in the GB models (Table 1). Further, all the mixed-layer models require parameter choices, and perhaps those for the GB models are just “better.”
5. Summary and discussion
In this study, we investigate biases in the climatological mean state of the northern Arabian Sea (NAS) that are present in 31 coupled ocean–atmosphere models ( appendix A and Table 1). Model differences lead to large variations in the biases (Fig. 2). Based on these differences, we divide the models into four groups: two groups depending on whether the model lacks (G1) or includes (G2) a Persian Gulf, and two groups depending on whether D20 values increase to unrealistically large values (GA) or remain small (GB).
Basic bias properties are captured in the multimodel-mean (MMM) fields for all the models (Figs. 1, 3, and 4). In particular, errors in the depth of the 20°C isotherm and wintertime (January) mixed-layer thickness (ΔMLT) are largest in the northwest corner of the basin (Figs. 3d,f), and subsurface tongues of warm temperature and high salinity spread away from the northern boundary (Figs. 4b,d). These properties suggest that the NAS biases arise from errors in the models’ specification of PGW. In support of this idea, PGW does spread into the NAS in the G2A models, within or just below the mixed layer (left column in Fig. 11). Whether PGW spreads into the NAS appears to be linked to depth of PGW relative to MLT in the northwest corner of the basin : If the PGW is below the mixed layer (; G2B models) PGW remains near the western boundary, whereas if MLT in the northwest corner of the basin is thick enough to entrain the PGW salinity maximum (; 8 of 12 G2A models) it spreads efficiently into the NAS.
Other bias properties, however, point toward as the primary cause of . Perhaps most convincingly, similar biases occur in the G1A and G2A models despite the former lacking a Persian Gulf (cf. G1A and G2A panels in Figs. 7 and 8), and there are no subsurface biases in the G1B and G2B models for which MLT remains realistically thin (cf. G1B and G2B panels in Figs. 7 and 8). In addition, subsurface salinity and temperature tongues originate within the mixed layer near the northern boundary for the G1A and G2A models (Figs. 7e,gand 8e,g), and the structures of and are similar along the northern boundary (Figs. 7a,c and 8a,c). These properties suggest that the biases are formed along the northern boundary during winter by the deep mixed layer there and spread southward during the rest of the year (Figs. 6a–d), essentially forming ASHSW that is too deep (e.g., Prasad and Ikeda 2002b).
Figure 12 provides scatterplots that sequentially illustrate the chain of processes that connect error to the dry bias associated with the models’ weak summer monsoon rainfall. There is a strong link between and (Fig. 12a), which supports the idea that biases cause biases through errors in the generation of model PGW and ASHSW. Surprisingly, is not highly correlated with surface heat flux (Fig. 12b), but rather with , the inverse of the stratification just beneath the bottom of the mixed layer (Fig. 12c). These correlations do not indicate that errors in have no effect on ; rather, they show that the influence of biases is so large that it blurs the impact of the errors. The high – and – correlations (Figs. 12d,e), together with quantitative estimates based on the equation of state, indicate that