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    Analysis domains for Q1 profiles (over Amazonia) and zonal surface wind (over the equatorial Atlantic Ocean), the location of LBA (star), mean AMIP2 surface wind biases against the ICOADS data (vectors; magnitude >0.5 m s−1), and mean continental precipitation (>6 mm day−1) from observations (shaded) and the AMIP2 simulations (contours) during MAM.

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    Monthly-mean biases in surface zonal wind us over the equatorial Atlantic in (a) AMIP2 models, (b) CMIP3 models, and (c) AMIP models of CMIP5. The ICOADS data were used to estimate the biases.

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    Mean profiles of diabatic heating from LBA observations and reanalyses at the LBA location, averaged over the LBA period of Nov 1998–Feb 1999. The RMSEs of the reanalyses are given.

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    Continental precipitation from CMAP observations and reanalyses averaged over the LBA period of Nov 1998–Feb 1999. The RMSEs of the reanalyses are given.

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    Probability distributions of biases in (a) surface zonal wind us and (b) zonal SLP gradient force P′ over the equatorial Atlantic in the AMIP2 ensemble during MAM. Dashed lines separate the total population into terciles.

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    Differences in (a),(e) surface zonal wind (shaded; every 0.5 m s−1) and surface wind vectors, (b),(f) precipitation (mm day−1), (c),(g) SLP (Pa), and (d),(h) equatorial distributions of SLP (Pa) between the top and bottom terciles in (left) surface zonal wind us and (right) zonal SLP gradient force P′ biases in the AMIP2 ensemble during MAM.

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    Mean Q1 profiles over Amazonia in the top and bottom terciles of surface zonal wind biases (us) from the AMIP2 ensemble. The vertically integrated Q1 ratio (QR) between both profiles (top over bottom tercile) is given.

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    Probability distributions of Q1 at low levels (850–700 hPa) over Amazonia in the top (shaded bars) and bottom (open bars) terciles of (a) surface zonal wind us and (b) zonal SLP gradient force P′ biases from the AMIP2 ensemble during MAM.

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    Correlation coefficients (black line) and their 95% confidence level limits (shaded) between standardized Q1 over Amazonia and biases in (a) surface zonal wind us and (b) zonal SLP gradient force P′ from the AMIP2 ensemble during MAM.

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    Differences in Q1 over Amazonia (δQ1; shaded colors) and zonal wind (δu; contours, m s−1) over the equatorial Atlantic between the top and bottom terciles in surface zonal wind biases us from the AMIP2 ensemble.

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    Differences in Q1 over Amazonia between the top and bottom terciles in surface zonal wind biases us from individual AMIP2 models with deficient Q1 (a) at all levels and (b) only at low levels during MAM.

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    Scatter diagram between (a) low-level (850–700 hPa) Q1 over Amazonia and (b) entrainment over the equatorial Atlantic E against mean surface zonal wind biases us over the equatorial Atlantic from each AMIP2 model during MAM. In (a), the symbol size is proportional to the vertically (1000–100 hPa) averaged Q1 for each model. In (b), biases in zonal SLP gradient force (P′; 105 m s−2) are contoured.

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    Mean Q1 profile over Amazonia for each AMIP2 model with its vertically averaged Q1 in the range of (a) 1.8°–1.9°C day−1, (b) 1.2°–1.3°C day−1, and (c) 0.9°–1.1°C day−1 during MAM.

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    Monthly (a) entrainment E and (b) the ratio of E and zonal SLP gradient force P over the equatorial Atlantic from the AMIP2 ensemble and ICOADS data.

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    Correlation coefficients (dots) and their limits of the 95% confidence level (vertical bars) between surface zonal wind biases us and entrainment biases E′ in a given bin of zonal SLP gradient force P′ from the AMIP2 ensemble during MAM. The sample size is given for each bin as its percentage of the total (540 months); their sum accounts for 95% of the total, bins with sample sizes less than 2% of the total (on the tails of the P′ distribution) were excluded.

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Possible Root Causes of Surface Westerly Biases over the Equatorial Atlantic in Global Climate Models

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  • 1 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
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Abstract

Most global climate models (GCMs) suffer from biases of a reversed zonal gradient in sea surface temperature (SST) and weak surface easterlies (the westerly bias) in the equatorial Atlantic during boreal spring. These biases exist in atmospheric GCMs (AGCMs) and are amplified by air–sea interactions in atmospheric–oceanic GCMs. This problem has persisted despite considerable model improvements in other aspects. This study proposes a hypothesis that there are two possible root causes for the westerly bias. The first is insufficient lower-tropospheric diabatic heating over Amazonia. The second is erroneously weak zonal momentum flux (entrainment) across the top of the boundary layer. This hypothesis is based on a scale analysis of a simple model for a well-mixed equatorial boundary layer and diagnoses of simulations from eight AGCMs. Severe westerly biases in AGCMs tend to occur when the diabatic heating at low levels (850–700 hPa) over Amazonia is too weak. Deficient low-level diabatic heating weakens the zonal gradient in sea level pressure along the Atlantic equator, introducing westerly biases. In addition, westerly biases may also occur when easterly momentum flux due to entrainment is underestimated.

Corresponding author address: David Zermeño, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098. E-mail: dzermeno@rsmas.miami.edu

Abstract

Most global climate models (GCMs) suffer from biases of a reversed zonal gradient in sea surface temperature (SST) and weak surface easterlies (the westerly bias) in the equatorial Atlantic during boreal spring. These biases exist in atmospheric GCMs (AGCMs) and are amplified by air–sea interactions in atmospheric–oceanic GCMs. This problem has persisted despite considerable model improvements in other aspects. This study proposes a hypothesis that there are two possible root causes for the westerly bias. The first is insufficient lower-tropospheric diabatic heating over Amazonia. The second is erroneously weak zonal momentum flux (entrainment) across the top of the boundary layer. This hypothesis is based on a scale analysis of a simple model for a well-mixed equatorial boundary layer and diagnoses of simulations from eight AGCMs. Severe westerly biases in AGCMs tend to occur when the diabatic heating at low levels (850–700 hPa) over Amazonia is too weak. Deficient low-level diabatic heating weakens the zonal gradient in sea level pressure along the Atlantic equator, introducing westerly biases. In addition, westerly biases may also occur when easterly momentum flux due to entrainment is underestimated.

Corresponding author address: David Zermeño, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098. E-mail: dzermeno@rsmas.miami.edu

1. Introduction

The tropical Atlantic atmosphere and ocean host a large variety of important and intriguing weather and climate phenomena. They include the intertropical convergence zone (ITCZ), trade winds, easterly waves, hurricanes, the equatorial branches of the meridional overturning circulations in both the ocean and atmosphere, an equatorial cold tongue, and zonal and meridional modes of the tropical Atlantic variability (Xie and Carton 2004). This region is influenced by many remote factors. They include two major centers of atmospheric deep convection over Amazonia (Wang and Fu 2007) and West Africa (Ruiz-Barradas et al. 2003), the North Atlantic decadal variability (Xie and Tanimoto 1998), and teleconnections with the Pacific Ocean (Aceituno 1988; Chiang et al. 2002; Klein et al. 1999; Enfield and Mayer 1997). Given this complexity, it is of little surprise that most state-of-the-art global climate models (GCMs) suffer from misrepresentations of variability mechanisms (Breugem et al. 2006) and persistent systematic biases in this region (Davey et al. 2002; Deser et al. 2006; Richter and Xie 2008).

The most notable model biases in the tropical Atlantic region include excessively high sea surface temperature (SST) associated with an erroneously deep mixed layer in the Gulf of Guinea. These errors lead to a reversed zonal gradient of equatorial SST, namely, warm to the east and cold to the west. These biases peak during boreal summer but start during boreal spring (DeWitt 2005). Notable biases during boreal spring are an underestimation of low-level clouds (also known as stratocumulus cloud decks) off the African coast and over the southeast Atlantic (Huang et al. 2007; Hu et al. 2011), a southward shift of the ITCZ (Deser et al. 2006), deficient (excessive) rainfall over Amazonia (West Africa) (Richter and Xie 2008), an erroneous east-to-west equatorial gradient in sea level pressure (SLP) (Chang et al. 2007; Richter and Xie 2008), and weak equatorial surface easterlies (DeWitt 2005) known as the westerly bias. These problems have shown an enigmatic persistency through decades of considerable model improvements in other aspects. In this study, we focus on the westerly bias of boreal spring.

There are several possible reasons for the westerly bias and the SST bias (or warm bias) in coupled ocean–atmosphere models. Huang et al. (2007) suggested that the major cause of the warm SST bias in the east Atlantic is an excess of shortwave radiation associated with a common underestimation of the stratocumulus cloud decks, a mechanism similar to that proposed by Ma et al. (1996) for the warm bias in the southeast Pacific Ocean. Hu et al. (2011) found that a realistic representation of the vertical distribution of the clouds (the cloud liquid water path) in the region may significantly alleviate the warm bias. Breugem et al. (2008) suggested that spurious barrier layers tend to inhibit the surging of the east Atlantic cold tongue enhancing the warm SST bias during boreal spring and summer. Patricola et al. (2012), however, found no essential role of these barrier layers. Seo et al. (2006) showed that low model resolutions not resolving ocean eddies can potentially contribute to the warm bias in the annual mean. The warm bias in the eastern equatorial Atlantic may weaken or reverse the zonal gradient in SST, introducing a westerly bias through the mechanism of Lindzen and Nigam (1987).

DeWitt (2005) showed that reducing the equatorial Atlantic surface westerly bias significantly improves upwelling in the east Atlantic and the cross-Atlantic equatorial SST gradient in coupled models. The westerly bias exists in atmospheric GCMs (AGCMs) with prescribed SST (Chang et al. 2007; Richter and Xie 2008, section 3). This problem may be exacerbated by air–sea interactions in most coupled models (Biasutti et al. 2006). So, in addition to oceanic sources, there must be atmospheric sources for the westerly bias as well. As will be discussed in this article, based on a simple model of a well-mixed tropical boundary layer (Stevens et al. 2002) there are two possible causes for the westerly bias in AGCMs: erroneous zonal gradient in SLP as suggested by previous studies (Chang et al. 2007; Richter and Xie 2008) and erroneous momentum flux between the lower troposphere and the boundary layer, also known as boundary layer entrainment.

An erroneous zonal gradient in SLP along the Atlantic equator can be introduced by deficient rainfall over Amazonia (Chang et al. 2008; Wahl et al. 2010) or excessive rainfall over West Africa (Richter et al. 2012) during boreal spring and by the influence of the monsoon in the Gulf of Guinea during the spring–summer transition (Okumura and Xie 2004). Chang et al. (2008) showed that a reduction in Amazonian rainfall deficit in a model can lead to a better simulation of the zonal gradient in SLP and thus a reduction in the westerly bias. A more accurate simulation of Amazonian rainfall may come from better representations of convection (Betts and Jakob 2002), land processes, land–atmosphere interactions (Richter et al. 2012), and a better representation of the remote forcing from the Pacific (Tozuka et al. 2011). In a similar manner, a better simulation of the West African rainfall can also lead to improvements in the westerly bias (Richter et al. 2012). Other studies, however, have shown contradicting results in the role of the rainfall bias over West Africa (Chang et al. 2008).

An interesting result from Chang et al. (2008) is that the zonal gradient in SLP along the Atlantic equator in their AGCM is relatively insensitive to the vertical profile of diabatic heating over Amazonia. This issue needs to be revisited. Many studies have shown that it is the vertical gradient of diabatic heating, and not the vertically integrated heating (which is proportional to surface precipitation), that determines the vertical structure of the atmospheric circulation (DeMaria 1985; Hartmann et al. 1984; Wu et al. 2000; Wu 2003; Schumacher et al. 2004). Zhang and Hagos (2009) demonstrated that a robust steady-state response of surface and low-level winds to an isolated heating source exists only when there is sufficient heating in the lower troposphere. It is more intuitive to relate the westerly bias over the equatorial Atlantic Ocean to the vertical structure of diabatic heating than to its vertically integrated heating or total precipitation over the Amazonia. However, surface pressure is not the only process that controls equatorial surface winds. Studies of the momentum balance in the tropical eastern Pacific boundary layer have shown that the strength and variability of tropical surface winds cannot be properly explained without taking into consideration the momentum entrainment at the top of the boundary layer (Stevens et al. 2002; McGauley et al. 2004; Back and Bretherton 2009).

In this study, we present diagnoses that form the base of a hypothesis that there are two possible root causes of equatorial Atlantic westerly biases of boreal spring in AGCMs: insufficient low-level diabatic heating over Amazonia and erroneously weak momentum flux from the lower troposphere into the boundary layer. Our analyses show evidence of connections between the westerly bias and these possible causes. A formal proof of this hypothesis would require more rigorous investigations.

2. Data

In this study, westerly biases are diagnosed in eight models of the Atmospheric Model Intercomparison Project phase 2 (AMIP2; Glecker 1996), their coupled versions from phase 3 of the Coupled Model Intercomparison Project (CMIP3; Meehl et al. 2005), and the AMIP models from phase 5 of the Coupled Model Intercomparison Project (CMIP5; Meehl et al. 2009). Biases in model surface wind and SLP were estimated from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS; Worley et al. 2005) and biases in precipitation from the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP; Xie and Arkin 1997) dataset.

The apparent heating source Q1 (Yanai et al. 1973) was estimated to represent the vertical structure of diabatic heating in the AMIP2 models and European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim; Dee et al. 2011). The term Q1 was also estimated from radiosonde data of the Large-Scale Biosphere–Atmosphere Experiment (LBA; Silva Dias et al. 2002). Direct outputs of diabatic heating profiles from the Climate Forecast System Reanalysis (CFSR; Saha et al. 2006) and the Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011) were also used. The term Q1 was computed using centered and forward difference schemes for horizontal and vertical derivatives, respectively:
e1
where T is mean temperature, ω is vertical velocity, V is the horizontal velocity vector, cp is the heat capacity at constant pressure, and α is the specific volume. All data were interpolated to a horizontal grid of 1°. There are 14 vertical levels (10 m and 1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, and 70 hPa) in all model simulations. Table 1 lists the temporal resolutions and periods covered by the used data.
Table 1.

Observations, reanalyses, and model simulations. Diabatic heating available as temperature tendency terms in MERRA and CFSR.

Table 1.

Two main domains were analyzed. One domain is over the equatorial Atlantic Ocean (as in Richter and Xie 2008) and the other is over Amazonia (Fig. 1). Surface zonal winds and momentum entrainment were averaged over the equatorial Atlantic domain. Because of missing data in observations (ICOADS), the zonal SLP gradient was estimated as the slope of a least squared line fitting all data points along the equatorial Atlantic domain. Diabatic heating profiles were averaged over the Amazonian domain. The total number of March–May (MAM) samples (540) in the AMIP2 simulations was used as the degree of freedom in the correlation significance tests.

Fig. 1.
Fig. 1.

Analysis domains for Q1 profiles (over Amazonia) and zonal surface wind (over the equatorial Atlantic Ocean), the location of LBA (star), mean AMIP2 surface wind biases against the ICOADS data (vectors; magnitude >0.5 m s−1), and mean continental precipitation (>6 mm day−1) from observations (shaded) and the AMIP2 simulations (contours) during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

3. Potential sources of the westerly bias

Westerly biases in most atmospheric–oceanic GCMs of CMIP3 (Fig. 2b) are more severe in all seasons than those in their atmospheric-only counterparts of AMIP2 (Fig. 2a). In both coupled and uncoupled GCMs, maximum westerly biases occur during MAM. In the latest generation of AGCMs from CMIP5 (Fig. 2c), these westerly biases are only modestly reduced from those in CMIP3 (Fig. 2a). It is obvious that some root causes of the westerly bias exist in the atmospheric models, and they, if detectable, should be more evident during MAM.

Fig. 2.
Fig. 2.

Monthly-mean biases in surface zonal wind us over the equatorial Atlantic in (a) AMIP2 models, (b) CMIP3 models, and (c) AMIP models of CMIP5. The ICOADS data were used to estimate the biases.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Stevens et al. (2002) demonstrated that mean surface winds over the tropical oceans can be studied using a simple well-mixed boundary layer model. The zonal momentum equation for this mixed-layer model at the equator is
e2
where U is the zonal component of the mixed-layer bulk wind vector U, which represents surface wind, UT is the zonal component of the wind vector immediately atop the mixed layer, ωE is the entrainment velocity across the top of the mixed layer, Cd is the surface drag coefficient, h is the depth of the mixed layer, and α is the specific volume. This equation describes the momentum balance of equatorial boundary layer winds by the pressure gradient force (first term), surface drag or friction (second), and entrainment (third).
For simplicity, ignoring the meridional component and assuming a mean easterly wind we obtain from Eq. (2)
e3
A scale analysis using ωE = 1.2 × 10−2 m s−2 (McGauley et al. 2004), UT = 10 m s−1, h = 1000 m, −αp/∂x = 2 × 10−5 m s−2 (see section 4b), and Cd = 1/900 (Garratt 1992) indicates that the terms with ωE in Eq. (3) cannot be neglected in comparison to the pressure gradient term on the right-hand side of Eq. (3). The surface westerly bias can therefore come from errors in the pressure gradient force (Chang et al. 2008; Richter and Xie 2008), the momentum entrainment, or both.

Two factors determine the SLP gradient force over the equatorial oceans. The first is an isolated diabatic-heating source in the troposphere (Gill 1980) or, more precisely, its vertical gradient (DeMaria 1985; Hartmann et al. 1984; Wu et al. 2000; Wu 2003; Schumacher et al. 2004). The second is the SST gradient (Lindzen and Nigam 1987). Biases in the SLP gradient force can be introduced via biases in SST in coupled simulations but not in AMIP simulations. AMIP simulations are forced by observed monthly SST. We therefore focus on two possible root causes for the westerly bias in AGCMs: erroneous vertical profiles of diabatic heating over Amazonia (section 4) and erroneous entrainment of momentum over the equatorial Atlantic Ocean (section 5).

4. Heating profiles

a. Ensemble analysis

There are no observed profiles of diabatic heating in Amazonia. The first issue to address is whether profiles of diabatic heating from the three reanalysis products, either as their direct output of temperature tendency terms (MERRA and CFSR) or estimated as Q1 (ERA-Interim), could be used as surrogates for unavailable observations to estimate biases in Q1 in the AGCM simulations. To evaluate the reliability of reanalysis heating profiles, we compared them to the mean LBA heating profile (Fig. 3). CFSR correctly captures the maximum amplitude of the LBA profile, but it overestimates its strength at low levels (800–500 hPa) and its peak is slightly lower than the peak of the LBA profile. The ERA-Interim profile has the smallest root-mean-square error (RMSE), but its heating peak is weaker than the observed by 20% and it also overestimates its amplitude at low levels. The MERRA profile differs the most from the LBA profile; its amplitude is the smallest and it does not have any clear peak. In addition, none of the reanalyses reproduced the spatial pattern of the observed rainfall, and all of them underestimated the total rainfall amount at the LBA location and over Amazonia (Fig. 4). This simple comparison suggests that errors in the three reanalyses not only come from incorrect vertical structure of diabatic heating over the LBA region, but they also come from incorrect spatial distribution of rainfall. It might be safer to assume that their heating profiles over Amazonia during boreal spring are not reliable either. Therefore, reanalysis heating profiles were not used as surrogates of observations.

Fig. 3.
Fig. 3.

Mean profiles of diabatic heating from LBA observations and reanalyses at the LBA location, averaged over the LBA period of Nov 1998–Feb 1999. The RMSEs of the reanalyses are given.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Fig. 4.
Fig. 4.

Continental precipitation from CMAP observations and reanalyses averaged over the LBA period of Nov 1998–Feb 1999. The RMSEs of the reanalyses are given.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Without a reliable reference of heating profiles, we took a different approach to diagnose connections between diabatic heating in Amazonia and the westerly bias. We calculated the errors in surface zonal wind (us, hereafter primes denote biases) with respect to ICOADS for each month of simulation in each of the eight AMIP2 models (Table 1). We treated each model simulation as a member of an ensemble (hereafter AMIP2 ensemble), which includes the simulations from the eight models. The probability distribution of us (Fig. 5a) demonstrates that westerly biases exist in more than 75% of all months in the AMIP2 ensemble during MAM. All samples of us were grouped into three equal parts (terciles) based on their amplitude. The top tercile (to the right of the right vertical dashed line in Fig. 5a) represents the portion of the AMIP2 ensemble with large us or westerly biases, and the bottom tercile (to the left of the left vertical dashed line) represents the portion with small or no westerly biases or even easterly biases. The corresponding distribution of monthly errors in the zonal SLP gradient force (−α∂p/∂x, hereafter P′) is shown in Fig. 5b. Positive P′ represents eastward SLP gradient force corresponding to the surface westerly bias. Possible connections of biases in surface zonal wind us and zonal SLP gradient force P′ with diabatic heating profiles in Amazonia can be diagnosed by comparing the top and bottom terciles of us and P′.

Fig. 5.
Fig. 5.

Probability distributions of biases in (a) surface zonal wind us and (b) zonal SLP gradient force P′ over the equatorial Atlantic in the AMIP2 ensemble during MAM. Dashed lines separate the total population into terciles.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

The first result from this ensemble approach is given in Fig. 6. The panels show the difference between the top and bottom terciles of us (left) and P′ (right) in surface zonal wind, surface wind vectors, precipitation, and SLP. The tercile difference (hereafter denoted by δ) is the average over the top tercile subtracted by the average over the bottom tercile. Larger westerlies in the top terciles (positive δus in Figs. 6a,e) are expected by our difference definition. Positive δP with higher pressure over Amazonia and lower pressure over the eastern Atlantic (Figs. 6c,g) is consistent with positive δus. The difference in the zonal gradient in SLP is about 80 Pa from 10° to 40°W (Figs. 6d,h), which is consistent with its analogous using observations in Richter and Xie (2008). The corresponding force is 2 × 10−5 m s−2. If the zonal gradient in SLP bias is related to insufficient rainfall over Amazonia as previously suggested (Richter and Xie 2008), one would expect a precipitation deficit there in the top tercile. There is no obvious deficit in precipitation over Amazonia (Figs. 6b,f). Instead, excessive precipitation is found over the Brazilian Nordeste and tropical Atlantic Ocean, which is possibly related to a characteristic southward drift or expansion bias of the Atlantic ITCZ in models (Biasutti et al. 2006; Deser et al. 2006). Tercile differences in SST, consistent with the notion that SST is not responsible for the westerly bias in AGCMs, are very small and do not show any identifiable pattern (not shown). The similar patterns in the tercile differences in us and P′ further confirm that surface westerlies and the zonal SLP gradient force biases are closely connected.

Fig. 6.
Fig. 6.

Differences in (a),(e) surface zonal wind (shaded; every 0.5 m s−1) and surface wind vectors, (b),(f) precipitation (mm day−1), (c),(g) SLP (Pa), and (d),(h) equatorial distributions of SLP (Pa) between the top and bottom terciles in (left) surface zonal wind us and (right) zonal SLP gradient force P′ biases in the AMIP2 ensemble during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

We now present an explanation for us and P′ in terms of Q1 over Amazonia. Figure 7 shows the vertical profiles of Q1 over Amazonia (Fig. 1) averaged in the top and bottom us terciles. In each month of March, April, and May (and during MAM), the amplitude of lower-tropospheric Q1 in the top tercile (larger westerly biases) is smaller than that in the bottom tercile. The probability distributions of Q1 at 850–700-hPa levels in the top and bottom terciles of us substantially differ (at the 95% confidence level according to the Kolmogorov–Smirnov test), with more months of weak low-level Q1 in the top tercile (larger westerly biases) than in the bottom tercile (Fig. 8a). These differences are not all due to a deficit in the total rainfall amount in the bottom tercile (Figs. 6b,f); the ratios of the vertically integrated Q1 (proportional to the total rainfall amount) between the two terciles are 0.85–0.96. The linear correlation coefficients between us and Q1 reach a negative peak (−0.36) at 850 hPa (Fig. 9a) and a positive peak (0.12) at 300 hPa. This is consistent with Fig. 7 in that larger westerly biases are associated with weaker low-level Q1. If larger westerly biases were caused by an underestimation of precipitation alone regardless of the vertical structure of Q1, months of larger westerly bias (larger us) would be drier months. No correlation between us over the equatorial Atlantic and rainfall over Amazonia was found.1 Similar analyses showed no evident connection between us and Q1 over equatorial West Africa.

Fig. 7.
Fig. 7.

Mean Q1 profiles over Amazonia in the top and bottom terciles of surface zonal wind biases (us) from the AMIP2 ensemble. The vertically integrated Q1 ratio (QR) between both profiles (top over bottom tercile) is given.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Fig. 8.
Fig. 8.

Probability distributions of Q1 at low levels (850–700 hPa) over Amazonia in the top (shaded bars) and bottom (open bars) terciles of (a) surface zonal wind us and (b) zonal SLP gradient force P′ biases from the AMIP2 ensemble during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Fig. 9.
Fig. 9.

Correlation coefficients (black line) and their 95% confidence level limits (shaded) between standardized Q1 over Amazonia and biases in (a) surface zonal wind us and (b) zonal SLP gradient force P′ from the AMIP2 ensemble during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

The plausible physical connections between us and Q1 in Amazonia are further supported by their connection to P′. Consistent with Fig. 8a, the probability distributions of Q1 at 850–700-hPa levels substantially differ (at the 95% confidence level) between the top and bottom P′ terciles, with more samples of weak low-level Q1 in the top tercile (larger biases of positive P′) than in the bottom tercile (Fig. 8b). The correlation between P′ and Q1 (Fig. 9b) also reaches a negative peak at 850 hPa, suggesting that positive P′ is related to insufficient Q1 at this level. Figures 9a and 9b indicate that biases in surface westerly and zonal SLP gradient force are both related to insufficient lower-tropospheric Q1. The correlation between us and P′ is 0.41 (significant at the 95% confidence level).

To provide a broader perspective of the connection between the westerly bias over the equatorial Atlantic and Q1 over Amazonia we examined the us tercile differences in tropospheric zonal wind δu and those in Q1 δQ1 through the entire year (Fig. 10). Excessive low-level westerlies in the top tercile compared to the bottom tercile (δu > 0) exist through the entire year, but become stronger and deeper during boreal spring. Maximum westerlies are located at 850 hPa during MAM. During June and July they extend up to the 200-hPa level but with smaller amplitude than during MAM. After July they gradually become weaker and shallower. The terms δQ1 and δu roughly correspond to each other. In the lower troposphere, excessive westerlies (δu > 0) in the top tercile are generally accompanied by a deficit in Q1 (δQ1 < 0), and excessive easterlies in the upper troposphere (δu < 0) are accompanied by excessive Q1 (δQ1 > 0). The Q1 deficit in low levels begins after December and continues through the early months of the year. During MAM, negative δQ1 at 850 hPa roughly matches the maximum in westerly δu at that level. In May, the deficit in δQ1 reaches its maximum near 600 hPa and becomes shallower and weaker afterward, as correspondingly do the excessive westerlies. In the upper troposphere, there are excessive easterlies with much larger amplitude and two peaks: one from February to May and the other from August to October, both at 150 hPa. Upper-level excessive easterlies appear to be associated with excessive upper-level Q1. Their peaks occur roughly in the same seasons. The upper-level excessive Q1 alone, however large, is obviously not the reason for the excessive surface westerlies. Excessive low-level westerlies and upper-level easterlies indicate a weakening of the Atlantic zonal circulation in the top tercile. This is possibly a combined result of insufficient Q1 in the lower troposphere and excessive Q1 in the upper troposphere. The correspondence between δu and δQ1 is, however, not perfect. For example, there is an apparent lag between the peaks of low-level δQ1 and lower-tropospheric δu. Other factors for the westerly bias must also exist.

Fig. 10.
Fig. 10.

Differences in Q1 over Amazonia (δQ1; shaded colors) and zonal wind (δu; contours, m s−1) over the equatorial Atlantic between the top and bottom terciles in surface zonal wind biases us from the AMIP2 ensemble.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

b. Comparison of individual models

Figure 11 shows the difference in Q1 over Amazonia between the top and bottom us terciles in each individual AMIP2 model during MAM. Although δQ1 shows different vertical structures, all models suffer from weaker 850–700-hPa Q1 in the top tercile compared to the bottom tercile. Deficient Q1 exists at all levels in some models (Fig. 11b), while only at low levels in others (Fig. 11b). Can the mean vertical Q1 explain the degree of the westerly biases among the models? Fig. 12a shows a scatter diagram of mean low-level Q1 and mean westerly biases during MAM. The symbol size is proportional to the vertically integrated heating over Amazonia. The severity of the westerly biases among these models does not depend on the vertically integrated Q1 and apparently neither on the mean low-level Q1. The latter relationship, however, can be better analyzed by comparing models with similar vertically integrated Q1 (Fig. 13). The two models with the largest vertically integrated Q1 (1.8°–1.9°C day−1; Fig. 13a) share similar vertical structures; however, the one with slightly stronger low-level Q1 (open star) suffers from slightly less severe westerly biases (Fig. 12a). The two models with intermediate vertically integrated Q1 (1.2°–1.3°C day−1; Fig. 13b) best exemplify the possible effect of low-level Q1 on the westerly biases. The one with weaker lower low-level Q1 (solid diamond) suffers from more severe westerly biases (Fig. 12a) than the one with stronger low-level Q1 (solid triangle). There is no relationship between low-level Q1 and the westerly biases among the four models with relatively weak vertically integrated Q1 (0.9°–1.1°C day−1; Fig. 13c). Other factors must be in play. One of them is explained in the next section.

Fig. 11.
Fig. 11.

Differences in Q1 over Amazonia between the top and bottom terciles in surface zonal wind biases us from individual AMIP2 models with deficient Q1 (a) at all levels and (b) only at low levels during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Fig. 12.
Fig. 12.

Scatter diagram between (a) low-level (850–700 hPa) Q1 over Amazonia and (b) entrainment over the equatorial Atlantic E against mean surface zonal wind biases us over the equatorial Atlantic from each AMIP2 model during MAM. In (a), the symbol size is proportional to the vertically (1000–100 hPa) averaged Q1 for each model. In (b), biases in zonal SLP gradient force (P′; 105 m s−2) are contoured.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Fig. 13.
Fig. 13.

Mean Q1 profile over Amazonia for each AMIP2 model with its vertically averaged Q1 in the range of (a) 1.8°–1.9°C day−1, (b) 1.2°–1.3°C day−1, and (c) 0.9°–1.1°C day−1 during MAM.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

5. Momentum entrainment

As discussed in section 3, entrainment is an essential component of the momentum balance in the boundary layer over the tropical oceans. Its mistreatment in AGCMs may potentially lead to biases in surface wind. In this section, we examine the possible relation between erroneous entrainment and the westerly bias over the equatorial Atlantic in addition to biases in the zonal SLP gradient force in the AMIP2 ensemble.

Calculating momentum entrainment in GCM simulations requires the entrainment velocity ωE, wind throughout the boundary layer, and the boundary layer depth h. They are not available from standard model output. We estimated the entrainment term E in the AMIP2 models and observations over the tropical Atlantic domain (Fig. 1) as a residual of the zonal momentum in Eq. (2):
e4
where is surface friction and . We assumed the mean boundary layer wind U as us and a boundary layer height h of 1000 m. Mean E in observations is negative (Fig. 14a), indicating easterly momentum is mixed downward from the lower troposphere into the mixed layer and helps to maintain or enhance the surface easterlies. During MAM, when the westerly bias is the largest, mean E in the AMIP2 ensemble is negative but weaker than in observations. The amplitude of E during these months is larger than that in the zonal SLP gradient force P (Fig. 14b), suggesting a dominant role of E. During the other months, mean E in the AMIP2 ensemble is positive, but its amplitude is much smaller than that of P, suggesting that the role of E is not dominant. In observations, however, the amplitude of E is larger than that of P all the time. This indicates systematic errors in the treatment of entrainment relative to the SLP gradient in the models.
Fig. 14.
Fig. 14.

Monthly (a) entrainment E and (b) the ratio of E and zonal SLP gradient force P over the equatorial Atlantic from the AMIP2 ensemble and ICOADS data.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

Larger us is mainly due to larger positive P′ (Fig. 12b). The possible effect of entrainment on the westerly bias us, however, must be evaluated with respect to a constant pressure gradient force bias P′. Among models with similar P′ (e.g., between 0.8 and 1.2 × 105 m s−2 in Fig. 12b), models with weaker negative entrainment E suffer from larger westerly biases us than those with stronger negative E. This partially explains the independence of us from low-level Q1 in Fig. 12a (e.g., open square and shaded dot). This suggests that insufficient easterly momentum flux because of entrainment (small negative E) could lead to westerly biases.

The connection between monthly westerly biases us and errors in entrainment (E= D− P′) is examined through their correlation in bins of similar P′ from the AMIP2 ensemble (Fig. 15). The correlation between us and E′ is positive in all P′ bins. This positive correlation indicates that, at fixed P, westerly biases tend to become more severe (us > 0) when models suffer from westerly entrainment biases (E′ > 0): namely, insufficient easterly entrainment.

Fig. 15.
Fig. 15.

Correlation coefficients (dots) and their limits of the 95% confidence level (vertical bars) between surface zonal wind biases us and entrainment biases E′ in a given bin of zonal SLP gradient force P′ from the AMIP2 ensemble during MAM. The sample size is given for each bin as its percentage of the total (540 months); their sum accounts for 95% of the total, bins with sample sizes less than 2% of the total (on the tails of the P′ distribution) were excluded.

Citation: Journal of Climate 26, 20; 10.1175/JCLI-D-12-00226.1

These results suggest that erroneous entrainment may lead to surface westerly bias in an AGCM regardless of whether the zonal SLP gradient force is adequately represented or not. This may explain the apparent insensitivity of the westerly bias to the vertical structure of diabatic heating in Chang et al. (2008).

6. Summary and conclusions

We have used a simple model for a well-mixed boundary layer over the tropical oceans and simulations from eight AGCMs to diagnose possible root causes of the surface westerly bias over the equatorial Atlantic during boreal spring. We examined the possible roles of the vertical structure of diabatic heating and zonal momentum entrainment across the top of the boundary layer. Larger westerly biases in AGCMs tend to occur when the lower-tropospheric diabatic heating over the Amazonia is weak and easterly momentum flux into the boundary layer is insufficient. Based on these results, we propose a hypothesis that unrealistic diabatic heating profiles over Amazonia and unrealistic vertical momentum mixing across the top of the boundary layer over the equatorial Atlantic are two possible root causes of the equatorial Atlantic westerly bias in AGCMs.

Our hypothesis along with previous studies suggest that a westerly bias in an AGCM would occur when 1) Amazonian rainfall is underestimated, 2) low-level diabatic heating in Amazonia is too weak (even if the total rainfall amount is well reproduced), and 3) the vertical mixing of zonal momentum across the top of the equatorial Atlantic boundary layer is too weak (in the presence of low-tropospheric easterlies), even if the total rainfall amount and vertical structure of diabatic heating in Amazonia are well reproduced. There can certainly be other causes. One of those could be the bias in diabatic heating over the tropical Atlantic related to the erroneous southward shift of the ITCZ. We tried to identify a relation between the ITCZ bias and the westerly bias in the AMIP2 models we diagnosed but found none.

The results from this study lay the foundation for our hypothesis, not its proof. Further diagnoses and modeling work, as well as reliable observations of diabatic heating profiles over Amazonia and boundary layer entrainment over the equatorial Atlantic Ocean, are needed to test our hypothesis. We have conducted numerical simulations using a regional mesoscale atmospheric model covering the tropical Atlantic, South America, and Africa. When the diabatic heating profiles over Amazonia were modified to be weaker in the lower troposphere, the model produced more severe westerly bias over the equatorial Atlantic. This result is expected. It is consistent to previous studies that examined the sensitivity of the vertical structure of the atmospheric large-scale circulation to vertical heating profiles (Hartmann et al. 1984; Wu et al. 2000; Wu 2003; Schumacher et al. 2004; Li et al. 2009; Zhang and Hagos 2009). Our experiments showed insensitivity of westerly bias to the diabatic heating profiles and precipitation amounts over equatorial West Africa, consistent to Chang et al. (2008). It would be interesting to investigate the sensitivity of the westerly bias to boundary layer parameterization schemes with different efficiencies of vertical momentum mixing.

The implication of our results is that there might be no simple or single remedy for the westerly bias in GCMs. This may be why this problem has been so stubborn and persistent up to the new generation of CMIP5 models. Efforts of advancing models in a holistic way must continue before this problem is completely solved.

Acknowledgments

The authors thank three anonymous reviewers for their careful and critical comments on this study. The authors also benefitted from discussions with Courtney Schumacher and Ben Kirtman on this work. The Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the World Climate Research Program (WCRP) Working Group on Coupled Modeling (WGCM) organized the CMIP3 and CMIP5. The U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provided coordinating support for CMIP and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. Appreciations also go to the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output. The CMAP data were downloaded from the website of NOAA/OAR/ESLR/PSD (http://www.esrl.noaa.gov/psd/). This study was supported by NSF Grants ATM-0739402, AGS-1062202, and AGS1062202, NOAA Grants NA08OAR4320889 and NA17RJ1226, and DOE Grant SC0006808.

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1

Richter and Xie (2008) did not calculate the correlation between Amazonian rainfall and westerly biases in the models.

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