Abstract

As key variables in general circulation models, precipitation and moisture in four leading models from CMIP5 (phase 5 of the Coupled Model Intercomparison Project) are analyzed, with a focus on four tropical oceanic regions. It is found that precipitation in these models is overestimated in most areas. However, moisture bias has large intermodel differences. The model biases in precipitation and moisture are further examined in conjunction with large-scale circulation by regime-sorting analysis. Results show that all models consistently overestimate the frequency of occurrence of strong upward motion regimes and peak descending regimes of 500-hPa vertical velocity . In a given regime, models produce too much precipitation compared to observation and reanalysis. But for moisture, their biases differ from model to model and also from level to level. Furthermore, error causes are revealed through decomposing contribution biases into dynamic and thermodynamic components. For precipitation, the contribution errors in strong upward motion regimes are attributed to the overly frequent . In the weak upward motion regime, the biases in the dependence of precipitation on and the probability density function (PDF) make comparable contributions, but often of opposite signs. On the other hand, the biases in column-integrated water vapor contribution are mainly due to errors in the frequency of occurrence of , while thermodynamic components contribute little. These findings suggest that errors in the frequency of occurrence are a significant cause of biases in the precipitation and moisture simulation.

1. Introduction

General circulation models (GCMs) are important tools for simulating climate changes under different scenarios, and for a better understanding of historical and future climates. Although many efforts have been made to improve the performance of GCMs through improving model physical parameterizations (Richter and Rasch 2008; Neale et al. 2008) or increasing model resolutions (Reichler and Kim 2008), notable model errors still exist in state-of-the-art models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012; Sheffield et al. 2013a,b; Sun et al. 2016, among others).

Many studies have investigated the model biases in precipitation and water vapor simulation separately, particularly in tropical regions. For coupled models, they revealed that most models still suffered from the well-known double-ITCZ (intertropical convergence zone) problem accompanied by cold tongue bias at the equator (e.g., Mechoso et al. 1995; Meehl et al. 2005; Sun et al. 2006; Sun et al. 2009; Zhang and Song 2010; Sun et al. 2013; Hirota and Takayabu 2013; Tian 2015). Besides, the simulated precipitation amount also has large biases in GCMs although they vary from model to model. Liu et al. (2014) studied the continental precipitation of 34 CMIP5 models and showed that at global scale all models overestimated the total precipitation amount and large intermodel spread existed in selected tropical regions, particularly in winter season. Yin et al. (2013) evaluated 11 CMIP5 models and found that most models overestimated rainfall associated with the Atlantic ITCZ or the eastern Pacific ITCZ. Stanfield et al. (2015) demonstrated that GCMs tend to overestimate precipitation compared to Global Precipitation Climatology Project (GPCP) and Tropical Rainfall Measuring Mission (TRMM) observations. Also, some systematic errors have been found in moisture when compared with satellite observations and reanalysis data (e.g., Soden and Bretherton 1994; Bates and Jackson 1997; Allan et al. 2003; Brogniez et al. 2005; Pierce et al. 2006; John and Soden 2007; Jiang et al. 2012). These studies found that most models have a dry bias in the tropics and a moist bias in subtropical areas. John and Soden (2007) analyzed 16 CMIP3 model results globally and showed that water vapor has a dry bias in the boundary layer and a large moist bias in the free troposphere. On the other hand, Tian et al. (2013) showed that CMIP5 models are too dry in the whole tropical troposphere but too moist in the extratropical troposphere compared to NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) data.

Precipitation is tightly related to water vapor in the atmosphere. Thus, biases in precipitation are likely related to biases in water vapor in GCMs. Bretherton et al. (2004) found an exponential relationship between water vapor path and precipitation. Vertically, a high correlation is found between rainfall and moisture variability in the free troposphere and a low correlation is found in the boundary layer (Bretherton et al. 2004; Holloway and Neelin 2009). Furthermore, Li et al. (2014) found that the underestimation of specific humidity mostly occurred over strongly convective regions of the tropics, such as the warm pool, the ITCZ, the South Pacific convergence zone (SPCZ), and convectively active continental regions. This suggests that water vapor and precipitation are closely associated with deep convection, which in turn interacts strongly with large-scale circulation (e.g., Gill 1980; Lau et al.1997; Hirota et al. 2011; Oueslati and Bellon 2013a,b). Because of this, a number of researchers have tried to evaluate GCM performance by using the regime sorting proposed by Bony et al. (2004), which provides a concise metric for measuring systematic errors in the representation of the coupling between the large-scale circulation and precipitation (e.g., Bellucci et al. 2010; Hirota et al. 2011), as well as cloud properties (e.g., Su et al. 2008; Su et al. 2013). It facilitates the investigation of model errors associated with different large-scale circulation conditions. Bellucci et al. (2010) used this method to identify the cause of anomalous rainfall in southeastern Pacific (double-ITCZ regions) in several coupled models. They found that the overly frequent deep convection activities amplified the double-ITCZ problem in the coupled models, whereas errors in precipitation magnitude within each regime already exist in the corresponding atmosphere models. Their findings were confirmed by Oueslati and Bellon (2015), who analyzed the double-ITCZ bias in 17 coupled models in CMIP5 and their corresponding AMIP simulations. Furthermore, they decomposed the precipitation contribution error into dynamic (error in large-scale circulation) and thermodynamic (error in precipitation within each regime) components following Bony et al. (2004). Their results suggested that precipitation errors in double-ITCZ regions were mainly from weak-to-moderate ascending regimes, where model errors were controlled by errors in probability distribution frequency of vertical motion rather than errors in precipitation intensity within each regime.

Although these studies showed systematic biases in precipitation and water vapor in GCMs and shed light on their underlying causes, further studies are needed for a deeper and more systematic understanding of the causes of the model errors to improve the performance and fidelity of the model simulations. Following previous work and methodology, in this study we examine the simulated precipitation and humidity biases in four leading CMIP5 coupled models, and their corresponding AMIP simulations. Different from previous work, we investigate precipitation and moisture jointly and focus on tropical oceans where deep convection occurs most frequently. We further divide the tropical oceans into four regions—the tropical Pacific ITCZ, the SPCZ, the Indian Ocean, and the Atlantic ITCZ—as we are interested in finding out whether there are significant regional differences; if there are, we hope that these differences can be used to better understand the causes of the precipitation and humidity biases. We will apply the regime sorting method of Bony et al. (2004) to better understand the role of large-scale circulation in precipitation and humidity biases. For a detailed understanding of model biases, we also attempt to address the question whether the biases in precipitation and humidity are caused by errors in the frequency of vertical velocity at 500 hPa or errors in precipitation and humidity within different regimes of large-scale circulation, through the decomposition analysis following Bony et al. (2004) [also see Oueslati and Bellon (2015)].

In the following section, we briefly describe the model and observation data used in our analysis, as well as the regime-sorting and decomposition methodology. In section 3, an evaluation of models’ performance in precipitation and humidity is conducted. In section 4, we dissect the sensitivity of model biases in precipitation and humidity to the large-scale circulation by using a regime sorting method. In section 5, we decompose the precipitation and humidity biases into dynamic and thermodynamic components to identify the main source for those biases. The concluding remarks are provided in section 6.

2. Data and method

This study employs the fully coupled simulations as well as the corresponding atmosphere-only runs from four leading CMIP5 models over the period 1996–2005. These four models can generally represent the leading general circulation models in the world. They are, respectively, the Community Climate System Model version 4 (CCSM4) of the National Center for Atmospheric Research (Neale et al. 2010), the HadGEM2-ES and HadGEM2-A from the Met Office and the Hadley Center (Collins et al. 2011; Jones et al. 2011), the GFDL-CM3 from the Geophysical Fluid Dynamics Laboratory (Donner et al. 2011; Griffies et al. 2011), and MPI-ESM-MR from the Max Planck Institute for Meteorology (Giorgetta et al. 2013). The atmosphere-only runs have the sea surface temperatures and sea ice prescribed to the observed values (hereafter referred to as AMIP runs). The fully coupled simulations are the historical runs with only the external radiative forcing prescribed (hereafter referred to as CMIP runs; Taylor et al. 2012). More details about the models including spatial resolutions and the parameterization schemes for convection are given in Table 1.

Table 1.

List of models participating in this study. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)

List of models participating in this study. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)
List of models participating in this study. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)

The variables for analysis include monthly mean precipitation, vertical velocity at 500 hPa and specific humidity q at 10 levels (1000, 925, 850, 700, 600, 500, 400, 300, 250, and 200 hPa). ERA-Interim (hereinafter ERA-I) reanalysis data, for the same variables and same time period (1996–2005), are used for comparison with the simulations by the models. The resolution of reanalysis data is 2.5° × 2.5°. Since precipitation from the reanalysis data is largely a model product, we also analyzed Tropical Rainfall Measuring Mission 3A12 precipitation data for a more precise comparison. Because of the time limitation of TRMM data, we use 1998–2007 for our study. Note that the TRMM data are interpolated into the same resolution as ERA-I in the regime-sorting analysis. To validate the ERA-I humidity data, we used monthly integrated water vapor (IWV) data from the Special Sensor Microwave Imager (SSM/I; Wentz et al. 2012) produced by Remote Sensing Systems (RSS), which are available at www.remss.com/missions/ssmi.

We focus on the oceanic regions in the tropics, where the most active convection occurs climatologically. Since large-scale circulation and physical processes may differ over different ocean basins, the analysis area is divided into four regions, the Pacific ITCZ (0°–20°N, 120°E–90°W; orange box in Fig. 1a), the SPCZ (0°–20°S, 140°E–150°W; red box in Fig. 1a), the Indian Ocean (15°N–30°S, 50°–110°E; yellow box in Fig. 1a), and the Atlantic ITCZ (15°N–5°S, 50°W–20°E; magenta box in Fig. 1a).

Fig. 1.

Annual mean precipitation distribution of (a) TRMM data (1998–2007), (b) ERA-Interim reanalysis data (1996–2005), and models’ difference (1996–2005) from TRMM data for the (c) CCSM4 coupled model, (d) CCSM4 atmosphere-only model, (e) GFDL-CM3 coupled model, (f) GFDL-CM3 atmosphere-only model, (g) HadGEM2-ES coupled model, (h) HadGEM2-A atmosphere-only model, (i) MPI-ESM-MR coupled model, and (j) MPI-ESM-MR atmosphere-only model. Four analyzed regions in this study are marked in (a), including the Pacific ITCZ (orange box), SPCZ (red box), Indian Ocean (yellow box), and Atlantic ITCZ (magenta box) regions.

Fig. 1.

Annual mean precipitation distribution of (a) TRMM data (1998–2007), (b) ERA-Interim reanalysis data (1996–2005), and models’ difference (1996–2005) from TRMM data for the (c) CCSM4 coupled model, (d) CCSM4 atmosphere-only model, (e) GFDL-CM3 coupled model, (f) GFDL-CM3 atmosphere-only model, (g) HadGEM2-ES coupled model, (h) HadGEM2-A atmosphere-only model, (i) MPI-ESM-MR coupled model, and (j) MPI-ESM-MR atmosphere-only model. Four analyzed regions in this study are marked in (a), including the Pacific ITCZ (orange box), SPCZ (red box), Indian Ocean (yellow box), and Atlantic ITCZ (magenta box) regions.

For regime-sorted analysis, we use the monthly-mean midtropospheric (500 hPa) vertical velocity as a proxy for large-scale ascent or descent . Before examining the relationship among large-scale circulation, precipitation and humidity, we calculate the probability density function (PDF) of , using an interval of 0.01 Pa s−1. Defining the PDF of as , where refers to , then one has

 
formula

In our specific case, the lower and upper limits use the minimum and maximum of for each given region. Results are shown for the range −0.25 to 0.15 Pa s−1, which covers over 99.95% of data.

We then relate precipitation and humidity to large-scale circulation by binning them against . More specifically, the total precipitation in a region, say the ITCZ region, can be viewed as functions of . For each bin, the mean precipitation within that bin Prec(ω) can be obtained. The total precipitation can be written as

 
formula

where the summation is over all bins. To get reliable results of statistical significance, those with mean precipitation that falls within bins where PDF is lower than 0.01% are neglected. The contribution of precipitation from a given bin to the total regional mean precipitation is For model simulations, both and are obtained from model outputs. For ERA-I, and are obtained in the same way as they are obtained from the models. However, when TRMM precipitation is used, we first interpolate TRMM data into the same resolution as the ERA-I data (2.5° × 2.5°), and then collocate the interpolated TRMM data with the ERA-I data. The period of ERA-I data we used here is set to the same period as the TRMM data (1998–2007). We then calculate the bin-averaged precipitation for each bin from the ERA-I data . For moisture, in addition to the average specific humidity at each level within each regime , the column integrated water vapor

 
formula

is also used to represent the moisture condition. Similar to precipitation, the contribution at a given bin is given by .

To identify the causes of model errors in precipitation and moisture, we calculate the biases of precipitation contributions from each bin to the total precipitation: Here the subscript ERA signifies that the PDF of is obtained from the ERA-I data for the period 1996–2005 to make it consistent with model data. The PDFs of in the period 1998–2007 and 1996–2005 are almost the same, so are trustable for use as a reference standard. Then, this difference can be decomposed to bias in Prec and bias in the PDF of for each bin:

 
formula

Similarly, for IWV

 
formula

where indicates the difference between model results and ERA-I reanalysis data (or TRMM for precipitation). As shown in Eqs. (4) and (5), model errors in precipitation and moisture are decomposed into three components. The first term is the dynamic component, representing errors arising from model bias in frequency. This term is associated with model circulation biases. The second term is the thermodynamic component, representing errors caused by the model biases in mean precipitation/IWV at each bin; it is related to simulation bias in hydrological processes. The third term can be regarded as the covariance component, due to combined errors from biases in frequency and mean precipitation/IWV at each bin.

3. Evaluation of simulations in precipitation and humidity

Tropical annual mean precipitation distributions from observations and the simulations by the four chosen CMIP5 models are shown in Fig. 1. Figure 1a shows the observed precipitation from TRMM. Figure 1b is the precipitation from the ERA-I reanalysis. The precipitations from the simulations by the four models—both the CMIP and the AMIP simulations—are presented as the differences from the TRMM data (Figs. 1c–h). The four oceanic regions we have chosen for the present study are marked by the boxes in Fig. 1a. Compared with TRMM data (Fig. 1a), ERA-I reanalysis data (Fig. 1b) show a significantly stronger tropical precipitation in the Indo-Pacific warm pool region. The differences between these two datasets underscore the fact that precipitation in reanalysis data is largely a by-product of model physics parameterizations (Dee et al. 2011). Thus we measure the model biases from the differences between the model simulations and the TRMM observations.

From Figs. 1c, 1e, 1g, and 1i, we see that all CMIP coupled models suffer from the double-ITCZ problem in the Pacific—too little precipitation along the equator and too much precipitation on the off-equatorial regions in both hemispheres. On the other hand, although AMIP models (Figs. 1d,f,h,j) have a less severe double-ITCZ problem, they overestimate precipitation in most tropical regions.

In the Indian Ocean, the differences in precipitation distribution between CMIP and AMIP are relatively small. But they differ from the observations considerably. The observed precipitation is mainly located in the eastern part of the Indian Ocean along the equator (Figs. 1a). Three of the four models (except CCSM4), in both the AMIP and CMIP runs, overestimate the precipitation amount in the western and central equatorial Indian Ocean. MPI-ESM-MR has a more realistic precipitation center but has an excessive precipitation amount. Unlike in the Pacific Ocean, coupled ocean–atmosphere feedback has much less impact on precipitation simulation in the Indian Ocean.

In the Atlantic ITCZ region (the magenta box in Fig. 1a), similar to the double-ITCZ problem in the Pacific Ocean, all four CMIP models produce a spurious precipitation band south of the equator, leading to negative precipitation biases along the equator and positive biases south of the equator as shown in Figs. 1c, 1e, and 1i. This deficiency also exists in AMIP runs but with smaller amplitude, underscoring an earlier finding by Lin (2007) that the coupled ocean–atmosphere feedbacks are responsible for most of the double-ITCZ bias not only in the Pacific but also in the Atlantic.

Figure 2 shows the IWV distribution of ERA-I (Fig. 2a), SSM/I (Fig. 2b), and model biases from ERA-I reanalysis data (Figs. 2c–j). Compared with SSM/I passive microwave data, the IWV computed from ERA-I reanalysis has a similar distribution. Although the magnitude of ERA-I IWV is slightly larger than that in SSM/I (no greater than 4 kg m−2), the difference between these two datasets has little spatial variation. Thus, in our further analysis, we will only focus on model IWV biases from ERA-I reanalysis data. The variation of atmospheric water vapor is largely controlled by sea surface temperature (SST). This relationship was confirmed both by radiosonde data and model outputs (e.g., Sun and Oort 1995; Wentz and Schabel 2000; Soden et al. 2005; Trenberth et al. 2005). The patterns of IWV biases in CMIP models are similar to the SST biases (not shown here). However, from our AMIP results (Figs. 2d,f,h,j), where models were forced by observed SST, biases in IWV still exist. This indicates that besides SST, other factors also contribute to IWV biases in the models. Unlike precipitation biases in the models (whose patterns look very similar across the models), biases in IWV vary from model to model in their patterns. Despite a strong relationship between moisture and precipitation in observations (e.g., Bretherton et al. 2004), IWV biases in the models do not correspond well to the precipitation biases. This also indicates that the relationships between IWV and precipitation are not simulated well in the models. Figure 3 shows the relationship between precipitation and IWV (binned at 1 kg m−2 interval) for the models and the observation. It is found that precipitation has exponential relationship with IWV, consistent with the findings from Bretherton et al. (2004) and Peters and Neelin (2006). The differences between TRMM and ERA-I results here serve as a measure of uncertainty in reanalysis precipitation data. In all four regions chosen for the analysis of AMIP and CMIP runs, precipitation–IWV relationships in models deviate from observations, although the differences vary from model to model. Little regional difference is observed. All models produce too much precipitation for the given IWV under moist conditions (IWV > 45 kg m−2). The largest biases are found in the HadGEM2-ES/A (blue line in Fig. 3), explaining why the spatial biases in precipitation and IWV are opposite in that model. On the other hand, since the GFDL model has the most realistic simulations of the IWV–precipitation relationships, its biases in precipitation have the most consistent distribution with the IWV bias among models.

Fig. 2.

Integrated water vapor distribution of (a) ERA-Interim reanalysis data, (b) SSM/I data, and the models’ difference from ERA-Interim reanalysis data for the (c) CCSM4 coupled, (d) CCSM4 atmosphere-only, (e) GFDL-CM3 coupled, (f) GFDL-CM3 atmosphere-only, (g) HadGEM2-ES coupled, (h) HadGEM2-A atmosphere-only, (i) MPI-ESM-MR coupled, and (j) MPI-ESM-MR atmosphere-only models.

Fig. 2.

Integrated water vapor distribution of (a) ERA-Interim reanalysis data, (b) SSM/I data, and the models’ difference from ERA-Interim reanalysis data for the (c) CCSM4 coupled, (d) CCSM4 atmosphere-only, (e) GFDL-CM3 coupled, (f) GFDL-CM3 atmosphere-only, (g) HadGEM2-ES coupled, (h) HadGEM2-A atmosphere-only, (i) MPI-ESM-MR coupled, and (j) MPI-ESM-MR atmosphere-only models.

Fig. 3.

Monthly mean precipitation binned by IWV with 1 kg m−2 interval for (a) AMIP and ERA-Interim reanalysis and (b) CMIP and ERA-Interim reanalysis in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 3.

Monthly mean precipitation binned by IWV with 1 kg m−2 interval for (a) AMIP and ERA-Interim reanalysis and (b) CMIP and ERA-Interim reanalysis in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Biases in the IWV in the four chosen regions are further examined through looking at the biases in the vertical structure of specific humidity, which are shown in Fig. 4. The results of AMIP and CMIP are found similar, so only the CMIP results are presented. In CCSM4, there is a moist bias throughout the troposphere in all regions, particularly at the surface and in midtroposphere. On the other hand, HadGEM2-ES has a dry bias at every level in all regions, especially in the lower troposphere. The GFDL-CM3 model exhibits a large dry bias in the lower troposphere below 800 hPa and a relatively small moist bias in the upper troposphere. MPI-ESM-MR shows different moisture bias in different regions in the lower troposphere, but a common dry bias above 600 hPa for all the regions.

Fig. 4.

Vertical structure of specific humidity bias from ERA-Interim reanalysis data for CMIP models, including (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the Pacific ITCZ (red lines), SPCZ (green lines), Indian Ocean (blue lines), and Atlantic ITCZ (yellow lines) regions.

Fig. 4.

Vertical structure of specific humidity bias from ERA-Interim reanalysis data for CMIP models, including (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the Pacific ITCZ (red lines), SPCZ (green lines), Indian Ocean (blue lines), and Atlantic ITCZ (yellow lines) regions.

4. Regime dependence of model biases in precipitation and humidity

The above analysis reveals model biases in precipitation, humidity, and the IWV–precipitation relationship. The results indicate that the hydrological processes are not simulated well in these four leading CMIP5 models. Because of the strong interaction among precipitation, moisture, and large-scale circulation, in this section we examine model biases from the perspective of dynamical processes—large-scale circulation. We will investigate precipitation and moisture biases in different circulation regimes since the time-mean fields shown in the previous section cannot reveal the cancellation of compensating errors. Thus, this regime-dependence analysis is necessary to help to untangle model biases and identify their causes.

Toward this goal, we first evaluate how well the models simulate the large-scale atmospheric circulation. Figure 5a shows the annual mean vertical velocity at 500 hPa in ERA-I reanalysis data. Large-scale upward motions are located at Indo-Pacific warm pool regions, corresponding well with regions of large precipitation and IWV amount. Model differences from ERA-I in are presented in Figs. 5b–i. Positive biases (blue shadings) indicate that models simulate too weak upward motions or too strong downward motions, whereas negative biases (red shadings) indicate too strong upward motions or too weak downward motions. All models except CCSM4, for both AMIP and CMIP runs, produce too strong upward motion in the western and central Indian Ocean. In the Pacific and Atlantic Ocean, due to the double-ITCZ problem in the coupled models, all CMIP runs produce a stronger downward motion band along equator and two parallel stronger upward motion regions on both sides of the equator. This bias disappears in AMIP runs. However, AMIP runs of different models show different biases in ω500. Especially in the SPCZ region, the CCSM4 and GFDL models produce weaker upward motions than ERA-I, while HadGEM2-A and MPI-ESM-MR have stronger upward motions. This indicates that may respond differently to SST forcing in different models. Here we further examine this response in four oceanic regions. We computed the average within each SST bin from 292 to 305 K, with a 0.5-K interval, for CMIP runs, AMIP runs, and ERA-I, respectively. The results are presented in Fig. 6. They show that the responses of large-scale circulation to SST are different among the models, and model biases are more noticeable in the CMIP runs than in the AMIP runs. In the AMIP runs, all the model results are closer to ERA-I than in the CMIP runs. This is expected as the AMIP runs are forced by the observed SST conditions and coupled ocean–atmosphere interaction is not involved, which often amplifies the errors. The responses are more diverse in the CMIP and intermodel differences are much larger. In the GFDL-CM3 and the HadGEM2-A/ES models, ocean–atmosphere coupling makes the onset of large-scale ascending motion happen at a lower SST than in ERA-I, whereas in CCSM4 and MPI-ESM-MR the corresponding SST value at which large-scale circulation changes from downward to upward is similar in CMIP to that in AMIP. In addition, the relationship between and SST is different in different ocean basins. Under the high SST conditions, stronger upward motions are produced in the Pacific ITCZ and SPCZ than in the Indian Ocean or Atlantic ITCZ. Large-scale downward motions happening at the lower SST value are stronger in the Indian Ocean than in other regions.

Fig. 5.

Annual mean vertical velocity at 500 hPa of (a) ERA-I reanalysis data, and models’ difference from ERA-I for the (b) CCSM4 coupled, (c) CCSM4 atmosphere-only, (d) GFDL-CM3 coupled, (e) GFDL-CM3 atmosphere-only, (f) HadGEM2-ES coupled, (g) HadGEM2-A atmosphere-only, (h) MPI-ESM-MR coupled, and (i) MPI-ESM-MR atmosphere-only models.

Fig. 5.

Annual mean vertical velocity at 500 hPa of (a) ERA-I reanalysis data, and models’ difference from ERA-I for the (b) CCSM4 coupled, (c) CCSM4 atmosphere-only, (d) GFDL-CM3 coupled, (e) GFDL-CM3 atmosphere-only, (f) HadGEM2-ES coupled, (g) HadGEM2-A atmosphere-only, (h) MPI-ESM-MR coupled, and (i) MPI-ESM-MR atmosphere-only models.

Fig. 6.

Mean as a function of SST for (a) AMIP and ERA-I reanalysis and (b) CMIP and ERA-I reanalysis in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 6.

Mean as a function of SST for (a) AMIP and ERA-I reanalysis and (b) CMIP and ERA-I reanalysis in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Before investigating the model biases in precipitation and IWV in different large-scale circulations, we examine how models simulate the relationship among precipitation, IWV, and large-scale circulation . Figure 7 shows the joint pdf of precipitation intensity dependence on IWV and for ERA-I–TRMM combined data and four CMIP models. The precipitation is binned by IWV at 1 kg m−2 intervals and by at 0.01 Pa s−1 intervals. It has a tilted structure from the bottom-right corner to the top-left corner in observations. These results confirm that both large-scale circulation and IWV are indispensable factors for precipitation production. Weak precipitation (smaller than 2 mm day−1) is produced in downward motion and low IWV regimes. Precipitation increases with increasing intensity of upward motion and increasing amount of IWV in the atmosphere. Little regional difference is found, except in the Atlantic ITCZ region where higher column-integrated water vapor is needed to produce the weak precipitation in the weakly upward motion regimes than in the other three regions. All four models can simulate this structure well. As pointed out in section 3, models simulate too much precipitation in high-IWV regimes. From Fig. 7, it is clear that precipitation is overestimated in the high-IWV and upward motion regimes in all four models. For a given upward motion, less IWV is required to produce the same precipitation intensity in models than in the observation. The HadGEM2-ES is drier than other models in upward motion regimes, especially in SPCZ, Indian Ocean and Atlantic ITCZ regions, with no values of IWV above 56 kg m−2. This is consistent with the IWV distribution results seen in section 3. Obviously, the relationships among precipitation, IWV, and large-scale circulation are not simulated well in models. Especially in the upward motion regimes, the model biases are larger than those in the downward motion regimes.

Fig. 7.

The joint distribution of precipitation as a function of and IWV for (a) ERA-Interim–TRMM combined data, (b) CCSM4, (c) GFDL-CM3, (d) HadGEM2-ES, and (e) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 7.

The joint distribution of precipitation as a function of and IWV for (a) ERA-Interim–TRMM combined data, (b) CCSM4, (c) GFDL-CM3, (d) HadGEM2-ES, and (e) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Next, we will look into the dependence of precipitation and IWV on large-scale circulation separately. But first we will examine how well the dynamic regimes (as represented by ) are simulated in the CMIP (Fig. 8a) and AMIP runs. Although the dependence of on SST and the spatial distribution of bias are different between the CMIP and AMIP runs, in all the studied regions the frequencies of occurrence of large-scale circulation are similar (for brevity, only CMIP results are shown here). This similarity indicates that the atmosphere–ocean coupling and the control of SST may have influence on the spatial distribution of , but the biases in the intensity and frequency of are a problem independent of the atmosphere–ocean coupling. The PDF of has its peak in the weakly subsiding regimes at 0.02 Pa s−1. A broad secondary peak occurs in the moderate ascent regimes (roughly from 0 to −0.05 Pa s−1). Different responses of to SST in the different regions have an impact on the PDF pattern especially in its tail region. We can see that the PDF values in the regime where is stronger than −0.06 Pa s−1 are larger in the Pacific ITCZ and SPCZ than in the other two regions, and that PDF values in the regime where downward is stronger than 0.04 Pa s−1 are larger in the Indian Ocean. Most models simulate a similar PDF pattern to ERA-I, but overestimate the occurrence of the dominant weakly subsiding regimes (around 0.02 Pa s−1) and strong ascending motion . Similar results were found by Bellucci et al. (2010) and Oueslati and Bellon (2015) in the double-ITCZ region. From this regime-sorting analysis, more information that cannot be seen in the geographical distribution is revealed. For example, in the SPCZ region, all models overestimate the frequency of downward motion stronger than 0.02 Pa s−1. This overestimation was compensated by the overestimation in the frequency of the strong upward motion in HadGEM2-A and MPI-ESM-MR. This cancellation results in a stronger mean upward motion in the SPCZ. On the other hand, CCSM4 and GFDL-CM3 simulate the PDF of upward motion well. Thus, they show a weaker upward motion mean state. The precipitation dependence on as shown in Fig. 8b underscores the control of large-scale circulation on precipitation. Stronger large-scale ascending motions correspond to stronger convection, and thus lead to larger precipitation. TRMM–ERA combined results have relatively less precipitation in the strong upward motion regimes in the Indian Ocean and the Atlantic ITCZ than in the Pacific ITCZ and SPCZ. This indicates that other than circulation, factors such as SST, temperature, or humidity can also have important influences on precipitation under strong upward motion condition. All coupled models, as well as the reanalysis data, overestimate the sensitivity of precipitation to large-scale circulation, especially in strong ascending regimes. This is consistent with results from Fig. 7. For a given upward motion strength, there is more precipitation in models than in observations and the reanalysis data in all regions. Intermodel spread is large in ascending motion regimes stronger than −0.12 Pa s−1, probably a consequence of different model representation of deep convection. Shown in Fig. 8c are contributions to total precipitation from each bin for each model as well as for the reanalysis data and TRMM observations in the four regions. Similar to TRMM observations and ERA-I reanalysis, all models show large contribution to precipitation in weakly ascending regimes . However, CCSM4 and GFDL-CM3 tend to overestimate the peak contribution while MPI-ESM-MR and HadGEM2-ES slightly underestimate it in the Pacific ITCZ, SPCZ, and the Indian Ocean. In the Atlantic ITCZ all models underestimate the peak precipitation contribution in weakly upward motion regimes. For upward motion regimes with , all models greatly overestimate contributions to precipitation in all four regions. Both the positive bias in the frequency of occurrence of intense upward motion (Fig. 8a) and the stronger than observed dependence of precipitation on 500-hPa vertical velocity (Fig. 8b) are responsible for these excessive contributions. In the weak subsidence regime, there is also a considerable amount of contribution to the total precipitation, probably associated with shallow convection. All four models simulate the contribution well in these weak subsidence regimes.

Fig. 8.

The (a) PDF of , (b) mean precipitation as a function of and (c) contribution to the mean precipitation as a function of for observations and CMIP model outputs in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 8.

The (a) PDF of , (b) mean precipitation as a function of and (c) contribution to the mean precipitation as a function of for observations and CMIP model outputs in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Figure 9 shows the variation of the mean IWV as a function of and the contributions to IWV from different circulation regimes as measured by . The IWV increases from downward motion regimes toward the upward motion regimes and the increase plateaus off when reaches about −0.06 Pa s−1. In all four regions, the atmosphere in HadGEM2-ES is the driest in the upward motion regimes among the four models, and the GFDL-CM3 is the closest to the ERA-I reanalysis. All models have too much contribution to IWV in strong ascending regimes and weak descending regime (roughly from 0.02 to 0.04 Pa s−1). Most models do not have enough contribution to IWV in the weakly ascending regimes .

Fig. 9.

(a) Mean integrated water vapor (IWV) and (b) the contribution to mean IWV as a function of for ERA-Interim reanalysis data and CMIP5 model outputs in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 9.

(a) Mean integrated water vapor (IWV) and (b) the contribution to mean IWV as a function of for ERA-Interim reanalysis data and CMIP5 model outputs in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

To gain further insights into the vertical distribution of moisture biases and its relationship to large-scale circulation, we examine the vertical structure of specific humidity in each regime. The differences between the results from the models and ERA-I are shown in Fig. 10. The vertical structure of model biases and their dependence on dynamic regimes vary from model to model. The CCSM4 shows a moist bias throughout the troposphere in the descending regime in three of the four regions (except the Atlantic ITCZ region). In the ascending regime, the CCSM4 has a moist bias in the planetary boundary layer (PBL) and midtroposphere and a dry bias in the lower troposphere above the PBL. The GFDL-CM3 has the smallest bias in most of the dynamic regimes, although it also has a noticeable dry bias in the lower troposphere and moist bias in the middle and upper troposphere in ascending motion regimes. The HadGEM2-ES and MPI-ESM-MR have very similar moisture bias structures in all dynamic regimes. Both models have a dry bias throughout the troposphere in the upward motion regimes and moist bias in descending motion regimes. The moist bias is larger in the MPI-ESM-MR model and dry bias is larger in the HadGEM2-ES model.

Fig. 10.

Vertical distribution of specific humidity bias (g kg−1) from ERA-Interim as a function of for CMIP model outputs in (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

Fig. 10.

Vertical distribution of specific humidity bias (g kg−1) from ERA-Interim as a function of for CMIP model outputs in (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions.

5. Attribution of model bias to dynamic and thermodynamic components

In the previous section, we have examined the model biases under different large-scale circulation conditions. Both the frequency of occurrence of and the dependence of precipitation and humidity on are found to contribute to model precipitation and humidity biases. In this section, we attempt to attribute the contribution biases to the dynamic and thermodynamic factors. From Eqs. (7) and (8), biases in contributions to precipitation and IWV in a given circulation regime can be decomposed into three components: bias in the frequency of occurrence of that regime (dynamic component), bias in the mean precipitation or IWV corresponding to that regime (thermodynamic component), and the covariance of the two biases (nonlinear component).

Figure 11 presents the three components for precipitation contribution bias in each bin. In general, the dynamic and thermodynamic components have comparable contributions to the bias, and the nonlinear component is relatively small. In strong ascending regimes , the positive precipitation bias is mainly due to errors in the dynamic component. In contrast, the contribution to the bias from the thermodynamic component is negligible. Strong upward motion occurs too frequently in the models, leading to an overestimated precipitation contribution. In weakly ascending or descending regimes, contributions from both the dynamic and thermodynamic components are important, although these two components often have the opposite signs. Mostly the dynamic contribution is negative, and the thermodynamic contribution is positive, with the former dominating over the latter in all models and regions except the GFDL model in the SPCZ region. Therefore, errors in the simulation of the occurrence of dynamic regimes are the dominant contributors to the precipitation biases in the models although excessive precipitation in a given regime also makes important contribution.

Fig. 11.

Decomposed terms of the model bias in precipitation contribution for (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions. The black line represents the model bias in precipitation contribution, the green line represents the dynamical component, the blue line represents the thermodynamic component, and the yellow line represents the covariance component.

Fig. 11.

Decomposed terms of the model bias in precipitation contribution for (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions. The black line represents the model bias in precipitation contribution, the green line represents the dynamical component, the blue line represents the thermodynamic component, and the yellow line represents the covariance component.

For the column-integrated water vapor, the biases are almost entirely controlled by the dynamic component in all regimes for all models (Fig. 12). However, caution should be exercised in interpreting this result. First, IWV is an integral of moisture content in all levels and small errors in IWV can be due to error cancellation at different levels. For instance, CCSM4 has a moist bias in the PBL and midtroposphere but a dry bias in the lower troposphere above the PBL in the ascending motion regimes. This is obscured in Fig. 12 because of error cancellation. Second, although the thermodynamic contribution is small to biases in IWV, moisture biases across the circulation regimes are still an important issue to address. For example, in HadGEM2-ES and MPI-ESM-MR, although the thermodynamic contributions are small, moisture biases in the troposphere in each bin (Figs. 10c,d) are large. Reducing these biases is by no means a scientifically trivial issue.

Fig. 12.

Decomposed terms of the model bias in the IWV contribution for (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions. The black line represents the model bias in the IWV contribution, the green line represents the dynamical component, the blue line represents the thermodynamic component, and the yellow line represents the covariance component.

Fig. 12.

Decomposed terms of the model bias in the IWV contribution for (a) CCSM4, (b) GFDL-CM3, (c) HadGEM2-ES, and (d) MPI-ESM-MR in the (left to right) Pacific ITCZ, SPCZ, Indian Ocean, and Atlantic ITCZ regions. The black line represents the model bias in the IWV contribution, the green line represents the dynamical component, the blue line represents the thermodynamic component, and the yellow line represents the covariance component.

6. Summary and conclusions

Global climate models such as those archived in CMIP5 are primary tools for studying the present climate and future climate projection. The reliability of these models depends critically on how accurately the precipitation and moisture fields are simulated. This study dissects biases in precipitation and moisture in four leading state-of-the-art climate models that participate in the IPCC (Intergovernmental Panel on Climate Change) assessment (IPCC 2013). We choose four tropical regions where deep convection dominates: the tropical Pacific ITCZ, the SPCZ, the Indian Ocean, and the Atlantic ITCZ.

All four models still suffer from the double-ITCZ problem in both the Pacific and Atlantic Ocean, with excessive precipitation on both sides of equator and insufficient precipitation along the equator. The amount of precipitation is overestimated in most of the areas studied, except some areas over the equator where precipitation is generally underestimated. The vertical structure of specific humidity is found to have large intermodel spread. Compared to ERA-I data, CCSM4 exhibits a moisture bias throughout the troposphere in all four regions while HadGEM2-ES has large dry biases. GFDL-CM3 has dry biases in the lower troposphere with little moist bias in the upper levels. Moisture biases in MPI-ESM-MR are region dependent, with moist bias in the Pacific ITCZ and dry bias in SPCZ in the lower half of the troposphere but dry bias in all regions above 600 hPa.

Results from regime-sorting analysis show that large-scale circulation is not well simulated in either the CMIP or their corresponding AMIP models. All models overestimate the frequency of occurrence of strong ascending motion and the peak frequency of descending motion ( around 0.02 Pa s−1). Precipitation is too sensitive to in each ascending motion regime, especially in strong upward motion regimes. For a given upward , there is too much precipitation compared to TRMM observations or ERA-I reanalysis in all models and regions, indicating that the hydrological cycle is too active in the models. This might be related to the fact that convection is too active in models. For moisture, biases vary from model to model. CCSM4 shows moist biases in descending or weakly ascending regimes, but moist biases in the PBL and midtroposphere and dry biases in the lower troposphere above the PBL in strong upward motion regimes. The GFDL model shows dry biases in the lower troposphere in all circulation regimes. The Hadley Center and Max-Planck Institute models show very similar structures of moisture biases, with moist bias in descending regimes and dry bias in ascending regimes. Further investigation is needed to identify the sources of these biases.

The errors in precipitation and column-integrated water vapor are decomposed into contributions from those related to dynamic circulation and thermodynamic factors for each regime. Under strong upward motion conditions, excessive precipitation contributions to total precipitation are mainly due to too frequent occurrence of this regime. In weakly ascending regimes, both dynamic and thermodynamic contributions, often of opposite signs, are important to the precipitation biases. The frequency of occurrence of weakly ascending regimes is underestimated in models, leading to insufficient contribution from these regimes to the total precipitation. This bias is largely offset by the positive precipitation bias under a given regime. For IWV, biases in contribution to total IWV from all regimes are almost all due to dynamic contribution, that is, the frequency of occurrence of each dynamic regime.

The errors in dynamical component (large-scale circulation) is the dominant cause for errors in precipitation and moisture in the models, especially in strong upward motion regimes. The error in thermodynamic component plays an important role in precipitation bias in weakly upward motion regimes but has little impact on moisture bias in all regimes. These results underscore the importance of accurately simulating the large-scale circulation in CMIP5 models.

Acknowledgments

This material is based upon work supported by the National Key Research and Development Program of China Grant 2017YFA0604000, the U.S. National Science Foundation Grant AGS-1549259, and the U.S. Department of Energy, Office of Science, Biological and Environmental Research Program (BER), under Award DE-SC0016504. De-Zheng Sun was in part supported by the U.S. National Science Foundation Grant AGS-1444489. The authors thank two anonymous reviewers for their constructive comments that helped improve the manuscript.

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