1 Introduction

The Yellow River and the Yangtze River are both known as “the cradle of Chinese civilization.” Since ancient times, people have lived alongside these two rivers, depending on them to irrigate crops and make a living. Even in modern times, China remains an agricultural country. Agricultural production in these two river basins is a very important component of total national production. It is widely known that climate conditions have tremendous impacts on agricultural production, and the conditions in the two basins are extremely sensitive. Hence, climate change in the basins has aroused recent concern (Jiang et al. 2009; Feng and Zhou 2012; Wei et al. 2012; Zhang et al. 2013). Since China is in the East Asian monsoon region, its climate is strongly influenced by a typical monsoon circulation. In summer, most parts of the country are affected by southwesterly surface winds accompanied by heavy rain. Precipitation is concentrated in summer, and water vapor transport is one of the most important components of the East Asian monsoon system (Zhou and Yu 2005). Therefore, understanding the long-term changes of summer precipitation and other hydrologic elements has been an issue of considerable urgency.

Climate models are fundamental for improving the understanding of the climate system and providing estimates of future climate change. The Coupled Model Intercomparison Project (CMIP) was established in 1995 under the auspices of the Working Group on Coupled Modelling (WGCM). The project provides a standard experimental protocol for studying the output of coupled atmosphere–ocean general circulation models (AOGCMs) and a community-based infrastructure in support of climate model diagnosis, validation, intercomparison, documentation, and data access. The latest version of this project is CMIP5, which was begun in September 2008 and is expected to provide valuable information to all three IPCC working groups (Taylor et al. 2012). Previous studies have made some progress in evaluating model performance of certain hydrological variables. Deng et al. (2013) evaluated spring and summer precipitation changes with nine CMIP5 models in the Yangtze River basin and found that the models generally simulated the annual cycle well but most overestimated precipitation, especially during January through June. Su et al. (2013) found that only half of 24 general circulation models (GCMs) were able to reproduce the observed seasonal patterns over the Tibetan Plateau. Kumar et al. (2013) analyzed 20th century precipitation trends by using 19 CMIP5 models. They found large uncertainties in simulation of local-scale precipitation trends. Huang et al. (2013) analyzed the uncertainty of simulated summer precipitation over eastern China through intercomparison of 14 CMIP5 models and a multi-model ensemble (MME). They indicated that the MME had the ability to reproduce summer precipitation in this region, but there was large model spread between models in terms of climatology and interannual variation. The authors argued a possible reason for this large spread was uncertainty in simulating large-scale circulation. Song et al. (2013) evaluated summer water vapor transport (WVT) and cross-equatorial flow across Asian–Australian monsoon regions as simulated by 22 AOGCMS. They revealed that most models produced reasonable representations of summer monsoon WVT, characterized by a southeast water vapor conveyor belt over the South Indian Ocean and a southwest belt from the Arabian Sea to East Asia. However, previous studies mainly focused on evaluations of individual hydrological variables and did not investigate whether models were able to capture the relationships among these variables and the possible regimes behind the results, which may be of great importance to the further development of the models.

In general, local evaporation and externally atmospheric water vapor transport are two main sources of precipitation in a specific region. Several studies have concurred that precipitation in a region is mainly dominated by water vapor transport (Benton et al. 1950; Trenberth 1999; Zhou and Yu 2005; Lin et al. 2014). However, no consensus has been reached for the relationship between precipitation and evaporation. Li et al. (2013) compared annual cycles of moisture supply over southwest and southeast China. They found that evaporation over these regions was significantly negatively correlated with precipitation in most months. Teuling et al. (2009) compared the correlation between yearly evaporation over land and precipitation for the period 1986–1995. They revealed that in very dry regions such as the Sahara, evaporation over land was positively correlated with precipitation. Such relations were also founded in the western part of Midwest US (water-limited) (Kumar et al. 2010). Nevertheless, the relationship between summer precipitation and evaporation in the Yellow River basin and the Yangtze River basin remains unclear.

In this study, we assess CMIP5 model simulations for the historical run from 1986–2005 over the Yellow and Yangtze River basins. We focus on intercomparison of individual model performance and investigate possible reasons for their differences. This paper is organized as follows. Section 2 describes datasets and analysis methods. Section 3 evaluates model performances of summer precipitation, evaporation, and water vapor transport from perspectives of climatological spatial distribution, interannual variations, and their relationships. Section 4 contains discussions, and conclusions are provided in section 5.

2 Study domain, data, and methodology

2.1 Analysis regions

Figure 1 shows the two analysis regions in this study. Region I comprises mainly the Yellow River basin (33–41°N and 100–119°E), and region II is mainly the Yangtze River basin (26–33°N and 100–119°E). In this study, we selected rectangular analysis regions instead of irregular realistic regions to facilitate the calculations of water vapor flux along the boundaries. Furthermore, these rectangular regions cover main areas of the river basins and are able to represent the same characteristics as those in the realistic regions. Thus, we believe that it is reasonable to choose these two rectangular analysis regions to represent the Yellow and Yangtze River basins, respectively.

Fig. 1
figure 1

Domain of the study regions. I: Yellow River basin (Yellow RB), II: Yangtze River basin (Yangtze RB)

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2.2 Datasets

Our evaluation is based on the results of 16 models that have participated in CMIP5 (data are available online at http://pcmdi9.llnl.gov/esgf-web-fe/). We used CMIP5 historical simulations in which all forcings have been applied to the models for the period 1986–2005. Table 1 provides basic information about the 16 models. The CMIP5 model output used in this study consists of monthly precipitation, evaporation, convective precipitation, geopotential height, zonal wind, meridional wind, specific humidity, and surface pressure.

Table 1 Information about CMIP5 climate models used
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To assess the skills of model simulations of the present climate, observational and reanalysis data were used as references to compare with model results. The observed precipitation is from gauge-based gridded data (Xie et al. 2007). Evaporation, geopotential height, and convective precipitation data are from ERA-Interim, which is the latest global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (Dee 2011), and its validity has been widely tested and verified in many previous studies (Feng and Zhou 2012; Sun and Wang 2013; Lin et al. 2014). Reference water vapor transport was calculated by monthly zonal wind, meridional wind, surface pressure, and specific humidity data from ERA-Interim. In addition, water vapor transport calculated from NCEP-US Department of Energy (DOE) Atmospheric Model Intercomparison Project II reanalysis (NCEP2) (Kanamitsu et al. 2002) was also used to verify the model results. All data were selected from the period 1986–2005 to correspond with the simulations.

2.3 Methodology

The general atmospheric water vapor balance equation can be expressed as (Schmitz and Mullen 1996)

$$ \frac{\partial W}{\partial t}=-\nabla \cdot \overrightarrow{Q}+E-P. $$
(1)

Here, \( \frac{\partial W}{\partial t} \) is the change in atmospheric water vapor storage, and W is the total precipitable water; E and P are the evaporation and precipitation, respectively; \( -\nabla \cdot \overrightarrow{Q} \) is the convergence of water vapor flux. This equation means that within a region changes in atmospheric water vapor storage, the convergence of water vapor flux, precipitation, and evaporation should be balanced. Besides, when considering relatively long periods such as over a month, the change in local water vapor term is usually small in comparison with the other terms (Brubaker et al. 1993), which is not analyzed in the present study.

The total water vapor flux can be separated into two parts: the stationary and transient components (Trenberth 1991). Previous studies found that stationary component dominated the total water vapor flux over East Asia while transient water vapor flux contributed little (Simmonds et al. 1999). Therefore, in our analysis, we focused on the stationary component.

We adopted the approach of Trenberth (1991) to calculate vertically integrated water vapor flux:

$$ \overrightarrow{Q}=-\frac{1}{g}{\displaystyle {\int}_{ps}^{pt}\overrightarrow{V}q}dp, $$
(2)

where q is the specific humidity, \( \overrightarrow{V} \) is the horizontal wind vector, g is the acceleration due to gravity, and p s is the surface pressure. The pressure of the top layer p t is 300 hPa, as the water vapor above 300 hPa is negligible (Xu et al. 2008).

Water vapor flux along the four boundaries is calculated as follows:

$$ {Q}_b=\frac{1}{g}{\displaystyle {\int}_L\overrightarrow{Q}\cdot \overrightarrow{n} dl}, $$
(3)

where L is the length of the boundary, \( \overrightarrow{n} \) is the outward normal vector of the regional boundary, and \( \overrightarrow{Q}\cdot \overrightarrow{n} \) is the moisture transport across the regional boundary (Schmitz and Mullen 1996).

For the model ensemble, arithmetic means were used. We interpolated all monthly fields of variables to 1° × 1° grids by using the bilinear interpolation method to facilitate model intercomparison and validation against observations.

To quantitatively evaluate model performance, we calculated the correlation coefficient (COR) and standard deviations (STDs) of the variables in this study.

The MME standard deviations are calculated as follows:

$$ STDMME=\sqrt{\frac{{\displaystyle \sum_{i=1}^{i=n}\sigma {i}^2}}{n}}, $$
(4)

where σ is the standard deviation in individual CMIP5 models and n is the number of the models.

3 Results

3.1 Biases of precipitation, evaporation, and water vapor transport

Figure 2 shows the spatial distribution of summer mean precipitation biases for 1986–2005 from the 16 CMIP5 models, the MME (relative to observations), and observations. Observations show that maximum precipitation was mainly over South China, decreasing northward. The summer mean precipitation over the Yellow River basin was 3.13 mm/day based on observations from 1986–2005 (Table 2). Most models tend to overestimate precipitation in the Yellow River basin. Among the models, BNU-ESM, NorESM1-M, CESM-CAM5, and CCSM4 models simulated the greatest regional mean precipitation in the Yellow River basin (Table 2), whereas HadGEM2-ES and IPSL-CM5A-LR models performed well with very small biases in simulating summer mean precipitation distribution in the Yellow River basin. The MME mean summer precipitation in the Yellow River basin was 4.30 mm/day. In the Yangtze River basin, the observed summer mean precipitation was 6.36 mm/day. Compared with observations, models generally performed well in simulating precipitation in this region with small biases. The MME mean summer precipitation was 6.45 mm/day, which is very close to the observational result.

Fig. 2
figure 2

Spatial distribution of summer mean precipitation biases (units: mm/day) for 1986–2005 from 16 CMIP5 models and MME (relative to observations) and observations

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Table 2 Statistical summary of regional average summer mean precipitation (P, units: mm/day), evaporation (E, units: mm/day), and water vapor convergence (WVC, units: mm/day) between model simulations, observations, and reanalysis data for 1986–2005
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To assess potential causes and implications of the systematic biases shown above, we compared CMIP5 model simulations of evaporation and water vapor transport with the reanalysis data. Figure 3 displays the spatial distribution of summer mean evaporation biases for 1986–2005 from the 16 models, the MME (relative to ERA-Interim), and ERA-Interim. The distribution pattern of evaporation by ERA-Interim was similar to that of observational precipitation. The regional average summer mean evaporation based on ERA-Interim over the Yellow River basin and Yangtze River basin were 2.61 and 3.54 mm/day, respectively. Most of the models were capable of simulating the distribution pattern of evaporation. However, considerable biases still existed. Most of the models exhibited strong overestimation of evaporation in the west of the Yellow River basin, which is likely to be related to the corresponding overestimation of precipitation mentioned above. Furthermore, in the Yellow River basin, models simulating greater precipitation also simulated higher evaporation. As NorESM1-M, BNU-ESM, CCSM4, and CESM-CAM5 models overestimated evaporation with the largest biases, which were the same models that simulated the most precipitation as discussed above. In the Yangtze River basin, large negative biases existed in BCC-CSM1.1 and FGOALS-g2 models, covering most of the basin, whereas the CCSM4, CSIRO-Mk3.6.0, and NorESM1-M models showed significant positive biases in this region.

Fig. 3
figure 3

Spatial distribution of summer mean evaporation biases (units: mm/day) for 1986–2005 from 16 CMIP5 models, MME (relative to ERA-Interim), and ERA-Interim results

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Figure 4 shows the vertically integrated summer water vapor flux across four boundaries from 1986–2005. ERA-Interim and NCEP2 results concurred that both the Yellow and Yangtze River basins were moisture sink regions in summer. In addition, ERA-Interim showed that in the Yellow River basin, there was a predominant southerly water vapor influx of 60.84 × 106 kg/s and another of 31.83 × 106 kg/s across the western basin boundary. Water vapor influx across the north was relatively weak, with magnitude 10.15 × 106 kg/s. Water vapor flowed outward across the eastern boundary at 85.53 × 106 kg/s. The corresponding net budget of water vapor flux is a gain of 17.28 × 106 kg/s. In the Yangtze River basin, water vapor inputs were from the southern boundary at 208.71 × 106 kg/s and the western boundary at 26.50 × 106 kg/s. Water vapor flowing outward from the eastern boundary is 82.95 × 106 kg/s and from the northern boundary at 60.84 × 106 kg/s. The corresponding net budget of water vapor flux is a gain of 91.41 × 106 kg/s. Results from NCEP2 also displayed similar features. Most models were able to reproduce the same directions of water vapor transport. Except for IPSL-CM5A-LR model, all models indicated that the Yellow River basin was the moisture sink region. In addition, models that overestimated precipitation, such as BNU-ESM, CESM1-CAM5, FIO-ESM, and NorESM1-M models, also tended to produce stronger water vapor convergence. Their pronounced overestimation of water vapor convergence was likely caused by their strong overestimation of water vapor influx across the southern boundary.

Fig. 4
figure 4

Vertically integrated summer water vapor flux across boundaries from 1986–2005 (units, 1e + 6 kg/s)

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3.2 Uncertainties in simulating large-scale circulations and mesoscale convective systems

Analyses of the summer mean geopotential height at 500 hPa for 1986–2005 from the 16 CMIP5 models, the MME and ERA-Interim are provided in Fig. 5. Since China is in the East Asian monsoon region, its summer climate is significantly influenced by the location and movement of the western Pacific subtropical high (WPSH). As subtropical highs are usually associated with atmospheric subsidence, they transport moisture from oceans, influencing monsoonal rainfall (Lau and Weng 2002; Li et al. 2012). Compared with ERA-Interim, the WPSH strengthened and advanced further westward and northward in the BNU-ESM, CCSM4, and CESM-CAM5 models, which is related to strong overestimation of precipitation in the Yellow River basin (Fig. 2). In addition, WPSH simulated by FIO-ESM was more southward, resulting in the stronger overestimation of precipitation in the Yangtze River basin. However, in GISS-E2-R, GISS-E2-H, HadGEM2-ES, and IPSL-CM5A-LR, the WPSH retreated eastward and southward, which is associated with small positive precipitation biases in the Yellow River basin (Fig. 2).

Fig. 5
figure 5

Summer mean geopotential height (units:gpm) at 500 hPa for 1986–2005 from 16 CMIP5 models, MME, ERA-Interim, and NCEP2

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Figure 6 displays vertically integrated summer mean water vapor flux and its divergence from 16 CMIP5 models, the MME (biases relative to ERA-Interim), ERA-Interim (summer mean), and NCEP2 (summer mean) for 1986–2005. The general characteristics in NCEP2 were consistent with those in ERA-Interim. However, NCEP2 presented an artificial water vapor convergence maximum area over the Sichuan basin along the eastern edge of the Tibetan Plateau. This unrealistic water vapor convergence is corresponded with the artificial precipitation maximum in NCEP2, which is not consistent with precipitation observations. Considering that ERA-Interim successfully eliminated this artificial water vapor convergence, we preferred to apply ERA-Interim results as reference. ERA-Interim product indicated that three branches of water vapor transport are responsible for the summer precipitation in China. The first is cross-equatorial flow around 105°E, associated with strong anticyclonic circulation over Australia. The second is from the tropical Pacific Ocean, transported by southerly flow west of the WPSH, bringing abundant warm and moist air into China. The third is transported by the southwest flow of the Indian summer monsoon across the Arabian Sea and the Bay of Bengal. The results also indicated that in summer, most parts of China are dominated by water vapor convergence; the magnitude of this convergence is stronger in the Yangtze River basin than that in the Yellow River basin. Most models reasonably capture the aforementioned water vapor characteristics. Among them, BNU-ESM, CCSM4, and CESM-CAM5 models simulated stronger water vapor convergence in the Yellow River basin than that by ERA-Interim. This result may have occurred because these three models simulated a stronger and more westward and northward WPSH, generating more moisture convergence in that region. Moreover, FIO-ESM model simulated stronger water vapor convergence in the Yangtze River basin, which is associated with the more southward WPSH simulated by this model. Although compared with ERA-Interim, NorESM1-M model simulated weaker WPSH, this model still exhibited stronger water vapor convergence in the Yellow River basin, which was caused by the overestimation of specific humidity in the moisture source region by NorESM1-M model. The other models simulated very weak water vapor transport, resulting in less moisture convergence. Hence, uncertainties in simulated climatological summer precipitation over these regions are closely related to uncertainties in simulating large-scale circulations.

Fig. 6
figure 6

Vertically integrated summer mean water vapor flux (vectors, units: kg/(m*s)) and its divergence (contours, units: mm/day) from 16 CMIP5 models, MME (bias relative to ERA-Interim), ERA-Interim, and NCEP2 for 1986–2005

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Apart from the uncertainties in simulating large-scale circulations, we also attribute model performance of precipitation to the simulations of mesoscale convective systems. A large fraction of rainfall over East Asia originates from large, deep convective storms (Xu 2013). This study examines the spatial distribution of summer mean convective precipitation biases for 1986–2005 from the 16 CMIP5 models, the MME (relative to ERA-Interim), and ERA-Interim results (Fig. 7). In the Yellow River basin, BNU-ESM, CESM1-CAM5, CSIRO-Mk3.6.0, FIO-ESM, and NorESM1-M models strongly overestimated convective precipitation, which makes certain contributions to the overestimation of total precipitation in that region. In the Yangtze River basin, however, underestimation of convective precipitation by some models partially resulted in their negative total precipitation biases.

Fig. 7
figure 7

Spatial distribution of summer mean convective precipitation biases (units: mm/day) for 1986–2005 from 16 CMIP5 models, MME (relative to ERA-Interim), and ERA-Interim results

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3.3 Interannual variations of water cycle and relationships among precipitation, evaporation, and water vapor convergence

Time series of regional mean summer precipitation, evaporation, and water vapor convergence in the Yellow River basin (left) and Yangtze River basin (right) are shown in Fig. 8. In the Yellow River basin, there is no evident trend of these variables in observations and reanalysis data from 1986 to 2005. For interannual variations, precipitation tended to strongly vary after 1995, whereas evaporation varied smoother than precipitation. STDs in terms of interannual variations of regional mean summer precipitation, evaporation, and water vapor convergence over the Yellow River basin in the observations and reanalysis were 0.49, 0.12, and 0.77/0.70 mm/day, respectively (Table 3). Regarding the individual models, most of them overestimated STDs of precipitation and evaporation, and six models tended to underestimate interannual variations of water vapor convergence. As shown by observations and reanalysis data, interannual variations of these three variables were stronger in the Yangtze River basin than those in the Yellow River basin. Precipitation began to decline in 1980, and a strong upward tendency appeared after 1990 and continued through the late 1990s. Maximum precipitation appeared in 1998, with water vapor convergence peaked as well. Interannual variations of water vapor convergence exhibited similar features, whereas those of evaporation displayed opposite variations. STDs in terms of interannual variations of regional mean summer precipitation, evaporation, and water vapor convergence in the Yangtze River basin in the observations and reanalysis were 0.78, 0.15, and 0.88/0.95 mm/day, respectively (Table 3). For the models, models capture the interannual variability well with some overestimations, particularly in the Yellow River basin. Furthermore, models that overestimated interannual variations of precipitation also tended to simulate stronger water vapor convergence variations.

Fig. 8
figure 8

Time series of regional average summer mean precipitation (units: mm/day), evaporation (units: mm/day), and water vapor convergence (units: mm/day) in the Yellow River basin (left) and Yangtze River basin (right) for 1986–2005. All values are anomalies relative to averages in 1986-2005

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Table 3 Statistical summary of STDs of interannual variations of precipitation (P, units: mm/day), evaporation (E, units: mm/day), and water vapor convergence (WVC, units: mm/day) between model simulations, observations, and reanalysis data for 1986–2005
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To investigate the possible underlying relationships among precipitation, evaporation, and water vapor convergence and to assess whether CMIP5 models have the ability to simulate these connections, we used scatter plots to compare their possible links. First, we calculated the regional average monthly mean precipitation, evaporation, and water vapor convergence of June, July, and August, respectively, and then we obtained anomalies by subtracting the climatological monthly mean values of the same month during 1986–2005. Figure 9 exhibits the summer precipitation anomaly (P anomaly) versus evaporation anomaly (E anomaly) within the Yellow River basin (red) and the Yangtze River basin (blue). Solid lines in the figure were the best least-squares fit lines. OBS represents the case between precipitation from observations and evaporation from ERA-Interim. Figure 9 reveals that in the Yellow River basin, there is a weak positive correlation between precipitation and evaporation in the OBS as we see the slope of the best least-squares fit line is gentle and the COR is only 0.15, which is insignificant based on the t test. Regarding model performance, most models also exhibited very weak correlations between P and E. Apart from that, FGOALS-g2, CSIRO-Mk3.6.0, HadGEM2-ES, and IPSL-CM5A-LR models simulated strong positive correlations with respective CORs of 0.70, 0.55, 0.51, and 0.53, which are statistically significant at the 99 % confidence level, whereas MPI-ESM-LR and NorESM1-M simulated a significant negative correlation. In the Yangtze River basin, OBS displayed a strong negative relationship between precipitation and evaporation that is statistically significant at the 99 % confidence level. Except for CSIRO-Mk3.6.0, FGOALS-g2, and IPSL-CM5A-LR models, the other 13 models were able to reproduce negative correlations, with 9 models statistically significant at a 99 % confidence level. This result indicated that most models were able to capture the significant negative relationship between precipitation and evaporation in the Yangtze River basin. The above analyses also suggest that the relationship between precipitation and evaporation varies among regions. The implications and possible regimes that relate to the different relationships in the two river basins are analyzed in following discussions.

Fig. 9
figure 9

Summer precipitation anomaly (P anomaly, units: mm/day) versus evaporation anomaly (E anomaly, units: mm/day) within the Yellow River basin (red dots) and the Yangtze River basin (blue dots). Solid lines are best least-squares fit lines. The red (blue) numbers are CORs between P and E anomaly in the Yellow River basin (Yangtze River basin)

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Figure 10 exhibits the summer precipitation anomaly (P anomaly) versus water vapor convergence anomaly (WVC anomaly) within the Yellow River basin (red) and the Yangtze River basin (blue). In the Yellow River basin, both OBS and CMIP5 models clearly demonstrate positive relationships between summer precipitation and water vapor convergence. The CORs of OBS (ERA-Interim) and OBS (NCEP2) are 0.68 and 0.72, respectively. Most models had higher CORs than these values, indicating that those models tended to overestimate the positive relationship between precipitation and water vapor convergence in the Yellow River basin. Very strong positive correlations between summer precipitation and water vapor convergence were also found for the Yangtze River basin. As shown in Fig. 10, all models appeared to perfectly reproduce the highly correlated precipitation and water vapor convergence in the Yangtze River basin. The CORs of OBS (ERA-Interim) and OBS (NCEP2) were 0.82 and 0.78, respectively, higher than those in the Yellow River basin, which means that positive relationship between precipitation and water vapor convergence was more pronounced in the Yangtze River basin, which implies that summer water vapor convergence plays a more important role in this region.

Fig. 10
figure 10

Summer precipitation anomaly (P anomaly, units: mm/day) versus water vapor convergence anomaly (WVC anomaly, units: mm/day) within the Yellow River basin (red dots) and the Yangtze River basin (blue dots). Solid lines are best least-squares fit lines. The red (blue) numbers are CORs between P and WVC anomaly in the Yellow River basin (Yangtze River basin)

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4 Discussions

In section 3.3, we concluded that the relationships between precipitation and evaporation in these two river basins are different and such differences are dominated by different feedback regimes between precipitation and evaporation. The regional mean summer precipitation was 6.36 mm/day in the Yangtze River basin and 3.13 mm/day in the Yellow River basin, which demonstrates that soil moisture in the Yangtze River basin is greater. It is highly probable that in summer, the Yangtze River basin is characterized by an energy-limited regime (Teuling et al. 2009; Seneviratne et al. 2010; Mueller and Seneviratne 2014) with strong negative correlation between precipitation and evaporation. This result is consistent with the conclusions drawn by Meng and Shen (2014) that southeast and southwest regions in China are primarily within energy-limited regimes and by Li et al. (2013) that during the rainy season, interannual variation of local evaporation is opposite to that of precipitation in southeast and southwest China. In humid regions like Yangtze River basin, increased precipitation does not necessarily mean increased evaporation; because it is already very wet, more precipitation does not make any difference, only higher temperature or radiation can increase evaporation. Moreover, Tang and Leng (2013) found that there was a significant negative relationship between summer mean daily maximum temperature and cloud cover over most areas of North American and a significant negative relationship between summer mean daily maximum temperature and precipitation in the southern USA. They suggested that an increase in cloud cover associated with an increase in the top of the atmosphere (TOA) reflected shortwave radiation and the increase of precipitation might contribute to the observed summer cooling in the USA. Likewise, here we consider that in the Yangtze River basin, it is likely that the higher precipitation amount accompanied with more cloud cover led to an increase in TOA reflected shortwave radiation, thus contributing to the decrease of net radiation, which directly decreased the temperature, resulting in a reduction in evaporation. This process describes an energy-limited regime. A different regime is a soil moisture-limited regime prevailing in arid regions where the evapotranspiration (ET) rate is limited by water availability. Even if the temperature is high, which provides energy for evaporation, ET is still low because insufficient water is available for evaporation. The feedback with precipitation is that enhanced precipitation provides more water and more soil moisture, thereby increasing ET and evaporation, which is a positive relationship. The northwest of China is strongly under the influence of this regime, as indicated by the plot of the P anomaly versus E anomaly within the northwest of China (38–46°N and 82–92°E) where it is extremely dry (Fig. S1). The results suggest that a strong positive correlation between precipitation and evaporation exists there, which agrees with the soil moisture-limited regime. Finally, in the Yellow River basin, it is not obvious which regime prevails because the relationship between precipitation and evaporation is not significant.

5 Conclusions

This study provides estimations of summer precipitation, evaporation, and water vapor transport from 16 CMIP5 models for the Yellow River basin and Yangtze River basin over the period 1986–2005. The results indicate that most models tend to overestimate precipitation in the Yellow River basin, whereas precipitation in the Yangtze River basin is well simulated by most models. Moreover, most models display an artificial precipitation maximum area in the west of the Yellow River basin. This artificial precipitation maximum area simulated by some models is corresponded to an artificial evaporation maximum area in the evaporation field, as most models also exhibit strong overestimation of evaporation in the west of the Yellow River basin.

Both basins are moisture sinks in summer, and most models are able to reproduce the same directions of water vapor transport as reanalysis data do, except that the IPSL-CM5A-LR model simulates the Yellow River basin as a moisture source region. Models that overestimate precipitation tend to produce strong water vapor convergence. In the Yellow River basin, BNU-ESM, NorESM1-M, and CESM-CAM5 models simulate the most precipitation, and simultaneously they produce the strongest water vapor convergence in that region. This result is likely related to large-scale circulations simulated by these models, which the WPSH strengthens and advances further westward and northward, resulting in stronger water vapor convergence in the Yellow River basin. In addition, NorESM1-M model simulates weak WPSH, but the simulated water vapor convergence in the Yellow River basin is strong, which is caused by the overestimation of specific humidity in the moisture source region by NorESM1-M model. Convective precipitation biases simulated by models are also partially responsible for their total precipitation biases. In the Yellow River basin, BNU-ESM, CESM1-CAM5, CSIRO-Mk3.6.0, FIO-ESM, and NorESM1-M models strongly overestimate convective precipitation, which makes certain contributions to the overestimation of total precipitation in that region. In the Yangtze River basin, however, underestimation of convective precipitation by some models partially results in their negative total precipitation biases.

No obvious trend is noted in summer precipitation, evaporation, and water vapor convergence in observations, reanalysis data, and individual models. Relationships between summer precipitation and evaporation in the Yellow and Yangtze River basins differ significantly. This result is likely to be associated with different feedback regimes in these basins, which are soil moisture-limited regime and energy-limited regime. In the Yangtze River basin, there is strong negative relationship between precipitation and evaporation, because Yangtze River basin is likely to be characterized by an energy-limited regime. Nine models are capable of simulating this negative relationship between precipitation and evaporation. In the Yellow River basin, it is not obvious which regime prevails as the correlation between precipitation and evaporation is not significant. Finally, summer precipitation and water vapor convergence are closely related in both OBS and the models. Most models tend to overestimate the positive relationship between precipitation and water vapor convergence.