As an indicator of atmospheric evaporating capability over a hypothetical reference surface, reference evapotranspiration (ET0) is the most important hydrological and meteorological variable to reflect climate change. This is particularly true for the Yellow River Basin, which faces serious water shortages and is vulnerable to climate change. In this study, the ET0 at 80 sites during 1957–2008 in the Yellow River Basin was calculated using the Penman-Monteith method with the calibrated Angstrom coefficients. Spatial and seasonal patterns of changes in ET0 as well as the concerned climatic variables are specially focused on using advanced statistical tests and GIS method. The entire Yellow River Basin is characterized by complicated spatial variability in the change of ET0. Significant negative trends are mainly distributed in the southeast corner, northern side, and midwest of the Yellow River Basin, while significant increases of ET0 mainly occur in the middle part and southwest corner of the basin. Still, no coherent spatial patterns in ET0 trends are seen in any season. The dominance of warming trends in temperature and decreasing trends in wind speed and sunshine duration can be found in the basin. Relative humidity presents insignificant or weak trends at many sites but with a mixed spatial structure of positive and negative trends at both annual and seasonal scales. The combined effects of climatic variables to ET0 changes and their spatial and seasonal variability are revealed by further analysis of sensitivity of ET0 to climatic variables and the contribution of climatic variables to ET0 changes over six homogenous regions identified by a rotated empirical orthogonal function (REOF) clustering method on annual and seasonal scales. The decline of surface wind speed offsets the increasing effect of the temperature increase and is mainly responsible for the ET0 reduction in the west and north of the Loess Plateau. The reduced sunshine duration is the leading factor for ET0 decrease in the middle-lower Yellow River Plain, especially during the summer time. The increasing mean temperature plays the most important role in the ET0 increase in the source area of the Yellow River Basin. Furthermore, regional actual evapotranspiration and ET0 present complementary behavior, but does not accurately fall in the 1:1 complementary relationship of the Bouchet's hypothesis, especially for the high elevation subregions. In addition, although precipitation changes are the main driving factors for drought variation, increasing ET0 intensified the drought in middle regions.
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 From the latest report of the Intergovernmental Panel on Climate Change (IPCC), the Fourth Assessment Report (IPCC, 2007), there is no doubt that the climate system has warmed in recent decades. Although the uncertainties about the extent and pace of future projected temperature are large, IPCC global climate models reveal unambiguously that the warming trend will continue. Despite responding to climatic changes in different ways [Kundzewicz and Somlyody, 1997], the alterations of precipitation, runoff, infiltration, groundwater flow, evapotranspiration, and soil moisture in many parts of the world during the past century suggest that one of the most significant potential consequences of global warming may be the ongoing intensifications in regional hydrological cycles [Alan et al., 2003; Huntington, 2006].
 The Yellow River Basin, hosting a population of 107 million people [McVicar et al., 2007] and consisting of 1200 million ha of farmland [Yang et al., 2004], is one of the most important basins in China. However, the serious water-related issues, such as soil erosion, sedimentation, water shortages, and drying up, hinder the sustainable development of the region, resulting in severe environmental and ecological problems. Qualitative analysis and quantitative estimation for the ET0 trend will provide insight into the impact of climate change on the future water balance and improve the regional strategy for water resource management for the Yellow River Basin. Recent studies suggested that the pan evaporation in the Yellow River Basin presented a steady decreasing trend during the past decades [Qiu et al., 2003; Xu and He, 2005]. As for the ET0, the study on assessment of its changes in the Yellow River Basin is scare in the literature. Recently, Liu et al.  explored the temporal trends of ET0 in the Yellow River Basin at an annual scale using monthly meteorological data and concluded that increasing temperature and decreasing relative humidity are mainly responsible for the increasing trends of ET0 in the upper, middle, and whole basin. The same research group also investigated spatial distribution and temporal variation of ET0 and found that the upward and downward trends were mainly detected in the middle and lower region of the basin, respectively [see Yang et al., 2011].
 However, seasonal patterns of ET0 changes and their underlying causes have not been investigated in their study. As the Yellow River Basin presents distinct seasonal climatic changes with cold and dry winters and wet and warm summers [Wang et al., 2007], it is important to understand the seasonal variation of the climate factors and their relative significance to the ET0 changes. In addition, from an agricultural point of view, seasonal trends in ET0 may have more impact on human and natural system than annual trends particularly due to seasonal behaviors of crop growth, irrigation, and water resources allocation. Furthermore, frequent drying up in main river and seasonal drought across the basin during past decades [Cong et al., 2009], which make the Yellow River become a seasonal river, greatly emphasize the urgent need to investigate the patterns of seasonal contributions of climatic factor to ET0 changes.
 On the other hand, spatial heterogeneity for ET0 trends and corresponding driving factors are expected in the Yellow River Basin due to complex spatial patterns in climate conditions in this region, from arid zone in the resource area, special arid Loess Plateau zone, and semiarid zone in the middle reach, to semihumid and humid zone in the lower reach [Huang et al., 2009]. However, the results from previous study on ET0 trends are only based on regional averaging across the stations without consideration of spatial pattern of the stations or subjective subregions selection. The heterogonous spatial distribution of a long record may make such an aggregation into region-wide trends deviate from the real situation. Meanwhile, there may also be spatial variability in the trigger mechanism for ET0 trends, which have not been adequately revealed in a previous study.
 More detailed investigation is required to address these limitations mentioned above. In this study, we therefore concentrate on the spatial and seasonal differences in the contributing factors to the ET0 trends across the Yellow River Basin, which has not been specifically investigated in previous studies. Moreover, by investigating the possible change in ETa related with changing ET0, whether ETp and ETa follow the Bouchet's complementary relationship in the Yellow River Basin is clarified. Meanwhile, as the important implication of ET0 changes, the relative importance to droughts due to changes in ET0 compared with changes in precipitation regime is also analyzed. But first, spatial patterns of the long-term ET0 trends and the climate factors concerned will be detected at annual and seasonal scales based on daily meteorological data, and the regionalization of ET0 is presented and the entire Yellow River Basin is categorized according to major results from REOF.
2. Study Area and Data Processing
 The Yellow River, regarded as the “Mother River of China” because human inhabitants have existed in this region since prehistoric times [Wang et al., 2000], is the second longest river in China. Originating from the eastern Qinghai-Tibet Plateau at an elevation of higher than 5000 m, the Yellow River flows eastward through northwestern China over a total length of 5464 km before discharging into the Bohai Sea (see Figure 1). It has a drainage area of more than 750,000 km2 and exhibits a variety of geological and climatic features. From the source to the river mouth, the Yellow River experiences three typical landforms: the Tibet Plateau with elevations from 2000 to 5000 m, the Loess Plateau with elevations from 500 to 2000 m, and the alluvial plain in the eastern part [Yang et al., 2004]. From northwest to southeast, the basin is characterized by an arid, semiarid continental monsoon climate and semihumid climate. The basin's average annual temperature ranges from 4 to 14°C. The mean annual precipitation is highly heterogeneous across the basin, increasing from 368 mm in the upper reaches to 530 mm in the middle reaches and 670 mm in the lower reaches [Wang et al., 2007]. As the important source for water supply in northwestern and northern China, the river supports 9% of China's population and 17% of agricultural land (IWMI and YRCC, 2003). The Yellow River is well known not only for its history and large drainage area but also for its high sand content, frequent floods, and limited water resources. Affected by climatic change and human activities in recent years, the ecoenvironment and hydrological processes tend to increasing change as reflected by a more fragile ecoenvironment, the aggravation of soil erosion, and more frequent zero-flow events in the Yellow River Basin during the last decades [Zhang et al., 2009; Wang et al., 2008].
 Meteorological data from 80 National Meteorological Observatory (NMO) stations, which were provided by the National Meteorological Information Centre of China (NMIC) of the China Meteorological Administration (CMA), including daily observations of air temperatures, relative humidity, wind speed, and sunshine duration for the period of 1957–2008, were used in this study to calculate ET0 of the Yellow River Basin. Precipitation data from these meteorological stations were also collected. The location and distribution of meteorological stations over the Yellow River Basin are shown in Figure 1. These stations are well distributed in space and can reflect the characteristics of the regional climate. The detailed information of these stations including name, WMO number, latitude, longitude, and altitude are also given in Table 1. Among these stations, five stations located in the Tibetan Plateau and three stations located in the Loess Plateau began from year 1959 (Nos. 56,067, 53,704, 53,615, 53,545, and 56,065) and 1960 (Nos. 56,041, 52,943, and 56,173). Missing daily data account for about 0.59% as an average for the 80 stations and were reconstructed by the median meteorological data from at least three neighboring stations. In addition, 12 of these 80 stations (see Table 2) have radiation observations records and were used to calibrate the Angstrom coefficients for estimating the solar radiation in the FAO Penman-Monteith method. Annual discharge data for 14 stations widespread in the entire basin were also collected to test Bouchet's hypothesis (Figure 1). The length of records for Huayuankou, Lijin, Toudaoguai, Huangheyan, and Tangnaihai is 1958–2005, but 1958–2001 for the remainder stations except Lanzhou with 1967–2005.
Table 1. Information for the National Meteorological Observatory Stations Used in This Study
Table 2. Calibration of the Angstrom Coefficients for the 12 Stations With Radiation Observations
Length of Record
3.1. Fao Penman-Montieth (PM) Method
 As mentioned in section 1, ET0 has to be estimated from meteorological records. In literature, there are many methods available for ET0 estimation, among which the most reliable method for various climatic conditions is the FAO PM method because it is physically based and explicitly incorporates both physiological and aerodynamic parameters [Xu et al., 2006]. Although the ET0 is only a theoretical climatic parameter without considering actual surface soil type and water availability, its values can provide a standard to compare evapotranspiration capability under various climatic conditions. The FAO PM method requires data on sunshine duration, temperature, relative humidity, and wind speed and is given in the form of
[Allen et al., 1998], where is the reference evapotranspiration (mm d−1), is the net radiation at the crop surface (MJ m−2 d−1), is the soil heat flux density (MJ m−2 d−1), is the mean daily air temperature (°C), is the daily average wind speed at 2 m above ground level (m s−1), is the saturation vapor pressure (kPa), is the actual vapor pressure (kPa), is the saturation vapor pressure deficit (kPa), is the slope of the saturated vapor pressure in relation to air temperature (kPa °C−1), and is the psychrometric constant (kPa °C−1).
 The solar radiation can be estimated from sunshine duration (or hours of sunshine) with the help of the Angstrom formula
[Allen et al., 1998], where is solar or shortwave radiation (MJ m−2 d−1), is actual duration of sunshine (h), is the maximum possible duration of sunshine or daylight hours (h), is thus the relative sunshine duration, is the extraterrestrial radiation (MJ m−2 d−1), and and are the regression coefficients. Differing from the study by Liu et al.  which used the averaged values the coefficients and of the whole China reported by Chen et al. , we calibrated the Angstrom coefficient according to the measured solar radiation and hours of sunshine in this study.
 The coefficients and at 12 stations with radiation observation (see Figure 1 and Table 2) were estimated based on the observations of and using nonlinear least-squares data fitting by the Gauss-Newton method. Meanwhile, and were computed based on date and latitude according to the equations provided by the FAO PM method. The length of data selected in this study (see Table 2) is much longer than that in related work by Chen et al.  (based on the climatic data during the period of 1 January 1994–31 December 1998), ensuring more accuracy and reliability in the calibrated parameters. The fraction of extraterrestrial radiation (i.e., the magnitudes of ) reaching the earth on clear days vary in different stations along with different altitude (above 0.8 in higher altitude areas but below 0.8 in lower altitude areas), resulting in spatial variability, which is also reported by Zhang et al. . Overall, the Angstrom model is suitable for daily global radiation estimation in the Yellow River Basin as indicated by high values (see Table 2). and of the other stations with no solar radiation but sunshine duration were estimated by Kringing interpolation method. The mean annual and seasonal ET0 were computed for each station by accumulating the daily values. The seasons are defined in the standard climatological way: spring is defined as occurring from March to May, summer from June to August, autumn from September to November, and winter from December to February.
3.2. Trend Analysis Method
 In this study, a simple linear regression method was used to quantify the magnitude of overall trend (i.e., the change per unit time) in ET0 and other climatic variables used in the PM method, while the Mann–Kendall method was used to test the significance of the trend. The linear regression is the most common method for detect trends in climate variables [da Silva, 2004]. The linear regression method was chosen to test the long-term trends because of its simplicity for an unknown trend. The rank-based Mann–Kendall method [Mann, 1945; Kendall 1975] is a nonparametric method and is highly recommended by the World Meteorological Organization for analyzing hydrological series because it does not need any distribution assumption for the data but has the same power as its parametric competitors [Yue and Pilon, 2004]. Moreover, temporal patterns of drought index, precipitation, and ET0 were detected in this study by the sequential version of the Mann–Kendall test, which is to identify the beginning of a trend within a time series [Gerstengarbe and Werner, 1999]. Different from the common version of the Mann–Kendall test mentioned previously, the sequential version of the Mann–Kendall test is mainly used to analyze changing processes [e.g., Ma and Fu, 2003; Zhang et al. 2008; Wang et al., 2011] and the change points [e.g., Partal and Kahya, 2006] of hydrometeorological variables over time.
3.3. The Rotated Empirical Orthogonal Function (REOF) Method
 In this study, REOF, a widely used method to study the spatial pattern of various meteorological parameters [Wang et al., 2006], was employed to investigate the most dominant spatial patterns of ET0 and identify the homogenous regions in the Yellow River Basin. EOF analysis tends to find a relatively small number of independent variables which convey as much of the original information as possible without redundancy. The EOF method is a statistical technique to estimate both the patterns of physical processes (spatial variability) and time series coefficients modulating each process (temporal variability) by decomposing a multivariate data set into an uncorrelated linear combination of separate functions of the original variables. The eigenvectors (EOFs), one of the outputs of the EOF method, are usually plotted as vector maps to describe spatial variability by showing the regions which are closely related, inversely related, or unrelated. The EOF analysis finds linear combinations of the measured variables so that leading EOF describes the spatially coherent that maximize its variance. However, sometimes the high-order EOFs have smaller spatial scales and are not physically meaningful due to the orthogonality [Su et al., 2008]. This limitation has led to the development of the rotated empirical orthogonal function (REOF) [Richman, 1986]. REOF yields localized structures by compromising some of the EOF properties such as orthogonality. The effect of the rotation to simple structure is to cluster within each mode a small number of high valued variables and a large number of near-zero value variables. REOF was found to be better in dividing climatic patterns in a comparison study [Kim and Wu, 1999]. In this paper, the varimax REOF method was chosen, which maximizes the variance of the squared correlation between each rotated principal component (RPCs) and each variable, to give the simplest pattern description while explaining the maximum amount of variance.
3.4. Contribution Estimation Method and Sensitivity Analysis Method
 In order to quantify the relative contributions of a climatic variable to the changing trends in ET0 at annual and seasonal scales, a recovered stationary series method [Xu et al., 2006] was employed as follows: (1) The trend in a climatic variable was removed to obtain a stationary time series; (2) ET0 was recalculated by using the detrended data series while original data for other variables were retained in each time; and (3) the ET0 values from the detrended and original time series were compared and the difference was considered as the influence of the trend by that variable. Besides the magnitude of change of climatic variables themselves, the sensitivity of climatic variables to the ET0 also plays a crucial role to the ET0 trends. Therefore, to fully understand the results of contribution estimation, it is necessary to evaluate the impact of meteorological variables on ET0 by examining the sensitivity of ET0 to meteorological variables. A simple but practical sensitivity analysis is to calculate and plot the relative changes of an input variable against the corresponding relative change of the output variable, and then the corresponding relative change of outcome can easily be read from the plot for a certain relative change of the variable. The procedure of this method can be described as follows: (1) The scenarios for changes in climatic variables were determined by adjusting the observed data series by adding delta changes; (2) the ET0 were recalculated by using one scenario at each time; and (3) the relative changes between the recalculated and the original ET0 against the relative changes in each climatic variable were calculated and plotted.
4.1. Spatial Distributions of Annual ET0 and Related Meteorological Variables
 The spatial distribution of mean annual ET0 is plotted in Figure 2. The annual distribution has a rich spatial structure with a relatively low values in the southwestern part of the basin (Qinghai and Sichuan Provinces) and high values in northwestern (Inner Mongolia) and southeastern (Shandong Province) parts. The spatial patterns of the mean annual values of the major meteorological variables are shown in Figure 3. From high to low value, a clear northwestern-southeastern and south-north gradient can be found in the spatial distribution of sunshine duration and reverse pattern in relative humidity. The highest and lowest air temperature values mainly occur in the southeastern and southwestern parts of the basin, respectively. Compared with other climatic variables, wind speed has a fairly homogenous spatial distribution except for a few high values at a few isolated points. A comprehensive view of Figures 2 and 3 suggests a combined effect of all climatological factors on the ET0 and its complex spatial patterns. It can be seen that the high ET0 values in the southeastern part are mainly due to the very high air temperature in this region since, as being seen from Figure 3, in this region the sunshine duration is lower, the relative humidity is higher, and the wind speed is similar as compared with other regions. The northwestern part, also presenting the high ET0 values, is attributed by the very long sunshine duration and very low relative humidity in this region. The very low air temperature and relative high relative humidity are mainly responsible for the low ET0 values in the southwestern part of the Yellow River Basin.
4.2. ET0 Trends
 The trends for the annual ET0 in the period of 1957–2008 are shown in Figure 4. It can be seen from the map that the entire Yellow River Basin is characterized by complicated spatial variability in the change of ET0, which reflects considerable climatic variation and complex causal mechanisms for ET0 change. There are 36 stations presenting negative trends in annual ET0 (i.e., 45% of all stations), of which 22 stations (i.e., 27.5% of all stations) are statistically significant at 95% confidence level. While positive trends were found in 44 stations (i.e., 55% of all stations), 26 stations (i.e., 32.5% of all stations) are dominated by significant increasing trends at the 95% confidence level. The stations showing significant negative trends mainly distribute in three areas, i.e., southeast corner, northern sides, and midwest of the basin. The significant increases of annual ET0 mainly occur in the middle part and southwest corner of the basin. The magnitudes of trends in annual ET0 (i.e., the change per unit time) is not necessarily associated with the significance of this kind of change due to the different level of annual ET0 values in different stations. Except in only a few stations, the annual ET0 with positive/negative trends increased/decreased by 0–3 mm yr−1. A remarkably large positive and negative trends in annual ET0 are found in Zeku station (4.8 mm yr−1) and Jingtai station (−4.9 mm yr−1), located southwest and midwest of the basin, respectively. The overall pattern of change in ET0 trends at an annual scale presented in Figure 4 (i.e., upward trends in upper and middle regions and downward trends in lower regions) is generally in line with the findings by Liu et al. , although time step of analyses processes performed in the study of Liu et al.  (monthly) are different with ours (daily). However, compared with only temporal trends of regional average ET0 series showed by Liu et al. , this study provides spatial distribution maps of ET0 trends containing trends slopes as well as the statistical significances (see Figure 4) and therefore captures more detailed spatial information and shows more findings. For instance, despite the positive trends in mean annual ET0 series detected in the upper and middle basin [Liu et al., 2010], many stations dominated by negative trends in annual ET0 can be found in the northern sides and midwest of this region.
 Furthermore, the trends (including significance and magnitudes of change) and their spatial patterns of change in ET0 trends at seasonal scale are also depicted in Figure 5. It can be seen that no coherent spatial patterns in ET0 trends are shown in any season with mixed positive and negative sign in all of the basin, especially for the upper and middle regions. Concurrently, there are large differences in spatial distribution patterns of trends in ET0 for different seasons. Stations with different changing direction of seasonal ET0 trends can be easily found in the basin. Moreover, by jointly viewing Figures 4 and 5, although it is clear that for most stations with significant change trends in annual ET0, significant change trends can be found in at least two seasons, compared with that of annual ET0, similar spatial distribution patterns for trends in all four seasonal ET0 can only be found in parts of the basin. Among them, the summer ET0 presents relatively the most similar spatial patterns with that of annual ET0. For most stations in the middle and lower region, significant seasonal ET0 changes can only be found in spring and summer, respectively (see Figure 5). Apart from some stations in the center part of the basin, presenting significant increasing trends in spring ET0, the largest slopes of seasonal ET0 trends in most stations with significant change trends in annual ET0 can be found in summer. Moreover, the spatial and seasonal variability in ET0 has been further confirmed by the results (not reported here because of space limitation) of the homogeneity test (mostly used in recent ET0 studies, e.g., Jhajharia et al.  and Dinpashoh et al. ) when the entire basin is considered, which indicated heterogeneities in ET0 trends between the stations and between seasons. This may not be surprising, as evapotranspiration is a very complex random processes influenced by various climatic and geographical factors.
4.3. Climate Factors for ET0 Change
 In order to understand the intrinsic causal mechanism behind the ET0 changes, the same trend detection procedure is conducted with the major meteorological variables at both the annual and seasonal scales. The meteorological variables examined in this study include sunshine duration, air temperature, relative humidity, and wind speed. The results of trend analysis for annual and seasonal meteorological variables and their spatial patterns are demonstrated in Figures 6 and 7. Starting with the annual air temperature, we find that significant warming trends occur across the entire basin covered by the station network. Over 90% of the stations have statistically significant (at the 95% confidence level) increasing trends in annual air temperature, reflecting the general sharp warming in this basin, which is consistent with global warming as reported across most of the world. The largest warming trends (often >0.04°C yr−1) mainly occur in the northern part, whereas the trends in the middle part are generally smaller (around 0.01°C yr−1). Contrarily, although some stations distributed in the midwest area of the basin present increasing wind speed, the map for annual mean wind speed generally shows widespread decreasing trends. Fifty-four stations (i.e., 67.5% of all stations) are dominated by negative trends in wind speed, among which 44 stations (i.e., 55% of all stations) are statistically significant, with most significant trends being over 0.01 m s−1 yr−1. Similar changes with respect to wind speed can be observed in the annual sunshine duration. About 2/3 (53 stations) that present negative trends in annual sunshine duration are significant with most the slope of decrease being between 0.01 and 0.04 h d−1 yr−1. And the majority of these negative trends (38 stations accounting for almost half of the entire basin) happened in the eastern, northern, and western sides of the basin. In contrast to the three meteorological variables (i.e., air temperature, wind speed, and sunshine duration) analyzed above, the relative humidity has the lowest number of stations with significant changes; only 38.75% of the station trends (including positive and negative trends) are significant at the 95% confidence level. In addition, no coherent trends are seen in any subregions, indicating irregular station trend patterns. The annual relative humidity trends have mixed positive and negative signs in the entire basin.
 The seasonal spatial distributions of the four climatic variables are demonstrated in Figure 7. The main impression is that the direction of the trends for these climatic variables and their spatial patterns are similar to that in the annual scale described above. However, the differences in magnitudes between different seasons can also be observed. The warming trends in temperature for seasonal data are overwhelming, and most of them in all four seasons are statistically significant. An interesting point to be noted is that for most stations the largest slopes of temperature trends can be found in winter, confirming the consecutive warm winter phenomenon recently in China [Deng et al., 2008]. The map for seasonal data (Figure 7(d)) reveals that significant decreasing trends in wind speed are frequent over the Yellow River Basin, and most significant negative trends are found in at least three seasons. The stations with larger slopes are mainly located in the western, southeastern, and northern parts of the basin. The middle and southwestern parts of the basin have either insignificant or rather weak change trends in seasonal wind speed. For seasonal sunshine duration, significant decreasing trends occur mainly in the eastern area of the basin, where larger slopes of trends (often 0.04–0.06 h d−1 yr−1) can mostly be found in summer and winter. Generally, a dominance of insignificant seasonal relative humidity trends is seen on the Yellow River Basin. Even though some stations present significant change trends in seasonal relative humidity, most of them are only detected in one or two seasons.
 Overall, the station based analysis suggests that the trends of climatic variables vary spatially and seasonally. Although the spatial patterns of annual and seasonal trends in climatic variables are quite different, the dominance of warming trends in temperature, negative trends in wind speed, and sunshine duration can be found in the Yellow River Basin. For annual and seasonal relative humidity, the basin has many insignificant or weak trends and a mixed spatial structure of positive and negative trends. Furthermore, analysis of the seasonal patterns of climatic variables change generally indicate that springs and winters have experienced the largest increase in temperature, and summers and winters have experienced the largest decrease in wind speed in this basin.
4.4. Spatial Variability of ET0 and Identification of Homogenous Regions by REOF
 The REOF analysis was performed on annual ET0 to further explore the spatial anomalies of ET0 over the Yellow River Basin and make a reasonable partition. The first 10 EOFs together explain 85.5% of the variance and the first 6 EOFs together can explain 74% of the variance. The fact that more than 70% of the total variability can be captured by only six EOFs suggests that the complexity of spatial pattern of ET0 over the entire Yellow River Basin can largely be explained by a small number of spatial structures. Therefore, six significant orthogonal functions were used to identify the spatial characteristics of possible physical significance in this study. A new set of REOF modes were produced by rotating the first six loading vectors of the initial EOFs. The percentages of variance captured by each REOF for annual ET0 data are listed in Table 3. At the same time, the annual ET0 patterns of the (varimax) rotated EOFs for the Yellow River Basin by plotting the isolines of the loading factor values, with the absolute value of rotated loading vector at the mode's center >0.7 and at the boundaries of the regions >0.3, are demonstrated in Figure 8. The first REOF pattern has the highest loadings and accounts for 18.7% of the total ET0 variance. Almost all loadings are positive throughout the basin, and a center can be found in the middle area of the Yellow River Basin (104.7°E, 36.6°N) with a rotated loading vector value equal to 0.85. The dominated area with the rotated loading vector value >0.3 mainly covered over the Loess Plateau (see Figure 8a). This region is characterized by the lower amount (see Figure 2) and weaker variation (see Figure 4) of ET0. The second REOF pattern (see Figure 8b) indicates a center in the lower mainstream section (111.0°E, 34.1°N) with a rotated loading vector value equal to 0.9. The area with a rotated loading vector value >0.3 mainly locates in the plain of middle and lower reaches of the basin. The amount and variation of ET0 are highest around this region (see Figures 2 and 4), which is a humid climatic area. The famous Hetao Plain (Hetao means the bend of a river in Chinese) is associated with the third REOF pattern and a center of this mode is located in the northern side of the basin (112.5°E, 40.0°N) (see Figure 8c). The fourth REOF pattern (Figure 8d) represents mainly the western area of the Hetao Plain and Longxi Plateau with 9.7% explained variance. There are also two scattered centers on northwestern (107.1°E, 40.9°N) and midwestern parts (101.8°E, 36.7°N) of the basin with rotated loading vector values 0.64 and 0.79, respectively. The fifth REOF pattern (Figure 8e) shows a center in the Ningxia Hui autonomous region (106.8°E, 39.2°N) with a rotated loading vector value equal to 0.89. Those areas with a rotated loading vector value >0.3 include the western parts of the basin. The last REOF pattern (Figure 8f) is centered in the part of the Qinghai-Tibetan Plateau (102.6°E, 32.8°N), the upper mainstream section and the highest area of the Yellow River Basin, with the rotated loading vector value 0.89. According to the output of REOF analyses of annual ET0, the 80 stations widespread over the basin are separated into six clusters (Figure 9). It should be particularly interesting to point out that unlike the way to divide the Yellow River Basin into three parts according to the topography and elevation in the study of Liu et al. , we identify the homogenous regions by the virtue of the REOF method. There may be some uncertainty in subregion selection on the basis of visual inspection of the geographical distribution or administrative practices due to its vulnerability to subjective discretion. For example, the subregions of upper, middle, and lower reach of the Yellow River Basin defined in literature [e.g., Huang et al., 2009] are different from the study of Liu et al. . Compared with boundaries determined in term of topography, climatic homogeneous area partitioned objectively by clustering algorithms can capture more realistic spatial information. Investigation on spatial and seasonal differences in the reason and the contributing climatic variables for the ET0 trends over the Yellow River Basin presented in section 4.5 is based on the regional average data of the six homogenous regions identified above.
Table 3. Before and After the First 11 Rotate Principal Components of the Variance Contribution (%)
% of Variance
% of Variance
4.5. Contributions to ET0 Trend
 The results of trend analysis for the area-averaged ET0 and four major meteorological variables in categorized six subregions are summarized in Table 4. The area averaged ET0 for 1957–2008 presents significant negative trends for subregions II and IV at confidence level of 95%, with slopes of about −1.5 and −1.8 mm yr−1, respectively. Significant positive trends at confidence level of 95% are found in subregions I, V, and VI with the slopes of about 0.7, 1.7, and 1.1 mm yr−1, respectively. In addition, a weak downward trend in subregion III can also be detected for recent decades. Although there are differences in magnitudes of change between seasonal and annual series, all the seasonal series present the same directions of change with that of annual series except the spring ET0 series in subregions II and III. The overall impression from the trends in meteorological variables is that except for the trend in temperature, other trends in the regional averaged series display obvious variability in time and space, which are similar to the results based on the individual station performed above. The significant positive trends in annual mean temperature can be found in all the subregions. As for relative humidity, only subregion VI was dominated by significant negative trend. The significant negative trends in all seasonal sunshine duration series except spring series are mainly found in subregions II, III, and IV. Almost all of the four seasons are dominated by increasing temperatures in all subregions. The highest positive slope of 0.06°C yr−1 is found in subregion VI during winter. Significant decreasing trends in seasonal relative humidity series can only be found in subregion VI, while positive trends mainly occur during winter. For seasonal wind speed, the significant decreasing trends can be found in all the seasons in subregions II, III, IV, and VI.
Table 4. Slope Values of Annual and Seasonal of ET0 and Four Climatic Variables of Six Subregions in the Yellow River Basin During 1957–2008
Note: * indicates significant trends at the 5% level of significance determined by MK test.
ET0 (mm yr−1)
Sunshine Duration (h d−1 yr−1)
Air Temperature ( °C yr−1)
Relative Humidity (% yr−1)
Wind Speed (m s−1 yr−1)
 In order to quantify the impacts of these variables on ET0, the meteorological variables were detrended and the difference between the original reference evapotranspiration and the recalculated evapotranspiration with detrended series was identified. These contribution analyses (see section 3.4) were done for all the subregions at annual and seasonal scales. For illustrative purposes, the annual original meteorological series and the detrended series of subregions I and II are plotted in Figure 10, and the original ET0 and the recalculated ET0 for the annual and seasonal series are demonstrated in Figures 11 and 12, respectively. The original annual values, the detrended ones, and their trend lines shown in Figure 10 suggest that after detrended, the trend of original series can be extracted and removed, and the original series with variation become stationary time series. The difference between the original ET0 and recalculated ET0 can reveal the contribution of the meteorological variables to the ET0 trends. Taking the annual wind speed series of subregion IV as an example (see Figure 11), the result shows that if the detrended wind speed is used, the recalculated ET0 will have a positive trend. In other words, the difference between original ET0 series and recalculated ET0 with detrended wind data represents the contribution of wind speed to the trend in ET0. In subregion IV, a large positive difference can be found between the original ET0 and recalculated ET0 with the detrended, and a smaller but still remarkable positive and negative difference can be found between the original ET0 and recalculated ET0 with detrended sunshine duration and temperature, respectively. The contribution analysis in annual meteorological variables in subregion IV reveals that there is a combined effect of all variables and the decreasing trend in wind speed was the main cause of the decrease in ET0 on subregion IV. The same explanation applies to the other subregions. Overall, it is concluded from Figure 11 that the dominated factors vary in different subregions, indicating that the contribution to annual ET0 variation is different spatially. Wind speed is recognized as the major driving force for the decreasing trends in ET0 in subregions III and IV. While temperature is mainly responsible for the increasing trends in ET0 in subregions I and VI. The decrease of ET0 in subregion II and the increase of ET0 in subregion V are mainly attributed to the decrease of sunshine duration and the relative humidity, respectively. Furthermore, the contribution analysis in seasonal series (see Figure 12) indicates that the relative importance of the climate factors on the changes in ET0 may also vary with seasons. In spring, relative humidity is dominant factor for subregions I, II, and V, and wind speed for subregions III and IV, while mean temperature for subregion VI. In summer, compared with the spring, the dominant factor becomes sunshine duration for subregions I and II, and wind speed for subregion V. Compared with summer, except for subregion V, the almost dominant factor for the changes of ET0 in autumn is relative humidity. In winter, the impact of mean temperature in subregions I, III, V, and VI become the strongest, while for subregions II and IV, the dominant factors are sunshine duration and wind speed, respectively.
4.6. Sensitivity of the ET0 to Climatic Variables
 The fact that the climatic variables (such as the relative humidity in subregion V in winter) present insignificant trends but provide the largest contribution to the changes of ET0 makes it necessary to conduct the sensitivity of the ET0 to climatic variables. There are many sensitivity analysis methods, such as derivative analyses, regression technique, Bayesian analysis, and Fourier analyses, that can be used to assess the impact of one variable to model output. In this study, sensitivity curve method, with the procedure of plotting relative changes of a dependent variable against relative changes of an independent variable as a curve, was employed to determine the change in ET0 expected for change in one of the climatic variables. This method has been used by many researchers due to its simplicity and practicability [e.g., Paturel et al., 1995; Goyal, 2004; Xu et al., 2006; Wang et al., 2011]. Seven climate change scenarios (i.e., of , where is the meteorological variable) were used as the input for the FAO PM model. The results of the sensitivity analysis in six subregions for seasonal and annual scales are illustrated in Figure 13. For the same relative change of the variable, the larger the corresponding relative changes of ET0, the stronger the sensitivity of the variable. The sensitivity of ET0 to the meteorological variables varies in time and space. Annually, the positive relation of the relative change in ET0 with mean temperature, wind speed, and sunshine duration and the negative relation with relative humidity indicate that ET0 decreases with decrease of mean temperature, wind speed, and sunshine duration but increases with the reduction of relative humidity. Although there are differences in sensitivity of ET0 to the relative humidity among subregions, it is clear that relative humidity is the most sensitive variable for all the seasons and the year. This is in accordance with Yin et al. , which reported that relative humidity was the most sensitive variable in all different climate regions of China. This result has also been confirmed by other regional studies in China [e.g., Xu et al., 2006; Gong et al., 2006; Zheng et al., 2009]. Furthermore, in most subregions and seasons, sunshine duration generally is the second sensitive variables, while mean temperature exhibited the least sensitivity.
4.7. Test of the Bouchet's Complementary Relationship
 Compared with ET0, ETa, the hydrologic flux of interest, is a more complicated variable reflecting complex interactions among climate, vegetation and soil characteristics, and condition of water supply. As for the relationship between ETp and ETa, there is a famous Bouchet's complementary hypothesis [Bouchet, 1963], which states that for large homogeneous surfaces with minimal advection of heat and moisture, ETp and ETa fall in a complementary relationship. The complementary relationship can be theoretically expressed as ETa = λETw − ETp, where ETw is wet environment evapotranspiration and λ is a constant. This implies that all available energy not used by ETa goes to heat and dry the atmosphere, driving ETp above ETw by the amount that ETa allows [Zhang et al., 2007]. With ignoring the interannual change of water storage in the catchments, ETa was estimated from the annual water balance (ETa = P − RO, where P is basin-wide precipitation and RO is runoff), which was used as the “measured” ETa for analysis. As a very good representative of ETp under a given condition, ET0 was used as ETp value to examine the Bouchet's hypotheses. Meanwhile, the Priestley-Taylor equation [Priestley and Taylor, 1972], which was widely used [e.g., Hobbins et al., 2001; Yang et al., 2006], was employed to estimate ETw. To analyze possible change in ETa related to changing ET0, we examined the relationship between precipitation and evapotranspiration processes in the six subregions and found the apparent complementary relationship came about in all subregions (Figure 14). Moreover, λ (the ratio of ETa + ETp to ETw) in the complementary relationship for different subregions are estimated as 1.36, 1.61, 1.38, 1.24, 1.24, and 1.2 for subregions I, II, III, IV, V, and VI, respectively, which are far less than the theoretical value of 2.0 and decline with the increase of elevation. Similar phenomenon also has been obtained from the recent countrywide analysis in China [Yu et al., 2009].
4.8. The Implication of ET0 Changes for Drought Variation
 As a serious environmental problem, droughts always have tremendous economic and social implications. From a hydrological perspective, change in seasonality and regionality of hydroclimatic variables including ET0 and precipitation are important for recent occurrence of seasonal drought in the Yellow River Basin. Thus, the surface humid index (SHI) (written as SHI = P/ETp, here ET0 was used as ETp), a parameter considering two major surface hydrological processes—precipitation and ETp—suggested by Hulme et al. , was employed to analyze the changes in state of dry and wet in the Yellow River Basin. Also, the relative importance for changes in ET0 and precipitations to drought trends are investigated by means of stepwise regression method. The trends in annual and seasonal scales in six subregions are shown in Figures 15 and 16, respectively. At an annual scale, there is a decrease in the SHI trends in subregions I, III, and V, indicating that the magnitude of drought are intensified in these regions (Figure 15). However, only the dry trends in subregion I passed the statistical test at significance level of 95%, exactly confirming the fact that the drought issues are most pronounced in the middle regions [Wang et al., 2004; Kang et al., 2004]. Furthermore, a notable observation for temporal evolution of SHI, precipitation, and ET0 is that generally similar changing pattern can be found between SHI and precipitation. Whereas the ET0 presents rather different or even opposite (e.g., in subregions I, IV, and V) changing characteristics in comparison with that of SHI. A similar behavior is seen for seasonal series (Figure 16). Concurrently, remarkable seasonality for SHI change can be found for almost all the subregions. Take subregion I as an example, it appears that significant drying trends can be found in spring and autumn, while converse behaviors emerge in winter. Similar with the annual results, seasonal drying trends are mainly found in subregions I and II. What is the main contribution factor for the drought in the Yellow River Basin, precipitation or ET0? The phenomenon that SHI exhibits resemble evolution processes with precipitation and obviously distinct behavior with ET0 over time easily suggest that precipitation plays a more important role in drought change than ET0. However, the credibility of this deduction needs to be tested statistically. Therefore, the stepwise regressions analysis was performed to determine the relative contributions of precipitation and ET0 change to SHI trends (Table 5). Compared with ET0, precipitation has overwhelmingly dominant influence on the SHI change for all the subregions in all the seasons. This finding holds also for all individual station series (map not shown here because of space limitation) for annual and seasonal scales. Nevertheless, ET0 changes undoubtedly intensify the drought variation, particularly for the recent two decades. For example, for subregion V, although precipitation shows almost no variation after the 1990s, apparent decrease in SHI can be easily found due to remarkable increase in ET0 in this region (Figure 15). While for subregion III, suppressive effect from ET0 changes on drying trends is observed. Therefore, it can be concluded that although increasing ET0 in subregions I and V is not the main reason, it intensified the drought in these regions. This conclusion gives a catchment-scale perspective on previous findings by Ma and Fu , which reported that the drought in the center of north China main resulted from the decrease in precipitation and was partly due to the increase in ETp.
Table 5. Trend Slope and Absolute Value of the Standardized Regression Coefficient of the Precipitation and ETp for Six Subregions During 1957–2008 on the Yellow River Basin
SHI (% yr−1)
P (m yr−1)
Standardized Regression Coefficient
Note: * indicates significance at 95% confidence level through the MK test.
 It is easy to understand that whether or not one climatic variable is the main reason to long-term trends of ET0 depends on the combined effect between sensitivity of this climatic variable to ET0 and slopes of the variable itself. Therefore, we demonstrated the result of the magnitudes of the climatic variable, the sensitivity of climatic variable to ET0, and the contribution of climatic variable to ET0 trends over different subregions on annual and seasonal scales in the same chart (Figures 17 and 18) to illustrate the reason for the detected ET0 changes more easily. Taking subregion I as an example, the fact that although mean temperature is the least sensitive variable to ET0 among the four major climatic variables, it presents the largest contribution (see Figure 17) to the increasing trend in ET0 (see Table 4) and is the only variable showing significant trend (see Figure 17). Another example is that although relative humidity is the most sensitive variable to annual ET0 in subregion III, it presents the smallest impact on the ET0 change since relative humidity is the only variable showing an insignificant trend (see Figure 17). Generally, significant increase of mean temperature should be the main causes of the increase of annual ET0 in subregions I and VI, followed by decreasing relative humidity. The leading factor for annual ET0 change in subregions II and V is sunshine duration and relative humidity, respectively, followed by wind speed. The significant decreasing wind speed mainly attributes to the decreasing ET0s in subregions III and IV. In the light of the analyses above, one can appreciate that high spatial heterogeneity can be found not only in ET0 change but also in the influencing variables. Three subregions show upward trends in ET0 with two being significant and the other three show downward trends with two being significant (see Table 4). Also, there are complex spatial patterns in the leading factor (see Figure 17). As the largest river basin, the Yellow River experiences a variety of geomorphologic patterns from origins to the river mouth [Yang et al., 2004], the Tibet Plateau with elevations from 2000 to 5000 m, the Loess Plateau with elevations from 500 to 2000 m, and the alluvial plain in the eastern part. More significantly, the climate conditions vary from cold to warm zones and change from arid and semiarid regions [Cheng, 1996]. Multifarious climatic features, coupled with complicated geographic conditions in such a large basin are bound to determine the spatial differences in ET0 trends and its contributing factors. Similar results exhibiting quite obvious spatial and regional differences in controlling climatic factors have also been identified in the Qinghai-Tibetan Plateau [Zhang et al., 2009], the Yangtze River Basin [Xu et al., 2006], and the Haihe River Basin [Wang et al., 2011]. At the seasonal scale, the variations of the main causes to the ET0 trends are mainly found in subregions I and V. In four seasons, three different controlling climatic variables can be found in subregions I and V. While subregion VI is predominated by mean temperature of all the seasons, and changes of ET0 in subregions III and IV are attributed to wind speed in all the seasons. The fact that ET0 changes should be explained with the combined effect between changing trends of the climatic variables and their sensitivity have been confirmed again by the seasonal patterns. For instance, in spring, despite presenting the significant increasing trends in all the subregions, mean temperature is only responsible for the ET0 increase in subregion VI. In contrast, despite presenting insignificant trends in all the subregions, relative humidity has the greatest impact on ET0 in subregions I, II, and V due to its strongest sensitivity. Presenting simultaneously the change patterns of the climatic variables, sensitivity to ET0 and contribution to ET0 trends in forms of quantification and combination can provide comprehensive and well-understood information and interpolation for ET0 change in the region. Generally, although we confirm the results that the ET0 changes are driven by the combination of climatic variables including sunshine duration, temperature, relative humidity, and wind speed, as identified by Liu et al. , our results indicate that there have been significant seasonally and regionally variation in the contributing factors to ET0 changes across the Yellow River Basin, which have not been revealed in previous studies. For example, Liu et al.  suggested that mean temperature was the leading factor for ET0 increase in middle regions. However, our results show that mean temperature is the main influencing factors for ET0 change only in subregion I, a part of middle regions defined in the study of Liu et al. , while ET0 change in subregions III and V (other parts of the middle region) should be attributed to wind speed and relative humidity, respectively. Regional diversity of the ET0 response to climatic factors in the Yellow River Basin was not conducted in the previous study. In addition, although for annual series, mean temperature have the first role in ET0 changes in subregion I, three different dominant climatic variables can be found in this region at the seasonal scales (see Figure 15).
 Overall, it can be concluded from the above analyses that the decrease of surface wind speed is mainly responsible for the ET0 reduction in the west and north of the Loess Plateau mostly including subregions III and IV. The reduced sunshine duration is the leading factor for ET0 decrease in the middle-lower Yellow River Plain mainly including subregion II. Furthermore, increasing mean temperature plays the most important role in ET0 increase in subregion VI, the source area of the Yellow River Basin, which belongs to part of the Qinghai-Tibetan Plateau. The decrease of wind speed presented in most areas of the Yellow River Basin confirms the recent research results by Fu et al.  and Guo et al. , which revealed that China is dominated by a declining trend in wind speed during the past several decades. At the same time, wind speed as the decisive factor for the ET0 or pan evaporation change have been also reported in some places, such as, Australia [Roderick et al., 2007; Rayner, 2007], the north of the Qinghai-Tibetan Plateau [Zhang et al., 2009], Canadian Prairies (Burn and Hesch, 2007), the Haihe River Basin [Zheng et al., 2009; Wang et al., 2011], north China [Yin et al., 2010], and most parts of China [Yang and Yang, 2012]. Recently, writing in Nature Geoscience, McVicar and Roderick  reviewed the recent slow-down in global near-surface winds and emphasized that one of its obvious implications is partially offsetting any rise in evaporation at higher elevation regions. McVicar et al.  showed that terrestrial stilling is a globally widespread phenomenon through a global review of 148 studies reporting wind speed trends and highlighted the contribution of wind speed to the declining evaporative rates. Vautard et al.  proposed that the decline of wind speed at least partially attribute to increases in terrestrial surface roughness. This finding can be confirmed by the study of Fu et al.  and Bandyopadhyay et al. , which both partly relate the wind speed decreases with increasing artificial structures originated from urbanizations. However, Jiang et al.  suggested that the main reason for the decreasing trends in China were considered as the decreasing East Asian winter and summer monsoons under the background of global warming, a similar conclusion by Xu et al. . Zhang et al.  indicated that significant decreases in wind speed over the Qinghai-Tibetan Plateau were in accordance with the decreasing trends of upper-air zonal wind and the decline of the pressure gradient. Furthermore, McVicar et al.  recently found that wind speed has declined more rapidly at higher than lower elevations by the observational evidence from two mountainous regions. Many researchers found potential reasons for the decline of wind speed, such as the above mentioned, up to now it is difficult to reach consensus as it is a complicated issue.
 Decreasing global radiation or sunshine duration has also been considered an important leading factor for ET0 or pan evaporation decrease in many parts of the world. Roderick and Farquhar  found that the general decrease in pan evaporation in the Northern Hemisphere was associated with observed widespread decreases in sunlight as a consequence of increased cloud coverage and/or aerosol concentration. Jhajharia et al.  also indicated that sunshine duration was the most influencing variable for pan evaporation changes in northeast India in winter, monsoon, and premonsoon seasons. There is consensus among many researchers that increasing aerosol loading should be responsible for the sunshine hour decrease [e.g., Kaiser and Qian 2002; Forster et al., 2007; Ramanathan et al., 2007]. Decreasing global radiation or sunshine duration is a regional phenomenon in eastern China, which may be due to the increased air pollution [Zhang et al., 2004]. Another study by Liu et al.  also found that unlike some parts of the world, the decrease in solar irradiance in China was not always accompanied by increase in precipitation, confirming that aerosols may play a critical role in the decrease of solar irradiance in China. Furthermore, the consistent spatial and temporal patterns of trends in annual sunshine duration and surface air temperature on the Yunnan-Guizhou Plateau in southwest China support the currently accepted reason that the cooling in southwest China might have been caused by negative radiative forcing of aerosols from enhanced pollutants [Zheng et al., 2008]. However, the recent study by Yang et al.  argued that wind speed may be another important influencing factor of sunshine duration apart from the aerosols in north China since the spatial average distribution of wind speed is very consistent with the declining trend in sunshine duration, and concurrently the interactions between wind speed and aerosol loading may be enabling forces behind wind speed to strongly drive changes in sunshine duration. It is easy to understand that a great deal of uncertainties about investigating the reason for decline of sunshine duration should exist due to numerous factors and complex climatic and physical mechanism, which thus need to be further studied.
 It should be noted that although ET0 and pan evaporation can provide a useful clue to the direction of the change in ETa [Ohmura and Wild, 2002; Xu et al., 2006], as the important component of hydrologic flux, ETa is the more interesting variable. However, as we mentioned in section 1, ETa is difficult to be evaluated due to its numerous influencing factors including climatic factors, vegetation, soil characteristics, and available water restriction. Therefore ETa is usually estimated through less complex physically based or empirical approaches. As for the Yellow River Basin, ETa calculated by the simple two-parameter steady state model presented significant decreasing trends in all regions of the Yellow River Basin [Liu and Yang, 2010]. However, the study by Gao et al.  on ETa trend estimated by modified water balance methodology by Thornthwaite and Mather  suggested that the Qinghai-Tibet Plateau parts of the Yellow River dominated by increasing ETa. Despite that both of them considered that precipitation plays the more important role for the ETa change, it cannot be denied that the choice of model and parameter will lead to the uncertainty of ETa change. For instance, the phenomenon that the different picture of evaporative demand changes will be painted from temperature-based ETp formulation and a physically based one considering multiple variables have been discussed and confirmed [Hobbins et al., 2008; Roderick et al., 2009b; Donohue et al., 2010]. Furthermore, adverse changing direction between ETp, pan evaporation, and ETa can be found in certain cases, indicating decreasing/increasing ET0 and pan evaporation did not necessarily mean decreasing/increasing ETa [Linacre, 2004; Zhang et al., 2009]. For example, the argument that the decrease in pan evaporation actually provided a strong indication of increasing actual evapotranspiration in many situations have been used to explained the evaporation paradox by Brutsaert and Parlange . In addition, direct observational evidence has been provided by Ramírez et al.  to verify the complementary relationship between ETp and ETa derived by Bouchet . However, several extremely water-limited regions are difficult to reconcile to this interpretation where decline in ETa is concurrent with a decline in pan evaporation or ETp (e.g., southeastern Australia, Roderick and Farquhar ). Roderick et al. [2009b] pointed out that energy-limited and water-limited conditions should be distinguished and changes in supply under water-limited conditions should be inspected when employing pan evaporation record to interpret changes in the surface water balance.
 According to our analysis, ETa and ETp exhibit the complementary relationship in all the subregions of the Yellow River Basin, but they increasingly deviate from 1:1 complementary relationship along with the increase of elevation. Similar conclusions have been drawn in national scale [Yu et al., 2009], which are attributed to increasing radiation energy budget and decreasing vapor transfer power at the high elevation. In nonhumid regions like the Yellow River Basin, ETa obeys the complementary relationship with ETp, indicating that change in ETa is dominated by change in precipitation rather than ETp. In despite of decrease in ETp or ET0, ETa may increase when the decreasing magnitude of ETp or ET0 are greater than that of λETw. Nevertheless, the current results and recent related studies on this topic generally suggest that the full trigger mechanism for evapotranspiration is far from resolved. Therefore, further studies still need to be conducted to identify the roles played by the choices of models and parameters when ETa is estimated, and more comprehensive work should be conducted to investigate the change in evapotranspiration processes with consideration of local condition and factors.
 In our study, special efforts are made in providing a more detailed spatial description than in previous studies, which are necessary due to the large spatial variability of climate and geography in the Yellow River Basin. Change in seasonality of hydroclimatic variables may be more important for recent occurrence of seasonal drought in the Yellow River Basin and also in broader perspectives of hydrological environment and agricultural ecology. We thus attempt to address these concerns by extensively examining changes in ET0 and related climatic variables and find some seasonal behaviors. Spatial pattern of ET0 and related climatic variable changes on station basis documented here offers more comprehensive demonstration. This, in combination with distinctly different seasonal characteristics for ET0 changes and their contributing factors which were not examined in a previous study, as well as the implication of spatial heterogeneity and seasonality of ET0 changes for drought, delivers new information and aspects on the ET0 changes of the Yellow River Basin and thus highlights the significance of the present study.
 In this study, ET0, an indicator of atmospheric evaporating capability over a specifically hypothetical reference surface, was estimated using the Penman-Monteith method with the calibrated Angstrom coefficients for 80 stations across the Yellow River Basin during 1957–2008. Spatial and seasonal patterns of the ET0 trends were specially focused with the help of REOF clustering method together with some advanced statistical tests. Further analysis of sensitivity of ET0 to climatic variables and the contribution of climatic variables to ET0 changes over six homogenous regions on annual and seasonal scales revealed the combined effects of climatic variables to ET0 changes and their spatial and temporal variability. Furthermore, complementary feedback mechanism between ETp and ETa within the framework of Bouchet's hypothesis in this basin was examined. Also, the relative contributions of ET0 and precipitation changes to drought were evaluated. Some interesting findings are obtained from this investigation as follows:
 1. The annual ET0 over the Yellow River Basin has a rich spatial structure with relatively low values in the southwestern part of the basin (Qinghai and Sichuan Provinces) and high values in northwestern (Inner Mongolia) and southeastern (Shandong Province) parts. Concurrently, the entire Yellow River Basin is characterized by complicated spatial variability in the change of ET0. Twenty-two stations (i.e., 27.5% of all stations) present significant negative trends at the 95% confidence level, and mainly distribute in three areas, i.e., southeast corner, northern sides, and midwest of the Yellow River Basin. Twenty-six stations (i.e., 32.5% of all stations) are dominated by significant decreasing trends, mainly occurring in the middle part and southwest corner of the basin. Spatial heterogeneities have also been detected in trends in seasonal ET0. Trends in summer ET0 have relatively similar spatial distribution patterns to that of annual ET0 and present the largest slope among four seasons. For most stations in the middle and lower regions, significant seasonal ET0 changes can only be found in spring and summer, respectively.
 2. The trends of climatic variables in the Yellow River Basin vary spatially and seasonally. However, the dominance of warming trends in temperature and negative trends in wind speed and sunshine duration can be found in the Yellow River Basin. For the annual and seasonal relative humidity, the basin has many insignificant or weak trends and a mixed spatial structure of positive and negative trends. There are differences in magnitudes of change for the climatic variables between different seasons. Springs and winters have experienced the largest increase in temperature, and summers and winters have experienced the largest decrease in wind speed in the basin.
 3. The Yellow River Basin can be categorized into six subregions by REOF analysis based on the ET0 data at 80 stations for 1957–2008. Six subregions can be roughly described respectively as below. Subregion I: the middle area of the Yellow River Basin, subregion II: the plain in lower reaches of the Yellow River Basin, subregion III: the northern sides of the basin, subregion IV: the western area of the Hetao Plain and Longxi Plateau, subregion V: the western parts of the basin, and subregion VI: the upper mainstream section of the Yellow River Basin.
 4. The sensitivity of ET0 to the climatic variables varies in different seasons. However, relative humidity and mean temperature are apparently the most and least sensitive variables, respectively, for almost all the seasons and for annual series. Moreover, in most seasons, sunshine duration or wind speed are generally the second sensitive variables. There are no obvious differences in the sensitivity for the same climatic variable over different subregions except for the relative humidity, whose sensitivity is remarkably larger in the lower section of the Yellow River Basin than other areas.
 5. The ET0 change is the results of the combined influence of wind speed, sunshine duration, relative humidity, and temperature. Concurrently, the contribution of climatic variable to the trend in the ET0 depends on not only the actual temporal change of the variable but also the sensitivity of ET0 to this variable. The dominant variables for the ET0 change vary spatially and seasonally. The decline of surface wind speed is mainly responsible for the ET0 reduction in the west and north of the Loess Plateau mostly including subregions III and IV, almost throughout the year. The reduced sunshine duration is the leading factor for ET0 decrease in the middle-lower parts of the Yellow River Plain mainly including subregion II, especially during the summer period. In addition, increasing mean temperature plays the most important role in ET0 increase in subregion VI, the source area of water in the Yellow River Basin, which belongs to part of Qinghai-Tibetan Plateau. Although mean temperature and relative humidity are, respectively, the main controlling factors for the ET0 change in subregions I and V, three different controlling climatic variables can be found at the seasonal scales.
 6. ETa and ETp in all the subregions exhibited complementary behaviors although the accurate 1:1 complementary relationship within the Bouchet's hypothesis is not followed. Concurrently, the ratio of sum of ETa and ETp to evapotranspiration in a wet environment appears to decrease along with the increase of elevation in the Yellow River Basin. In addition, contribution analysis of ET0 and precipitation changes on drought reveals that the regionality and seasonality of drought variations are predominated by precipitation regime changes and intensified by ET0 changes.
 In this paper we attempted to conduct a systematic analysis of spatial and temporal characteristics of changes in ET0 and the related differences in the contributing factors to the ET0 trends in the Yellow River Basin. We concentrated on the spatial and seasonal differences in the leading factors to the ET0 trends over the basin, which has not been specifically revealed in the previous studies. The distinct seasonal patterns of ET0 and spatial variability of the influencing climatic variables for the ET0 change in the study, highlighting the importance of investigating the hydrological and meteorological processes at high time and space resolution. Simple but practical sensitivity and contribution analysis in this study can avoid the uncertainties from the determination of the derivatives by using the mean partial derivatives. Furthermore, combining and quantitatively demonstrating the change patterns of the climatic variables, their sensitivities to ET0 and contributions to ET0 trends at both annual and seasonal scales in this study can provide comprehensive and well-understood information and interpolation for ET0 change in the basin. In addition, a complementary relationship between the ETa and ETp identified may give a theoretic basis for explanation of complex feedback hydrological processes. A larger picture of significance of regional and seasonal difference in ET0 changes was depicted by the analysis of implication of ET0 and precipitation changes for drought variation.
 This work was financially supported by the National Science Foundation of China (51009046, 50839002), the Natural Science Foundation of Jiangsu Province (BK2010519), the Open Research Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science (2009B053), and CSIRO Transformational Capability Platform-Computational and Simulation Sciences. We thank the National Climatic Centre (NCC) of the China Meteorological Administration (CMA) for providing the valuable meteorological data. Cordial thanks are extended to the Editor-in-Chief Professor Praveen Kumar, the Associate Editor, and three anonymous referees for their valuable comments which greatly improved the quality of the paper.