# Reference Evapotranspiration Changes: Sensitivities to and Contributions of Meteorological Factors in the Heihe River Basin of Northwestern China (1961–2014)

Authors: Chaoyang Du; Jingjie Yu; Ping Wang; Yichi Zhang
Journal: Advances in Meteorology
 (2016)

---

## Abstract

This paper investigates reference evapotranspiration(ET0) changes, sensitivities to and contributions of meteorological factors in the Heihe River Basin (arid and inland region). Results show that annual ET0 over the whole basin has increasing trend (2.01 mm·10 yr−2) and there are significant increasing spatial variations from the upper (753 mm yr−1) to the lower (1553 mm yr−1) regions. Sensitivity analysis indicates that relative humidity is the most sensitive factor for seasonal and annual ET0 change, and the influence is negative. The sensitivity of minimum temperature is the weakest and negative. Contribution analysis shows that the main contributors to ET0 changes are aerodynamic factors rather than radiative factors. This study could be helpful to understand the response of ecoenvironment to the meteorological factors changes in the Heihe River Basin.


---

## Body

## 1. Introduction

Evapotranspiration is an excellent indicator of hydroclimatic change and the response of water management, food security, and ecoenvironment [1]. Among different evapotranspiration terms, such as actual evapotranspiration (ETa), potential evapotranspiration (ETp), pan evaporation (Epan), and reference evapotranspiration (ET0), Epan and ET0 are often used as surrogates of ETp to reflect the evaporation capability in a specific region. Because ETp and ET0 are dependent only on meteorological condition not underlying surface and are measurable or calculable, they are important hydroclimatic indicators for reflecting regional water-energy balance changes and the effect of climate change. Spatiotemporal variations of ET0 in different climatic regions have been globally reported over the past decades [2, 3]. Many regions have experienced significant decreasing trends of Epan or ET0, such as the US [4], China [5], Canada [6], Australia [7], India [8], Japan [9], and Romania [10]. However, ET0 changes with significant positive trends have been reported in other regions, such as the Mediterranean region [11], Iran [12], Spain [13], and Serbia [14]. Moreover, the interannual fluctuations of ET0 for some regions are very significant; ET0 may increase during one period but decrease during the next period [5, 7]. Therefore, the temporal variations of ET0 are complex and diverse in different climatic zones. Reasons for the different temporal variations of ET0 in different climatic zones need to be explored in further detail.The causes ofET0 changes in many regions have been studied. First, the effects of different methods on ET0 changes have been discussed in different climatic zones. Popular methods for ET0 calculation mainly include FAO P-M, Priestley-Taylor, Hargreaves, Makkink, Blaney-Criddle, and Samani-Hargreaves methods [15]. Comparisons showed that FAO P-M performs better among the different methods due to having the clear physical meaning and is recommended as a standard method for the ET0 calculation [16, 17]. Second, a sensitivity coefficient was used to investigate the effects of meteorological factors on ET0 change [18–20]. Most studies showed that aerodynamic factors are the major factors in different regions. For example, air temperature, wind speed, and relative humidity have stronger effects on ET0 change in Spain [20]. Air temperature and wind speed are the dominant variables influencing ET0 in Iran [12]. Air temperature is the most sensitive variable to ET0 change in India [21]. Similar results have also been found in some regions of China, in which wind speed, air temperature, and vapor pressure deficit are the major sensitive factors for ET0 change in such areas as the Loess Plateau Region [22], the Liaohe delta [23], the Tibet Plateau [24], the Changjiang River Basin [19], and the Haihe River Basin [25]. Some studies proposed a close agreement between changes in ET0 and solar energy in Greece [26], Korea [27], and the Yellow River Basin [28]. Sensitivity analysis could only describe the responses of ET0 to changes in individual factor. However, it cannot determine how much the impact of each meteorological factor on ET0 change is.The Heihe River basin (HRB), the second largest inland river basin in northwestern China, consists of three regions with different landscapes and climate conditions, where the upper mountainous region is semiarid and natural with little human interference, the middle region is dry and intensively irrigated plain, and the lower region is an extremely dry Gobi desert plain. The spatial variation ofET0 in such basin may supply more information of regional response to the climate. The previous studies only reported the spatiotemporal variations of ET0 [29, 30] at a given period, but there is no common understanding of ET0 change so far due to different data time series. The aim of this paper is to clarify the effect of meteorological factors on ET0 change by comprehensively analyzing the sensitivity of ET0 change and contributions of meteorological factors in the HRB using reliable and complete daily meteorological data from 16 stations for the period 1961–2014. This paper will determine (1) the spatial pattern and temporal trends of ET0 for the HRB, (2) the sensitivity of ET0 to meteorological factors, and (3) the contributions of the meteorological factors to ET0 change.


## 2. Study Area and Data

### 2.1. Study Area

As shown in Figure1, the drainage map and the basin border of the HRB are extracted using a 90 m resolution digital elevation model (DEM) data from the Shuttle Radar Topography Mission (SRTM) website of the NASA (http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp) (basin length: 820 km; total area: 143,000 km2; elevation: 870–5545 m).Figure 1
Location of the HRB and spatial distribution of the meteorological and radiation stations. U, M, and L represent the upper, middle, and lower regions in the basin, respectively.The HRB is divided into three regions according to basin characteristics, shown in Figure1. The upper mountainous region belongs to the cold and semiarid mountain zone with an elevation from 2000 to 5000 m, annual mean temperature of less than 2°C, pan evaporation of 700 mm yr−1, and precipitation of 350–400 mm yr−1. The middle region is the main irrigation zone and residential area with more than 90% of the total population of the basin; it has a precipitation of 100–250 mm yr−1 and pan evaporation of 2000 mm yr−1. The lower region is covered by the arid Gobi desert in the north of the basin with an elevation of 870–1500 m and is characterized by an extremely arid climate, with pan evaporation of 3500 mm yr−1 and precipitation of 10–50 mm yr−1.


### 2.2. Data

In this study, daily meteorological data of 16 stations from 1961 to 2014 in and around the HRB are available from the National Climatic Centre of the China Meteorological Administration. The three solar radiation stations correspond to the upper, the middle, and the lower region (Figure1). The data set includes daily observations of atmospheric pressure, maximum and minimum air temperatures at 2 m height (Tmax, Tmin), relative humidity at 2 m height (RH), daily sunshine duration, pan evaporation measured using a metal pan, 20 cm in diameter and 10 cm high, installed 70 cm above the ground, and wind speed measured at 10 m height which was transformed to wind speed at 2 m height (WS) by the wind profile relationship from Chapter 3 of the FAO paper 56 [16]. In addition, the three radiation stations were used to calibrate the Ångström parameters of extraterrestrial radiation reaching the earth on clear days in the FAO P-M equation. The spatial patterns of the meteorological factors, ET0, and sensitivity coefficients were obtained by the inverse distance weight (IDW) interpolation method.In this study, the four seasons of the HRB are defined as spring (from March to May), summer (from June to August), autumn (from September to November), and winter (from December to February).


## 2.1. Study Area

As shown in Figure1, the drainage map and the basin border of the HRB are extracted using a 90 m resolution digital elevation model (DEM) data from the Shuttle Radar Topography Mission (SRTM) website of the NASA (http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp) (basin length: 820 km; total area: 143,000 km2; elevation: 870–5545 m).Figure 1
Location of the HRB and spatial distribution of the meteorological and radiation stations. U, M, and L represent the upper, middle, and lower regions in the basin, respectively.The HRB is divided into three regions according to basin characteristics, shown in Figure1. The upper mountainous region belongs to the cold and semiarid mountain zone with an elevation from 2000 to 5000 m, annual mean temperature of less than 2°C, pan evaporation of 700 mm yr−1, and precipitation of 350–400 mm yr−1. The middle region is the main irrigation zone and residential area with more than 90% of the total population of the basin; it has a precipitation of 100–250 mm yr−1 and pan evaporation of 2000 mm yr−1. The lower region is covered by the arid Gobi desert in the north of the basin with an elevation of 870–1500 m and is characterized by an extremely arid climate, with pan evaporation of 3500 mm yr−1 and precipitation of 10–50 mm yr−1.


## 2.2. Data

In this study, daily meteorological data of 16 stations from 1961 to 2014 in and around the HRB are available from the National Climatic Centre of the China Meteorological Administration. The three solar radiation stations correspond to the upper, the middle, and the lower region (Figure1). The data set includes daily observations of atmospheric pressure, maximum and minimum air temperatures at 2 m height (Tmax, Tmin), relative humidity at 2 m height (RH), daily sunshine duration, pan evaporation measured using a metal pan, 20 cm in diameter and 10 cm high, installed 70 cm above the ground, and wind speed measured at 10 m height which was transformed to wind speed at 2 m height (WS) by the wind profile relationship from Chapter 3 of the FAO paper 56 [16]. In addition, the three radiation stations were used to calibrate the Ångström parameters of extraterrestrial radiation reaching the earth on clear days in the FAO P-M equation. The spatial patterns of the meteorological factors, ET0, and sensitivity coefficients were obtained by the inverse distance weight (IDW) interpolation method.In this study, the four seasons of the HRB are defined as spring (from March to May), summer (from June to August), autumn (from September to November), and winter (from December to February).


## 3. Methodology

### 3.1. FAO Penman-Monteith Method

The Penman-Monteith method can be used globally to estimate potential evapotranspiration. Allen et al. simplified the Penman-Monteith equation and defined the hypothetical reference grass with an assumed height of 0.12 m, a fixed surface resistance of 70 s m−1, and an albedo of 0.23 [16]. This method can provide good and reliable results for ET0 because it is physically based and explicitly incorporates both physiological and aerodynamic parameters and has been accepted as a standard to compare evapotranspiration capability for various climatic regions [31]. Moreover, this method has been successfully applied across the whole of China [32, 33]. The FAO P-M for calculating daily ET0 is described as (1)ET0=0.408ΔRn-G+γ900/Tmean+273u2es-eaΔ+γ1+0.34u2,where ET0 is the reference evapotranspiration (mm day−1), Rn is the net radiation at the crop surface (MJ m−2 day−1), G is the soil heat flux density (MJ m−2 day−1), Tmean is the mean daily air temperature at 2 m height (°C), u2 is the wind speed at 2 m height (m s−1), es is the saturation vapor pressure (kPa), ea is the actual vapor pressure (kPa), Δ is the slope vapor pressure curve (kPa°C−1), γ is the psychrometric constant (kPa°C−1); the atmospheric pressure used in this study is the measured value. More details regarding the data processing in (1) can be found in FAO paper 56.In (1), the solar radiation (Rs) is obtained with the following Ångström formula:(2)Rs=a+bnNRa,where Rs is the solar radiation (MJ m−2 day−1), n is the actual sunshine duration (hours), N is the maximum possible sunshine duration or daylight hours (hours), Ra is the extraterrestrial radiation (MJ m−2 day−1), and a and b are regression constants.Because of the effects of the atmospheric conditions (humidity, dust) and solar declination (latitude and month) as well as the elevation variations, the Ångström valuesa and b in the HRB were calibrated using the observed radiation data at the three solar radiation stations (Figure 2).Figure 2
Calibration of the Ångström coefficients for the three radiation stations: (a) Gangcha station in the upper region, (b) Jiuquan station in the middle region, and (c) Ejina station in the lower region.
(a)
(b)
(c)


### 3.2. Trend Analysis

The long-term trends and changes ofET0 and meteorological factors are detected using the linear fitted method: (3)y^=a^t+b^,where y^ is the fitted trend during a given period and a^ and b^ are the estimated regression slope and the regression constant, respectively. Positive slope indicates an increasing trend and negative slope indicates a decreasing trend.For data sets without seasonality, the significance of a trend is described using the Mann-Kendall (MK) test method [34, 35], which is to statistically assess if there is a monotonic trend of the variable of interest over time [36], whilst the Seasonal Kendall (SK) test is extension of the MK test and is suitable for trend applicable to data sets with seasonality, missing values, and serial correlation over time [37, 38]. The SK test begins by computing the MK test separately for each month or season and then summing the statistic Si and variance Var(Si). Following Hirsch et al. [37], the entire sample X is made up of subsamples X1 through X12 (one for each month), and each subsample Xi contains the ni annual values from month i:(4)X=X1,X2,…,X12,Xi=Xi1,Xi2,…,Xi12.The null hypothesisH0 for the SK test is that the X is a sample of independent random variables (xij) and that each X1 is a subsample of independent and identically distributed random variables over years. The alternative hypothesis H1 is that for one or more months the subsample is not distributed identically over years.According to the MK test, the statisticSi is defined by(5)Si=∑k=1ni-1∑j=k+1nisign⁡xij-xik,where(6)sign⁡θ=1,θ>0,0,θ=0,-1,θ<0.Now, the subsampleXi satisfies the null hypothesis of Mann’s test. Therefore relying on Mann and Kendall we have(7a)ESi=0(7b)VarSi=118nini-12ni+5-∑tigititi-12ti+5,where gi is the number of tied groups for the ith month and tip is the number of data in the pth group for the ith month. Si is normal in the limit as ni→∞. The SK test statistic S is given by(8)S=∑i=1mSi,where m is the number of months for which data have been obtained over years. The expectation and variance can be derived as follows:(9a)ES=∑i=1mESi,(9b)VarS=∑i=1mVarSi+∑i=1m∑j=1mcov⁡SiSj,where Si and Sj(i≠j) are function of independent random variables, so cov(SiSj)=0.Forn1>10, the standard normal deviate Z is estimated by (10) to test the significance of trends:(10)Z=S-1VS,S>0,0,S=0,S+1VS,S<0.For the SK test, the null hypothesisH0 means that there is no monotonic trend over time; when Z>Z1-α/2, the original null hypothesis is rejected; this means that the trend of the time series is statistically significant. In this study, significance level of α=0.1 is employed.


### 3.3. Sensitivity Analysis

Saxton [18] and Smajstrla et al. [39] defined the sensitivity coefficient by drawing a curve of the change of a dependent variable versus the changes of independent variables. For multifactor models (e.g., the FAO P-M), due to different dimensions and ranges of different factors, the ratios of ET0 changes and factors changes cannot be compared. In addition, this approach could introduce errors to understand the response of model behaviors to the factors because of changing one of the factors but holding other factors stationary [27]. To avoid the above two disadvantages, the dimensionless sensitivity coefficient defined by the dimensionless partial derivative with respect to the independent factors is used in this study:(11)Sxi=limΔxi→0ΔET0/ET0Δxi/xi=∂ET0∂xi·xiET0,where xi is the ith meteorological factor and S(xi) is the dimensionless sensitivity coefficient of reference evapotranspiration related to xi. Greve et al. [40] used this method to estimate the effects of variation in meteorological factors and measurement error on evaporation change. If the sensitivity coefficient of a factor is positive (negative), ET0 will increase (decrease) as the factor increases. The larger the absolute value of the sensitivity coefficient, the more ET0 is sensitive to a factor.In this study, the meteorological factorsTmax, Tmin, WS, RH, and Rs are chosen for sensitivity analysis. Sensitivity coefficients (STmax, STmin, SWS, SRH, and SRs) were calculated on a daily dataset. Monthly and annual average sensitivity coefficients were obtained by average daily values. Regional sensitivity coefficients were obtained by averaging station values.


### 3.4. Contribution Estimation

Although sensitivity coefficients can reflect the sensitivity ofET0 change to the perturbation of a factor, it cannot describe the contribution of a factor change to ET0 change. Because both of the sensitivity and changes in meteorological factors affected ET0 change, an approach to integrating the sensitivity and changes of meteorological factors is proposed to quantify influence magnitude individual meteorological factors changes to the trends of ET0.Mathematically, for the functionET0=f(x1,x2,…,xn), where x1,x2,…,xn are independent variables, the first order Taylor approximation of the dependent variable ET0 in terms of the independent variables is expressed as(12)ΔET0=∑∂ET0∂xi·Δxi+δ,where ΔET0 is the change of ET0 during a period, xi is the ith meteorological factor, Δxi is the change of xi during the same period, ∂ET0/∂xi is the partial differential of ET0 with respect to xi, and δ is the Lagrange remainder.If both sides of (12) are divided by ET0¯ (the average value of ET0 during a period), (12) can be written as(13)ΔET0ET0¯=∑∂ET0∂xi·ΔxiET0¯+ε,where ΔET0/ET0¯ is the relative change of ET0 during a given period; ε=δ/ET¯0 is the error item, which can be neglected because of its small value.The first term in the right side of equation is multiplied byx-i/x-i; (13) can be written as(14)ΔET0ET0¯=∑∂ET0∂xi·x-iET0¯Δxix-i+ε,where ∂ET0/∂xi·x-i/ET0¯ is the average sensitivity coefficient of factor xi during a period, denoted as S-xi. If we let C(xi)=∑S¯xi·Δxi/x-i, (14) can be written as(15)ΔET0ET0¯≈∑CxiC(xi) is the relative change in ET0 contributed by Tmax, Tmin, WS, RH, and Rs.


## 3.1. FAO Penman-Monteith Method

The Penman-Monteith method can be used globally to estimate potential evapotranspiration. Allen et al. simplified the Penman-Monteith equation and defined the hypothetical reference grass with an assumed height of 0.12 m, a fixed surface resistance of 70 s m−1, and an albedo of 0.23 [16]. This method can provide good and reliable results for ET0 because it is physically based and explicitly incorporates both physiological and aerodynamic parameters and has been accepted as a standard to compare evapotranspiration capability for various climatic regions [31]. Moreover, this method has been successfully applied across the whole of China [32, 33]. The FAO P-M for calculating daily ET0 is described as (1)ET0=0.408ΔRn-G+γ900/Tmean+273u2es-eaΔ+γ1+0.34u2,where ET0 is the reference evapotranspiration (mm day−1), Rn is the net radiation at the crop surface (MJ m−2 day−1), G is the soil heat flux density (MJ m−2 day−1), Tmean is the mean daily air temperature at 2 m height (°C), u2 is the wind speed at 2 m height (m s−1), es is the saturation vapor pressure (kPa), ea is the actual vapor pressure (kPa), Δ is the slope vapor pressure curve (kPa°C−1), γ is the psychrometric constant (kPa°C−1); the atmospheric pressure used in this study is the measured value. More details regarding the data processing in (1) can be found in FAO paper 56.In (1), the solar radiation (Rs) is obtained with the following Ångström formula:(2)Rs=a+bnNRa,where Rs is the solar radiation (MJ m−2 day−1), n is the actual sunshine duration (hours), N is the maximum possible sunshine duration or daylight hours (hours), Ra is the extraterrestrial radiation (MJ m−2 day−1), and a and b are regression constants.Because of the effects of the atmospheric conditions (humidity, dust) and solar declination (latitude and month) as well as the elevation variations, the Ångström valuesa and b in the HRB were calibrated using the observed radiation data at the three solar radiation stations (Figure 2).Figure 2
Calibration of the Ångström coefficients for the three radiation stations: (a) Gangcha station in the upper region, (b) Jiuquan station in the middle region, and (c) Ejina station in the lower region.
(a)
(b)
(c)


## 3.2. Trend Analysis

The long-term trends and changes ofET0 and meteorological factors are detected using the linear fitted method: (3)y^=a^t+b^,where y^ is the fitted trend during a given period and a^ and b^ are the estimated regression slope and the regression constant, respectively. Positive slope indicates an increasing trend and negative slope indicates a decreasing trend.For data sets without seasonality, the significance of a trend is described using the Mann-Kendall (MK) test method [34, 35], which is to statistically assess if there is a monotonic trend of the variable of interest over time [36], whilst the Seasonal Kendall (SK) test is extension of the MK test and is suitable for trend applicable to data sets with seasonality, missing values, and serial correlation over time [37, 38]. The SK test begins by computing the MK test separately for each month or season and then summing the statistic Si and variance Var(Si). Following Hirsch et al. [37], the entire sample X is made up of subsamples X1 through X12 (one for each month), and each subsample Xi contains the ni annual values from month i:(4)X=X1,X2,…,X12,Xi=Xi1,Xi2,…,Xi12.The null hypothesisH0 for the SK test is that the X is a sample of independent random variables (xij) and that each X1 is a subsample of independent and identically distributed random variables over years. The alternative hypothesis H1 is that for one or more months the subsample is not distributed identically over years.According to the MK test, the statisticSi is defined by(5)Si=∑k=1ni-1∑j=k+1nisign⁡xij-xik,where(6)sign⁡θ=1,θ>0,0,θ=0,-1,θ<0.Now, the subsampleXi satisfies the null hypothesis of Mann’s test. Therefore relying on Mann and Kendall we have(7a)ESi=0(7b)VarSi=118nini-12ni+5-∑tigititi-12ti+5,where gi is the number of tied groups for the ith month and tip is the number of data in the pth group for the ith month. Si is normal in the limit as ni→∞. The SK test statistic S is given by(8)S=∑i=1mSi,where m is the number of months for which data have been obtained over years. The expectation and variance can be derived as follows:(9a)ES=∑i=1mESi,(9b)VarS=∑i=1mVarSi+∑i=1m∑j=1mcov⁡SiSj,where Si and Sj(i≠j) are function of independent random variables, so cov(SiSj)=0.Forn1>10, the standard normal deviate Z is estimated by (10) to test the significance of trends:(10)Z=S-1VS,S>0,0,S=0,S+1VS,S<0.For the SK test, the null hypothesisH0 means that there is no monotonic trend over time; when Z>Z1-α/2, the original null hypothesis is rejected; this means that the trend of the time series is statistically significant. In this study, significance level of α=0.1 is employed.


## 3.3. Sensitivity Analysis

Saxton [18] and Smajstrla et al. [39] defined the sensitivity coefficient by drawing a curve of the change of a dependent variable versus the changes of independent variables. For multifactor models (e.g., the FAO P-M), due to different dimensions and ranges of different factors, the ratios of ET0 changes and factors changes cannot be compared. In addition, this approach could introduce errors to understand the response of model behaviors to the factors because of changing one of the factors but holding other factors stationary [27]. To avoid the above two disadvantages, the dimensionless sensitivity coefficient defined by the dimensionless partial derivative with respect to the independent factors is used in this study:(11)Sxi=limΔxi→0ΔET0/ET0Δxi/xi=∂ET0∂xi·xiET0,where xi is the ith meteorological factor and S(xi) is the dimensionless sensitivity coefficient of reference evapotranspiration related to xi. Greve et al. [40] used this method to estimate the effects of variation in meteorological factors and measurement error on evaporation change. If the sensitivity coefficient of a factor is positive (negative), ET0 will increase (decrease) as the factor increases. The larger the absolute value of the sensitivity coefficient, the more ET0 is sensitive to a factor.In this study, the meteorological factorsTmax, Tmin, WS, RH, and Rs are chosen for sensitivity analysis. Sensitivity coefficients (STmax, STmin, SWS, SRH, and SRs) were calculated on a daily dataset. Monthly and annual average sensitivity coefficients were obtained by average daily values. Regional sensitivity coefficients were obtained by averaging station values.


## 3.4. Contribution Estimation

Although sensitivity coefficients can reflect the sensitivity ofET0 change to the perturbation of a factor, it cannot describe the contribution of a factor change to ET0 change. Because both of the sensitivity and changes in meteorological factors affected ET0 change, an approach to integrating the sensitivity and changes of meteorological factors is proposed to quantify influence magnitude individual meteorological factors changes to the trends of ET0.Mathematically, for the functionET0=f(x1,x2,…,xn), where x1,x2,…,xn are independent variables, the first order Taylor approximation of the dependent variable ET0 in terms of the independent variables is expressed as(12)ΔET0=∑∂ET0∂xi·Δxi+δ,where ΔET0 is the change of ET0 during a period, xi is the ith meteorological factor, Δxi is the change of xi during the same period, ∂ET0/∂xi is the partial differential of ET0 with respect to xi, and δ is the Lagrange remainder.If both sides of (12) are divided by ET0¯ (the average value of ET0 during a period), (12) can be written as(13)ΔET0ET0¯=∑∂ET0∂xi·ΔxiET0¯+ε,where ΔET0/ET0¯ is the relative change of ET0 during a given period; ε=δ/ET¯0 is the error item, which can be neglected because of its small value.The first term in the right side of equation is multiplied byx-i/x-i; (13) can be written as(14)ΔET0ET0¯=∑∂ET0∂xi·x-iET0¯Δxix-i+ε,where ∂ET0/∂xi·x-i/ET0¯ is the average sensitivity coefficient of factor xi during a period, denoted as S-xi. If we let C(xi)=∑S¯xi·Δxi/x-i, (14) can be written as(15)ΔET0ET0¯≈∑CxiC(xi) is the relative change in ET0 contributed by Tmax, Tmin, WS, RH, and Rs.


## 4. Results

### 4.1. Correlation ofET0 and Epan

The coefficients of determinationR of monthly Epan and ET0 for different stations (Table 1) are between 0.939 and 0.986, which means that the monthly Epan and ET0 have a very close linear relationship in the HRB. Such a close linear relationship suggests that ET0 can be a good estimation using the observed Epan in the HRB if the regression coefficients are given. Moreover, Figures 3(a) and 3(b) show that monthly and annual Epan and ET0 both present good linearity. The monthly and annual R values are 0.967 and 0.906, respectively. And the correlation of monthly Epan and ET0 appears to be a strong seasonal characteristic and becomes less centralized from winter to summer.Table 1
Coefficient of determination of monthlyEpan and ET0 for nine meteorological stations.
Station
U1
U2
U3
M1
M2
M3
M4
L1
L2
R
2
0.945
0.939
0.966
0.969
0.973
0.959
0.968
0.965
0.986Figure 3
Relationship betweenEpan and ET0 at monthly (a) and annual (b) scales for nine meteorological stations from 1961 to 2001.
(a)
(b)


### 4.2. Evolution and Spatial Pattern ofET0 at Different Time Scales

Figure4 shows the average monthly ET0 change during a year for the whole basin during 1961 and 2014. The mean monthly ET0 is 97.8 mm month−1 over the whole basin in the last 50 years. Monthly ET0 first increases and then decreases during a year. The peak value occurs in June and July, approximately 177 mm month−1, whereas the bottom values occur during November and February and are less than 50 mm month−1. This strong monthly variation has a similar shape feature to the natural change in temperature and solar radiation (Figures 4 and 7). In addition, ET0 in summer months differs more dramatically than that in winter months. And the difference between the maximum and the minimum of ET0 reaches 50 mm in July, whereas the difference in December is only 10 mm. The evaporation capability in summer months accounts for 44% of annual ET0.Figure 4
Box and whisker plots of monthlyET0 of the HRB from 1961 to 2014. The line inside the boxes represents the median, and the upper and lower lines of the boxes indicate the 75th and 25th percentiles, respectively. The upper and lower parts of the whiskers indicate the maximum and the minimum of monthly ET0, respectively.Figure5 shows the trends of annual and seasonal ET0 for the whole basin from 1961 to 2014. The mean annual ET0 is 1175 mm yr−1. The increasing trend of annual ET0 is 2.01 mm·10 yr−2 over the 54 years and has no statistical significance. Annual ET0 variations exhibit three different phases, which has a significant increasing trend during 1961–1974 and 1997–2014 but clearly decreases during 1975–1996 at 0.05 levels (Figure 5(e)). The 1961–2014 means of ET0 from spring to winter are 363 mm yr−1, 511 mm yr−1, 220 mm yr−1, and 81.4 mm yr−1, respectively. The climatic trends of ET0 in spring and winter are 2.07 mm·10 yr−2 and 0.52 mm·10 yr−2, respectively, whereas ET0 changes in summer and winter have decreasing trends of −0.7 mm·10 yr−2 and −0.06 mm·10 yr−2.Figure 5
Annual and seasonalET0 trends for the HRB during 1961 and 2014. NS means not significant at the level of α<0.05 by the MK test.
(a)
(b)
(c)
(d)
(e)Table2 reports the mean values and trends of seasonal and annual ET0 in the three subregions from 1961 to 2014. The seasonal and annual ET0 have gradually increasing spatial gradients from the upper region to the lower region. The mean annual ET0 of the upper, middle, and lower regions are 902 mm yr−1, 1051 mm yr−1, and 1289 mm yr−1, respectively. The ET0 change in the upper region appears to be a statistically increasing trend at 6.61 mm·10 yr−2. The climatic trends of annual ET0 in the middle and lower regions are 2.25 mm·10 yr−2 and 0.91 mm·10 yr−2, respectively, without statistical significance.Table 2
Means of seasonal and annualET0 and their trends in the three subregions during 1961–2014.
Region
Annual
Spring
Summer
Autumn
Winter
Upper region
Mean (mm yr−1)
902
280
380
171
71.1
Trend (mm⋅10 yr−2)
6.61∗
2.41∗
1.33
1.19∗
1.54∗
Middle region
Mean (mm yr−1)
1051
330
446
196
78.6
Trend (mm⋅10 yr−2)
2.25
2.03
-
0.33
-
0.21
0.58
Lower region
Mean (mm yr−1)
1289
395
568
241
84.8
Trend (mm⋅10 yr−2)
0.91
2.02
-
1.31
-
0.26
0.31
Note:∗ means the significance level of 0.1.The maximum and minimum values of seasonalET0 consistently occur in summer and winter, respectively, for the three regions. Whereas the seasonal ET0 trends are different, ET0 for the upper region has significant increasing trends in spring, autumn, and winter, with increasing rates of 2.41, 1.19, and 1.54 mm·10 yr−2, respectively. Seasonal ET0 has no significant trend for the middle and lower regions.The spatial patterns of seasonal and annualET0 in the HRB from 1961 to 2014 are plotted in Figure 6. There are clear spatial gradients for annual ET0 from the upper region to the lower region. The maximum occurs in the lower region and is up to 1553 mm yr−1 near station L2, and the minimum is found in the upper region and is as low as 757 mm yr−1 near station U2 in the upper region.Figure 6
Spatial patterns of the seasonal and annual meanET0 in the whole HRB from 1961 to 2014. Max and Min denote the maximum and minimum values, respectively, of ET0 over the whole basin. SD indicates the standard deviation of the spatial variations of ET0.Figure 7
Monthly variations of meteorological factors (Tmean, WS, RH, and Rs) in the upper (U), middle (M), and lower (L) regions and the whole basin (W). The 54-year mean (solid line) and standard deviation (error bar) are shown.The spatial variation of seasonalET0 is smaller than that of annual ET0. The ET0 changes in spring, summer, and autumn have similar spatial features. The ET0 changes only in summer have a clear spatial pattern, ranging from 300 mm yr−1 to 700 mm yr−1 over the whole basin. Variations of ET0 in the other three seasons have very small spatial gradients across the whole basin. The spatial difference in ET0 in spring is between 232 mm yr−1 and 472 mm yr−1, with a SD of 49 mm yr−1, and the ET0 variation in the autumn ranges from 145 mm yr−1 to 290 mm yr−1, with a SD of 30 mm yr−1. The spatial distribution of ET0 in winter varies little, and its SD is only 5.8 mm yr−1 over the whole basin.


### 4.3. Trends in Meteorological Factors

According to the FAO P-M method described in (1), Tmax, Tmin, WS, RH, and Rs are selected as the major meteorological factors having an important influence on ET0. Tmean (the average of Tmax and Tmin) is a comprehensive indicator for analyzing temperature variation.Figure7 shows monthly variations of meteorological factors in the upper, middle, and lower regions and the whole basin during 1961 and 2014. The variations of monthly Tmean and Rs are similar to those of monthly ET0 (Figure 4), and their peak values occur in the middle of the year, with a minimum at the ends of the year. The air temperature in the upper region is the smallest over the whole basin, which ranges from −12.6°C month−1 to 12.9°C month−1. Although the average monthly Tmean in the middle and lower regions are both 8.1°C month−1, the maximum value of Tmean in the lower region is larger than that in the middle region, and the minimum value in the lower region is smaller than that in the middle region. Moreover, the standard deviation of monthly Tmean in the middle region is the smallest.The variation of wind speed during a year is relatively small. The peak of monthlyWS occurs in April. There are similar variation features of WS for the three subregions. The monthly WS in the lower region is the largest, with an average of 2.8 m s−1 month−1 during the year, whereas that in the lower region is the smallest, with an average of 1.8 m s−1 month−1. The higher error bar means that the monthly WS has significant fluctuations during the year.The monthlyRH from the lower to the upper region gradually increases and the fluctuations of RH are also substantial. The monthly RH in the upper region increases at first and then decreases, and its peak is during June and August. The monthly RH in the middle and lower regions decreases at first and then increases, and its bottom is in April.The monthlyRs in different regions have the same variation features and standard deviations during the year. The high value of monthly Rs is found during June and August, and the low value occurs in winter. The standard deviation during May and August is larger than that from November to February.Figure8 shows trends of annual Tmean, WS, RH, and Rs for the upper, middle, and lower regions and the whole basin during 1961 and 2014. Positive trends of annual Tmean during 1961 and 2014 are detected in the upper, middle, and lower regions and the whole basin, with significant rates of change of 0.32°C·10 yr−2, 0.33°C·10 yr−2, 0.38°C·10 yr−2, and 0.36°C·10 yr−2, respectively.Figure 8
Trends of annualTmean, WS, RH, and Rs for the upper (U), middle (M), and lower (L) region and the whole basin (W). S indicates that the trend is statistically significant, and NS indicates that the trend is not significant at the 0.05 level.The mean annualWS in the lower region is 2.5 m s−1yr−1 and is larger than that in other regions. The interannual oscillations of annual WS for the middle and lower regions and the whole basin are similar and have three phases: two relatively steady periods from 1961 to 1968 and 1969 to 1974, followed by a long-term statistically significant decline phase from 1974 to the 1990 s. However, the trend of annual WS in the upper region has only a statistically significant decline phase from 1961 to 2014. There are significant decreasing trends for the upper, middle, and lower regions, with change rates of −0.13 m s−1·10 yr−2, −0.17 m s−1·10 yr−2, and −0.20 m s−1·10 yr−2, respectively.The mean annualRH in the lower, middle, and upper regions is 41% yr−1, 50% yr−1, and 52% yr−1, respectively. During 1961 and 2014, decreasing trends in the upper and middle regions are not statistically significant, whereas the changes in annual RH in the lower region and whole basin have significant decreasing trends. Therefore, the changes in RH across the whole basin are mainly affected by the trend of RH in the lower region.The change of annualRs for the different regions has no significant decreasing trend during the 54-year period, whereas the interannual oscillations of Rs are clearer than those of RH.


### 4.4. Variations of the Sensitivity Coefficients

Mean daily sensitivity coefficients for major meteorological factors that exhibit large fluctuations during a year (Figure11). Although annual Tmax and Tmin have the same trend, the variations of STmaxand STmin are different. STmax gradually increases from negative to positive at first and then decreases from positive to negative and achieves a larger and stable peak value during May and August (Figure 9(a)). The daily variation patterns of STmin have a unimodal distribution, and the peak occurs on the 200th day of the year (Figure 9(b)). STmax and STmin are positive during summer, and the former is larger than the latter. STmax and STmin are negative during winter days, and the latter is smaller than the former. Thus, ET0 is sensitive to Tmax in summer but Tmin in winter. The value of STmax is greater in the lower region than in the other two regions. STmin for the middle and lower regions is almost the same and is greater than that in the upper region.Figure 9
Mean daily sensitivity coefficients for maximum temperature (a), minimum temperature (b), wind speed (c), relative humidity (d), and shortwave radiation (e) in the upper (U), middle (M), and lower (L) regions of the HRB. (f) Comparison of the mean daily sensitivity coefficients for major meteorological factors in the whole basin.
(a)
(b)
(c)
(d)
(e)
(f)The values ofSWS in the three regions are positive throughout the year. ET0 is most sensitive to WS in the beginning and end of a year but is insensitive to WS in summer (Figure 9(c)). The variation patterns of SWS for the three regions are the same. The values of SWS for the three regions have significant differences during a year. The value in the lower region is the largest; thus, ET0 is more sensitive to WS in the lower region than in the other two regions.Relatively strong negative sensitivity coefficients were obtained forRH (Figure 9(d)). ET0 is less sensitive to RH in the winter for the upper region compared with the two other regions. However, ET0 is more negative sensitive to RH in the lower region during April and September.The daily variation patterns ofSRs agree with those of shortwave radiation (Figure 9(e)). ET0 is insensitive to Rs in winter, and SRs increases and achieves its maximum value in summer. The variations of SRs for the three regions show similar patterns, whereas SRs in the lower region is significantly less than that in the upper and middle regions. The variation of daily SRs and SWS appears to be an opposite pattern during a year. Similar findings were reported by Gong et al. [19]. STmax and SRs have a similar variation pattern, whereas STmin and SWS appear to have opposite patterns. RH is the most sensitive factor and WS and Tmin are the least sensitive factors in the whole basin throughout the year.Figure10 shows the interannual variations of annual sensitivity coefficients from 1961 to 2014. The variation of annual SWS has a significant increasing trend, whereas the absolute values of STmin and SRH show that they have statistically significant decreasing trends during 1961 and 2014. ET0 becomes more sensitive to WS but less sensitive to Tmin and RH. The annual STmax and SRs have increasing and decreasing trends, respectively, but their trends are not statistically significant during the period of 1961–2014. This shows that the relative changes of the meteorological factors Tmin and Rs and the relative change of ET0 maintain a stable ratio [41].Figure 10
Interannual variations of sensitivity ofET0 in relation to Tmax, Tmin, WS, RH, and Rs.Figure 11
Spatial distribution of the mean annual sensitivity coefficients forET0 to the major meteorological factors (Tmax, Tmin, WS, RH, and Rs) during 1961–2014.Figure11 describes the spatial patterns of the sensitivity coefficients of ET0 to the major meteorological factors across the whole HRB. The mean annual values of sensitivity for Tmax, Tmin, WS, RH, and Rs are 0.28, −0.04, 0.27, −0.38, and 0.29 at the basin scale, respectively. RH is the most sensitive factor, and Tmin is less sensitive to ET0 over the whole basin. It seems that STmax and STmin have similar spatial patterns, whereas spatial distributions of the absolute values of STmax and STmin are opposite due to the negative sign of STmin. Overall, there are three different spatial distributions for the five meteorological factors. (1) STmax and SWS have a similar spatial pattern, increasing from the south to the north of the basin with significant spatial gradients. (2) The spatial patterns of STmin and SRs are similar, and the sensitivity for the two factors decreases from the upper region to the lower region. (3) The spatial variation of SRH has no significant gradient from the lower region to the upper region.


### 4.5. Contribution of the Trends of the Meteorological Factors to That ofET0

The sensitivity coefficient describes the response ofET0 to changes in meteorological factors but is not able to reflect change magnitude in ET0 caused by meteorological factors. Namely, ET0 change is strongly sensitive to a meteorological factor, but the meteorological factor must not cause a significant change in ET0. This is because, other than the sensitivity coefficients, changes in ET0 are influenced by changes in meteorological factors as well. Consequently, (15) is used to diagnose the contribution of meteorological factors to ET0 changes.As shown in Figure12, the relative changes of monthly, seasonal, and annual ET0 calculated using (15) well fit those of the actual ET0 from observed data. This result illustrates that sensitivity coefficients and changes in meteorological factors could be used to analyze the contribution of one or more meteorological factors to ET0 changes in the HRB.Figure 12
Relationship ofC(ET0) to TR(ET0) at different time scales for all stations in the HRB. C(ET0) is the sum of the relative change of ET0 contributed by changes in meteorological factors using (15). TR(ET0) is the long-term relative change of ET0 from the observed data.Figure13 shows the contributions of meteorological factor changes to relative changes in annual and seasonal ET0 for the 9 stations in the HRB during 1961–2014. WS is the largest contributor to ET0 change among meteorological factors in the middle and lower regions. The decreasing trends of WS cause ET0 decreases, with relative changes in ET0 of −3% to −18%, corresponding to changes of −30 to −250 mm. However, Tmin and Rs trends from 1961 to 2014 have little influence on the changes in ET0 for the middle-lower regions. For the upper region, the trends of Tmax and Tmin for all stations significantly increase ET0, and relative changes of ET0 are between 2.3% and 3.2%, corresponding to changes of 19 to 26 mm. The positive effects of WS and RH on ET0 change are similar to air temperature, which cannot be ignored for station U3.Figure 13
Contributions of meteorological factor changes to relative changes inET0 at annual and seasonal time scales for the stations in the HRB. An upward bar means that the factor trend causes a positive change in ET0, and a downward bar means that the factor trend causes a negative change in ET0.The contribution of the seasonal change of meteorological factors toET0 change is similar to that at an annual scale. WS is still the dominant contributor to ET0 change for the middle-lower regions at all seasons. The relative changes of ET0 caused by WS change are greater than 5% for most stations in the middle and lower regions, whereas the relative changes of ET0 caused by other factors are less than 5%. The trends of seasonal Tmax and Tmin still result in an increase in ET0 for the upper region. However, there are differences for the contribution levels of each meteorological factor in different seasons and regions. For example, the trends of Rs for stations U1, U2, and M1 have more significant contributions to the changes of ET0 only in summer, whereas the Rs trends for all stations have little effect on the changes of ET0 in other seasons. Moreover, the Tmin trends in lower regions do not contribute to changes in ET0 in autumn, whereas the contribution of Tmin to ET0 change is strong in the other three seasons. RH and WS for station U3 have similar effects on ET0 change, for which the effect is stronger in summer than that in other regions.


## 4.1. Correlation ofET0 and Epan

The coefficients of determinationR of monthly Epan and ET0 for different stations (Table 1) are between 0.939 and 0.986, which means that the monthly Epan and ET0 have a very close linear relationship in the HRB. Such a close linear relationship suggests that ET0 can be a good estimation using the observed Epan in the HRB if the regression coefficients are given. Moreover, Figures 3(a) and 3(b) show that monthly and annual Epan and ET0 both present good linearity. The monthly and annual R values are 0.967 and 0.906, respectively. And the correlation of monthly Epan and ET0 appears to be a strong seasonal characteristic and becomes less centralized from winter to summer.Table 1
Coefficient of determination of monthlyEpan and ET0 for nine meteorological stations.
Station
U1
U2
U3
M1
M2
M3
M4
L1
L2
R
2
0.945
0.939
0.966
0.969
0.973
0.959
0.968
0.965
0.986Figure 3
Relationship betweenEpan and ET0 at monthly (a) and annual (b) scales for nine meteorological stations from 1961 to 2001.
(a)
(b)


## 4.2. Evolution and Spatial Pattern ofET0 at Different Time Scales

Figure4 shows the average monthly ET0 change during a year for the whole basin during 1961 and 2014. The mean monthly ET0 is 97.8 mm month−1 over the whole basin in the last 50 years. Monthly ET0 first increases and then decreases during a year. The peak value occurs in June and July, approximately 177 mm month−1, whereas the bottom values occur during November and February and are less than 50 mm month−1. This strong monthly variation has a similar shape feature to the natural change in temperature and solar radiation (Figures 4 and 7). In addition, ET0 in summer months differs more dramatically than that in winter months. And the difference between the maximum and the minimum of ET0 reaches 50 mm in July, whereas the difference in December is only 10 mm. The evaporation capability in summer months accounts for 44% of annual ET0.Figure 4
Box and whisker plots of monthlyET0 of the HRB from 1961 to 2014. The line inside the boxes represents the median, and the upper and lower lines of the boxes indicate the 75th and 25th percentiles, respectively. The upper and lower parts of the whiskers indicate the maximum and the minimum of monthly ET0, respectively.Figure5 shows the trends of annual and seasonal ET0 for the whole basin from 1961 to 2014. The mean annual ET0 is 1175 mm yr−1. The increasing trend of annual ET0 is 2.01 mm·10 yr−2 over the 54 years and has no statistical significance. Annual ET0 variations exhibit three different phases, which has a significant increasing trend during 1961–1974 and 1997–2014 but clearly decreases during 1975–1996 at 0.05 levels (Figure 5(e)). The 1961–2014 means of ET0 from spring to winter are 363 mm yr−1, 511 mm yr−1, 220 mm yr−1, and 81.4 mm yr−1, respectively. The climatic trends of ET0 in spring and winter are 2.07 mm·10 yr−2 and 0.52 mm·10 yr−2, respectively, whereas ET0 changes in summer and winter have decreasing trends of −0.7 mm·10 yr−2 and −0.06 mm·10 yr−2.Figure 5
Annual and seasonalET0 trends for the HRB during 1961 and 2014. NS means not significant at the level of α<0.05 by the MK test.
(a)
(b)
(c)
(d)
(e)Table2 reports the mean values and trends of seasonal and annual ET0 in the three subregions from 1961 to 2014. The seasonal and annual ET0 have gradually increasing spatial gradients from the upper region to the lower region. The mean annual ET0 of the upper, middle, and lower regions are 902 mm yr−1, 1051 mm yr−1, and 1289 mm yr−1, respectively. The ET0 change in the upper region appears to be a statistically increasing trend at 6.61 mm·10 yr−2. The climatic trends of annual ET0 in the middle and lower regions are 2.25 mm·10 yr−2 and 0.91 mm·10 yr−2, respectively, without statistical significance.Table 2
Means of seasonal and annualET0 and their trends in the three subregions during 1961–2014.
Region
Annual
Spring
Summer
Autumn
Winter
Upper region
Mean (mm yr−1)
902
280
380
171
71.1
Trend (mm⋅10 yr−2)
6.61∗
2.41∗
1.33
1.19∗
1.54∗
Middle region
Mean (mm yr−1)
1051
330
446
196
78.6
Trend (mm⋅10 yr−2)
2.25
2.03
-
0.33
-
0.21
0.58
Lower region
Mean (mm yr−1)
1289
395
568
241
84.8
Trend (mm⋅10 yr−2)
0.91
2.02
-
1.31
-
0.26
0.31
Note:∗ means the significance level of 0.1.The maximum and minimum values of seasonalET0 consistently occur in summer and winter, respectively, for the three regions. Whereas the seasonal ET0 trends are different, ET0 for the upper region has significant increasing trends in spring, autumn, and winter, with increasing rates of 2.41, 1.19, and 1.54 mm·10 yr−2, respectively. Seasonal ET0 has no significant trend for the middle and lower regions.The spatial patterns of seasonal and annualET0 in the HRB from 1961 to 2014 are plotted in Figure 6. There are clear spatial gradients for annual ET0 from the upper region to the lower region. The maximum occurs in the lower region and is up to 1553 mm yr−1 near station L2, and the minimum is found in the upper region and is as low as 757 mm yr−1 near station U2 in the upper region.Figure 6
Spatial patterns of the seasonal and annual meanET0 in the whole HRB from 1961 to 2014. Max and Min denote the maximum and minimum values, respectively, of ET0 over the whole basin. SD indicates the standard deviation of the spatial variations of ET0.Figure 7
Monthly variations of meteorological factors (Tmean, WS, RH, and Rs) in the upper (U), middle (M), and lower (L) regions and the whole basin (W). The 54-year mean (solid line) and standard deviation (error bar) are shown.The spatial variation of seasonalET0 is smaller than that of annual ET0. The ET0 changes in spring, summer, and autumn have similar spatial features. The ET0 changes only in summer have a clear spatial pattern, ranging from 300 mm yr−1 to 700 mm yr−1 over the whole basin. Variations of ET0 in the other three seasons have very small spatial gradients across the whole basin. The spatial difference in ET0 in spring is between 232 mm yr−1 and 472 mm yr−1, with a SD of 49 mm yr−1, and the ET0 variation in the autumn ranges from 145 mm yr−1 to 290 mm yr−1, with a SD of 30 mm yr−1. The spatial distribution of ET0 in winter varies little, and its SD is only 5.8 mm yr−1 over the whole basin.


## 4.3. Trends in Meteorological Factors

According to the FAO P-M method described in (1), Tmax, Tmin, WS, RH, and Rs are selected as the major meteorological factors having an important influence on ET0. Tmean (the average of Tmax and Tmin) is a comprehensive indicator for analyzing temperature variation.Figure7 shows monthly variations of meteorological factors in the upper, middle, and lower regions and the whole basin during 1961 and 2014. The variations of monthly Tmean and Rs are similar to those of monthly ET0 (Figure 4), and their peak values occur in the middle of the year, with a minimum at the ends of the year. The air temperature in the upper region is the smallest over the whole basin, which ranges from −12.6°C month−1 to 12.9°C month−1. Although the average monthly Tmean in the middle and lower regions are both 8.1°C month−1, the maximum value of Tmean in the lower region is larger than that in the middle region, and the minimum value in the lower region is smaller than that in the middle region. Moreover, the standard deviation of monthly Tmean in the middle region is the smallest.The variation of wind speed during a year is relatively small. The peak of monthlyWS occurs in April. There are similar variation features of WS for the three subregions. The monthly WS in the lower region is the largest, with an average of 2.8 m s−1 month−1 during the year, whereas that in the lower region is the smallest, with an average of 1.8 m s−1 month−1. The higher error bar means that the monthly WS has significant fluctuations during the year.The monthlyRH from the lower to the upper region gradually increases and the fluctuations of RH are also substantial. The monthly RH in the upper region increases at first and then decreases, and its peak is during June and August. The monthly RH in the middle and lower regions decreases at first and then increases, and its bottom is in April.The monthlyRs in different regions have the same variation features and standard deviations during the year. The high value of monthly Rs is found during June and August, and the low value occurs in winter. The standard deviation during May and August is larger than that from November to February.Figure8 shows trends of annual Tmean, WS, RH, and Rs for the upper, middle, and lower regions and the whole basin during 1961 and 2014. Positive trends of annual Tmean during 1961 and 2014 are detected in the upper, middle, and lower regions and the whole basin, with significant rates of change of 0.32°C·10 yr−2, 0.33°C·10 yr−2, 0.38°C·10 yr−2, and 0.36°C·10 yr−2, respectively.Figure 8
Trends of annualTmean, WS, RH, and Rs for the upper (U), middle (M), and lower (L) region and the whole basin (W). S indicates that the trend is statistically significant, and NS indicates that the trend is not significant at the 0.05 level.The mean annualWS in the lower region is 2.5 m s−1yr−1 and is larger than that in other regions. The interannual oscillations of annual WS for the middle and lower regions and the whole basin are similar and have three phases: two relatively steady periods from 1961 to 1968 and 1969 to 1974, followed by a long-term statistically significant decline phase from 1974 to the 1990 s. However, the trend of annual WS in the upper region has only a statistically significant decline phase from 1961 to 2014. There are significant decreasing trends for the upper, middle, and lower regions, with change rates of −0.13 m s−1·10 yr−2, −0.17 m s−1·10 yr−2, and −0.20 m s−1·10 yr−2, respectively.The mean annualRH in the lower, middle, and upper regions is 41% yr−1, 50% yr−1, and 52% yr−1, respectively. During 1961 and 2014, decreasing trends in the upper and middle regions are not statistically significant, whereas the changes in annual RH in the lower region and whole basin have significant decreasing trends. Therefore, the changes in RH across the whole basin are mainly affected by the trend of RH in the lower region.The change of annualRs for the different regions has no significant decreasing trend during the 54-year period, whereas the interannual oscillations of Rs are clearer than those of RH.


## 4.4. Variations of the Sensitivity Coefficients

Mean daily sensitivity coefficients for major meteorological factors that exhibit large fluctuations during a year (Figure11). Although annual Tmax and Tmin have the same trend, the variations of STmaxand STmin are different. STmax gradually increases from negative to positive at first and then decreases from positive to negative and achieves a larger and stable peak value during May and August (Figure 9(a)). The daily variation patterns of STmin have a unimodal distribution, and the peak occurs on the 200th day of the year (Figure 9(b)). STmax and STmin are positive during summer, and the former is larger than the latter. STmax and STmin are negative during winter days, and the latter is smaller than the former. Thus, ET0 is sensitive to Tmax in summer but Tmin in winter. The value of STmax is greater in the lower region than in the other two regions. STmin for the middle and lower regions is almost the same and is greater than that in the upper region.Figure 9
Mean daily sensitivity coefficients for maximum temperature (a), minimum temperature (b), wind speed (c), relative humidity (d), and shortwave radiation (e) in the upper (U), middle (M), and lower (L) regions of the HRB. (f) Comparison of the mean daily sensitivity coefficients for major meteorological factors in the whole basin.
(a)
(b)
(c)
(d)
(e)
(f)The values ofSWS in the three regions are positive throughout the year. ET0 is most sensitive to WS in the beginning and end of a year but is insensitive to WS in summer (Figure 9(c)). The variation patterns of SWS for the three regions are the same. The values of SWS for the three regions have significant differences during a year. The value in the lower region is the largest; thus, ET0 is more sensitive to WS in the lower region than in the other two regions.Relatively strong negative sensitivity coefficients were obtained forRH (Figure 9(d)). ET0 is less sensitive to RH in the winter for the upper region compared with the two other regions. However, ET0 is more negative sensitive to RH in the lower region during April and September.The daily variation patterns ofSRs agree with those of shortwave radiation (Figure 9(e)). ET0 is insensitive to Rs in winter, and SRs increases and achieves its maximum value in summer. The variations of SRs for the three regions show similar patterns, whereas SRs in the lower region is significantly less than that in the upper and middle regions. The variation of daily SRs and SWS appears to be an opposite pattern during a year. Similar findings were reported by Gong et al. [19]. STmax and SRs have a similar variation pattern, whereas STmin and SWS appear to have opposite patterns. RH is the most sensitive factor and WS and Tmin are the least sensitive factors in the whole basin throughout the year.Figure10 shows the interannual variations of annual sensitivity coefficients from 1961 to 2014. The variation of annual SWS has a significant increasing trend, whereas the absolute values of STmin and SRH show that they have statistically significant decreasing trends during 1961 and 2014. ET0 becomes more sensitive to WS but less sensitive to Tmin and RH. The annual STmax and SRs have increasing and decreasing trends, respectively, but their trends are not statistically significant during the period of 1961–2014. This shows that the relative changes of the meteorological factors Tmin and Rs and the relative change of ET0 maintain a stable ratio [41].Figure 10
Interannual variations of sensitivity ofET0 in relation to Tmax, Tmin, WS, RH, and Rs.Figure 11
Spatial distribution of the mean annual sensitivity coefficients forET0 to the major meteorological factors (Tmax, Tmin, WS, RH, and Rs) during 1961–2014.Figure11 describes the spatial patterns of the sensitivity coefficients of ET0 to the major meteorological factors across the whole HRB. The mean annual values of sensitivity for Tmax, Tmin, WS, RH, and Rs are 0.28, −0.04, 0.27, −0.38, and 0.29 at the basin scale, respectively. RH is the most sensitive factor, and Tmin is less sensitive to ET0 over the whole basin. It seems that STmax and STmin have similar spatial patterns, whereas spatial distributions of the absolute values of STmax and STmin are opposite due to the negative sign of STmin. Overall, there are three different spatial distributions for the five meteorological factors. (1) STmax and SWS have a similar spatial pattern, increasing from the south to the north of the basin with significant spatial gradients. (2) The spatial patterns of STmin and SRs are similar, and the sensitivity for the two factors decreases from the upper region to the lower region. (3) The spatial variation of SRH has no significant gradient from the lower region to the upper region.


## 4.5. Contribution of the Trends of the Meteorological Factors to That ofET0

The sensitivity coefficient describes the response ofET0 to changes in meteorological factors but is not able to reflect change magnitude in ET0 caused by meteorological factors. Namely, ET0 change is strongly sensitive to a meteorological factor, but the meteorological factor must not cause a significant change in ET0. This is because, other than the sensitivity coefficients, changes in ET0 are influenced by changes in meteorological factors as well. Consequently, (15) is used to diagnose the contribution of meteorological factors to ET0 changes.As shown in Figure12, the relative changes of monthly, seasonal, and annual ET0 calculated using (15) well fit those of the actual ET0 from observed data. This result illustrates that sensitivity coefficients and changes in meteorological factors could be used to analyze the contribution of one or more meteorological factors to ET0 changes in the HRB.Figure 12
Relationship ofC(ET0) to TR(ET0) at different time scales for all stations in the HRB. C(ET0) is the sum of the relative change of ET0 contributed by changes in meteorological factors using (15). TR(ET0) is the long-term relative change of ET0 from the observed data.Figure13 shows the contributions of meteorological factor changes to relative changes in annual and seasonal ET0 for the 9 stations in the HRB during 1961–2014. WS is the largest contributor to ET0 change among meteorological factors in the middle and lower regions. The decreasing trends of WS cause ET0 decreases, with relative changes in ET0 of −3% to −18%, corresponding to changes of −30 to −250 mm. However, Tmin and Rs trends from 1961 to 2014 have little influence on the changes in ET0 for the middle-lower regions. For the upper region, the trends of Tmax and Tmin for all stations significantly increase ET0, and relative changes of ET0 are between 2.3% and 3.2%, corresponding to changes of 19 to 26 mm. The positive effects of WS and RH on ET0 change are similar to air temperature, which cannot be ignored for station U3.Figure 13
Contributions of meteorological factor changes to relative changes inET0 at annual and seasonal time scales for the stations in the HRB. An upward bar means that the factor trend causes a positive change in ET0, and a downward bar means that the factor trend causes a negative change in ET0.The contribution of the seasonal change of meteorological factors toET0 change is similar to that at an annual scale. WS is still the dominant contributor to ET0 change for the middle-lower regions at all seasons. The relative changes of ET0 caused by WS change are greater than 5% for most stations in the middle and lower regions, whereas the relative changes of ET0 caused by other factors are less than 5%. The trends of seasonal Tmax and Tmin still result in an increase in ET0 for the upper region. However, there are differences for the contribution levels of each meteorological factor in different seasons and regions. For example, the trends of Rs for stations U1, U2, and M1 have more significant contributions to the changes of ET0 only in summer, whereas the Rs trends for all stations have little effect on the changes of ET0 in other seasons. Moreover, the Tmin trends in lower regions do not contribute to changes in ET0 in autumn, whereas the contribution of Tmin to ET0 change is strong in the other three seasons. RH and WS for station U3 have similar effects on ET0 change, for which the effect is stronger in summer than that in other regions.


## 5. Discussion

This paper carefully and thoroughly analyzed the trends and spatial variations of the annual and seasonalET0 for different regions over the HRB. The spatial patterns of annual and seasonal ET0 during the last 54 years in this study are consistent with the previous studies [34, 35]. However, the overall increasing trend (2.01 mm·10 yr−2) of annual ET0 for the whole basin in this paper is different from the significant decreasing trend reported by previous studies [29, 30]. After serious comparison and analysis, the causes of the differences come from inconsistent study areas and from differences in the data time series, treatment of missing data, and analysis methods. (i) Because the lower region of the HRB is the desert area and is difficult to fix the basin divides, four different basin areas have been defined by the Yellow River Conservancy Commission during different periods. The basin area defined most recently in 2005 is larger than the basin areas defined in 1985, 1995, and 2000 and can better describe the hydrological characteristics, especially for the lower region of the basin. This study adopted the latest basin area data defined in 2005, and previous studies adopted the earlier basin area data defined in 1995. (ii) Different data time series may result in different trends of annual ET0. The trends of annual and seasonal ET0 calculated by the data series of 1959–1999 or 1961–2000 were earlier and shorter than the data series of 1961–2014 in this study. This latest data series, covering more than 50 years of climate stage and data quality during this latest period, is more reliable and is without missing data. (iii) Because meteorological stations are scarce in the inland arid basin in China, the stations around the basin must be considered to increase the precision of calculation of regional ET0. Clearly, the results obtained using only the 10 stations in the previous studies are less reliable than those using 16 stations related to the basin.Equation (15) was used to assess the contribution of meteorological factors to ET0 trends. Figure 12 shows that correlation of the estimated and the actual relative changes of ET0 are very good, whereas the correlation coefficients decrease with increasing time scales from monthly scale to annual scale. This illustrated that the accuracy of (15) decreases with increasing time scale. The error sources of (15) are that (i) the five major meteorological factors cannot completely cover all impact factors of the FAO P-M equation; (ii) the selected factors interact with each other and are not totally independent; and (iii) the annual averaging variations of the daily sensitivity coefficient could produce different offsets to ET0 changes contributed by different meteorological factors.


## 6. Summary

In arid regions, investigating the causes of reference evapotranspiration(ET0) change is important for understanding hydroclimatic change and the response of ecoenvironment. The Heihe River Basin (HRB), the second largest inland river basin in China, is divided into the upper, middle, and lower subregions to diagnose the causes of ET0 changes in different dryness environment.First, theET0 changes for the HRB were obtained by FAO P-M method and meteorological data series from 16 stations during 1961–2014. The seasonal and annual ET0 have no significant increasing trends for the whole basin, whereas there is a clear increasing spatial gradient from the upper region to the lower region.Second, the dimensionless sensitivity analysis showed that relative humidity is most sensitive toET0 change and negative, followed by maximum temperature and shortwave radiation but with positive sensitivity. The sensitivity of minimum temperature is weakest and negative.Finally, to quantify the influence magnitude of the major meteorological factors onET0 changes, an approach to integrating the sensitivity and changes of meteorological factors is proposed. Contribution analysis showed that wind speed is the dominant factor to cause the decrease of ET0 for the middle and lower regions. And the maximum and minimum temperatures are the main contributors to the increasing trends of ET0 for the upper region. Therefore, the ET0 changes are mainly affected by aerodynamic factors rather than radiative factors as dryness increase.



---

*Source: 4143580-2015-12-29.xml*