Influence of Meteorological Factors on the Potential Evapotranspiration in Yanhe River Basin, China

Abstract

Potential evapotranspiration (ET₀) is an essential component of the hydrological cycle, and quantitative estimation of the influence of meteorological factors on ET₀ can provide a scientific basis for studying the impact mechanisms of climate change. In the present research, the Penman–Monteith method was used to calculate ET₀. The Mann–Kendall statistical test with the inverse distance weighting were used to analyze the spatiotemporal characteristics of the sensitivity coefficients and contribution rates of meteorological factors to ET₀ to identify the mechanisms underlying changing ET₀ rates. The results showed that the average ET₀ for the Yanhe River Basin, China from 1978–2017 was 935.92 mm. Save for a single location (Ganquan), ET₀ increased over the study period. Generally, the sensitivity coefficients of air temperature (0.08), wind speed at 2 m (0.19), and solar radiation (0.42) were positive, while that of relative humidity was negative (−0.41), although significant spatiotemporal differences were observed. Increasing air temperature and solar radiation contributed 1.09% and 0.55% of the observed rising ET₀ rates, respectively; whereas decreasing wind speed contributed −0.63%, and relative humidity accounted for −0.85%. Therefore, it was concluded that the decrease of relative humidity did not cause the observed ET₀ increase in the basin. The predominant factor driving increasing ET₀ was rising air temperatures, but this too varied significantly by location and time (intra- and interannually). Decreasing wind speed at Ganquan Station decreased ET₀ by −9.16%, and was the primary factor underlying the observed, local “evaporation paradox”. Generally, increase in ET₀ was driven by air temperature, wind speed and solar radiation, whereas decrease was derived from relative humidity.

1. Introduction

According to the sixth report of the IPCC(Intergovernmental Panel on Climate Change)[1], the increase in global mean surface temperature has reached 0.87 °C in 2006–2015. Warming temperatures intensify hydrological cycling and affect the spatiotemporal allocation of water resources, increasing the frequency and intensity of water-related disasters [2] and posing challenges to people’s safety, socioeconomic development, and environmental security. Therefore, hydrological research is of utmost importance.

Evapotranspiration (ET), composed of water evaporation and transpiration from the surface, water, and plants, is an essential component of the water cycle, with corresponding control over the balances of water and energy. In practical applications, the concepts are divided into actual and potential (ET₀), where the former refers to ET under the true conditions of the surface, and latter describes ET levels when the surface is theoretically supplied with limitless water [3]. ET₀ represents the limit value of actual ET in a region [4], determines the dry and wet condition of a basin, and is an important indicator for estimating basin ET capacity [2]. Although ET under warming climates has been increasing in some regions, such as western Africa [5], Israel [6], and southern China [7], ET₀ is largely decreasing around the globe in a phenomenon known as the “evaporation paradox” [8,9,10,11]. Scholars exploring the causes of changes in ET₀ have found that the decline in ET₀ in Australia [8], Iran [12], and southern Canada [10] were mainly caused by wind speed; whereas a decline in ET₀ in India was most closely related to relative humidity [13]. In China, the most critical factor linked to the decline of ET₀ is water vapor pressure [14]; however, due to the large geographical differentiation of natural conditions across the diverse regions of China, the drivers of ET₀ display significant spatial heterogeneity. ET₀ of the Yellow River Basin has been increasing, with patterns most closely associated with air temperature, followed by incoming solar radiation [15]. The most important meteorological factor for ET₀ in the Yangtze River Basin was relative humidity [16], but decreases in solar radiation and wind speed were the main factors influencing lowered levels of ET₀ [17]. ET in the upper reaches of the Heihe River Basin was also most correlated to relative humidity, but the observed changes were mainly driven by wind speed [18]. The observed decrease of ET₀ on the Qinghai-Tibet Plateau was related to a decrease of wind speed as well, in addition to a decrease in net radiation, and increase in air temperature [19]. The increasing ET₀ of the Loess Plateau was caused by the combined effect of rising air temperatures and declining in relative humidity, wind speed, and sunshine hours [20]. As indicated by the varied response of ET₀ to the complexities of the changing climate across spatially heterogeneous areas, the precise influence of climate factors on ET₀ are still highly uncertain and deserving of further exploration. Further, Liu et al. [21] found that the change of ET₀ was not only affected by the climate sensitivity coefficient but is also related to the changing trend of meteorological factors. Thus, only by combining the sensitivity coefficient and contribution rate can we systematically and quantitatively analyze the driving mechanisms of change for ET₀ [22].

Since the 1990s, climate change and anthropogenic activity have had a pronounced impact on the hydrological cycle of the Loess Plateau. The Yanhe River Basin (YRB), a typical watershed in the hilly and gully region of the Loess Plateau, provides an optimal opportunity for a more in-depth understanding of the impacts of climate change on ET₀ in a region of great significance for understanding the allocation of water resources and components of the water cycle for the region. Therefore, the YRB was selected as the study area for the present research. The Penman–Monteith method was used to calculate ET₀, with the objectives of analyzing sensitivity to four major meteorological variables and changing trends of various climate factors. Subsequently, the contribution of these factors were quantitatively estimated, so as to reveal the mechanisms of observed ET₀ changes in the YRB over the past 40 years. Broadly, this study contributes to a more thorough understanding of the impact mechanisms of climate change on the hydrological cycle and provides a scientific basis for water resource evaluation and management, in addition to informing agricultural planting structures.

2. Data and Methods

2.1. Study Area

The YRB is a first-level tributary of the middle reaches of the Yellow River, extending 286.9 km over a total drainage area of 7725 km². It originates from Zhoushan, Tianciwan Township, Jingbian County, and proceeds to flow through four primary counties and cities—Zhidan, Ansai, Baota, and Yanchang—and enters the Yellow River near the bank of Nanhegou Township in Yanchang County. The YRB maintains a continental monsoon climate, which is dry-windy in spring, warm-rainy in summer, cool-rainy in autumn, and cold-dry in the winter [23]. Average annual levels are: precipitation, about 520 mm; air temperature, 8.8–10.2 °C; evaporation 898–1678 mm; and sunshine duration, 2450 h [24].

2.2. Data

The meteorological data in the present study were acquired from China Meteorological Data Network (http://data.cma.cn/ (accessed on 20 June 2020)), and included the daily average, maximum, and minimum air temperatures (T, T_max, and T_min, respectively), wind speed at 10 m (U₁₀), sunshine duration (n, in h), daily average relative humidity (RH), and the daily precipitation (P). The U₁₀ was converted into wind speed of 2 m (U₂) by $U_2=0.75\cdot U_{10}$. Data were collected across a time series from 1978–2017, derived from the specific control hydrological station of Ganguyi, and meteorological stations in Jingbian, Wuqi, Zhidan, Ansai, Yan’an, Zichang, Yanchuan, Yanchang, Ganquan and Yichuan (Figure 1).

2.3. ET₀

The Penman-Monteith method, a commonly accepted standard in the literature, was used in the present research to calculate ET₀ (Equation (1)) [25]:

$$E{T}_0=\frac{0.408\mathsf{\Delta }\left(R_n-G\right)+\gamma \frac{900}{\left(T+273\right)}{U}_2\left(e_s-e_a\right)}{\mathsf{\Delta }+\gamma \left(1+0.34U_2\right)}$$

(1)

where $E{T}_0$ is potential evapotranspiration (mm); $R_n$ is the net radiation (MJ·mm⁻²·day⁻¹); G is the soil heat flux (MJ·mm⁻²·day⁻¹); γ is the psychrometric constant (kPa·°C⁻¹); T is mean daily air temperature (°C); U₂ is the wind speed at 2 m height(m·s⁻¹); e_s and e_a are saturation and actual vapor pressure (kPa), respectively; and ∆ is the slope of the vapor pressure curve (kPa·°C⁻¹).

2.4. Calculation of Sensitivity Coefficient

The dimensionless sensitivity coefficient $S_i$ [26,27,28,29] was used to characterize the sensitivity of ET₀ to climate change. This method analyzes the impact of a single climatic factor on ET₀, while holding all others constant, and is calculated according to Equation (2):

$$S_i=\frac{\partial E{T}_0}{\partial i}\frac{i}{E{T}_0 }$$

(2)

where $i$ is change in the climate factor being assessed, and $\partial E{T}_0/\partial i$ is the partial derivative of $E{T}_0$ with respect to climate factor $i$.

A positive (negative) sensitivity coefficient indicates that $E{T}_0$ will increase (decrease) as the variable increases; and the absolute value of the sensitivity coefficient indicates the climatic factor’s degree of influence. An $S_i$ of −0.1, for example, indicates that a 10% increase (decrease) of factor $i$ will cause a 5% decrease (increase) in $E{T}_0$ when the other meteorological variables are held constant. In the present study, the sensitivity coefficients of average air temperature, humidity, wind speed, and solar radiation were calculated and denoted as $S_T$, $S_{RH}$, $S_{U_2}$, $S_{R_S}$, respectively. In this study, we regarded March to May as spring, June to August as summer, September to November as autumn and December to February as winter. Further, the monthly and annual values of the sensitivity coefficients were obtained by averaging the daily sensitivity coefficients.

2.5. Calculation of Contribution Rate

In the research here, the contribution rate of climatic factors to ET₀ was indicated by multiplying $S_i$ by the relative change rate of factor i [7], and computed according to Equations (3) and (4).

$$C_i=S_i·R_i$$

(3)

$$R_i=\frac{N·L_i}{M_i}100\%$$

(4)

where $C_i$ is the contribution rate of change of $i$ to $E{T}_0$ (%), $R_i$ is the relative rate of change of climatic factor $i$, $N$ is the number of years in the study period, $L_i$ is the linear trend rate of climatic factor $i$, and $M_i$ is the average value of the climatic factor.

Similarly to S_i, positive (negative) $C_i$ indicates the positive (negative) effect of climatic factor $i$ on the change of $E{T}_0$, and the greater its absolute value, the greater its contribution.

2.6. Analytical Method

The non-parametric Mann–Kendall statistical test [30,31] was used to detect the trends of the sensitivity coefficients, and resulting contribution rates of ET₀ in the YRB from 1978 to 2017. The inverse distance weighting method was used to further interpolate the sensitivity coefficient and contribution rate [32].

3. Results

3.1. Temporal and Spatial Characteristics of ET₀ and Meteorological Factors

The changes in multi-year average monthly $E{T}_0$ and meteorological factors for the YRB are shown in

Table 1. Temporal characteristics of ET₀ and meteorological factors in Yanhe River Basin.

Time	Mean						M-K Statistics
	T/°C	RH/%	U2/(m s−1)	Rs/(MJ mm−2 Day−1)	P/mm	ET0/(mm)	T	RH	U2	Rs	P	ET0
Jan.	−6.07	53.85	1.03	304.92	3.00	23.37	1.68	0.72	0.93	0.51	0.63	0.49
Feb.	−2.05	52.44	1.13	336.89	5.65	33.90	2.73	1.1	−0.09	0.61	2.14	1.7
Mar.	4.33	50.53	1.32	478.71	14.28	66.43	3.12	−2.31	−0.19	2.42	−2.33	3.36
Apr.	11.76	46.48	1.48	580.06	24.05	104.39	2.24	−0.47	−3.03	1.44	1.07	0.49
May.	17.20	50.93	1.40	664.94	43.40	133.22	0.75	−0.37	−2.07	1	0.54	0.28
Jun.	21.29	57.66	1.26	655.36	60.54	139.72	1.68	−1.17	−0.93	0.93	−1.1	1
Jul.	22.99	69.01	1.11	631.68	115.24	134.55	2.63	−1.24	0.72	0.72	0.3	1.63
Aug.	21.24	74.17	1.03	573.99	107.19	114.22	1.7	−2.21	1.12	−0.42	−1	0.7
Sep.	16.04	74.92	0.98	453.95	71.85	78.29	2.82	−0.21	1.84	−1.86	0.98	−0.49
Oct.	9.63	70.20	1.02	384.49	34.76	53.65	1.61	1.26	0.05	−1.05	0.72	−0.21
Nov.	2.22	62.64	1.07	304.19	12.64	32.13	1.98	−0.19	−0.23	−0.02	−0.3	0.68
Dec.	−4.23	57.03	1.04	276.63	2.60	22.07	0.89	−0.68	1.35	0.63	0.56	0.96
Year	9.59	60.05	1.16	5645.81	495.19	935.92	3.8	−1.12	−0.7	0.56	0.42	1.65

. Averages from 1978–2017 were: air temperature, 9.59 °C (maximum observed from June to August); RH, 60.05% (maximum observed from August to October); wind speed at 2 m height, 1.16 m·s⁻¹ (maximum observed from March to May); solar radiation, 5645.81 MJ·mm⁻²·day⁻¹ (maximum observed from May to July); and precipitation, 495.19 mm (maximum observed from July to September). The results of the Mann–Kendall statistical test indicated that air temperature (p < 0.01), solar radiation, and precipitation showed an increasing trend with time, while RH and wind speed at 2 m height were decreasing. The average ET of YRB was 935.92 mm, peaking from May to July. Overall, $E{T}_0$showed an increasing trend (p < 0.1), while $E{T}_0$ values for September–October were decreasing, although not at a statistically significant level.

Average annual air temperature of YRB from 1978 to 2017 presented a geographical distribution pattern of southeastern highs and northwestern lows, both of which increased over time (Figure 2). RH displayed highs in the west and east, and lows in the north and south. Only the Zichang and Yanchang stations showed an insignificant rising trend in RH, indicating that the YRB underwent significant warming and drying. U₂ reached lows in the east and west, highs to the north and south, with an overall downward trend save for the Zichang, Yanchang, Yanchuan, and Yichuan stations showing an increase. The incoming solar radiation in the southeast was less than that in the south, and displayed a decreasing trend; whereas the solar radiation at Yan’an and Jingbian stations were the highest in the basin, showing an upward trend. Precipitation in the YRB had a distribution pattern of south > southeast > northwest, peaking at Yan’an and Ganquan stations. Save for the sole location of Yan’an, precipitation in the basin showed an upward trend. $E{T}_0$ was greatest in the south and least in the west. An upward trend was observed for all sites except Ganquan, where decreasing $E{T}_0$ levels with increasing air temperature indicated the local existence of the “evaporation paradox” phenomenon. It can be seen that the intra-annual characteristics of meteorological factors and ET₀ were variable, and spatial heterogeneity was significant throughout the study region.

3.2. Sensitivity of ET₀ to Meteorological Factors

3.2.1. Temporal Characteristics

$S_T$, $S_{RH}$, and $S_{R_S}$ showed an intra-annual, single peak pattern, indicating that ET₀ was more sensitive to temperature conditions and sunshine duration in the summer over this scale. In addition, $S_{U_2}$ showed a unimodal distribution, displaying that ET₀ was most sensitive to wind speed in the winter (Figure 3). On an interannual scale, $S_T$, $S_{R_S}$, and $S_{U_2}$ increased, whereas $S_{RH}$ decreased. The absolute value of $S_{R_S}\left(0.42\right)$ was the largest of the factors examined, indicating that ET₀ was most sensitive to solar radiation, and increased by 4.2% for every 10% increase in solar radiation (while holding all other factors constant;

Table 2. Temporal characteristics of sensitivity coefficient of ET₀ to meteorological factors.

Time	Mean				M-K Statistics
	ST	SRH	SU2	SRs	ST	SRH	SU2	SRs
Jan.	−0.12	−0.51	0.32	0.09	1.33	−2.31	1.35	−0.56
Feb.	−0.05	−0.43	0.25	0.27	2.10	−1.77	0.56	−0.58
Mar.	0.04	−0.36	0.20	0.40	−0.33	1.82	2.82	−2.21
Apr.	0.09	−0.28	0.20	0.48	0.19	0.89	0.16	1.12
May.	0.12	−0.25	0.16	0.56	−0.19	1.07	0.30	0.09
Jun.	0.14	−0.24	0.13	0.63	−0.89	1.24	0.93	−0.07
Jul.	0.19	−0.28	0.09	0.70	−1.98	−0.02	1.70	−1.07
Aug.	0.22	−0.33	0.07	0.70	−2.54	−1.37	2.63	−2.83
Sep.	0.20	−0.44	0.09	0.61	−1.33	−2.77	1.37	−2.38
Oct.	0.13	−0.54	0.16	0.43	0.61	−1.82	−0.42	−0.37
Nov.	0.02	−0.62	0.29	0.16	1.00	−0.91	1.12	−1.19
Dec.	−0.07	−0.61	0.37	−0.01	2.84	−0.93	1.40	−1.21
Year	0.08	−0.41	0.19	0.42	0.82	−1.51	2.80	−1.82

). Examining each month across all years, $S_T$ was positive except for in the winter, $S_{RH}$ was consistently negative, $S_{U_2}$ was positive throughout, and $S_{R_S}$ was positive except for December. From analyses of the absolute values for the sensitivity coefficients of ET₀, it was revealed that spring–summer values were mainly affected by solar radiation, and autumn-winter values by RH. Examining the M-K statistics, the monthly sensitivity coefficients of ET₀ in the YRB were variable: $S_T$ increased over the study period, but declined in the months from March–September (save for April); $S_{RH}$ decreased annually, but increased within each year from March–June; $S_{U_2}$ increased overall, but decreased in the month of October; and $S_{R_S}$ mostly decreased annually, but increased each year in April and May. It was found that over the 40-year study period, the sensitivity of ET₀ to air temperature and wind speed had increased, while sensitivity to solar radiation and RH decreased. The sensitivity of ET₀ to the climatic factors examined varied by month throughout the year, and within each month of the year as well.

3.2.2. Spatial Characteristics

$S_T$, $S_{U_2}$, and $S_{R_S}$ at each site in the YRB were positive values, whereas $S_{RH}$ was the sole factor with a negative value. The absolute values of $S_{RH}$ at the Jingbian, Zichang, Ansai, Yan’an, Ganquan, and Yichuan stations were the largest of all factors, indicating the importance of RH when determining ET₀. The absolute values of $S_{Rs}$ at the Wuqi, Zhidan, Yanchuan, and Yanchang stations were larger than elsewhere, confirming the importance of solar radiation on ET₀. $S_T$ tended to increase across all stations, save for Yan’an, Yanchang, and Yichuan; whereas $S_{RH}$ tended to decrease save for Jingbian, Wuqi, Yan’an, and Ganquan stations. Except for Wuqi station, sensitivity of $S_{U_2}$ was increasing. $S_{R_S}$ was increased only at Ansai, Ganquan, and Wuqi stations, while decreasing at all other sites (

Table 3. M-K statistics of Sensitivity coefficient of ET₀ to meteorological factors of Yanhe River Basin.

Station	Mean				M-K Statistics
	ST	SRH	SU2	SRs	ST	SRH	SU2	SRs
Jingbian	0.03	−0.46	0.26	0.34	1.12	3.05	2.89	−0.40
Wuqi	0.07	−0.36	0.17	0.43	0.56	2.07	−0.07	1.54
Zichang	0.07	−0.43	0.21	0.40	0.51	−3.57	1.42	−1.30
Zhidan	0.08	−0.34	0.16	0.45	2.77	−1.21	2.10	−0.77
Ansai	0.08	−0.45	0.20	0.41	1.26	−0.16	1.07	0.72
Yan’an	0.08	−0.44	0.21	0.41	−1.56	0.05	1.33	−1.30
Ganquan	0.09	−0.46	0.17	0.45	2.68	3.38	0.54	1.72
Yanchuan	0.08	−0.28	0.17	0.44	0.61	−2.68	4.24	−3.36
Yanchang	0.10	−0.39	0.18	0.45	−1.72	−2.96	3.36	−3.22
Yichuan	0.09	−0.45	0.20	0.42	−1.56	−2.49	3.61	−3.84

). Therefore, the ET₀ of the YRB was most sensitive to RH and solar radiation, but this influence appears to be weakening. Contrarily, the sensitivity of ET₀ to air temperature and wind speed was small, but sensitivity is increasing.

The geographic distribution of ET₀ sensitivity to climatic factors was derived by spatial interpolation of the sensitivity coefficients for each station (Figure 4): $S_T$ gradually decreased from SE to NW of the basin, peaking in the Yanchang area; $S_{RH}$ increased from the central to SE and SW of the basin, reaching its maximum in Zhidan and Yanchuan, respectively; $S_{U_2}$ was roughly opposite of $S_{RH}$, with a minimum in the Zhidan area; the distribution pattern of $S_{R_S}$ was similar to that of $S_{RH}$, reaching maximums in Zhidan, Ganquan, and Yanchang. Thus, the sensitivity of ET₀ to each climate factor analyzed varied significantly by geographic location.

3.3. Contribution Rate of Meteorological Factors

On an annual scale, when the T increased by 14.35%, ET₀ increased by 1.09%. Since S_RH was negative, an increase in RH by 2.09% led to a decrease in ET₀ by 0.85%. If U₂ decreased by 3.24%, ET₀ decreased by 0.63%; and when solar radiation increased by 1.32%, ET₀ increased by 0.55%. Overall, air temperature was the dominant meteorological factor contributing to ET₀ of the YRB from 1978–2017. From an intra-annual perspective, the increase in air temperature in January and February led to an increase in ET₀. The increases of ET₀ in March, July, and August were most strongly correlated with the decrease in RH. The observed increase in ET₀ in April and May was primarily caused by the decrease in U₂. The most significant driver of ET₀ in June was solar radiation, and the observed increase in ET₀ caused by U₂ nearly offset the decrease driven by lowered RH. In September and October, the most significant factor determining lowered ET₀ was the decline in solar radiation. T was the dominant controlling factor of ET₀ in November. In November, although ET₀ had the greatest level of sensitivity to RH, its contribution rate was only 0.03%, permitting the inference that the decreasing trend of RH was not the primary cause of the observed decrease in ET₀. The most significant contribution to ET₀ in December was U₂. In December, although ET₀ was sensitive to RH, its decline did not lead to a decrease of ET₀ (

Table 4. Temporal characteristic of contribution rate of meteorological factors to ET₀ in Yanhe River Basin.

Time	RT/%	CT/%	RRH/%	CRH/%	RU2/%	CU2/%	RRS/%	CRS/%
Jan.	−16.15	1.95	3.10	−1.59	2.34	0.76	0.53	0.05
Feb.	−123.61	6.68	8.25	−3.57	0.71	0.18	1.79	0.49
Mar.	63.48	2.86	−23.68	8.61	−4.53	−0.92	11.87	4.79
Apr.	12.65	1.15	−4.60	1.26	−23.55	−4.70	5.30	2.54
May.	2.77	0.33	−3.47	0.88	−22.31	−3.66	4.09	2.31
Jun.	4.57	0.64	−6.65	1.58	−11.78	−1.57	2.65	1.68
Jul.	6.11	1.16	−5.64	1.59	3.95	0.34	2.25	1.58
Aug.	4.48	0.96	−6.40	2.09	6.20	0.43	−2.29	−1.60
Sep.	9.70	1.95	−0.57	0.25	8.53	0.73	−9.20	−5.58
Oct.	11.47	1.44	4.18	−2.25	−5.09	−0.81	−6.80	−2.89
Nov.	66.20	1.26	−0.04	0.03	−4.10	−1.17	−2.04	−0.33
Dec.	−21.83	1.46	−4.92	3.01	10.80	3.96	2.62	−0.04
Year	14.35	1.09	2.09	−0.85	−3.24	−0.63	1.32	0.55

).

Across the entire study region, a relatively equal change of a single climatic factor had significantly variable contributions to ET₀. For example, an increase of RH by 0.74%, lead to a decrease in ET₀ at the Zichang station by 0.34%, and a decrease at the Yanchang station of 0.24% (

Table 5. Contribution rate of meteorological factors to ET₀ of stations in Yanhe River Basin.

Station	RT/%	CT/%	RRH/%	CRH/%	RU2/%	CU2/%	RRS/%	CRS/%
Jingbian	27.75	2.02	−9.00	3.91	−31.68	−6.76	2.79	1.12
Wuqi	12.34	0.94	−3.92	1.35	−17.78	−2.82	8.81	3.95
Zichang	16.19	1.25	0.74	−0.34	10.52	2.10	−0.21	−0.08
Zhidan	19.71	1.86	−4.56	2.10	−8.13	−1.40	4.27	1.90
Ansai	11.10	0.89	−1.46	0.40	−18.65	−3.13	2.23	0.98
Yan’an	12.91	1.25	−7.57	2.93	0.16	0.03	4.43	1.98
Ganquan	18.00	0.54	−2.99	1.37	−35.71	−9.16	−2.18	−0.74
Yanchuan	8.27	0.54	−0.51	0.18	40.06	6.90	−1.17	−0.50
Yanchang	4.70	0.39	0.74	−0.24	34.65	6.51	−3.42	−1.48
Yichuan	15.34	1.33	−4.67	2.12	8.13	1.64	−2.58	−1.09

). Through comparison, it was found that the dominant meteorological factor at Jingbian, Zichang, Ansai, Ganquan, Yanchang, and Yanchuan stations was U₂. Solar radiation contributed the most to ET₀ at Wuqi station, and RH was the controlling factor at Zhidan, Yan’an, and Yichuan stations. Air temperature contributed positively to the increase of ET₀ across the entire basin, whereas the effects of RH, U₂, and solar radiation on ET₀ displayed significant spatial variability. For example, the contribution rate of RH to the recorded ET₀ values of Zichang and Yanchang stations was negative, but all other stations recorded positive rates (Table 5). Because ET₀ of Zichang and Yanchang stations had a negative sensitivity coefficient to RH, the observed increase in RH had a negative effect on ET₀. Conversely, other sites had a positive effect on ET₀ due to the decreasing levels of RH.

Thus, the geographic zonality each meteorological factor’s contribution to ET₀ was significant. The influence of T and solar radiation on ET₀ gradually decreased from NW to SE of the basin, whereas U₂ displayed precisely the opposite pattern. The contribution of RH to ET₀ decreased radially from Zhidan to the surrounding areas (Figure 5). By combining Figure 2 and Figure 5, it can be ascertained that the high ET in the Yan’an area was primarily driven by RH and solar radiation, whereas the low ET observed in the Zhidan area was mainly affected by U₂. Because the sensitivity coefficient of ET₀ to RH in Ganquan was negative, the recorded decrease in RH had a positive effect on ET₀. Similarly, the sensitivity coefficient of ET₀ to U₂ and solar radiation was positive, so the recorded decrease in U₂ and solar radiation contributed to the observed decrease in ET₀. Therefore, the main factors behind the “evaporation paradox” phenomenon observed in Ganquan were decreasing values of U₂ and solar radiation.

4. Discussion

Previous studies have found that a combination of the changing meteorological factors, sensitivity coefficients, and contribution rates can more accurately analyze the drivers of ET₀ [21,22].

4.1. Dominant Factors of ET₀ Variation in the YRB

The calculated absolute values (i.e., strengths) for the sensitivity coefficients of the climatic factors analyzed on ET₀ were Rs > RH > U₂ > T; however, sensitivities varied significantly by month. For example, the sensitivity coefficient of ET₀ to solar radiation in December was −0.01, but reached 0.7 in July and August from1978 to 2017. Additionally, the sensitivity coefficient of T in the winter (December, January, February) was negative, but positive throughout the remainder of the year. Combined with the results of trend analysis of meteorological factors, it was found that T still maintained a positive correlation with ET₀, since T in the winter months was low as well.

The absolute values of the contribution rates for each meteorological factor to ET₀ were T > RH > U₂ > solar radiation; and furthermore, these rates for each individual factor varied significantly by month. For example, the contribution rates of T to ET₀ for January, February, and December were 1.95%, 6.68%, and 1.46%, respectively; but these rates in June, July, and August were 0.64%, 1.16%, and 0.96%, thus indicating that the contribution of T to the increase of ET₀ was higher in winter months than in summer. Furthermore, although the sensitivity coefficient of ET₀ to T was small, its contribution was large as the significantly increasing trends of air temperature (p < 0.01) led to an increase of ET₀. These findings are similar to the results of a study on ET₀ climate sensitivity coefficients in the Yellow River Basin [15]. In the YRB, although the sensitivity coefficient of ET₀ to solar radiation was the greatest, its overall contribution to ET₀ was low due to its relatively stable rate over time.

Combined with precomplaint sensitivity analysis and contribution rate analysis in the present study, it can be seen that only by combining the sensitivity coefficients of changing meteorological factors to ET₀, can we ascertain their true contribution rates for a more comprehensive understanding of the causes of changes in ET₀.

In the present study, the multi-year average air temperature of the YRB showed an increasing trend, with a positive sensitivity coefficient, and a contribution rate of 1.09%. RH has displayed a decreasing trend with time, a sensitivity coefficient of −0.41, and contribution rate of −0.85%. It can be seen, however, that the decreasing trend of RH did not cause the increase in ET₀ in the YRB. U₂ also displayed a decreasing trend with time, a positive sensitivity coefficient of ET₀, and a contribution rate of −0.63%. Solar radiation showed an increasing trend with time, a positive sensitivity coefficient, and contribution rate of 0.55%. Thus, it can be concluded that the negative contribution rates of meteorological factors ET₀ were less than the positive. Accordingly, ET₀ in the YRB has shown an increasing trend from 1978–2017 mostly related to T, U₂, and solar radiation, whereas observed decreases in ET₀ were primarily driven by RH.

4.2. Evaporation Paradox in the YRB

Another pertinent point was that although the ET₀ of the YRB showed an overall increasing trend, ET₀ at the Ganquan Station decreased, indicating a sole, local existence of the “evaporation paradox”. The absolute value of the sensitivity coefficients for the meteorological factors in the Ganquan area were RH > solar radiation > U₂ > T; and the absolute values of their contribution rates were U₂ > RH > solar radiation > T. In the Ganquan area, the increasing trend of air temperature was significant, but its corresponding contribution rate was relatively low. Solar radiation decreased with time, and its corresponding contribution rate to ET₀ was −0.74%, nearly offsetting the positive contribution rate of air temperature. The sensitivity coefficient for RH was −0.46, with a contribution rate of 1.37%, indicating that the downward trend of RH had a positive effect on ET₀. Lastly, the sensitivity coefficient for U₂ was only 0.17, but its significant downward trend resulted in a contribution rate of −9.16%, making it the dominant factor driving the observed decreasing trend in ET₀. This is similar to results found by Roderick & Farquhar [8], Dinpashoh et al. [12], Burn & Hesch [10], and Luo et al. [18].

5. Conclusions

In this paper, the effects of air temperature (T), relative humidity (RH), wind speed at 2 m (U₂), and solar radiation on the potential evapotranspiration (ET₀) in the Yanhe River Basin (YRB), China were quantitatively estimated using sensitivity coefficients and contribution rates, combined with the changing trend of meteorological factors observed from 1978–2017. The main conclusions of this study can be summarized as follows:

The absolute value of the sensitivity coefficients of ET₀ to meteorological factors in the YRB was solar radiation > RH > U₂ > T, although sensitivities displayed significant temporal (intra- and interannual) and spatial differences. The absolute values of the contribution rates for each meteorological factor were T > RH > U₂ > solar radiation. Similarly, the contribution rates for the same climatic factors displayed significant spatiotemporal heterogeneity.

The observed increase of ET₀ in the YRB was related to T, U₂, and solar radiation; whereas decreases in ET₀ were mostly related to RH. The most dominant factor controlling ET₀ across the entire YRB was T, but this displayed significant spatiotemporal differences at local scales. The “evaporation paradox” phenomenon observed in the Ganquan area was driven primarily by wind speed.

It can be seen from this study only by combining the sensitivity coefficients of changing meteorological factors to ET₀, with their respective contribution rates, we can systematically and quantitatively analyze the driving mechanisms of observed changes in ET₀.