Potential EvapotranspirationReduction and Its InfluenceonCrop Yield in the North China Plain in 1961–2014

China Meteorological Administration Training Centre, Beijing 100081, China Key Laboratory of Ecosystem Network Observation and Modeling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China Mentougou Meteorological Service, Beijing 102308, China College of Resources and Environmental Sciences, China Agricultural University, Beijing 100193, China Department of Geography, University of North Texas, Denton, TX 76203, USA College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100190, China


Introduction
Hydrological processes and crop water requirements have been modified by climate change on local, regional, and global scales [1,2]. e modification of climate change has coincided with surface air temperature increase.
In the hydrological cycle, actual evapotranspiration (ET) and potential evapotranspiration (ET 0 ) played important roles [3], particularly in soil evaporation and crop transpiration, eventually impact crop productivity. ET is measured as the quantity of water evaporating from an area under existing atmospheric conditions [4]. ET is controlled by two processes occurring simultaneously: evaporation from the soil and transpiration from the leaf surface [5]. ET 0 is calculated as the maximum quantity of water that can be lost as water vapor in a given climate, by a continuous, extensive stretch of vegetation covering the ground when there is no shortage of water [6]. ET 0 is determined by the meteorological conditions and the surface type [7]. Because ET 0 is computed from precipitation, temperature, relative humidity, wind speed, and sunshine hours [8][9][10], any change in these variables is likely to change the ET 0 . Furthermore, these changes created more benign or stressful conditions for ET 0 [11,12]. ET 0 had a significant impact on the availability of water resources [13], consequently influencing agricultural productivity. Plant growth planning often requires information on ET 0 [14,15] to estimate crop transpiration.
erefore, the study of ET 0 under climate change has become an interesting research issue to scientists around the world. Also, it is important to identify the changes in ET 0 on a regional scale. e humidity index (K), change in precipitation, and ET 0 were applied to estimate dry-wet variations. Previous research studies on climate type only considered the influence of temperature and precipitation [16,17] without including the influence of relative humidity, solar radiation, wind speed, and sunshine hours. erefore, to understand the changing characteristics of climate variations, it is important to integrate water resource management. Furthermore, K can be applied to predict model scenarios that would persist in critical agricultural areas. erefore, assessing ET 0 and K distribution would explain the relationships between climate change and hydrological processes. is would lead to reasonable water regulation and management to maintain the ecohydrological system.
In the NCP, summer maize (Zea mays L.) represents 33% of the national grain yield, while winter wheat represents 50% of the national grain yield [18]. Increasing temperature and decreasing precipitation are likely to reduce the yields of several primary crops over the next two decades [19]. Water shortage would be aggravated in the main grain production belt of North China [20,21]. Bergamaschi et al. [22] indicated that crop yields would reduce by 10-20% up to 2050 because of warming and drying. Hence, understanding the hydrological distribution in these regions is critical for managing agricultural water resources and adjusting the planting pattern.
At present, there are few studies on the spatiotemporal variations in climate type by integrating the input (precipitation) and output (evapotranspiration) of atmospheric water vapor in the NCP. erefore, the objectives of this study were to (1) quantify the changes in spatial and temporal variations in ET 0 and K in the NCP from 1961 to 2014, (2) quantitatively explain the reasons for the changes in ET 0 by analyzing the sensitivity coefficients and contribution rates, and (3) analyse the relationship between ET 0 and the crop yield. e results might be useful to agricultural planning and layout.

Study Area and Data.
e study area, located in the NCP (31-43°N and 110-123°E), has a warm, temperate monsoon climate. e precipitation changes significantly in summer. e main crops are summer maize and winter wheat. e mean annual temperature and average annual precipitation were 13.0°C and 586 mm, respectively [23]. e soil has a silt-loam texture in the cultivated layer in general. is study was based in Beijing, Tianjin, Hebei province, Henan province, and Shandong province.
In this study, daily meteorological data from January 1961 to December 2014 were obtained from 60 stations in the NCP (Table 1). ese data contained daily mean, minimum and maximum temperature, sunshine hours, wind speed, precipitation, and relative humidity provided by the National Climatic Centre of China Meteorological Administration (http://cdc.cma.gov.cn).
e wind speed at 10 m height was converted to wind speed at 2 m height using the wind profile relationship introduced in Allen et al. [24], as shown in equation (1). e observed dataset has been subjected to strict quality and homogenization control. e geographical location of the stations is shown in Figure 1.
where u 2 is the wind speed at 2 m above the ground surface (m·s −1 ), u z is the wind speed at z m above the surface (m·s −1 ), and z is the height of measurement above the ground surface (m).

Estimation of Humidity Index (K).
Humidity index is the ratio of precipitation to potential evapotranspiration and is calculated by where P is the daily precipitation (mm·d −1 ) and ET 0 is the daily potential evapotranspiration (mm·d −1 ). e classification of climate region based on humidity index is listed in Table 2 [25].
ET 0 is calculated by the Penman-Monteith formula [24]: where R n is the net radiation at the surface, MJ·m −2 ·d −1 , G is soil heat flux density, MJ·m −2 ·d −1 , cis the psychrometric constant, kPa°C −1 , T is the mean daily air temperature,°C, U 2 is the wind speed at a height of 2 m, m·s −1 , e s is the saturation vapor pressure, kPa, e a is the actual vapor pressure, kPa, and Δ is the slope of the saturated water-vapor pressure curve, kPa°C −1 . e computation of all data required for calculating ET 0 followed the method and procedure given in Chapter 3 of FAO-56 [24].

Sensitivity Analysis and Sensitivity Coefficient.
Sensitivity analysis of the ET 0 equation is an effective way to analyze the effect of meteorological factors on ET 0 [26]. Previous studies showed the usage of nondimensional relative sensitivity coefficients to explain climate variables influence on ET 0 [27]: where S Vi is the sensitivity coefficient of the ith climate variable, ET 0 is the potential evapotranspiration, mm·d −1 , ΔET 0 is the daily change of ET 0 , V i is the ith climate variable, and ΔV i is the change of V i . A positive/negative S Vi of a variable indicated that ET 0 would increase/decrease as climate variables. e greater the S Vi , the greater effect of the climate factor on ET 0 .
where G vi is the contribution of the ith climate variable to ET 0 , S vi is the sensitivity coefficient, and R vi is the relative change rate for the ith climate variation, which was given by equation (5). e meaning of G vi is the same as S vi . In this study, S vi and G vi for daily air temperature, solar radiation, relative humidity, and wind speed were estimated to quantify the contribution of each factor to the variation of ET 0 .
where Trend Vi is the climate tendency rate for the ith climate variation and is calculated by equation (6), V i is the mean value for the climate variation, and n is the time in years. In this study, n � 54.

Climate Trend.
Climate tendency rate (Trend Vi ) was calculated by the least square method: where X i is the ith climate variation, t is the time in years, a is the regression coefficient, 10×a is the climate tendency rate, and b is the constant parameter.

Annual and Spatial Variation and Tendency of Humidity
Index. e humidity index (K) showed an upward trend from north to south, changing from 0.34 to 1.20 (Figure 2(a)), which indicated that the climate of the region varied from semiarid to humid from north to south. e climate in Northwest and mid-west Hebei was semiarid, while that in South Henan was humid, with K above 1. e other regions had semihumid climate, with K ranging from 0.5 to 1.0. e tendency rate of K was −0.005 decade −1 (P � 0.63), which showed a slight drying trend from south to north (Figure 2(b)).
irty-five percent of the sites (total � 60) mainly distributed in southern NCP had a tendency rate of K above 0, which indicated that these regions were wet. e other sites with a tendency rate of K below 0, especially East Shandong and North Hebei, were dry with a tendency rate of K below −0.01 decade −1 .

Interdecadal Changes in Precipitation and ET 0 .
e tendency rate of precipitation was −12.4 mm decade −1 , which indicated a downward trend of precipitation. e abrupt decline in precipitation tendency rate was mainly observed in Southeast Hebei and Southeast Shandong (Figure 3(a)). Only 10.0% of all the sites had a tendency rate of precipitation over 0. e ET 0 tendency rate was −13.5 mm decade −1 (Figure 3(b)), which showed a downward trend from 1961 to 2014. e ET 0 tendency rate was significant at the 0.05 level in 71.0% of the sites, especially in mid-east Hebei and midsouth Shandong.   Figure 4(a)), which meant that ET 0 increased with temperature. S T in the southeast was higher, especially in the Henan province, while it peaked in the mid-region, such as North Shandong, Beijing, Tianjin, and North Hebei. S RH varied from−0.70 to−0.19 (Figure 4(b)), which indicated that ET 0 decreased as the relative humidity increased. e spatial distribution of S RH showed a downward trend from south to east. e S RH was higher in East Shandong, with an absolute value above 0.5. In South Hebei and Beijing, the absolute value of S RH was below 0.4. e S SH in all regions was above 0, with a mean value of 0.18 (Figure 4(c)). e S SH showed an upward trend from north to south. S WS ranged from 0.10 to 0.31 (Figure 4(d)) and showed a downward trend from north to south. e S WS in the northern part of the region, e.g., North Hebei, Beijing, and Tianjin, was above 0.21, while in South Henan, it was below 0.18.

Climate Factor Attribution Rate to ET 0 on Annual and
Spatial Scales. G vi was applied in this study to indicate the relative change in ET 0 resulting from each meteorological factor. e attribution rate of air temperature to ET 0 (G vT ) ranged from−0.5% to 4.0% ( Figure 5(a)). G vT in the northern and eastern parts of the NCP was over 1%, while it was less than 1% in the other regions. e attribution rate of relative humidity to ET 0 (G vRH ) ranged from−4.7% to 10.1% ( Figure 5(b)). G vRH in North Hebei and Southwest Shangdong was below 0. e attribution rate of sunshine hours to ET 0 (G vSH ) ranged from−8.4% to 0.2% ( Figure 5(c)). G vSH was above 0 in only one site. e spatial distribution of G vSH showed a downward trend from north to south. e attribution rate of wind speed to ET 0 (G vWS ) ranged from−19.1% to 4.9% ( Figure 5(d)). e highest absolute value of G vWS was in Beijing and Tianjin. e attribution rate of air temperature and relative humidity to ET 0 was positive, which indicated that ET 0 increased with an increase in these two climate factors. However, the mechanisms of G vT and G vRH were different. G vT was positive when the sensitivity coefficient was positive and the tendency rate (0.24°C decade −1 ) of air temperature increased (Figure 6(a)). G vRH was positive when the sensitivity coefficient was negative and the tendency rate Advances in Meteorology (0.44 decade −1 ) of relative humidity decreased (Figure 6(c)). e attribution rate of sunshine hours and wind speed was negative, which indicated that the change in the two climate factors decreased ET 0 . e attribution rate of climate factor to ET 0 was in the following order: wind speed > sunshine hour > relative humidity > air temperature.

Discussion
e change in climate types was due to the sensitivity to various meteorological variables and their attribution to ET 0 in the NCP. ET 0 was most sensitive to relative humidity, which had a negative effect. is was consistent with the study by Hu et al. [28] in Northeast China. e factor that impacted ET 0 significantly varied depending on the location. Huo et al. [3] indicated that ET 0 was very sensitive to 2 m wind speed and relative humidity in Northwest China. In southern Spain, ET 0 was sensitive to air temperature and radiation in the warmer season and to 2 m wind speed in cooler seasons [29]. In Australia, temperature was found to be the most important factor for ET 0 , but the second-most important factors differed between dry and humid catchments [30]. Yang et al. [31] showed that the sensitivity of ET 0 to climate factors varied from low elevations to high elevations. e sensitivity of ET 0 to climate factors is regional variation because climate conditions and climate factors differ with regional variation [30,31]. In this study, wind speed reduction was the main reason for the decline in ET 0 from 1961 to 2014. However, the climate tendency rate was low and resulted in a relatively low attribution rate.
In general, warm climates led to an increase in evaporation and evapotranspiration. However, the observation of pan evaporation rate has been declined in most parts of the world in the past several decades [8,9,32,33], which is called the pan evaporation paradox phenomenon [34]. Also, those only considered the influence of air temperature on ET 0 , without considering other meteorological factors, e.g., wind speed, relative humidity, and sunshine hours. It revealed significant increasing trends in ET 0 (P � 0.1) during 1961-1990 over the entire West African region [35]. Although the air temperature significantly increased at the rate of 0.24°C decade −1 , the effect of decrease in wind speed and sunshine hours was greater than that of the increase in air temperature, which led to a significant decline of ET 0 in the NCP. is pattern of variations is in agreement with the findings of Dinpashoh et al. [36] in North-West Iran where most of the stations selected (86% of the sites) also showed increasing trends in ET 0 between 1997 and 2016. However, Hou et al. [37]     Advances in Meteorology 7 contributing to increasing ET 0 due to its sensitivity to ET 0 and the significant increase trend. Agriculture accounts for at least 90% of the total water use in the arid and semiarid regions [38]. An important way to alleviate water stress is to improve agricultural water management. Comprehensively understanding an agrohydrological process lays a foundation for minimizing agricultural water use. In the presence of a shallow water table, groundwater provides an important source for crop water use in arid and semiarid regions [39,40], which impact crop productive. Climate type depended on the rate of change of precipitation and ET 0 . e important issue involves the evaluation of drought impacts on agriculture. Crop yields and drought occurrence statistics are closely related [42,42], but consistency analysis of drought trends derived from humidity index and agricultural drought survey is sparse. Crop yield increased significantly (P ≤ 0.001) in the study area (Figure 7), in accordance with K in each area. e crop yield was greater in Shandong and Henan province, with a K of 0.70 and 0.77, compared with that in Tianjin, Beijing, and Hebei (Table 3). e lowest K (0.53) was in Hebei province, along with the lowest crop yield. erefore, regional water balance should be considered and drought or flood risk might be reduced in these areas. China has investigated agricultural drought area for decades, so it is important to investigate the degree that K and ET 0 with agricultural drought surveys, especially in their climatic trends.

Conclusions
e NCP has experienced a semiarid to humid climate from north to south based on the humidity index due to the slight change in precipitation and the significant decline of ET 0 on annual and spatial scales. In the study region, 71.0% of the sites showed a "pan evaporation paradox" phenomenon. ET 0 was the most sensitive to relative humidity, particularly in East Shandong, followed by wind speed. e dominant cause of ET 0 decline was wind speed, with the highest attribution rates, particularly in Beijing and Tianjin. e higher the humidity index in Shandong and Henan province was, the higher the crop yield was. e lower the humidity index in Hebei province was, the lower the crop yield was. It is necessary to analyze the influence of ET 0 on crop yield at various crop growth stages.

Data Availability
e data used to support the findings of this study have been deposited in the 3691421data-2019.xls repository and are included within the article. Disclosure e first author is Wanlin Dong.