Spatiotemporal Characteristics of Evapotranspiration Paradox and Impact Factors in China in the Period of 1960–2013

Downward trend of potential evaporation accompanied with upward of air temperature which is denoted as evaporation paradox has been reported in many regions over the past several decades in the world. In this paper, evaporation paradox and key factors attributed to ET 0 changes are systematically analyzed based on data from 599 meteorological stations during 1960–2013. Results show that (1) Evaporation paradox exists in all regions in1960–2013 and 1960–1999 except SWRB in 1960–2013 but no evaporation paradox in 2000–2013. (2) Evaporation paradox exists in large areas in spring and summer, the extent and range fall in autumn, and there is no evaporation paradox in winter. (3)The evaporation paradox area accounts for 73.7% of China in 1960–2013 and 91.2% in 1969–1999. (4) Sunshine hours, humidity, wind speed, andmaximum temperature appear to be the most important variables which contributed to ET 0 change in China.


Introduction
Climate change characterized by global warming has been the focus of diversified research fields such as water resource, agriculture, ecosystem, and human health.It is widely accepted that global air temperature had been increasing in recent decades, it has risen by about 0.85 (0.65-1.06) ∘ C from 1951 to 2012, and the average rising rate was 0.12 (0.08-0.14) ∘ C (IPCC [1]).In China, temperature has increased by about 0.5-0.8∘ C and precipitation has large regional fluctuation but no significant trend in the recent 100 years (Wang et al. [2]).
In fact pan evaporation observations mostly ended in 2001 in China; evaporation paradox was concluded based on annual pan evaporation of 1960-2000 (H.Yang and D. Yang [33]) or potential evaporation from 1960-2010 without no data segment.However, change of temperature and potential evaporation transformed around 2000.In this paper observed meteorological variables are divided into two parts taking year 2000 as the boundary and the objectives of this study are (1) to investigate changes in ET 0 and temperature in China since 1960s; (2) to examine the existence of evaporation paradox in different periods and regions; (3) to determine potential key factors attributed to ET 0 changes in the whole country as well as different river basins.

Data and Methodology
2.1.Data.Daily meteorological data were obtained from 754 stations from the China Meteorological Administration (CMA) and National Meteorological Information Center of China (NMIC); 599 stations (Figure 1) of these had complete records of all climatic factors calculating ET 0 in time series of 1960-2013.The daily meteorological data included precipitation, relative humidity, sunshine hours, vapor pressure, wind speed, maximum, minimum, and mean air temperature.A few missing data (mainly in 1967, 1968, 1969) were estimated by averaging the value of the other years observed at the same station.
In the data set, the 10 river basins are the first-order basin in China (Figure 1).56 stations are in the Songhua River basin (SRB), 36 are in the Liao River basin (LRB), 33 are in the Hai River basin (HaRB), 67 are in the Yellow River basin (YeRB), 38 are in the Huai River basin (HuRB), 143 are in the Yangtze River basin (YaRB), 28 are in the southeast rivers basin (SERB), 67 are in the Pearl River basin (PRB), 35 are in the southwest rivers basin (SWRB), and 97 are in the Northwest Rivers Basin (NWRB).In the 599 stations, the Taiwan Island is the one that we could not collect observation data from; therefore, it is excluded from the study region.

Methodology
2.2.1.Penman-Monteith Method.In this paper, potential evapotranspiration (ET 0 ) was estimated using the Penman-Monteith (PM) method (Allen et al. [34]); the formula is given as where ET 0 is the daily potential evapotranspiration (mm d −1 ), and the yearly and monthly value of ET 0 will be used in this paper;   is the net radiation at the top surface (MJ⋅m −2 ⋅d −1 ); G is the soil heat flux density (MJ⋅m −2 ⋅d −1 );  is the mean daily air temperature at 2 m height ( ∘ C);  2 is daily average wind speed at 2 m height (m⋅s −1 );   is the saturation vapor pressure (kPa);   is the actual vapor pressure (kPa); Δ is the slope of the vapor pressure curve (kPa ∘ C −1 );  is the psychrometric constant (kPa ∘ C −1 ).In the model the radiation term was calculated by experience formula and its accuracy depends on the experience coefficients which were often only effective in particular regions.In this paper, ET 0 was calculated by corrected radiation.The correcting net radiation is as follows (Yin et al. [35]): where  is constant of Stefan-Boltzmann (4.903 × 10 −9 MJ⋅K −4 ⋅m −2 ⋅d −1 ),  , ,  , is the absolute maximum and minimum temperature (K),  is the actual sunshine hours (h),  is the duration of possible sunshine (h), and  sa is the Sunny radiation (MJ⋅m −2 ).Soil heat flux  is small compared with the relative net radiation and  ≈ 0 in the day time scale.

Trend Analysis Method.
The simple linear regression method was used to estimate the trend magnitudes (slope) in ET 0 and other climatic variables.The linear equation is where X is the simulated value of climatic variables;  × 10 is the trend which denoted the change trend of climatic variables per decade; and  is the time series (Yang et al. [36]).Meanwhile, the nonparametric Mann-Kendall (M-K) method (Mann [37], Kendall et al. [38]) is highly recommended by the World Meteorological Organization for analyzing hydrological series as it did not need any distributional assumption for the data and it was used to detect the significance of the trend.

Stepwise Regression.
The basic idea is to introduce the influencing factors into regression equation one by one.Significant test is carried out when introducing one variable into the model, retaining the significant factors and rejecting the insignificant ones until there are no variables introduced into the model and no one rejected.This method can eliminate the variables which contribute little to principal component or those existing linear relations and can overcome the multicollinearity based on guaranteeing the regression effects.

Region Average of Variables.
In previous researches, regional value was obtained by using an arithmetic mean method from meteorological station.However, meteorological stations are not distributed evenly but dense in the east and sparse in the west in China.Therefore, it is necessary to assign different weights for different stations when evaluating climate change accurately for different regions.When calculating the average value of an area, the weight of a station is determined by the percentage of the Thiessen polygon in the whole area.Thiessen polygon method was more accurate than simple mean method and less workload grid data set method.

Observed Changes of
Temperature and ET 0 .In 1960-2013, 98.2% of the 599 stations show upward trend (91.2% of all stations are at 95% significance level).The average daily temperature in China as a whole (Figure 2) rises at the rate of 0.24 ∘ C per decade (95% significance level).Corresponding with significant warming trend, the mean national ET 0 declines at the rate of −3.9 mm per decade (95% significance level), so there exists evaporation paradox in China as a whole.The mean annual temperature in the 10 river basins all rose at 95% significance level and ET 0 all showed downward trend except in SERB, YeRB, and SWRB in 1960-2013; all river basins indicated upward in temperature and downward in ET 0 in 1960-1999.The maximum downward in ET 0 and upward in temperature appeared in NWRB and SRB with values being −27.65 mm per decade and 0.44 ∘ C per decade, respectively, in 1960-1999.In 2000-2013, ET 0 in YaRB, SERB, SWRB, NWRB, and PRB increased while temperature in SWRB and PRB decreased.In other basins the trend in temperature and ET 0 was the same.In this period temperature only in YaRB and SWRB increased, whether the increase was a fluctuation in the whole upward process or the beginning of decrease needs further investigation.Summer (June to August): in 1960-2013, ET 0 and temperature were the highest values in a whole year; the slope of ET 0 and percent of downward stations were the highest values too.ET 0 descended in YaRB, HaRB, HuRB, YeRB, LRB, NWRB, and China as a whole; temperature rose in all regions, except HuRB which was at 99% confidence level.In 1960-1999, evaporation paradox existed in all river basins except SWRB and HuRB; in China as a whole the percent of ET 0 downward climaxed 77% and 8 river basins were more than 70%, and so evaporation paradox was the most prominent in all statistical periods.In 2000-2013, the variation of ET 0 and temperature was the same except the HuRB.

Seasonal Change of Evaporation Paradox
Autumn (September to November): the slope and range of ET 0 decline reduced in autumn comparing with that of spring and summer.In 1960-2013, ET 0 in HaRB, LRB, SERB, SRB, and NWRB decreased and temperature increased significantly.The phenomenon existed in the 5 river basins in 1960-1999 too.In 2000-2013, HuRB, LRB, SRB, and PRB showed evaporation paradox.
Winter (December to February next year): change in temperature was the most severe compared with the other seasons.Except in PRB in 1960-1999, temperature in 1960-2013 and 1960-1999 all rose significantly.Opposite to the severe increase in temperature, decrease of ET 0 in winter was moderate.In 1960-2013, ET 0 only in HuRB, HaRB, LRB, and NWRB declined slightly and other regions showed upward trend.In 1960-1999, ET 0 in HaRB, HuRB, PRB, YaRB, NWRB, and China as a whole insignificantly decreased.In 2000-2013, temperature showed biggest fall and only SWRB showed upward trend.In winter ET 0 changed the smallest in the four seasons and evaporation paradox was moderate.

Spatial Distribution of Evaporation Paradox.
In 1960-2013 and 1960-1999, the percent of rising stations in temperature exceeded 90%, so stations in which ET 0 decreased can be judged as where evaporation paradox existed (Figure 4).The evaporation paradox distribution can be obtained from the interpolation of  statistic of ET 0 .In 1960-2013, 57.6% of the site of annual ET 0 decreased in China, the regions where ET 0 increased were mainly located in the northeast of the NWRB, northwest of SRB, three rivers sources regions, middle reach in YeRB, northeast and southeast of HuRB, SWRB, coastal area of PRB, middle of YaRB, and so on.Overall coastal areas in the south of 37 ∘ N, most of the regions between 30 ∘ N and 40 ∘ N, 90 ∘ E-110 ∘ E, northwestern of the northeast China, and southeastern of SWRB were the areas where evaporation paradox does not exist.The evaporation paradox area accounted for 73.7% of the 10 river basins.In 1960-1999, ET 0 of 75.1% stations showed downward trend; northwestern of SRB, Ningxia and middle Shaanxi section of the YeRB, three rivers sources regions and northeastern of HuRB, there is no evaporation paradox in such areas.The evaporation paradox area accounted for 91.2%.In 2000-2013, ET 0 and temperature of 223 stations change oppositely and 322 stations were the same; 54 stations of  statistics of ET 0 or temperature were 0.

Impacts of Meteorological
Factors on ET 0 .Meteorological factors change had profound impacts on ET 0 ; in this paper stepwise regression was used to extract the influencing factors of ET 0 .Yearly ET 0 and 7 meteorological factors such as mean temperature ( mean ), maximum temperature ( max ), minimum temperature ( min ), relative humidity (RH), sunshine hours (), average wind speed (), and average water pressure () were firstly normalized in order to remove the impacts of inconsistent units.The entering order of climate variability was showed in Table 2.  was the primary contributor which caused ET 0 change in China as a whole, SERB, YeRB, and SWRB and the standardized coefficients were 0.75, 0.54, 0.87, and 0.54, respectively. contributed most to ET 0 change in YaRB, HuRB, LRB, and PRB with the standardized coefficients of 0.56, 0.66, 0.82, and 0.70. max had maximum impact on ET 0 in HaRB with standardized coefficients being 0.80.The largest contribution in SRB was RH which was negative with ET 0 .Table 2 indicated that ,  max , , and RH were the most important factors influencing ET 0 .Table 3 showed slope of the listed meteorological elements and ET 0 in different statistical period.In 1960-2013, ET 0 decreased in all regions expect SERB, YeRB, and SWRB; in NWRB, LRB and HaRB ET 0 decreased at 99% level of confidence.In 1960-1999, ET 0 decreased in all regions and the decline rate was much more than that of 1960-2013; in 2000-2013, ET 0 in 5 river basins was downward trend. which was in positive relationship with ET 0 decreased at the rate of −0.11 m s −1 per decade significantly in China as a whole and it was found to be the primary contributor which caused ET 0 to decrease in the past 54 years; except PRB in 1960-2013,  decreased in all regions significantly. which was in positive relationship with ET 0 too had decreased with a significant trend of −0.The change of ET 0 was influenced comprehensively by all these factors; ET 0 was in a positive relationship with , ,  max and negative relationship with RH.In China, the decline of ,  made ET 0 reduce and decline RH and ascension of  max made ET 0 ascend.The comprehensive effect of the four elements was the decline of ET 0 .In 1960-1999, the decline rate of ,  strengthened corresponding to the weakness in  max rising and RH decreasing strengthened the decline rate of ET 0 to −14.78 mm per decade.In 2000-2013, the trend of meteorological factors changed compared with that of 1960-1999, decline rate of ,  reduced greatly,  max switched from increase into decrease, and decline rate of RH increased substantially.The combination caused ET 0 switch from decrease to increase.

Conclusions
(1) In 1960-2013, temperature in 98.2% stations of 599 stations increased in China.The decline rate of annual national ET 0 was −3.9 mm per decade so evaporation paradox existed.In 1960-1999, ET 0 of 75.1% stations was downward and temperature of  (3) There was no evaporation paradox in the southeastern coastal areas south of 37

Figure 1 :
Figure 1: Spatial distribution of meteorological stations and firstorder basin in China.
Paradox.According to Figure2, the mean annual temperature climaxed in around year 2000 and then decreased slowly, and ET 0 reached the lowest value around 1993 and then rose slowly.Taking the change into account comprehensively, this paper took the year 2000 as the dividing line.At the same time in order to compare with the proceeding results of other researchers, we analyzed the characteristics of evaporation paradox in the period of1960-2013, 1960-1999, and 2000-2013 (
Figure 3 showed trends of evaporation paradox in 4 seasons.Spring (March to May): in 1960-2013, evaporation paradox existed in HaRB, LRB, SRB, NWRB, SWRB, PRB, and China as a whole.In 1960-1999, evaporation paradox existed in all regions except SRB; in 2000-2013, there was no evaporation paradox; change of temperature and ET 0 was the same in eight river basins and temperature in 5 river basins dropped.The opposite changes of temperature and ET 0 in 1960-1999 and 2000-2013 weakened the evaporation paradox of 1960-2013.

4. 1 .
Relationship between ET 0 and Precipitation.Precipitation and ET 0 were two important segments of the hydrologic

Figure 3 :
Figure 3: Seasonal change of temperature and ET 0 in different regions.

Figure 4 :
Figure 4: Distribution of evaporation paradox in different periods.

Figure 5 :
Figure 5: Change of precipitation and ET 0 in China.

Table 1 :
Change trends of temperature and potential evapotranspiration (ET 0 ) in China.
slope of ET 0 (mm per decade);  percent of downward (%);  slope of temperature ( ∘ C per decade);  percent of upward; *  = 0.05, * *  = 0.01, the significance in 2000-2013 was not calculated because of the short time.

Table 2 :
Results of the stepwise regression.

Table 3 :
Slope of climate variables and ET 0 in China.−14.78 * * −17.64 * * −20.93 * * −18.08 * * −8.16 −5.94 −12.67 −3.77 −27.65 * * −3.26 −14.65 * * ∘ N, most of areas in 30 ∘ N-40 ∘ N, 90 ∘ E-110 ∘ E, northwestern in SRB, and southeastern of SWRB in China in 1960-2013; the area accounted for 26.3% of the 10 river basins.No evaporation paradox area was only in NWRB, northeastern of SRB, middle reach of YeRB, three river source regions, and northeastern of HuRB which accounted for 8.8% merely.(4) Precipitation in NWRB, SERB, three river source regions, lower reaches of YaRB, northwestern of SRB, northwestern of HuRB, and lower reaches of PRB increased and in such regions ET 0 decreased in 1960-2013.Most of stations in which ET 0 and precipitation change inversely were located south of 27 ∘ N and north of 32 ∘ N; the number of the stations was 346 in 1960-1999.In 2000-2013, the stations which precipitation increased were located in north of 32 ∘ N and the number of stations in which ET 0 and precipitation change inversely was 352.(5) ,  max , , RH were the most important variations affecting ET 0 change; , ,  max were positive and RH was negative relationship with ET 0 ; , , RH mainly decreased and  max mainly increased in China and the comprehensive function of them made ET 0 decrease in 1960-2013 and 1960-1999 and increase in 2000-2013.