Evaporation paradox and its mechanism in coastal wetlands of northern China

Over the past few centuries, global warming has become an indisputable fact, while many researches found that the potential evapotranspiration throughout the world showed a consistently decreasing over the past 50 years, and called this phenomenon as “evaporation paradox”. In this study, we validated that it did exist in coastal wetlands of northern China and tried to understand the mechanism. The conclusions include: (i) The temperature of in coastal wetlands of northern China shows a significantly decreased trend while potential evapotranspiration is significantly increased, and suggests “evaporation paradox” actually exists in study area; (ii) The sensitivities of climate factors were that a 10% increase in T, Tmax, Tmin, RH, W and S would result in a 2.169% (increase 2.169%), 2.440%, 0.640%, -4.310% (decrease 4.310%), 1.413% and 4.416% in potential evapotranspiration (Eo), respectively; (iii) among the 6 climatic factors, the contribution rate of the effects on potential evapotranspiration were sunshine duration (41.65%) > wind (25.23%) > air temperature (18.04%) > relative humidity (12.51%). And the phenomenon of evaporation paradox in coastal wetlands of northern China was caused by the decrease of wind speed and sunshine duration.


Introduction
Global warming caused by anthropogenic-driven emissions of greenhouse gases has become a serious issue worldwide in recent years and the evapotranspiration would be expected to increase in both capacity and amount in view of the rise in temperature, however, the evapotranspiration showed a trend of decrease in various part of the world, including China. Observations have shown that the temperature throughout China has risen by (0.09±0.017) ℃/10a in the past 50 years , but the trend of the rate of the Pan evaporation in China has been consistently decreasing in the past 50 years. The phenomenon of the decreasing of evapotranspiration under rising temperature is called evaporation paradox.
However, there is no clear conclusion about the mechanism of evaporation paradox yet  and the existing researches mainly concentrated on the qualitative analysis and lacking the studies of how the other climate factors affect the evapotranspiration and the contributions other climate factors made to affect it. Potential Evapotranspiration plays an important role in water cycle and energy cycle in a watershed and shows a specific characteristic under certain climate and landscape  (Lin et al., 2018, Luo et al., 2017. It is affected by characteristics of meteorological variables, vegetation cover rate and management methods (Pandey et al., 2016). The reasons for the decline of pan evaporation can be summed up as follows: the increase in atmospheric cloudiness, resulting in a decline of solar radiation . The decrease of solar radiation results from the increase of atmospheric aerosols and other pollutants, as the air humidity increases, the difference of the vapor pressure decreases (Huang et al., 2015). According to the present research, global radiation decline caused by cloud cover or aerosol increase is the main reason of pan evaporation and potential evapotranspiration decrease, while it differs in different regions. Schaake and Waggoner (1990) first proposed the concept of climate elasticity. Many previous researches estimated climate elasticity towards understanding the effects of climate change and most of them were studying the hydrologic (streamflow) response (Xu et al., 2013;Ma et al., 2010;Zheng et al., 2009;Sun et al., 2013). The sensitivities of the hydrological responses to climate changes have been studied recently (Hamlet et al., 2005;Wang and Zeng, 2011). In this study, we attempted the concept of sensitivity in potential evapotranspiration and tried to analyze the sensitivities of climatic factors on potential evapotranspiration. Based on the sensitivity coefficients, the effects of climate change on potential evapotranspiration could be calculated.
The coastal wetlands of northern China is located in semi-arid region, water resources in there are more important for maintaining wetland environment and habitat, taking them as the study object to analyze the change of potential evapotranspiration and its mechanism has a better importance. The purpose of this study is to: (i) identify if the phenomenon of "evaporation paradox" does exist in northern China; (ii) analyze the relationship of potential evapotranspiration with other climatic factors and indicate the cause of evaporation paradox; (iii) analyze the attributions of potential evapotranspiration change based on the sensitivity coefficients of other climatic factors and understand the mechanism of evaporation paradox.

Study area
The coastal wetlands in China and their adjacent land areas cover about 580 × 10 4 ha. And the coastal wetlands in northern China, which located in north of the Yellow River estuary, are mainly distributed in the Liaoning, Hebei, Tianjin and Shandong provinces and cities with an area of about 155.23 × 10 4 ha. The location and distribution of wetlands are shown in Fig. 1. The region has a continental monsoon climate with a mean annual precipitation of 500~800 mm. It is warm and humid and has distinct seasons, with an average annual temperature of 12~14 ℃.

Data
Daily meteorological data were obtained from 21 national meteorological stations in the coastal wetlands of northern China from China Meteorological Administration (CMA) and National Meteorological Information Center of China (NMIC). All of these stations had complete records of all climate factors for calculating potential evapotranspiration (E o ) in the time series of 1960-2010, including atmospheric pressure, maximum, minimum and mean daily air temperature, relative humidity, wind speed and sunshine hours. The location of all meteorological stations can be seen in Fig. 1.

Potential evapotranspiration calculation
The potential evapotranspiration data are calculated based on the FAO model (Allen et al., 1998). This model has been widely used worldwide and is expressed briefly as: where: E o = daily potential evapotranspiration (mm)  = slope of the saturation water vapor pressure versus air temperature (kPa﹒℃ -1 ) R n = total net radiation (MJ/m 2 ) G = total soil heat flux (MJ/m 2 , assumed zero in this study)  = psychrometric constant (kPa﹒℃ -1 ) e s = saturation vapour pressure (kPa) e a = actual vapour pressure (kPa)  2 = mean wind speed at 2 m height (m/s) C = unit conversion factor with a value of 900.

Mann-Kendall test
Mann-Kendall test is recommended by the international meteorological organization to detect significant trends of climatic variables in time series (Hamed, 2008;Liang et al., 2010). The test statistic value of "Z" is calculated as follows: The statistic S: where x i and x j are two generic sequential data values of the variable, n is the length of the data set.
The statistic S [Var(S)] can be calculated as: ( 1)(2 5) () 18 n n n Var S    2.3.3. Sensitivity analysis method Schaake (1990) introduced a concept of "elasticity" to evaluate the sensitivity of hydrological process to climate changes. Reference to the sensitivity analysis of hydrology, the sensitivity coefficient (ε) represents the proportional change in potential evapotranspiration (E o ) divided by the proportional change in a climatic variable (X) and is expressed as: when, X approachingX, X would be infinitely small and ε X approaches infinity. To overcome the numerical problem, Sankarasubramanian et al. (2001) have further verified the nonparametric estimator as: and then the effects of climatic factors could be expressed as:

Evaporation paradox in coastal wetlands of northern China
Potential evapotranspiration and temperature are the most obvious indicators to reflect climatic characteristics. The temperature data were obtained directly from the national weather station and the mean annual potential evapotranspiration of coastal wetlands in northern China was calculated by the method of Penman Monteith Equation with meteorological data from the national weather station within the study watershed area of the time series of 1951-2010.
Trend analysis is widely used for understanding dynamics and behaviors of hydrological and climatic variables over a long-term period. The long-term variations of potential evapotranspiration (E o ) and temperature (T) of the meteorological stations in coastal wetlands of northern China were shown in Figs. 2(a&b), suggested that the annual potential evapotranspiration (E o ) of the meteorological stations all showed decreased trend and the annual temperature showed increased trend. And Fig. 3 showed the change of the mean value of all meteorological stations, also suggested that the mean annual potential evapotranspiration in northern China had a decreased trend and the mean annual temperature was an increased trend.
The Mann-Kendall test was applied to detect the change trend of climate over the study period of 1951 to 2010. Based on the Mann-Kendall test results, the Z statistic of annual mean potential evapotranspiration of coastal wetlands in northern China was -4.36, which suggested that over the whole study period from 1951 through 2010, the annual mean potential evapotranspiration of northern China showed a downward trend at the 0.01 confidence level. And the Z statistics of daily average temperature, daily maximum temperature and daily minimum temperature of northern China were 5.68, 4.76 and 6.33, respectively. Those mean the longterm variation of air temperature showed an obvious increase trend over the period of 1951 to 2010 in northern China and was at the 0.01 confidence level. Therefore, we can conclude that the phenomenon of evaporation paradox does exist in in coastal wetlands of northern China.  The correlation between Eo and other weather factors

Relations between potential evapotranspiration and other climate factors
A correlation analysis was conducted between potential evapotranspiration (E o ) with 6 basic climate factors, as mean daily air temperature (T), maximum daily air temperature (T max ), minimum daily air temperature (T min ), relative humidity (RH), wind (W), sunshine duration (S). Correlation coefficients results are shown in Table 1 and the bivariate correlation statistics was used to analyze the significance to potential evapotranspiration of independent variables. Table 1, we can find that the potential evapotranspiration got significantly positive correlations at a 0.01 level with wind speed and sunshine duration and got significantly negative correlations with factors of mean daily temperature at a 0.01 level. While the minimum daily temperature, the maximum daily temperature and the relative humidity were not so related with potential evapotranspiration, the correlation coefficients were -0.055, -0.123 and 0.073, respectively.

The change trends of correlative factors
According to the results of Mann-Kendall test, the Z statistic of the mean daily temperature was 5.68. And also, the Z statistic of wind speed (W) and sunshine duration (S) were -6.82 and -4.37, respectively, which suggested that they showed downward trends during the study period of 1951 to 2010 at a 0.01 level. Then, we can draw a conclusion that the phenomenon of evaporation paradox in coastal wetlands of northern China may be caused by the combined effects the increase of temperature and the decrease of atmospheric pressure, wind speed and sunshine duration.

The attribution analysis of evaporation paradox
Based on Eqs. 8, we got the sensitivity coefficients (ε) of potential evapotranspiration (E o ) to mean daily air temperature (T), maximum daily air temperature (T max ), minimum daily air temperature (T min ), relative humidity (RH), wind (W) and sunshine duration (S). The values of ε T , ε Tmax , ε Tmin , ε RH , ε W and ε S were 0.2169, 0.2555, 0.0786, -0.4440, 0.1401 and 0.4826, respectively. These mean that a 10% increase in T, T max , T min , RH, W and S would result in a 2.169% (increase 2.169%), 2.440%, 0.640%, -4.310% (decrease 4.310%), 1.413% and 4.416% in potential evapotranspiration (E o ), respectively.   could be divided into a reference period ) and a change period . Comparing the mean values between the two periods, the changes of E o and the other 6 climatic factors (T, T max , T min , RH, W, S) could be simply calculated and can be seen in Table 2. Results showed that, in the change period, the E o of coastal wetlands in northern China has decreased 24.95 mm.
According to the sensitivity coefficients (ε) and the change values, the effects of other climatic factors (T, T max , T min , RH, W, S) on potential evapotranspiration could be simulated by Eqs. 9 and the results were shown in Table 3. Results show that S (sunshine duration) had the largest effect on potential evapotranspiration which decreasing 33.03 mm accounting for 41.65% followed was wind (W), its effects was decreasing potential evapotranspiration 20.01 mm and accounting for 25.23% and the average effect of temperature rise on potential evapotranpiration was increasing 18.04 mm and accounting for 18.04% and the least effect was caused by relative humidity (RH) which increasing 9.92 mm and accounting for 12.51%.

Discussion
"Evaporation paradox" is a hot topic in evapotranspiration research and had been verified in Australia (Roderick and Farquhar, 2004), New Zealand (Roderick and Farquhar, 2005), Canada (Burn and Hesch, 2007), Italy (Moonen et al., 2002), India (Jhajharia et al., 2012) and many regions in China (Cong et al., 2008;Ma et al., 2012;Jiang et al., 2013). Many researchers tried to figure out its mechanism, while did not get a unified understanding about the evaporation paradox. Many researchers discussed the mechanism of the decrease in potential evapotranspiration and suggested some reasons likely as the sunlight decrease due to the increase in cloud coverage (Peterson et al., 1995; or aerosol concentration (Stanhill and Cohen et al., 2001), vapor pressure deficit decrease due to increasing air humidity (Huang et al., 2015), or wind speed decrease due to monsoon change (Cohen et al., 2002). And other researchers discussed that decreasing in solar radiation or sunlight, referred as global dimming, could be the primary cause, but this trend changed to the reverse direction in 1980s (Wild et al., 2005;Pinker et al., 2005).
In this study, the annual daily average temperature in coastal wetlands of northern China showed an upward trend at 0.01 confidence level, while the annual potential evapotranspiration showed a downward trend and that indicated a phenomenon of evaporation paradox. The correlation analysis of potential evapotranspiration and other climatic factors showed that, not only temperature, wind speed and sunshine duration also obviously affected potential evapotranspiration, they all showed positive correlations. Based on Mann-Kendall trend analysis, the annual wind speed and sunshine duration both showed significantly decreased trends and those might be the cause of potential evapotranspiration decrease. More scientifically, to reveal possible causes, the attribution of historical potential evapotranspiration to climatic forcings, like air temperature, sunshine duration, wind speed and relative humidity, has been undertaken. In our study, the annual potential evapotranspiration in coastal wetlands of northern China had an obvious decreasing trend and we want to separate the effects and contributions of other climatic factors on potential evapotranspiration. Sensitivity analysis method was widely used in studying the impacts of climatic variation in stream flow (Potter et al., 2011;Sankarasubramanian et al., 2001), and here we used this method in our research to study the effects of factors on potential evapotranspiration. Our results showed the calculation was obviously accurate, the sum effect quantity of 7 factors was 38.01 mm, comparing with the actual change (39.68 mm), the method was appropriate for studying the effects of factors on potential evapotranspiration.
It is important to highlight that there remains some uncertainty in this statistical assessment of climate impacts on potential evapotranspiration. Many researches suggested the reason of evaporation paradox was the decrease of solar radiation which called "dimming" phenomenon. In our research, we used sunshine duration as the substitution and that may lead to some error in our results. And we analyzed the effects of mean daily air temperature (T), maximum daily air temperature (T max ), minimum daily air temperature (T min ), relative humidity (RH), wind (W) and sunshine duration (S) and whether they were all the factors? Some other possible reasons may need to discussed and we would make some modification in the future research.

Conclusions
Climate change is an indisputable fact over the past centuries, a better understanding of climate change is becoming increasingly important for hydrologic cycle, ecology system and other fields. In this study, we test the phenomenon of "evaporation paradox" and quantify the attribution analysis of potential evapotranspiration change to understand the mechanism. The findings can be summarized as follows: (i) The potential evapotranspiration of in coastal wetlands of northern China is significantly decreased at the 0.1 confidence level and temperature is significantly increased at the 0.01 confidence level and "evaporation paradox" actually exists in study area.
(iii) The effects of 6 climatic factors on potential evapotranspiration were sunshine duration (41.65%) > wind (25.23%) > air temperature (18.04%) > relative humidity (12.51%). And the phenomenon of evaporation paradox in coastal wetlands of northern China was caused by the decrease of wind speed and sunshine duration.