Climatic Characteristics of Reference Evapotranspiration in the Hai River Basin and Their Attribution

Based on the meteorological data from 46 stations in the Hai River Basin (HRB) from 1961–2010, the annual and seasonal variation of reference evapotranspiration was analyzed. The sensitivity coefficients combined with the detrend method were used to discuss the dominant factor affecting the reference evapotranspiration (ET o). The obtained results indicate that the annual reference evapotranspiration is dominated by the decreasing trends at the confidence level of 95% in the southern and eastern parts of the HRB. The sensitivity order of climatic variables to ET o from strong to weak is: relativity humidity, temperature, shortwave radiation and wind speed, respectively. However, comprehensively considering the sensitivity and its variation strength, the detrend analysis indicates that the decreasing trends of ET o in eastern and southern HRB may be caused mainly by the decreasing wind speed and shortwave radiation. As for the relationship between human activity and the trend of ET o , we found that ET o decreased more significantly on the plains than in the mountains. By contrast, the population density increased more considerably from 2000 to 2010 on the plains than in the mountains. Therefore, in this paper, the 1483 correlation of the spatial variation pattern between ET o and population was further analyzed. The spatial correlation coefficient between population and the trend of ET o is −0.132, while the spatial correlation coefficient between the trend of ET o and elevation, temperature, shortwave radiation and wind speed is 0.667, 0.668, 0.749 and 0.416, respectively. This suggests that human activity has a certain influence on the spatial variation of ET o , while natural factors play a decisive role in the spatial variation of reference evapotranspiration in this area.


Introduction
Hydrologists have found that climate change has resulted in some changes in the water cycle [1][2][3].One major challenge of recent hydrological modeling activities is the assessment of the effects of climate change on the terrestrial water cycle [4].Hydrological models are usually based on the calculation of reference evapotranspiration and reducing it to the actual evapotranspiration by considering the soil moisture status [5] or the number of days since the last rainfall event [6].Therefore, analyzing how climate change affects reference evapotranspiration (ET o ) is critical for understanding the impact of climate change on the hydrological cycle.According to Allen et al. [7], ET o is the evapotranspiration from the reference surface, which is a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m −1 and an albedo of 0.23.
The Hai River Basin (HRB) is one of seven largest river basins and also one of the most developed areas in China, with the population accounting for about 10% of the nation's total.The middle and lower reaches of the basin are important wheat production regions in China.This region has a semi-humid and semi-arid climate and has been strongly influenced by human activities.The annual precipitation is 539 mm, while the annual pan evaporation is 1100 mm, making the basin vulnerable to climatic variations [7].In recent decades, several eco-environmental problems in that area have come to the fore under the combined impacts of climate change and intensified human activities.Water resources in the HRB are currently used for irrigation, aquaculture and industries.Due to the very limited available water resources in the basin, water has been diverted from other basins to supply it for agriculture and to maintain essential ecosystem functions [8].
In order to understand how climatic variables affect ET o , some studies have been carried out to evaluate evapotranspiration in the context of climate change.Zheng et al. [9] analyzed the cause of the decreased pan evaporation during 1957-2001 in the HRB, and found the reason to be the declining wind speed.Xu et al. [10] proved that the decreasing wind speed and net radiation were responsible for the ET o changes in the Changjiang River Basin of China.Liu [11], who analyzed the pan evaporation from 1955 to 2000 in China, found that the decrease in solar radiance was most likely the driving force of the reduced pan evaporation in China.Furthermore, sensitivity analysis has also been performed on the impacts of climate change [12][13][14][15][16][17][18].However, the temporal pattern of ET o is not only influenced by the sensitivity of climatic variables, but also by their variation patterns.
The spatial pattern of ET o in HRB has not been addressed in the literature, yet.In this study, we calculated ET o using the FAO-56 Penman-Monteith equation and analyzed the temporal-spatial pattern in ET o and its driving variables.Attribution analysis was then performed to quantify the contribution of each input variable to ET o variation.The objective of this paper is to exhibit the temporal-spatial variation pattern of ET o over the past 50 years in the HRB, then to detect the reason for these characteristics and to quantify the contribution of the climatic variation to ET o .

Study Area and Data
The Hai River Basin is located in north China and is one of seven largest river basins in the country.The basin is bounded in the north by Mount Tangshan, in the west by Mount Taihang and in the east by the Bohai Sea.Land surface elevation in the mountainous north and west of the study area is generally above 2000 m a.s.l.On the floodplains, however, surface elevation hardly exceeds 100 m a.s.l.The basin occupies an area of 3.2 × 10 5 km 2 (34.9-42.8°N, 112.0-119.8°E) and includes five provinces and the two megacities of Beijing and Tianjin (Figure 1).Climatically, the HRB belongs to the East Asian monsoon region.The annual mean temperature varies from 8 °C to 12 °C, while annual precipitation is about 539 mm; relative humidity varies from 50% to 70%.

Penman-Monteith Method
The Penman-Monteith method recommended by FAO (Food and Agriculture Organization) [19] as the standard method for determining reference evapotranspiration was used in this study.The method was selected because it is physically based and explicitly incorporates both physiological and aerodynamic parameters.

(
) ( ) where, ET o is the reference evapotranspiration (mm/day); R n is net radiation at the crop surface (MJ/m 2 /day); G is soil heat flux density (MJ/m 2 /day); T is mean daily air temperature (°C), U 2 is wind speed at 2 m height (m/s); e s is saturation vapor pressure (kPa); (e s -e a ) is the saturation vapor pressure deficit (kPa); Δ is the slope of vapor pressure (kPa/°C) and γ is the psychometric constant (kPa/°C).
The computation of all data required for the calculation and relevant procedures are given in Chapter 3 of the FAO Paper 56 [19].

Trend Detection and Sensitivity Analysis Method
The rank-based nonparametric Mann-Kendall statistical test [20,21] is commonly used for trend detection, because of its robustness for non-normally distributed and censored data, which are frequently encountered in hydroclimatic time series.In this method, the test statistic, Z, is as follows: sgn( ) ( 1)(2 5) ( 1)(2 5) 18 Equation ( 2) gives the standard deviation of S with correction for ties in the data, with e i denoting the number of ties of extent i.The upward or downward trend in the data is statistically significant if , where is the (1 / 2) Z Original measurements of air temperature (T a ), wind speed (U) and relative humidity (Rh) were chosen for the sensitivity analyses.The fourth applied variable is shortwave radiation (R s ).This is because shortwave radiation is one of the input variables in a number of semi-physical and semi-empirical equations that are used to derive the net energy flux required by the Penman method [22].Following the procedure described by Allen [19], R s can be estimated with the following formula that relates surface shortwave radiation to extraterrestrial radiation and daily sunshine duration: (6) where R s is shortwave radiation, n is daily sunshine duration (h); N is maximum possible duration of sunshine or daylight hours (h); n/N is relative sunshine duration; R a is extraterrestrial radiation and a s and b s are the regression constants.The recommended values a s = 0.25 and b s = 0.75 were used in this study.
In multivariate models, different variables have different dimensions and different ranges of values, which make it difficult to compare the sensitivity by partial derivatives.Consequently, the partial derivative is transformed into a non-dimensional form: Basically, a positive/negative sensitivity coefficient of a variable indicates that ET o increases/decreases as the variable increases; the larger the sensitivity coefficient, the larger the effect a given variable has on ET o .

Spatial Correlation Coefficient
Correlation coefficients depict the spatial relationship between two datasets.The correlation between two variables is a measure of dependency between these variables.It is the ratio of the covariance between the two datasets divided by the product of their standard deviations.Because it is a ratio, it is a unit-less number.The equation to calculate the correlation is [23]: (8) where, Cov ij is the covariance; are the standard deviations of dataset i and j, respectively.
The calculated covariance matrix in this paper contains values of variances and covariances.The variance is a statistical measure showing how much variance there is from the mean.The remaining entries within the covariance matrix are the covariances between all pairs of the input datasets.The following formula is used to determine the covariance between datasets i and j: (9) where, Z ik , Z jk are the values of dataset i and dataset j, respectively in location k; μ i , μ j are the average values of datasets i and j, respectively; i, j is the order of dataset; N is the number of dataset; K denotes a particular location.
Correlation ranges from +1 to −1.A positive correlation indicates a direct relationship between two datasets, such as when the cell values of one datasets increase, the cell values of another datasets are also likely to increase.A negative correlation means that one variable changes inversely to the other.A correlation of zero means that two datasets are independent of one another.

Detrend Method
The variation pattern of ETo is determined by multi-climatic variables, including their sensitivity to ETo and variation fluctuations.The detrend method is a combination method that considers both the sensitivity coefficient and the fluctuation of the climatic variables.
The detrend method is a way of quantifying the contribution of climatic variables to the annual variation of ET o .This method shows the contribution in graphs and vividly describes how the climatic variables influence ET o .In this study, the following steps were performed: (1) use of the simple linear regression method to detect the changing slope of the main climatic variables; (2) detection of the significance of the slope by the t-test; (3) removal of the significant slope of main climatic variables to  make them stationary time series; (4) recalculation of reference evapotranspiration using each time the original series of three variables and the detrend data of one variable; (5) comparison of the results with the original reference evapotranspiration; the observed difference is considered as the influence of those variables on the trend [22].

Correlation between ET o and E pan
Figure 2 shows the monthly correlation coefficients (R 2 ) between ET o and E pan in HRB.As can be seen, the lowest correlation coefficient is 0.93, while the highest is 0.97.Spatially, mountain areas in the northwest and coastal areas in the southeast have higher correlation coefficients than plains in the central part of the study area.Mountain and coastal areas are more humid than plains, which is consistent with the research conclusion of Brutsaert [24] that in humid areas, reference evaporation has a better relationship with pan evaporation.

Spatial-Temporal Variation of ET o in HRB
To study the spatial distribution of the trend of ET o from 1960 to 2010 in the HRB, the Mann-Kendall test was used for each station to establish the ET o trends.The trends of annual and seasonal ET o were tested at the 95% confidence level.Decreasing trends in annual ET o were observed at 28 stations located mostly on the eastern and southern plains of the HRB.However, increasing trends in the annual ET o were observed at three sites (Datong, Wutaishan, Weixian) located in the western mountain region of the HRB (Figure 3).

Variation Pattern of Climatic Variables
Shortwave radiation decreases in the whole basin, and most trends are significant at the 0.05 significance level (Figure 5).The maximum and minimum temperatures increased in the whole HRB (Figure 5).The maximum temperatures in the southern mountain area increase more significantly than on the northern plains; the average p-value of the Mann-Kendall test for the whole basin is 2.9 (Table 2).The minimum temperatures increase more obviously than the maximum ones; the average p-value of the Mann-Kendall test for the whole basin is five.Relative humidity decreases in most of the basin, and this trend is significant in most sites of the mountain areas.As to the wind speed, the decreasing trends are significant in most parts of the basin at the 0.05 significance level.The increasing temperature and decreasing relative humidity will make ET o increase, while the decreasing short wave radiation and wind speed will make ET o decrease.Therefore, the decreasing trends of ET o in the HRB suggest that the increasing temperature and decreasing relative humidity slightly discount the decreasing trend, but do not change its direction; the decreasing shortwave radiation and wind speed commonly result in the decreasing ET o in the southeastern coastal area of the HRB.
In order to detect the reasons for the increasing trend of ET o in Datong, Wutaishan and Weixian stations, this paper analyzed the climate variables at these three locations.We found a Mann-Kendall test value of temperature as large as at the other investigated stations.However, relative humidity decreased faster, while shortwave radiation and wind speed (except Wutaishan) were slower compared to the mean value calculated for the whole HRB.Therefore, it can be concluded that the increasing temperature, decreasing faster relative humidity and decreasing slower shortwave radiation and wind speed result in the increasing trend of ET o at these three stations.

Sensitivity of Climatic Variables
Since ET o is an important indicator of climatic changes, the sensitivity coefficient was used in this study to analyze how climatic variables affect ET o .The non-dimensional form of the sensitivity coefficient was employed to estimate the sensitivity of climatic variables in the HRB. Figure 6 gives the annual sensitivity coefficient of four climatic variables (T a , Rh, R s and U) to ET o from 1960 to 2010 estimated by the FAO-56 Penman-Monteith method.Figure 6 suggests that temperature, wind speed and short wave radiation are less sensitive in the mountain areas than on the coastal plains, while relative humidity is less sensitive in the area closest to the coast than on the plains and in the mountains.

(c) (d)
As for the trend of sensitivity to the climatic variables, the decreasing trends are found in temperature, short wave radiation and relative humidity, while the increasing trend is in wind speed.As variations in sensitivity coefficients to main climatic variables are detected before and after 1990, so the data series of sensitivity coefficients were divided into two groups of 1960-1990 and 1991-2010, respectively, to calculate mean sensitivity coefficients to climatic variables.The obtained results show that before 1990, the sensitivity coefficients to T a , Rh, U and R s were 0.500, −0.641, 0.205 and −0.357, respectively, while after 1990, they were 0.477, −0.586, 0.221 and 0.349, respectively.

ET o with Detrend Climatic Variables
Figure 7 gives the trend of ET o estimated with the detrend data series.The trends of ET o with detrend temperature are decreasing, except one station, while the variation pattern of ET o with detrend relative humidity is similar to the original ET o .This shows that there are larger differences between the original ET o and the recalculated one with detrend wind speed or detrend shortwave radiation than that with the detrend temperature or relative humidity.This suggests that the decreasing wind speed and shortwave radiation may be the main causes of the decreasing ET o in the HRB.As for the decreasing trend of shortwave radiation, previous studies have shown that the decrease in global radiation is the most likely the cause, which is a regional phenomenon.By examining the regional total radiation in eastern China, Zhang [25] concluded that the regional total radiation is decreasing due to the increased air pollution in that area.Another study by Liu [26] also proved that air pollution may result in the decrease of R s in HRB.Therefore, they speculate that aerosols may play a critical role in the decrease of solar radiation in China.

Relationship between ET o and Human Activity
The relationship between the variation pattern of ET o and human activity refers to how human activity affects climatic variables.In order to detect the relationship between human activity and the variation of climatic variables, the investigated sites were divided into two groups; elevation was taken as the sole criterion of that division.Areas with an elevation higher than 500 m a.s.l. are usually defined as mountains, while below 500 m a.s.l. as plains.In general, the population density is higher and human activity is more intense on the plains than in the mountain areas.Figure 8 gives the GDP (Gross Domestic Product) increase from 2000 to 2010 and the distribution of plains in the HRB, respectively.As can be seen, the GDP increased noticeably from 2000 to 2010 on the plains of the HRB.This may suggest that human activity is concentrated on the plains.At the same time, the decrease of ET o is more visible on the plains than in the mountains.Table 2 gives the trend of the investigated climatic variables in these two elevation groups.It can be seen that the trend of the shortwave radiation, wind speed and minimum temperature on the plains is more obvious than that in the mountain areas.The detrend results show that the decreasing shortwave radiation and wind speed are the main causes of the decreasing ET o on the plains of the HRB.Therefore, we deduce that there is a relationship between the human activity and the decreasing shortwave radiation and wind speed.Liu et al. [26] found that during the period from 1957 to 2008, the solar radiation decreased significantly in the HRB and that the trend was more significant in the densely populated areas than in the sparsely populated ones.The spatial distribution of the aerosol index increase is consistent with the solar radiation decrease.The aerosol increase resulting from human activities was an important reason for the decrease in solar radiation.This phenomenon was also found by some other studies [27][28][29].As for the wind speed, Jiang et al. [30] analyzed the change of wind speed over China from 1956 to 2004.They found that the effect of urbanization on annual MWS (Mean Wind Speed) is more and more obvious with time, especially in the 1980s.It corresponds with the substantial development of urbanization.At the same time, the declining trend of mean wind speed at the urban stations is more serious than that at the rural ones over the last 50 years.This is coincident with the results given in Table 3.Furthermore, in order to determine the relationship between ET o and human activities, this paper analyzed with the use of the spatial correlation coefficient method the spatial correlation between ET o , population and meteorological factors, which have a definite effect on ET o .The results show that the spatial correlation coefficient between population and ET o is −0.132, while the spatial correlation coefficients between population, R s and Rh are −0.307 and −0.144, respectively.Moreover, the spatial correlation coefficients between elevation and ET o is 0.667, while the spatial correlation coefficients between ET o , R s , U and T a are 0.749, 0.416 and 0.668, respectively.This proves that human activity has a certain influence on the spatial variation of ET o , while natural factors play a decisive role in the spatial variation character of reference evapotranspiration (Table 4).With increasing altitude and decreasing pressure, the atmosphere is getting thinner and the heat radiation losses become faster.Therefore, the temperature decreases with increasing altitude.At the same time, when the sunlight scattering and reflection decrease, the solar radiation increases.While the proportion of water vapor in the air is relatively large, it is usually concentrated in the lower parts of the atmosphere.Relatively small air moisture content at high altitudes results in low relative humidity there.Friction caused by the uneven Earth surface retards the air flow, so that the wind speed is relatively smaller near the ground.With higher elevation (up to 6000 m a.s.l.), the wind speed becomes less impacted by the uneven ground.

Conclusions
In this paper, the spatial and temporal characteristics of annual and seasonal ET o  in the Hai River Basin (HRB) were examined, and the possible causes of changes in ET o were detected.The following conclusions may be drawn from the study: (1) Most stations in the HRB have decreasing trends in the annual ET o at a confidence level of 95%.These stations are distributed mainly in the southern and eastern coastal areas of HRB.Three stations (Datong, Wutaishan and Weixian) in the western area of HRB show significant increasing trends in the annual ET o .As for the seasonal changes, similar characteristics with

Figure 1 .
Figure 1.The location of the Hai River Basin (HRB).
Z indicates an increasing trend in the time series, while negative Z, a decreasing one.

Figure 2 .
Figure 2. Correlation between ET o and E pan in the HRB.

Figure 3 .
Figure 3.The annual trend of ET o in the HRB.

Figure 6 .Figure 6 .
Figure 6.The sensitivity coefficients of climatic variables in the HRB.(a) The sensitivity coefficients of T a ; (b) The sensitivity coefficients of Rh; (c) The sensitivity coefficients of U; (d) The sensitivity coefficients of R s .

Figure 7 .
Figure 7.The annual trend of ET o with detrend climatic variables in the HRB.(a) The annual trend of ET o in the HRB; (b) The trend of ET o with detrend U; (c) The trend of ET o with detrend T a ; (d) The trend of ET o with detrend R s ; (e) The trend of ET o with detrend Rh.

Figure 8 .
Figure 8.The GDP variation and distribution of plain areas in the HRB.(a) GDP variation during 2010 to 2000 in HRB; (b) DEM below 500 m a.s.l. in HRB.

Table 1 .
listed in Table1.In Table1, the annual ET o is the average value from 1960 to 2010 calculated using the FAO-56 Penman-Monteith method.Basic data on the investigated stations in HRB.

Table 2 .
The Mann-Kendall test value of the main climate variables at the three stations.

Table 3 .
The trend of climatic variables in different elevation groups.

Table 4 .
The spatial correlation coefficients between ET o and different factors.