Temporal variations of reference evapotranspiration and its sensitivity tometeorological factors in Heihe River Basin，China

Jie Zhao，Zong-xue Xu*，De-peng Zuo，Xu-m ing WangCollege ofWater Sciences，Beijing Normal University，Beijing 100875，PRChina Received 12 July 2014；accepted 22 December 2014 Available online 21 January 2015

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Temporal variations of reference evapotranspiration and its sensitivity tometeorological factors in Heihe River Basin，China

Jie Zhao，Zong-xue Xu*，De-peng Zuo，Xu-m ing Wang
College ofWater Sciences，Beijing Normal University，Beijing 100875，PRChina Received 12 July 2014；accepted 22 December 2014 Available online 21 January 2015

Abstract

On the basis of daily meteorological data from 15meteorological stations in the Heihe River Basin（HRB）during the period from 1959 to 2012，long-term trends of reference evapotranspiration（ET0）and keymeteorological factors thataffect ET0were analyzed using the Mann-Kendall test.The evaporation paradox was also investigated at 15meteorological stations.In order to explore the contribution of key meteorological factors to the temporal variation of ET0，a sensitivity coefficientmethod was employed in this study.The results show that:（1）mean annual air temperature significantly increased at all 15meteorological stations，while themean annual ET0decreased atmost of sites；（2）the evaporation paradox did existin the HRB，while theevaporation paradoxwasnotcontinuous in spaceand time；and（3）relativehumiditywas the mostsensitivemeteorological factorwith regard to the temporalvariation of ET0in the HRB，followed byw ind speed，air temperature，and solar radiation.Air temperature and solar radiation contributedmost to the temporal variation of ET0in the upper reaches；solar radiation and w ind speed were the determ ining factors for the temporal variation of ET0in them iddle-lower reaches.

?2015 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license（http:// creativecommons.org/licenses/by-nc-nd/4.0/）.

Reference evapotranspiration；Evaporation paradox；M eteorological factor；Heihe River Basin

1.Introduction

Evapotranspiration plays an important role in the hydrological cycleaswellas theglobalenergy budget.Itcontributes 2/3 of annual precipitation and has an essential influence on the Earth's climate system（Jayawardena，1989；Chahine，1992；Zhan et al.，2011；Zuo et al.，2012；Duhan et al.，2013）. In addition，evapotranspiration is a key input to hydrological m odels（Liang et al.，1994；Gerten et al.，2004；Zhao et al.，2013）.Therefore，a comprehensive understanding of temporal trends and spatial distribution of evapotranspiration is highly significant towater resourcemanagement，especially in places where thewater availability is limited.

Globalwarm ing hasbeen oneof themostconcerning issues forgovernments.As reported in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change（IPCC），the surface temperature of the Earth has increased by about 0.13°C per decade over the past 50 years（IPCC，2007）.This has significant impacts on environmental system s，by causing glaciers tomelt，the sea level to rise，etc.Globalwarm ing also breaks thebalance of eco-systemsand threatens food supplies. Some studieson climate change have predicted thatone of the phenomena thatglobalwarm ingw illbring about isan increase in the rate of evaporation from terrestrial open water bodies，which will enhance the scarcity of water resources in arid regions（Jackson，2001；Scheffer et al.，2001；Yang et al.，2009；Jayantha et al.，2011；Sjoegersten，2013）.

Observed pan evaporation data have revealed the fact that evaporation from open water bodies has been decreasing over the past several decades in different regions around theworld（Brutsaert et al.，1998；Gao et al.，2012；Yesihrmak，2013），including Australia（Roderick and Farquhar，2004），Canada（Aziz and Burn，2006），Eurasia（Velichko et al.，2008），China（Cong et al.，2009），and India（Rao and Wani，2011）.The contrast between the increase in air temperature and the decrease in observed pan evaporation rate is referred to as the evaporation paradox（Roderick and Farquhar，2002）.Furthermore，a similar decreasing trend of reference evapotranspiration（ET0）wasalso found by Thomas（2000）and Roderick and Farquhar（2004）.

In order to investigate the evaporation paradox，many studies have been carried out.Generally，these studies can be divided into two categories.One includes studies meant to determ ine the key factors that impact pan evaporation and ET0and analyze variations of these key factors so as to explain the reason why pan evaporation and ET0have decreased over the past several decades.The other includes studies that focus on determining whether decreasing pan evaporation or ET0definitely leads to the decrease in actual evapotranspiration.Studies concerning spatial and temporal variations in pan evaporation and ET0have been carried out by researchers worldw ide.Gao et al.（2006）studied spatial and temporal variations in ET0at 580 stations in China during the period from 1956 to 2000，and，through a partial correlation analysis，the study determ ined that sunshine duration，w ind speed，and relative humidity have asignificant impact on ET0.Wang etal.（2014）analyzed the relationship between the variations of ET0and each climatic variable at Linhe Station，a representative weather station in the Hetao Irrigation District of China，during the period from 1954 to 2012.The results showed that ET0in the Hetao Irrigation District is most sensitive to mean daily air temperature，followed by w ind speed.Changes in sunshine duration had only a m inor effect on ET0during the study period.Recent analysis from Wang et al.（2012）indicated that the aerodynam ic component of ET0accounted for 86%of the longterm changes in global ET0from 1973 to 2008.However，Matsoukas et al.（2011）showed the opposite conclusion: trends in ET0more closely followed trends in energy availability than trends in atmospheric holding capability for vapor transfer.

These studies have come to quite different conclusions in different regions，indicating a need for new methods to identify the most important meteorological factors in explaining changes in ET0at the regional level.Besides，most of these studies focused on the theoretical sensitivity of ET0，which is the expected variation of ET0due to changes in variables under the assumption that only one variable changes while other variables remain the same.In fact，the theoretical sensitivity of ET0does not consider the actual changes in meteorological variables.However，the explanation ofmeteorological factors controlling changes in ET0must consider both the sensitivity of and long-term changes in the meteorological factors themselves.

In this study，overallanalysisof the variation of ET0in the arid region in northwestern Chinaw as carried out.The study mainly focused on both the temporal trends of annual and seasonal ET0and quantitative analysis of the contributions of different meteorological variables to the variation of ET0. The objectives of this study included:（1）to detect the longterm trends in ET0and air temperature using the Mann-Kendall（M-K）test；（2）to investigate the evaporation paradox at 15 stations by comparing the changing trends in annual ET0w ith the changing trends in air temperature，in order to compensate for the lack of pan evaporation data in the Heihe River Basin（HRB），because Zuo et al.（2010）found a linear relationship between pan evaporation and ET0in northwestern China and a coefficient of determ ination greater than 0.97，verifying the rationality of using the variation of ET0to reflect the variation of pan evaporation in this study；and（3）to quantify the contribution of key meteorological factors（air temperature，solar radiation，relative hum idity，and w ind speed）to the variation of ET0and explain the reason for the evaporation paradox using the sensitivity coefficientmethod.

Fig.1.Meteorological stations in and around HRB.

2.Study area and data

2.1.Study area

The HRB，covering an area of approxim ately 134 000 km2，is the second largest inland river basin in northwestern China and spans Qinghaiand Gansu provinces as well as the Inner Mongolia Autonomous Region from upper reaches to lower reaches.The HRB is located between latitude 37.50°N and 42.40°N，and longitude 98°E and 102°E（Fig.1）.

The HRB is situated in the interior of the Eurasian continentand dominated by arid hydrological characteristicsw ith a mean annual precipitation of approximately 400 mm and a m ean annual ET0of approximately 1 600 mm.The precipitation，temperature，evaporation，and runoff in the HRB vary greatly at both spatial and temporal scales.The dom inant land use types are desert land and grass land，occupying approximately 60%and 25%of the total area，respectively.Due to its important role inwater resourcesmanagement in northwestern China，the HRB has long been a focus of studies on inland rivers in arid regions.

2.2.Data

Six daily meteorological variables（observed daily mean，maximum and minimum air temperatures，relative humidity，w ind speed at the height of 2 m，and sunshine duration）derived from the ground surface climatic data sets at 15 nationalmeteorological stations from 1959 to 2012（Fig.1）in and around the HRB were obtained from the Environmental and Ecological Science Data Center forWest China.The six variables were used as input data for the FAO56 Penman-Monteith（FAO56 P-M）method to estimate daily values of ET0.The autocorrelation method was emp loyed in this study to analyze the persistence，which is the tendency for successive values of a m eteorological data series to remember the antecedent values（Gilesand Flocas，1984）.The results reveal that，forall15 stations in theHRB，autocorrelation coefficients of annual and seasonal air temperatures and ET0series are quite low，whichmeans a low persistence in the data series.

3.M ethods

3.1.FAO56 P-M method

The FAO56 P-M method，which is considered the most accurate method to estimate ET0under different climatic conditions，was employed to estimate the daily values of ET0in this study.Monthly and annualvaluesof ET0wereobtained by adding up thedaily values.The equation of the FAO56 P-M method（Allen et al.，1998）is as follows:

where ET0is reference evapotranspiration（mm），⊿is the slope of the saturated vapor pressure（kPa/°C），Rnis net radiation at the surface（MJ/（m2·d）），G is soil heat flux density（M J/（m2·d）），γis thepsychrometric constant（kPa/°C），T is the mean air temperature at the height of 2 m（°C），u2is w ind speed at the heightof 2m（m/s），esissaturation vapor pressure（kPa），and eais actual vapor pressure（kPa）.Each term in Eq.（1）was obtained usingmethods described by Allen et al.（1998）.

3.2.M-K test

TheM-K test，whichwas developed by Mann and Kendall and is superior for detecting linear or non-linear trends（Hisdal et al.，2001），was employed to analyze the long-term trends in ET0and air temperature.This method has been w idely used for detecting trends in hydro-meteorological variables such as stream flow，air temperature，ET0，and precipitation in different regions around the world（Zuo et al.，2012；Gong et al.，2011）.

The related equations for calculating the M-K test statistic S and the standardized test statistic ZMKare as follow s:

where Xiand Xjare the sequential data values of the time series in theyears i and j，n is the length of the timeseries，tpis the number of ties for the p th value，and q is the number of tried values.Positive valuesof ZMKindicate increasing trends，while negativevaluesof ZMKindicate decreasing trends in the time series.When，the null hypothesis，which assumes that there is no significant trend in the time series，is rejected and a significant trend exists in the time series.Z1-α/2is the critical value of Z from the standard normal table，and for the 5%significance level the value of Z1-α/2is 1.96.

3.3.Sensitivity coefficientmethod

Formultivariablemodels，such as the FAO56 P-M method，different variables have different dimensions and ranges of values，which makes it difficult to compare sensitivity w ith partial derivatives（Zuo et al.，2012）.Therefore，the partial derivative is transform ed into a non-dimensional form to interpret the sensitivity of the variables（M cCuen，1974；Beven，1979）:

where SViis the sensitivity coefficient and Viis the i th variable.SVirepresents the subtle change in ET0resulting from the subtle change in Vi.GViindicates the contribution of the i th variable to thevariation of ET0.The sensitivity coefficienthas been w idely used in studies on evapotranspiration（Estevez et al.，2009）.The positive SViof one variablemeans that the changing trends in ET0and thevariableare thesame，while the negative SViof one variablemeans that the changing trends inET0and the variable are opposite.It is the same for GVi. Sensitivity coefficients are different for different variables at different times.The larger the absolute value of the sensitivity coefficient is，the greater the effect the variable exertson ET0. Also，the larger the absolute value of GViis，the greater the contribution thevariablemakes to thevariation of ET0.In this study，SViand GVifor daily air temperature，solar radiation，relative humidity，and w ind speed were estimated to quantify the contribution of each factor selected to thevariation of ET0.

Fig.2.Temporal variations of seasonal ET0of HRB from 1959 to 2012.

4.Result analysis and discussion

4.1.Temporal trend of ET0

Fig.2 shows inter-annual variation of seasonal ET0in each season.Itcan be seen that seasonal ET0in themiddle reaches was similar to that across the whole basin in both values of seasonal ET0and the inter-annual trends.

The M-K testwas carried out at the 15 stations to investigate the changing trends in annual ET0seriesduring the period from 1959 to 2012 in the HRB at the significance levelof 5%. The results show that the annual ET0series exhibited decreasing trends at most of meteorological stations（Fig.3（a））.Fig.3（a）also show s thatseven stations in the basin showed a significant decreasing trend.In the legend of Fig.3，Decrease Sig，Decrease Insig，Increase Sig，and Increase Insig mean decrease significant，decrease insignificant，increase significant，and increase insignificant，respectively.

Changing trends in seasonal ET0at each station were also detected using theM-K test.Results reveal that the spring ET0of all15 stationsexhibited an insignificantdecreasing trend.A decreasing trend in the summer ET0took place atmostof the 15 stations，except at Yeniugou，M azongshan，and Guaizihu stations.Of the three stations，Guaizihu Station，located in the lower reaches of the HRB，exhibited a significant increasing trend，while Yeniugou Station in the upper reaches and Mazongshan Station in the lower reaches exhibited an insignificant increasing trend.In autumn，eight stations showed an increasing trend in ET0，much m ore than in other seasons.For the eightstations，the autumn ET0at five stations increased significantly.The other seven stations showed a significant decreasing trend，except for Jiuquan Station and Zhangye Station in themiddle reaches.Four stations showed an increasing trend in thew inter ET0，two ofwhich are located in the upper reaches，while Shandan Station and Guaizihu Station are in them iddle and lower reaches，respectively.

Generally，at the temporal scale，most of the stations showed a decreasing trend over the four seasons，especially in spring.An increasing trend in annual and seasonal ET0m ostly took p lace at stations in the upper and lower reaches.

4.2.Temporal trend of air temperature

In order to investigate the evaporation paradox in the HRB，it is necessary to study the changing trend in air temperature. Fig.4 shows the results of the M-K test performed on the annualmean air temperature aswell as the seasonalmean air temperature.The HRB is dominated by an increasing trend in air temperature at the annual and seasonal scales，w ith all 15 stations experiencing warmer conditions.The seasonalmean air temperature in autumn and w inter increases significantly at most stations，while the increase of the seasonal mean air temperature in spring and summer is insignificant.Thismeans that the increase of air temperature in autumn and w inter contributes more to the increase of annual mean air temperature.

4.3.Evaporation paradox

As described above，therewasawarm ing trend in the HRB during the period from 1959 to 2012，and annual ET0exhibited a decreasing trend in the m iddle and lower reaches of the HRB.Accordingly，it can be concluded that the evaporation paradox did exist in the HRB，except in the upper reachesandat two stations in the lower reaches，where the annual ET0showed an increasing trend oran insignificantdecreasing trend（Fig.5）.In other words，the evaporation paradox mainly existed in them idd le-lower reaches of the HRB.

Fig.3.Spatial distributions of annual and seasonal ET0trends in HRB from 1959 to 2012.

4.4.Sensitivity of keymeteorological factors for ET0

In order to quantify the contribution of keymeteorological factors to the spatial and temporal variations of ET0and determine the reasonwhy theevaporation paradox exists in the HRB，the sensitivity coefficients ofmain meteorological variablesof ET0，i.e.，air temperature（STA），solar radiation（SRS），relative humidity（SRH），and w ind speed（SWS），in different regions of the HRB were calculated and are plotted in Fig.6.

From Fig.6（a），it can be seen that the sensitivities of relative hum idity are all negative in different regions of the HRB，which means that ET0w ill decreasewhen relative hum idity increases.SRHreaches its peak in summer around July and attains its minimum value in December and January. Generally，the curvesexhibita single-peak shape，though they retain fluctuation over short temporalperiods.SRHin the lower reaches is obviously smaller than in other regions.In other words，relative humidity has a greater negative effect on the variation of ET0in the lower reaches than in the upper-middle reaches.Similarly，the sensitivity coefficient curves shown in Fig.6（b）for the air temperature present a single-peak shape and reach their peak in May and June.STAin the lower reaches ishigher than in the upper-m iddle reaches throughout the year.Curves of SRS（Fig.6（c））are sim ilar to those of SRHand STA，reaching theirmaximum andminimum values in summer and w inter，respectively.In the m iddle-lower reaches，the effect of solar radiation on ET0in early summer（May and June）is the greatest，while in the upper reaches the peak comes around a little later in August.Fig.6（d）shows that，in themiddle-lower reaches，ET0ismoresensitive tow ind speed in summer，while SWSin the upper reaches，which ismuch smaller than that in themiddle-lower reaches，remainsalmost unchanged throughout the year，and does not show a significant peak.

A comparison of the four subgraphsof Fig.6 shows that for the fourmeteorological factors considered in this study，relative humiditywas themost sensitive factor for ET0at the daily scale with absolute values of sensitivity coefficients reaching 6.0 in summer，several times higher than that of othermeteorological factors.Wind speed was the second greatest sensitive factor to ET0，especially in the middle-lower reaches.Air temperature and solar radiation were the two least sensitivemeteorological factors to ET0.

Fig.4.Spatial distributions ofmean annual and seasonal air temperature trends in HRB from 1959 to 2012.

Fig.5.Evaporation paradox in HRB from 1959 to 2012.

The sensitivity coefficient（SVi）indicates the sensitivity of ET0to themeteorological factor（Vi），under the condition that changes in allmeteorological factors are the same.However，at the 15 selected stations in the HRB，the changing percentage varies greatly for each meteorological factor.Thus，GViwas employed in this study to indicate the relative change in ET0resulting from eachmeteorological factor.Table 1 lists the annual GVivalue for eachmeteorological factor estimated by Eq.（7）.The total estimated contribution was obtained by summ ing up the GViof each factor.From the tablewe can see that，in the upper reaches，GVivalues of air temperature and solar radiation aremuch larger than those of other two factors，which means that air temperature and solar radiation contribute the most to the variation of ET0，while relative humidity and w ind speed hardly make contributions to the variation of ET0，due to the quite low relative change of hum idity and w ind speed in the upper reaches.In the middle reaches，the large decrease in solar radiation and w ind speed lead to the decrease in ET0at all stations except Shandan Station，which is consistentw ith results of the changing trend of ET0（Fig.3（a））.Though relative hum idity is themost sensitive factor for ET0，its relative change is little during the study period，and contributed least to the variation of ET0.In the lower reaches，solar radiation and w ind speed are the two determining factors for the variation of ET0because of theirlarge impacton ET0and significantvariations during the study period.

Fig.6.Sensitivity coefficients in different regions of HRB.

Table 1 Contribution ofmeteorological factors to variation of ET0.

5.Conclusions

In thisstudy，temporalvariation of ET0wasestimated using the FAO56 P-M method and keymeteorological factorswere analyzed at 15meteorological stations in the HRB during the period from 1959 to 2012.Conclusions can be summed up as follow s:

（1）Both annual and seasonal ET0for most of the HRB displayed a decreasing trend throughout years，especially in spring.As for air temperature，all 15 stations showed increasing trends，whichmeans that therewasawarm ing trend in the HRB during the period from 1959 to 2012.

（2）From the fact thatmean annual ET0and air temperature exhibited contrasting trends，it can be concluded that the evaporation paradox did exist in the HRB，mainly in the middle-lower reaches.

（3）The resultsof sensitivity analysis show that relative humiditywas themostsensitive factor for ET0atthedaily scale in the HRB，followed by w ind speed，air temperature，and solar radiation.In the upper reaches，air temperature and solar radiation contributedmost to the temporal variation of ET0，and in them iddle-lower reaches，solar radiation and w ind speed were the determ ining factors for the temporal variation of ET0.

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This work was supported by the National Natural Science Foundation of China（Grant No.91125015）and the Central Nonprofit Research Institutes Fundamental Research of the Yellow River Institute of Hydraulic Research（Grant No.HYK-JBYW-2013-18）.

*Corresponding author.

E-mail address:zongxuexu@vip.sina.com（Zong-xue Xu）. Peer review under responsibility of HohaiUniversity.

http://dx.doi.org/10.1016/j.w se.2015.01.004

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