Spatiotemporal Characteristics of Reference Evapotranspiration and Its Sensitivity Coefficients to Climate Factors in Huang-Huai-Hai Plain, China

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1 Joural of Itegrative Agriculture 2013, 12(12): December 2013 RESEARCH ARTICLE Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai Plai, Chia YANG Jia-yig 1, 2, 3*, LIU Qi 1, 2, 3*, MEI Xu-rog 1, 2, 3, YAN Chag-rog 1, 2, 3, JU Hui 1, 4 ad XU Jia-we 1, 4 1 Istitute of Eviromet ad Sustaiable Developmet i Agriculture, Chiese Academy of Agricultural Scieces, Beijig , P.R.Chia 2 State Egieerig Laboratory of Efficiet Water Use ad Disaster Reductio for Crops, Miistry of Agriculture, Beijig , P.R.Chia 3 Key Laboratory of Drylad Agriculture, Miistry of Agriculture, Beijig , P.R.Chia 4 Key Laboratory of Agricultural Eviromet, Miistry of Agriculture, Beijig , P.R.Chia Abstract Climate chage will have importat implicatios i water shore regios, such as Huag-Huai-Hai (3H) plai, where expected warmer ad drier coditios might augmet crop water demad. Sesitivity aalysis is importat i uderstadig the relative importace of climatic variables to the variatio i referece evapotraspiratio (ET 0 ). I this study, the 51-yr ET 0 durig witer wheat ad summer maize growig seaso were calculated from a data set of daily climate variables i 40 meteorological statios. Sesitivity maps for key climate variables were estimated accordig to Krigig method ad the spatial patter of sesitivity coefficiets for these key variables was plotted. I additio, the slopes of the liear regressio lies for sesitivity coefficiets were obtaied. Results showed that ET 0 durig witer wheat growig seaso accouted for the largest proportio of aual ET 0, due to its log pheological days, while ET 0 was detected to decrease sigificatly with the magitude of 0.5 mm yr -1 i summer maize growig seaso. Solar radiatio is cosidered to be the most sesitive ad primarily cotrollig variable for egative tred i ET 0 for summer maize seaso, ad higher sesitive coefficiet value of ET 0 to solar radiatio ad temperature were detected i east part ad southwest part of 3H plai respectively. Relative humidity was demostrated as the most sesitive factor for ET 0 i witer wheat growig seaso ad decliig relativity humidity also primarily cotrolled a egative tred i ET 0, furthermore the sesitivity coefficiet to relative humidity icreased from west to southeast. The eight sesitivity cetrals were all foud located i Shadog Provice. These ET 0 alog with its sesitivity maps uder witer wheat-summer maize rotatio system ca be applied to predict the agricultural water demad ad will assist water resources plaig ad maagemet for this regio. Key words: ET 0, spatial distributio, temporal treds, sesitivity coefficiet, 3H plai INTRODUCTION A global chage i the mai meteorological variables has bee observed i the last decades. Accordig to the IPCC report, i recet 100 years ( ), the global temperature has raised by 0.74 C (IPCC 2007), ad it is likely to cotiue i the 21st cetury, ad caused chages i the hydrological cycle by affectig precipitatio ad evaporatio (Hutigto 2006). The climate chage with the characteristic of global warmig has become a hot spot of research i field of water Received 21 Jauary, 2013 Accepted 26 Jue, 2013 YANG Jia-yig, Tel: , yagjy@ieda.org.c; Correspodece MEI Xu-rog, Tel/Fax: , meixurog@caas.c * These authors cotributed equally to this study. doi: /S (13)

2 Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai 2281 resources, agriculture, ecology, ad other disciplies. Chages i climatic elemets such as temperature, precipitatio, radiatio, humidity, ad wid speed could have profoud implicatios for hydrologic processes (McKeey ad Roseberg 1993). Previous studies have focused attetio o two aspects, followed by the quatificatio of climate chages (Türkeş et al. 2002; Wu et al. 2006; Toreti ad Desiato 2008; de Luis et al. 2009; El Keawy et al. 2009; Gozalez Hidalgo et al. 2009; Espadafor et al. 2011c) ad the assessmet of the impacts of those chages o differet fields (Walther et al. 2002; Izaurralde et al. 2003; Gog et al. 2006; Mizyed 2009). As oe of the importat parameters of the hydrologic cycle, referece crop evapotraspiratio (ET 0 ) plays a key role i estimatig ad predictig actual crop evapotraspiratio, water maagemet, establishig irrigatio scheme ad other practice of agricultural productio. ET 0 refers to the crop evapotraspiratio i the ope short grass lad where the soil moisture is adequate, groud is completely covered, ad grass grew ormally with the similar height (grass height is about 8-15 cm). ET 0 is a itegrated climate parameter that gives a measure of the evaporatio demad of the air. Several researches have poited out that ET 0 is expected to icrease with temperature rise (McNulty et al. 1997; Goyal 2004). However, decreasig treds of ET 0 were foud i some areas of Chia (Thomas 2000; Shebi et al. 2006; Wag et al. 2007), Idia (Chattopadhyay ad Hulme 1997), USA (Hobbis et al. 2004), ad Australia (Roderick ad Farquhar 2004). Besides, ET 0 is essetially depedet o four meteorological variables: air temperature, solar radiatio, relative humidity ad wid speed (Alle et al. 1998). Oe or more of those four meteorological variables ca be take ito accout, depedig o the ET 0 calculatio method selected. The mai advatage of the Pema- Meteith approach is that it takes ito accout the most sigificat variables, so that the ifluece of each of them ca be aalyzed, physically based equatios requirig daily data for temperature ad relative humidity of the air, solar radiatio ad wid speed (Alle et al. 1998). To uderstad the relative importace of climatic variables i the Pema-Meteith formulatio, a sesitivity aalysis is required ad the results from sesitivity aalysis are of vital sigificace for determiig the effect of climate chage o ET 0. Several papers have carried out sesitivity aalysis of ET 0 to meteorological data i differet climates (Raa ad Katerji 1998; Goyal 2004; Irmak et al. 2006), but they restricted to a sigle statio. Furthermore, what has bee reported to be the most effective variable detected is wid speed (Cohe et al. 2002; Wag et al. 2007; Todisco ad Vergi 2008), solar radiatio (Gao et al. 2006; Wag et al. 2007) ad relative humidity (Gog et al. 2006) i other papers, however, they almost restricted to mothly, seasoal or aual ET 0. Liu Y et al. (2010) reported the aual ET 0 ad its costituets (ET rad ad ET aero ) were sigificatly declied ad that the highest ET 0 ad ET rad were i summer, the lowest i witer, while the sprig ET aero value was the highest across the North Chia Plai (NCP). Sog et al. (2010) also reported that for the whole NCP, aual ET 0 showed a statistically sigificat decrease of mm per decade over the 46 years of data collectio ad that the decreasig et radiatio ad wid speed had a bigger impact o ET 0 rates tha the icreases observed by the maximum ad miimum temperatures. However, studies about sesitivity aalysis of ET 0 durig typical crop growig seaso ad its variatio tred are rarely see. The objectives of this study were (1) to ivestigate the treds for ET 0 i Huag-Huai-Hai (3H) plai i the past 51 years, (2) to evaluate the major factors related to the chage i ET 0 ; ad (3) to develop the temporal variatios of climatology sesitivity coefficiets for differet crops (witer wheat ad summer maize), i a attempt to uderstad the relative roles of mai climatic variables for witer wheat ad summer maize. RESULTS Variatio of ET 0 Ivestigatio of treds ad persistece of historical meteorological data is helpful i uderstadig the status of ET 0. We performed a compariso of ET 0 for witer wheat ad summer maize estimated usig the FAO-56 Pema-Moteith formulatio. As described i Table 1, average aual ET 0 was mm, with maximum value mm, ad miimum value

3 2282 YANG Jia-yig et al mm. Statistically sigificat decreasig tred at sigificace level of P<0.01were foud i the aalysis of aual ET 0, with slope of -1.3 mm yr -1. ET 0 i witer wheat growig seaso was detected with higher value compared with ET 0 i summer maize growig seaso. A sigificat tred was foud (P<0.01) for ET 0 i summer maize growig seaso, with a decreasig tred of -0.8 mm yr -1, lower tha the decreasig tedecy of aual ET 0. A Table 1 Aual variatio tedecy ad statistics of ET 0 i study area Average ET 0 (mm) Maximum ET 0 (mm) Miimum ET 0 (mm) Slope (mm yr -1 ) Aual ** Witer wheat Summer maize ** r B ** represets liear coefficiets sigificat at P<0.01. The same as below. Usig the Pema-Meteith equatio, ET 0 was calculated i 40 statios from 1961 to A large spatial variability was foud for ET 0 i witer wheat ad summer maize growig seaso i 3H plai, ad differet treds were detected i study area. ET 0 i witer wheat growig seaso was higher i the cetral part tha i souther ad orther parts as described i Fig. 1. Sigificat tedecy was detected for ET 0 i 23 statios, amog which ET 0 i 17 statios decreased ad was maily located i Shadog ad Hea provices, while ET 0 i 6 statios icreased ad was maily located i Hebei Provice. O the other had, a dowward tred i ET 0 i summer maize growig seaso was detected from east to west across to the study area. ET 0 was observed to decrease sigificatly i aroud 24 statios, which maily located i Hea Provice ad orth part of Ahui Provice. Variatio of the sesitivity coefficiets Slopes of the liear regressio lies for sesitivity coefficiets are listed i Table 2, ad it was foud that the most effective meteorological factor impactig ET 0 varied with regio ad seaso. ET 0 i summer maize growig seaso showed more sesitive to temperature ad solar radiatio, sice the sesitivity coefficiets of temperature (S T ) ad sesitivity coefficiets of solar radiatio (S RS ) i summer maize growig seaso Fig. 1 Spatial patter of ET 0 ad its tred i witer wheat seaso ad summer maize seaso i Huag-Huai-Hai plai (3H plai). A, witer wheat. B, summer maize. were bigger tha that i witer wheat growig seaso. Solar radiatio was the domiat factor to ET 0 i summer maize growig seaso, for its sesitivity coefficiet value was Treds of S T are egative i the time series aalysis, which meas that the egative ifluece i ET 0 got bigger i the 51 yr, combiig with the egative value of S T. Compared with S T i summer maize growig seaso, chages of S RS was detected with more obvious tedecy, with a tred of per decade at the sigificat level of P<0.01, which meas that chages i solar radiatio cotributed less to the fluctuatio of ET 0 i summer maize growig seaso i the 51 yr. RH was demostrated as the most sesitive factor for ET 0 i witer wheat growig seaso, with the sesitivity coefficiets of relative humidity (S RH ) value of ,

4 Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai 2283 followed by solar radiatio, temperature ad wid speed. Obvious icreasig tred was detected i S RH i witer wheat growig seaso, with a slope of per decade. However, ifluece of relative humidity to ET 0 i witer wheat growig seaso had get to be smaller, because of the egative value of S RH i witer wheat growig seaso. Sesitivity surfaces for climate variables i growig period of witer wheat ad summer maize are Table 2 Aual variatio tedecy ad statistics of sesitivity coefficiet of ET 0 i 3H plai Mea Maximum Miimum Slope (per decade) r S T Aual ** Witer wheat ** Summer maize ** S RS Aual ** Witer wheat * Summer maize ** S WS Aual ** Witer wheat ** Summer maize ** S RH Aual ** Witer wheat ** Summer maize Sesitivity coefficiets for mea temperature (S T ), solar radiatio (S RS ), wid speed (S WS ), relative humidity (S RH ). * represets liear coefficiets sigificat at P<0.05. The same as below. preseted i Figs. 2 ad 3. These maps are obtaied from the iterpolated meteorological surfaces accordig to Krigig method i Geostatistical aalysis module. The spatial patter of sesitivity coefficiets for S RS, S RH, S T ad wid speed (S WS ) durig witer wheat ad summer maize was plotted i these maps. Spatial patter of sesitivity coefficiets of ET 0 were mapped i witer wheat ad summer maize growig seaso i 3H plai respectively, ad tedecy of sesitivity coefficiets has bee calculated i every sigle statio, i order to detect their sigificatly chage i time series. Results showed that the S T decreased from orth to south i witer wheat growig seaso, which meas that chages i temperature may lead to greater decrease of ET 0 i witer wheat growig seaso i the south part of the study area. 18 statios had bee detected with sigificat decreasig tred (P<0.01), maily located i Hea ad Hebei provices. Higher value was detected i S RS i the orth part of 3H plai. S RS i 9 statios decreased at the sigificace level of P<0.01, ad the decreasig tedecy was more obvious i Hebei ad Ahui provices. While S RS i the other 9 statios icreased, more slow tred maily located i Hea ad Jiagsu provices. S WS i witer wheat growig seaso showed opposite chage patter to S RS, with higher value detected i the south part. More sharply decreasig tedecy was located i Hebei Provice ad orther part of Ahui Provice, ad more sharply icreasig tred maily located i Hea ad orther part of Jiagsu provices. S RH icreased from west to southeast, with 29 statios sigificatly icreased, especially i Hebei ad Hea provices. ET 0 i summer maize growig seaso was more sesitive to temperature fluctuatig i east part of 3H plai tha i west part. S T i 26 statios sigificatly icreased, especially i Hebei ad Hea provices. S RS icreased from ortheast to southwest i summer maize growig seaso, which meas that chages i solar radiatio may lead greater decrease of ET 0 i southwest part of study area. 26 statios had bee detected with sigificat decreasig tred (P<0.01), more obvious decreasig tedecy of S RS maily located i Hebei ad Shadog provices. Higher value was detected i S WS i the orth part of 3H plai. S WS i 26 statios icreased at the sigificace level of P<0.01, ad S WS i summer maize growig seaso icreased more sharply i Hebei Provice. Higher value was detected i S RH i summer maize growig seaso i the orthwest of 3H plai. S RH i 12 statios sigificatly icreased, which maily located i Hea Provice, while there were also 5 statios detected with decreasig tedecy i S RH, which maily located i Hebei Provice. Sesitivity cetral of ET 0 Sesitivity cetrals of ET 0 were calculated based o the data set of sesitivity coefficiet i 40 statios i order to better uderstad the characteristics ad spatial differetiatio of sesitivity coefficiets for ET 0 i witer wheat ad summer maize growig seaso. It ca be see from Fig. 4 that the eight sesitivity cetrals (icludig S T, S RS, S WS ad S RH of ET 0 i witer wheat growig seaso, ad S T, S RS, S WS ad

5 2284 YANG Jia-yig et al. A B C D Fig. 2 Spatial variability i sesitivity coefficiet of ET 0 i witer wheat seaso to temperature (S T, A), solar radiatio (S RS, B), wid speed (S WS, C) ad relative humidity (S RH, D). S RH of ET 0 i summer maize growig seaso) were all located i Shadog Provice. Sesitivity cetrals of S T, S RS, S WS ad S RH of ET 0 i witer wheat growig seaso located i Jiaxiag, Dogpig ad Weshag couties i Shadog Provice respectively, while sesitivity cetrals of S T, S RS, S WS ad S RH of ET 0 i summer maize growig seaso located i Weshag, Weshag, Pigyi ad Yazhou couties. Sesitivity cetrals of S RS i summer maize growig seaso ad i witer wheat growig seaso showed the farthest distace (aroud 33.6 km), followed by S RH, S WS ad S T. ET 0 regioal respose to climate chage Although sesitivity aalysis aims to idetify the most sesitive variable to ET 0 durig witer wheat ad summer maize growig seaso, further study eed to be coducted for ET 0 with the purpose of fidig out cotrollig factors because of variatio i climatic variables. The tedecy ad magitude of climate variables ad relatioships betwee ET 0 ad T, WS, RH ad RS i witer wheat ad summer maize growig seasos are preseted i Table 3. As described, climate variables sigificatly chaged i the past 51 yr except relative humidity i summer maize growig seaso, ad maximum magitude was all foud i witer wheat growig seaso. As for witer wheat growig seaso, the maximum value was detected for correlatio coefficiet of relative humidity, that is to say, the decliig relative humidity also primarily cotrolled a egative tred i ET 0,

6 Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai 2285 A B C D Fig. 3 Spatial variability i sesitivity coefficiet of ET 0 i summer maize seaso to temperature (S T, A), solar radiatio (S RS, B), wid speed (S WS, C) ad relative humidity (S RH, D). Latitude T T Witer wheat WS RS RS WS Summer maize Logitude Fig. 4 Sesitivity cetral of ET 0 i witer wheat-summer maize growig seaso i 3H plai. RH RH wid speed. Solar radiatio also was the primarily cotrollig variable for egative tred i aual ET 0, followed by relative humidity, mea temperature ad wid speed. These fidigs idicate that each climate variable has a importat role to play i the tred ad magitude ad their roles chage with regioal characteristics. Thus, oly oe or two meteorological variables caot be resposible for the tred ad magitude of ET 0 ad they all eed be accouted for i a combiatio-based eergy balace equatios whe used i climate chage studies. DISCUSSION while the primarily cotrollig variable tured to be solar radiatio i summer maize seaso, followed by ET 0 durig witer wheat growig seaso accouted for the largest proportio of aual ET 0 due to its

7 2286 YANG Jia-yig et al. Table 3 The tred ad correlatio coefficiets betwee aual ET 0 with key climatic variables i 3H plai Mea temperature ( C per decade) Solar radiatio (MJ m -2 yr -1 ) Relativity humidity (%) Wid speed (m s -1 ) Tred Aual 0.26 ** * ** Witer wheat 0.33 ** ** * ** Summer maize 0.19 ** ** ** Correlatio coefficiet Aual ** 0.57 ** 0.54 ** Witer wheat ** 0.35 * Summer maize ** ** log pheological days, while it is characterized by sigificatly decreasig with the magitude of 0.5 mm yr -1 i summer maize growig seaso. Similar results have bee reported for Wuqiao Agricultural Experimet Statio i North Chia plai by Kog (2012). Furthermore, a sigificat ET 0 decrease was foud i aalysis of aual ET 0. This is i agreemet with some other researches (Thomas 2000; Shebi et al. 2006; Wag et al. 2007; Liu Y et al. 2010; Sog et al. 2010), which have poited i this directio, although ET 0 is expected to icrease i the ext years o a par with temperature rise accordig to climate chage model predictios. For the agriculture regios of water shortage, such as 3H plai, relativity humidity is the most sesitive variable i the whole witer wheat-summer maize rotatio system. This is partially agreed by Chattopadhyay ad Hulme (1997), who poited out that relative humidity is a major limitig factor to ET 0 if warmig is accompaied by higher humidity. However, this cotrasts with the result poited out by Gao et al. (2006) ad Wag et al. (2007). They poited out that solar radiatio reductio alog with wid speed was the mai cotributig variables. As for summer maize growig seaso, solar radiatio is the most sesitive ad primarily cotrollig variable for egative tred i ET 0, similar to the results reported by Bo et al. (2011). The fluctuatio of ET 0 is expected to have importat cosequeces due to its overlap with the precipitatio chages. This will lead to a correspodig chages of irrigatio, or a ecessity to modify the preset croppig patters ad agroomic techiques (Olese ad Bidi 2002; Vergi ad Todisco 2011). From ET 0 estimates, ad usig adequate crop coefficiets (Doorebos ad Pruitt 1975; Alle et al. 1998), irrigatio schedules ca be defied. I additio, it could be of great help to simulate optimizatio procedures uder water restrictios. With the results provided i this study, agroomic effects due to chages i ET 0 i witer wheat-summer maize rotatio system could be iferred for irrigated agriculture i 3H plai. Thus, the chages i ET 0 would redefie irrigatio requiremets if crop coefficiet curves were ot affected by the weather coditios. However, a marked iter-aual ad iterdecadal variatio of drought occurred i North Chia accordig to the revised Palmer drought severity idex (PDSI) ad there have bee more drought years i North Chia sice 1970 (Wei et al. 2003). It is ecessary to develop feasible late sowig, straw mulchig, regulated deficit irrigatio ad soil water storage ad preservatio especially for witer wheat i North Chia. I additio, it would be expected for the crop cycle to modify due to chages of weather ad crop water requiremet. I Spai, Döll (2002) has estimated a decrease i irrigatio requiremets i 2020 due to the possibility of sowig earlier i time whe higher temperature is more favorable. Fially, it is difficult to quatify the ifluece of the detected chages o soil moist i the regio, especially whe ET 0 decreases with the absece of tred i precipitatio. This would ted to icrease aquifer recharge, beig ot well i agreemet with the reported dryig tred i this regio (Liu et al. 2011). It is therefore ecessary to model the aquifers behavior i order to uderstad the possible impacts of crop actual evapotraspiratio ad of future climate chage o water resources. CONCLUSION The 51-yr ET 0 durig witer wheat ad summer maize growig seaso for 3H plai were calculated from a data set of daily climate variables i 40 meteorological statios. Sesitivity maps for key climate variables i witer wheat ad summer maize seaso were estimated from the iterpolated meteorological surfaces accordig to Krigig method ad the spatial patter variability i sesitivity coefficiets because these key variables was plotted i these maps. I additio, the slopes of the liear regressio lies for sesitivity coefficiets were described i Table 2. These ET 0 alog with its sesitivity maps uder witer

8 Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai 2287 wheat-summer maize rotatio system ca be applied to predict the agricultural water demad ad will assist water resources plaig ad maagemet for this regio. ET 0 durig period of witer wheat accouted for the largest proportio of aual ET 0, due to its log pheological days, while as for summer maize growig seaso ET 0 decreased sigificatly with the magitude of 0.5 mm yr -1. Solar radiatio is cosidered to be the most sesitive ad primarily cotrollig variable for egative tred i ET 0 for summer maize growig seaso, ad more sesitivity to solar radiatio ad temperature were detected i east part ad southwest part of 3H plai respectively. While i witer wheat growig seaso relativity humidity became the predomiat factor, furthermore, decliig relativity also primarily cotrolled a egative tred i ET 0. ET 0 i summer maize growig seaso was more sesitive to temperature fluctuatio i east part of study area ad S RS icreased from ortheast to southwest. As for witer wheat growig seaso, S RH tured to icrease from west to east ad south. The eight sesitivity cetrals (icludig S T, S RS, S WS ad S RH of ET 0 i witer wheat ad summer maize growig seaso, respectively) were all foud located i Shadog Provice. This fact is probably derived from the locatio of selected 40 meteorological sites ad spatial patter of sesitivity coefficiets for these four key variables. sufficiet irrigatio water ad fertilizers. Accordigly, the mai croppig system i the 3H plai is the witer wheatsummer maize rotatio system (Zhao et al. 2006; Liag et al. 2011; Su et al. 2011). Usually, witer wheat is sow at the begiig of October ad harvested at Jue i the followig year, summer maize is sow directly afterwards ad harvested at the ed of September. Data set from 1961 to 2011 i 40 weather statios provided by Chia Meteorological Admiistratio (CMA) were used i this study (Fig. 5). Daily observed maximum (T max ) ad miimum air temperature (T mi ), wid speed (WS) measured at 10 m height, average relative humidity (RH) ad daily sushie duratio (SD) data were available. The weather statios were selected by the followig two criteria. First, the spatial distributio had to guaratee such a coverage could be represetative of irrigated lads i 3H plai. I additio, time series had to be log eough to obtai statistically sigificat results i tred aalyses. Thus, the 51-yr period from 1961 to 2011 was studied whe MATERIALS AND METHODS Study area ad climate data The 3H plai, oe of the largest plais i Chia, is located i the orth of Chia ad exteds from N ad E. The climate is temperate, subhumid, ad cotietal mosoo with a cumulative temperature (>0 C) of to C, average aual precipitatio ragig from 5 00 to 800 mm (Re et al. 2008). The aual raifall cocetrates i the summer period, from July to September. However, witer ad sprig is characterized by a lack of water for agricultural productio. Although precipitatio is isufficiet for cultivatio i this area, it is oe of the mai Chiese crop productio ceters, providig about 61 ad 31% of wheat ad maize productio respectively ( with itesive maagemet characterized by the applicatio of Fig. 5 The locatio of meteorological statios i 3H plai. it was possible. Calculatio of ET 0 The Pema-Moteith formula recommeded by the Food ad Agriculture Orgaizatio of the Uited Natios (FAO) was used to calculate ET 0 over the past 51-yr. The Pema- Moteith formula is give as followig: ( R-G ) + γ U2( es-ea) ET T 273 0= + + γ ( U ) I this formula, ET 0, crop referece evapotraspiratio (mm d -1 );, saturatio vapor pressure/temperature curve 2 (1)

9 2288 YANG Jia-yig et al. (kpa C -1 ); R, et radiatio from caopy (MJ m -2 d -1 ); G, soil heat flux (MJ m -2 d -1 ); T, the average daily temperature, equal to the mea of daily average maximum temperature (T max ) ad average miimum temperature (T mi ), C; U 2, wid speed of 2 m height above the groud (m s -1 ); e s, saturatio vapor pressure (kpa); e a, actual water vapor pressure (kpa); e s -e a, vapor pressure deficit (kpa); γ, psychrometer costat (kpa C -1 ). The related parameters of calculatio methods i the formula were showed i the referece (Alle et al. 1998). All the above variables ca be calculated from daily meteorological observatio data. R ca be approached by the followig formula: R= Rs-Rl (2) Where, R is the et radiatio (MJ m -2 d -1 ), R s is the differece betwee the icomig et shortwave radiatio (MJ m -2 d -1 ), R l is the outgoig et logwave radiatio (MJ m -2 d -1 ). R s = ( 1-α ) R s (3) Where, R s is et solar or shortwave radiatio (MJ m -2 d -1 ), α is albedo or caopy reflectio coefficiet, which is 0.23 for the hypothetical grass referece crop, R s is the icomig solar radiatio (MJ m -2 d -1 ). R s ( 0.34 e ) T max, k + Tmi, k Rl = σ a 35 (4) 2 Rso Where, R l is et outgoig logwave radiatio (MJ m -2 d -1 ), σ is Stefa-Boltzma costat ( MJ K -4 m -2 d -1 ), T max, k is maximum absolute temperature durig the 24-h period, T mi, k is miimum absolute temperature durig the 24-h period, e a is actual vapour pressure [kpa], R s -R so is relative shortwave radiatio, R s is solar radiatio (MJ m -2 d -1 ), R so clear-sky radiatio (MJ m -2 d -1 ). The solar radiatio (R s ) ca be calculated with the Agstrom formula which relates solar radiatio to extraterrestrial radiatio ad relative sushie duratio: R s= a + b R a (5) N Where, R s is solar or shortwave radiatio (MJ m -2 d -1 ), is actual duratio of sushie (h), N is maximum possible duratio of sushie or daylight hours (h), R a is extraterrestrial radiatio (MJ m -2 d -1 ). The values of a (=0.25) ad b (=0.5) are recommeded by FAO. Soil heat flux (G) is small compared to R, particularly whe the surface is covered by vegetatio ad calculatio time step is 24 h or loger. Thus, as the magitude of the day or 10-d soil heat flux beeath the grass referece surface is relatively small, it ca be igored. That is G day 0. For the calculatio of ET 0, wid speed measured at 2 m above the surface is required. It ca be coverted from the ormal measuremet at 10 m wid speed based o the equatio give by the FAO Pema-Moteith method (Alle et al. 1998) as followig: U 4.87 U 2= Z (6) log e ( ) Where U 2 is the wid speed at 2 m above groud surface (m s -1 ), U Z is the measured wid speed at Z m above groud surface (m s -1 ), ad Z is the height of measuremet above groud surface. Here Z is 10 m. Sesitivity aalysis of ET 0 to meteorological variables Sesitivity aalysis was performed to evaluate the effect of meteorological variables o ET 0. For a geeral defiitio of sesitivity, the variable V is cosidered, which is a fuctio of the iput variables x 1, x 2, x 3,, x 4 : V = f ( x1,..., x ) (7) If the variables x 1, x 2, x 3,, x 4 are idepedet of V, it may be writte: V+ V = f ( x1 + x1,..., x + x ) (8) From a Taylor series expasio we have, eglectig higher-order terms: V V V = X X (9) 1 X 1 X V By defiitio, the partial differetials,, are the X i sesitivities, SX i is the depedet variable V to the idepedet iput variable X i (McCue 1974; Saxto 1975; Beve 1979; McCue ad Beighley 2003). They deote the chage i V per uit chage i X i. From eq. (9) we have: V V SX i = = (10) X i X i Which shows that SX i may be obtaied by calculatig directly the value of the partial differetial, or by applyig a step chage i X i, while leavig the variables other tha X i costat. Here SX i may be sesitive to the relative magitude of V ad X i. Therefore, SX i may be divided V by the ratio, which leads to the relative sesitivity or X i sesitivity coefficiet RSX i : VX i RSX i = (11) X iv Now, the relative chage i V ca be expressed as (Saxto 1975), which shows that the relative sesitivity coefficiet deotes the part of the relative chage i X i that is trasferred to the relative chage i V. If, for example, RSX i =25%, a 10% chage i X i will result i a 2.5% chage i V. V X1 X = RSX RSX (12) V X X 1 Sesitivity coefficiets ceter aalysis I order to evaluate characteristic of sesitivity coefficiets of meteorological parameters o ET 0, sesitivity coefficiets ceters were calculated based o gravity ceter aalysis o the sesitivities of meteorological parameters. The gravity

10 Spatiotemporal Characteristics of Referece Evapotraspiratio ad Its Sesitivity Coefficiets to Climate Factors i Huag-Huai-Hai 2289 ceter (Gaile 1984) is the poit of equality of the regioal force from all directios, which is usually deoted by certai attributes ad geographic coordiates of the subuit (compared to the etire study area). ( X ijeij ) ( ) Yij Eij j = 1 j = X i =, Yi = 1 (13) E E X i, Y i are the latitude ad logitude of the sesitive ceter of meteorological parameter i; X ij, Y ij are the latitude ad logitude of grid j of i. E ij is the sesitivity coefficiets of i i grid j. E is the accumulate sesitivity coefficiets of i i all grids. Time series aalysis method I order to uderstad the temporal variatio of the climate variables, the liear tred ad the associated periods were aalyzed by a liear fitted model. The least-square liear model is the most commo method used for statistical diagosis i moder climatic aalysis studies (Zeg ad Heilma 1997; Doohue et al. 2010; Liu et al. 2010), ad is a fudametal techology to forecast chages i moder climate. The liear tred was chose because of beig the simplest model for a ukow tred. The level of adequacy of the fitted model was measured by the percetage of variace explaied by it. Liear treds for the series of aual total precipitatio were calculated by the least square regressio. The estimated slopes were tested agaist the hypothesis of ull slope by meas of a 2-tailed T-test at a cofidece level of 95% (Serrao et al. 1999). A series y 1, y 2, y i,, y, ca be expressed by the polyomial: ( t) = a + a t + + a t ( m ) yˆ 0 1 m < (14) Where, t is year. Geerally, the liear tred of a time series ca be estimated by the least square method ad ca be expressed by the liear regressio equatio as: ( t) a a t yˆ = (15) Where, the slope a 1 is the estimated tred. Ackowledgemets This research was supported by the Key Techologies R&D Program of Chia durig the 12th Five-Year Pla period (2012BAD09B01), the Natioal 973 Program of Chia (2012CB955904), the Project of Food Security ad Climate Chage i the Asia-Pacific Regio: Evaluatig Mismatch betwee Crop Developmet ad Water Availability ad Project of Natioal No-profit Istitute Fud, Chia- Australia (BSRF201206). We gratefully ackowledge the aoymous reviewers for their valuable commets o the mauscript. Refereces Alle R G, Pereira L S, Raes D, Smith M Crop evapotraspiratio: Guidelies for computig crop water requiremets. Irrigatio ad Draiage Paper 56. FAO, Rome, Italy. Beve K A sesitivity aalysis of the Pema- Moteith actual evapotraspiratio estimates. Joural of Hydrology, 44, Chattopadhyay N, Hulme M Evaporatio ad potetial evapotraspiratio i Idia uder coditios of recet ad future climate chage. Agricultural ad Forest Meteorology, 87, Cohe S, Iaetz A, Stahill G Evaporative climate chages at Bet Daga, Israel, Agricultural ad Forest Meteorology, 111, Döll P Impact of climate chage ad variability o irrigatio requiremets: a global perspective. Climatic Chage, 54, Doohue R J, McVicar T R, Roderick M L Assessig the ability of potetial evaporatio formulatios to capture the dyamics i evaporative demad withi a chagig climate. Joural of Hydrology, 386, Doorebos J, Pruitt W O Guidelies for predictig crop water requiremets. Irrigatio ad Draiage Paper. Food ad Agriculture Orgaizatio, Rome, Italy. ElKeawy A M, LpezMoreo J I, Vicete-Serrao S M, Mekld M S Temperature treds i Libya over the secod half of the 20th cetury. Theoretical ad Applied Climatology, Espadafor M, Lorite I J, Gavil P, Beregea J A aalysis of the tedecy of referece evapotraspiratio estimates ad other climate variables durig the last 45 years i Souther Spai. Agricultural Water Maagemet, 98, Gaile G L Measures of spatial equality. Spatial Statistics ad Models. D. Reidel Publishig Compay, USA. pp Gao G, Che D, Re G, Che Y, Liao Y Spatial ad temporal variatios ad cotrollig factors of potetial evapotraspiratio i Chia: Joural of Geographical Scieces, 16, Gog L, Xu C, Che D, Halldi S, Che Y D Sesitivity of the Pema-Moteith referece evapotraspiratio to key climatic variables i the Chagjiag (Yagtze River) basi. Joural of Hydrology, 329, Gozalez-Hidalgo J C, Lopez-Bustis J A, Stepek P, Marti-Vide J, de Luisa M, Mothly precipitatio treds o the Mediterraea frige of the Iberia Peisula durig the secod half of the twetieth cetury ( ). Iteratioal Joural of Climatology, 29, Goyal R K Sesitivity of evapotraspiratio to global warmig: a case study of arid zoe of Rajastha (Idia). Agricultural Water Maagemet, 69, Hargreaves G H, Samai Z A Estimatig potetial evapotraspiratio. Joural of the Irrigatio ad Draiage Divisio, 108, Hobbis M T, Ramrez J A, Brow T C Treds i

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