Dominant Climatic Factor Driving Annual Runoff Change at Catchments Scale Over China

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , such ff to estimate ff and a 1–3 % de- ff . The results show that the n change, we chose the climate elastic- is precipitation in the most part of China, ff ff erent regions of China. The reduction of pre- . In addition, there are large spatial variations 12912 12911 ff ff response to climate variables change and detect the ff 1 was represented by a parameter ff . It is of great significance of climate elasticity of runo ff and H. Yang change at catchments scale over 1,2,3 ff have been observed in many di ff This discussion paper is/has beenSciences under (HESS). review Please for refer the to journal the Hydrology corresponding and final Earth paper System in HESS if available. State Key Laboratory of Hydro-Science and Engineering, Department of Hydraulic Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic University of Chinese Academy of Sciences, Beijing, 100049, China crease in evapotranspiration atriver most basins in regions north in Chinaas China have the exhibited (Liu Shiyang obvious River et decline Basin in al.,Tang (Ma mean et et 2014). annual al., al., runo Most 2008), 2007; the of Cong Yellow River the et Basin (Yang al., et 2009), al., 2004; and the Hai River Basin (Ma et al., 2010). The cipitation occurred in theand Hai River the Basin, Yellow the River upper(Yang Basin, et reach of al., and the 2014). the Yangtze1966 River A increase to Basin 29 occurred 2011, % which in decline would the of have in surface lead wind the to speed western a occurred 1–6 China % in increase China in during runo in climate type and geographying characteristics the over spatial China. variation To ofdominant get runo a climatic better factor understand- drivingity annual method runo proposed bycharacteristics on Yang runo and Yang (2011), where thenet impact radiation of in the the lowerRiver catchment reach Basin of and Yangtze River the Basin, southeast the area, Pearl and River wind Basin, speed the in Huai part of1 the northeast China. Introduction Climate change has becomehydrology increasingly cycle significant, and and the it waterruno has resource management. important Changes impacts in on climatic factors and dominant climatic factor driving annual runo Abstract With global climate changes intensifying, thehas hydrological attracted response to more climate attentions. changes also It for is water beneficial resourceschange not planning on only and runo for management hydrologythe to impacts and reveal of ecology the climatic but impacts factors of on climate runo Dominant climatic factor driving annual runo China Z. Huang 1 Engineering, Tsinghua University, Beijing,2 100084, China Sciences and Natural Resources Research,Beijing, Chinese 100101, Academy China of3 Sciences, Received: 13 November 2015 – Accepted: 5Correspondence December to: 2015 H. – Yang Published: ([email protected]) 15 December 2015 Published by Copernicus Publications on behalf of the European Geosciences Union. Hydrol. Earth Syst. Sci. Discuss.,www.hydrol-earth-syst-sci-discuss.net/12/12911/2015/ 12, 12911–12945, 2015 doi:10.5194/hessd-12-12911-2015 © Author(s) 2015. CC Attribution 3.0 License. 5 25 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ff ff . The φ ), net ra- to climate change to P ff ff ) were derived, 2 U ), mean air tempera- P change as: ects of precipitation and air ff ) is the derivation to ff ), and relative humidity (RH), φ ( 0 U 0 ects of climatic factors on runo F ff ): , (4) erent climatic factors. For example, ff R elasticity to precipitation ( ( ff RH ff change is still unknown in many catch- dRH ff RH , (3) ε E + 12913 12914 E ∆ ), wind speed ( 2 elasticity to precipitation ( ) 2 T U ) U ff φ d ( φ 2 ( 0 are the runo 0 U 0 F ε ect water generation and concentration. However, the − ff RH φF + ) on annual runo ε 1 P T − d was evaluated in the upper reach of the Yellow River Basin T ) is a Budyko formula and ), relative humidity (RH), and wind speed ( P ε ff n φ P ( , and ∆ R + 2 0 , Fu et al. (2007) calculated the runo U # F n ff n ) ε , (2) R ) to precipitation and potential evaporation change: R and then detecting the dominant climatic factor driving annual runo , φ T d , (1) are the precipitation elasticity and air temperature elasticity, respec- ( T φ T ff d ( ff 0 and 0 ε P b Rn 0 b F P erent climatic factors. By taking advantage of the mean annual climatic d change can be expressed as follows: ε , ε ε ) n ff − at catchments scale over China, and (3) estimating the impact of climate ff φF R + + R 1 ff E/P ε , ), mean air temperature ( is the precipitation elasticity. To consider the e P and P n + , P P P = d d ( P R P a 1 P a P ε ε φ ε ), net radiation ( " ε ε ε T = = = = A simple climate elasticity method was firstly defined by Schaake (1990) to estimate There are several approaches to investigate the feedback of annual runo Five categories of methods can be used to estimate climate elasticity (Sankarasub- There are large spatial variations in both geography characteristics and climate type R R R R R R R R d ∆ d d change, such as theArnold hydrologic and models Fohrer, 2005), (Yang the et climate elasticitymanian al., method et (Schaake, 1998, al., 1990; 2000; 2001) Sankarasubra- and Arnoldelasticity the et method statistics was al., method widely (Vogel 1998; used et insuch al., quantifying as 1999). the in Therein, e the the Yellow climate RiverRiver Basin Basin (Zheng (Xu et et al., al.,River 2013), 2009; Basin the Yang and (Ma Chao–Bai Yang, et Rivers 2011), Basin al., the (Ma 2008; Luan et Yang and al., Yang, 2010), 2011). andthe the impacts Hai of precipitation ( ments of China. diation ( where where climate elasticity of runo by using Eq. (3) (Zheng etYang and al., 2009). Yang To (2011) evaluate the proposedman impact an from equation analytical other and climatic method, factors, the whichchanges annual was in water based di balance on equation, the to Pen- quality the runo ture ( factors in the study period, the runo temperature on runo response of runo ramanian et al., 2001),many and studies the analytical because derivation itamount method of is has historical observed not been data. widely only Arora used (2002) clear in projected in a equation theory to calcuated but the also does not need a large decline in land surfacechanges wind in speed precipitation could may lead a dominant to climatic decrease factor driving in annual evapotranspiration and runo where where tively. and the runo variation on runo change. over China, which wouldmate result change. in Therefore, a theproposed large current by variation Yang study and in aims Yang (2011), thetors to: (2) to hydrologic evaluating (1) runo the response further climate to elasticity validating of cli- the climatic method fac- hydrologic processes have been influenced by di respectively. However, this method washumid only Northern tested China. in several catchments of the non- 5 5 15 10 25 20 10 20 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 0 0 E ∂T and ∂E , the 0 0 2 1 T E ∂U ∂E = , 4 and n 0 ε 0 , ∂E ∂R at catchment n 0 E , R 0 ∂E ∂R n + 0 ∂E ∂E E R E , = = ∂P ∂E 3 , respectively; and they ε P , Yang and Yang (2011) 0 ff , (8) E /λ s . (10) . The potential evaporation e and 0 E P to runo 0 E RH RH) 0 dRH − to changes caused by the changing in 6 E P − ff ε ff ∂E/∂E 2 )(1 ε − 2 and change. + U = ff P 2 2 2 U ε U erence method, while d 12915 12916 ff , (9) 5 0.536 ε and + 2 RH ε dRH P ) 6 + can be expressed as follows: erential method. ε E T ff ff − + d 6.43(1 symbolize the runo 4 P ∂E/∂P 2 . Due to the complex relationship between ∗ γ , (11) 2 ε − ∗ 0 U 2 U γ (1 RH d ε represents the characteristics of the catchment, for exam- ∂E ∂ 5 ∆ + RH = + ε 0 n + 1 E + n RH . (6) + n ∗ ε 2 and RH , (7) R R /n = 0 T U ∗ /λ 2 are the elasticity of potential evaporation to net radiation, air temper- d 0 1 ) d 6 E , (5) 3 U 6 + E 4 are the climate elasticity of runo d ε G ε n , ε ∗ ε ∗ /n 2 P 2 2 , T P − 1 0 5 T ε ε ε + n was calculated by finite di ε , and RH, respectively. The largest one among them is considered as the E + + n n 0 , + + ∗ n R n ∗ P n n 0 2 4 0 ( , and E R ) can be evaluatedby the Penman equation (Penman, 1948): 0 R R P P R ε and U 0 2 E ∂T 1 d γ P P , ∂E E , + d d ∗ , − 3 1 3 + ∂U ∂E 1 1 n ∆ T ε ε P ∗ ε − 0 2 ε ε P , ∆ + U E P = were calculated by finite di n P = = R = 0 = = 0 0 Substitution of Eq. (9) into Eq. (7) leads to: Similar to Eq. (7), the response of potential evaporation to climatic factors can be = = ∗ , R E R 0 RH 5 R E R ∂E ∂ d d d To attribute the contribution of changes in derived a new equation: where value of Denoted Eq. (10) as follows: R ature, wind speed and relative humidity, respectively. Therein, ε where P estimated as: can be estimated as E and the physical meaning of these symbols were shown in Table 1. 3 Data and method 3.1 Study region and data Catchment information data setof was the collected People’s from Republic the of Ministry China of (Water Water Resources Resources and Hydropower Planning and dominant climatic factor driving annual runo (mmday where where the parameter 2 Climate elasticity method based onAt the catchment Budyko hypothesis scale, thereand potential is evaporation, abvious which is relationshipAn referred analytical between as equation the evaporation, of Budyko precipitation the hypothesis Budyko (Budyko, 1961). hypothesis was inferred by YangE et al. (2008): ple land use andet al., coverage 2014). change, The vegetation, water slope balance equation and can climate be simplified seasonality as (Yang scale for the long term, so runo R 5 5 10 15 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ratio ff was calculated s R n N 0.9 + 0.1 are parameters which were was calculated according to s . (14) n # b 4 and min s T a 237.3 273.15) + + ) can be calculated by the observed wind 17.27 min 1 min T − T 12918 12917 ( + 2 4 , ms ) can be estimated as follows: exp 2 α . (15) + U 10 , (12) U ! 273.15) ratio ( s is estimated as: max e ff + s 0.75 . (16) T 237.3 e = /n + RH ) was calculated as: max 1 100 , (13) 1 T a ( − n r 17.27 max R 0 " P T 5.42) E σ day + − n N 0.14 2 n − 0 z − s − E × 4.87 exp R s . ) s b − is the extra-terrestrial radiation; and P α 0.34 + 1 (MJm a ln(67.8 s − n

R = z a in two inland catchments in Xinjiang province. Hence 207 third-level catchments and R (1 U × 0.3054 ff P R 0 = = = E = To validate Eq. (7), two catchments were chosen, namely the Luan River Basin and Since only 118 weather stations directly measured solar radiation, the daily net radi- To get the annual climatic factors in each catchment, firstly, a 10 km grid data set, Meteorological data, obtained from 736 weather stations during the period 1961– = n s , 2 s speed at 10 m height (Allen et al., 1998): U Wind speed at a height of 2 m ( α Based on Eq. (6), the runo the upper Hanjiang Rivernorth Basin China, (shown is in a part Fig.75–85 of % 1b). Hai of The River Basin. which Luan Itlying River concentrates has in Basin, a from mean the located June annual middle in precipitation totributary and of September. of lower 455 mm, the reaches The Yangtze of River, Hanjiang finally the River flows Yangtze River Basin, into Basin, Danjiangkou reservoir which and is has the a largest length 3.2 Validation of the climate elasticityTwo method steps were taken for theing validation of Eq. the (7) climate and elasticity validating method, Eq. namely9). ( validat- where calibrated using the dataet at al., 2006). the In 118 Eq. (12), stations with solar radiatione observations (Yang Furthermore, the catchment characteristicsα parameter ation climatic factors were anwhich inverse-distance must weighted consider technique, the except influence of air elevation temperature (Yang et al., 2006). which covers the studyteorological area, data. Secondly, was according preparedof to for the cliamte interpolation 10 factors km from grid of the data each observed set, catchment the me- were average values calculated. The interpolation method for R the period 1961–2010 was collected from 118 weather stations. and the physical meaning of these symbols were shown in Table 2. 2010 from the China Meteorologicalface Administration mean (CMA), air included temperature, precipitation, maximumtive sur- air humidity, temperature, sunshine minimum hours, air and temperature, wind rela- speed. In addition, daily solar radiation during were available. Chinese water resourcesare 10 zoning first-level was basins, divided 80in level s-level Fig. river by 1a). basins level, Therein, and and there areruno 210 there no third-level observed river meteorological basins data in (shown were Taiwan selected Island and in no this study. by using the Angström formula (Angström, 1924): R Design General Institute, 2011). In the data set, catchment boundary and runo 5 5 20 15 10 15 10 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . ∗ 0 ∗ 0 E E has ff 3–1 %. High − ective statisti- erent methods ) as: ff ff ∗∗ 0 to anthropogenic E ff which were estimated , (17) ff to climate change both in ,RH) ff 2 U , 0 indicates an increasing trend, n R , β > T ( change were analyzed by hydrologi- f ff − 19.0 % in the upper Hanjiang River Basin, − dRH) 12920 12919 + 0 ,RH E 2 U 19.6 and d − + 2 U , n , (18) 21.4 % in the upper Luan River Basin, 12.4 and 9.1 % in the , to evaluation the error of Eq. (9). change in Danjiangkou Basin by using three di R # ∗∗ − 0 d ) ff represents the Penman equation. Then, the first approximation is the magnitude of trend, and i E ) + f i x β n − − R j j , ( x T 14 and ( . The relative errors (shown in Fig. 2b) mostly ranged from d − x " + ; where = is T 0 indicates a decreasing trend. ( y ff f i < j = β < median 0 0 Figure 2a showed the relationship between the potential evaporation change eval- Equation (9) is the first-order Taylor expansion of Penman equation. On one hand, = E E d was compared with The mean annual precipitation, nethumidity radiation, for air each temperature, catchment wind during speed, 1961–2010 and were shown relative in Fig. 3. The mean annual correlativity of them and the smallmaked relative it errors showed possible the accuracy tofactors of variation. express Eq. (9), potential which evaporation change as4.2 a function The of mean cliamtic annual climatic factors β for all and 4 Result 4.1 Validation of the climate elasticityTable method 3 showed the comparison of climate contribution to runo the line uated by Eq. (9) and that evaluated by Eq. (17), and most of the point were around which were estimated by thespectively. climate The result elasticity provided method a and strong theto evidence for hydrological evaluate using models the the re- climate climate elasticity elasticityhumid method and and arid the catchments. response of runo where the function 3.3 Trend analysis The Mann–Kendall (MK) nonparametric test (Kendall, 1990) is an e lower Luan River Basin and cal tool for trend(Mainment, detection, 1993). especially The MK for nonparametric hydrological testtion and is processes. widely meteorological The used time sample for its data series but convenient are calcula- they not necessary must to becance obey serially levels some of specific indenpendent. the distribution, trend In ofset this the at study, hydrological 0.05 and we and meteorological firstly 0.1, time and series evaluated then which the estimated were signifi- the slope of the trend: by the climate elasticity methodto and runo the hydrological models. The climate contribution of about 925 km and an elevation of 3500–88 m. In the two catchments, runo activities and climate change inet the al. Luan (2014) River Basin exploredties by the variation using to contributions the runo GBHM from model. climate Sun change and catchment proper- we firstly evaluated the climate elasticityradiation, of relative potential evaporation humidity, to wind airfurther speed temperature, net estimated and the the change in change potential in evaporation according these Eq. climatic (9), denoted factors, as and a remarkable change, and the causes for runo including climate elasticity and decompositionmodeling methods, method. To and validate the the dynamic climatewere elasticity hydrological compared method, with the the results results given in by Eq. references (7) Xu et al. (2013) and Sun et al. (2014). On the other hand, we calculated the potential evaporation change ( cal models. Xu et al. (2013) assessed the response of annual runo 5 5 20 15 10 15 20 25 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . 2 1 3 ff U − − 0.5 ε − 0.05), in the ). The < 1 C, with 1 ◦ − 2 − U p < , 1 < ε − 3.3–23.8 0.95 change. The high − − which had a similar ff 0.5 %decade 1 11 %decade − 0.05), while small de- − − p < 2.5 %decade 10–10 % increase in runo − ranged from 1.1 to 4.75 (2.0 1.7 to − ) and decreased in the south- 1 − P ranged from 0.05 to 3 (0.74 on ) in China, of which the largest − ε 1 5 to 0.1 to 0.1, indicted that a 1 centi- − RH − − ε day to the climatic factors for each catch- 2 in the northwest inland to 1883 mma ff − 1 0.5 on average) runo , and the high value occurred in the north − 1 − − ) occurred in the majority of the southeast. 1 0.05), while small decrease (ranging from 12922 12921 − 0.5 mostly occurred in southern and northwest 2 % ( − − p < < n R had a range of 0 to 1176 mma 0.22 on average). The high value of 0.05) increase in wind. Relative humidity increased in ff Cdecade 0.1 to ◦ < ε , ranged from 1.1 to 1.5, occurred in southern China. The − in the upper reach of Yangtze River Basin. Only 5 catch- − P 1 ε p < − 0.1 − 2.0 mostly occurred in the Huai River Basin, the Liao River to the air temperature change varied from geographic position 0.94 ( ered from 3–10 (MJm − ff ff − ) occurred in the Hai River Basin, the Huai River Basin and the 1 < 0.05) and decreased in Yellow River Basin, Hai River Basin and the mostly occurred in the Huai River Basin, the Liao River Basin, and − n R P ) occurred in the majority of the northern China. No significant change 1 ε p < ) mainly occurred in the northern China ( − 1 , 1 %decade < ε 0.01 to 1 − − − − change caused 0.5 n − R 3 %decade − . The annual mean runo . The lowest value of ff ff Cdecade 0 %decade ◦ − The net radiation di Air temperature increased all over the China. Large increase (rangingWind from speed 0.4 to decreased in most catchments, ranging from Net radiation showed a decrease in most catchments. Large decrease (ranging from A 1 % 6 to crease (ranging from 0 to 0.4 lower reach of Yangtze River Basin ( trend was shown in the Qinghai–Tibet Plateau. 0.8 ment showed significant ( the western China (the maximum is about 3 %decade ranged from mostly occurred in theaverage), north and China. the distributions The of value them of agreed with that4.4 of precipitation. Changes in the climatic factors The changes in climatiction factors in were precipitation change shown which11 in %decade increased Fig. in 5. the northwest There China is (ranging a from large 5but to spatial there varia- were no significant change trend shown in 63− % of these 207 catchments. to southeast to east China and the Yangtzechange River trend Basin of (ranging relative from humidity agreed with the change of precipitation. upper reach of Yangtze River Basin (ranging from and had no rules, and the reason will be discussed in discussion part. The value of in the southeast coastalthe area, southeast and to it the had northwest. a typical spatial variation of decreasing from a typical spatial variation of2 decreasing m from height the in south Chinaand to ranged the the from coastland north. 1 and The to the windity, 4 lowest ms which speed value occurred in ranged in from Sichuan 35correlation Basin. % The with in relative precipitation. humid- the According northwestruno to to Eq. 82 (6), % in we can the evaluate southeast, the had mean a annual positive precipitation in China, ranged from 30 mma value occurred in the Qinghai–TibetBasin. Plateau The and mean the lowest annual value air occurred temperature in Sichuan in China had a range of ment. In the 207on catchments, average), indicating precipitation that elasticity 1runo % change in precipitation leads to 1.1–4.75 % change in highest value of spatial variation with that of pricipitation. 4.3 Climate elasticity of the 207Figure catchments 4 showed the climate elasticity of runo value of the Hai River Basin, and the lower reach of Yellow River Basin. Basin, and the Hairelatively River small value Basin, of and the downstream of Yellow River Basin, and the China. The air temperature elasticity,grade ranging degree from increase inThe sensibility air of temperature runo will result in 5 5 15 20 10 10 15 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | P ε occurred . 1 change to small. ff − ff ff change were ff change. The contri- ff change, which was de- in the 207 catchments. change ranges from 12 10 %decade ff − ff ff ected the runo ff 18 to change change occurred in most catch- . − change ff 1 change occurred in the Qinghai– , while the largest negative contri- ff ff − , while in other catchments the net 1 ff 1 − − change occurred in most catchments change occurred in most catchments had a distinctspatial variation. Positive ff ff in Hai River Basin, part of the Liao River ff ff 12924 12923 . 1 − change was dominated by precipitation. In addition, the ranges 0–2 %decade ff small. ff ff 8 %decade − . While negative contribution mainly occurred in the central and north- 1 − 13 to , while in other catchments the wind speed e − 1 ected the runo − ff change was mainly determined by net radiation in the lower reach of the Yangtze ff Positive contribution of net radiation to runo Positive contribution of wind speed to runo Negative contribution of relative humidity to runo Positive contribution of air temperature to runo Figure 7 showed the contribution of climate factors to runo Wind speed elasticity, which stands for the sensitivity of annual runo Tibet Plateau and the northernmainly part occurred of the in northeast northwestPositive China, contribution and while and negative negative the contribution contribution eastern ofboth air China small temperature except to when runo compared for with the other northeast climatic factors. China. except for part ofthe the upper Liao reach River of Basin,6 Yangtze %decade River the Basin. positive In the contribution Hai reached River the Basin and most, ranging from 2 to except for the Qinghai–Tibet Plateau.reached In the the most, Hai rangingradiation River from e Basin, 3 the to positive 9 %decade contribution to 25 %decade east China.In the middle reachnegative contribution of reaches the the Yellow River most, Basin ranging from and the Hai River Basin, the ments except for partmidity of to the the change northwest of where runo the positive contribution of relative hu- contribution occurred in thethe western northwest China where and the the contribution of southeast precipitation of to China, runo especially in fined as the sumchange had of a the negative contribution contributionBasin, on the of runo middle climatic and factors. lower Generally reaches speaking, of climate Yellow River Basin and the southeast China, runo Figure 8 showed theIn dominant most catchments, climatic the factors runo driving runo River Basin, the Pearl River Basin,wind the speed Huai in River part Basin and of the theArea. southeast northeast, area, part and of by the Inner Mongolia and part of the northeast 5 Discussion 5.1 Climate elasticity The climate elasticity method is widelyments used in to evaluate China. hydrologic cycle Yang et inChina, many al. catch- which (2014) is calibrated the precipitationtation same elasticity elasticity with to were our be evaluated as result. 1.1in 2.6 to What’s the in more, 4.8 Chao–Bai the in in Rivers Luan previous Basinet River study, (Ma Basin al., the et (Xu 2013), precipi- al., et as 2010), al.,et as 1.4 2013), al., 1.4 as for to 2.4 2013), the 1.7 Beijiang as(Jiang in River et the 1.0–2.0 al., catchment Poyang in Lake 2007). of (Sun Those the the results Dongjiang Pearl were River River also in Basin catchment good (Wang of agreement with the our Pearl results River for Basin in the northwest, rangingbution from occurs 10 in to 30 the %decaderanging middle from reach of the Yellow River Basin4.6 and the Hai The River dominant climatic Basin, factors driving runo in the same regions. wind speed change, was negative across China with small sensitivity in the southern and had a positive contribution inChina. the Therein, northwest, the part largest of positive the contribution northeast from and climate the southeast change to runo bution of precipitation to the change of runo Figure 6 showed the contributions of climatic factors to the runo 4.5 Contributions of climatic factors to the runo 5 5 10 15 20 15 20 10 25 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0 − ∂T ∂E )(1 2 5.5 to but ig- U − ff 0.536 . The climate ff + 3 to 0 in China. − to climate change ff ranged from was negative mostly, 6.43(1 0 0 ects of climate change is small and the sign of γ ∆ ), and we can express ff γ ∂ ∂T 0 s ∂E s ∂E ∆+ e . ∂e ∂E , erent basins, but it had in- T with respect to temperature = ects on runo 0.1 in the 89 catchments of ff C, ∆ ◦ ff 0 s ( s − 1 e f and ∂e ∂E 10 and 0 = ), respectively. Due to their sub- ∆ s 0 ∂ T ∂E e increase caused by cliamte change T < ( 0.8 to E and 3 ff f − 0.59 for the entire Yellow River Basin; . Figure 9 showed the relationship be- 0.1 to 0.1, which were similar to other i varied in di 0 = s − as the change of temperature according − . e s 0 ∂T 0 ∂E s = . What’s more changeing air temperature e ∂T e ff ∂E ∂T RH) U ∂E − ε ect the atmosphere, which results in potential 12926 12925 ff )(1 ff 2 U ranging of ) and and between T U ( T 2 ε ranged from 0.3 to 1.9 (0.85 on average). From the λ f 0.536 + 0 s ecting runo ff and ∂e ∂E ∆ = 0.3 for the Futuo River catchment of the Hai River Basin ∆ 6.43(1 − was positive mostly. Next, we will analyze the value of . , (19) , (20) − ff ) s X 0 = G = ∂T − U ∂E ∂T would be important, and a degree global warming will result in X n ∂e | elasticity to potential evaporation, ranging from ε R 0 0 s ff ( ff . Furthermore, the derivatives and C, h is mainly determined by (kPa) as 0 ◦ increasing. What’s more, when ∂T ∆ 2 ∂e ∂E in 207 basins of China. ∂E ) T ∂ s ∂E γ T 0 10 ε 0 e γ + 1 E ∂T ect atmospheric movement, resulting in precipitation change (Gardner, ∆+ ∂E 2 ( ∆ can be expressed as: ff ε T > ∂T ∂ 0 = erential method. Denoting Eq. (8) as 0 = ∂T is the runo 0 ) and ∂E ff ∆ and . Xu et al. (2013) reported that the runo ∆ 4 1 ect of climate change to runo 2 ∂ ∂ ff ∂E ε ∂E − ff T ε . Figure 10 showed the trend of and 2 C ε = ◦ depends on /λ 0 = 0 The air temperature elasticity ranges from Changing in air temperature would a The net radiation elasticity and the relative humidity elasticity agreed with the result 10–3 % changes in runo T ∂T ∂T ∂E ∂E RH) to the connection between studies in the2014). same However, the regions air temperature (Yang elasticity andclimatic is obvious elasticities. Yang, small 2011; when Next, compared we Tang tosmall. et other will Air temperature discuss al., elasticity the 2013; is cause calculated Yang by why et the air following al., equation: temperatureε elasticity is would also a 2009). In fact, changeselasticity in method only air analyzes temperaturenores the have the direct indirect great impact impact. e temperature of Chiew on et air runo al. temperature (2009) on− evaluated runo that the indirect impact of air on runo 5.2 E similar to the result calculated by Tang et al. (2013) in the Yellow River Basin. where 9.3 (0.22 on average), while is small, which leads to the small value of evaporation change, further a Recently, many studies have been carried out to assesswere the 8.8 e and 9.2River mm Basin. simulated Tang et by al.in GBHM (2013) the analyzed and Yellow River response Basin the of bythe climate natural using two runo the elasticity methods climate also model elasticityin gave method in similar this and study. Luan conclusion. SWAT model, Their and results agreed with that revealed evaluated by Yang and Yangand (2011) 89 in catchments of Futuo the River Hai catchment River of and the the Yellow Hai River Basins River of Basin China and are also the Hai River andresult the in Yellow River the Basins same regions. of China. Those results were similar to our results, it could be found that the absolute value of crease trend as while when by the di Yang and Yang (2011) estimated tween where So the value of China and highwind sensitivity speed in elasticity theby Northern using China. the Yang climate andcatchment. elasticity Tang Yang et method, (2011) al. which calculated (2013) was estimated same with our result for the same (kPa stitution, 5 5 15 15 10 20 10 20 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | n R 0.1 to − 0.22 on change. − ff 10 mm and = P ∆ 0.01 to 0.94 ( − by adopting the Variable were considered as two . When P P T ε ) are not large, the error of ε change for each catchment. P ff ∆ ect of change in air temperature to ff 100 mm. Bao et al. (2012) estimated that change was determined by the geographic = 12927 12928 ff P . To verify the impact of the relationship between ∆ T ) and precipitation ( erences in climate and geography characteristics, 0 ff and the air temperature E in China, wind speed declines were often identified as n ∆ When ff R P but ignores the relation between climatic factors. And the ε must be evaluated as follows: ff n 0.1 to 0.1. Net radiation elasticity which ranges from was situation dependent. Wind speed decline tended to result was ignored, the relative error was less than 1 %, which was R − n ff change over China. We first validated the climate elasticity method R ff on in Futuo River catchment (Yang and Yang, 2011) and the Yellow River change. T ff . (21) ff T d n T ect of R ff ∆ ∆ to precipitation, net radiation, air temperature, wind speed and relative humidity, change by the climate elasticity method which only stresses on the direct impact 0.5 on average), wind speed elasticity which ranged from ff ff = − caused by first-order approximation can be discounted, but the error will increase n In addition, Eq. (10) is a first-order approximation, which probably results in errors in The dominant climatic factor to runo Previous studies reported that precipitation decrease was the dominantRemarkably, factor in of some catchments of the northeast, the Inner Mongolia and the In the 207 catchments, precipitation elasticity, which was low in in southern China 2 ( P R evaluated by Yang and Yang (2011) in the Futuo River Basin. the estimating of climate elasticity.in Yang et potential al. evapotranspiration (2014) ( evaluated that when the changes McVicar et al. (2012) stressedtranspiration that and the runo impact of wind speed change on actual evapo- in the decline of actualin evapotranspiration wet and complementary river increase basinssimilar of to but streamflow our has results. littlemeteorological In factors impacts previous on in runo studies, when dry assessing basins the (Liu impacts et of al., changes in 2014), which was conditions and climate. In thisruno study, we analyzed the contributionof of climate climatic change factors to on runo ε with changes increasing with a 0.5–5 % relative error in being important (Tang etpart al., 2011; of the Liu Inner etchanges Mongolia al., and and 2014). the stable part And precipitation, of in windfactor speed the the to decline northwest runo part became area, the of main due the contribution to northeast, the small hydrology northwest Area, declining wind speed has the greatest contribution to runo a 5–50 % relative error in or small part ofthe the Huai northwest River and Basin,elasticity, high ranged ranging in from from the 1.1 Liao to− River 4.75 Basin, (2.0 the on Hai average). The River Basin, air temperature Basin (Tang et al., 2013), which agreed with our result. we divided Chinaruno into 207 catchments,and and estimated then the contribution evaluated of the climate factors climate to elasticity runo of a 100 mm increase in precipitationInfiltration causes Capacity 20 % (VIC) increase model. in 6 Conclusions In this study, we used the climatedriving elasticity annual method runo to reveal the dominantwhich climatic was factor firstly derived bycountry Yang with and remarkable Yang (2011). spatial On di account of China being a vast net radiation and air temperaturechange on in Eq. (12), net the radiation e d is associated to the air temperature If the e independent elements. But in fact, according to Eqs. (12) and13) ( the net radiation 5.3 Error analysis In Eq. (10), the net radiation relationship needs further study. declining runo 5 5 25 10 15 20 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ff , J. Hydrol., 379, ff ect on annual runo ff in the middle reach of 1 − change, it was precipitation ff in part of the Liao River Basin, ff in the northwest China, while the ects of surface wind speed decline ff 1 8 %decade − − 13 to − 12930 12929 ect of climate change on mean annual runo ff ects on annual streamflow, Water Resour. Res., 43, W11419, ff This research was partly supported by funding from the National Natural ranged from 10 to 30 %decade ff impact assessment, J. Hydrol., 379, 172–180, 2009. ff There was a large spatial variation in climatic factors change. Precipitation increased Climate change had a negative contribution on runo Regarding the dominant climatic variable driving runo on modeled hydrologicaldoi:10.5194/hess-18-2803-2014, 2014. conditions in China, Hydrol. Earthon streamflow Syst. decrease in Sci., the Miyun 18, Reservoir catchment, 2803–2813, J.human Hydrol., 389, activity 317–324, on 2010. streamflow352, for 239–249, a 2008. river basin in arid region of northwest China, J. Hydrol., J. Hydrol., 265, 164–177, 2002. variables to climate change2306, 2012. in the Haihe River Basin, China, Hydrol. Process., 26,runo 2294– River Basin using a distributed hydrological model, Water Resour. Res., 45,to 335–345, assess 2009. climate changedoi:10.1029/2007WR005890, e 2007. 351–359, 2009. impacts of climate change simulated byChina, six hydrological J. models Hydrol., in 336, the 316–333, Dongjiang Basin, 2007. south 1990. assessment Part 1: Model development, J. Am. Water Resour. As., 34, 73–89, 1998. ing crop water requirements, FAO Irrigation Drainage Paper 56, FAO, Rome, 1998. applied watershed modelling, Hydrol. Process., 19, 563–572, 2005. Ma, H., Yang, D., Tan, S. K., Gao, B., and Hu, Q.: ImpactMa, of Z., climate variability Kang, and S., human Zhang, activity L., Tong, L., and Su, X.: Analysis ofMainment, impacts D. of R.: climate Handbook variability of and Hydrology, McGraw-Hill, New York, 1993. Bao, Z., Zhang, J., Liu, J., Wang, G., Yan, X., Wang, X., and Zhang, L.: Sensitivity of hydrological Budyko, M. I.: The heatChiew, balance F., of Teng, the J., Earth’s surface, Vaze, Sov. J., Geogr., 2, and 3–13, Kirono,Cong, 1961. D.: Z., Influence Yang, D., of Gao, global B., climate Yang, H., modelFu, G., and selection Charles, Hu, S. on P.,and H.: Chiew, F.H. Hydrological S.: A trend two-parameter climate analysis elasticity of in streamflow index the Yellow Gardner, L. R.: Assessing the e Jiang, T., Chen, Y. D., Xu, C. 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Research Program 51379098 (20131089284). and In addition, 91225302), this research and benefited the from Tsinghua University in most of the 207and catchments, the net southeast, radiation and in wind the speed lower inAcknowledgements. reach part of of Yangtze the River northeast. Basin in the northwest Chinaupper and reach decreased of in Yangtze Yellow River Riverments. Basin, Basin. Air Hai Net temperature River radiation increased Basin showedcatchments all and and a the over the decrease change the of in relative China. most humidity Wind agrees catch- with speed the decreased change of in precipitation. most average) and relative humidity elasticity whichhad ranged similar from distributions 0.05 with to precipitation 3 elasticity. (0.74 on average) the Hai River Basin, the middleeast and China, lower reaches and of Yellowand River had Basin the a and southeast the positive south- China.change contribution what’s to in more, runo the thelargest largest northwest, negative contribution positive part ranged contribution from of from the climate northeast the Yellow River Basin and the Hai River Basin. 5 5 25 30 10 15 20 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | to recent ff ects of climate ff ects of climate change ff to assess the e ff erent distributed hydrological models ff 12932 12931 across China, J. Hydrol., 517, 607–616, 2014. ff in the Luan River Basin, China, Hydrol. Res., 44, 940–952, 2013. ff , Water Resour. Res., 47, 197–203, 2011. ff erent methods, J. Hydrol., 508, 170–180, 2014. ff energy balance equation, Water Resour. 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Yang, H., Yang, D., Lei, Z., and Sun, F.:Yang, New H., analytical Qi, derivation J., of Xu, the X., mean Yang, annual D., water– and Lv, H.: The regional variation in climate elasticity and Zheng, H., Zhang, L., Zhu, R., Liu, C., Sato, Y., and Fukushima, Y.: Responses of streamflow to Yang, D., Herath, S., and Musiake, K.: Comparison ofYang, di D., Li, C., Hu, H., Lei, Z., Yang, S., Kusuda, T.,Yang, Koike, D., T., Sun, and F., Musiake, Liu, K.: Z., Analysis Cong, of Z., and Lei, Z.:Yang, H. Interpreting and the Yang, D.: complementary Derivation relationship of climate elasticity of runo Mcvicar, T. R., Roderick, M. L., Donohue, R. J., and Van Niel, T. G.: Less bluster ahead?Penman, Ecohy- H. L.: Natural evaporation from open water,Sankarasubramanian, bare A., soil Vogel, and R. grass, M., P. Roy. and Soc. Limbrunner, Lond., J. F.:Schaake, Climate J. elasticity C.: of From streamflow climate to flow, in:Sun, Climate S., Change Chen, and H., US Ju, W., water Song, resources, J., edited Zhang, H., by: Sun, J., and Fang,Sun, Y.: E Y., Tian, F., Yang, L., and Hu, H.: Exploring theTang, B., spatial Tong, L., variability Kang, of S., contributions and Zhang, from L.: Impacts of climate variabilityTang, on Q., reference Oki, evapo- T., Kanae, S., and Hu,Tang, H.: Y., Tang, The Q., influence Tian, of precipitation F., Zhang, variability and Z., partial and Liu, G.: Responses of natural runo Vogel, R. M., Wilson, I., and Daly, C.: Regional regressionWang, models Z., of Shen, annual Y., and streamflow Song, for L.: the Hydrologic response ofWater the Resources climatic change and based Hydropower on SWAT Planning andXu, Design X., General Yang, H., Institute: Yang, D., and Specification Ma, for H.: AssessingYang, the D., impacts of Herath, climate S., variability and and human Musiake, K.: Development of geomorphology-based hydrological 5 5 10 15 10 15 20 30 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cient ffi Stefan–Boltzmann constant 12934 12933 9 − 10 × 4.903 – solar radiation 1 − – wind speed at a height of 2 m –– slope of– the saturated vapor net pressure radiation vs.– air temperature curve soil heat flux psychrometric constant 1 2.45 latent heat of vaporization day − 2 − day 1 1 m − − 2 4 − 1 1 d d − 1 − − 2 2 − − − C C 1 ◦ ◦ − CC – – daily maximum air temperature daily minimum air temperature ◦ ◦ hh – – daily actual sunshine duration daily maximum possible duration of sunshine MJK dimensionlessMJm – albedo or the canopy reflection coe ms kPa – saturated vapor pressure kPa MJm kPa MJkg MJm Principal parameters of Eq. (12). Principal parameters of Penman equation. s s max min T T n N RH % – daily relative humidity R σ α Symbol Unit Value Physical meaning n 2 s RHU % – relative humidity Symbol Unit4 Value Physical meaning e R G γ λ Table 2. Table 1. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | two basins for and are M ) 0 (b) E ε R/R ∆ and P ε is the percentage 0.6 11.3 % 27.6 % 19.6 % 19.0 % O ) − Upper Hanjiang River Basin − − − − R by using the climate elasticity ff R/ ∆ is the percentage of 0 E / 0 E ∆ change (mm); ( 1.1 8.0 %31.4 % 3.0 % ff is mean annual potential evaporation (mm); − Lower Luan River Basin − − 0 E 12936 12935 is the characteristics parameter; change that was estimated by hydrological models n ff is the runo R ∆ 1.2 14.0 % 12.4 % 9.8 %6.2 % 30.8 % 1.8 % 21.4 % 9.1 % − − 2.2 2.1 1.6 − 34.0− 1.4 92.6− 1.4 352.0 1.0 River Basin 402.41257.4− 512.4 1207.5 850.0 1178.0 M O E ) ) ) 0 are the percentage of runo change that was observed; E E P ) ff / is the percentage of precipitation change (%); 0 R/R R/R R/R 0 P E R P/ 0 E P Spatial distribution of the third-level river basins in China and ∆ ∆ ∆ R/R is the mean annual precipitation (mm); ( ε ∆ ∆ ( n ε ( Catchments Upper Hanjiang P E ∆ P/ ∆ of runo P ∆ potential evaporation change; the precipitation elasticity and potential( evaporation elasticity, respectively; ( and the climate elasticity method, respectively. Comparison between the climate contribution to runo validation. Figure 1. (a) method and by using the hydrological models. Table 3. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | net are 02 (c) E C), ◦ and d 01 E (%) from 1961–2010, ∗∗ 0 E wind speed in 2 m height (e) air temperature (unit: (b) relative humidity, (d) 12938 12937 precipitation (unit: mm), (a) ), wind speed, 1 (unit: mm) in the 207 catchments during 1961–2010. − ff day (%) and that evaluated by Eq. (17) denoted as 2 ∗ 0 − runo E (f) Comparison between the potential evaporation change evaluated by equation ), and The mean annual 1 − the relative error (%) caused by the first-order approximation, where d (b) Figure 3. radiation (unit: MJm (unit: ms Figure 2. (a) Eq. (9), denoted as and the potential evaporation change (mm) calculated by Eq. (9) and that by Eq. (17), respectively. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | N N N

net ° ° ° 0 0 0 1 5 3 relative (b2) )

in the 207 ( in the 207 ﬀ E E

(e1) ° ° ﬀ 0 0 2 2 1 1 ), 1 − N N N

° ° ° net radiation (unit: of runo 0 0 0 5 3 1 E E

° ° air temperature elas- 0 0 RH 0 0 5 precipitation, 1 1 0 1 . . ε 0 0

(b1) 0 5 ) -

0 - - . (c)

E 5 0

1 0 ( . . - 0 , ), . 0 0 d - - 0 0 n n 1 E E e

(a2) R ° ° g − e 0 0 2 2 E E L ε

1 1 ° ° 0 0 8 8 0 0 0 . . . E E

1 2 3

° ° - - -

0 0 6 6 6 0 0 . . . ) 1 1

0 1 2 relative humidity to runo B

( E E

5 5 5 ° ° . . . 0 0 wind speed (unit: decade 0 1 2

2 2 - - - 1 1

0 1 1 . . . d (e2) 0 1 2 n E E

e ° ° g 0 0 e 8 8 L (d1) ), E E

1 ° ° relative humidity elasticity 0 0 − 0 0 1 1 12940 12939 net radiation elasticity )

D (e)

5 0 5 . . . ( 0 . 1 1 0 - - - 0 precipitation (unit: decade

- - - - (b)

E E

1 4 9 4 . . . . ° ° , 2 1 0 0 0 0 d - - - - wind speed, E E 2 2 n

and P 1 1 ° ° e 0 0 g e 8 8 2 ε (a1) L U ε (d2) E E

° ° 0 0 )

0 0 1 1 A

( 0 5 5 0 5 7 2 . . . 0 . 0 0 0 E E - - 0 -

° ° - - - -

0 0 ); and the signiﬁcance of the trends for 4 4 4 9 2 2 7 9 2 4 1 1 . . . . 1 0 0 0 0 d - - - - − n E E e

° ° g e 0 0 8 8 L 0 0 0 . . . E E 3 4 2

- - ° ° -

0 0 N N N 6 6 6

. . 0 0 . ° ° ° air temperature (unit: decade 2 3 1 1 1 0 0 0 air temperature, 1 5 3 Precipitation elasticity 5 5 5 8 . . . . wind speed elasticity 1 2 3 4

- - - - (c1)

1 1 1 1 d . . . . The changing trends for (c2) 1 2 3 4 n E E ), e

g ° ° (d) 1 e 0 0 8 8 L , − T ε N N N

1 ° ° ° 0 0 0 − 1 5 3 wind ) (d)

( E E

° ° 0 0 2 2 1 1 N N N

° ° ° 0 0 0 N N N 5 3 1

° ° ° E E 0 0 0

1 5 3 ° ° 0 0 0 0 ) 1 1

( 0

- % air temperature, 1

% - E E

1 ° ° - 0 d 0 0 n 2 2 e 1 1 E E

° ° ° ° 0 0 % 0 0 % 0 0 2 2 6 ) 6 .

1 1 1 1 % 2 1 . B - 0

1 ( - -

% % % 9 9 E E

1 2 5 ° ° . . 0 . 0 0 3 1 - - 0 2 2 1 1 d n net radiation, E E

e ° ° g 0 0 e 8 8 L in the 207 catchments from 1961 to 2010 (unit: (b) E E ﬀ

° ° 0 0 E E

0 0 ° ° 1 1 12942 12941 0 0 0 0 ) 1 1

D % % % %

% 2 4 6 8 ( . . . . 0 % %

% 2 4 6 8 5 5 - E E 5

- - - - % 1 2

° ° 5 - - -

% 0 0

- % % % %

5 2 2 1 1 1 1 % % 2 % 1 1 E E . 0 2 4 6 % 1 1

d 9 . . . . 0 ° ° 1 0 0 in the 207 catchments from 1961–2010 (unit: decade 9 n - 0 2 4 6 . . . 0 0 0 e . 0 0 9 8 8 g - 0 1 2 e ﬀ L precipitation, % % E E

% 0 3 % % ° ° 0 2 3 0 0

0 0

(a) 1 - - 1 -

0 0 -

E E

1 1 -

)

% %

° ° % % 1 1 0 0 9 A %

1 0 0 8 8 9 . . ( . 3 0 . 5 5 4 1 % % % % d - 5 1 2 - 0 E E

4 6 2 n

- e ° °

- - -

g 0 0 e 2 2 % % % % L 1 1 1 1 1 1 1 . 0 0 0 E E . . .

0 d 2 4 - 0 ° ° n 0 0 e 8 8 g e L N N N

° ° ° 0 0 0 5 3 1 E E

° ° N N N

ect of climate change to runo 0 0 ° ° ° 0 0 0 0 0 1 1 ﬀ 1 5 3 % % % 2 6 7 % % - 1

2 8 % - 0

1 9

- - -

- -

% % % % 9 % 1 % 3 9 9 . . relative humidity to runo 1 0 1 9 . The contribution of 7 . 1 0 0 . 8 . The e 1 1 5 ). E E 9 1 - - - 0 d

n ° ° 1 e 0 0 g 8 8 e − (e) L N N N

° ° ° 0 0 0 1 5 3

0.0012

- 20 E E

° ° R² = = 0.2783 R² 0 0 2 2 change in the 207 catchments from 1 1 y y = 0.0001x ﬀ 10 E E

° ° 12944 12943 0 0 0 0 in the 207 basins of China. 1 1 0 n ∂T n o ∂E i d o t i e t a e i a p t d i S a

p i d R and

c n t e i e r T W N P 0 d n 0 E E e

° ° g 0 0 e 8 8 0.006 0.004 0.002 -0.002 -0.004 -0.006 L N N N

° ° ° 0 0 0 3 1 5 -10 Dominant climatic factor driving annual runo Relationship between Figure 9. Figure 8. 1961 to 2010. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | s e and 4 5 2 (B) 2 9 1 5 5 . 1 8 0 2 7 +

9 . x T 0 4 0 = 8 0 . R² 0 =

y 5 5 5 5 2 1 0

. . .

2 1 0 s e -5 5 2 ) with temperature change. The blue curves are the 12945 s (A e (b) 8 5 9 1 3 0 . and 9 C), respectively. 0 9 ◦ 7 +

9 4 , respectively; the pink curves show the linear slope of . x T 0 7 T 4 = 0 (a) 0 . R² 5 0 = 2 to 20 with

y s − e 1 2 5 5 0 . . 0 1

0 0 . .

0 0 △ -5 of and 4 Relationship of ranging from T ( T with Figure 10. relationship