A global quantitation of factors affecting evapotranspiration variability

Journal Pre-proofs Research papers A global quantitation of factors affecting evapotranspiration variability Feng Shuyun, Jianyu Liu, Qiang Zhang, Yongqiang Zhang, Vijay P. Singh, Xihui Gu, Peng Sun PII: DOI: Reference:

S0022-1694(20)30148-7 https://doi.org/10.1016/j.jhydrol.2020.124688 HYDROL 124688

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Journal of Hydrology

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30 June 2019 24 January 2020 12 February 2020

Please cite this article as: Shuyun, F., Liu, J., Zhang, Q., Zhang, Y., Singh, V.P., Gu, X., Sun, P., A global quantitation of factors affecting evapotranspiration variability, Journal of Hydrology (2020), doi: https://doi.org/10.1016/ j.jhydrol.2020.124688

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1

A global quantitation of factors affecting evapotranspiration

2

variability Feng Shuyun1, Jianyu Liu1, Qiang Zhang2,3,4, Yongqiang Zhang5, Vijay P. Singh6, Xihui

3

Gu7, Peng Sun8

4 5 6

1Laboratory

of Critical Zone Evolution, School of Geography and Information Engineering,

7

China University of Geosciences, Wuhan 430074, China

8

2Key

9

Beijing Normal University, Beijing 100875, China

Laboratory of Environmental Change and Natural Disaster, Ministry of Education,

10

3State

Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal

11

University, Beijing 100875, China

12

4Faculty

13

Management, Beijing Normal University, Beijing 100875, China

14

5CSIRO

15

6Department

16

Engineering, Texas A&M University, College Station, Texas, USA

17

7Department

18

Geosciences, Wuhan 430074, China;

19

8College

20

Corresponding author: Qiang Zhang ([email protected]); Jianyu Liu ([email protected])

of Geographical Science, Academy of Disaster Reduction and Emergency

Land and Water, GPO Box 1700, Canberra ACT 2601, Australia of Biological and Agricultural Engineering and Zachry Department of Civil

of Atmospheric Science, School of Environmental Studies, China University of

of Geography and Tourism, Anhui Normal University, Anhui 241000, China

21

1

22

Abstract: Scientific viewpoints on the long-term hydrological responses to factors

23

other than climatic change remain controversial and yet the impacts of these factors are

24

often neglected at the short-term (such as monthly and annual) timescale. We developed

25

an analytical method to decompose evapotranspiration (E) variability to the variability

26

of precipitation (P), potential evapotranspiration (E0), total water storage change (∆S),

27

and catchment characteristics (n), such as vegetation, soil and climate seasonality.

28

Global assessment showed that P enhanced E variability in most regions, while

29

restrained E variability in some extremely humid regions. E0 controlled monthly E

30

variability in most the energy-constrained regions. ∆S had much larger impacts on E

31

variability at monthly scale compared to the annual scale, and restrained E variability

32

in many arid regions (P/E0 < 0.66). Catchment characteristics had larger impacts on E

33

variability in humid regions (P/E0 > 0.66), especially at annual scale. The dominant

34

factors of E variability varied with timescales and regions. At a global scale, P and

35

catchment characteristics are the dominant factors controlling global E variability at

36

monthly and annual scales, respectively; In humid regions, however, the impacts of E0

37

on monthly E variability are generally larger than the impacts of precipitation and

38

catchment characteristics. We highlight the necessity to consider the impacts of

39

catchment characteristics even at the short-term timescales, otherwise the simulation

40

and attribution of E variability would be significantly underestimated.

41

Keywords: Climate change; Global evapotranspiration; Attribution; Budyko

42

framework; Different timescales

43 2

44

1

Introduction

45

Quantitatively attributing the causes of global hydrometeorological change is

46

important to understanding the global hydrological cycle and energy balance, and

47

supports hydrological modeling, prediction, and management (Berghuijs et al., 2017;

48

Berghuijs and Woods, 2016a; Haddeland et al., 2014; Liu et al., 2017a; Yang et al.,

49

2017; Zhou et al., 2015). Recent global studies indicated that catchment characteristics

50

(as summarized by n or ω in Budyko framework, also named as “other factors”), such

51

as vegetation, soil and climate seasonality, have important impacts on water cycle at

52

long-term timescale (Berghuijs et al., 2017; Berghuijs and Woods, 2016a; Berghuijs

53

and Woods, 2016b; Chen et al., 2016; Gudmundsson et al., 2016; Gudmundsson et al.,

54

2017; Zhou et al., 2015).

55

Zhou et al. (2015) found that catchment characteristics had a larger impact on water

56

yield (runoff/precipitation, R/P) in more humid regions, and their contribution tended

57

to

58

evapotranspiration, P/E0). On the contrary, Gudmundsson et al. (2017) advocated that

59

catchment characteristics influenced water yield in more arid conditions and their

60

contribution decreased with the increase of wetness index. These discrepancies

61

demonstrated limited understanding of the roles of catchment characteristics in water

62

availability and variability under different dry-wet conditions, and their conflicting

63

results may cause divergence in both scientific conclusions and water management.

64

Therefore, revisiting the factors affecting hydrometeorological changes globally and

65

clarifying of the impacts of catchment characteristics are necessary for a better

increase

with

the

increase

of

wetness

3

index

(precipitation/potential

66

understanding of hydrometeorological processes under the changing environment.

67

The variability of E, which is directly related to water yield, reflects the sensitivity

68

of hydroclimatic responses to the changes of climatic variables and catchment

69

characteristics (Zeng and Cai, 2016; Zhang et al., 2016a). Recent years have witnessed

70

increasing efforts in the quantification of causes behind the E variability in different

71

regions and basins. Koster and Suarez (1999) were the first to derive the standard

72

deviation of E at annual scale based on the Budyko framework. Some studies extended

73

the Budyko hypothesis to a finer time scale for hydrological sensitivity and variability

74

analysis by considering total water storage change (ΔS) (Liu et al., 2018; Wang and

75

Alimohammadi, 2012; Ye et al., 2015; Zeng and Cai, 2015). Integrating the effect of

76

ΔS, Zeng and Cai (2015) developed a theoretical framework to assess the sources of E

77

variability from variance and covariance of P, E0 and ΔS:

78 79

𝜎2𝐸 = 𝑤2𝑃𝜎2𝑃 + 𝑤2𝐸0𝜎2𝐸0 + 𝑤2𝑇𝑊𝑆𝐶𝜎2𝑇𝑊𝑆𝐶 + 𝑤𝑃,𝐸0𝑐𝑜𝑣(𝑃,𝐸0) +𝑐𝑜𝑣(𝑃,𝑇𝑊𝑆𝐶) + 𝑤𝐸0,𝑇𝑊𝑆𝐶 ∙ 𝑐𝑜𝑣(𝐸0,𝑇𝑊𝑆𝐶)

(1)

80

This equation is meaningful to extend the hydrological attribution from long-term

81

timescale to short-term timescales, such as monthly and annual scales. Based on this

82

equation, Zeng and Cai (2016) evaluated the influencing factors behind monthly and

83

annual E variability across 32 large rivers over the globe. Also, some studies applied

84

this framework in attribution analysis of E and runoff (R) variability across China (Wu

85

et al., 2017; Zhang et al., 2016a). However, some issues need to be addressed in the

86

derivation and application of this equation in attribution analysis: (1) This method

87

attributes the variance of E to the variance and covariance of P, E0 and ΔS, e.g., 𝜎2𝑃 4

88

and 𝑐𝑜𝑣(𝑃,𝐸0), which makes it impossible to know individual contribution of a single

89

factor. (2) As shown later in this paper, such an approach prohibits accounting for the

90

impacts of catchment characteristics, such as vegetation, soil and climate seasonality,

91

on E variability, which biases the simulation and attribution, and needs to be resolved

92

if we want to a better quantify the attribution of E variability. Previous studies have

93

verified the significant impacts of catchment characteristics on hydrometeorological

94

changes at long-term timescale (Berghuijs et al., 2017; Jaramillo and Destouni, 2014;

95

Lin et al., 2014; Lin et al., 2010; Renner and Bernhofer, 2012), which may also play a

96

role in E variability at short-term timescales, such as monthly and annual scales.

97

However, no reports were found to quantify the impacts of catchment characteristics on

98

monthly and annual E variability, especially at global scale. As suggested by Zhang et

99

al. (2016a), future research is needed to assess the influences of catchment

100

characteristics on the E variability. Therefore, a new analytical method needs to be

101

developed with considering the impacts of catchment characteristics, as well as

102

focusing on the individual contribution of each factor instead of the covariance of two

103

factors.

104

Overall, previous global assessments only attributed the hydrometeorological

105

changes at long-term timescale (Berghuijs et al., 2017; Gudmundsson et al., 2017; Yang

106

and Yang, 2011; Zhou et al., 2015), and there are conflicting findings in the dominant

107

factors of hydrometeorological changes (Gudmundsson et al., 2017; Zhou et al., 2015).

108

Limited attention has been paid to quantitative attribution at short-term timescale (Wu

109

et al., 2017; Zeng and Cai, 2015; Zeng and Cai, 2016; Zhang et al., 2016a), but the 5

110

methods used in these studies only can assess the impacts of climatic factors without

111

considering the impacts of catchment characteristics. Furthermore, no systematic study

112

concerning the sources of monthly and annual E variability across the globe has been

113

published yet. Therefore, the objectives of this study are: (1) to propose a Budyko-based

114

E variability decomposition method with the inclusion of catchment characteristics to

115

assess the sources of E variability; (2) to clarify the impacts of catchment characteristics

116

on E variability under different dry-wet conditions; and (3) to evaluate global patterns

117

of the effects of P, E0, ΔS and catchment characteristics on the variability of E at

118

monthly and annual scales. This study can help shed a new light on

119

hydrometeorological responses to affecting factors over the globe in a changing

120

environment.

121 122

2

Methods and Data

123

2.1 Data

124

Global monthly terrestrial water cycle dataset (Greenland and Antarctica were

125

excluded), including P, E, R and ∆S (1984-2010, 0.5º spatial resolution), were collected

126

from

127

(http://stream.princeton.edu:8080/opendap/MEaSUREs/WC_MULTISOURCES_WB

128

_050) (Zhang et al., 2018). This dataset was merged from multiple data sources, such

129

as in-situ observations, remotely sensed data, land surface model outputs, and

130

reanalysis datasets. For example, the ∆S was merged by simulations from VIC model

131

and ensemble mean of ∆S product derived from GRACE. Compared to most dataset

Terrestrial

Hydrology

Research

6

Group

at

Princeton

University

132

from only one single data source, this dataset was known as the best available global

133

monthly dataset (Wu et al., 2018). Besides, a constrained Kalman filter data

134

assimilation technique was used to obtain the water balance for each month. In addition,

135

this dataset was validated by in-situ observations, such as the observed E data from the

136

FluxNet towers, and the runoff data from the Global Runoff Data Centre (GRDC), and

137

the United States Geological Survey (USGS), which shown that the dataset was reliable

138

and can be used to investigate the impacts of climate variability on hydrological cycle.

139

More details about this dataset, in terms of data sources, data assimilation procedures

140

and uncertainty quantification, can be found in Zhang et al., (2018). The global long-

141

term (1901-2015) monthly E0 dataset was calculated at 0.5° grid resolution by Harris et

142

al. (2014) from Climatic Research Unit (CRU) in the University of East Anglia

143

(https://crudata.uea.ac.uk/cru/data/hrg/), by using the Penman–Monteith equation

144

(Monteith, 1965; Penman, 1948).

145

2.2 Analytical derivation of E variability

146

The Budyko framework shows the water supply and available energy are the

147

controlling factors behind the mean E, which can be presented by a function of P and

148

E0. Based on the Budyko framework, several water-energy balance equations have been

149

deduced, among which the equations by Choudhury (1999) and Yang et al. (2008) have

150

been widely used：

151

𝐸=

𝑃𝐸0

(𝑃

𝑛

+ 𝐸𝑛0)

1/𝑛

(2)

152

where n is the controlling parameter, which can be calibrated by minimizing the least

153

squares errors between the simulated E by equation (2) and assessed E from Global 7

154

monthly terrestrial water cycle dataset. The n accounts for catchment characteristics

155

that impact the partitioning of P on E, such as vegetation, soil and climate seasonality.

156

Limited by steady-state assumption of Budyko framework, the equation (2) was

157

generally used at long-term timescale. Although several studies have applied it to

158

annual timescale, the assumption on ignoring the impacts of Δ S may be not valid.

159

Therefore, by considering the impacts of ΔS, previous studies have extended the

160

Budyko framework to shorter timescale (Wang and Alimohammadi, 2012; Zeng and

161

Cai, 2015):

162

𝐸𝑖 =

(𝑃𝑖 ― ∆𝑆𝑖)𝐸0𝑖

((𝑃𝑖 ― ∆𝑆𝑖)𝑛𝑖 + 𝐸0𝑖𝑛𝑖)

(3)

1/𝑛𝑖

163

where i is the time. If i is the month, this equation is a monthly water-energy balance

164

equation at monthly scale. Then the ni is the mean parameter in the Budyko model for

165

the ith month within one year during all the study periods (Tang et al., 2017; Xing et

166

al., 2018). If i is the year, that is an annual water-energy balance equation at annual

167

scale.

168

Hydrological cycle and water balance are not only controlled by climatic changes,

169

such as P and E0, but also regulated by catchment characteristics (n), such as vegetation,

170

soil and climate seasonality (Fig. 1). Besides, ΔS plays a more important role in the

171

water-energy balance at short-term timescale (Fig. 2), since water storage dynamics is

172

significant at monthly and annual scales (Chen et al., 2013). The E can be expressed as

173

the function of P, E0, ΔS and n, E=f (P, E0, ΔS, n). The total differential of E can be

174

expressed as:

175

𝑑𝐸𝑖 =

∂𝑓

∂𝑃𝑑𝑃𝑖

∂𝑓

∂𝑓

∂𝑓

+ ∂𝐸0𝑑𝐸0𝑖 + ∂∆𝑆𝑑∆𝑆𝑖 + ∂𝑛𝑑𝑛𝑖 8

(4)



176 177

Using a first-order approximation of E change, Eq. (4) can be rewritten as:

178

∆𝐸𝑖 ≈

∂𝑓

∂𝑃∆𝑃𝑖

∂𝑓

∂𝑓

∂𝑓

(5)

+ ∂𝐸0∆𝐸0𝑖 + ∂∆𝑆∆𝑆𝑖 + ∂𝑛∆𝑛𝑖

179

where ∆ represents the departure of a quantity during year/month i from its long-term

180

mean value.

181

To avoid variance and covariance in the analytical derivation, here we evaluate the

182

variability of E by using the mean absolute deviation (MAD), which shows a similar

183

ability to standard deviation (σ) in the evaluation of E variability (Fig. 3).

184

1

1

𝑁

1

𝑁

𝑁

𝑀𝐴𝐷𝐸 = 𝑁∑𝑖 = 1|𝐸𝑖 ― 𝐸| = 𝑁∑𝑖 = 1|∆𝐸𝑖| = 𝑁∑𝑖 = 1𝑠𝑖𝑔𝑛(∆𝐸𝑖) × ∆𝐸𝑖

(6)



185 186

where N is the sample size. Substituting ∆𝐸𝑖 from Eq. (4) into Eq. (5), we can develop

187

an analytical derivation for E variability:

188

1

𝑁

𝑀𝐴𝐷𝐸 = 𝑁∑𝑖 = 1𝑠𝑖𝑔𝑛(∆𝐸𝑖) ×

(

∂𝑓

∂𝑃𝑑𝑃𝑖

∂𝑓

∂𝑓

∂𝑓

)

+ ∂𝐸0𝑑𝐸0𝑖 + ∂∆𝑆𝑑∆𝑆𝑖 + ∂𝑛𝑑𝑛𝑖

(7)

189

The E variability predicated by Eq. (7) is referred to “simulation”; while the E

190

variability assessed by standard deviation with the E data from Zhang et al. (2018) is

191

referred to “assessment”. Eq. (7) can be presented as:

192

𝑀𝐴𝐷𝐸 = 𝐼𝑃 + 𝐼𝐸0 + 𝐼∆𝑆 + 𝐼𝑛

(8)

193

where 𝐼𝑃, 𝐼𝐸0, 𝐼∆𝑆 and 𝐼𝑛 indicate the impacts of P, 𝐸0, ∆𝑆 and catchment

194

characteristics on the E variability, respectively: 1

∂𝑓

𝑁

195

𝐼𝑥 = 𝑁∑𝑖 = 1𝑠𝑖𝑔𝑛(∆𝐸𝑖) × ∂𝑥𝑑𝑥𝑖

196

where x denotes each factor, including P, E0, ∆S, and n.

9

(9)

The absolute contribution of each influencing factor to the E variability (Cx) can be

197 198

quantified as (Hobbins, 2016):

199

𝐶𝑥 = |𝐼

𝑃|

𝐼𝑥 + |𝐼𝐸0| + |𝐼∆𝑆| + |𝐼𝑛|

× 100%

(10）

200

The E variability is subject to temporal shifts at different time scales, such as daily,

201

monthly, annual, and long-term time scales (Zeng and Cai, 2015). Ideally, the analytical

202

derivation of E variability can be applied to assess the sources of E variability at an

203

arbitrary time scale if the E variability can be calculated at that scale. In the current

204

study, we mainly evaluate the influences of P, E0, ∆S and catchment characteristics on

205

the monthly and annual E variability.

206 207

3

Results

208

3.1 Performance of analytical method

209

To verify the reliability of the analytical attribution method, we compared the

210

simulated E variability evaluated by analytical method with the assessed E variability

211

calculated by standard deviation (Fig. 4). Results shown that the analytical method can

212

well capture the E variability at both monthly and annual scales. At the monthly scale,

213

the determination coefficient (R2) and Nash-Sutcliffe coefficient (NSE) between

214

assessed and simulated E variabilities were 0.92 and 0.89, respectively, with a Root

215

Mean Square Error (RMSE) of 2.96 mm (Fig. 4a). If catchment characteristics were not

216

considered in the simulation, the simulated E variability was significantly

217

underestimated with a regression coefficient of 0.78, and the simulation accuracy

218

decreased with R2 and NSE of0.85 and 0.63, respectively (Fig. 4b). 10

219



220

At the annual scale, the R2 and NSE values were 0.90 and0.89, respectively, with a

221

RMSE of 5.16 mm (Fig. 4c). If catchment characteristics were not considered, R2 and

222

NSE reduced to 0.27 and -0.65, and the simulated E variability was also undervalued

223

(Figs. 4d). Furthermore, the simulation accuracy of E variability by the analytical

224

method in arid regions (P/E0 < 0.66) (Feng and Fu, 2013) (R2 ≥ 0.95) was higher than

225

in humid regions (P/E0 > 0.66) (R2 < 0.84) at both monthly and annual scales (Figs. 5),

226

implying larger uncertainty in the E behavior in humid regions than in arid regions.

227



228

The simulation errors also varied with latitude, and there are relatively larger errors

229

around equator. By contrast, the E variability was simulated using the method proposed

230

by Zeng and Cai (2015) , who deduced the variance of E into P, E0 and ΔS without

231

considering the n. Results shows that the E variability simulated by the method from

232

Zeng and Cai (2015) was subject to larger errors than that by the newly-proposed

233

method, and the simulated E variability was underestimated at most latitudes (Figs. 6).

234

This difference mainly because the method developed by Zeng and Cai (2015) ignored

235

the impacts of catchment characteristics.

236 237

3.2. Global patterns of E variability sources

238

Based on Eq. (9-10), we quantified the global pattern of contributions of P, E0, ∆S

239

and catchment characteristics to the E variability. Figures 7 and 8 shows the

240

contributions (measured by percentages) of each factor to E variability, as well as their 11

241

relationships with wetness index (WI; P/E0), at monthly and annual scales, respectively.

242

The positive value means the variability of one factor enhancing the E variability, while

243

the negative value means restraining effect. In general, similar global patterns of

244

contributions at the monthly scale can be observed when compared to that at the annual

245

scale. However, the P and catchment characteristics had larger impacts on the E

246

variability at annual scale, while E0 and ∆S had larger impacts at the monthly scale. In

247

addition, the impacts (including the positive and negative impacts) of P on E variability

248

tend to increase with the WI (wetness index; P/PET), while the impacts of ∆S, E0 and

249

catchment characteristics tend to decrease with the WI.

250



251

P had a positive impact on E variability in most regions across the globe. The

252

contribution of P in arid regions was evidently larger than that in humid regions,

253

epically at annual scale (Figs. 9 and 10), such as West Asia, North Africa, South Africa,

254

Gobi Desert, most regions of Australia, Southwestern America, and Patagonian Desert,

255

with the contribution larger than 50% (Fig. 7 and 8). On the contrary, the contributions

256

of P show negative values in some extreme humid regions, such as Amazon basin,

257

Congo basin, southeast Asia, which implies that more P lead to less E in these regions.

258

Because in these extremely humid regions E is mainly controlled by E0 rather than P.

259

More precipitation is often associated with less solar radiation and larger relative humid

260

(Díaz‐Torres et al., 2017; Solomon, 1967), which reduces the E0 and further leads to

261

the decrease of E (Fig. 11).

262

12

263

∆S had a larger influence on E variability at monthly scale than that at annual scale.

264

The contributions of ∆S are negative in many arid regions. Especially at annual scale,

265

the median contribution of ∆S for arid regions is -2.9%.

266

E0 had much great impacts on E variability in humid regions than that in arid

267

regions, especially at monthly scale, with median contribution of 36.3% for the former

268

while 1.9% for the later.

269

Catchment characteristics enhanced E variability across most regions across the

270

globe, while restrained E variability in some extreme arid regions, such as Sahara Desert,

271

Gobi Desert. Besides, the contributions of n to E variability at annual scale are much

272

larger than that at monthly scale, with median contribution of 41.9% for the former but

273

15.2% for the later.

274

3.3 Identification of key factors behind E variability

275

The key factors behind the E variability were different spatially (Fig. 12).

276

Precipitation is a more important factor behind monthly and annual E variability for 46%

277

and 42% of the global land grid cell, which mainly located in the arid regions.

278

Meanwhile, ∆S had the largest contribution to the E variability across 12% and 2% of

279

the globe at the monthly and annual scales, respectively. In this sense, ∆S had larger

280

impacts on E at shorter time scales, which is agree with the findings in previous study

281

(Wu et al., 2017; Zeng and Cai, 2016; Zhang et al., 2016a). Therefore, Budyko

282

framework should be cautious to use at short-term timescales when the ∆S data is not

283

available.

284

13

285

Regions with a largest contribution of E0 to the annual E variability only accounted

286

for 2%. On the contrary, E0 plays a key role in E variability at monthly scale, and

287

controls the E variability for 32% of global regions. Moreover, in the humid regions,

288

the impacts of E0 on E variability (with median contribution of 36.3%) were generally

289

larger than the impacts of P and catchment characteristics. Catchment characteristics

290

controlled monthly and annual E variability for 10% and 51% of global regions,

291

respectively, implying that catchment characteristics are the dominant factor for global

292

E variability at annual scale.

293

The above-mentioned results indicated that P is the largest contributor to monthly

294

E variability, while catchment characteristics is the largest contributor to annual E

295

variability. ∆S play an important role in E variability at monthly scale. E0 mainly

296

controlled monthly E variability in energy-constrained and moisture-adequate regions.

297

4

Discussion

298

This study has made incremental process on several important aspects of

299

hydrometeorological attributing study. First, a new quantitative framework was

300

developed to attribute E variability at short-term timescales, which has better

301

performance in simulation and attribution of E variability. Second, although several

302

global assessments have investigated the causes of long-term hydrometeorological

303

changes (Berghuijs et al., 2017; Berghuijs and Woods, 2016b; Gudmundsson et al.,

304

2016; Zhou et al., 2015), this study proposed the first quantification attribution of global

305

E variability at short-term timescales, i.e., monthly and annual timescales. Third, the

306

results clarified the roles of catchment characteristics in E variability and challenged 14

307

the widely held view that climate is the primary source of E variability while catchment

308

characteristics are secondary (e.g., Berghuijs et al., 2017; Wu et al., 2017). Our results

309

indicated that the dominant factor of E variability varied with timescales and dry-wet

310

conditions. At a global scale, precipitation played a dominant role in E variability at

311

monthly timescale while catchment characteristics dominated E variability at annual

312

scale; In humid regions, however, the impacts of E0 on monthly E variability are

313

generally larger than the impacts of precipitation and catchment characteristics.

314

Correctly knowledge of the causes of E variability is crucial for understanding of

315

hydrometeorological processes (Wu et al., 2017). Finally, some interesting results were

316

found in the causes of E variability. It is generally recognized that precipitation played

317

a positive role in E variability (Zeng and Cai, 2016; Zhang et al., 2016a). However, the

318

new finding of study is that precipitation restrains E variability in many extremely

319

humid regions, such as Amazon and Congo basins. In contrast, total water storage

320

changes strengthened E variability in most humid regions while restrained E variability

321

in many arid regions.

322

Some previous studies have applied the long-term Budyko equation to annual scale

323

and seems to get reasonable results when neglecting ∆S (Ning et al., 2017; Potter and

324

Zhang, 2009). This is owing to the limited impacts of ∆S on variability at annual

325

timescale (Figure 9b). Nevertheless, the assumption on ignoring ∆S may be not valid

326

(Zeng and Cai, 2016). The regulating effect of ∆S on hydrological response has been

327

well documented (Wang and Alimohammadi, 2012; Zhang et al., 2016a). In the dry

328

months or years, ∆S can provide available water for E and causes larger E than P, which 15

329

enable the Budyko curves poorly capture the E variability (Figure 2a). Due to different

330

roles of ∆S under different arid/humid conditions, ∆S tends to enhance E variability in

331

humid regions but restrains it in the arid regions (Figures 7-8), which is also supported

332

by the findings from Zeng and Cai (2016), Zhang et al. (2016a) and Wu et al. (2017).

333

The ∆S regulated the temporal distribution of water availability for E. In humid regions,

334

∆S hold P from the energy-limited period to a warm period, which increases E in the

335

periods with high energy supply and enhances E variability (Zeng and Cai, 2016). These

336

results imply that, given exclusions of the impacts of ∆S, E variability would be

337

overestimated in arid regions, and underestimated in the humid regions.

338

The P plays a dominant role in E variability in most arid regions. However, in the

339

humid regions, the effect of P on E variability is going to be significantly diminished.

340

By contrast, the E0 has much larger impacts on E variability in humid regions than that

341

in arid regions. These are because the E variability in arid and humid regions are

342

prevalently limited by available water and energy, respectively (Karam and Bras, 2008).

343

The controlling parameter n in Budyko type equation is considered to represent the

344

catchment characteristics, which not only related to vegetation, soil moisture,

345

topography, but also include climate seasonality (Ning et al., 2017), snow rates (Zhang

346

et al., 2015), and storminess (Milly, 1994). Previous studies have found that the values

347

of n have positive relationship with vegetation coverage, soil moisture, while negative

348

relationship with basin slope, climate seasonality, storminess (Li et al., 2013; Liu et al.,

349

2019; Liu et al., 2017b; Padrón et al., 2017; Xu et al., 2013). Based on the Budyko

350

framework, a larger value of n tends to result in a smaller E (Figure 2). Consequently, 16

351

the regions with larger vegetation coverage, higher soil moisture, smaller slope, lower

352

climate seasonality, and less storminess would expect to have a higher n value and a

353

larger E. We emphasized the necessity to consider the impacts of catchment

354

characteristics on the E variability, since previous attributing studies often ignored

355

impacts of catchment characteristics on E changes (Wu et al., 2017; Zeng and Cai, 2016;

356

Zhang et al., 2016a). This argument is not just conceptually important; it play a key role

357

in the attributing results of E variability. For example, Wu et al. (2017) found that E0

358

was the dominant influencing factor behind the annual E variabilty in most regions of

359

South China, which was different from the results shown in Fig. 12. This was because

360

that they only assessed the sources of E variability from climatic factors, but excluded

361

the impacts of catchment characteristics. Our study updated the standing findings

362

concerning the factors behind E (Wu et al., 2017; Zeng and Cai, 2016; Zhang et al.,

363

2016a).

364

Moreover, previous studies showed large errors in the assessment of E variability

365

(Wu et al., 2017; Zeng and Cai, 2016; Zhang et al., 2016a). By attributing monthly E

366

variability to P, E0 and ∆S, Wu et al. (2017) found that the simulated E variability was

367

significantly underestimated, especially in humid regions. Also, the similar cases were

368

obtained in some large river basins over the world (Zeng and Cai, 2016) and lots of

369

small basins across China (Zhang et al., 2016a). Therefore, the remaining question to

370

address is then: why are there obvious underestimation in these studies? Our viewpoint

371

is that previous study ignored the influence of catchment characteristics. The results

372

showed that considering catchment characteristics can greatly improve the simulation 17

373

accuracy of E variability; while if excluding the impacts of catchment characteristics,

374

the E variability could be obvious underestimated and poorly simulated, especially in

375

humid regions. In addition, catchment characteristics had the largest contribution to E

376

changes in humid regions when compared to the impacts of P, E0 and ∆S. Therefore,

377

our study reveals the reason why E variability was often distinctly underestimated in

378

previous attributing study (Wu et al., 2017; Zeng and Cai, 2016), that is because they

379

ignored the contributions of catchment characteristics.

380

Although several studies have investigated the impacts of catchment characteristics

381

globally (Gudmundsson et al., 2016; Zhou et al., 2015), the contribution of catchment

382

characteristics to E is still open for debate (Berghuijs and Woods, 2016b; Chen et al.,

383

2016; Gudmundsson et al., 2017). Zhou et al. (2015) suggested that the contribution of

384

catchment characteristics to E was larger in humid regions than in arid regions, while

385

Gudmundsson et al. (2017) found a larger contribution of catchment characteristics in

386

arid regions, and the same findings were also from Gudmundsson et al. (2016) and

387

Berghuijs et al. (2017). Therefore, no consensus has been reached so far about the

388

impacts of catchment characteristics on E, which can be attributed to different

389

definitions of contributions. Gudmundsson et al. (2017) showed the relative average

390

contribution of finite difference change in m (controlling parameter of Fu’ equation,

391

also referring to the impacts of catchment characteristics) to water yield at the variable

392

range of [P/E0, P/E0 + ∆P/E0] and [m, m + ∆m], while Zhou et al. (2015) suggested the

393

relative contribution of infinitesimal change in m to water yield at exact values of P/E0

394

and m. Moreover, the afore-mentioned studies focused on the water availability changes 18

395

due to a unit change in P/E0 and m, instead of real-world changes. It is noted that a unit

396

change in P/E0 has entirely a different physical interpretation relative to a unit change

397

in m. Therefore, the current assessments are more a theoretical possibility rather than a

398

reality. Hence, taking the monthly and annual variability of E as examples, this study

399

helps shed new light on the real-world impacts of catchment characteristics. Our global

400

patterns of the contributions of P, E0, ∆S and catchment characteristics to the practical

401

E variability showed that catchment characteristics influenced E changes more in humid

402

regions. However, the previous global assessments deemed P or P/E0 as the primary

403

factors (Berghuijs et al., 2017; Gudmundsson et al., 2017; Zhou et al., 2015). For

404

example, Berghuijs et al. (2017) indicated that P controls 83% of the land grid cells for

405

runoff changes and catchment characteristics for the remaining 17%. The difference

406

can be due to different research objects, as well as the difference between practical

407

variability and theoretical changes.

408

The development in our study was based on the Budyko framework. However,

409

there are still some uncertainties and limitations. First, the total differential

410

decomposition of the Budyko formula has inherent errors and uncertainties. Here we

411

did not present uncertainty analysis for the analytical derivation based on the Budyko

412

framework. Yang et al. (2014) estimated the errors of the first-order Taylor expansion

413

of the Budyko-based equation and found that the errors increased with the variability

414

amplitude of the contributor. They showed that a 10 mm increase in precipitation would

415

bring about 0.5-5.0% error in the contribution of precipitation. In addition, we only

416

highlighted the relative contribution of each contributor to the E variability, without 19

417

providing the specific magnitudes of the impacts, since we mainly attempted to

418

investigate the relative importance of these contributors in the E variability.

419

5

Conclusions

420

In this study, we developed an analytical method to assess the sources of E

421

variability. The analytical method simulated the E variability well. We highlighted the

422

necessity to consider the impacts of catchment characteristics although at short-term

423

timescale, since the E variability would be significantly underestimated given exclusion

424

of catchment characteristics.

425

Precipitation played a more important role in E variability in the humid regions and

426

controlled monthly E variability in most regions across the globe. Catchment

427

characteristics were the primary contributor for the annual E variability with median

428

contributions of 51%. E0 had a limited impact on annual E variability, but played a key

429

role in monthly E variability, which controls 32% of global land grid cells. The ∆S had

430

a much large impact at the monthly scale than at the annual scale, which played a

431

dominant role in the monthly E variability for 12% of global land grid cells.

432

In conclusion, the development of analytical derivation for disentangling global E

433

variability has profound implication, which provides a new framework for hydrological

434

attribution analysis at short-term timescales, such as monthly and annual. The results

435

clarifying the role of catchment characteristics and its dominant regions are helpful to

436

improve our understanding on hydrometeorological processes.

437

20

438

Acknowledgments: This work is financially supported by the China National Key

439

R&D Program (Grant 2019YFA0606900), China Postdoctoral Science Foundation

440

funded project (BX20190301), Nature Science Foundation of Hubei Province

441

(2019CFB221), Fundamental Research Funds for the Central Universities, China

442

University of Geosciences (Wuhan) (162301182729), National Science Foundation for

443

Distinguished Young Scholars of China (Grant No. 51425903), the Fund for Creative

444

Research Groups of National Natural Science Foundation of China (Grant No.:

445

41621061), National Natural Science Foundation of China (No. 41771536, No.

446

41401052), Key Project of National Natural Science Foundation of China (Grant No.

447

51190091), and National Key Research and Development Program of China (Grant No.

448

2018YFA0605603). We would like to thank Ming Pan ([email protected]) at

449

Princeton University sharing the Global monthly terrestrial water cycle dataset. We also

450

gratefully acknowledge the hard work and efforts by the editor, Prof. Dr. Emmanouil

451

Anagnostou, and anonymous reviewers for their pertinent and professional comments

452

and suggestions which are greatly helpful for further quality improvement of our

453

manuscript.

454 455

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612 613

Figure captions

614

Fig. 1. The factors affecting evapotranspiration variability from climatic variability

615

(including precipitation and potential evapotranspiration variability), total water storage

616

change and other factors.

617

Fig. 2 Budyko framework (a) without and (b) with consideration of ∆S at annual

618

timescale. The Budyko curves from top to down are derived from Eq. (2) with n = ∞,

619

n = 5, n = 2, n = 1, n = 0.6, n = 0.4. The color bar indicates the counts of overlapping

620

grids.

621

Fig. 3. Comparing assessment E variability assessed by mean absolute deviation (MAD)

622

and that calculated by standard deviation (σ).

623

Fig. 4. Comparing simulated and assessed E variabilities at (a-b) monthly and (c-d)

624

annual scales for terrestrial (i.e., non-oceanic) 0.5º grid points across the globe.

625

Simulated E variabilities are calculated by equation (7) with and without consideration

626

of effects of other factors, while the assessment was evaluated by the standard deviation.

627

The black line is the fitting line and the color bar indicates the counts of overlapping

628

grids.

629

Fig. 5. Comparing simulation accuracy of the analytical method in arid regions (a, c)

630

and humid regions (b, d). The black line is the fitting line and the color bar indicates

631

the counts in overlapping grids.

632

Fig. 6. Modelling errors in the E variability (i.e., simulated values minus assessed

633

values) by latitude. The simulated E variability are evaluated by (a, c) the method

634

proposed in this study and (b, d) the method proposed Zeng and Cai (2015) at monthly 27

635

and annual scale. Black thick lines show the median of errors, and shading shows the

636

quantiles of errors in 30% - 70% and 10% - 90% in the order of darker to lighter shading.

637

Fig. 7. Global patterns for the contributions of (a) P, (b) ∆S, (c) E0 and (d) other

638

factors to monthly variability of E. (e-f) Relationship between the contributions and

639

wetness index (WI, P/E0) for each factor. The red dashed line shows the WI of 0.66,

640

which divides the globe into humid regions (i.e., WI > 0.66) and arid regions (i.e., WI

641

≤ 0.66).

642

Fig. 8. The same as Fig. 7, but for the annual variability of evapotranspiration.

643

Fig. 9. The median contributions of P, ∆S, E0 and n to the E variability for the grids in

644

arid regions, humid regions and globe at (a) monthly and (b) annual scales.

645

Fig. 10. The contributions of P, ∆S, E0 and n to the monthly and annual variability of E

646

in (a, c) arid regions and (b, d) humid regions.

647

Fig. 11. The relationship between monthly precipitation, potential evapotranspiration

648

and actual evapotranspiration in Amazon basin.

649

Fig. 12. Spatial patterns of dominant contributors to the E variability at (a) monthly and

650

(b) annual scale.

28

651 652

Fig. 1. The factors affecting evapotranspiration variability from climatic variability

653

(including precipitation and potential evapotranspiration variability), total water storage

654

change and other factors (e.g., vegetation dynamics and human activities).

655

29

656 657

Fig. 2 Budyko framework without and with consideration of ∆S at (a) monthly and (b)

658

annual scales. The Budyko curves from top to down are derived from Eq. (2) with n =

659

∞, n = 5, n = 2, n = 1, n = 0.6, n = 0.4. The color bar indicates the counts of overlapping

660

grids.

661

30

662 663

Fig. 3. Comparing assessment E variability calculated by mean absolute deviation

664

(MAD) and standard deviation (σ).

665

31

666 667

Fig. 4. Comparing simulated and assessed E variabilities at (a-b) monthly and (c-d)

668

annual scales for terrestrial (i.e., non-oceanic) 0.5º grid points across the globe.

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Simulated E variabilities are calculated by equation (8) with and without consideration

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of effects of other factors, while the assessment was evaluated by the standard deviation.

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The black line is the fitting line and the color bar indicates the counts of overlapping

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grids.

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Fig. 5. Comparing simulation accuracy of the analytical method in arid regions (a, c)

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and humid regions (b, d). The black line is the fitting line and the color bar indicates

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the counts in overlapping grids.

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Fig. 6. Modelling errors in the E variability (i.e., simulated values minus assessed

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values) by latitude. The simulated E variability are evaluated by (a, c) the method

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proposed in this study and (b, d) the method proposed Zeng and Cai (2015) at monthly

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and annual scale. Black thick lines show the median of errors, and shading shows the

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quantiles of errors in 30% - 70% and 10% - 90% in the order of darker to lighter shading.

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Fig. 7. Global patterns for the contributions of (a) P, (b) ∆S, (c) E0 and (d) other

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factors to monthly variability of E. (e-f) Relationship between the contributions and

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dryness index (WI) for each factor. The red dashed line shows the WI of 0.66, which

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divides the globe into humid regions (i.e., WI > 0.66) and arid regions (i.e., WI ≤

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0.66).

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Fig. 8. The same as Fig. 7, but for the annual variability of evapotranspiration.

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Fig. 9. The median contributions of P, ∆S, E0 and other factors to the E variability for

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the grids in arid regions, humid regions and globe at (a) monthly and (b) annual scales.

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Fig. 10. The contributions of P, ∆S, E0 and other factors to the monthly and annual

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variability of E in (a, c) arid regions and (b, d) humid regions.

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Fig. 11. The relationship between monthly precipitation, potential evapotranspiration

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and actual evapotranspiration in Amazon basin.

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Fig. 12. Spatial patterns of dominant contributors to the E variability at (a) monthly and

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(b) annual scale.

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Highlights

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1. We developed a quantitative method to attribute E variability at intra- and inter-

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annual scales. 2. P strengthened E variability in most regions while dampened E variability in extremely humid regions. 3. Catchment characteristics have larger impacts on E variability for humid regions and play a primary role in inter-annual E variability.

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S. Feng, J. Liu, and Q. Zhang designed the study. S. Fen and J. Liu conducted the calculations. S. Feng, J. Liu and Q. Zhang wrote the manuscript with contributions from Y. Zhang, VP Sing, X. Gu and P. Sun. All of the co-authors contributed to scientific interpretations and helped improve the manuscript.

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A global quantitation of factors affecting evapotranspiration

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variability Feng Shuyun1, Jianyu Liu1, Qiang Zhang2,3,4, Yongqiang Zhang5, Vijay P. Singh6, Xihui

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Gu7, Peng Sun8

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1Laboratory

of Critical Zone Evolution, School of Geography and Information Engineering,

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China University of Geosciences, Wuhan 430074, China

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2Key

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Beijing Normal University, Beijing 100875, China

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3State

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University, Beijing 100875, China

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4Faculty

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Management, Beijing Normal University, Beijing 100875, China

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5CSIRO

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6Department

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Engineering, Texas A&M University, College Station, Texas, USA

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7Department

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Geosciences, Wuhan 430074, China;

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8College

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Corresponding author: Qiang Zhang ([email protected]); Jianyu Liu ([email protected])

Laboratory of Environmental Change and Natural Disaster, Ministry of Education,

Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal

of Geographical Science, Academy of Disaster Reduction and Emergency

Land and Water, GPO Box 1700, Canberra ACT 2601, Australia of Biological and Agricultural Engineering and Zachry Department of Civil

of Atmospheric Science, School of Environmental Studies, China University of

of Geography and Tourism, Anhui Normal University, Anhui 241000, China

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41

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Abstract: Scientific viewpoints on the long-term hydrological responses to factors

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other than climatic change remain controversial and yet the impacts of these factors are

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often neglected at the short-term (such as monthly and annual) timescale. We developed

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an analytical method to decompose evapotranspiration (E) variability to the variability

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of precipitation (P), potential evapotranspiration (E0), total water storage change (∆S),

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and catchment characteristics (n), such as vegetation, soil and climate seasonality.

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Global assessment showed that P enhanced E variability in most regions, while

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restrained E variability in some extremely humid regions. E0 controlled monthly E

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variability in most the energy-constrained regions. ∆S had much larger impacts on E

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variability at monthly scale compared to the annual scale, and restrained E variability

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in many arid regions (P/E0 < 0.66). Catchment characteristics had larger impacts on E

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variability in humid regions (P/E0 > 0.66), especially at annual scale. The dominant

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factors of E variability varied with timescales and regions. At a global scale, P and

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catchment characteristics are the dominant factors controlling global E variability at

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monthly and annual scales, respectively; In humid regions, however, the impacts of E0

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on monthly E variability are generally larger than the impacts of precipitation and

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catchment characteristics. We highlight the necessity to consider the impacts of

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catchment characteristics even at the short-term timescales, otherwise the simulation

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and attribution of E variability would be significantly underestimated.

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Keywords: Climate change; Global evapotranspiration; Attribution; Budyko

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framework; Different timescales

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