Interaction of vegetation, climate and topography on evapotranspiration modelling at different time scales within the Budyko framework

Agricultural and Forest Meteorology 275 (2019) 59–68

Contents lists available at ScienceDirect

Agricultural and Forest Meteorology journal homepage: www.elsevier.com/locate/agrformet

Interaction of vegetation, climate and topography on evapotranspiration modelling at different time scales within the Budyko framework

T

Tingting Ninga,b, Sha Zhouc, Feiyang Changa, Hong Shend, Zhi Lia, Wenzhao Liua,

⁎

a

State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A&F University, Shaanxi, 712100, China b Key Laboratory of Ecohydrology of Inland River Basin, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China c Department of Earth and Environmental Engineering, Columbia University, New York, 10027, USA d Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, China

ARTICLE INFO

ABSTRACT

Keywords: Evapotranspiration Vegetation coverage Climate seasonality Budyko framework Loess plateau

Vegetation, climate and topography have been empirically formulated into the controlling parameter of the Budyko model (ω) to estimate evapotranspiration (ET). However, these variables, if simultaneously employed, may induce multicollinearity problems because of their potential interactions. Further, these interactions may vary with different time scales and subsequently result in the inaccurate estimation of ω. As such, we investigated the interactions of vegetation, climate and topography and their corresponding effects on ET modelling at different time scales by employing vegetation coverage (M), an improved climate seasonality and ¯ ), in 30 asynchrony index (SAI), the fraction of precipitation falling as snow (fs) and relative basin relief (BR/ BR catchments in China’s Loess Plateau. We found that, on annual scale, M and SAI were significantly related to ω, while being independent from each other; in consequence, both of them should be parameterized into the Budyko model on the annual scale for better ET modelling. However, the links between M and SAI became stronger with increased time scales, the parameterization of ω should thus be reformatted for longer periods. When extended to a 30-year period, ω was closely related to the above variables, but M was highly inter¯ , and fs was significantly related to BR/ BR ¯ . The independent M and fs were correlated with SAI and BR/ BR finally selected to fit ω, which allowed mean annual ET to be accurately modelled on long-term scale. Identification of the dominant factors applicable at different time scales can simplify the empirical parameterization of the Budyko formula and thereby facilitate more accurate estimation of ET.

1. Introduction

controlling parameter is considered to be governed both by land surface conditions and climate seasonality in current studies (Woods, 2003; Yang et al., 2007; Zhang et al., 2016). The term ‘land surface conditions’ mainly refers to the catchment topography, soil properties and vegetation condition, while ‘climate seasonality’ is associated with not only the amount of precipitation and potential evapotranspiration but also their seasonal distribution (Berghuijs and Woods, 2016a,b; Zhou et al., 2016). Vegetation participates in hydrological processes through rainfall interception, evapotranspiration and infiltration (Rodriguez-Iturbe, 2000; Zhang et al., 2016). Several studies have demonstrated that incorporation of vegetation information can improve the accuracy of the Budyko model in simulating catchment-scale ET, or runoff (Donohue et al., 2007; 2010; Ning et al., 2017; Peel et al., 2010; Zhang et al., 2001; Zhang et al., 2016). Topography also plays an important role in rainfall residence time and runoff yield (Appels et al., 2016; Frei et al.,

The Budyko hypothesis identifies that actual evapotranspiration (ET) could be calculated as a curvilinear function of available water and energy. Initially, this hypothesis assumed that the curve did not have any additional parameters and was suited for large basins and longterm scale (Budyko and Zubenok, 1961; Budyko, 1974). A series of empirical relationships for the Budyko curve were subsequently developed over the past decades. Recently, Zhou, G. et al. (2015), Zhou, S. et al. (2015) revisited the existing Budyko functions and suggested using Fu’s function (Fu, 1981) or Mezentsev-Choudhury-Yang’s function (denoted as M-C-Y hereafter) to describe catchment water-energy partitioning (Yang et al., 2010). Compared with the original function of the Budyko curve, more parameters have been defined in subsequent analytical derivations, such as ω in the Fu function and n in the M-C-Y function, which determine the shape of the Budyko curve. This kind of ⁎

Corresponding author. E-mail address: [email protected] (W. Liu).

https://doi.org/10.1016/j.agrformet.2019.05.001 Received 11 January 2019; Received in revised form 29 April 2019; Accepted 3 May 2019 0168-1923/ © 2019 Elsevier B.V. All rights reserved.

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

2010, Wörman 2006; Winter, 1999), rainfall infiltration (Fox et al., 1997; Heilweil et al., 2007) and groundwater table (Condon and Maxwell, 2015), and it has thus been formulated into the controlling parameter (Shao et al., 2012; Xu et al., 2013; Yang et al., 2007). Although climate seasonality can impact the controlling parameter (Berghuijs and Woods, 2016a,b; Zhou et al., 2016), many recent studies have ignored its potential effects. Several empirical formulae for the controlling parameter have been developed by enveloping topography, soil, vegetation and climate seasonality variables using the regression analysis method (Li et al., 2013; Ning et al., 2017; Xu et al., 2013; Yang et al., 2009). However, multicollinearity may occur when the explanatory variables are intercorrelated, which will, in turn, induce a series of problems. For example, the effects of individual explanatory variables may not be precisely estimated and the regression coefficients may become highly unstable (Mjelde et al., 1991; Willis and Perlack, 1978). Therefore, it is necessary to check the interactions between explanatory variables and select independent variables when developing expressions of the controlling parameters. Interactions between catchment landscape characteristics (vegetation, topography and/or soil) and climate properties, determine the mean annual water balance at the catchment scale (Gentine et al., 2012g; Troch et al., 2013; Xing et al., 2018), which provides insight into predictions of the hydrological partitioning in ungauged basins (Wang et al., 2016a,b). For example, Shao et al. (2012) found that both larger average storm depth in flat catchments and smaller average storm depth in hilly catchments resulted in more streamflow, while increasing forest cover was found to generally result in more mean annual evapotranspiration and less mean annual streamflow for flat catchments in Australia. Gentine et al. (2012) identified that both above- and below-ground vegetation had close relationships with the phase difference between precipitation and radiation (i.e. climate seasonality) around the conterminous US. Troch et al. (2013) used a physically-based hydrologic model to decouple the impact of climate and landscape properties in 12 American catchments across a climate gradient, and found that strong interactions existed between climate, vegetation and soil properties. Recently, the Budyko framework has been widely used to investigate the interannual variability in hydrological partitioning (Chen et al., 2013; Du et al., 2016) and to derive the analytic formula between the controlling parameter and the factors above (Ning et al., 2017). However, studies on the interactions between the main factors remains focused on the long-term scale. When it comes to the annual scale, catchment soil properties and topography are relatively stable, while vegetation and climate seasonality can vary greatly, and so relationships between variables and the dominant factors may vary at different time scales, which needs to be investigated, in order to improve parameterization of the controlling factors and lead to better ET modelling. The objectives of this study were, therefore, to investigate the interactions of vegetation, topography and climate at different time scales, and to identify the factors that could be beneficially incorporated to estimate the Budyko parameter at different time scales. The 30 catchments in China’s Loess Plateau (denoted as ‘CLP’ hereafter) have been used as examples for this purpose since this region has had substantial land use changes and resultant hydrological changes over the past decades. Our results will provide new insights into the application of the Budyko model.

unprecedented soil erosion which in the past contributed nearly 90% of the sediment load of the Yellow River (Wang et al., 2016a,b). In order to improve this situation, the Chinese government launched the “Grain to Green” project in 1999, and it has been reported that this project has achieved remarkable success in terms of increased vegetation cover in recent decades (Li et al., 2017). Furthermore, this re-vegetation has resulted in increased net primary productivity and evapotranspiration over the CLP, to the point where the available local water resources have been reported to be approaching their limits (Feng et al., 2016). Catchment streamflow records were obtained from the Yellow River Conservancy Commission. The lengths of the data records varied between 19–31 years. Daily meteorological data for the period 1960–2012, including precipitation, temperature, sunshine hours and relative humidity, were obtained from the China Meteorological Administration. The Global Inventory Modeling and Mapping Studies (GIMMS) Normalized Difference Vegetation Index version 3 (NDVI3g) dataset from Advanced Very High Resolution Radiometer (AVHRR) sensors was used to assess vegetation coverage change from 1982 to 2012. Digital elevation data, at 30 m resolution, was provided by the Geospatial Data Cloud site, Computer Network Information Center, Chinese Academy of Sciences. Detailed information on each catchment is presented in Supporting Information Table S1. 2.2. Methods 2.2.1. The Budyko function The Budyko framework can take a number of mathematical forms. In this study, Fu’s function was used to assess catchment water balance due to its more generalized form (Zhang et al., 2004):

ET ET0 =1+ P P ET P =1+ ET0 ET0

[1 + (

ET0 1/ ) ] P

[1 + (

P ) ]1/ ET0

or

(1)

where P is precipitation, and ET0 is potential evapotranspiration calculated using the method of Priestley and Taylor (1972). Annual ET is defined here as the difference between precipitation and streamflow and is referred to as “ETmeasure” in the following sections. The changes in water storage were directly ignored based on the results of previous studies. Specifically, using GRACE (Gravity Recovery and Climate Experiment), the water storage has no clear annual variations in the Yellow River basin for the period 2003–2008 (Zhao et al., 2011). Another study, used GRACE data and a bias-corrected method, found similar results in the rivers under dry climates during the period 1983–2006, including Yellow River (Liu et al., 2016). Therefore, compared with the ET of hundreds of millimeters, ignoring water storage change in the study area is reasonable. 2.2.2. Indices for vegetation, climate and topography Vegetation coverage (M) was chosen to represent the catchment vegetation condition and was estimated following Yang et al. (2009):

M=

NDVI NDVImin NDVImax NDVImin

(2)

where NDVImax and NDVImin are NDVI values for dense forest (0.80) and bare soil (0.05), respectively. The climate seasonality index (S), proposed by Milly (1994) and Woods (2003), has been widely used to reflect the seasonal variations between P and ET0 in previous studies (Abatzoglou and Ficklin, 2017; Ning et al., 2017; Yang et al., 2012). It can be expressed as:

2. Data and methods 2.1. Study area and data

S=|

CLP is located in the upper and middle reaches of the Yellow River (Fig. 1), and has sub-humid to semi-arid continental monsoon climates. Due to its sparse vegetation coverage, frequent heavy summer rainstorms and intensive agricultural practices, this region suffers from

P

ET0

|

(3)

where is the dryness index. P and ET0 are the seasonal amplitudes of P and ET0, respectively, and they are simulated by sinusoidal functions using monthly P and ET0 values: 60

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

Fig. 1. The 30 catchments in China’s Loess Plateau.

P (t ) = P¯ [1 +

P

sin(

¯ 0 [1 + ET0 (t ) = ET

2

ET0

t )] 12 sin(

2

SAI with a fixed phase determined by mean monthly P and ET0 performed better in explaining ω variations than did SAI with an annually fitted phase and S (Fig. S1). Thus, SAI with fixed SP and SET0 were used in this study to reflect climate seasonality. Further, it has been proven that changes in the ratio of precipitation in the form of snow to total precipitation (fs), have significant impact on catchment hydrological processes (Berghuijs et al., 2014; Zhang et al., 2015).We therefore calculated annual fs for each catchment following Berghuijs et al. (2014), i.e., P on days with an average temperature below 1℃ was considered to be entirely snowfall but other days considered to be entirely rainfall. Catchment averaged slope (tan ) and topographic wetness index (TWI) have been used to assess the impacts of topography on the controlling parameter by Yang et al. (2007; 2009) and Xu et al. (2013), respectively. Furthermore, basin relief (BR), firstly introduced by Ahnert (1970), can reflect topographic roughness (Hurtrez et al., 1999), and has thus been widely used to quantify water and soil loss, and to estimate potential soil erosion. The relationship between these above indices and parameter ω has been explored in this study. The specific BR and TWI calculation methods used were as follows:

(3a)

t )] 12

(3b)

where is the cycle of seasonality, which is 0.5 (6 months) in the tropics and 1 (12 months) outside the tropics; t is the time in month. Distributions of water and energy are not only reflected by differences in the seasonal amplitudes of P and ET0, however, but also by the phase mismatch between P and ET0 (Berghuijs and Woods, 2016a,b; Liu et al., 2018). Thus, Liu et al. (2018) proposed a climate seasonality and asynchrony index (SAI), to reflect the seasonality and asynchrony of water and energy distribution based on the work of Milly (1994) and Woods (2003):

SAI =

P

2

2

cos

P ET0

2 SP

SET0 12

+(

ET0

)2

1 2

(4)

where SP and SET0 are the phase shifts of P and ET0, which are fitted by their monthly values for each year. After considering SP and SET0, Eqs. 3a & 3b can be rewritten as:

P (t ) = P¯ [1 +

P

sin(

2 t

¯

ET0 (t ) = ET0 [1 +

ET0

SP )] 12

sin(

2 t

(4a)

SET0 )] 12

BR = elevationmax TWI = ln (A/ tan )

(4b)

elevationmin

(5) (6)

where elevationmax and elevationmin are respectively the maximum and minimum elevations for the optimal threshold window (1.44 km2), which was determined by using the mean change-point analysis method (Hui et al., 2015). A is the standardized upslope contributing area. BR and TWI for each catchment were scaled using the mean BR and TWI of ¯ and TWI/ the whole study area in a dimensionless form, i.e. BR/ BR ¯ . TWI

Liu et al. (2018) defined the time step of the P and ET0phase shifts (i.e. SP and SET0) as 1, implying that the time offsets for these two variables from a reference date was at least 1 month. However, several studies found that the phase difference of the precipitation peaks could be as short as a few days (Ho et al., 2003; Villarini et al., 2011), and so, the time step for SP and SET0 was defined as 0.1 in this study. 61

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

2.2.3. Statistical methods The linear correlation method was used to analyse the correlation between vegetation and climate seasonality as well as topographic factors, at different time scales. The stepwise regression method, which can directly reflect the dominance of different variables, was applied to develop the empirical equation of parameter ω. Further, the Variance Inflation Factor (VIF) statistic, where a greater VIF indicates stronger multicollinearity (Kroll and Song, 2013), was employed to test the multicollinearity among the variables. 3. Results 3.1. Interactions of multiple factors on short time scale Changes in landform, such as topography or soils, relatively gentle and no large abrupt events have occurred in CLP in recent decades (Liang and Yang, 2016; Tian et al., 2008). Therefore, we focused on the interactions among vegetation coverage, climate seasonality and the fraction of P falling as snow (fs), on annual scale. ω was positively correlated with vegetation coverage (M) (determining coefficient R2 = 0.18, p < 0.01) (Fig. 2a) while negatively correlated with climate seasonality and asynchrony index (SAI) (R2 = 0.22, p < 0.01) (Fig. 2b), which implied that catchment ET increased with increasing vegetation coverage while decreased with increasing seasonal difference between precipitation and potential evapotranspiration. There was no relationship between ω and fs (p > 0.05) (Fig. 2c). We therefore only considered the relationships between M and SAI in the 30 catchments. On annual scale, there was no relationship between M and SAI (p > 0.05) in 23 out of the 30 catchments (Fig. 3). Therefore, on annual scale, M and SAI were found to be highly related to parameter ω, while being independent from each other. Further, time series of M and SAI generated with 3-year, 7-year, 9year, 11-year, 15 -year and 19-year moving windows were used to evaluate their relationships at different time scales. Results showed that the longer time scales resulted in stronger relationships between M and SAI in most catchments (Fig. S2). In other words, the seasonal characteristics of water and energy supply were found to have more significant impacts on vegetation at longer time scales. It can be explained that, at shorter time scales, the effect of climate seasonality on vegetation lagged, due to the buffering effect of the soil reservoir on plant water use. At longer time scales, SAI reflects the regional climate conditions and climate dominates zonal vegetation. 3.2. Estimated ET with different ω formula on short time scale The combined dataset from 30 catchments was used to fit the relationships between annual ω and M as well as SAI in this study. To 1), the limiting conditions of M constrain the lower boundary of ω ( and SAI were achieved:

f1 (M )

0, i . e. ,

1, when M

f2 (SAI )

0, i. e . ,

1, when SAI

Fig. 2. Relationships between annual parameter ω and (a) M, (b) SAI, (c) fs based on 30 catchments.

0; (7)

conditions, the general form of parameter lows:

Thus, the specific expressions separately fitted by these two variables are:

= 1 + a1 × M b1 × exp (c1 SAI )

M 0.49

= 1 + 3.29 × (R2 adj = 0.19, F = 173)

= 1 + 3.22 × exp ( 0.30SAI ) adj = 0.23, F = 222.5)

(R2

can be expressed as fol(10)

Using the least linear square regression method, the semi-empirical formula for parameter on annual scale was derived as follows:

(8)

2 = 1 + 3.67 × M 0.27 × exp ( 0.21SAI ) (Radj = 0.27, F = 139)

(9)

(11)

Eq. (11) has a lower F value but higher R2adj value, compared to Eq.8. To compare the performances of the three empirical formulae above further, annual ET for each catchment was estimated, using Fu’s function with the three formulae above (Fig. 4). ETmeasure was introduced to evaluate the estimated ET, and it was seen that Eq.11 improved the annual ET modelling compared to Eqs. 8 & 9 by reducing the root mean

where R2adj is the adjusted determining coefficient, which can avoid the automatic and spurious increase in the R2 that occurs when extra explanatory variables are added (Nagappan and Ball, 2005); F is the statistic from the F test. Considering the relationships in Eqs. 8 & 9 and the above limiting 62

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

Fig. 3. Interactions between M and SAI for each catchment on annual scale.

square error mean (RMSE) from 20 mm and 18 mm respectively, to 16 mm. It can be concluded that, on annual scale, M and SAI are highly related to parameter ω, and considering their joint effects for ω calculations can improve ET modelling. Further, M and SAI are independent with each other, and so, can both be formulated into the Budyko model by the regression method on annual scale.

3.3. Interactions of multiple factors on the long-term scale

¯ and fs were explored on the longInteractions among M, SAI, BR /BR term scale (1982–2012). The results showed that ω was highly correlated with SAI and M with R2 of 0.46 and 0.23, respectively (Figs. 5a and b). However, M and SAI were also highly correlated (R2 = 0.65) (Fig. 5d). Thus, considering the dependence between M and SAI, they 63

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

¯ (R2 = 0.15) (Fig. 5d-f). Therefore, the multirelationship with BR /BR collinearity problem should be evaluated if these variables are all in¯ and SAI could corporated into the formula for ω. We found that BR /BR be removed from the formula on the long-term scale, using the stepwise regression method, and the results of collinearity tests have been listed in Table S2. Subsequently, the empirical formula for ω could be simplified as: 2 = 1 + 25.03 × M 0.43 × fs 0.71 (Radj = 0.56, F = 18.6)

Compared with Eq. 13, Eq.14 achieved a slightly higher R2adj and F value, of 0.56 and 18.6, respectively. To compare the performance of these two equations further, averaged annual ET was estimated for each of the 30 catchments, based on the Budyko model after estimating ω using Eq.13 and Eq.14 (which were denoted as ETmodel-multiple and ETmodel-M&fs, respectively). The results showed that the two ω formulation schemes gave similar R2, MAE and RMSE, indicating that Eq.14 with less explanatory variables, worked well without losing ET estimation accuracy (Fig. 6). Overall, on the long-term scale, although vegetation, climate and topography all influenced catchment water balance, to avoid the multicollinearity problem and simplify the formulation of ω, M and fs could be considered as the key variables for the parameterization of the Budyko model.

Fig. 4. Comparison of the RMSE between the annual ET estimated using the water balance equation and the modelled ET using the Fu equation, with the modelled ω based on M, SAI, and the joint effects of M-SAI. A distribution curve is shown to the right side of each box plot, and the data points are represented by diamonds.

should not be simultaneously incorporated into ω on the long-term scale. The linear relationships between ω and the three topographical indices are illustrated in Fig. S3. Among them, ω has a higher corre¯ (R2 = 0.38) than with other tanβ or TWI/ lation coefficient with BR /BR 2 ¯ TWI (R = 0.24), indicating that BR is more suitable for representing topographical conditions within the Budyko framework for this area. ¯ has been shown in Fig. 5e, The correlation between M and BR /BR where it can be seen that M has a positive exponential relationship with ¯ (R2 = 0.56, p < 0.01). Thus, M is closely linked with topoBR /BR graphical conditions in the CLP and the steeper regions seem to have higher vegetation coverage. ω also has a significant positive relationship with fs (R2 = 0.25) (Fig. 5c) on the long-term scale, which means that a precipitation shift from snow towards rain would lead to decreased ET for the given levels of P and ET0 in the CLP. No relationship was found between fs and M or ¯ , which indicated that the SAI, while fs was positively related to BR /BR steeper the topography, the more snow for the same level of P.

4. Discussion 4.1. Why is ω positively correlated with topography? The relationship between the Budyko controlling parameter and topographical factors has been investigated in previous studies. Most studies detected a negative relationship between parameter ω and topographical factors, at either the regional or global scale (Tang and Wang, 2017; Xu et al., 2013; Yang et al., 2007; Zhou, G. et al., 2015; Zhou, S. et al., 2015). In CLP, changes in vegetation depend greatly on topography, due to the significant eco-restoration efforts by the Chinese government since the 1950s. The “Grain to Green” Project, in particular, required that farmlands on slopes steeper than 25° were reverted to forest or grassland (Tang et al., 1998; Wang et al., 2005). At the same time, similar re-vegetation measures were carried out on slopes steeper than 15°. M showed an upward trend on the slopes greater than 15° from 1982 to 2012 in the CLP (R2 = 0.61; p < 0.05); further, slope gradients were significantly correlated with M (R2 = 0.82, p < 0.01) (Fig. S4). Therefore, in the CLP, steeper areas would have higher vegetation coverage, ET and ω, which is the possible reason why ω was ¯ . found to be positively correlated with both tan and BR/ BR The positive relationship between vegetation coverage and slope has also been detected in regions with little human interference, such as in eastern Mexico (Munoz-Villers et al., 2016), Israel (Carmel and Kadmon, 1999) and California (Deng et al., 2007). As such, the positive relationship between vegetation coverage and slope in the CLP reflects the combined effects of the “Grain to Green” Project and natural succession, although it is difficult to separate their individual effects, and this may lead to some uncertainties in our analysis.

3.4. Estimated ET with different ω formula on the long-term scale Based on the above analysis, on the long-term scale, parameter ω is ¯ , respectively. The functional highly related to M, SAI, fs and BR /BR forms of M and SAI on the annual scale (Eq.11) still apply here, and fs may be expressed in the form of power function according to the relationship between ω and fs in Fig. 5c. In the Loess Plateau, the influ¯ is special (Fig. 5e, Fig. S3c; see 4.1), which is expressed ence of BR/BR in the form of exponential function here. If all four variables are incorporated into parameter ω without considering correlations between the explanatory variables, ω can be determined as:

¯ ) = 1 + a2 × M b2 × fs c2 × exp (d2 SAI + e2 BR/ BR

(14)

4.2. Why is vegetation information the key variable?

(12)

Vegetation information is formulated into ω both on the annual and long-term scale in this study. It has been verified widely that vegetation greatly influences water balance (Donohue et al., 2007, 2010; Zhang et al., 2001). Eagleson (1982) emphasized that vegetation was both a cause and consequence of the hydrologic cycle. Feng et al. (2016) discovered that the re-vegetation program has led to significant increases in net primary productivity and ET over the CLP, which pushed local water availability to its upper limit. Further, the longer the time scale, the stronger the effects of vegetation on hydrological partitioning. For example, Jaramillo et al. (2018) found that forest biomass

Using the least linear square regression method, the final form of Eq.12 becomes: 2 = 1 + 12.18 × M 0.39 × fs 0.61 × exp (0.12SAI (Radj = 0.54, F = 9.6)

¯ ) + 0.23BR/BR (13) It should be noted that these four explanatory variables are highly intercorrelated. Specifically, M is correlated not only with SAI ¯ (R2 = 0.56), and fs also has a close (R2 = 0.65), but also with BR /BR 64

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

Fig. 5. Relationships between

-SAI (a),

-M (b),

¯ (e) and fs- BR/ BR ¯ (f) on the long-term scale (1982–2012). -fs (c), M-SAI (d), M-BR/ BR

Fig. 6. Comparison of long-term averaged annual ET estimates derived using Eq.13 and Eq.14 with that derived from catchment water balance (ET = P–Q).

65

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al.

(V) could well explain the variance of the residual effect on the evaporative ratio ((E/P)r) in Sweden during the period 1961–2012, and increasing time moving window would increase the explanation power of V on (E/P)r. It can be explained that there a time-lag effect exists, with respect to vegetation change on catchment hydrology, and that its effect is gradually amplified with increasing time scales. Therefore, vegetation information could be considered as the key variable for the parameterization of the Budyko model.

evapotranspiration. This simple and predictable outcome of hydrological partitioning results from the interactions between landscape characteristics and climate seasonality (Troch et al., 2013), and these landscape and climate variables have been empirically formulated into the Budyko controlling parameter using the regression method. To gain insight to the role of their interactions on hydrological partitioning and to avoid the multicollinearity problem when developing the empirical formula of the controlling parameter in Budyko equations at different time scales, the correlations between explanatory variables, including vegetation information, climate and topographic conditions, should be checked. Based on the 30 catchments of the Loess Plateau, we explored the interactions between vegetation coverage M, improved climate seasonality and asynchrony index SAI, the fraction of P falling as snow ¯ ) at different time scales. On annual fs and relative basin relief (BR/ BR scale, there was no relationship between M and SAI, in most catchments. Therefore, both M and SAI can be formulated into the controlling parameters to improve the performance of annual ET modelling. However, the longer the time scales, the closer the relationship between M and SAI. On the 30-year scale, M was highly correlated with SAI and ¯ , and BR /BR ¯ was also related to fs. Considering the above inBR/ BR teractions, M and fs were formulated into the parameter, using the step regression method. The empirical estimation of ω fitted by M and fs worked well for ET modelling for the 30 catchments on the long-term scale.

4.3. What is the potential influence of irrigation? Globally, irrigated land accounts for about 20% of the arable land area (Döll and Siebert, 2002), and this proportion reaches up to 40% in China (Jin and Young, 2001). Irrigation water diversion and consumption has significantly influenced the hydrological cycle (de Vrese et al., 2016; Jaramillo and Destouni, 2015; Nilsson et al., 2005). Therefore, irrigation has already been considered in the Budyko framework in recent studies (Han et al., 2011; Jiang et al., 2015; Wang and Hejazi, 2011; Xing et al., 2018). After calculating the effective irrigated area ratio (IA) for the 30 catchments of this study, following the method of Xing et al. (2018) (Table S1), we found that there was no relationship between parameter ω and IA. The possible reason for this was that the significant relationship between IA and M (R2 = 0.16, p < 0.05) weakened the effects of IA on ω, that is, vegetation could represent the effects of IA in these water-limited areas. Thus, it is not necessary to formulate irrigation information into parameter ω in CLP.

Acknowledgments This study was supported by the National Key Research and Development Program of China (No.2016YFC0501602), the National Natural Science Foundation of China (No. 41807160, 41571036), the Opening Fund of State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau (A3140214021804) and CAS "Light of West China" Program (Y929651001). The daily meteorological data are available at http://data.cma.cn/ data/detail/dataCode/SURF_CLI_CHN_MUL_DAY_CES_V3.0.html. The GIMMS NDVI3g data are available at https://nex.nasa.gov/ nex/projects/1349/. The Digital elevation data are available at http://www.gscloud.cn/. The constructive suggestions from the two referees are greatly appreciated.

4.4. What if correlated variables are incorporated into the controlling parameter? The statistical and inferential problems of multicollinearity in multiple regressions have been widely discussed for ecological data (Graham, 2003), and hydrologists are also starting to address these problems (Bassiouni et al., 2016; Okcu et al., 2016). However, the multicollinearity issues associated with developing the Budyko controlling parameter have rarely been discussed. The primary consequence of multicollinearity is that the separate effects of the explanatory variables may not be precisely presented in the regression equations (Willis and Perlack, 1978). In this study, parameter ω was significantly negative to SAI on the long-term scale (Fig. 5b), but this relationship was opposite in Eq.13. Considering relative infiltration capacity ks/ i¯r , M and average slope in the Haihe Basin, Yang et al. (2009) developed a formula for the controlling parameter n in M-C-Y’s function as n = 2.721 (ks /i¯r ) 0.393M 0.301exp (4.351tan ) . In this equation, the controlling parameter was positively correlated with tanβ, but this is opposite to their real relationship (Fig. S5). This inconsistent phenomenon could be explained as follows: the weak n-tan relationship was offset by the strong tan - ks/ i¯r relationship during regression analysis, which subsequently impacted the correct expression of the regression equation. In this study, the formula for ω that incorporated M, SAI, fs and BR/ ¯ (Eq.13) achieved a lower F value than the version that only conBR sidered the effects of M and fs (Eq.14). This is another consequence of multicollinearity, that is, multicollinear explanatory variables will decrease statistical power. Moreover, multicollinearity may also cause the exclusion of significant variables during model creation (Graham, 2003). Therefore, even considering more variables in the Budyko controlling parameter is helpful in achieving a deeper understanding of the impacts of catchment climate, vegetation and topography on water balance variation, and the multicollinearity caused by the interactions of these variables cannot be ignored.

Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.agrformet.2019.05. 001. References Abatzoglou, J.T., Ficklin, D.L., 2017. Climatic and physiographic controls of spatial variability in surface water balance over the contiguous United States using the Budyko relationship. Water Resour. Res. 53 (9), 7630–7643. https://doi.org/10. 1002/2017wr020843. Ahnert, F., 1970. Functional relationships between denudation, relief, and uplift in large mid-latitude drainage basins. Am. J. Sci. 268 (3), 243–263. https://doi.org/10.2475/ ajs.268.3.243. Appels, W.M., Bogaart, P.W., van der Zee, S.E.A.T.M., 2016. Surface runoff in flat terrain: how field topography & runoff generating processes control hydrological connectivity. J. Hydrol. (Amst) 534, 493–504. https://doi.org/10.1016/j.jhydrol.2016. 01.021. Bassiouni, M., Vogel, R.M., Archfield, S.A., 2016. Panel regressions to estimate low-flow response to rainfall variability in ungaged basins. Water Resour. Res. 52 (12), 9470–9494. https://doi.org/10.1002/2016wr018718. Berghuijs, W.R., Woods, R.A., 2016a. A simple framework to quantitatively describe monthly precipitation and temperature climatology. Int. J. Clim. 36 (9), 3161–3174. https://doi.org/10.1002/joc.4544. Berghuijs, W.R., Woods, R.A., 2016b. Correspondence: space-time asymmetry undermines water yield assessment. Nat. Commun. 7, 11603. https://doi.org/10.1038/ ncomms11603. Berghuijs, W.R., Woods, R.A., Hrachowitz, M., 2014. A precipitation shift from snow towards rain leads to a decrease in streamflow. Nat. Clim. Change 4 (7), 583–586. https://doi.org/10.1038/nclimate2246.

5. Conclusions Budyko (1974) suggested that mean annual catchment water balance is controlled to the first order by precipitation and potential 66

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al. Budyko, M.I., 1974. Climate and Life. 508 pp. Academic, New York. Budyko, M.I., Zubenok, L.I., 1961. Determination of evaporation from the land surface (in Russian). Izv. Akad. Nauk SSR, Ser. Geogr. 6, 3–17. Carmel, Y., Kadmon, R., 1999. Effects of grazing and topography on long-term vegetation changes in a Mediterranean ecosystem in Israel. Plant Ecol. 145 (2), 243–254. https://doi.org/10.1023/a:1009872306093. Chen, X., Alimohammadi, N., Wang, D., 2013. Modeling interannual variability of seasonal evaporation and storage change based on the extended Budyko framework. Water Resour. Res. 49, 6067–6078. https://doi.org/10.1002/wrcr.20493. Condon, L.E., Maxwell, R.M., 2015. Evaluating the relationship between topography and groundwater using outputs from a continental-scale integrated hydrology model. Water Resour. Res. 51 (8), 6602–6621. https://doi.org/10.1002/2014wr016774. de Vrese, P., Hagemann, S., Claussen, M., 2016. Asian irrigation, African rain: remote impacts of irrigation. Geophys. Res. Lett. 43 (8), 3737–3745. https://doi.org/10. 1002/2016gl068146. Deng, Y., Chen, X., Chuvieco, E., Warner, T., Wilson, J.P., 2007. Multi-scale linkages between topographic attributes and vegetation indices in a mountainous landscape. Remote Sens. Environ. 111 (1), 122–134. https://doi.org/10.1016/j.rse.2007.03. 016. Döll, P., Siebert, S., 2002. Global modeling of irrigation water requirements. Water Resour. Res. 38 (4), 1037. https://doi.org/10.1029/2001WR000355. Donohue, R.J., Roderick, M.L., McVicar, T.R., 2007. On the importance of including vegetation dynamics in Budyko’s hydrological model. Hydrol. Earth Syst. Sci. 11 (2), 983–995. https://doi.org/10.5194/hess-11-983-2007. Donohue, R.J., Roderick, M.L., McVicar, T.R., 2010. Can dynamic vegetation information improve the accuracy of Budyko’s hydrological model? J. Hydrol. (Amst) 390 (1-2), 23–34. https://doi.org/10.1016/j.jhydrol.2010.06.025. Du, C., Sun, F., Yu, J., Liu, X., Chen, Y., 2016. New interpretation of the role of water balance in an extended Budyko hypothesis in arid regions. Hydrol. Earth Syst. Sci. 20, 393–409. https://doi.org/10.5194/hess-20-393-2016. Eagleson, P.S., 1982. Ecological optimality in water-limited natural soil-vegetation systems: 1. Theory and hypothesis. Water Resour. Res. 18 (2), 325–340. Feng, X., Fu, B., Piao, S., Wang, S., Ciais, P., 2016. Revegetation in China’s Loess Plateau is approaching sustainable water resource limits. Nat. Clim. Change 6, 1019–1022. https://doi.org/10.1038/nclimate3092. Fox, D.M., Bryan, R.B., Price, A.G., 1997. The influence of slope angle on final infiltration rate for interrill conditions. Geoderma 80 (1-2), 181–194. https://doi.org/10.1016/ s0016-7061(97)00075-x. Frei, S., Lischeid, G., Fleckenstein, J.H., 2010. Effects of micro-topography on surfacesubsurface exchange and runoff generation in a virtual riparian wetland - A modeling study. Adv. Water Res. 33 (11), 1388–1401. https://doi.org/10.1016/j.advwatres. 2010.07.006. Fu, B., 1981. On the calculation of the evaporation from land surface (in Chinese). Sci. Atmos. Sinica 5 (01), 23–31. Gentine, P., D’Odorico, P., Lintner, B.R., Sivandran, G., Salvucci, G., 2012g. Interdependence of climate, soil, and vegetation as constrained by the Budyko curve. Geophys. Res. Lett. 39, L19404. https://doi.org/10.1029/2012gl053492. Graham, M.H., 2003. Confronting Multicollinearity in Ecological Multiple Regression. Ecology 84 (11), 2809–2815. https://doi.org/10.1890/02-3114. Han, S., Hu, H., Yang, D., Liu, Q., 2011. Irrigation impact on annual water balance of the oases in Tarim Basin, Northwest China. Hydrol. Processes 25 (2), 167–174. https:// doi.org/10.1002/hyp.7830. Heilweil, V.M., McKinney, T.S., Zhdanov, M.S., Watt, D.E., 2007. Controls on the variability of net infiltration to desert sandstone. Water Resour. Res. 43 (7), W07431. https://doi.org/10.1029/2006wr005113. Ho, C.H., Lee, J.Y., Ahn, M.H., Lee, H.S., 2003. A sudden change in summer rainfall characteristics in Korea during the late 1970s. Int. J. Clim. 23 (1), 117–128. https:// doi.org/10.1002/joc.864. Hui, Y., Yong, L., Liu, S., Yong, W., Yong, Y., Liu, W., 2015. The influences of topographic relief on spatial distribution of mountain settlements in Three Gorges Area. Environ. Earth Sci. 74 (5), 4335–4344. https://doi.org/10.1007/s12665-015-4443-2. Hurtrez, J.E., Lucazeau, F., Lave, J., Avouac, J.P., 1999. Investigation of the relationships between basin morphology, tectonic uplift, and denudation from the study of an active fold belt in the Siwalik Hills, central Nepal. J. Geophys. Res-Sol. Ea. 104 (B6), 12779–12796. https://doi.org/10.1029/1998jb900098. Jaramillo, F., Destouni, G., 2015. Local flow regulation and irrigation raise global human water consumption and footprint. Science 350 (6265), 1248–1251. https://doi.org/ 10.1126/science.aad1010. Jaramillo, F., Cory, N., Arheimer, B., Laudon, H., van der Velde, Y., Hasper, T.B., Teutschbein, C., Uddling, J., 2018. Dominant effect of increasing forest biomass on evapotranspiration: interpretations of movement in Budyko space. Hydrol. Earth Syst. Sci. 22 (1), 567–580. https://doi.org/10.5194/hess-22-567-2018. Jiang, C., Xiong, L.H., Wang, D.B., Liu, P., Guo, S.L., Xu, C.Y., 2015. Separating the impacts of climate change and human activities on runoff using the Budyko-type equations with time-varying parameters. J. Hydrol. (Amst) 522, 326–338. https:// doi.org/10.1016/j.jhydrol.2014.12.060. Jin, L., Young, W., 2001. Water use in agriculture in China: importance, challenges, and implications for policy. Water Policy 3 (3), 215–228. https://doi.org/10.1016/ S1366-7017(01)00015-0. Kroll, C.N., Song, P., 2013. Impact of multicollinearity on small sample hydrologic regression models. Water Resour. Res. 49 (6), 3756–3769. https://doi.org/10.1002/ wrcr.20315. Li, D., Pan, M., Cong, Z.T., Zhang, L., Wood, E., 2013. Vegetation control on water and energy balance within the Budyko framework. Water Resour. Res. 49 (2), 969–976. https://doi.org/10.1002/wrcr.20107. Li, J., Peng, S., Li, Z., 2017. Detecting and attributing vegetation changes on China’s Loess

Plateau. Agr. Forest Meteorol. 247, 260–270. https://doi.org/10.1016/j.agrformet. 2017.08.005. Liang, P., Yang, X.P., 2016. Landscape spatial patterns in the Maowusu (Mu Us) Sandy Land, northern China and their impact factors. Catena 145, 321–333. https://doi. org/10.1016/j.catena.2016.06.023. Liu, W.B., Wang, L., Zhou, J., Li, Y.Z., Sun, F.B., Fu, G.B., Li, X.P., Sang, Y.F., 2016. A worldwide evaluation of basin-scale evapotranspiration estimates against the water balance method. J. Hydrol. 538, 82–95. https://doi.org/10.1016/j.jhydrol.2016.04. 006. Liu, J., Zhang, Q., Singh, V.P., Song, C., Zhang, Y., Sun, P., 2018. Hydrological effects of climate variability and vegetation dynamics on annual fluvial water balance at global large river basins. Hydrol. Earth Syst. Sci. 22, 4047–4060. https://doi.org/10.5194/ hess-22-4047-2018. Milly, P.C.D., 1994. Climate, soil-water storage, and the average annual water-balance. Water Resour. Res. 30 (7), 2143–2156. https://doi.org/10.1029/94wr00586. Mjelde, J.W., Cothren, J.T., Rister, M.E., Hons, F.M., Coffman, C.G., Shumway, C.R., Lemon, R.G., 1991. Integrating data from various field experiments: the case of corn in Texas. J. Produ. Agri. 4 (1), 139–147. Munoz-Villers, L.E., Geissert, D.R., Holwerda, F., McDonnell, J.J., 2016. Factors influencing stream baseflow transit times in tropical montane watersheds. Hydrol. Earth Syst. Sci. 20 (4), 1621–1635. https://doi.org/10.5194/hess-20-1621-2016. Nagappan, N., Ball, T., 2005. Use of relative code churn measures to predict system defect density. International Conference on Software Engineering, ACM. pp. 284–292. Nilsson, C., Reidy, C.A., Dynesius, M., Revenga, C., 2005. Fragmentation and flow regulation of the world’s large river systems. Science 308 (5720), 405–408. https://doi. org/10.1126/science.1107887. Ning, T., Li, Z., Liu, W., 2017. Vegetation dynamics and climate seasonality jointly control the interannual catchment water balance in the Loess Plateau under the Budyko framework. Hydrol. Earth Syst. Sci. 21 (3), 1515–1526. https://doi.org/10.5194/ hess-21-1515-2017. Okcu, D., Pektas, A.O., Uyumaz, A., 2016. Creating a non-linear total sediment load formula using polynomial best subset regression model. J. Hydrol. (Amst) 539, 662–673. https://doi.org/10.1016/j.jhydrol.2016.04.069. Peel, M.C., McMahon, T.A., Finlayson, B.L., 2010. Vegetation impact on mean annual evapotranspiration at a global catchment scale. Water Resour. Res. 46, W09508. https://doi.org/10.1029/2009wr008233. Priestley, C., Taylor, R., 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev. 100 (2), 81–92. Rodriguez-Iturbe, I., 2000. Ecohydrology: A hydrologic perspective of climate-soil-vegetation dynamics. Water Resour. Res. 36 (1), 3–9. https://doi.org/10.1029/ 1999wr900210. Shao, Q.X., Traylen, A., Zhang, L., 2012. Nonparametric method for estimating the effects of climatic and catchment characteristics on mean annual evapotranspiration. Water Resour. Res. 48, W03517. https://doi.org/10.1029/2010wr009610. Tang, Y., Wang, D., 2017. Evaluating the role of watershed properties in long-term water balance through a Budyko equation based on two-stage partitioning of precipitation. Water Resour. Res. 53 (5), 4142–4157. https://doi.org/10.1002/2016wr019920. Tang, K., Zhang, K., Lei, A., 1998. The research on upper limit of abandoning farmland slope in the Loess Plateau Hilly Region (in Chinese). Chin. Sci. Bull. 43 (2), 200–203. Tian, Y., Lun, W.U., Gao, Y., Wang, D., Zhang, Y., 2008. DEM-based Modelling and Simulation of Modern Landform Evolution of Loess, 257-276 Pp. Springer, Berlin Heidelberg. Troch, P.A., Carrillo, G., Sivapalan, M., Wagener, T., Sawicz, K., 2013. Climate-vegetation-soil interactions and long-term hydrologic partitioning: signatures of catchment co-evolution. Hydrol. Earth Syst. Sci. 17 (6), 2209–2217. https://doi.org/10.5194/ hess-17-2209-2013. Villarini, G., Smith, J.A., Ntelekos, A.A., Schwarz, U., 2011. Annual maximum and peaksover-threshold analyses of daily rainfall accumulations for Austria. J. Geophys, Res. D: Atmos. 116, D05103. https://doi.org/10.1029/2010JD015038. Wang, D., Hejazi, M., 2011. Quantifying the relative contribution of the climate and direct human impacts on mean annual streamflow in the contiguous United States. Water Resour. Res. 47, W00J12. https://doi.org/10.1029/2010wr010283. Wang, S., Huang, Y., Chen, Z., 2005. Remote sensing study of returning farmland to forest or grassland in the Yellow River Basin (in Chinese). J. Tsinghua Univ. (Sci. Technol.) 45 (3), 306–309. Wang, C., Wang, S., Fu, B.J., Zhang, L., 2016a. Advances in hydrological modelling with the Budyko framework: A review. Prog. Phys. Geog. 40 (3), 409–430. https://doi. org/10.1177/0309133315620997. Wang, S., Fu, B., Piao, S., Lü, Y., Ciais, P., Feng, X., Wang, Y., 2016b. Reduced sediment transport in the Yellow River due to anthropogenic changes. Nat. Geosci. 9 (1), 38–41. https://doi.org/10.1038/ngeo2602. Willis, C.E., Perlack, R.D., 1978. Multicollinearity: effects, symptoms, and remedies. J. Northeast. Agric. Econ. Counc. 7, 55–61. Winter, T.C., 1999. Relation of streams, lakes, and wetlands to groundwater flow systems. Hydrogeol. J. 7 (1), 28–45. https://doi.org/10.1007/s100400050178. Woods, R., 2003. The relative roles of climate, soil, vegetation and topography in determining seasonal and long-term catchment dynamics. Adv. Water Resources 26 (3), 295–309. https://doi.org/10.1016/s0309-1708(02)00164-1. Wörman, A., Packman, A.I., Marklund, L., Harvey, J.W., Stone, S.H., 2006. Exact three‐dimensional spectral solution to surface‐groundwater interactions with arbitrary surface topography. Geophys. Res. Lett. 33 (7), L07402. https://doi.org/10. 1029/2006GL025747. Xing, W.Q., Wang, W.G., Shao, Q.X., Yong, B., 2018. Identification of dominant interactions between climatic seasonality, catchment characteristics and agricultural activities on Budyko-type equation parameter estimation. J. Hydrol. (Amst) 556, 585–599. https://doi.org/10.1016/j.jhydrol.2017.11.048.

67

Agricultural and Forest Meteorology 275 (2019) 59–68

T. Ning, et al. Xu, X.L., Liu, W., Scanlon, B.R., Zhang, L., Pan, M., 2013. Local and global factors controlling water-energy balances within the Budyko framework. Geophys. Res. Lett. 40 (23), 6123–6129. https://doi.org/10.1002/2013gl058324. Yang, D., Sun, F., Liu, Z., Cong, Z., Ni, G., Lei, Z., 2007. Analyzing spatial and temporal variability of annual water-energy balance in nonhumid regions of China using the Budyko hypothesis. Water Resour. Res. 43 (4), W04426. https://doi.org/10.1029/ 2006wr005224. Yang, D., Shao, W., Yeh, P.J.F., Yang, H., Kanae, S., Oki, T., 2009. Impact of vegetation coverage on regional water balance in the nonhumid regions of China. Water Resour. Res. 45, W00A14. https://doi.org/10.1029/2008wr006948. Yang, J., Wang, B., Bao, Q., 2010. Biweekly and 21-30-Day variations of the subtropical summer monsoon rainfall over the lower reach of the Yangtze River Basin. J. Clim. 23 (5), 1146–1159. https://doi.org/10.1175/2009JCLI3005.1. Yang, H., Lv, H., Yang, D., Hu, Q., 2012. Seasonality of precipitation and potential evaporation and its impact on catchment water-energy balance (in Chinese). J. Hydroelectric Eng. 31 54–59+93. Zhang, L., Dawes, W.R., Walker, G.R., 2001. Response of mean annual evapotranspiration to vegetation changes at catchment scale. Water Resour. Res. 37 (3), 701–708. https://doi.org/10.1029/2000wr900325. Zhang, L., Hickel, K., Dawes, W.R., Chiew, F.H.S., Western, A.W., Briggs, P.R., 2004. A rational function approach for estimating mean annual evapotranspiration. Water

Resour. Res. 40, W02502. https://doi.org/10.1029/2003WR002710. Zhang, D., Cong, Z., Ni, G., Yang, D., Hu, S., 2015. Effects of snow ratio on annual runoff within the Budyko framework. Hydrol. Earth Syst. Sci. 19 (4), 1977–1992. https:// doi.org/10.5194/hess-19-1977-2015. Zhang, S., Yang, H., Yang, D., Jayawardena, A.W., 2016. Quantifying the effect of vegetation change on the regional water balance within the Budyko framework. Geophys. Res. Lett. 43 (3), 1140–1148. https://doi.org/10.1002/2015gl066952. Zhao, Q.L., Liu, X.L., Ditmar, P., Siemes, C., Revtova, E., Hashemi-Farahani, H., Klees, R., 2011. Water storage variations of the Yangtze, yellow, and Zhujiang river basins derived from the DEOS mass transport (DMT-1) model. Sci. China-Earth Sci. 54, 667–677. https://doi.org/10.1007/s11430-010-4096-7. Zhou, G., Wei, X., Chen, X., Zhou, P., Liu, X., Xiao, Y., Sun, G., Scott, D.F., Zhou, S., Han, L., Su, Y., 2015. Global pattern for the effect of climate and land cover on water yield. Nat.Commun. 6, 5918. https://doi.org/10.1038/ncomms6918. Zhou, S., Yu, B., Huang, Y., Wang, G., 2015. The complementary relationship and generation of the Budyko functions. Geophys. Res. Lett. 42 (6), 1781–1790. https://doi. org/10.1002/2015gl063511. Zhou, S., Yu, B., Zhang, L., Huang, Y., Pan, M., Wang, G., 2016. A new method to partition climate and catchment effect on the mean annual runoff based on the Budyko complementary relationship. Water Resour. Res. 52 (9), 7163–7177. https://doi.org/10. 1002/2016wr019046.

68