Modeling water balance using the Budyko framework over variable 1 timescales under diverse climates 2

10 Understanding the effects of climate and catchment characteristics on overall water balance at different temporal scales 11 remains a challenging task due to the large spatial heterogeneity and temporal variability. Based on a long-term (1960–2008) 12 land surface hydrologic dataset over China, this study presented a systematic examination of the applicability of the Budyko 13 model (BM) under various climatic conditions at long-term mean annual, annual, seasonal and monthly temporal scales. The 14 roles of water storage change (WSC, dS/dt) in water balance modeling and the dominant climate control factors on modeling 15 errors of BM are investigated. The results indicate that BM performs well at mean annual scale and the performance in arid 16 climates is better than humid climates. At other smaller timescales, BM is generally accurate in arid climates, but fails to 17 capture dominant controls on water balance in humid climates due to the effects of WSC not included in BM. The accuracy 18 of BM can be ranked from high to low as: dry seasonal, annual, monthly, and wet seasonal timescales. When WSC is 19 incorporated into BM by replacing precipitation (P) with effective precipitation (i.e., P minus WSC), significant 20 improvements are found in arid climates, but to a lesser extent in humid climates. The ratio of the standard deviation of WSC 21 to that of evapotranspiration (E), which increases from arid to humid climates, is found to be the key indicator of the BM 22 simulation errors due to the omission of the effect of WSC. The modeling errors of BM are positively correlated with the 23 temporal variability of WSC and hence larger in humid climates, and also found to be proportional to the ratio of potential 24 evapotranspiration (PET) to E. More sophisticated models than the BM which explicitly incorporate the effect of WSC are 25 required to improve water balance modeling in humid climates particularly at all the annual, seasonal, and monthly 26 timescales. 27 Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-441 Manuscript under review for journal Hydrol. Earth Syst. Sci. Discussion started: 25 August 2017 c © Author(s) 2017. CC BY 4.0 License.


Introduction
Precipitation (P) partitioning into evapotranspiration (E), runoff (R) and soil water storage is controlled by climate and catchment characteristics, such as soil, topography, and vegetation (Zhang et al., 2008).Quantifying the effects of climate and catchment characteristics on water balance is a major scientific challenge for hydrologists.Budyko (1958) postulated that the first-order control on the partitioning of P is the balance between available water (P) and energy (represented by potential evapotranspiration, PET).The empirical relationship proposed, widely known as the Budyko's curve, has shown good agreement with long-term water balance data for numerous watersheds globally (Budyko, 1974).Based on the Budyko hypothesis, various functional forms associated with the relation between the evaporation ratio (E/P) and climate aridity index (PET/P) have been developed for quantifying long-term water balance (Pike, 1964;Fu, 1981;Choudhury, 1999;Zhang et al., 2001Zhang et al., , 2004;;Porporato et al., 2004;Yang et al., 2008;Gerrits et al., 2009).The parameters of the analytically derived Budyko-type equations (e.g., Fu, 1981;Zhang et al., 2004;Yang et al., 2008) well account for the effects of rainfall seasonality and soil water storage capacity (Milly, 1994a(Milly, , 1994b;;Potter et al., 2005;Hickel and Zhang, 2006;Yokoo et al., 2008;Gerrits et al., 2009;Feng et al., 2012) and vegetation dynamics (Zhang et al., 2001;Donohue et al., 2007;Oudin et al., 2008;Yang et al., 2009;Peel et al., 2010;Li et al., 2013;Zhang et al., 2016) on the long-term mean water-energy balance.
Recently numerous research efforts have been directed to extend the applicability of the original Budyko framework to smaller temporal scales than the long-term average, such as annual (Koster and Suarez, 1999;Sankarasubramanian and Vogel, 2002;Zhang et al., 2008;Yang et al., 2007Yang et al., , 2009;;Potter and Zhang, 2009;Cheng et al., 2011;Tekleab et al., 2011;Carmona et al., 2014;Yu et al., 2013), seasonal (Chen et al., 2013), monthly (Zhang et al., 2008;Tekleab et al., 2011;Du et al., 2016), and daily (Zhang et al., 2008) timescales.For example, Koster and Suarez (1999) proposed an analytical Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.framework based on the Budyko equation to quantify the interannual variability of E, and compared the theoretical framework with the global climate model simulations.Zhang et al. (2008) extended the Budyko framework to predict water balance at the mean annual, annual, monthly, and daily timescales in Australia.The results indicated that the models perform well in most catchments in Australia at the mean annual and annual timescales, but more complicated models are required at the shorter timescales primarily due to the importance of water storage change (WSC, dS/dt) at these smaller timescales.Yang et al. (2009) incorporated the impact of vegetation coverage into the Budyko framework to improve parameter estimation in the coupled water-energy balance equation.Chen et al. (2013) extended the Budyko framework to the seasonal timescale and also developed a model for incorporating interannual variability of E and WSC.The WSC has been found to be a significant component on water balance variability at annual or smaller timescales in many regions around the world (Eltahir and Yeh, 1999;Yeh and Famiglietti, 2008;Yokoo et al., 2008;Istanbulluoglu et al., 2012;Wang and Alimohammadi, 2012;Wang, 2012;Chen et al., 2013;Du et al., 2016).Wu et al. (2017) investigated the effects of climate and WSC on the temporal variability of E over China.They found that the effect of WSC in accommodating climatic fluctuations is larger at monthly timescale than at annual timescale, and even becomes the dominant controlling factor on the temporal variability of E in some extremely arid regions.Therefore, when applying to smaller timescales, the Budyko framework should be extended to incorporate the effect of WSC (Zhang et al., 2008;Zeng and Cai, 2015).Wang (2012) suggested that the effective precipitation (i.e., P minus WSC) can be used in Budyko's framework to account for the storage change and satisfy the water balance under the non-steady-state condition.
Although advances have been made in water balance simulations over variable timescales within the Budyko framework, our knowledge about the effects of climate and catchment characteristics on the water balance is still limited due to its spatial heterogeneity and temporal variability.The research question asked in this study is whether the Budyko framework is applicable for water balance modeling at smaller timescales when WSC becomes increasingly significant, and under various hydroclimate conditions particularly for the extremely humid or arid climates.On the basis of a long-term  gridded land surface dataset over China, the objectives here are: (1) to test the Budyko framework under various climatic conditions over four different timescales (mean annual, annual, seasonal, and monthly) at both the basin and the grid scales;

Data sources
A long-term  meteorological and hydrologic gridded dataset, covering the entire China with a 0.25° spatial resolution, is provided by Zhang et al. (2014).The observed meteorological data, including P, maximum temperature T max , minimum temperature T min and wind speed WS, are derived from the total 756 monitoring stations maintained by the Chinese Meteorological Administration (CMA).The hydrologic flux data including E, surface runoff (R s ) and baseflow (B s ), are obtained from the Variable Infiltration Capacity (VIC) model simulation forced by daily observed climate forcing data of P, T max , T min , and WS.The dataset used here provides a more reliable estimate of R, E and other hydrologic variables over China compared with the global products of a similar nature (e.g., Nijssen et al., 2001;Adam et al., 2006;Rodell et al., 2004;Sheffield et al., 2006;Sheffield and Wood, 2007;Pan et al., 2012), and hence it will be treated and termed as the "observed data" in this paper, particularly in contrast to the "predicted data" from the Budyko models.This dataset has been successfully used for the quantitative assessment of effects of climate and WSC on the temporal variability of actual evapotranspiration in China (Wu et al., 2017).The PET data spanning the period 1960-2008 with a 1° resolution is provided by the Hydroclimatology Group of Princeton University (Sheffield et al., 2006(Sheffield et al., , 2012)).The PET is estimated based on the Penman equation (Penman, 1948;Shuttleworth, 1993) using the updated meteorological dataset obtained from Sheffield et al. (2006Sheffield et al. ( , 2012)).
All the data used are disaggregated into 0.5° × 0.5° grids over China (for a total of 3814 grids) using the linear interpolation.
Gridded WSC at the time interval i dt is computed using the water balance equation: A total of 14 large river basins in China under a large diversity of climates, are chosen for analysis (Figure 1(a)).The monthly and annual P, E, R s , B s and PET for each of the 14 basins are estimated from the grid data within the basin boundary.
The basic and detailed information of the 14 basins and their long-term  mean water balances are given in Table 1.As seen, the mean annual aridity index (PET/P) is less than 1.0 in the Southeast Drainage, Pearl and Yangtze River basins belonging to humid climates, and in the range of 1.19-8.63for the other eleven basins belonging to arid climates.
The net primary productivity (NPP) is an important component of the global carbon budget directly reflecting the production capacity of vegetation, and it is the basis of organic material and energy cycles in the global ecosystem (Field et al. 1998;Houghton et al. 1999;Field, 2001).The formation of NPP can effectively indicate the ecological response of catchment characteristics.In this study, the 1-km NPP data set in 2010 covering the entire China as obtained from the Research Center for Natural resources and Environment Science Data of the Chinese Academy of Science, is used to represent the vegetation characteristics of catchments over China.Figure 1(b) show the spatial distribution of NPP over China.The value of NPP generally decreases from southern to northwest China, which is generally opposite to the pattern of mean annual aridity index.Scatterplot of NPP versus the mean annual aridity index for the 3814 grids of China is shown in Figure 1(c).As seen, the NPP decreases rapidly with the increasing aridity index for all regions with the aridity index smaller than 3.However, under the extremely dry conditions (the aridity index > 3) the NPP falls within a narrow range fluctuating around zero.NPP is negligible in the extremely dry regions such as some regions of Xinjiang.

Dry and wet seasons
For a given catchment, the dry and wet months among the twelve months of a year are identified based on the mean monthly aridity index expressed as (Chen et al., 2013)  , 1 where N d and N w represent the numbers of dry and wet months within a year (i.e.N d + N w =12).

The Budyko model (BM)
The Budyko curves are the equations coupling the concepts of water and energy balances which usually contain one or more parameters to be estimated (Turc, 1954;Pike, 1964;Fu, 1981;Choudhury, 1999, Zhang et al., 2001, 2004;Porporato et al., 2004;Yang et al., 2008;Gerrits et al., 2009).One of the commonly used functional forms is the Fu's equation (Fu, 1981;Zhang et al., 2004) expressed as follows: where the parameter ω represents the effects of land surface characteristics and climate seasonality on the water-energy balance (Li et al., 2013).The Fu's equation with a clear physical basis is considered to be more applicable for estimating mean annual evapotranspiration than other empirical formulas (Zhang et al., 2004).
As the timescale becomes finer, WSC becomes more significant in closing water budget since it controls the supply and demand of water fluxes with a delayed effect (Chen et al. 2013).Therefore, the effect of WSC has to be incorporated into BM particularly when applied to smaller timescales.Following Wang (2012), the water availability is defined as the effective (5) In this study, both equations ( 4) and ( 5) will be applied to the smaller timescales (i.e.annual, seasonal and monthly).The parameters ω is estimated by using the least-square method.

Model performance evaluation
The model performance is evaluated by using the Nash-Sutcliffe Coefficient of Efficiency (CE) and the Relative Error (RE).
The CE is calculated as where ,, and EE are the observed and simulated E at the ith time step, respectively.N is the number of the time steps.
CE ranges from  to 1.A positive CE value indicates acceptable model performance, and a CE closer to 1 indicates more efficient model performance (Moriasi et al., 2007).
The RE is a percentage measurement of mean bias of model simulations relative to observations, defined as ,, , 100% where ,, and EE represent the mean observed and simulated E over the N time steps.annual timescale with the correlation coefficient (r) of 0.97 and the RE of -2.9%.In addition, the estimated mean annual E under dry climates is more accurate than that under humid climates.water balance well for most grids.Consistent with the above, it is found that the model performs more accurately in the grids with a larger aridity index (i.e.smaller NPP) than more humid grids.

Basin scale
The BM is also applied to annual water balance modeling at the basin scale.The comparison of observed and BM-simulated annual E in the 14 river basins is shown in Figure 3.It demonstrates that the dynamic BM model generally produces a reasonably good fit to annual E for most of basins.The majority of arid basins with the aridity index > 1.0 (e.g.Inner Mongolia, Qiangtang, Qinghai, Xinjiang, Hexi) have a high CE ranging between 0.70 and 0.97, and a small RE ranging between -0.11% and 0.58%, indicating the performance of BM is rather reliable in arid basins at the annual scale.In contrast, for humid basins with the aridity index < 1.0 (e.g.Southeast Drainage and Pearl, and Yangtze), although RE is generally small, the model fails to capture the significant interannual variability of E and results in a negative CE in Southeast Drainage and Pearl River basin.
As WSC can play a significant role in affecting annual E, the extended BM (equation ( 5)), which incorporates the effect of WSC is also used to model annual water balance.The improvement relative to the original BM in the simulated annual E can be observed from Figure 3 for the arid basins (with the aridity index > 1.0): the CE (RE) in these arid basins is ranging from 0.4-0.98 (-0.17% -0.06%).However, virtually no improvement can be seen for the humid basins (Southeast Drainage, Pearl, and Yangtze basins) in which the performance (CE) becomes worse than the BM.Therefore, the extended BM may not provide significant improvement over the BM when applied to humid basins at the annual scale.

Grid scale
Similar to the basin scale, the BM for annual water balance modeling is applied to the 3814 grids over the entire China (Figure 4).As seen from Figure 4a, there are 81%, 63.7% and 37.3% of grids with CE greater than 0, 0.5, and 0.8, respectively.The RE for all grids ranges between -16.1% and 8.2% (Figure 4b).For the grids with the aridity index ≤ 3, CE is considerably small under humid conditions and increases rapidly toward nearly 1.0 with the increasing aridity index (Figure 4c).Similarly, RE is relatively large (small) under the humid (extremely dry) conditions (Figure 4e). Figure 4g compares the observed and simulated interannual variability of E (as quantified by the standard deviation of annual E) for the 3814 grids with the mean annual aridity index also given in the color bar.All the grids have the interannual variability of E less than 120 mm.The correlation coefficient between observed and simulated interannual variability of E for all grids is 0.819, but the simulated E interannual variability is generally higher than observations (Figure 4g).Although performing well for most grids in dry regions, the BM performs rather poorly for a large portion of grids in humid regions mainly due to the impacts of interannual variability of WSC which have not been included in the BM.
The validation of the extended BM against the observed E (red line in Figure 4a) indicates that 83.5%, 70.1% and 48.1% of grids with the CE > 0, 0.5 and 0.8, respectively.The RE ranges between -16.1% to 6.9% (Figure 4b) rather close to the performance of BM.The correlation coefficient between observed and simulated interannual variability of E is 0.835, slightly larger than 0.819 of the BM.However, the overestimated interannual variability of E in BM in humid grids is significantly improved by the extended BM (Figure 4h).Overall the extended BM provides potential improvements of annual water balance at the grid scale mainly in correcting the overestimated interannual variability of E, but the improvement is limited for the grids with the underestimated interannual variability (Figures 4g and 4h).

Basin scale
Following the definition of the wet-and dry-season (equations ( 2) and ( 3)), the wet and dry seasonal PET/P, PET/P e , E/P, and E/P e are calculated respectively in each basin.For some extremely humid (arid) basins, the mean monthly aridity indices can be all smaller (larger) than 1.0 for all twelve months so that there is only wet (dry) season without any dry (wet) season.
Figure 5 shows the validation of the BM and extended BM against observed E at the dry seasonal scale for all 13 basins except the Southeast Drainage basin which does not have any dry season.As seen, the BM performs poorly in capturing the peaks and troughs of E in the Pearl, Yangtze, Southwest Drainage and Huaihe basins, with the CE all below 0.4.For the other 9 less humid basins in Figure 5, the simulated E by the BM agrees well with observed E with the CE (RE) ranging from 0.52 to 0.97 (0.02% and 0.24%).Significant improvements in the extended BM simulations are found for all basins, particularly notable in the Pearl, Southwest Drainage, Huaihe and Liaohe basins.The CE of the extended BM ranges between 0.44-0.98,and there are seven out of 13 basins with CE > 0.9, indicating that the extended BM simulation is generally accurate in the dry seasonal scale.
The validations of the BM and extended BM against observed E in the wet seasonal scale are shown in Figure 6 for the only 8 out of the 14 basins with the wet season.As seen, the BM is unable to simulate E accurately with all CE less than 0.5.
Similar to that found in the BM simulation, the extended BM simulations still show large discrepancy in reproducing the observed interannual variability of E at the wet seasonal scale.Particularly for the Huaihe basin, both the BM and the extended BM significantly underestimate the long-term mean E, with the RE -10.93% and -10.33% respectively.The simulated E cannot well capture the sharp rises and falls of interannual variability of E, likely due to the strong variability of water balance at the wet seasonal scale.

Grid scale
Similar to the basin scale, the PET/P, PET/P e , E/P and E/P e are calculated separately for wet-and dry-season at the grid scale.The validation of the BM and extended BM against observed E in dry season for the selected grids is shown in Figure 7.There are 3538 out of the total 3814 grids (92.8%) with dry season identified within twelve months.For the performance of BM, the CE is larger than 0, 0.5 and 0.8 for 83.1%, 64.5% and 39.9% of grids, respectively.The CE is small in humid grids and increases as the aridity index increases.When moving toward increasingly drier climates, the CE gradually becomes insensitive to the aridity index (> 20) and approaches to the upper limit of 1.0.Strong correlation (~0.94) is found between the observed and simulated interannual variability of E in dry season (Figure 7g).However, the BM tends to overestimate the interannual variability of E particularly for the humid basins with the RE as large as 124.3% (Figure 7e).
The results suggest that the BM is more applicable to arid than humid climates, similar to that found in analyzing annual water balance.The validation of the extended BM performance against observed E indicates a significant improvement over the BM.There are more than 96.3%, 85.4%, and 60% of grids with CE > 0, 0.5 and 0.8, respectively.The RE in humid climates is reduced from >100% in BM to only about 10-20% in the extended BM (Figure 7f), also the overestimated variability of simulated E in humid climates is largely corrected by the extended BM (Figure 7h) to achieve excellent performance in water balance modeling in dry season.
The validation of the BM and extended BM against observed E in the wet season at the grid scale is shown in Figure 8.
There are in total 1982 out of 3814 grids (52%) with the wet season identified within twelve months.For these 1982 grids, the CE of the BM simulation are all < 0.73, and only 41.3% of grids with CE > 0. The RE of the BM simulation is negative for 83.4% of grids, and it tends to perform even worse in more arid climates (Figure 8e).Based on these results, it can be concluded that the BM performance is not satisfactory in the wet season at the grid scale, similar to that found at the basin scale.The performance of the extended BM in the wet season is similarly poor as the BM for most grids.Therefore, more sophisticated water balance models with the capability of simulating important mechanisms in wet season are required to model the interannual variability of water balance more accurately for all basins and grids under diverse climates.

Basin scale
The BM and the extended BM are applied to model monthly water balance for the 14 river basins.The comparisons between the observed and simulated monthly E from both models are presented in Figure 9. Overall, the BM performs well in all basins with the RE (CE) between -16.6% and 9.5% (0.69 and 0.98).However, the BM tends to underestimate the peaks of E in some basins (Southeast Drainage, Pearl, Yangtze, Southwest Drainage and Huaihe).In contrast, the extended BM performs poorly for most basins (particularly in humid basins), with 8 out of 14 basins having CE lower than the BM and 11 out of 14 basins having the absolute value of RE larger than the BM.Improvements caused by using the extended BM can only be found in several dry basins (e.g., Qinghai, Xinjiang, and Hexi).

Grid scale
The validation of the BM and the extended BM against observed E at the monthly scale is presented in Figure 10.For the BM, there are 97.1% and 57.2% of the 3814 grids with the CE > 0 and 0.8, respectively.For the extended BM, almost all the grids have CE > 0 and 68.1 % of grids have CE > 0.8.The RE in the BM (the extended BM) ranges between -40.8% and 449.5% (-49.6% and 72.2%).The BM tends to be more accurate in arid climates, consistent with the findings at the annual and seasonal timescales.However, the extended BM performs poorly in arid climates, significantly underestimating the intra-annual variability of E in humid climates (Figure 10h).Comparisons between Figure 10c and 10d reveal that the BM performs better performance (with larger CE) than the extended BM mainly in the grids with the aridity index > 20, while the extended BM performs better than BM mainly in the grids with a smaller aridity index (< 10).

The role of water storage change (WSC) in water balance modeling
In general, the influence of WSC is more significant in the annual and smaller timescales (Wu et al., 2017), and this has been recognized to have an impact on the water balance modeling of BM (Zhang et al., 2008;Donohue et al., 2010;Chen et al., 2013).Figure 11  with that of WSC for all the four timescales examined.In addition, the correlation tends to be stronger in dry season (Figure 11b) than in wet season (Figure 11c).Figure 12 shows the relations between CE and σ WSC /σ E (the ratio between the standard deviations of observed WSC and E) at four different timescales.As shown, WSC is significant on the variability of water balance at annual and smaller timescales (particularly at the seasonal timescale) and the variability of WSC tends to be more significant than that of E in humid climates.The correlation coefficients of CE and σ WSC /σ E range between -0.67 and -0.44 at four timescales, indicating that a larger σ WSC /σ E would lead to low accuracy in the BM simulations particularly in humid climates .These results suggest that the BM is not suitable for water balance modeling in humid climates at the smaller timescales when the temporal variability of WSC is significant.

Primary controlling factors in the modeling errors of BM in humid climates
As mentioned before, the BM performs poorly in humid climates with large modeling errors over the long-term mean annual, annual, seasonal, and monthly timescales.In humid climates, the partitioning of P into E and runoff is mainly controlled by PET, which is commonly termed as the energy-limited condition (Zhang et al., 2004(Zhang et al., , 2008;;Yang et al., 2009, Zeng andCai, 2015).Therefore, the performance of the BM in modeling E should be dependent on both PET and E under the energy-limited condition.
According to McVicar et al. (2012), the climate conditions can be classified into three cases: the energy-limited areas (mean annual aridity index < 0.76), the 'equitant' areas (0.76 < mean annual aridity index < 1.35), and the water-limited areas (mean annual aridity index > 1.35).In this study, a total of 622 grids categorized as the energy-limited condition with mean annual aridity index < 0.76 are identified from the total 3814 grids in China.The RE of the BM simulations for each of the 622 grids at mean annual, annual, seasonal, and monthly timescales are compared with the mean ratio of PET/E in Figure 13.
As seen, the mean RE is generally smaller than zero at all mean annual, annual, seasonal, and monthly timescales when the mean PET/E < 1.5.It is clear that the mean RE is positively correlated with the mean PET/E, particularly at the mean annual scale with a large correlation coefficient of 0.976.The pattern of the scatterplot at the annual scale is similar to that at the wet seasonal scale.When the mean PET/E < 1.5, the mean RE is sensitive to the mean PET/E.However, when the mean PET/E > 1.5, the mean RE becomes insensitive to the mean PET/E and falls within a narrow range fluctuating around zero.As the timescale decreases to the month scale, the mean RE tends to become large with the increasing mean PET/E when the mean Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.(2) to investigate the role of WSC in water balance modeling at various timescales and under different climate conditions; and (3) to identify the dominant climatic controlling factors on the modeling errors of the Budyko framework.It is anticipated that the knowledge obtained from this study would enhance understanding of the controls of climatic and catchment characteristics on the water balances from arid to humid climates and across a variety of timescales.
the 1960-2008 monthly climatology of potential evaporation, precipitation and storage Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.change, respectively.The classification between dry and wet months are based upon the criterion wet) for each month from January through December, and this classification remains the same for all years.Based on the identified dry and wet months, the dry and wet seasonal precipitation, potential evaporation, and storage changes are calculated by summing up the dry-and wet-months values for each year during 1960-2008.For example, the dry seasonal PET (PET d ) and the wet seasonal PET (PET w ) are computed as , 1 Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.precipitation P e, (i.e.,

Figure 2
Figure2(a) shows the mean annual E/P versus PET/P over the 14 river basins in China.As seen, the BM (equation (4)) with Figure 2(c) shows the comparison between the "observed" and the BM-predicted mean annual E in the 14 river basins.Results indicate that the estimated E using the Fu's equation agrees well with observations at the long-term mean

Figure 2
Figure 2(b) plots the mean annual E/P versus PET/P along with the distribution of NPP, while Figure 2(d) shows the comparison between observed and BM-simulated mean annual E. Both subplots include all the total 3814 grids in China.It is clear that most of grids follow the Budyko curve reasonably well with a fitted ω of 1.97, and the aridity index increases with the decreasing NPP.The high r (~0.94, Figure 2(d)) indicates that the BM can be calibrated and simulates mean annual Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.
plots the mean variability (i.e. standard deviation) of the modeling errors of BM (the simulated minus the observed E) versus the mean variability (i.e. standard deviation) of WSC from the annual, dry season, wet season and monthly timescales.As seen, both the variability of the modeling errors in E and the variability of WSC are larger under more humid climates.The variability of modeling errors in E shows a strong positive correlation (ranging from 0.6 to 0.8) Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.
Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.PET/E > 1.5.Overall the mean RE is strongly correlated with the mean PET/E at the monthly timescale, and this is likely due to the in-phase seasonality between PET and E under the energy-limited condition.The results suggest that the PET/E (especially for the condition PET/E < 1.5) can be one of the main factors controlling the errors of the BM simulation under the energy-limited condition.5Summary and future workOn the basis of a long-term land surface hydrologic data, this paper presents a systematic examination of the applicability of the Budyko framework at four temporal scales (long-term mean annual, annual, seasonal, and monthly) under a wide variety of climatic conditions in China.The original Budyko model and the extended Budyko model (which incorporates the effect of WSC by using the effective precipitation P-WSC to replace P) are validated at both the 14 river basins and the total 3814 0.5° × 0.5° grid scales for the entire China.The role of WSC in modeling water balance and the dominant climate factors controlling the modeling errors of E by the original Budyko model are emphasized.At the long-term mean annual scale which the effect of WSC is negligible, the Budyko model generally performs well in terms of simulated E, and the performance in arid climates is better than that in humid climates.The effect of WSC becomes significant in modeling E at the smaller temporal scales particularly in humid climates.Under such circumstances, the original BM is generally accurate for modeling water balance under arid climates, but it fails to capture the dominant controls of WSC on water balance partitioning under humid climates.Overall the accuracy of the original Budyko model can be ranked from high to low as follows: dry seasonal, annual, monthly, and wet seasonal scales.As the effective precipitation is used as a substitute for precipitation in the extended Budyko model, an improvement of water balance modeling can be found in arid climates, but to a much lesser extent in humid climates.The performance of the extended Budyko model is generally better than the original Budyko model at the dry seasonal timescale, but tends to be worse at both the wet seasonal and monthly timescales.More sophisticated models explicitly accounting for the effect of WSC are required to improve water balance modeling particularly in humid climates and at smaller timescales.The WSC and the modeling errors in E both show larger temporal variability in humid climates.The temporal variability of Hydrol.Earth Syst.Sci.Discuss., https://doi.org/10.5194/hess-2017-441Manuscript under review for journal Hydrol.Earth Syst.Sci. Discussion started: 25 August 2017 c Author(s) 2017.CC BY 4.0 License.modelingerrors in E shows a strong positive correlation with that of WSC at all annual, seasonal and monthly timescales (the correlation coefficient between 0.6-0.8,Figure11).The accuracy of the Budyko model simulations decrease with the increased ratio between the standard deviations of WSC and E particularly in humid climates.In addition, under the energy-limited condition (mainly in humid climates), the mean relative errors of the Budyko model show a strong positive correlation with the mean ratio of PET/E at the long-term mean annual timescale.However, at the annual and seasonal timescales, the mean relative errors are sensitive to the mean ratio of PET/E only under the condition PET/E < 1.5.Future research will be focused on the identification and quantifications of controlling factors in the modeling errors of the Budyko model from the arid to humid climates over variable timescales, particularly when PET/E is greater than 1.5.

Figure 1 .
Figure 1.(a) Location of the 14 river basins in China, (b) the spatial distribution of the NPP over China, and (c) the relationship between the NPP and the aridity index for the 3814 grids over China.

Figure 2 .
Figure 2. The mean annual evaporation ratios as a function of the mean annual aridity indices for (a) the 14 river basins and (b) the 3814 grids over China with the color bar of NPP (gC.m -2 yr -1 ) for the 14 river basins and 3814 grids.The comparison of observed and simulated mean annual E for (c) the 14 river basins and (d) the 3814 grids over China with the color bar of the mean annual aridity index for the 14 river basins and 3814 grids.The red-lines in subplots (a) and (b) are fit by using the long-term mean data points of the 14 basins and 3814 grids, respectively.

Figure 3 .
Figure 3.Comparison of annual time series of observed E (black dots) with that predicted by the BM (blue line) and that predicted by the extended BM (red line) for each of the 14 basins.The number in the parentheses is consistent with that given inTable 1.

Figure 4 .
Figure 4. Model validation at the annual timescale: (a) the cumulative distribution of the percentage of grids with the CE larger than or equal to a specific value for the BM (blue line) and the extended BM (red line); (b) same as (a), but for RE.The relationship between CE and the aridity index for (c) the BM and (d) the extended BM for the total 3814 grids over China.The relationship between RE and aridity index for (e) the BM and (f) the extended BM.Comparison of observed and simulated E variability for (g) the BM and (h) the extended BM.The color bar indicates the mean annual aridity index for the total 3814 grids over China.

Figure 5 .
Figure 5.Comparison of dry season time series of observed E (black dots) with that predicted by the BM (blue line) and that predicted by the extended BM (red line) for each of the 13 basins.The number in the parentheses is consistent with that given inTable 1.

Figure 7 .
Figure 7. Model validation at the dry seasonal timescale: (a) the cumulative distribution of the percentage of grids with the CE larger than or equal to a specific value for the BM (blue line) and the extended BM (red line); (b) same as (a), but for RE.The relationship between CE and the aridity index for (c) the BM and (d) the extended BM for the total 3538 grids over China identified with the dry season.The relationship between RE and aridity index for (e) the BM and (f) the extended BM.Comparison of observed and simulated E variability for (g) the BM and (h) the extended BM.The color bar indicates the mean annual aridity index for the total 3538 grids over China.

Figure 8 .
Figure 8. Model validation at the wet seasonal timescale: (a) the cumulative distribution of the percentage of grids with the CE larger than or equal to a specific value for the BM (blue line) and the extended BM (red line); (b) same as (a), but for RE.The relationship between CE and the aridity index for (c) the BM and (d) the extended BM for the total 1982 grids over China identified with the wet season.The relationship between RE and aridity index for (e) the BM and (f) the extended BM.Comparison of observed and simulated E variability for (g) the BM and (h) the extended BM.The color bar indicates the mean annual aridity index for the total 1982 grids over China.

Figure 9 .
Figure9.Comparison of monthly time series of observed E (black dots) with that predicted by the BM (blue line) and that predicted by the extended BM (red line) for each of the 14 basins.The number in the parentheses is consistent with that given in Table1.

Figure 10 .
Figure 10.Model validation at the monthly timescale: (a) the cumulative distribution of the percentage of grids with the CE larger than or equal to a specific value for the BM (blue line) and the extended BM (red line); (b) same as (a), but for RE.The relationship between CE and the aridity index for (c) the BM and (d) the extended BM for the total 3814 grids over China.The relationship between RE and aridity index for (e) the BM and (f) the extended BM.Comparison of observed and simulated E variability for (g) the BM and (h) the extended BM.The color bar indicates the mean annual aridity index for the total 3814 grids over China.

Figure 11 .
Figure 11.The temporal variability (i.e., standard deviation) of the modeling errors in E (i.e., the simulated E of the BM minus the observed E) versus that of WSC at the (a) annual, (b) dry season, (c) wet season, and (d) monthly timescales.The color bar indicates the mean annual aridity index of the selected grids.

Figure 12 .
Figure 12.The ratio of the standard deviation of WSC to that of E versus the CE of the BM simulations at the (a) annual, (b) dry season, (c) wet season, and (d) monthly timescales.The color bar indicates the mean annual aridity index of the selected grids.

Figure 13 .
Figure 13.The relationship between the mean RE of E and the mean ratio of PET/E for the 622 grids under the energy-limited condition with (a) mean annual, (b) annual, (c) wet seasonal, and (d) monthly timescales.
Figure 6.Comparison of wet season time series of observed E (black dots) with that predicted by the BM (blue line) and that predicted by the extended BM (red line) for each of the 8 basins.The number in the parentheses is consistent with that given inTable 1