A Multi-Dimensional Hydro-Climatic Similarity and Classification Framework Based on Budyko Theory for Continental-Scale Applications in China

Our knowledge of the similarities and differences in ecological systems is vital to understanding the co-evolution of ecological factors. This study proposes a multi-dimensional hydro-climatic similarity and classification framework based on Budyko theory. The framework employs the dryness index (DI), evaporative index (EI), and an empirical parameter (ω) to further sub-divide four climatic zones (humid, semi-humid, semi-arid, and arid zones) in terms of DI. A criterion that define the similarities between stations is proposed to verify the classification to obtain optimal results. This method is applied to Mainland China, and 637 stations are adopted for continental-scale classification experiments. The point cloud of the Budyko curve for all the stations in Mainland China is plotted. We find that the hydrothermal conditions of the vertically distributed stations on the Budyko curve can be quite different in the same climatic zone when DI < 4.0. The higher the vertical locations of the stations on the Budyko curve are, the drier and colder the climates and corresponding natural landscapes. Under the proposed hydro-climatic classification framework, the four climatic zones are further divided into 17 sub-regions, and the hydrothermal conditions for each sub-region are discussed. The results suggest that regional differences of long-term water balance are resulted by not only mean annual hydrothermal factors and catchment forms but also annual distribution of hydrothermal factors. Our framework can provide hydrologically-based classification across continental scale and, thus, provide a profound understanding of hydrothermal conditions of continental-scale hydrological cycles.


Introduction
The ecological systems are an open, relatively stable hierarchical system in space-time [1].Similarities and differences in ecological systems have attracted widespread attention in recent years, suggesting that there is considerable interest in extending our understanding of the co-evolution of terrain, climate, soil, vegetation, human activities and numerous other factors [2][3][4][5][6].Climate is an important factor that has a strong impact on ecology [7][8][9], and understanding environmental conditions and regional differences is the basis of the study of ecological systems.Thus, hydro-climatic classifications are of great significance for ecological zoning, resource and environment evaluation, and ecosystem change and management.
Initially, studies of natural regional differences mostly focused on a single factor such as temperature, precipitation, soil, and vegetation [10] but individual natural factors are in a state of interaction and mutual restraint [11,12].The classification of differences among single factors is one-sided, and many other factors should be taken into account [13].For example, Fernandez and Sayama [14] proposed a classification framework for large river basins based on temporal patterns of precipitation, evaporation, storage and runoff utilizing a global dataset.Another famous approach is the Köppen Climate Classification, which considers temperature and precipitation [15] and offers clear standard boundaries, but its operation is tedious, and it lacks hydrologically relevant details in the form of the interaction between water and energy availability and so on [3,16].
In addition, many hydro-climatic classification studies have been conducted by examining synthetic climate indices [17], such as the humidity index [18], potential evaporation and dryness tolerance [19,20], latent potential evaporation, moisture levels [21], biological temperature, dryness index (DI, which is often refer to as aridity index) [22], and temperature and humidity/aridity values [23].Budyko [24] found that the DI drives the partitioning of precipitation into runoff and evaporation across the large-scale long-term average water balance, and the DI is widely applied as an indicator to large-scale climate classifications [25][26][27].For instance, Wu et al. [27] classified China into four climatic zones using the DI.But hydro-climatic classifications based on a synthetic climate index still involve one-dimensional mapping, which cannot reflect overall regional differences [28].Recent studies (e.g., [16,29,30]) all show that three climatic indices can help characterize flow regimes.As pointed by Knoben et al. [16], at least two aspects, e.g., available water (precipitation) and energy (temperature and evaporation) should be considered to conceptualize regional hydro-climatic characteristics.Understanding of this principle has led to the Budyko curve for assessing annual water balance [16].
In 1974, Budyko [24] proposed a well-known hydro-climatic scheme based on the DI and evaporative index (EI).He found that the relationship between the DI and EI is basically represented as a single line though he acknowledged that small variations around the curve can arise depending on local conditions.Subsequent studies have further detected the deviations from the Budyko curve, indicating that the DI and EI do not purely reflect a single line relationship, which indicates that, in addition to the DI, other variables besides the DI can influence variability in the regional water balance [13,[31][32][33].Land surface conditions [32,[34][35][36][37][38][39][40][41] and climate variability [42][43][44][45][46][47][48] have been identified as responsible for such deviations.In fact, Fu [49] found a theoretical non-monomial relationship between the DI and EI and derived Fu's equation in which parameter ω was introduced to the Budyko hypothesis to reflect deviations from the Budyko curve.In other words, parameter ω can reflect similarities and differences among regions.The parameter (ω) is assumed to represent the synthesized effects of vegetation cover, soil properties, and catchment topography on water balance [31,32].
Based on Fu's theoretical works, the physical significance of parameter ω has been widely discussed.For example, Zhang et al. [31] found that parameter ω is higher for forested catchments than grass-covered catchments.Merz and Blöschl [50] manually divided Austria into five hydro-climatic regions through an assessment of the hydro-climatic variability of catchments and found that each region is plotted differently on the Budyko curve.Yang et al. [32] analyzed 108 catchments in the Yellow River basin and found that parameter ω presents significant regional distribution characteristics.In fact, the value of parameter ω can be directly estimated through long-term mean water balance and average climate using Fu's equation.Furthermore, Yang et al. [32] suggested an empirical formula for estimating it in terms of the dimensionless landscape parameters.
Above studies have shown that different values of parameter ω on the Budyko curve represent different hydro-climatic attributes.However, so far it is only used to reveal the differences of hydro-climatic conditions caused by different land covers in regional scale.In continental scale, Greve et al. [51] assessed the predictability of water availability in regions by using a probabilistic Budyko framework assuming a certain distribution of the parameter ω.While as noted by Greve et al. [51], ω is not a constant and differs between catchments that are characterized by different land surface and climatic conditions.That is to say ω varies according to climatic conditions.Hence, Budyko theory should have the potential to be used for continental-scale classifications.
Our objective is to develop a theoretical framework for hydrologic classification by assessing mean annual water balance based on Budyko theory.The suggested multiple-dimensional classification strategy applied in this study uses three climatic indices, i.e., the DI, EI, and parameter ω, to repartition a traditional climatic zone in terms of the DI.To verify the classification results, a similarity standard is proposed: optimal partition results are obtained when most similar stations within each sub-region are selected.In this study, the multi-dimensional classification framework is applied to Mainland China to obtain optimal partition results, and the hydrothermal conditions for each type of station and differences and similarities among stations in the same climatic zone are discussed.Finally, we evaluate the results of our hydro-climatic classification for Mainland China.

Study Area and Data
China is located in eastern Asia on the west bank of the Pacific Ocean, which is heavily affected by the monsoon climate.Climatic patterns range from tropical, subtropical, warm-temperate, and temperate to cold-temperate from south to north in the eastern regions of the country.Moreover, due to the continental climate, climatic patterns shift from humid to arid from east to west.At the same time, more than half of China is occupied by mountains and plateaus, and these local climates and complex physiognomic features produce a large variety of biomes across the country.
The climate data considered (1961-2012) include the observed monthly mean temperature, precipitation, relative humidity, wind speed and sunshine period values (from the National Data Center of the China Meteorological Administration) from 637 stations across Mainland China (Figure 1).Thus, Mainland China is selected as the study area and islands without data are not considered in sub-region classification in this study.(Figure 1).The 90 m Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM) data was obtained from the Geographical Spatial Data Cloud of the Computer Network Information Center of the Chinese Academy of Sciences [52].Soil types were provided by the Institute of Soil Science of the Chinese Academy of Sciences [53], and soil texture data were collected from the Data Center for Resources and Environmental Sciences of the Chinese Academy of Sciences (RESDC) [54].

Budyko Theory
The general form of Budyko theory is given as follows: (1) where DI is the dryness index; EI is the evaporative index; P is the mean annual precipitation (mm); E0 is the mean annual potential evapotranspiration (mm), and Ea is the mean annual actual evapotranspiration (mm).
Based on the Budyko hypothesis, Fu [49] obtained a theoretical analytical formula for the Budyko curve through dimension analysis and mathematical derivation [31] that is referred to as Fu's equation: where ω > 1 is a dimensionless parameter.As has been documented (e.g., [31,32]), parameter ω represents the synthesized effects of catchment characteristics on water balance, and its value can be calibrated through long-term mean water balance and average climate using Fu's equation.As is impacted not only by climate but also catchment factors, local long-term water balance should not vary along a single Budyko curve and, thus, only a group of such curves can be able to represent the regional differences.

Potential Evapotranspiration
According to the FAO [55], the Penman-Monteith method for potential evapotranspiration can be expressed as:

Budyko Theory
The general form of Budyko theory is given as follows: (1) where DI is the dryness index; EI is the evaporative index; P is the mean annual precipitation (mm); E 0 is the mean annual potential evapotranspiration (mm), and E a is the mean annual actual evapotranspiration (mm).
Based on the Budyko hypothesis, Fu [49] obtained a theoretical analytical formula for the Budyko curve through dimension analysis and mathematical derivation [31] that is referred to as Fu's equation: where ω > 1 is a dimensionless parameter.As has been documented (e.g., [31,32]), parameter ω represents the synthesized effects of catchment characteristics on water balance, and its value can be calibrated through long-term mean water balance and average climate using Fu's equation.As is impacted not only by climate but also catchment factors, local long-term water balance should not vary along a single Budyko curve and, thus, only a group of such curves can be able to represent the regional differences.

Potential Evapotranspiration
According to the FAO [55], the Penman-Monteith method for potential evapotranspiration can be expressed as: where G is the soil heat flux density (MJ m −2 d −1 ); T is the air temperature measured at a height of 2 m ( • C); u 2 is the wind speed measured at a height of 2 m (m s −1 ); e s is the saturation vapour pressure (kPa); e a is the actual vapour pressure (kPa); e s − e a is the saturation vapour pressure deficit (kPa); ∆ is the slope vapour pressure curve (kPa • C −1 ); γ is the psychrometric constant (kPa • C −1 ); and R n is the net radiation measured from the crop surface (MJ m −2 d −1 ).R n is calculated as follows: where Ab is the ground reflectance, which is related to surface conditions and soil moisture content levels; s denotes periods of sunshine; S is the maximum possible length of sunny periods; a s and b s are dimensionless parameters, a s is a regression constant that expresses the fraction of extraterrestrial radiation reaching the earth on overcast days (s = 0), a s + b s represents the fraction of extraterrestrial radiation reaching the Earth on clear days (s = S); R a is the solar shortwave radiation; and R nl is the net long wave radiation.
The computation of all the data required to calculate of E 0 followed Chapter 3 of FAO Paper 56 [55].Moreover, recommended values for parameters a s and b s for Mainland China were used to calculate solar radiation levels [56].The monthly accumulated values of potential evapotranspiration are used for estimating actual evapotranspiration in the following section.

Actual Evapotranspiration
Actual evapotranspiration is estimated through a water balance model is based on the Thornthwaite-Mather approach [21] in this study.Here E a is calculated as follows: where W fc is the field capacity, W p is the wilting point, and W is the soil water content (W p ≤ W ≤ W fc ).The field capacity (W fc ) and wilting point (W p ) data can be estimated from soil texture data.The soil moisture retention function β is based on the ratio of the available soil water content to the maximum available soil water content and expressed as Accordingly, β will decrease linearly until all available water is used.
The governing equation of the water balance model is written as follows: where L is the water surplus; ∆W is the monthly change in W; and ∆t is the time step.Soil moisture content levels measured at the beginning and end of each month are used to calculate ∆W.In the model, the soil depth of the model is set to 1 m.Gao et al. [56] used this method to estimate monthly actual evapotranspiration for 686 stations over China.According to their suggestions, as the initial soil water content for each station is unknown a 60 months warm-up period (balancing routine) is used to force the net change in soil moisture from the beginning to the end of a specified balancing period to zero.They also suggested that the actual evapotranspiration can be assumed to be 0 mm when the monthly air temperature is less than or equal to 0 • C as frozen soil or snow cover prevents effective evapotranspiration from the ground surface.

The Multi-Dimensional Classification Framework
From the traditional climate classification framework in terms of the DI, Wu et al. [27] classified Mainland China into four climatic zones: a humid zone with DI ≤ 0.99, a semi-humid zone with DI∈(1.00,1.49), a semi-arid zone with DI∈(1.50, 3.99), and an arid zone with DI ≥ 4.00.In this study, EI and parameter ω are further employed to repartition climatic zones.As shown in Figure 2, five main procedures are applied under the classification framework.First, the mean annual DI and EI values are calculated for each station, and point clouds for these values are plotted on the Budyko curve.Second, four climatic zones are classified based on the DI according to the method of Wu et al. [27].Third, by setting different values of ω, a cluster of Fu's curves is obtained, which divide each climatic zone into n sub-regions (see Figure 3).Here, the values of ω are determined to make Fu's curves cross equipartition points on the line segment between intersections of the lower and upper envelope lines, namely, EI = a and EI = b while DI = 1 (Figure 3).Line DI = 1 was used as it forms the turning point of the Budyko theoretical boundary, and it is the dividing line between the humid zone and the non-humid zone.Moreover, as the EI is close to 1 when DI > 4, the arid zone is classified into two sub-regions with DI = 20 used as an indicator [57].The similarities of stations derived from multivariate statistics are used to verify the classification results.Traditionally, multivariate statistical tools based on hydro-climatic and physical characteristics [6,58,59] have been used in hydro-climatic classification and regionalization studies.Thus, eight climatic and physical factors that can comprehensively characterize climatic, topographical, and surface conditions for each station were adopted in this study to establish an eight-dimensional vector space as follows: where x1 to x5 represent average annual values of climatic factors (i.e., wind speed, vapour pressure, temperature, sunshine, and precipitation), x6 is station altitude, and x7 and x8 denotes the soil textures (namely, sand and clay content, respectively).Similarities between any two stations are characterized by the distance in the vector space, namely, the Euclidean distance.The Euclidean distance between two meteorological stations can be obtained from Equation (10): where  , and  , are normalized values of the eight-dimensional vectors Xi and Xk for the ith and kth stations, respectively, and ρ(Xi,Xk) and ρ(Xi,Xk) are the Euclidean distances of Xi and Xk, respectively.When this value is larger, the two stations are less similar.Optimal classification results can be obtained when the mean level of similarity between stations within each sub-region is the highest.The similarities of stations derived from multivariate statistics are used to verify the classification results.Traditionally, multivariate statistical tools based on hydro-climatic and physical characteristics [6,58,59] have been used in hydro-climatic classification and regionalization studies.Thus, eight climatic and physical factors that can comprehensively characterize climatic, topographical, and surface conditions for each station were adopted in this study to establish an eight-dimensional vector space as follows: where x 1 to x 5 represent average annual values of climatic factors (i.e., wind speed, vapour pressure, temperature, sunshine, and precipitation), x 6 is station altitude, and x 7 and x 8 denotes the soil textures (namely, sand and clay content, respectively).Similarities between any two stations are characterized by the distance in the vector space, namely, the Euclidean distance.The Euclidean distance between two meteorological stations can be obtained from Equation (10): (10) where x i,j and x k,j are normalized values of the eight-dimensional vectors X i and X k for the ith and kth stations, respectively, and ρ(X i ,X k ) and ρ(X i ,X k ) are the Euclidean distances of X i and X k , respectively.When this value is larger, the two stations are less similar.Optimal classification results can be obtained when the mean level of similarity between stations within each sub-region is the highest.

General Classification Results
All 637 meteorological stations across Mainland China were used for the classification experiment.
Mean annual E 0 and E a values for each station were calculated using long-term climatic data and the point cloud of the Budyko curve was plotted for all stations in Mainland China (Figure 4).First, four basic climatic zones-humid, semi-humid, semi-arid and arid-were classified based on the DI according to the method of Wu et al. [27].It was found that stations from the same climatic zone cover a broad range of the Budyko curve (see Figure 4), with the exception of the arid zone.EI is close to 1, but DI covers a broad span of values ranging from 4 to 57 in the arid zone.
Water 2019, 10, x FOR PEER REVIEW 8 of 26

General Classification Results
All 637 meteorological stations across Mainland China were used for the classification experiment.Mean annual E0 and Ea values for each station were calculated using long-term climatic data and the point cloud of the Budyko curve was plotted for all stations in Mainland China (Figure 4).First, four basic climatic zones-humid, semi-humid, semi-arid and arid-were classified based on the DI according to the method of Wu et al. [27].It was found that stations from the same climatic zone cover a broad range of the Budyko curve (see Figure 4), with the exception of the arid zone.EI is close to 1, but DI covers a broad span of values ranging from 4 to 57 in the arid zone.For each experiment, the average Euclidean distance between any two stations within a climatic zone was obtained, and the number of sub-regions as a function of the average Euclidean distance For each experiment, the average Euclidean distance between any two stations within a climatic zone was obtained, and the number of sub-regions as a function of the average Euclidean distance within a climatic zone is shown in Figure 5.As shown in the figure, the Euclidean distance for the humid zone is shortest when it is sub-divided into five sub-regions, and the optimal quantities of semi-humid and semi-arid zones are measured as 6 and 4, respectively.Using DI = 20 as an indicator, the arid zone is sub-divided into two sub-regions, so all 637 stations across China can be divided into 17 groups under the hydro-climatic classification framework (Figure 6a).Therefore, the four basic climatic zones of Mainland China are classified into 17 sub-regions (Figure 6b).
Water 2019, 10, x FOR PEER REVIEW 9 of 26 within a climatic zone is shown in Figure 5.As shown in the figure, the Euclidean distance for the humid zone is shortest when it is sub-divided into five sub-regions, and the optimal quantities of semi-humid and semi-arid zones are measured as 6 and 4, respectively.Using DI = 20 as an indicator, the arid zone is sub-divided into two sub-regions, so all 637 stations across China can be divided into 17 groups under the hydro-climatic classification framework (Figure 6a).Therefore, the four basic climatic zones of Mainland China are classified into 17 sub-regions (Figure 6b).As shown in Figure 6, the 17 sub-regions cover vast areas from the west coast of the Pacific Ocean to central Asia and from the tropical South China Sea to the harsh Mongolian Plateau.As shown in As shown in Figure 6, the 17 sub-regions cover vast areas from the west coast of the Pacific Ocean to central Asia and from the tropical South China Sea to the harsh Mongolian Plateau.As shown in Figure 7, different hydrothermal conditions shape and affect the landscape characteristics of sub-regions, and the relative positions of sub-regions on a point cloud are also provided.In the humid, semi-humid, and semi-arid zones, we find that the higher the vertical locations of stations on the Budyko curve, the drier and colder the climate and corresponding natural landscapes.For example, the semi-arid zone is divided into four sub-regions (C31, C32, C33, and C34) from the bottom to the top of the Budyko curve, and the related stations are typical of the North China Plain, the Inner Mongolia Grassland and the alpine region with the average precipitation and temperature decreasing from 570 mm to 449 mm and from 11.2 • C to 1.9 • C, respectively, as shown in Table 1.
There are various climate classifications across Mainland China.First, dry-wet climate zones based on DI index were compared with other similar studies.It was found that the four basic climatic zones, i.e., humid, semi-humid, semi-arid and arid are comparable with the results of Yuan et al. [60] that employs data from 1961 to 2015.However, there are some biases especially in sub-dividing semi-humid and semi-arid zones while comparing with the regionalization results of Zheng et al. [61] which used climate data over 1981-2010.It is believed that China has experienced obviously climate wetting as the climate warming due to the significantly decreasing E 0 over the period of 1961 to 2014 [61].This can partly explain why the transitional zones between dry and wet climates have alternated over the past 50 years.The results were also compared with the China climate classification based on Köppen method [62], and a similar transition of climate zones was found.However, accurate assessments of our framework with other methods, e.g., the Köppen climate classification [62] and the so-called standard method for China climate regionalization [61], are difficult.The reasons are that they are always different in methods and criterions.For instance, all the climate classification will focus on mean annual characteristics of climatic factors.In those methods, the temporal variations of some factors especially precipitation cannot be considered adequately, let alone actual evapotranspiration and runoff, which determine to a great extent regional dry-wet conditions [56].However, our framework can provide hydrologically based classification by considering annual distribution of hydrothermal factors and actual evapotranspiration.

Effects of Hydrothermal Relationships on Sub-Region Classification
As stated in the section above, Mainland China was divided into 17 sub-regions according to hydrothermal conditions under the Budyko framework.The results shown in Figure 8 illustrate that the hydrothermal factors, e.g., precipitation and sunny periods, that characterize Mainland China are strongly related with climatic zones.As shown in Figure 8, DI = 1 and DI = 4 contour lines can roughly coincide with the 1000-mm and 300-mm isohyetal lines, and precipitation heavily shapes the sub-region classifications.However, some obvious deviations are observed; e.g., in Northeastern China, DI = 1.5 and the 700-mm isohyetal line do not overlap, as is found for the southeastern part of Mainland China.In Northeastern China, precipitation levels in most parts of Heilongjiang Province range from 300-700 mm, while due to relatively low levels of radiation, the value of DI (<1.5) is small, which may explain why these areas receiving relatively little precipitation belong to the semi-humid zone.It is evident that the classification results are affected by both hydrological and thermal factors (e.g., precipitation, temperature, and sunny periods).The spatial and temporal distributions of hydrothermal factors are essential for categorizing a sub-region, and their distributions are basically analogous in many areas of Mainland China.A correlation diagram of the hydrothermal conditions for each sub-region is presented below (Figure 9).

Effects of Hydrothermal Relationships on Sub-Region Classification
As stated in the section above, Mainland China was divided into 17 sub-regions according to hydrothermal conditions under the Budyko framework.The results shown in Figure 8 illustrate that the hydrothermal factors, e.g., precipitation and sunny periods, that characterize Mainland China are strongly related with climatic zones.As shown in Figure 8, DI = 1 and DI = 4 contour lines can roughly coincide with the 1000-mm and 300-mm isohyetal lines, and precipitation heavily shapes the subregion classifications.However, some obvious deviations are observed; e.g., in Northeastern China, DI = 1.5 and the 700-mm isohyetal line do not overlap, as is found for the southeastern part of Mainland China.In Northeastern China, precipitation levels in most parts of Heilongjiang Province range from 300-700 mm, while due to relatively low levels of radiation, the value of DI (<1.5) is small, which may explain why these areas receiving relatively little precipitation belong to the semi-humid zone.It is evident that the classification results are affected by both hydrological and thermal factors (e.g., precipitation, temperature, and sunny periods).The spatial and temporal distributions of hydrothermal factors are essential for categorizing a sub-region, and their distributions are basically analogous in many areas of Mainland China.A correlation diagram of the hydrothermal conditions for each sub-region is presented below (Figure 9).As precipitation is a controlling factor of the sub-region classification, the relationships between mean annual precipitation and other hydrothermal indices were explored (Figure 9).Average annual precipitation values for each sub-region decrease from 1717 mm in C12 to 47 mm in the arid C42, and total precipitation levels decrease accordingly with DI and EI (Figure 9a,b).Compared to Figure 9a, the diagram for P and EI shown in Figure 9b is more scattered.In addition, as the DI values for climatic zone classification are set according to Wu et al. [27], the point cloud of every climatic zone does not overlap (Figure 9a).A similar phenomenon can be observed in Figure 9c.It was found that E0 tends to remain constant (1030 mm on average) as precipitation levels increase in the semi-arid, semi-humid, and humid zones.However, the P and EI point clouds for the sub-regions of different climatic zones seem to present several intersections (Figure 9b).For instance, the mean EI values are 0.67 and 0.73 for C14 and C15, respectively, and 0.64 for C21, creating overlap between these subregions because Ea is not only impacted by precipitation (Figure 9d) but also by sunny periods (Figure 9e) and other heat factors.For all stations in Mainland China, mean annual precipitation and sunny periods are inversely related.In fact, the inverse relationship between mean annual precipitation and heat conditions causes these variables to perform distinct functions in the hydrologic cycle.In heatrich arid and semi-arid zones, actual evapotranspiration is mainly controlled by precipitation.As is shown in Figure 9d, Ea is nearly equal to P in arid zones and some semi-arid zones.These regions are characterized by low levels of precipitation and by relatively high heat conditions (e.g., sunny periods as shown in Figure 9e).However, for the semi-humid and humid zones, the point cloud is scattered, showing that once precipitation levels reach a certain value, actual evapotranspiration is dominated by heat conditions.In humid sub-regions, Ea is typically less than P; for example, the average value of Ea for the humid zone is approximately 850 mm, while the average value of P exceeds 1400 mm.As precipitation is a controlling factor of the sub-region classification, the relationships between mean annual precipitation and other hydrothermal indices were explored (Figure 9).Average annual precipitation values for each sub-region decrease from 1717 mm in C12 to 47 mm in the arid C42, and total precipitation levels decrease accordingly with DI and EI (Figure 9a,b).Compared to Figure 9a, the diagram for P and EI shown in Figure 9b is more scattered.In addition, as the DI values for climatic zone classification are set according to Wu et al. [27], the point cloud of every climatic zone does not overlap (Figure 9a).A similar phenomenon can be observed in Figure 9c.It was found that E 0 tends to remain constant (1030 mm on average) as precipitation levels increase in the semi-arid, semi-humid, and humid zones.However, the P and EI point clouds for the sub-regions of different climatic zones seem to present several intersections (Figure 9b).For instance, the mean EI values are 0.67 and 0.73 for C14 and C15, respectively, and 0.64 for C21, creating overlap between these sub-regions because E a is not only impacted by precipitation (Figure 9d) but also by sunny periods (Figure 9e) and other heat factors.For all stations in Mainland China, mean annual precipitation and sunny periods are inversely related.In fact, the inverse relationship between mean annual precipitation and heat conditions causes these variables to perform distinct functions in the hydrologic cycle.In heat-rich arid and semi-arid zones, actual evapotranspiration is mainly controlled by precipitation.As is shown in Figure 9d, E a is nearly equal to P in arid zones and some semi-arid zones.These regions are characterized by low levels of precipitation and by relatively high heat conditions (e.g., sunny periods as shown in Figure 9e).However, for the semi-humid and humid zones, the point cloud is scattered, showing that once precipitation levels reach a certain value, actual evapotranspiration is dominated by heat conditions.In humid sub-regions, E a is typically less than P; for example, the average value of E a for the humid zone is approximately 850 mm, while the average value of P exceeds 1400 mm.As shown by the station cloud of the Budyko curve (Figure 4) as well as the correlation diagrams of the hydrothermal conditions (Figure 9), although the scatter diagram of the values of DI, EI, and other hydrothermal indices can be fitted by a parabolic curve, the parameters are not related by a single valued relation.It is consistent with the findings presented in most of the catchment studies, e.g., in the non-humid regions of China [32].As suggested by Zhang et al. [31] and Yang et al. [32], local long-term water balance is impacted not only by climate but also catchment factors.Thus, inter-differences of long-term water balance across a very large scale should be represented by a group of Budyko curves.Regions located between top curves (e.g., C15, C26) on the Budyko scatterplot in Figure 4 are characterized by evaporation favorited and the evaporation rates are determined by precipitation and potential evapotranspiration.Regions on bottom areas of the Budyko curves (e.g., C11, C21) are generally not favourable for evaporation.For example, the evapotranspiration efficiencies (E a /E 0 ) for C15 and C26 are 0.92 and 0.76, which are higher than 0.70 and 0.52 for C11 and C21.The values of E a /E 0 decrease accordingly from the humid zone to the semi-humid zone, which indicates that the E 0 -forced evaporation in C1 zones is transiting to the P-forced evaporation in C2 zones.These findings are consistent with the results of Zhang et al. [31].Moreover, through comparisons of monthly hydrothermal factors in typical stations for each sub-region, it was found that stations with closely annual values (e.g., C22 and C23 as listed in Table 1) can behave quite differently in hydrological characters due to the different annual distribution of precipitation and sunshine (Figure 10c,d).

Hydro-Climatic Characteristics of the Sub-Regions
In this section, the hydro-climatic characteristics of each sub-region in the humid, semi-humid, semi-arid, and arid zones are discussed.Within each zone, several climatic factors (e.g., precipitation, sunshine time, temperature, etc.) measured as the mean values for stations in each sub-region are determined (Table 1), and eight typical stations that represents the average hydro-climatic conditions of the given sub-region is used to further explore the relationships among precipitation, sunny periods, and temperature (see in Figure 10).

Humid Zone
Average precipitation for C11-C15 of the humid zone range from 1090 to 1717 mm, and the potential evapotranspiration, actual evapotranspiration, air temperature, and sunny period values range from 845-1195 mm, 779-934 mm, 14.8-20.0• C, and 1402-2131 h, respectively.In the humid zone, temperature, annual sunny periods and potential evapotranspiration decrease from C11 to C15. Figure 9e shows that C15, located in the Sichuan Basin and the Guizhou Plateau (dark green area in Figure 8b), where "no three days are clear" (a Chinese adage), receives the least amount of sunlight among the sub-regions and that average annual sunny periods measured at some C15 stations are even less than 1000 h.
In addition to the C11 sub-region, a decreasing trend in precipitation and actual evaporation from region C12 to region C15 (Table 1) was observed.C11 receives less precipitation than C12.As both temperature and sunny periods in C11 are greater than those of C12, and its potential evapotranspiration value is greater than that of C12, too.However, average annual actual evaporation for C11 is 93 mm less than that of C12.The reason is that rainfall and heat values for C12 to C15 are synchronous.However, C11 includes different periods of rain and heat (Figure 10a).In the summer, when precipitation are higher, sunny periods are the shortest of the year for C11.Therefore, although monthly precipitation reaches 300 mm in the summer, actual evaporation is controlled by latent heat and is low.Although latent heat levels are high in other seasons, actual evaporation is controlled by precipitation, creating relatively low levels of evaporation in this sub-region.
Sub-region C11 covers 0.42% of the Chinese territory and is mainly located in the western part of Yunnan Province.It is characterized by high altitudes (over 800 m), abundant sunshine (2131 h), high potential evapotranspiration levels and intense precipitation (1595 mm).Precipitation falling from May to September accounts for 78% of the annual total (e.g., Ruili station (97.9 • E, 24.0 • N), Figure 10a).As rain and heat are not synchronous, the average annual actual evapotranspiration is only 841 mm and is lower than that of other sub-regions in the humid zone.
Sub-region C12 occupies 2.53% of the Chinese territory and is largely located in coastal areas of Guangdong Province and Hainan Province, and in southcentral Jiangxi Province.The vegetation is dominated by tropical monsoon rainforest and subtropical evergreen broad-leaved forest.Due to the tropical cyclones, the highest wind speed (2.6 m/s) and precipitation (1717 mm) are the highest in the humid zone.Precipitation mainly falls from May to August, and average monthly precipitation levels for these 4 months are close to 400 mm.However, the duration of sunny periods is not as long as that in the C11.
Sub-region C13 accounts for 6.75% of the Chinese territory.Stations in C13 are broadly distributed in Fujian, Guangdong, and Guangxi Provinces.C13 and C12 are positioned in southcentral zones of Mainland China.The annual sunny periods and annual precipitation decrease from those of C12.Monthly sunny periods vary from 72 h to 253 h, and monthly mean rainfall reaches approximately 120 mm.Sub-region C14 occupies 6.00% of the Chinese territory.Stations in C14 are positioned in the south, north and northeast of the humid zone; they cross the Sichuan Basin, the periphery of the Guizhou Plateau and Hunan Province and extend even to Anhui, Zhejiang and Jiangsu Provinces.Maximum monthly precipitation reach 204 mm.Rain and heat processes are recorded in the same period.
Sub-region C15 covers 3.90% of the Chinese territory and is mainly located in the Sichuan Basin and Guizhou Plateau.Annual sunny periods cover 1402 h, which is the lowest value found in sub-regions of the humid zone, and they are consistent with monthly precipitation trends (e.g., Xishui station (106.2 • E, 28.3 • N), Figure 10b).The average annual precipitation is 1090 mm, and the highest monthly precipitation of 180 mm occurred in June.

Semi-Humid Zone
The precipitation recorded for the semi-humid zone range from 660 mm to 1029 mm, and the potential and actual evapotranspiration range from 795 mm to 1266 mm and from 607 mm to 662 drier and colder the climatic conditions and corresponding natural landscapes.Hence, to obtain comprehensive classification results, the DI, EI, and curve-fitting index ω should be combined.Under the proposed hydro-climatic classification framework, the four climatic zones were further divided into 17 sub-regions, and the hydrothermal conditions were examined for each sub-region.We found that the spatial and temporal distributions of hydrothermal factors are essential for sub-region categorizing.
In conclusion, our classification method based on Budyko theory can identify differences in dry-wet conditions and thus serves as an objective tool for large-scale hydro-climatic classification.Our method that classifies regions through quantitatively assessing the interaction between water and energy availability could underpin sustainable water resources development and even guide crop planting by considering the synthetic climate indices of the framework.Finally, mapping hydro-climatic zones across continental scale would transfer knowledge to ungagged areas, which can guide modelling and promote predictive power for hydrological community.

Figure 1 .
Figure 1.Map of meteorological stations and provinces in China.Grey points on the map denote the meteorological stations used in this study.

Figure 1 .
Figure 1.Map of meteorological stations and provinces in China.Grey points on the map denote the meteorological stations used in this study.

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10, x FOR PEER REVIEW 6 of 26and parameter ω are further employed to repartition climatic zones.As shown in Figure2, five main procedures are applied under the classification framework.First, the mean annual DI and EI values are calculated for each station, and point clouds for these values are plotted on the Budyko curve.Second, four climatic zones are classified based on the DI according to the method of Wu et al.[27].Third, by setting different values of ω, a cluster of Fu's curves is obtained, which divide each climatic zone into n sub-regions (see Figure3).Here, the values of ω are determined to make Fu's curves cross equipartition points on the line segment between intersections of the lower and upper envelope lines, namely, EI = a and EI = b while DI = 1 (Figure3).Line DI = 1 was used as it forms the turning point of the Budyko theoretical boundary, and it is the dividing line between the humid zone and the nonhumid zone.Moreover, as the EI is close to 1 when DI > 4, the arid zone is classified into two subregions with DI = 20 used as an indicator[57].

Figure 2 .
Figure 2. Flow chart of main procedures within the classification framework.

Figure 2 .
Figure 2. Flow chart of main procedures within the classification framework.

Figure 3 .
Figure 3. Schematic diagram of sub-region classifications on the Budyko curve.Points a and b, shown as red triangles, denote the intersection of lower and upper envelope lines when DI = 1.Line segment ab is divided into n equal segments, and Fu's curves cross equipartition points to divide each climatic zone into n sub-regions.

Figure 3 .
Figure 3. Schematic diagram of sub-region classifications on the Budyko curve.Points a and b, shown as red triangles, denote the intersection of lower and upper envelope lines when DI = 1.Line segment ab is divided into n equal segments, and Fu's curves cross equipartition points to divide each climatic zone into n sub-regions.

Figure 4 .
Figure 4.The optimal classification of stations on the Budyko curve.The humid zone is divided into sub-regions C11, C12, C13, C14, and C15.The semi-humid zone is divided into sub-regions C21, C22, C23, C24, C25, and C26.The semi-arid zone is divided into sub-regions C31, C32, C33, and C34.The arid zone is divided into sub-regions C41 and C42.The large range of point clouds found on the Budyko curve at DI < 4.0 (in which EI has a relatively larger span) shows that the hydrothermal conditions are quite different within the same climatic zone, so EI can be used as an indicator to further sub-divide of each zone.Firstly, the lower envelope line with ω = 2.05 and the upper envelope line with ω = 8.40 were fitted according to Fu's equation on the Budyko curve.As shown in Figure 4, when DI = 1, EI is in the range of 0.59-0.91,a = 0.59, and b = 0.91.Thus, equipartition points of the EI interval (0.59 ≤ EI ≤ 0.91) at DI = 1 can be obtained by setting different numbers of sub-regions.For this classification experiment, the default maximum number of sub-regions is set as 8, which is sufficiently large for an optimal classification through trial and error tests.The three climatic zones (humid, semi-humid, and semi-arid) were then sub-divided from one sub-region (the initial climatic zone in terms of the DI) to eight sub-regions, and eight experiments were conducted on each climatic zone.For each experiment, the average Euclidean distance between any two stations within a climatic zone was obtained, and the number of sub-regions as a function of the average Euclidean distance within a climatic zone is shown in Figure 5.As shown in the figure, the Euclidean distance for the

Figure 5 .
Figure 5.The number of sub-regions as a function of the average Euclidean distance measured within a climatic zone.The three red pentagrams represent optimal values with the lowest Euclidean distance for each zone.

Figure 5 .
Figure 5.The number of sub-regions as a function of the average Euclidean distance measured within a climatic zone.The three red pentagrams represent optimal values with the lowest Euclidean distance for each zone.

Figure 6 .
Figure 6.The classification results of national climatic stations (a) and climatic zones (b).

Figure 6 .
Figure 6.The classification results of national climatic stations (a) and climatic zones (b).

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Figure 8 .
Figure 8.The distribution of the dryness index with average annual precipitation (a) and sunny periods (b) for Mainland China.