Under the framework of the HiWATER (http://hiwater.westgis.ac.cn/), hydrometeorological observation network dataset, including eddy coevolution (EC) systems and automatic weather stations (AWS), were deployed at typical ecosystem across upstream, middle stream, and downstream in the Heihe River Basin (97.1 E-102.0°E and 37.7°N-42.7°N) for ecohydrological and micrometeorological monitoring. The total area of the HRB is 14.3 million km² which integrates alpine glaciers, alpine grassland, oases, and the Gobi desert (Cheng et al., 2014). In the upper reaches in the Qilian Mountains, at an altitude between 1674 and 5564 m, the climate is cold and arid. With characteristics of wet and cold climate (an average annual temperature of 0.54℃) and an average annual precipitation of 300-600 mm, the vegetation distribution is more obvious in the vertical zone, which mainly consists of sparse alpine vegetation, alpine meadows, swamp meadow and alpine desert. The middle reaches, at an altitude between 1352 m and 1700 m, have a temperate continental arid climate with an annual average precipitation of 90-160 mm and an annual evaporation of 2000-2500 mm. The vegetation type is natural and artificial oases, which are the areas with the greatest intensity of human activity. The lower reaches have an altitude less than 1352 m and are more arid, with rare precipitation and strong evapotranspiration. The average annual temperature is 8.7℃, the average annual rainfall is 36.6 mm, and the vegetation is mainly desert and riparian forest. There are series of hydrometeorological observatory in the upstream, midstream and downstream of the HRB (Liu et al., 2018), covering the main vegetation types of the HRB. As shown in Figure 1, the alpine meadow and alpine swamp meadow, and alpine desert ecosystems in the upper reaches, the cropland ecosystem in the middle reaches, and the Tamarix ramosissima Ledeb, Populus euphratica ecosystems in the lower reaches were selected for investigation in the present study. All sites have continuous observation data from eddy covariance systems (EC) and automatic weather stations (AWS) from January 2014 to December 2016. Table 1 lists detailed descriptions of each ecosystem.

The GLASS leaf area index (LAI) products (http://glassproduct.bnu.edu.cn/) from Beijing Normal University, available every 8 days and interpolated onto a daily time interval, were used to represent vegetation dynamics in this study. Vegetation heights of riparian forest in the lower reaches were acquired by a field quadrat survey, and vegetation heights of alpine meadow in the upper reaches were obtained by reference to a research dataset of ecohydrological transects in the HRB in 2013. The heights of maize in cropland were as given by Wen et al. (2016).

The study data were obtained from a hydrometeorological observation network dataset provided by HiWATER (http://hiwater.westgis.ac.cn/), which includes EC systems and AWS. The data collection has been described in detail (Liu et al., 2018; Xu et al., 2013). The EC systems were mounted on towers ranging from 3.5 to 22 m above the various canopy heights (Table 1). Post-processing calculations were performed using EdiRe (Liu et al., 2011), and the results were gap-filled using a set of general algorithms (Reichstein et al., 2005). After gap-filling, daily energy budget closure was used to elevate the EC data, which was determined by the linear regression statistics between (lET+H) and (Rn-G) (Liu et al., 2011). The energy balance closure for daily-mean dataset ranged from 53% to 96% (Figure 2), which indicated that energy balance closure problem in our sites was not a big issue. Meteorological data including air temperature (Ta, ℃), humidity (RH, %), wind speed (u, m/s), air pressure (P, Pa), soil temperature (Ts, ℃), moisture profile (θ, %), and solar radiation/soil heat flux (R_n, W m^-2), were used for model input. The energy balance closure for the daily-mean datasets ranged from 74% to 96% (Table 1), which indicated that energy balance closure issue was not a big concern in our sites (Pan et al., 2017).

A two-layer source model was used to partition energy between plant and soil layer. The main equations of the model are illustrated in supplementary materials (Text S1). This model was chosen for the following reasons. First, this model, using the energy balance between the soil surface and the vegetation canopy and taking into account the energy interaction between them, achieved good performance in partitioning energy flux in the humid grasslands of Japan (Wang and Yamanaka, 2014; Wang et al., 2015), the cropland ecosystem of the HRB (Wang et al., 2016), and arid and semiarid grassland in Inner Mongolia of China (Wang et al., 2017; Wang et al., 2018). Second, the model uses the Newton-Raphson iteration scheme to solve the governing equations for the canopy and the ground surface separately without the need for radiometric temperature. Third, the model considers stomatal control of transpiration, including its dependence on soil moisture, and solar radiation is explicitly included. The model was localized to fit the characteristics of each ecosystem; Text S1 summarizes the parameters used for each site in this study. More details about the model can be found in Wang and Yamanaka (2014). The root mean square error (RMSE) and I index (Willmott et al., 1985; Wang and Yamanaka, 2014), as well as R² (R is the correlation coefficient), were used to validate and test the model for energy partitioning.

According to the eddy covariance measurements, the β was estimated based on the measured sensible (H) divided by latent heat fluxes (lET):

where H and lET are sensible (H) and latent heat flux (lET) respectively.

Based on the two-source model output, the β_V was estimated based on the simulated sensible (H_V) divided by transpiration fluxes (lT):

The β_G was estimated based on the simulated sensible (H_G) divided by evaporation fluxes (lE):

The observed day-to-day variations in energy balance components of net radiation, sensible heat flux, and latent heat flux and ground heat flux were shown at six sites in the HRB (Figure 2). Energy partitioning was dominated by latent heat, followed by sensible heat and the soil heat flux for six ecosystems during 2014-2016. Among the six ecosystems, the maximum latent heat was observed in riparian forest ecosystem of Hunhelin, followed by agriculture ecosystem of Daman and Sidaoqiao. There are larger fluctuations of lET for ecosystems of riparian forest and agriculture ecosystem than ecosystems in upstream. The detailed statistics of monthly mean dataset of latent (lET) and sensible heat flux (H) were summarized in Table 2. Using gap-filling dataset, daily energy budget closure was evaluated by the linear regression statistics between (lET+H) and (R_n-G) (Liu et al., 2011b).

Seasonal day-to-day variations of leaf area index (LAI) and observed β for Dashalong, Ya kou, A’rou, Daman, Hunhelin and Sidaoqiao from 2014 to 2016 were shown in Figure 3.

Bowen ratio (β) among the six sites exhibited significant seasonal variations with smaller inter-annual fluctuations. All ecosystems exhibit a “U-shaped” pattern, characterized by smaller value of β in growing season, with a minimum value in July, and fluctuating day to day. Statistics of measured Bowen ratio show that there is significant difference (P < 0.01) between growing season and non-growing season for all ecosystems (Table 3). We find there is negative fluctuation between leaf area index and β. There is smaller β with higher LAI during the growing season while higher β with lower LAI during non-growing season. For non-growing season, there were higher β values than growing season, indicating that there were other environmental factors (e.g. snow, freeze soil surface) rather than vegetation dominating the energy partitioning. During the growing season, average Bowen ratio was the highest for the alpine swamp meadow (0.60 ± 0.30), followed by the desert riparian forest Populus euphratica (0.47 ± 0.72), the alpine desert (0.46 ± 0.10), the Tamarix ramosissima desert riparian shrub ecosystem (0.33 ± 0.57), alpine meadow ecosystem (0.32 ± 0.17), and cropland ecosystem (0.27 ± 0.46).

There is reasonable agreement between observed and simulated Bowen ratio (β), with high Iindex (0.64-0.85), and R² (0.28-0.31) and lower RMSE (0.22-0.50) values of the six ecosystems (Table 4), which indicate that our model is reasonable for reconstructing the energy partition process for various ecosystems. There is similar seasonal pattern of β with larger values during non-growing seasons while smaller values during growing seasons for the six ecosystems. Our model can not only simulate the total energy flux, but also partition β between soil and vegetation surface. Seasonal day-to-day variations of measured Bowen ratio (β) and simulated Bowen ratio between canopy (β_V) and ground soil surface (β_G) showed the similar seasonal pattern for Dashalong, Yakou, A’rou, Daman, Hunhelin and Sidaoqiao from 2014 to 2016 (Figure 4). There are similar seasonal patterns of β, β_V and β_G, which indicate the convergent ecosystem response for both soil and vegetation surface_.

The dependence of ecosystem energy partitioning on LAI was shown in Figure 5 for sites of Dashalong, Yakou, A’rou, Daman, Hunhelin and Sidaoqiao. The relationship between daily mean volumetric soil moisture and Bowen ratio for each site was shown in Figure 6. There was a trend of convergence of Bowen ratio with both development of LAI and increase of soil moisture. The amplitude of convergence of Bowen ratio was more obvious with the development of LAI compared with increase of soil moisture, suggesting that the leaf development dominates the energy partition for the six ecosystems in the HRB. The results indicate that leaf development explains the seasonality of Bowen ratio and dominates the lET flux for the six ecosystems.

Bowen ratio, generally measured by Bowen ratio system or EC system, failed to separate total energy flux into soil and vegetation surface by traditional methods. Two-source model is a useful tool for integrating the energy/water processes with separate lE (H_G) and lT (H_V) in terrestrial ecosystems and has the advantage of enabling process-based assessment of energy partitioning between soil and vegetation surface. Although previous studies used other methods to partition energy flux at vineyard (Zhao et al., 2017), there are several advantages of our modeling approach. First, the model treats the radiation/energy balance properly in both vegetative canopy and at the ground surface with interaction between them, enabling us to estimate all the total energy balance components, which can be comparable with measured Bowen ratio for model validation and to separate the Bowen ratio between canopy and soil surface. In this way, we can assess qualitatively the role of soil and plant for ecosys-tem energy partitioning. The model is solved by Newton-Raphson iteration scheme to simply, stably and rapidly estimate leaf temperature (T_L) and ground soil temperature (T_G) without directional radiometric temperature. The estimated T_L and T_G can be useful for model validation and reconstructing the surface temperature of various ecosystems. Second, changes of surface albedo with leaf development, and stomatal control of latent heat flux by transpiration including its dependence on soil moisture are explicitly considered in the model. Finally, the differences of ecohydrological (e.g. root depth, maximum and minimum stomatal resistance, canopy structure) and soil property (e.g. soil saturation moisture) among alpine vegetation, agriculture ecosystem and riparian ecosystem were taken into consideration in the model. However, there also exist many uncertainties for energy partitioning with separation of plant and soil surface, which still need to be improved. In reality, the terrestrial ecosystems have complex land surface (e.g. snow cover in winter). The amount of LAI ranged from close to nil after snow melt, up to 3-5 m² m^-2 (Figure 3). During periods of snow cover almost all shortwave radiation was reflected by the white surface and midday means of the albedo (α) varied between 0.7-0.8 with observed dataset. In this study, the land was mainly covered by vegetation and soil, this assumption accounted for errors of energy partitioning with separation of plant and soil surface. The values of some parameters (e.g. r_{st_min}, r_{st_max}, α_v and α_g) were fixed throughout the periods investigated; water source of plant of each ecosystems was fixed throughout the periods investigated which may change seasonally or yearly. Those uncertainties may result in errors for energy partitioning.

Previous studies have shown biophysical control on energy partitioning of temperate mountain grassland (e.g. Hammerle et al., 2008) and vineyard (Zhao et al., 2017). Our results support this view for the typical ecosystems within the HRB. Strictly speaking, the daily and seasonal variations of β, β_V and β_G are mainly controlled by LAI through changes of surface albedo and regulating permittivity. The surface albedo increased with increased LAI, and changing surface albedo was mainly controlled by LAI during growing seasons for the six ecosystems. The permittivity decreased with increased LAI, and controlled solar radiation partitioning between soil and plant surface. Also, the daily or seasonal variations of β, β_V and β_G are primarily controlled by LAI through regulating canopy conductance. With leaf development, more and more water was lost through plant transpiration with increased canopy conductance. Besides, the present study suggests soil moisture variation has impact on β, β_V and β_G (Figure 6), which indicate that soil water is primarily controlled energy partitioning through regulating canopy conductance during the drought period.

Strong biophysical controls of β were commonly found in previous studies. However, the relationship or its functional form varied among sites. Our results also showed different relationships for the typical ecosystems within the HRB. Figure 7 shows the statistics of LAI and β for the six ecosystems. Although there is close relationship between LAI and β, but differences are still shown in sensitivities of LAI to regulation of β. We find the riparian forest ecosystem (Sidaoqiao) has higher sensitivity to regulating energy partitioning, followed by alpine desert ecosystem characterized by smaller variations of LAI (Figure 7). From Figure 8, we find there are larger fluctuations of β for ecosystems of riparian forest and agriculture ecosystem, but conserve day to day fluctuations for A’rou (alpine meadow ecosystem), Dashalong (alpine swamp meadow ecosystem) and Yakou (alpine desert eco-system) during the growing season (from May to September). The di-vergent changes of β among the ecosystems are probably influenced by climate (T_a, and VPD) and soil water. The ecosystems in upper, middle and downstream show similar behavior of energy partitioning. Because the larger and rapid changes of VPD regulated by groundwater fluctuations of riparian ecosystems in downstream, the monthly fluctuations of lET, H and β are the largest. On the contrary, for alpine ecosystems, the monthly fluctuations of lET, H and β are the smallest because of the smallest changes of air temperature, which is the dominant factor for energy parti-tioning. Daman (agriculture ecosys-tem) has larger changes in LAI, but a smaller change in Bowen ratio, which is mainly due to the regulation of irri- gation and soil water dynamics. The ecosystems in upstream show subtle difference, the smallest variations of H and β of Dashalong site which may be related by its largest heat storage as alpine swamp meadow ecosystem. The smallest values of H and lET of Yakou, followed by Dashalong and A’rou, corresponded their elevations. Hunhelin showed a lower value of β than Sidaoqiao, which can be explained by the ecohydrlogical difference of plants and the distance between the sites and river channel.