The Budyko hypothesis (BH) is an effective approach to investigating long-term water balance at large basin scale under steady state. The assumption of steady state prevents applications of the BH to basins, which is unclosed, or with significant variations in root zone water storage, i.e., under unsteady state, such as in extremely arid regions. In this study, we choose the Heihe River basin (HRB) in China, an extremely arid inland basin, as the study area. We firstly use a calibrated and then validated monthly water balance model, i.e., the abcd model, to quantitatively determine annual and monthly variations of water balance for the sub-basins and the whole catchment of the HRB, and find that the roles of root zone water storage change and that of inflow from upper sub-basins in monthly water balance are significant. With the recognition of the inflow water from other regions and the root zone water storage change as additional possible water sources to evapotranspiration in unclosed basins, we further define the equivalent precipitation (P_e) to include local precipitation, inflow water and root zone water storage change as the water supply in the Budyko framework. With the newly defined water supply, the Budyko curve can successfully describe the relationship between the evapotranspiration ratio and the aridity index at both annual and monthly timescales, whilst it fails when only the local precipitation being considered. Adding to that, we develop a new Fu-type Budyko equation with two non-dimensional parameters (ω and λ) based on the deviation of Fu's equation. Over the annual timescale, the new Fu-type Budyko equation developed here has more or less identical performance to Fu's original equation for the sub-basins and the whole catchment. However, over the monthly timescale, due to large seasonality of root zone water storage and inflow water, the new Fu-type Budyko equation generally performs better than Fu's original equation. The new Fu-type Budyko equation (ω and λ) developed here enables one to apply the BH to interpret regional water balance over extremely dry environments under unsteady state (e.g., unclosed basins or sub-annual timescales).

Groundwater is critical for supporting socioeconomic development but has experienced gradual decreases in recent decades due to rapid population growth and economic development throughout the world. In recent years, the utilization of transboundary groundwater resources has received extensive attention globally. Because transboundary aquifers do not follow borders and are concealed, neighboring countries are prone to experiencing conflicts over the use of these transboundary groundwater resources. Therefore, an accurate and comprehensive assessment of the development potential of groundwater resources in these transboundary aquifers is necessary for the rational and fair use of those groundwater resources. Transboundary groundwater resources are an important water source for life, production, and ecological water use in Central Asia, which has a distinctive continental arid and semi-arid climate, and surface water resources in this region are relatively scarce. Considering the existing problems related to the utilization of groundwater resources in the transboundary aquifers in this region, we propose developing strategies for on-demand water abstraction, enhancing the ecological protection of transboundary aquifers, and strengthening international cooperation. This paper summarizes the distribution of 34 transboundary aquifers in Central Asia and analyzes the status and potential of groundwater resource uses in these transboundary aquifers.