Estimating long-term average annual water balance at the catchment scale has been an important scientific problem in hydrology and a reliable method for long-term estimates of evapotranspiration (D. Wang, 2012). Water and vegetation in the catchments have reached equilibrium through long-term evolution, so that there is an inextricable relationship between water balance and vegetation change (Gerten et al., 2004). Changes in vegetation affect the elements of water balance, thus vegetation coverage plays an influential role in regulating regional water balance (Heimann & Reichstein, 2008; Seddon et al., 2016). Precipitation (P), evapotranspiration (ET), streamflow (Q), and water storage changes (ΔS) are important components of water balance estimates. Previous studies (e.g., Shao et al., 2019) have demonstrated that vegetation restoration could lead to increases in regional ET over the Loess Plateau, thus changing the water availability. This could potentially exacerbate tensions between water supply and demand in water-stressed regions. Thus, it can be further hypothesized that the vegetation changes may influence the catchment-scale water balance. In addition, the relationship between ΔS and vegetation may be scale dependent and remains unclear, thus studying the time scale of ΔS in vegetation recovery areas is particularly important. The Loess Plateau, a typical arid and semi-arid region, accounts for 6.6% of China's total land area and supports 8.5% of the population (Fu et al., 2011). It is one of the most water scarce regions with the most fragile ecosystems in the world (Y. Wang et al., 2011; B. Zhang et al., 2016). In the past, the Loess Plateau, with its sparse vegetation coverage, frequent summer rains and intensive agricultural practices, suffered unprecedented water scarcity, soil erosion and fragile ecosystems (C. Wang et al., 2016; Z. Yang et al., 2016). These ecological and environmental problems significantly affect ecological environment and socioeconomic
