Hydrological modeling

    • Unifying water balance models: A new distribution function is proposed (Wang, 2018). In saturation excess runoff generation models (e.g., VIC and Xinanjing), a generalized Pareto distribution is usually used for describing the spatial distribution of soil water storage capacity. If the SCS distribution is used to replace the generalized Pareto distribution and the initial soil water storage is set to zero, it leads to the exact proportionality relationship of the SCS curve number (SCS-CN) method (Wang, 2018). When this distribution function is used for describing the spatial distribution of available water at the mean annual scale, it leads to a Budyko equation (Wang and Tang, 2014). When this distribution function is used for describing the spatial distribution of available water at the monthly scale, it leads to the monthly abcd model. Therefore, the proposed SCS distribution unifies saturation excess runoff models (VIC/Xinanjiang type), SCS-CN, abcd model, and Budyko equation. The roles of climate variability on runoff and baseflow at different time scales are quantified based on the unified daily, monthly, annual and long-term water balance models (Yao et al., 2020; Yao et al., 2021).

    • Unifying infiltration and evaporation model during a time period: The findings above indicate the similarity of infiltration and evaporation processes. For infiltration at the event scale, the water supply is rainfall depth for the event, and the water demand is infiltration capacity. For evaporation at the mean annual scale, the water supply is mean annual precipitation (for evaporation at the short time scale, water supply could be soil water storage and precipitation), and the water demand is potential evaporation. Using the supply/demand concept, infiltration and evaporation can be modeled as the same functional form (SCS-CN and Budyko equation).

    • Similarity between infiltration capacity and base flow recession: During a rainfall event, infiltration capacity declines with time. During a dry period, base flow declines with time. Here, f represents infiltration capacity (i.e., SCS-CN method) or the difference of infiltration capacity and saturated hydraulic conductivity (e.g., Horton equation, Philip equation). These three infiltration equations can be unified as the following functional form: -df/dt = a*f^b. b=1 is Horton equation, b=1.5 is SCS-CN method, and b=3 is Philip equation (Yao et al., 2018). Similarly, base flow (Q) recession can be modeled as a functional form: -dQ/dt = a*Q^b and b=1, 1.5, and 3. The similarity of infiltration capacity and base flow recession is underpinned by Darcy's law. The governing equations for both infiltration and base flow recession are based on Darcy's law. Infiltration is for unsaturated soil but base flow is for saturated soil. SCS-CN can be derived as a solution of Richards' equation (Hooshyar and Wang, 2016) like Horton equation and Philip equation.

Flow duration curve

River network

    • Network extraction:

        • Drainage and channel network extraction: A method for automatic extraction of valley and channel networks from high‐resolution digital elevation models (DEMs) is developed by (Hooshyar et al., 2016). This method utilizes both positive and negative curvature to delineate the valley network. The transition from unchannelized to channelized sections (i.e., channel head) in each first‐order valley tributary is identified independently by categorizing the corresponding contours using an unsupervised approach based on k‐means clustering.

        • Wet channel network extraction: A systematic method is developed to map wet channel networks by integrating elevation and signal intensity of ground returns of LiDAR data (Hooshyar et al., 2015).

    • Network density

        • Drainage density: The relationship between drainage density and basic geomorphic and topologic characteristics, which encapsulate the advective and diffusive transport processes acting on the landscape, are revealed through observed data and landscape evolution model simulations (Hooshyar et al., 2019a; Hooshyar et al., 2019b).

        • Perennial stream density: Perennial stream density is dominantly controlled by long-term climate (Wang and Wu, 2013).

    • Network structure

        • Junction angle: The flow regimes, debris‐flow dominated or fluvial, have distinct characteristic angles which are functions of the scaling exponent of the slope‐area curve (Hooshyar et al., 2017).

        • Branching structure: Climate has systematic impacts on the structure of river networks. The width functions of dry basins have higher entropy as compared to those of humid basins across spatial scales, suggesting more heterogeneity in drainage network of dry basins (Ranjbar et al., 2018; Ranjbar et al., 2020).