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This paper aims to investigate the connection between TOPography‐based hydrological model (TOPMODEL) and Variable Infiltration Capacity (VIC) model through virtual experiments from the perspective of water table and storage at the catchment scale. A simple finite‐difference groundwater flow model was built for a hypothetical catchment forced by a sequence of recharges. A steady‐state water table under a low recharge rate is used as the climatic lower limit, above which the pore space is considered as the maximum storage capacity. When the water table is shallow, the land surface is a good proxy of the water table as assumed in the original TOPMODEL, and the underlying water storage distribution curve is similar as the maximum storage capacity distribution curve. When the water table is deep, the climatic lower limit is a good proxy of water table, and the storage is approximately spatially uniform over the unsaturated area as assumed in the VIC model. The systematic variation of water table and storage distribution potentially provides a framework for unifying the TOPMODEL and VIC model. Plain Language Summary: The TOPography‐based hydrological model (TOPMODEL) and Variable Infiltration Capacity (VIC) model are two widely used saturation excess runoff models in the field of hydrology. They have different conceptualizations on the rainfall‐runoff process, but how to select between them when solving realistic problems is not clear. This paper revisits their assumptions in terms of water table and storage distribution by comparing the simulations from a groundwater flow model for a hypothetical catchment. Results show that the water table and storage distribution assumed by the TOPMODEL and VIC model are two extreme cases under very humid and arid conditions, respectively. This finding suggests that these two different saturation excess runoff models are possibly unified into a single general hydrological model in which the assumptions of water table and storage distribution could be considered as functions of recharge or water table depth. Key Points: The storage in unsaturated area is uniform in the Variable Infiltration Capacity (VIC) model but follows the maximum storage capacity distribution in TOPography‐based hydrological model (TOPMODEL)The water table is topography‐controlled in the TOPMODEL but climatic lower limit‐controlled in the VIC modelThe systematic variation of water table and storage distribution potentially provides a framework to unify the TOPMODEL and VIC model [ABSTRACT FROM AUTHOR]

For evaluating the climatic and landscape controls on long‐term baseflow, baseflow index (BFI, defined as the ratio of baseflow to streamflow) and baseflow coefficient (BFC, defined as the ratio of baseflow to precipitation) are formulated as functions of climate aridity index, storage capacity index (defined as the ratio of average soil water storage capacity to precipitation), and a shape parameter for the spatial variability of storage capacity. The derivation is based on the two‐stage partitioning framework and a cumulative distribution function for storage capacity. Storage capacity has a larger impact on BFI than on BFC. When storage capacity index is smaller than 1, BFI is less sensitive to storage capacity index in arid regions compared to that in humid regions; whereas, when storage capacity index is larger than 1, BFI is less sensitive to storage capacity index in humid regions. The impact of storage capacity index on BFC is only significant in humid regions. The shape parameter plays an important role on fast flow generation at the first‐stage partitioning in humid regions and baseflow generation at the second‐stage partitioning in arid regions. The derived formulae were applied to more than 400 catchments where storage capacity index was found to follow a logarithmic function with climate aridity index. The role of climate forcings at finer timescales on baseflow were quantified, indicating that seasonality in climate forcings has a significant control especially on BFI. Plain Language Summary: Baseflow is a portion of streamflow from delayed storage such as groundwater, and it is crucial for human water supply and ecological environments. Studies have indicated both climate and catchment landscape have impacts on baseflow generation. However, their respective roles on mean annual baseflow are not fully understood. This study derives new functions to analyze the mediation effects of soil water storage capacity on the process of precipitation partitioning, and uses numerical simulations to evaluate the role of climate forcings at finer timescales on mean annual baseflow. Two widely used baseflow metrics are focused on here: baseflow index (BFI), defined as the ratio of baseflow to total streamflow; and baseflow coefficient (BFC), defined as the ratio of baseflow to precipitation. Our results show that the spatial variability of soil water storage capacity plays an important role in baseflow generation, and the impact of soil water storage capacity on BFI spreads across regions with different climates, while its impact on BFC is only significant in humid regions. Numerical simulation shows that seasonality in climate forcings has a vital influence on BFI. Our study advances our knowledge of physical controls on baseflow generation. Key Points: Derived baseflow index (BFI) and baseflow coefficient (BFC) as functions of aridity index, storage capacity index, and a shape parameterWhen storage capacity index is small (large), BFI is less sensitive to climate aridity index in arid (humid) regionsThe control of climate variability (particularly seasonality) on BFI is strong, but not for BFC [ABSTRACT FROM AUTHOR]

Prediction of mean annual runoff is of great interest but still poses a challenge in ungauged basins. The present work diagnoses the prediction in mean annual runoff affected by the uncertainty in estimated distribution of soil water storage capacity. Based on a distribution function, a water balance model for estimating mean annual runoff is developed, in which the effects of climate variability and the distribution of soil water storage capacity are explicitly represented. As such, the two parameters in the model have explicit physical meanings, and relationships between the parameters and controlling factors on mean annual runoff are established. The estimated parameters from the existing data of watershed characteristics are applied to 35 watersheds. The results showed that the model could capture 88.2 % of the actual mean annual runoff on average across the study watersheds, indicating that the proposed new water balance model is promising for estimating mean annual runoff in ungauged watersheds. The underestimation of mean annual runoff is mainly caused by the underestimation of the area percentage of low soil water storage capacity due to neglecting the effect of land surface and bedrock topography. Higher spatial variability of soil water storage capacity estimated through the height above the nearest drainage (HAND) and topographic wetness index (TWI) indicated that topography plays a crucial role in determining the actual soil water storage capacity. The performance of mean annual runoff prediction in ungauged basins can be improved by employing better estimation of soil water storage capacity including the effects of soil, topography, and bedrock. It leads to better diagnosis of the data requirement for predicting mean annual runoff in ungauged basins based on a newly developed process-based model finally. [ABSTRACT FROM AUTHOR]

Following the Budyko framework, the soil wetting ratio (the ratio between soil wetting and precipitation) as a function of the soil storage index (the ratio between soil wetting capacity and precipitation) is derived from the Soil Conservation Service Curve Number (SCS-CN) method and the variable infiltration capacity (VIC) type of model. For the SCS-CN method, the soil wetting ratio approaches 1 when the soil storage index approaches ∞ , due to the limitation of the SCS-CN method in which the initial soil moisture condition is not explicitly represented. However, for the VIC type of model, the soil wetting ratio equals the soil storage index when the soil storage index is lower than a certain value, due to the finite upper bound of the generalized Pareto distribution function of storage capacity. In this paper, a new distribution function, supported on a semi-infinite interval x∈[0,∞) , is proposed for describing the spatial distribution of storage capacity. From this new distribution function, an equation is derived for the relationship between the soil wetting ratio and the storage index. In the derived equation, the soil wetting ratio approaches 0 as the storage index approaches 0; when the storage index tends to infinity, the soil wetting ratio approaches a certain value (≤1) depending on the initial storage. Moreover, the derived equation leads to the exact SCS-CN method when initial water storage is 0. Therefore, the new distribution function for soil water storage capacity explains the SCS-CN method as a saturation excess runoff model and unifies the surface runoff modeling of the SCS-CN method and the VIC type of model. [ABSTRACT FROM AUTHOR]

In this paper, we test the hypothesis that natural catchments utilize hedging strategy for evapotranspiration and water storage carryover with uncertain future precipitation. The hedging strategy for evapotranspiration in catchments under different levels of water availability is analytically derived with marginal utility principle. It is found that there exists hedging between evapotranspiration for present and future only with a portion of water availability. Observation data sets of 160 catchments in the United States covering the period from 1983 to 2003 demonstrate the existence of hedging in catchment hydrology and validate the proposed hedging strategy. We also find that more water is allocated to carryover storage for hedging against the future evapotranspiration deficit in the catchments with larger aridity indexes or with larger variability in future precipitation, i.e., long-term climate and precipitation variability control the degree of hedging. [ABSTRACT FROM AUTHOR]

The annual water storage changes at 12 watersheds in Illinois are estimated based on the long-term soil moisture and groundwater level observations during 1981-2003. Storage change is usually ignored in mean annual and interannual water balance calculations. However, the interannual variability of storage change can be an important component in annual water balance during dry or wet years. Annual precipitation anomaly is partitioned into annual runoff anomaly, annual evaporation anomaly, and annual storage change. The estimated annual storage change ratios vary from -60% to 40% at the study watersheds. The interannual variability of evaporation is not strongly correlated with the interannual variability of precipitation, but is correlated with the interannual variations of effective precipitation. As a response to the interannual variability of precipitation, the interannual variation of evaporation is smaller than those of runoff and storage change. The effect of annual water storage change increases the correlation coefficients between annual evaporation ratio and climate dryness index. Therefore, interannual water storage changes need to be included in the estimation of evaporation and total water supply in the Budyko framework. Effective precipitation can be used as a substitute for precipitation when computing evaporation ratio and climate dryness index. [ABSTRACT FROM AUTHOR]

The catchment water-energy balance at the interannual scale remains a challenge for bridging the important gap in our knowledge of the hydrologic cycle. This study investigates interannual evapotranspiration (ET) variability and water-energy balance at over 547 catchments across the contiguous United States in different climate zones. The investigation is based on ET data estimated from satellite images and surface daily meteorological data during the period of 1983-2006 provided by the University of Montana. We find that the interannual relationship between annual potential ET to annual precipitation (PET/P) and ET/P, the energy, and water factors defined with the Budyko curve framework can be captured by a linear function, with an average goodness of fit of 0.928 over all the catchments. The linear relationship is validated by another independent remote sensing ET product generated by the University of Washington and is demonstrated to be rational using regression diagnostics. Additionally, a comparison study using a water balance method and the Budyko curve is undertaken to examine the linear relationship. In addition to water supply and energy supply, the primary controls on evapotranspiration, soil water storage, response of vegetation to climate variability, and human interference are also major factors of the interannual relationship between PET/P and ET/P. [ABSTRACT FROM AUTHOR]

• A framework is proposed for hydrological modelling under nonstationary conditions. • Model parameters are quantified as functions of catchment properties for improving runoff estimations. • The impacts of data assimilation setup on the construction of parameter functions are assessed. Parameters are usually assumed to be stationary, and regarded as constants in hydrological modelling. However, studies have shown that model parameters may vary temporally due to human activities, and climate variability and changes. This study proposes a framework for quantifying hydrological model parameters as functions of time-variant catchment properties, aiming to improve the capability of capturing hydrograph and the extrapolative ability of hydrological models under a changing environment. The framework includes four steps: (1) estimating model parameters by using an ensemble Kalman filter based on the observations; (2) analyzing correlations between estimated parameter values and catchment properties; (3) constructing a set of parameter functions based on the identified catchment properties and the proposed functional forms; and (4) selecting and testing the best-performed model. As a demonstration of the framework, the monthly water balance for Tongtianhe and Ganjiang basins in China with different climate are simulated using a two-parameter monthly water balance model. Results from the Tongtianhe Basin show that considering the time-variant evapotranspiration parameter (C) brings improvement in low flows when water storage capacity (SC) is treated as constant since there is no significant improvement in runoff simulation when SC is treated as a time-variant parameter. The application to Ganjiang Basin shows that reasonable improvements are achieved when both C and SC are treated as time-variant, especially in low and high flows. The presented framework provides a useful tool for estimating time-variant parameters of hydrological models, thereby leading to more reliable model predictions under a changing environment. [ABSTRACT FROM AUTHOR]

A two-parameter annual water balance model was developed for reconstructing annual terrestrial water storage change (Δ TWS ) and groundwater storage change (Δ GWS ). The model was integrated with the Gravity Recovery and Climate Experiment (GRACE) data and applied to the Punjab province in Pakistan for reconstructing Δ TWS and Δ GWS during 1980–2015 based on multiple input data sources. Model parameters were estimated through minimizing the root-mean-square error between the Budyko-modeled and GRACE-derived Δ TWS during 2003–2015. The correlation of ensemble means between Budyko-modeled and GRACE-derived Δ TWS is 0.68 with p -value <0.05. The Δ GWS was reconstructed by subtracting soil moisture storage change from the Budyko-modeled Δ TWS and was validated (i.e., r = 0.74, p -value < 0.05) against well observations during the pre-GRACE period (i.e., 1985–1994). The negative values of the cumulative sum of the reconstructed Δ GWS during 1980–2015 (i.e., −13.6 ± 9.7 cm) indicate that the aquifer in Punjab has experienced depletion. The estimated depletion rate is −0.3 ± 0.2 cm/year and it has a negative correlation (i.e., r = −0.70, p -value < 0.0001) with the total number of tube wells installed in Punjab. The integration of the developed Budyko model with GRACE data provides a new way for evaluating long-term groundwater depletion in large-scale irrigation regions with parsimonious models. [ABSTRACT FROM AUTHOR]