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A three‐stage precipitation partitioning framework is proposed to study the climate controls on mean annual groundwater evapotranspiration (GWET) for 33 gauged watersheds in west‐central Florida. Daily GWET, total evapotranspiration (ET), groundwater recharge, base flow, and total runoff are simulated by the Integrated Hydrologic Model, which dynamically couples a surface water model (HSPF) and a groundwater flow model (MODFLOW). The roles of GWET on long‐term water balance are quantified by four ratios. The ratios of GWET to total available water, watershed wetting, ET, and recharge decrease exponentially with watershed aridity index (WAI), which is defined as the ratio of potential evapotranspiration to total available water. In the one‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and available water for ET (i.e., they‐axis of Budyko curve) decreases with WAI. In the two‐stage precipitation partitioning framework, the contribution of GWET to the ratio between total ET and watershed wetting (i.e., Horton index) decreases with WAI. The changes in GWET caused by intra‐monthly (IM) climate variability are the highest among the temporal scales of climate variability investigated to understand controls on GWET. The inter‐annual, intra‐annual, and IM climate variabilities lead to increase of GWET; but the sub‐daily climate variability results in decrease of GWET. For the third stage of partitioning, given the same ratio of potential GWET to available water for GWET, higher percentage of forest and wetland and lower percentage of impervious land contribute to higher ratio of GWET to available water for GWET.

 

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.

 

The available water for evaporation within a catchment is spatially variable. However, how the spatial variability of available water affects mean annual evaporation is not fully understood. For a specific catchment, a suitable distribution function defined for non‐negative random variables can be determined through statistical methods to represent the spatial variability of the available water when the point‐scale data are available. This article proposes that the distribution function representing the spatial variability of available water for evaporation determines the functional form of Budyko equation based on the one‐stage precipitation partitioning concept. Specifically, the available water for evaporation following a single‐parameter distribution function leads to a deterministic Budyko equation; whereas a two‐parameter distribution function of available water for evaporation leads to a single‐parameter Budyko equation. We identified the property of distribution function for symmetric Budyko equation, which suggests that precipitation partitioning and energy partitioning in the hydrological cycle follow the same functional form with respect to aridity index and humidity index, respectively. The lower bound of Budyko curve is explained as a result of probable distributions of available water for evaporation due to catchment co‐evolution.

 

Abstract. Prediction of mean annual runoff is of great interest but still poses achallenge in ungauged basins. The present work diagnoses the prediction inmean annual runoff affected by the uncertainty in estimated distribution ofsoil water storage capacity. Based on a distribution function, a waterbalance model for estimating mean annual runoff is developed, in which theeffects of climate variability and the distribution of soil water storagecapacity are explicitly represented. As such, the two parameters in themodel have explicit physical meanings, and relationships between theparameters and controlling factors on mean annual runoff are established.The estimated parameters from the existing data of watershed characteristicsare applied to 35 watersheds. The results showed that the model couldcapture 88.2 % of the actual mean annual runoff on average across thestudy watersheds, indicating that the proposed new water balance model ispromising for estimating mean annual runoff in ungauged watersheds. Theunderestimation of mean annual runoff is mainly caused by theunderestimation of the area percentage of low soil water storage capacitydue to neglecting the effect of land surface and bedrock topography. Higherspatial variability of soil water storage capacity estimated through theheight above the nearest drainage (HAND) and topographic wetness index (TWI)indicated that topography plays a crucial role in determining the actualsoil water storage capacity. The performance of mean annual runoffprediction in ungauged basins can be improved by employing better estimationof soil water storage capacity including the effects of soil, topography,and bedrock. It leads to better diagnosis of the data requirement forpredicting mean annual runoff in ungauged basins based on a newly developedprocess-based model finally. 

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.

 

The temporal variability of precipitation and potential evapotranspiration affects streamflow from daily to long‐term scales, but the relative roles of different climate variabilities on streamflow at daily, monthly, annual, and mean annual scales have not been systematically investigated in the literature. This paper developed a new daily water balance model, which provides a unified framework for water balance across timescales. The daily water balance model is driven by four climate forcing scenarios (observed daily climate and observed daily climate with its intra‐monthly, intra‐annual, and inter‐annual variability removed) and applied to 78 catchments. Daily streamflow from the water balance model is aggregated to coarser timescales. The relative roles of intra‐monthly, intra‐annual, and inter‐annual climate variability are evaluated by comparing the modeled streamflow forced with the climate forcings at two consecutive timescales. It is found that daily, monthly, and annual streamflow is primarily controlled by the climate variability at the same timescale. Intra‐monthly climate variability plays a small role in monthly and annual streamflow variability. Intra‐annual climate variability has significant effects on streamflow at all the timescales, and the relative roles of inter‐annual climate variability are also significant to the monthly and mean annual streamflow, which is often disregarded. The quantitative evaluation of the roles of climate variability reveals how climate controls streamflow across timescales.

 

The time compression (or time condensation) approximation (TCA) is commonly used in conjunction with an infiltration capacity equation for predicting the postponding infiltration rate, or, more generally, infiltration under time‐varying precipitation. In this paper a power function relationship for TCA between infiltration capacity and its time derivative is proposed for infiltration in the presence of a shallow water table. The results show that the exponent (β) in the power function relationship is not a constant but decreases as infiltration proceeds. The change ofβindicates that the TCA relationship changes during infiltration and further suggests the necessity of using different TCA relationships for predicting infiltration rate during different stages after ponding. We argue that the change ofβis due to the gradual dynamic change of the relative role of gravity and capillarity during infiltration. A Péclet number (Pe) is proposed for measuring the relative effect of gravity and capillarity. In the early times of infiltration when Pe < 1, with the increase ofPe,βdecreases roughly from 3.5 to 2 for clay, silty clay loam, and silty loam, and from 3 to 2 for sandy loam and sand; during the longer times whenPe > 1,βhas a linear relationship withPe. The relationship betweenPeandβprovides an objective approach to select the suitable TCA function during different infiltration stages after ponding.