Search for: All records

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.

 

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 flow duration curve (FDC) is a hydrologically meaningful representation of the statistical distribution of daily streamflows. The complexity of processes contributing to the FDC introduces challenges for the direct exploration of physical controls on FDC. In this paper, the controls of climate and catchment characteristics on FDC are explored using a stochastic framework that enables construction of the FDC from three components of streamflow: fast and slow flow (during wet days) and slow flow during dry days. The FDC during wet days (FDC_w) is computed as the statistical sum of the fast flow duration curve (FFDC) and the slow flow duration curve (SFDC_w), considering their dependency. FDC is modeled as the mixture distribution of FDC_wand the slow flow duration curve during dry days (SFDC_d), by considering the fraction of wet days (δ) for perennial streams and bothδand the fraction of days of zero streamflow for ephemeral streams. The Kappa distribution is employed to fit the FFDC, SFDC_w, and SFDC_dfor 300 catchments from Model Parameter Estimation Experiment (MOPEX) across the United States. Results show that the 0–20th percentile of FDC is controlled by FFDC and SFDC_w, the 90–100th percentile of FDC is controlled by SFDC_d, and the 20–90th percentile of FDC is controlled by three components. The relationships between estimated Kappa distribution parameters and climate and catchment characteristics reveal that the aridity index, the coefficient of variation of daily precipitation, timing of precipitation, time interval between storms, snow, topographic slope, and slope of recession slope curve are dominant controlling factors.

 

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. 

Abstract. Following the Budyko framework, the soil wetting ratio (the ratio betweensoil wetting and precipitation) as a function of the soil storage index (theratio between soil wetting capacity and precipitation) is derived from theSoil Conservation Service Curve Number (SCS-CN) method and the variableinfiltration capacity (VIC) type of model. For the SCS-CN method, the soilwetting ratio approaches 1 when the soil storage index approaches ∞,due to the limitation of the SCS-CN method in which the initial soil moisturecondition is not explicitly represented. However, for the VIC type of model,the soil wetting ratio equals the soil storage index when the soil storageindex is lower than a certain value, due to the finite upper bound of thegeneralized Pareto distribution function of storage capacity. In this paper,a new distribution function, supported on a semi-infinite interval $x\in [\mathrm{0},\mathrm{\infty })$, is proposed for describing the spatial distribution of storagecapacity. From this new distribution function, an equation is derived for therelationship between the soil wetting ratio and the storage index. In thederived equation, the soil wetting ratio approaches 0 as the storage indexapproaches 0; when the storage index tends to infinity, the soil wettingratio approaches a certain value (≤1) depending on the initial storage.Moreover, the derived equation leads to the exact SCS-CN method when initialwater storage is 0. Therefore, the new distribution function for soil waterstorage capacity explains the SCS-CN method as a saturation excess runoffmodel and unifies the surface runoff modeling of the SCS-CN method and theVIC type of model.