Exponential data fitting applied to infiltration, hydrograph separation, and variogram fitting

Most lumped rainfall-runoff models separate the interflow and groundwater components from the measured runoff hydrograph in an attempt to model these as hydrologic reservoir units. Similarly, rainfall losses due to infiltration as well as other abstractions are separated from the measured rainfall hyetograph, which are then used as inputs to the various hydrologic reservoir units. This data pre-processing is necessary in order to use the linear unit hydrograph theory, as well as for maintaining a hydrologic budget between the surface and subsurface flow processes. Since infiltration determines the shape of the runoff hydrograph, it must be estimated as accurately as possible. When measured infiltration data is available, Horton’s exponential infiltration model is preferable due to its simplicity. However, estimating the parameters from Horton’s model constitutes a nonlinear least squares fitting problem. Hence, an iterative procedure that requires initialization is subject to convergence. In a similar context, the separation of direct runoff, interflow, and baseflow from the total hydrograph is typically done in an ad hoc manner. However, many practitioners use exponential models in a rather “layer peeling” fashion to perform this separation. In essence, this also constitutes an exponential data fitting problem. Likewise, certain variogram functions can be fitted using exponential data fitting techniques. In this paper we show that fitting a Hortonian model to experimental data, as well as performing hydrograph separation, and total hydrograph and variogram fitting can all be formulated as a system identification problem using Hankel-based realization algorithms. The main advantage is that the parameters can be estimated in a noniterative fashion, using robust numerical linear algebra techniques. As such, the system identification algorithms overcome the problem of convergence inherent in iterative techniques. In addition, the algorithms are robust to noise in the data since they optimally separate the signal and noise subspaces from the observed noisy data. The algorithms are tested with real data from field experiments performed in Surinam, as well as with real hydrograph data from a watershed in Louisiana. The system identification techniques presented herein can also be used with any other type of exponential data such as exponential decays from nuclear experiments, tracer studies, and compartmental analysis studies.     

Hydrograph separation using tracers and digital filters to quantify runoff components in a semi‐arid mesoscale catchment

Chemical hydrograph separation using electrical conductivity and digital filters is applied to quantify runoff components in the 1,640 km² semi‐arid Kaap River catchment and its subcatchments in South Africa. A rich data set of weekly to monthly water quality data ranging from 1978 to 2012 (450 to 940 samples per site) was analysed at 4 sampling locations in the catchment. The data were routinely collected by South Africa's national Department of Water and Sanitation, using standard sampling procedures. Chemical hydrograph separation using electrical conductivity (EC) as a tracer was used as reference and a recursive digital filter was then calibrated for the catchment. Results of the two‐component hydrograph separation indicate the dominance of baseflow in the low flow regime, with a contribution of about 90% of total flow; however, during the wet season, baseflow accounts for 50% of total flow. The digital filter parameters were very sensitive and required calibration, using chemical hydrograph separation as a reference. Calibrated baseflow estimates ranged from 40% of total flow at the catchment outlet to 70% in the tributaries. The study demonstrates that routinely monitored water quality data, especially EC, can be used as a meaningful tracer, which could also aid in the calibration of a digital filter method and reduce uncertainty of estimated flow components. This information enhances our understanding of how baseflow is generated and contributed to streamflow throughout the year, which can aid in quantification of environmental flows, as well as to better parameterize hydrological models used for water resources planning and management. Baseflow estimates can also be useful for groundwater and water quality management.     

An approach for evaluating the hydrological effects of urbanization and its application

This study focuses mainly on observing urban development in Taiwan's Wu‐Tu watershed from the perspective of urban hydrological theory. An approach is proposed for developing a method for incorporating available meteorological data to define the degree of change in a runoff hydrograph for urbanizing basins. The mean rainfall was estimated using the Kriging method. For calibration, two methods of calculating the effective rainfall (the Φ‐index method and the non‐linear‐programming (NLP) method) were used as model inputs, and the optimal global parameters of the linear reservoir model were then obtained from the shuffled complex evolution (SCE) algorithm. Twenty‐six (1966–1991) and eight (1994–1997) rainfall–runoff events were used for calibration and verification, respectively. The NLP method yielded better results than the Φ‐index method, especially for multipeak rainfall–runoff events. The regression equation determined the relationship between the parameters of the model and impervious areas. A comparison based on the results of the instantaneous unit hydrograph of the study area revealed that three decades of urbanization had increased the peak flow by 27%, and the time to peak was decreased by 4 h. The study simply describes the results of the impact of imperviousness on hydrological modelling. Copyright © 2002 John Wiley & Sons, Ltd.     

An approach to analysing plot scale infiltration and runoff responses to rainfall of fluctuating intensity

Simulated rainfall of fluctuating intensity was applied to runoff plots on bare dryland soils in order to explore a new method for analysing the non‐steady‐state responses of infiltration and overland flow. The rainfall events all averaged 10 mm/h but included intensity bursts of up to 70 mm/h and lasting 5–15 min, as well as periods of low intensity and intermittency of up to 25 min. Results were compared with traditional steady‐state estimates of infiltrability made under simulated rainfall sustained at a fixed intensity of 10 mm/h. Mean event infiltration rate averaged 13.6% higher under fluctuating intensities, while runoff ratios averaged only 63% of those seen under constant intensity. In order to understand the changing soil infiltrability, up to three affine Horton infiltration equations were fitted to segments of each experiment. All equations had the same final infiltrability f_c, but adjusted values for coefficients f₀ (initial infiltrability) and K_f (exponential decay constant) were fitted for periods of rainfall that followed significant hiatuses in rainfall, during which subsurface redistribution allowed near‐surface soil suction to recover. According to the fitted Horton equations, soil infiltrability recovered by up 10–24 mm/h during intra‐event rainfall hiatuses of 15 to 20‐min duration, contributing to higher overall event infiltration rates and to reduced runoff ratios. The recovery of infiltrability also reduced the size of runoff peaks following periods of low intensity rainfall, compared with the predictions based on single Horton infiltration equations, and in some cases, no runoff at all was recorded from late intensity peaks. The principal finding of this study is that, using a set of affine equations, the intra‐event time variation of soil infiltrability can be tracked through multiple intensity bursts and hiatuses, despite the lack of steady‐state conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

A geomorphology-based semi-distributed watershed model

A semi-distributed watershed model was developed that conceptualizes the catchment as a cascade of nonlinear storage elements whose geometric dimensions are derived from the Horton–Strahler ordering of the stream network. Each storage element represents quick storm runoff over land or in a channel segment. The physically based groundwater submodel is parameterized through the application of the Brutsaert–Nieber recession flow analysis and it provides continuous baseflow separation. The model requires the calibration of seven parameters from a one year rainfall–runoff record. It was tested on the Mahantango Creek watershed in the Susquehanna River basin, Pennsylvania.     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

Power function decay of hydraulic conductivity for a TOPMODEL‐based infiltration routine

TOPMODEL rainfall‐runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power‐function‐based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low‐frequency 30 min design storm with 4·8 cm h^?1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field‐observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL‐based Ward Pound Ridge rainfall‐runoff simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Runoff production processes in small alpine catchments within the unconsolidated Pleistocene sediments of the Lainbach area (Upper Bavaria)

In the Lainbach catchment, unconsolidated Pleistocene moraine sediments are widely distributed. Because of the great natural risk of floods, together with extreme loads of sediments, investigations of runoff production processes have been conducted in this area. At hillslope scale three test sites with different states of soil development and vegetation cover were instrumented with V‐shaped weirs, precipitation gauges and measurement devices for electrical conductivity (EC) of discharge water. The EC has been used as a geochemical tracer for hydrograph separation, since the statistical relationship between content of dissolved Ca²⁺, Mg²⁺ cations and EC is highly significant for different stages of runoff. This method allows hydrograph separation at high temporal resolution for both the rising and falling limb of the hydrograph. The following results of the investigations can be resumed. If relief conditions are similar, the effectiveness of runoff production decreases with an increasing density of vegetation cover. The runoff delivery ratio decreases as well as the peaks of runoff. In contrast, concentration times of hillslope catchments are equal, even if vegetation cover is of great density and soils are well developed. As a reason for the short reaction times, different runoff production processes have been detected. On bare ground, infiltration excess overland flow intensified by surface sealing processes is the main source for quick runoff. On hillslopes well covered by vegetation, translatory flow processes indicated by soil water with high solute contents force a rapid runoff reaction only a few minutes after rainfall has begun. It is to be assumed that translatory flow is a runoff production process typical for hillslopes covered by vegetation in a steep alpine relief. By means of the areal distribution of the topographic index, concentration of runoff production on a small part of the catchment has been demonstrated for hillslopes densely covered by vegetation. The investigations have shown that there is a lack of studies on runoff production processes in steep alpine relief, as well as a deficit of methods to quantify hydraulic properties of coarse‐grained soils with a wide grain size distribution. Copyright © 2003 John Wiley & Sons, Ltd.     

Storm‐event rainfall–runoff modelling approach for ungauged sites in Taiwan

This work develops a top‐down modelling approach for storm‐event rainfall–runoff model calibration at unmeasured sites in Taiwan. Twenty‐six storm events occurring in seven sub‐catchments in the Kao‐Ping River provided the analytical data set. Regional formulas for three important features of a streamflow hydrograph, i.e. time to peak, peak flow, and total runoff volume, were developed via the characteristics of storm event and catchment using multivariate regression analysis. Validation of the regional formulas demonstrates that they reasonably predict the three features of a streamflow hydrograph at ungauged sites. All of the sub‐catchments in the study area were then adopted as ungauged areas, and the three streamflow hydrograph features were calculated by the regional formulas and substituted into the fuzzy multi‐objective function for rainfall–runoff model calibration. Calibration results show that the proposed approach can effectively simulate the streamflow hydrographs at the ungauged sites. The simulated hydrographs more closely resemble observed hydrographs than hydrographs synthesized using the Soil Conservation Service (SCS) dimensionless unit hydrograph method, a conventional method for hydrograph estimation at ungauged sites in Taiwan. Copyright © 2008 John Wiley & Sons, Ltd.     

A statistically based runoff‐yield model coupling infiltration excess and saturation excess mechanisms

A statistically based runoff‐yield model is proposed in this paper. The model considers spatial heterogeneities of rainfall, soil infiltration capacity and soil water storage capacity that are main factors controlling runoff‐yield process. It assumes that the spatial variation of rainfall intensity at each time step can be characterized by a probability density function, which is estimated by matching the hyetograph through goodness‐of‐fit measure, whereas the spatial heterogeneities of soil infiltration capacity and soil water storage capacity are described by parabola‐type functions. Surface runoff is calculated according to infiltration excess mechanism; the statistical distribution of surface runoff rate can be deduced with the joint distribution of rainfall intensity and soil infiltration rate, thus obtaining a quasi‐analytical solution for surface runoff. Based on saturation excess mechanism, the groundwater flow (flows below the ground are collectively referred to as groundwater flow) is calculated by infiltration and the probability distribution of soil water storage capacity. Consequently, the total runoff is composed of infiltration excess and saturation excess runoff components. As an example, this model is applied to flood event simulation in Dongwan catchment, a semi‐humid region and a tributary of Yellow River in China. It indicates that the proposed runoff‐yield model could achieve acceptable accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

A combined rainfall infiltration model based on Green–Ampt and SCS‐curve number

The Green–Ampt infiltration equation is an incomplete governing equation for rainfall infiltration due to the absence of an inertia term. The estimation of the capillary pressure head at the wetting front is difficult to determine. Thus, a major limitation of the Green–Ampt model is the constant, non‐zero surface ponding depth. This paper proposes an integrated rainfall infiltration model based on the Green–Ampt model and the SCS‐CN model. It achieves a complete governing equation for rainfall infiltration by momentum balance and the water budget based on the Green–Ampt assumption, and uses the curve number from the SCS‐CN method to calculate the initial abstraction, which is used as a basic parameter for the governing equation of the intensity of rainfall loss during the runoff period. The integrated rainfall infiltration model resolves the dilemma for capillary pressure head estimation, overcomes the limitation of constant, non‐zero surface ponding depth, and facilitates the calculation of runoff for individual flood simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Base flow separation for soil erosion simulation in a granitic forested headwater catchment using a process-based model,GeoWEPP

Distributed erosion models, which simulate the physical processes of water flow and soil erosion, are effective for predicting soil erosion in forested catchments. Although subsurface flow through multiple pathways is dominant for runoff generation in forested headwater catchments, the process-based erosion model, Geo-spatial interface for Water Erosion Prediction Project(Geo WEPP), does not have an adequate subsurface component for the simulation of hillslope water flow. In the current study, t...     

Hydrograph and unit hydrograph derivation in arid regions

Arid and semi‐arid regions expose special hydrological features that are distinctive from humid areas. Unfortunately, humid‐region hydrological empirical formulations are used directly in the arid and semi‐arid regions without care about the basic assumptions. During any storm rainfall in arid regions, rainfall, infiltration and runoff components of the hydrological cycle have impacts on water resources. The basis of the methodology presented in this paper is the ratio of runoff increment to rainfall increment during an infinitesimally small time duration. This is the definition of runoff coefficient for the same infinitesimal time duration. The ratio is obtained through rational, physical and mathematical combination of hydrological thinking and then integrated with the classical infiltration equation for the hydrograph determination. The parameters of the methodology are explained and their empirical estimations are presented. The methodology works for rainfall and runoff from ungauged watersheds where infiltration measurement can be performed. The comparison of the new approach with different classical approaches, such as the rational formula and Soil Conservation Service method, are presented in detail. Its application is performed for two wadis within the Kingdom of Saudi Arabia. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation of snowmelt runoff on experimental plots in Lulea,Sweden

Empirical characteristics of snowmelt runoff are derived from observations made during snowmelt in a six‐year period from 1980 to 1985 on three experimental plots and three plates located on the campus of the Lulea University of Technology in Lulea, Sweden. The plots had asphalt, gravel and grass surfaces. The plates were of different designs with one having the bottom cut out so that it was more like a frame. With the assumption that the asphalt surface of the plots was impervious, infiltration of meltwater into gravel and grass surfaces was deduced. Unlike rainfall infiltration, the graph of snowmelt infiltration rate resembled a flow hydrograph, with a distinct rise, a peak and a distinct recession. A strong linear relationship between the snowmelt runoff hydrograph peak and the snowmelt amount was found, which explained more than 90% of the variability in the snowmelt peak. This is in contrast with rainfall runoff where the relationship between runoff peak and volume is decidedly non‐linear. Hourly snowmelt runoff peak and daily snowmelt amount were found to exhibit nearly constant skew and follow approximately a Gumbel frequency distribution. Copyright © 2000 John Wiley & Sons, Ltd.     

FLOOD MODELLING WITH GIS-DERIVED DISTRIBUTED UNIT HYDROGRAPHS

The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km² watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Parameter sensitivity of automated baseflow separation for snowmelt‐dominated watersheds and new filtering procedure for determining end of snowmelt period

Automation in baseflow separation procedures allowed fast and convenient baseflow and baseflow index (BF and BFI) estimation for studies including multiple watersheds and covering large spatio‐temporal scales. While most of the existing algorithms are developed and tested extensively for rainfall‐ and baseflow‐dominated systems, little attention is paid on their suitability for snowmelt‐dominated systems. Current publishing practice in regional‐scale studies is to omit BF and BFI uncertainty evaluation or sensitivity analysis. Instead, “standard” and “previously recommended” parameterizations are transferred from rainfall/BF to snowmelt‐dominated systems. We believe that this practice should be abandoned. First, we demonstrate explicitly that the three most popular heuristic automated BF separation methods—Lyne–Hollick and Eckhardt recursive digital filters, and the U.K. Institute of Hydrology smoothed minima method—produce a wide range of annual BF and BFI estimates due to parameter sensitivity during the annual snowmelt period. Then, we propose a solution for cases when BF and BFI calibration is not possible, namely excluding the snowmelt‐dominated period from the analysis. We developed an automated filtering procedure, which divides the hydrograph into pre‐snowbelt, post‐snowmelt, and snowmelt periods. The filter was tested successfully on 218 continuous water years of daily streamflow data for four snowmelt‐dominated headwater watersheds located in Wyoming (60–837 km²). The post‐snowmelt BF and BFI metric can be used for characterizing summer low‐flows for snowmelt‐dominated systems. Our results show that post‐snowmelt BF and BFI sensitivity to filter parameterization is reduced compared with the sensitivity of annual BF and BFI and is similar to the sensitivity levels for rainfall/baseflow systems.     

Two‐dimensional physically based finite element runoff model for small agricultural watersheds: I. Model development

Soil erosion by water is the root cause of ecological degradation in the Shiwalik foothills of Northern India. Simulation of runoff and its component processes is a pre‐requisite to develop the management strategies to tackle the problem, successfully. A two‐dimensional physically based distributed numerical model, ROMO2D has been developed to simulate runoff from small agricultural watersheds on an event basis. The model employs the 2‐D Richards equation with sink term to simulate infiltration and soil moisture dynamics in the vadoze zone under variable rainfall conditions, and 2‐D Saint‐Venant equations under the kinematic wave approximation along with Manning's equation as the stage‐discharge equation for runoff routing. The various flow‐governing equations have been solved numerically by employing a Galerkin finite element method for spatial discretization using quadrilateral elements and finite difference techniques for temporal solutions. The ROMO2D computer program has been developed as a class‐based program, coded in C + + in such a way that with minor modifications, the model can be used to simulate runoff on a continuous basis. The model writes output for a runoff hydrograph of each storm. Model development is described in this paper and the results of model testing and field application are to be presented in a subsequent paper. Copyright © 2008 John Wiley & Sons, Ltd.