Sensitivity to space and time resolution of a hydrological model using digital elevation data

The space and time resolutions used for the input variables of a distributed hydrological model have a sufficient impact on the model results. This resolution depends on the required accuracy, experimental site and the processes and variables taken into account in the hydrological model. The influence of space and time resolution is studied here for the case of TOPMODEL, a model based on the variable contributing area concept, applied to an experimental 12 km² catchment (Coët-Dan, Brittany, France) during a two month winter period. A sensitivity analysis to space and time resolution is performed first for input variables derived from the digital elevation data, secondly for the optimized values of the TOPMODEL parameters and finally for modelling efficiency. This analysis clearly shows that a relevant domain of space and time resolutions where efficiency is fairly constant can be defined for the input topographic variables, as opposed to another domain of larger resolutions that induces a strong decrease of modelling efficiency. It also shows that the use of a single set of parameters, defined as mean values of parameters on this relevant domain of resolution, does not modify the accuracy of modelling. The sensitivity of the parameters to space and time resolution allows the physical significance of the parameter values to be discussed.     

A MATLAB implementation of TOPMODEL

The MATLAB SIMULINK programming language is applied to the TOPMODEL rainfall–runoff model. SIMULINK requires a good recognition of model dynamics, which has been achieved here in a version based on the first TOPMODEL (Beven and Kirkby, 1979). Introducing the topographic index distribution in a vector form allows the generalization and simplification of the SIMULINK structure. The SIMULINK version of TOPMODEL has a very easy to understand graphical representation, which shows, in a straightforward way, all the physical interactions that take place in the model. Moreover, owing to its modular structure it is easy to add new and/or develop old submodels, depending on the available data and the goal of the modelling. In the example given here TOPMODEL was extended by two submodels representing the soil moisture and evaporation distribution in the catchment. Preparation of the data and presentation of the results is done in MATLAB. Discharge predictions and spatial patterns of hydrological response are demonstrated for a separate validation period. © 1997 John Wiley & Sons, Ltd.     

Using TOPMODEL towards identifying and modelling the hydrological patterns within a headwater,humid, tropical catchment

Increasing pressure on the tropical environment requires a more thorough understanding of hydrological processes as part of reconciling the conflicting demands of economic development vis-à-vis sustainable land management. Using TOPMODEL, a physically based semi-distributed topohydrological model, we test its validity in modelling the stream flow dynamics (hydrograph) in a 1 ha tropical rainforest catchment in French Guiana. Another objective is through field validation of TOPMODEL to ascertain possible runoff generation mechanisms. The field validation of the temporal and spatial hydrodynamics across a rainfall–runoff event reveals that TOPMODEL may be suited for applications to this particular tropical rainforest environment; in fact, this is possibly the first successful application of such a model within the humid tropics. The main reasons why the model was successful are the presumed low hydraulic conductivities of the subsoil, coupled with the absence of an additional deep groundwater body, the contribution from which has caused difficulties in application of topographically, ‘physically’ based runoff models elsewhere in the humid tropics. © 1997 John Wiley & Sons, Ltd.     

Semi‐distributed flood runoff model at the subcontinental scale for southwestern Iran

Rainfall–runoff modelling, as a surface hydrological process, on large‐scale data‐poor basins is currently a major topic of investigation that requires the model parameters be identified by using basin physical characteristics rather than calibration. This paper describes the application of the TOPMODEL framework accompanied by a kinematic wave model to the Karun River sub‐basins in southwestern Iran with just one conceptual parameter for calibration. ISLSCP1, HYDRO1K and Reynolds data sets are presented in a geographical information system and used as data sources for meteorological information, hydrological features and soil characteristics of the study area respectively. The results show that although the model developed can adequately predict flood runoff in the catchment with only one calibrated parameter, it is suggested that the effect of surface reservoirs be considered in the proposed model. Copyright © 2007 John Wiley & Sons, Ltd.     

Analytical solution to a bias in the TOPMODEL framework balance

The increasing need for distributed hydrological modelling leads to an intense use of spatially distributed predictions of physically based models, such as TOPMODEL as addressed here. The ability of these models to reproduce the internal behaviour of catchments physically is increasingly tested through field experiments (geochemical investigation, distributed measurements network, etc.). This paper will show that, in the case of TOPMODEL, an implicit approximation remains in the classic derivation of the equations that consists in neglecting the surface of saturated areas with respect to the total surface of the catchment. This simplifying, though unnecessary, approximation leads to a systematic underestimation of the catchment water storage deficit and to divergence in the water budget accounting. This may also significantly change the predicted ratio between subsurface and surface water fluxes in the total discharge. An analytical solution is suggested that leads to water balance accounting which is better defined, and more consistent in comparison with field water storage recording. It is expected that this work will ensure more accurate TOPMODEL predictions, consistent with the assumptions of the model. This will then improve the interpretation of comparisons between results of simulation and field experiments. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling the hydrological response of mediterranean catchments,Prades, Catalonia. The use of distributed models as aids to hypothesis formulation

This paper attempts to extend the physical arguments underlying the distributed TOPMODEL concepts in an application to the strongly seasonal contributing area responses in two adjacent small mediterranean catchments in the Prades region of Catalonia, Spain. A perceptual model of hydrological response in these catchments is used to suggest possible modifications of the model in a hypothesis testing framework, including an attempt to modify the topographic index approach to reflect the expansion of the effective area of subsurface flow during the wetting-up sequence. It is found that slight improvements in modelling efficiency are possible but that different model parameter distributions are appropriate for different parts of the record. The model was much more successful for the catchment producing the higher runoff volumes. © 1997 John Wiley & Sons, Ltd.     

Sensitivity analysis of extended TOPMODEL for agricultural watersheds equipped with tile drains

An extension of TOPMODEL was developed for rainfall–runoff simulation in agricultural watersheds equipped with tile drains. Tile drain functions are incorporated into the framework of TOPMODEL. Nine possible flow generation scenarios are suggested for tile-drained watersheds and applied in the modelling procedure. In the model development, two methods of simulation of the flow in the unsaturated zone were compared: the traditional, physically based storage approach and a new approach using a transfer function. A regionalized sensitivity analysis was used to determine the sensitivity of parameters and to compare the behaviour of the transfer function with that of the simple storage-related formulation. The number of accepted combinations of parameter values, on average, was higher for the transfer function approach than when using a Monte Carlo method of parameter estimation. Since the rainfall–runoff response pattern tends to vary seasonally, seven events distributed throughout a year were used in the sensitivity analysis to investigate the seasonal variation of the hydrological characteristics. © 1997 John Wiley & Sons, Ltd.     

A distributed monthly hydrological model for integrating spatial variations of basin topography and rainfall

Hydrological models at a monthly time‐scale are important tools for hydrological analysis, such as in impact assessment of climate change and regional water resources planning. Traditionally, monthly models adopt a conceptual, lumped‐parameter approach and cannot account for spatial variations of basin characteristics and climatic inputs. A large requirement for data often severely limits the utility of physically based, distributed‐parameter models. Based on the variable‐source‐area concept, we considered basin topography and rainfall to be two major factors whose spatial variations play a dominant role in runoff generation and developed a monthly model that is able to account for their influences in the spatial and temporal dynamics of water balance. As a hybrid of the Xinanjiang model and TOPMODEL, the new model is constructed by innovatively making use of the highly acclaimed simulation techniques in the two existing models. A major contribution of this model development study is to adopt the technique of implicit representation of soil moisture characteristics in the Xinanjiang model and use the TOPMODEL concept to integrate terrain variations into runoff simulation. Specifically, the TOPMODEL topographic index ln(a/tanβ) is converted into an index of relative difficulty in runoff generation (IRDG) and then the cumulative frequency distribution of IRDG is used to substitute the parabolic curve, which represents the spatial variation of soil storage capacity in the Xinanjiang model. Digital elevation model data play a key role in the modelling procedures on a geographical information system platform, including basin segmentation, estimation of rainfall for each sub‐basin and computation of terrain characteristics. Other monthly data for model calibration and validation are rainfall, pan evaporation and runoff. The new model has only three parameters to be estimated, i.e. watershed‐average field capacity WM, pan coefficient η and runoff generation coefficient α. Sensitivity analysis demonstrates that runoff is least sensitive to WM and, therefore, it can be determined by a prior estimation based on the climate and soil properties of the study basin. The other two parameters can be determined using optimization methods. Model testing was carried out in a number of nested sub‐basins of two watersheds (Yuanjiang River and Dongjiang River) in the humid region in central and southern China. Simulation results show that the model is capable of describing spatial and temporal variations of water balance components, including soil moisture content, evapotranspiration and runoff, over the watershed. With a minimal requirement for input data and parameterization, this terrain‐based distributed model is a valuable contribution to the ever‐advancing technology of hydrological modelling. Copyright © 2006 John Wiley & Sons, Ltd.     

A BTOP model to extend TOPMODEL for distributed hydrological simulation of large basins

Topography is a dominant factor in hillslope hydrology. TOPMODEL, which uses a topographical index derived from a simplified steady state assumption of mass balance and empirical equations of motion over a hillslope, has many advantages in this respect. Its use has been demonstrated in many small basins (catchment areas of the order of 2–500 km²) but not in large basins (catchment areas of the order of 10 000–100 000 km²). The objective of this paper is to introduce the Block‐wise TOPMODEL (BTOP) as an extension of the TOPMODEL concept in a grid based framework for distributed hydrological simulation of large river basins. This extension was made by redefining the topographical index by using an effective contributing area af(a) (0?f(a)?1) per unit grid cell area instead of the upstream catchment area per unit contour length and introducing a concept of mean groundwater travel distance. Further the transmissivity parameter T₀ was replaced by a groundwater dischargeability D which can provide a link between hill slope hydrology and macro hydrology. The BTOP model uses all the original TOPMODEL equations in their basic form. The BTOP model has been used as the core hydrological module of an integrated distributed hydrological model YHyM with advanced modules of precipitation, evapotranspiration, flow routing etc. Although the model has been successfully applied to many catchments around the world since 1999, there has not been a comprehensive theoretical basis presented in such applications. In this paper, an attempt is made to address this issue highlighted with an example application using the Mekong basin. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of the catchment runoff coefficient on the performance of TOPMODEL in rainfall–runoff modelling

Effects of the catchment runoff coefficient on the performance of TOPMODEL in simulating catchment rainfall–runoff relationships are investigated in this paper, with an aim to improve TOPMODEL's simulation efficiency in catchments with a low runoff coefficient. Application of TOPMODEL in the semi‐arid Yihe catchment, with an area of 2623 km² in the Yellow River basin of China, produced a Nash–Sutcliffe model efficiency of about 80%. To investigate how the catchment runoff coefficient affects the performance of TOPMODEL, the whole observed discharge series of the Yihe catchment is multiplied with a larger‐than‐unity scale factor to obtain an amplified discharge series. Then TOPMODEL is used to simulate the amplified discharge series given the original rainfall and evaporation data. For a set of different scale factors, TOPMODEL efficiency is plotted against the corresponding catchment runoff coefficient and it is found that the efficiency of TOPMODEL increases with the increasing catchment runoff coefficient before reaching a peak (e.g. about 90%); after the peak, however, the efficiency of TOPMODEL decreases with the increasing catchment runoff coefficient. Based on this finding, an approach called the discharge amplification method is proposed to enhance the simulation efficiency of TOPMODEL in rainfall–runoff modelling in catchments with a low runoff coefficient. Copyright © 2004 John Wiley & Sons, Ltd.     

The information content theory for the estimation of the topographic index distribution used in TOPMODEL

This paper analyses the significance of the entropy concept in the topography parameterization within the model TOPMODEL proposed by Beven and Kirkby (1979), by means of the hydrological behaviour of an experimental basin in southern Italy. For a significant number of flood events recorded at the basin outlet, the performance of TOPMODEL for different spatial distributions of the topographic index, ln(a/tan β), has been observed. Performance is related to the information content estimated as an entropy measure, corresponding to each of the spatial distributions of the topographic index, with the aim of identifying the procedures most suitable to represent the hydrological process of rainfall–runoff. The results obtained have shown that for flood events corresponding to brief, heavy precipitation, some procedures provide better performances than others. Moreover, these improvements are justified by greater information content in the corresponding spatial distributions of the topographic index. Finally, TOPMODEL performances for some procedures have been analysed, varying the resolution scale of the topographic index. For analogous hydrological performances, scale change produced variations in some of the subsurface hydraulic parameters. These variations were proportional to a spatial variability measure of the topographic index distribution, derived from the corresponding information content. © 1997 John Wiley & Sons, Ltd.     

Continuous simulation for computing design hydrographs for water structures

The contribution discusses the problems with modelling design floods for water structures. The statistical extrapolations of observed flood series of, for example, 80 years “only” to the annual exceedance probability AEP = 0.01 is difficult due to the large variability in extreme values. For large dams, however, the AEP = 0.001 or 0.0001 is required. Most of the uncertainties in hydrological modelling are epistemic (uncertainties in model structure, model parameters, inputs, calibration data, and in measurements) and moreover some measurements can be disinformative. With powerful computers, it is now possible to produce very long series (100 to100,000 years in hourly time step) using precipitation and temperatures computed with a weather model. Within the framework of the Generalised Likelihood Uncertainty Estimation (GLUE) many (thousands) of such continuous simulations are produced and compared to the observed historical data. According to Keith Beven's Manifesto for the equifinality thesis the differences between modelled and observed values should not be larger than some limits of acceptability based on what is known about errors in the input and output observations used for model evaluation (e.g., for flow the current metering data are used). The unacceptable realisations are rejected. We have been working with the frequency version of TOPMODEL in various versions according to the unique characteristics of each catchment. Design hydrographs for water structures are then extracted from the acceptable realisations. The continuous simulation with uncertainty estimation seems nowadays the most promising method of computing design hydrographs for important water structures, even if issues associated with epistemic uncertainty of model assumptions remain.     

Simulation and comparative study of two types of Topographic Index model for a homogeneous mountain catchment

In order to expand the application range of the classic Topographic Index model (TOPMODEL) and develop a more appropriate submodel of hydrological processes for use in the land surface model, two types of TOPMODEL are investigated, one with saturated hydraulic conductivity change with depth obeying exponential law (classical e-TOPMODEL or e-TOPMODEL for short) and the other obeying general power law (general p-TOPMODEL or p-TOPMODEL for short). Using observation date in the Suomo River catchment located in the upper reaches of the Yangtze River, the sensitivity study of the p-TOPMODEL was conducted and the simulated results from the model were examined and evaluated first, and then the results were compared with the results from the e-TOPMODEL to find the similarities and differences between the two types of models. The main conclusions obtained from the above studies are (1) topographic index and its distribution derived from the p-TOPPMODEL for the Suomo Basin are sensitive to changes of parameter n and m; (2) changes of n and m have impacts on the simulation results of various hydrological components (such as daily runoff, monthly averaged runoff, monthly averaged surface runoff and subsurface runoff), but have the weaker impacts on forty-year averaged total runoff; and (3) for the same value of m, the simulated results of e-TOPMODEL display higher surface runoff and lower subsurface runoff than the general p-TOPMODEL does but multi-year averaged total runoffs produced from the two types of TOPMODEL show insignificant difference. The differences between the two types of models indicate that it is necessary to pay close attention to correct selection from different hydrological models for use in land surface model development. The result mentioned above is useful to provide some referential information for the model selection.     

Identifying storm flow pathways in a rainforest catchment using hydrological and geochemical modelling

The hydrological model TOPMODEL is used to assess the water balance and describe flow paths for the 9·73 ha Lutz Creek Catchment in Central Panama. Monte Carlo results are evaluated based on their fit to the observed hydrograph, catchment‐averaged soil moisture and stream chemistry. TOPMODEL, with a direct‐flow mechanism that is intended to route water through rapid shallow‐soil flow, matched observed chemistry and discharge better than the basic version of TOPMODEL and provided a reasonable fit to observed soil moisture and wet‐season discharge at both 15‐min and daily time‐steps. The improvement of simulations with the implementation of a direct‐flow component indicates that a storm flow path not represented in the original version of TOPMODEL plays a primary role in the response of Lutz Creek Catchment. This flow path may be consistent with the active and abundant pipeflow that is observed or delayed saturation overland flow. The ‘best‐accepted’ simulations from 1991 to 1997 indicate that around 41% of precipitation becomes direct flow and around 10% is saturation overland flow. Other field observations are needed to constrain evaporative and groundwater losses in the model and to characterize chemical end‐members posited in this paper. Published in 2004 by John Wiley & Sons, Ltd.     

Development of a modelling methodology for the investigation of riparian hydrological processes

The riparian zone is in intimate contact with the river and, as such, is a critical zone for understanding hydrological problems. This paper presents a general modelling methodology for the assessment of riparian hydrological processes. It is applicable to a wide range of riparian spaces and incorporates current expertise in numerical methods. A core part of the modelling methodology is the random walk particle method (RWPM). We develop an RWPM as part of the ESTEL2D subsurface flow model, test it against analytical solutions and apply it to the simulation of parcels of water as they move through the riparian zone. The modelling methodology provides a new opportunity to assess fundamental hydrological process issues such as the proportioning of pre‐event and event water storm runoff, and reversals of flow in floodplains. Copyright © 2005 John Wiley & Sons, Ltd.     

Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model

The Generalised Likelihood Uncertainty Estimation (GLUE) methodology is used to investigate how distributed water table observations modify simulation and parameter uncertainty for the hydrological model TOPMODEL, applied to the Sæternbekken Minifelt catchment in Norway. Errors in simulating observed flows, continuously-logged borehole water levels and more extensive, spatially distributed water table depths are combined using Bayes' equation within a `likelihood measure' L. It is shown how the distributions of L for the TOPMODEL parameters change as the different types of observed data are considered. These distributions are also used to construct corresponding simulation uncertainty bounds for flows, borehole water levels, and water table depths within the spatially-extensive piezometer network. Qualitatively wide uncertainty bounds for water table simulations are thought to be consistent with the simplified nature of the distributed model.     

Multi‐criterial validation of TOPMODEL in a mountainous catchment

The need for powerful validation methods for hydrological models including the evaluation of internal stages and spatially distributed simulations has often been emphasized. In this study a multi‐criterial validation scheme was used for validation of TOPMODEL, a conceptual semi‐distributed rainfall–runoff model. The objective was to test TOPMODEL's capability of adequately representing dominant hydrological processes by simple conceptual approaches. Validation methods differed in the type of data used, in their target and in mode. The model was applied in the humid and mountainous Brugga catchment (40 km²) in south‐west Germany. It was calibrated by a Monte Carlo method based on hourly runoff data. Additional information for validation was derived from a recession analysis, hydrograph separation with environmental tracers and from field surveys, including the mapping of saturated areas. Although runoff simulations were satisfying, inadequacies of the model structure compared with the real situation with regard to hydrological processes in the study area were found. These belong mainly to the concept of variable contributing areas for saturation excess overland flow and their dynamics, which were overestimated by the model. The simple TOPMODEL approach of two flow components was found to be insufficient. The multi‐criterial validation scheme enables not only to demonstrate limitations with regard to process representation, but also to specify where and why these limitations occur. It may serve as a valuable tool for the development of physically sound model modifications. Copyright © 1999 John Wiley & Sons, Ltd.     

A variable source area for groundwater evapotranspiration: impacts on modeling stream flow

Evapotranspiration (ET) plays a crucial role in catchment water budgets, typically accounting for more than 50% of annual precipitation falling within temperate deciduous forests. Groundwater ET is a portion of total ET that occurs where plant roots extend to the capillary fringe above the phreatic surface or induce upward movement of water from the water table by hydraulic redistribution. Groundwater ET is spatially restricted to riparian zones or other areas where the groundwater is accessible to plants. Due to the difficulty in measuring groundwater ET, it is rarely incorporated explicitly into hydrological models. In this study, we calibrated Topographic Model (TOPMODEL) using a 14‐year hydrograph record and added a groundwater ET pathway to derive a new model, Groundwater Evapotranspiration TOPMODEL (GETTOP). We inspected groundwater elevations and stream flow hydrographs for evidence of groundwater ET, examined the relationship between groundwater ET and topography, and delineated the area where groundwater ET is likely to take place. The total groundwater ET flux was estimated using a hydrological model. Groundwater ET was larger where the topography was flat and the groundwater table was shallow, occurring within about 10% of the area in a headwater catchment and accounting for 6 to 18% of total annual ET. The addition of groundwater ET to GETTOP improved the simulation of stream discharge and more closely balanced the watershed water budget. Copyright © 2013 John Wiley & Sons, Ltd.     

Towards the use of catchment geomorphology in flood frequency predictions

A further development of a topography-based model of catchment hydrology (TOPMODEL) is described and applied to the problem of predicting flood frequency characteristics. The model can simulate infiltration excess, saturation excess, and subsurface runoff contributions to peak flows. Catchment geomorphology plays a central role in predicting the nature of the hydrological response. Using stochastic rainfall and initial condition inputs based on measured data, the model satisfactorily reproduces the mean hourly flow flood frequency growth curve for the Wye catchment, but not the mean number of peaks greater than 3mm h^?1 each year. Suggestions for further improvements are made.