Effects of hillslope geometry on spatial infiltration using the TOPMODEL and SCS-CN models

ABSTRACT

The estimation of infiltration is a main issue in runoff simulation. The geometry of hillslopes (plan shape and profile curvature) may affect the responses, as well as infiltration over the hillslopes. In this study, the equations of TOPMODEL (a topography-based model) were applied to complex hillslopes to develop the complex TOPMODEL. This model was coupled with the SCS-CN (Soil Conservation Service Curve Number) model to examine the effects of geometry on infiltration and derive a saturation excess-based curve number (CN). The effects of plan shape and profile curvature upon the spatial distribution of CN and infiltration were studied. The results show that convergent hillslopes have 15.4% less infiltration and divergent hillslopes have 7.8% more infiltration than parallel ones. The infiltration over concave hillslopes is 13.5% lower and infiltration over convex hillslopes 5.8% higher than for straight ones. The degree of convergence/divergence has a greater effect on the CN compared to that of profile curvature.     

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.     

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.     

Refined conceptualization of TOPMODEL for shallow subsurface flows

The TOPMODEL framework was used to derive expressions that account for saturated and unsaturated flow through shallow soil on a hillslope. The resulting equations were the basis for a shallow‐soil TOPMODEL (STOPMODEL). The common TOPMODEL theory implicitly assumes a water table below the entire watershed and this does not conceptually apply to systems hydrologically controlled by shallow interflow of perched groundwater. STOPMODEL provides an approach for extending TOPMODEL's conceptualization to apply to shallow, interflow‐driven watersheds by using soil moisture deficit instead of water table depth as the state variable. Deriving STOPMODEL by using a hydraulic conductivity function that changes exponentially with soil moisture content results in equations that look very similar to those commonly associated with TOPMODEL. This alternative way of conceptualizing TOPMODEL makes the modelling approach available to researchers, planners, and engineers who work in areas where TOPMODEL was previously believed to be unsuited, such as the New York City Watershed in the Catskills region of New York State. Copyright © 2002 John Wiley & Sons, Ltd.     

TOPMODEL在珠江流域布柳河流域的应用及其与新安江模型的比较

TOPMODEL是一种以地形为基础的半分布式流域水文模型.对珠江流域布柳河流域的DEM信息进行处理,提取流域的水系、子流域边界、地形指数及水流路径距离的分布,将TOPMODEL应用于该流域中.另外将新安江模型也应用于该流域进行比较.此外,分析了两种模型结构差异所带来的模拟功能差异.两种模型模拟结果精度差异不大,而TOPMODEL实现了空间产流面积分布的可视化.     

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.     

TOPMODEL: A personal view

The minimum set of assumptions underlying TOPMODEL are explored, together with conditions under which they can or cannot be relaxed. It is concluded that it may be necessary to move towards spatially explicit solutions of the governing equations if the underlying q–D relationships are to be modified. The simplicity of TOPMODEL invites its use as a submodel within a range of geomorphological and ecological models that are driven by hydrology. Some example applications are outlined for both soil erosion and solution. © 1997 John Wiley & Sons, Ltd.     

TOPMODEL: A critique

TOPMODEL (a TOPography based hydrological MODEL) is now 20 years old and has been the subject of numerous applications to a wide variety of catchments. This paper represents a critical review of some of the issues involved in application of the TOPMODEL concepts, including the basic assumptions involved; the derivation of topographic index distributions from digital terrain data; additional model components; meaning and calibration of the model parameters; and issues involved in model validation and predictive uncertainty. The aim is to provoke a thoughtful approach to hydrological modelling and the interaction of modelling and field work. Some recommendations are made for future modelling practice. © 1997 John Wiley & Sons, Ltd.     

The in(a/tan/β) index: How to calculate it and how to use it within the topmodel framework

Topographic indices may be used to attempt to approximate the likely distribution of variable source areas within a catchment. One such index has been applied widely using the distribution function catchment model, TOPMODEL, of Beven and Kirkby (1979). Validation of the spatial predictions of TOPMODEL may be affected by the algorithm used to calculate the model's topographic index. A number of digital terrain analysis (DTA) methods are therefore described for use in calculating the TOPMODEL topographic index, In(a/tanβ) (a = upslope contributing area per unit contour; tanβ = local slope angle). The spatial pattern and statistical distribution of the index is shown to be substantially different for different calculation procedures and differing pixel resolutions. It is shown that an interaction between hillslope contributing area accumulation and the analytical definition of the channel network has a major influence on calculated In(a/tanβ) index patterns. A number of DTA tests were performed to explore this interaction. The tests suggested that an ‘optimum’ channel initiation threshold (CIT) may be identified for positioning river headwaters in a raster digital terrain model (DTM). This threshold was found to be dependent on DTM grid resolution. Grid resolution is also suggested to have implications for the validation of spatial model predictions, implying that ‘optimum’ TOPMODEL parameter sets may be unique to the grid scale used in their derivation. Combining existing DTA procedures with an identified CIT, a procedure is described to vary the directional diffusion of contributing area accumulation with distance from the channel network.     

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.     

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.     

Discharge and water table predictions using a generalised TOPMODEL formulation

A simple, generalized saturated zone formulation is presented in this paper to relax the assumption of an exponential function originally made in TOPMODEL. This saturated zone model is based on the concept of a ‘discharge:relative storage’ (QΔS) function which is derived empirically, using recession curve analysis, and may be of arbitrary form. The generalized formulation is applied to the Seternbekken MINIFELT catchment in Norway, where detailed distributed water table data have been measured. These water table data are used to suggest an empirical, power law modification of the topographic a/tan β index. Results for the simulation through time of discharges and water table depths at a few locations show that the generalized saturated zone formulation is as efficient a simulator of the observed data as a conventional TOPMODEL, but requires one parameter less to be calibrated. The simulation of detailed water table distributions is only approximate in both cases. The modified power law index shows only a small improvement but provides a basis for a discussion of possible sources of error in the TOPMODEL assumptions for this site. © 1997 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.     

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.     

Increased flexibility in base flow modelling using a power law transmissivity profile

The hydrological catchment model known as TOPMODEL, in its original and most widely‐used form, assumed that subsurface transmissivity decreases exponentially as subsurface water storage decreases. It has been shown that this leads to recession curves of discharge Q that take the form ? dQ/dt = aQ^b, where a is a constant and b = 2. In order to reproduce a wider range of recession, or base flow, behaviour, a power function for transmissivity was subsequently incorporated into TOPMODEL as an alternative to the exponential function. This was claimed to extend the realistic values of b to range from 1 to 2, inclusive. We show here that the power transmissivity function can also generate values of b > 2 without making unrealistic assumptions (beyond those arguably made in the original TOPMODEL), thus generating recession curves consistent with catchments showing prolonged base flow. Furthermore, the power transmissivity function can generate recession curves that steepen with time (b < 1). Copyright © 2007 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.     

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.     

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 network‐index‐based version of TOPMODEL for use with high‐resolution digital topographic data

This paper describes the preliminary development of a network‐index approach to modify and to extend the classic TOPMODEL. Application of the basic Beven and Kirkby form of TOPMODEL to high‐resolution (2·0 m) laser altimetric data (based upon the UK Environment Agency's light detection and ranging (LIDAR) system) to a 13·8 km² catchment in an upland environment identified many saturated areas that remained unconnected from the drainage network even during an extreme flood event. This is shown to be a particular problem with using high‐resolution topographic data, especially over large appreciable areas. To deal with the hydrological consequences of disconnected areas, we present a simple network index modification in which saturated areas are only considered to contribute when the topographic index indicates continuous saturation through the length of a flow path to the point where the path becomes a stream. This is combined with an enhanced method for dealing with the problem of pits and hollows, which is shown to become more acute with higher resolution topographic data. The paper concludes by noting the implications of the research as presented for both methodological and substantive research that is currently under way. Copyright © 2004 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.