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.     

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.     

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.     

Evaluation of digital channel network derivation methods in a glaciated subalpine catchment

The digital elevation model (DEM) has become an essential tool for an increasing array of mountain runoff analyses, particularly the derivation and mapping of stream channel networks. This study examines how well commonly applied DEM‐based channel derivation methods at different spatial resolutions can represent the channel network for a glaciated Rocky Mountain headwater catchment. The specific objectives are to (1) examine how differences in gridded DEM resolution affect spatially distributed values of local slope, specific contributing area, and topographic wetness index derived from both eight and infinite directional flow algorithms, (2) map the actual stream channel network to examine the influence of surface variables on channel initiation, and (3) assess accuracy of DEM‐derived networks compared with the field surveyed network. Results show that for the same contributing area threshold, increasing grid cell size leads to increased channelization of modeled networks. A plot of local slope versus contributing area reveals a negative relationship similar to that of prior studies in un‐glaciated areas but with breaks in slope at contributing areas that are too small to represent thresholds for channelization. Field survey results and evaluation of DEM‐derived channel networks suggest that channel network formation is not clearly related to surface topographic variables at Loch Vale. Digitally derived channel networks do not accurately predict low order channel locations, but approximations of the channel network with drainage density and headward extent of channelization similar to the observed network can be derived with both a 1 m and 10 m DEM using a contributing area threshold of approximately 4x10⁴ m². Copyright © 2014 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.     

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.     

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.     

A hillslope hydrology approach for catchment‐scale slope stability analysis

Regional analysis of slope stability is often constrained by availability of data. Model requirements for input data cannot be met at the desired spatial resolution because data are either site‐speci?c or non‐existent. Faced with these dif?culties it has often been the practice to assume that certain parameters are uniform throughout the area of interest. An alternative approach proposed here allows a more detailed discrimination of slope stability conditions. Based on the principles of hillslope hydrology, hydrologic information can be generated at suf?cient resolution to allow higher resolution slope stability analysis. Measurements from an instrumented network in a small area have been used to establish index‐based models for topographic and climate‐related controls of piezometric response. The ability to relate groundwater levels to rainfall and topographic parameters provides a means of up‐scaling to larger catchments and ultimately the opportunity to generate a catchment‐wide prediction of the distribution, magnitude and frequency of rainstorm‐generated groundwater levels. The example provided in this study uses the topography index of TOPMODEL in GIS to predict the spatial patterns of groundwater elevation for seasonal soil moisture conditions and given rainfall inputs. This allows modelling of catchment‐wide response of soil water to rainstorms with different return periods (representing different magnitudes), and is an essential prerequisite for a probabilistic regional slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd.     

Grid‐resolution effects on a model for integrating urban and rural areas

The impact of grid‐cell size on calibrated parameters and on the performance of a variable source area model intended for urbanizing catchments is studied in this research. The model uses TOPMODEL concepts that were modified to consider urban areas in both the topographic index and the mechanism of surface runoff generation. The revised model known as TOPURBAN, was applied to a small catchment of roughly 8 km² in southern Ontario. Ten different grid‐cell sizes ranging from 10 m to 100 m were selected to study scale effects in this catchment with mild to moderate relief, on three separate time periods. The model performed adequately with calibration efficiencies for all three time periods in the range of 0\65 to 0\85. The verification efficiencies were not as high and ranged from 0\4 to 0\6. Larger cell sizes produced higher averages of topographic index, and this resulted in larger calibrated transmissivities. The most important parameter in determining the quantity of urban runoff was slightly affected by grid resolution. During the calibration process, this parameter was also found to interact with important parameters that dealt primarily with rural runoff generation. As cell size increased, contributions from urban areas increased and overland flow contributions from rural areas decreased. Results showed that in this integrated model of urban and rural areas, predicted processes based on calibrated parameters were dependent on grid resolution. Calibration of internal state variables is recommended to draw conclusions on the influences between urban and rural areas on the overall flow. Copyright © 2000 John Wiley & Sons, Ltd.     

Development of a one-parameter variable source area runoff model for ungauged basins

This research develops a one-parameter model of saturated source area dynamics and the spatial distribution of soil moisture. The single required parameter is the maximum soil moisture deficit within the catchment. The concept behind the development of the model comes from the fact that the complexity of topographically-driven runoff generation can be reduced through the use of geomorphological scaling relations. The scaling formulation allows the prediction of the dynamics of saturated source areas as a function of basin-wide soil moisture state. This model offers a number of potential advantages. Firstly, the model parameter is independent of topographic index distribution and its associated scale effects. Secondly, it may be possible to measure this single parameter using field measurements or perhaps remote sensing, which gives the model significant potential for application in ungauged basins. Finally, the fact that this parameter is a physical characteristic of the basin, estimation of this parameter avoids regionalization and parameter transferability problems. The model is tested using rainfall–runoff data from the 10.4 ha experimental catchment known as Tarrawara in Australia, the 37 km² Town Creek catchment in U.S.A., and the 620 km² Balaphi and the 850 km² Likhu sub-catchments of the Koshi river in Nepal. In sub-catchments of Koshi river, the simulation results compare favorably against the calibrated TOPMODEL both in terms of direct runoff and the spatial distribution of soil moisture state. In the Tarrawara and Town Brook catchments, simulation results compare favorably against observed storm runoff using all observed data, without calibration.     

How does landscape structure influence catchment transit time across different geomorphic provinces?

Despite an increasing number of empirical investigations of catchment transit times (TTs), virtually all are based on individual catchments and there are few attempts to synthesize understanding across different geographical regions. Uniquely, this paper examines data from 55 catchments in five geomorphic provinces in northern temperate regions (Scotland, United States of America and Sweden). The objective is to understand how the role of catchment topography as a control on the TTs differs in contrasting geographical settings. Catchment inverse transit time proxies (ITTPs) were inferred by a simple metric of isotopic tracer damping, using the ratio of standard deviation of δ¹⁸O in streamwater to the standard deviation of δ¹⁸O in precipitation. Quantitative landscape analysis was undertaken to characterize the catchments according to hydrologically relevant topographic indices that could be readily determined from a digital terrain model (DTM). The nature of topographic controls on transit times varied markedly in different geomorphic regions. In steeper montane regions, there are stronger gravitational influences on hydraulic gradients and TTs tend to be lower in the steepest catchments. In provinces where terrain is more subdued, direct topographic control weakened; in particular, where flatter areas with less permeable soils give rise to overland flow and lower TTs. The steeper slopes within this flatter terrain appear to have a greater coverage of freely draining soils, which increase sub‐surface flow, therefore increasing TTs. Quantitative landscape analysis proved a useful tool for inter‐catchment comparison. However, the critical influence of sub‐surface permeability and connectivity may limit the transferability of predictive tools of hydrological function based on topographic parameters alone. Copyright © 2009 John Wiley & Sons, Ltd.     

A physically based distributed subsurface–surface flow dynamics model for forested mountainous catchments

This study was designed to develop a physically based hydrological model to describe the hydrological processes within forested mountainous river basins. The model describes the relationships between hydrological fluxes and catchment characteristics that are influenced by topography and land cover. Hydrological processes representative of temperate basins in steep terrain that are incorporated in the model include intercepted rainfall, evaporation, transpiration, infiltration into macropores, partitioning between preferential flow and soil matrix flow, percolation, capillary rise, surface flow (saturation‐excess and return flow), subsurface flow (preferential subsurface flow and baseflow) and spatial water‐table dynamics. The soil–vegetation–atmosphere transfer scheme used was the single‐layer Penman–Monteith model, although a two‐layer model was also provided. The catchment characteristics include topography (elevation, topographic indices), slope and contributing area, where a digital elevation model provided flow direction on the steepest gradient flow path. The hydrological fluxes and catchment characteristics are modelled based on the variable source‐area concept, which defines the dynamics of the watershed response. Flow generated on land for each sub‐basin is routed to the river channel by a kinematic wave model. In the river channel, the combined flows from sub‐basins are routed by the Muskingum–Cunge model to the river outlet; these comprise inputs to the river downstream. The model was applied to the Hikimi river basin in Japan. Spatial decadal values of the normalized difference vegetation index and leaf area index were used for the yearly simulations. Results were satisfactory, as indicated by model efficiency criteria, and analysis showed that the rainfall input is not representative of the orographic lifting induced rainfall in the mountainous Hikimi river basin. Also, a simple representation of the effects of preferential flow within the soil matrix flow has a slight significance for soil moisture status, but is insignificant for river flow estimations. Copyright © 2005 John Wiley & Sons, Ltd.     

Grid parameterization of a conceptual distributed hydrological model through integration of a sub-grid topographic index: necessity and practicability

Abstract

Grid-based distributed models have become popular for describing spatial hydrological processes. However, the influence of non-homogeneity within a grid on streamflow simulation was not adequately addressed in the literature. In this study, we investigated how the statistical characteristics of soil moisture storage within a grid impacts on streamflow simulations. The spatial variation of the topographic index, TI, within a grid was used to determine parameter B of the statistical curve of soil moisture storage in the Xinanjiang model. For comparison of influences of the non-homogeneity within a grid on streamflow simulation, two parameterization schemes of soil moisture storage capacity were developed: a grid-parameterization scheme for a distributed model and a catchment-averaged scheme for a semi-distributed model. The practicability and usefulness of the grid-parameterization method were evaluated through model comparisons. The two models were applied in Jiangwan experimental catchment Zhejiang Province, China. Streamflow discharge data at the catchment outlet from 1971 to 1986 at different temporal resolutions, e.g. 15 min and daily time step, were used for model calibration and validation. Statistical results for different grid scales demonstrated that the mean and variation of TI and B decline significantly as the grid scale increases. The simulated streamflow discharges of the two models were similar and the semi-distributed model outperformed the distributed model slightly when the streamflow at the outlet of the catchment was used as the only basis for comparison. In addition, a relatively larger bias in the predicted discharges between these two models was observed along with an abrupt increase of soil moisture saturation ratio. A further analysis of the simulated soil moisture content distribution revealed that the distributed model can provide a reasonable representation of the variable source area concept, which was justified to some extent by the field experiment data.

Editor D. Koutsoyiannis

Citation Liu, J.T., Chen, X., Wu, J.C., Zhang, X.N., Feng, D.Z. and Xu, C.-Y., 2012. Grid parameterization of a conceptual, distributed hydrological model through integration of a sub-grid topographic index: necessity and practicability. Hydrological Sciences Journal, 57 (2), 282–297.     

Testing the influence of topography and material properties on catchment‐scale soil moisture patterns using remotely sensed vegetation patterns in a humid temperate catchment,northern Britain

In order to evaluate the relationship between the apparent complexity of hillslope soil moisture and the emergent patterns of catchment hydrological behaviour and water quality, we need fine‐resolution catchment‐wide data on soil moisture characteristics. This study proposes a methodology whereby vegetation patterns obtained from high‐resolution orthorectified aerial photographs are used as an indicator of soil moisture characteristics. This enables us to examine a set of hypotheses regarding what drives the spatial patterns of soil moisture at the catchment scale (material properties or topography). We find that the pattern of Juncus effusus vegetation is controlled largely by topography and mediated by the catchment's material properties. Characterizing topography using the topographic index adds value to the soil moisture predictions relative to slope or upslope contributing area (UCA). However, these predictions depart from the observed soil moisture patterns at very steep slopes or low UCAs. Copyright © 2012 John Wiley & Sons, Ltd.     

A contour-based topographic model for hydrological and ecological applications

A digital model for discretizing three-dimensional terrain into small irregularly shaped polygons or elements based on contour lines and their orthogonals is described. From this subdivision the model estimates a number of topographic attributes for each element including the total upslope contributing area, element area, slope, and aspect. This form of discretization of a catchment produces natural units for problems involving water flow as either a surface or subsurface flow phenomenon. The model therefore has wide potential application for representing the three-dimensionality of natural terrain and water flow processes in the fields of hydrology, sedimentology, and geomorphology. Three example applications are presented and discussed. They are the prediction of zones of surface saturation, the prediction of the distribution of potential daily solar radiation, and the prediction of zones of erosion and deposition in a catchment.     

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.     

Paired‐basin comparison of hydrological response in harvested and undisturbed hardwood forests during snowmelt in central Ontario: I. Streamflow,groundwater and flowpath behaviour

Impacts of forest harvesting on groundwater properties, water flowpaths and streamflow response were examined 4 years after the harvest using a paired‐basin approach during the 2001 snowmelt in a northern hardwood landscape in central Ontario. The ability of two metrics of basin topography (Beven and Kirkby's ln(a/tan β) topographic index (TI) and distance to stream channel) to explain intra‐basin variations in groundwater dynamics was also evaluated. Significant relationships between TI and depth to potentiometric surface for shallow groundwater emerged, although the occurrence of these relationships during the melt differed between harvested and control basins, possibly as a result of interbasin differences in upslope area contributing to piezometers used to monitor groundwater behaviour. Transmissivity feedback (rapid streamflow increases as the water table approaches the soil surface) governed streamflow generation in both basins, and the mean threshold depths at which rapid streamflow increases corresponded to small rises in water level were similar for harvested (0·41 ± 0·05 m) and forested (0·38 ± 0·04 m) basins. However, topographic properties provided inconsistent explanations of spatial variations in the relationship between streamflow and depth to water at a given piezometer for both basins. Streamflow from the harvested basin exceeded that from the forested basin during the 2001 melt, and hydrometric and geochemical tracer results indicated greater runoff from the harvested basin via surface and near‐surface pathways. These differences are not solely attributable to harvesting, since the difference in spring runoff from the harvested basin relative to the forested control was not consistently larger than under pre‐harvest conditions. Nevertheless, greater melt rates following harvesting appear to have increased the proportion of water delivery to the stream channel via surface and near‐surface pathways. Copyright © 2005 John Wiley & Sons, Ltd.