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.     

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.     

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.     

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.     

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.     

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.     

Using targeted short‐term field investigations to calibrate and evaluate the structure of a hydrological model

This study combines the application of a hydrological model with the use of field data derived from short period measurement campaigns at two sites, one a low topography forested area and the other a steep grassland catchment. The main objective was to determine if the structure of the widely used Pitman model could be considered appropriate for simulating the field data. The model is typically applied at coarse spatial and temporal (1 month) scales, while the tests reported here use data from small catchments and are applied in a daily version of the model. The results demonstrate the importance of ensuring that field observations are measuring the same hydrological variables as the model simulations. At one study site, there was a mismatch in the soil moisture data that was corrected by incorporating a two‐layer soil algorithm into the model. The model results from both field sites identified the sensitivity of the model to assumptions about evaporative demands and indicate that the model structure is very sensitive to the potential evaporation inputs. The overall conclusion is that the model structure is generally appropriate for simulating the hydrological responses at the two sites, but that there remain some unresolved uncertainties about specific model components and the use of certain types of input data. The study lends support for the future development of a more complete daily version of this widely used model. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatial and temporal predictions of soil moisture dynamics,runoff, variable source areas and evapotranspiration for plynlimon,mid-wales

For many years hydrologists have tried to build physically realistic models which are still simple enough to be fitted to a range of observations made in the field. This is an ongoing process which will become even more difficult as the quality and variety of field and remotely sensed data improves. Hence models must be able to predict soil moisture patterns in time and in space as well as the outflow hydrograph. The model presented here (TOPMODEL) aims to predict the nature of variable source areas in a way that reflects their dynamics over space and time. All component processes are described and shown in operation. As TOPMODEL and similar models have a growing popularity, this paper can be seen as a demonstration of the model's predictive capabilities. The model is applied to the catchments of Plynlimon, mid-Wales for 1984, 1985 and 1986 data sets. The model has been thoroughly tested and cross-validated against independent data sets for different time periods, for a separate catchment, for internal gauges and for wet and dry periods. The resulting predicted soil moisture patterns show a small, semi-permanent variable source area that has the ability during large storms to expand dynamically over short time periods. Spatial predictions of evapotranspiration are also shown which reflect the influence of soil moisture patterns on this process. The weakest component of the model is the representation of root zone evaporation and how this pre-sets the antecedent condition of the catchment during long dry periods.     

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.     

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.     

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.     

Wavelet‐based regularization of the extracted topographic index from high‐resolution topography for hydro‐geomorphic applications

High‐resolution topography, e.g. 1‐m digital elevation model (DEM) from light detection and ranging (LiDAR), offers opportunity for accurate identification of topographic features of relevance for hydrologic and geomorphologic modelling. Yet, the computation of some derived topographic properties, such as the topographic index (TI), is characterized by daunting challenges that hamper the full exploration of topography‐based models. Particular problems, for example, arise when a distributed (or semi‐distributed) rainfall–runoff model is applied to high‐resolution DEMs. Indeed, the characteristic dependency between landscape resolution and the computed TI distribution results in the formation of un‐physical, unconnected saturated zones, which in turn cause unrealistic representations of rainfall–runoff dynamics. In this study, we present a methodology based on a multi‐resolution wavelet transformation that, by means of a soft‐thresholding scheme on the wavelet coefficients, filters the noise of high‐resolution topography to construct regularized sets of locally smoother topography on which the TI is computed. While the methodology needs a somewhat arbitrary definition of the wavelet coefficients threshold, our study shows that when the information content (entropy) of the TI distribution is used as a filtering efficiency metric, a critical threshold automatically emerges in the landscape reconstruction. The methodology is demonstrated using 1‐m LiDAR data for the Elder Creek River basin in California. While the proposed case study uses a TOPMODEL approach, the methodology can be extended to different topography‐based models and is not limited to hydrological applications. Copyright © 2012 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.     

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.     

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.     

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.     

Multisource hydrologic modeling uncertainty analysis using the IBUNE framework in a humid catchment

Hydrologic cycle is a complex system associated with both certain and uncertain constituents. The propagation of confidence bounds from different uncertainty sources to model output is of great significance for hydrologic modeling. In this paper, we applied the integrated bayesian uncertainty estimator to quantify the effects of parameter, input and model structure uncertainty on hydrologic modeling progressively. Two hydrologic models (Xinanjiang model and TOPMODEL) were applied to a humid catchment under three scenarios. Case I: the shuffled complex evolution metropolis (SCEM-UA) algorithm was conducted to determine the posterior parameter distribution of hydrologic models and analyze the corresponding forecast uncertainty. Case II: input uncertainty was also considered by assuming rain depth bias follows a normal distribution, and integrated with SCEM-UA. Case III: Simulations from two models were combined by the Bayesian model averaging to fully quantify multisource uncertainty effects. Results suggested that, from Case I to II, the containing ratio (percentage of observed streamflow enveloped by 95% confidence interval) obviously increased by an average magnitude of 10% for the study period 2000–2006. Besides, it also found that the width of 95% confidence interval became wider and narrower for Xinanjiang model and TOPMODEL, respectively, from Case I to II. This may indicate that the uncertainty of TOPMODEL results was more remarkable than Xinanjiang model in Case I. By combining results from two models, model structure uncertainty was also considered in Case III. The accuracy of uncertainty bounds further improved with the containing ratio of 95% confidence interval >95%. In addition, the optimized deterministic results from the uncertainty analysis showed that the average Nash–Sutcliffe coefficient increased continually from Case I to II and III (0.82, 0.84 and 0.90, respectively) for the study period. The analysis demonstrated the improvement of modeling accuracy when extra uncertainty sources were also quantified, and this finding also proved the applicability of IBUNE framework in hydrologic modeling.     

Use of a watershed hydrologic model to estimate interbasin groundwater flow in a Costa Rican rainforest

The watershed hydrologic model TOPMODEL was used to estimate interbasin groundwater flow (IGF) into a small lowland rainforest watershed in Costa Rica. IGF is a common hydrological process but often difficult to quantify. Four‐year simulations (2006–2009) using three different model approaches gave estimates of IGF that were very similar to each other (10.1, 10.2, and 9.8 m/year) and to an earlier estimate (10.0 m/year) based on 1998–2002 data from a budget study that did not use a hydrologic simulation model, providing confidence in the new estimates and suggesting each of the three model approaches is viable. Results show no significant temporal variation in IGF during 2006–2009 (or between this period and the earlier study from 1998–2002). Simulations of the 16 consecutive 3‐month periods in 2006–2009 gave 16 values of IGF rate with a mean (10.1 m/year, standard deviation = 0.6 m/year) very similar to the estimates above from the 4‐year simulations. This suggests the modified version of TOPMODEL can be used to model stream discharge and estimate IGF for sub‐annual time periods during which change in water storage is not necessarily equal to zero. Thus, simple watershed models may be used to estimate IGF based on even relatively short calibration periods, making such models useful tools in the study of this widespread hydrological process that affects water and chemical fluxes and budgets but is often difficult and costly to quantify. Copyright © 2013 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.