A test of TOPMODEL'a ability to predict spatially distributed groundwater levels

TOPMODEL was calibrated to a small catchment using precipitation and runoff data. Acceptable fits of simulated and observed runoff were obtained during both the calibration and validation periods. Predictions of groundwater levels using this calibration did not agree well with observations at the 37 points within the catchment where groundwater levels were measured, including three locations with continuous recordings. Groundwater level observations at one single point in time, however, sufficed to calibrate new topographic–soil indices that improved the prediction of the local groundwater levels at the observed tubes. This suggests that spatially distributed calibration data are necessary to exploit reliably TOPMODEL's ability to predict spatially distributed hydrology. The mean or recalibrated transmissivity values at these 37 points differed from the catchment mean as determined by the precipitation–runoff calibration. Thus, while groundwater information can help in predicting groundwater levels at specific locations, increasing the number of local groundwater level measurements is not sufficient to improve the spatially distributed representation of subsurface flow by TOPMODEL for the catchment as a whole, as long as the groundwater information is not integrated in the precipitation–runoff calibration. © 1997 John Wiley & Sons, Ltd.     

A model for distributed GIUH‐based flow routing on natural and anthropogenic hillslopes

Attempts to reduce the number of parameters in distributed rainfall–runoff models have not yet resulted in a model that is accurate for both natural and anthropogenic hillslopes. We take on the challenge by proposing a distributed model for overland flow and channel flow based on a combination of a linear response time distribution and the hillslope geomorphologic instantaneous unit hydrograph (GIUH), which can be calculated with only a digital elevation model and a map with field boundaries and channel network as input. The spatial domain is subdivided into representative elementary hillslopes (REHs) for each of which we define geometric and flow velocity parameters and compute the GIUH. The catchment GIUH is given by the sum of all REH responses. While most distributed models only perform well on natural hillslopes, the advantage of our approach is that it can also be applied to modified hillslopes with for example a rectangular drainage network and terrace cultivation. Tests show that the REH‐GIUH approach performs better than classical routing functions (exponential and gamma). Simulations of four virtual hillslopes suggest that peak flow at the catchment outlet is directly related to drainage density. By combining the distributed flow routing model with a lumped‐parameter infiltration model, we were also able to demonstrate that terrace cultivation delays the response time and reduces peak flow in comparison to the same hillslope, but with a natural stream network. The REH‐GIUH approach is a first step in the process of coupling distributed hydrological models to erosion and water quality models at the REH (associated with agricultural management) and at the catchment scale (associated with the evaluation of the environmental impact of human activities). It furthermore provides a basis for the development of models for large catchments and urban or peri‐urban catchments. Copyright © 2013 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.     

An improved method for single flow direction calculation in grid digital elevation models

This paper presents improvements to the global D8 (GD8) method for calculating single flow directions in a grid digital elevation model. Flow directions computed from grid digital elevation models serve as the foundation for much of the analysis and modeling of hydrological processes that are driven by topographic gradients. The literature includes both single flow direction methods, where flow goes to only one downslope cell, and multiple flow direction methods that apportion flow among multiple downslope cells. Among single flow direction methods, the standard D8 method, in which the flow direction is set based on the steepest local slope, results in bias on surfaces that do not align with the grid directions. Efforts to address this problem have led to the development of extended methods that account for elevation values further upslope in determining flow directions. We have identified discrepancies in one such method, GD8, and have examined ways to resolve these discrepancies. An improvement to GD8, named iGD8, is presented that allows replacing a reference cell from which path deviations are accumulated and that considers horizontal path deviation rather than global slope as a flow direction criterion. The improved method is found to be effective in resolving the problems encountered with GD8 and to be more efficient than a previously proposed alternative method (least transversal deviation (LTD) based D8, namely D8‐LTD) that uses recursive searching for the largest upstream area when multiple flow paths converge. The proposed improved GD8 method offers the opportunity for improved analysis and modeling of topographically driven hydrological processes by providing better foundational flow directions for these analyses.     

A rational runoff coefficient for a revisited rational formula

ABSTRACT

The Rational Formula (RF) is probably the most frequently applied equation in practical hydrology to compute the peak discharge, due to its simplicity and effective compromise between theory and data availability. Thus, after more than a century, the estimation of peak discharge through the RF is still an important and challenging issue in hydrology. The RF assumes response linearity and sometimes assumes that the return period does not depend on the runoff coefficient and neglects the time to ponding and the antecedent moisture condition. Moreover, the RF requires the critical duration of rainfall and the runoff coefficient to be estimated, both of which are highly controversial. This paper proposes an advanced RF that makes it possible to derive the peak discharge at the hillslope scale, where the above RF assumptions are mostly relaxed. Physically based runoff coefficient tables, which are not affected by subjectivity, are presented and application of the derived procedure is performed.     

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.     

Flood hazard mapping in Southern Brazil: a combination of flow frequency analysis and the HAND model

The Itajaí River basin is one of the areas most affected by flood-related disasters in Brazil. Flood hazard maps based on digital elevation models (DEM) are an important alternative in the absence of detailed hydrological data and for application in large areas. We developed a flood hazard mapping methodology by combining flow frequency analysis with the Height Above the Nearest Drainage (HAND) model – f2HAND – and applied it in three municipalities in the Itajaí River basin. The f2HAND performance was evaluated through comparison with observed 2011 flood extent maps. Model performance and sensitivity were tested for different DEM resolutions, return periods and streamflow data from stations located upstream and downstream on the main river. The flood hazard mapping with our combined approach matched 92% of the 2011 flood event. We found that the f2HAND model has low sensitivity to DEM resolution and high sensitivity to area threshold of channel initiation.     

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.     

A new tool for hillslope hydrologists: spatially distributed groundwater level and soilwater content measured using electromagnetic induction

New methods for obtaining and quantifying spatially distributed subsurface moisture are a high research priority in process hydrology. We use simple linear regression analyses to compare terrain electrical conductivity measurements (EC) derived from multiple electromagnetic induction (EMI) frequencies to a distributed grid of water‐table depth and soil‐moisture measurements in a highly instrumented 50 by 50 m hillslope in Putnam County, New York. Two null hypotheses were tested: H0₍₁₎, there is no relationship between water table depth and EC; H0₍₂₎, there is no relationship between soil moisture levels and EC. We reject both these hypotheses. Regression analysis indicates that EC measurements from the low frequency EM31 meter with a vertical dipole orientation could explain over 80% of the variation in water‐table depth across the test hillslope. Despite zeroing and sensitivity problems encountered with the high frequency EM38, EC measurements could explain over 70% of the gravimetrically determined soil‐moisture variance. The use of simple moisture retrieval algorithms, which combined EC measurements from the EM31 and EM38 meters in both their vertical and horizontal orientations, helped increase the r² coefficients slightly. This first hillslope hydrological analysis of EMI technology in this way suggests that it may be a promising method for the collection of a large number of distributed soilwater and groundwater depth measurements with a reasonable degree of accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

A combined algorithm for automated drainage network extraction from digital elevation models

Drainage networks are the basis for segmentation of watersheds, an essential component in hydrological modelling, biogeochemical applications, and resource management plans. With the rapidly increasing availability of topographic information as digital elevation models (DEMs), there have been many studies on DEM‐based drainage network extraction algorithms. Most of traditional drainage network extraction methods require preprocessing of the DEM in order to remove “spurious” sink, which can cause unrealistic results due to removal of real sinks as well. The least cost path (LCP) algorithm can deal with flow routing over sinks without altering data. However, the existing LCP implementations can only simulate either single flow direction or multiple flow direction over terrain surfaces. Nevertheless, terrain surfaces in the real world are usually very complicated including both convergent and divergent flow patterns. The triangular form‐based multiple flow (TFM) algorithm, one of the traditional drainage network extraction methods, can estimate both single flow and multiple flow patterns. Thus, in this paper, it is proposed to combine the advantages of the LCP algorithm and the TFM algorithm in order to improve the accuracy of drainage network extraction from the DEM. The proposed algorithm is evaluated by implementing a data‐independent assessment method based on four mathematical surfaces and validated against “true” stream networks from aerial photograph, respectively. The results show that when compared with other commonly used algorithms, the new algorithm provides better flow estimation and is able to estimate both convergent and divergent flow patterns well regarding the mathematical surfaces and the real‐world DEM.     

Lumped parameter sensitivity analysis of a distributed hydrological model within tropical and temperate catchments

Parameter sensitivity of the Distributed Hydrology‐Soil‐Vegetation Model (DHSVM) was studied in two contrasting environments: (1) Pang Khum Experimental Watershed (PKEW) in tropical northern Thailand; and (2) Cedar River basin (CRB) in Washington State of the temperate US Pacific Northwest. The analysis shows that for both basins, the most sensitive soil parameters were porosity, lateral saturated hydraulic conductivity, and the exponential decrease rate of lateral saturated hydraulic conductivity with soil depth. The most sensitive vegetation parameters were leaf area index, vegetation height, vapour pressure deficit, minimum stomatal resistance (for both grassland and forest scenarios), hemisphere fractional coverage, overstory fractional coverage, and trunk space (for the forest scenario only). Parameter sensitivity was basin‐specific, with the humid, temperate CRB being more influenced by vegetation parameters, while tropical PKEW was more influenced by soil properties. Increases and decreases in parameter values resulted in opposite and unequal changes in bias and root mean square error (RMSE), indicating the non‐linearity of physical process represented in the hydrological model. Copyright © 2011 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.     

Observational and predictive uncertainties for multiple variables in a spatially distributed hydrological model

In this study, uncertainty in model input data (precipitation) and parameters is propagated through a physically based, spatially distributed hydrological model based on the MIKE SHE code. Precipitation uncertainty is accounted for using an ensemble of daily rainfall fields that incorporate four different sources of uncertainty, whereas parameter uncertainty is considered using Latin hypercube sampling. Model predictive uncertainty is assessed for multiple simulated hydrological variables (discharge, groundwater head, evapotranspiration, and soil moisture). Utilizing an extensive set of observational data, effective observational uncertainties for each hydrological variable are assessed. Considering not only model predictive uncertainty but also effective observational uncertainty leads to a notable increase in the number of instances, for which model simulation and observations are in good agreement (e.g., 47% vs. 91% for discharge and 0% vs. 98% for soil moisture). Effective observational uncertainty is in several cases larger than model predictive uncertainty. We conclude that the use of precipitation uncertainty with a realistic spatio‐temporal correlation structure, analyses of multiple variables with different spatial support, and the consideration of observational uncertainty are crucial for adequately evaluating the performance of physically based, spatially distributed hydrological models.     

Multiple flow direction algorithms for runoff modelling in grid based elevation models: An empirical evaluation

When pathways for groundwater flow are defined in grid based elevation models, the grid structure creates some obstacles as it only allows for eight flow directions. Earlier algorithms have used arbitrarily designed flow distributions, which have resulted in either too diverging or too converging flow patterns. This study defines a computationally simple distribution function, where the converging nature (x) can be altered. A material of reference flow distributions was produced through simulation in four elevation models. The distribution function was tested for different values on x, against the reference. The results show a stable correlation pattern between the tested function and the reference. Optimum values on x were found, which suggest that the flow distribution from a grid cell should be weighted with the slope gradient raised to the power of 4–6.     

Computing spatially distributed sediment delivery ratios: inferring functional sediment connectivity from repeat high‐resolution digital elevation models

High‐resolution digital elevation models (DEMs) from repeat LiDAR (light detection and ranging) or SfM (structure from motion) surveys have become an important tool in process geomorphology. The spatial pattern of negative and positive changes of surface elevation on raster DEMs of difference (DoD) can be interpreted in terms of geomorphic processes, and has been used for morphological budgeting. We show how the application of flow routing algorithms and flow accumulation opens new opportunities for the analysis of DoD. By accumulating the values of the DoD along downslope flowpaths delineated on a DEM, these algorithms lend themselves to computing the net balance, i.e. sediment yield (SY), for the contributing area of each cell. Doing the same for the negative subset of the DoD yields a minimum estimate of erosion (E) within the contributing area. The division of SY by E yields (a maximum estimate of) the sediment delivery ratio (SDR), that is the proportion of material eroded within the contributing area of each cell that has been exported from that area. The resulting SDR is a spatially distributed measure of functional sediment connectivity. In this letter, we develop the computationally simple approach by means of an example DoD from a lateral moraine section in the Upper Kaunertal Valley, Austrian Central Alps. We also discuss advantages, assumptions and limitations, and outline potential applications to connectivity research using field‐, laboratory‐, and model‐based DoD. Copyright © 2018 John Wiley & Sons, Ltd.     

Efficient hybrid breaching‐filling sink removal methods for flow path enforcement in digital elevation models

Digital elevation models (DEMs) that are used in hydrological applications must be processed to remove sinks, mainly topographic depressions. Flow enforcement techniques include filling methods, which raise elevations within depressions, breaching, which carves channels through blockages, and hybrid methods. Despite previous research demonstrating the large impact to DEMs and subsequent analyses of depression filling, it is common practice apply this technique to flow enforcement. This is partly because of the greater efficiency of depression filling tools compared to breaching counterparts, which often limits breaching to applications of small‐ to moderate‐sized DEMs. A new hybrid flow enforcement algorithm is presented in this study. The method can be run in complete breaching, selective breaching (either breached or filled), or constrained breaching (partial breaching) modes, allowing for greater flexibility in how practitioners enforce continuous flow paths. Algorithm performance was tested with DEMs of varying topography, spatial extents, and resolution. The sites included three moderate sized DEMs (52 000 000 to 190 000 000 cells) and three massive DEMs of the Iberian Peninsula, and the Amazon and Nile River basins, the largest containing nearly one billion cells. In complete breaching mode, the new algorithm required 87% of the time needed by a filling method to process the test DEMs, while the selective breaching and constrained breaching modes, operating with maximum breach depth constraints, increased run times by 8% and 27% respectively. Therefore, the new algorithm offers comparable performance to filling and the ability to process massive topographic data sets, while giving practitioners greater flexibility and lowering DEM impact. Copyright © 2015 John Wiley & Sons, Ltd.