Application of distributed hydrological models for predictions in ungauged basins: a method to quantify predictive uncertainty

Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd.     

Calibration of rainfall-runoff models in ungauged basins: A regional maximum likelihood approach

Parameter estimation for rainfall-runoff models in ungauged basins is a challenging task that is receiving significant attention by the scientific community. In fact, many practical applications suffer from problems induced by data scarcity, given that hydrological observations are often sparse or unavailable. This study focuses on regional calibration for a generic rainfall-runoff model. The maximum likelihood function in the spectral domain proposed by Whittle [40] is approximated in the time domain by maximising the fit of selected statistics of the river flow process, with the aim to propose a calibration procedure that can be applied at regional scale. Accordingly, the statistics above are related to the dominant climate and catchment characteristics, through regional regression relationships. The proposed technique is applied to the case study of 4 catchments located in central Italy, which are treated as ungauged and are located in a region where detailed hydrological, as well as geomorphologic and climatic information, is available. The results obtained with the regional calibration are compared with those provided by a classical least squares calibration in the time domain. The outcomes of the analysis confirm the potential of the proposed methodology and show that regional information can be very effective for setting up hydrological models.     

Effect of spatial resolution on regionalization of hydrological model parameters

Lack of availability of historical data series is one of the major hindrances in hydrological modelling. Regionalization of hydrological model parameters is one of the solutions to obtain the parameters for ungauged basins. Recently, lots of methodologies have been developed. They can be categorized as model calibration then fitting regression between model parameters and catchments characteristics, using some kind of transfer function. The aim of this study was to compare different regionalization methods as well as to look how the spatial resolution affects regionalization. In this study, a modified Lipschitz and monotony condition was used for regionalization. To identify the effect of the model resolution, the parameters of a distributed and semi‐distributed version of the Hydrologiska Byråns Vattenbalansavdelning (HBV) model were regionalized. The study was conducted at the upper Neckar catchment of southwest Germany. It has been found that the combination of Lipschitz and monotony condition has performed reasonably. It has been seen that the distributed model structure has outperformed the semi‐distributed model structure. It shows under present data conditions that higher model resolution can describe processes of ungauged basins reasonably. Copyright © 2011 John Wiley & Sons, Ltd.     

Calibration of hydrological models in ungauged basins based on satellite radar altimetry observations of river water level

This paper proposes a new orientation to address the problem of hydrological model calibration in ungauged basin. Satellite radar altimetric observations of river water level at basin outlet are used to calibrate the model, as a surrogate of streamflow data. To shift the calibration objective, the hydrological model is coupled with a hydraulic model describing the relation between streamflow and water stage. The methodology is illustrated by a case study in the Upper Mississippi Basin using TOPEX/Poseidon (T/P) satellite data. The generalized likelihood uncertainty estimation (GLUE) is employed for model calibration and uncertainty analysis. We found that even without any streamflow information for regulating model behavior, the calibrated hydrological model can make fairly reasonable streamflow estimation. In order to illustrate the degree of additional uncertainty associated with shifting calibration objective and identifying its sources, the posterior distributions of hydrological parameters derived from calibration based on T/P data, streamflow data and T/P data with fixed hydraulic parameters are compared. The results show that the main source is the model parameter uncertainty. And the contribution of remote sensing data uncertainty is minor. Furthermore, the influence of removing high error satellite observations on streamflow estimation is also examined. Under the precondition of sufficient temporal coverage of calibration data, such data screening can eliminate some unrealistic parameter sets from the behavioral group. The study contributes to improve streamflow estimation in ungauged basin and evaluate the value of remote sensing in hydrological modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa

Abstract

The increasing demand for water in southern Africa necessitates adequate quantification of current freshwater resources. Watershed models are the standard tool used to generate continuous estimates of streamflow and other hydrological variables. However, the accuracy of the results is often not quantified, and model assessment is hindered by a scarcity of historical observations. Quantifying the uncertainty in hydrological estimates would increase the value and credibility of predictions. A model-independent framework aimed at achieving consistency in incorporating and analysing uncertainty within water resources estimation tools in gauged and ungauged basins is presented. Uncertainty estimation in ungauged basins is achieved via two strategies: a local approach for a priori model parameter estimation from physical catchment characteristics, and a regional approach to regionalize signatures of catchment behaviour that can be used to constrain model outputs. We compare these two sources of information in the data-scarce region of South Africa. The results show that both approaches are capable of uncertainty reduction, but that their relative values vary.

Editor D. Koutsoyiannis

Citation Kapangaziwiri, E., Hughes, D.A., and Wagener, T., 2012. Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa. Hydrological Sciences Journal, 57 (5), 1000–1019.     

Parameter regionalization of the FLEX-Global hydrological model

Global hydrological models(GHMs) are important tools for addressing worldwide change-related water resource problems from a global perspective. However, the development of these models has long been hindered by their low accuracy. In order to improve the streamflow simulation accuracy of GHMs, we developed a GHM—the FLEX-Global—based on the regionalization of hydrological model parameters. The FLEX-Global model is primarily based on the framework of the FLEX hydrological model coupled with the HAND-based Storage Capacity curve(HSC) runoff generation module to calculate net rainfall, and uses the global river-routing Ca Ma-Flood model to calculate river network routing. This new model allows for streamflow simulation at a spatial resolution of 0.5°×0.5° and a temporal resolution of 1 day in global catchments. To validate FLEX-Global accuracy, the FLEX-Global-simulated streamflow of 26 major rivers distributed in five different climate zones was compared with the observed data from the Global Runoff Data Center(GRDC). Next, the model performance of FLEXGlobal was further verified by comparing it with that of seven existing GHMs with varying accuracy in the five climate zones.Multi-metric evaluation indicated that the streamflow simulation accuracy was improved by the FLEX-Global model with regionalized parameters, especially in the tropical and dry climate zones. This newly-developed GHM with regionalized parameters can provide scientific support for the assessment of climate change impact, optimization of global water resource mangement, simulation of Earth's multi-sphere coupling, and implementation of the Inter-Sectoral Impact Model Intercomparison Project(ISIMIP).     

Use of a parsimonious rainfall–run‐off model for predicting hydrological response in ungauged basins

A new parameter parsimonious rainfall–run‐off model, the Distance Distribution Dynamics (DDD) model, is used to simulate hydrological time series at ungauged sites in the Lygne basin in Norway. The model parameters were estimated as functions of catchment characteristics determined by geographical information system. The multiple regression equations relating catchment characteristics and model parameters were trained from 84 calibrated catchments located all over Norway, and all model parameters showed significant correlations with catchment characteristics. The significant correlation coefficients (with p‐value < 0.05) ranged from 0.22 to 0.55. The suitability of DDD for predictions in ungauged basins was tested for 17 catchments not used to estimate the multiple regression equations. For ten of the 17 catchments, deviations in Nash–Sutcliffe efficiency (NSE) criteria between the calibrated and regionalised model were less than 0.1, and for two calibrated catchments within the Lygne basin, the deviations were less than 0.08. The median NSE for the regionalized DDD for the 17 catchments for two time series was 0.66 and 0.72. Deviations in NSE between calibrated and regionalised models are well explained by the deviations between calibrated and regressed parameters describing spatial snow distribution and snowmelt respectively. The quality of the simulated run‐off series for the ungauged sites in the Lygne basin was assessed by comparing flow indices describing high, medium and low flow estimated from observed run‐off at the 17 catchments and for the simulated run‐off series. The indices estimated for the simulated series were generally well within the ranges defined by the 17 observed series. Copyright © 2014 John Wiley & Sons, Ltd.     

Transferability of hydrological model parameters between basins in data-sparse areas, subarctic Canada

Hydrological models used for the simulation of runoff are often calibrated only on the basis of data obtained at the catchment outlet but the parameters thus derived are then applied to the simulations for the subbasins. Such a practice is common for the data-sparse areas such as the subarctic. However, it may yield erroneous results when the calibrated model parameters are applied to basins of various sizes, or with divergent physical characteristics. This study assesses the feasibility of transferring parameter estimates derived for one basin of a particular size to other basins of different dimensions, using the SLURP model for simulation and the Liard and two of its subbasins as an example. Results indicate that other than the snowmelt factor, the parameter values obtained from the subbasins are similar, but values of several parameters (e.g. maximum capacity of the soil water and groundwater storage, and snowmelt factor) are different from those derived for the large basin. Compared with applying the Liard basin parameters, the subbasins parameter sets generate higher evapotranspiration, earlier termination of the snowmelt period, more soil water storage, a shorter period with significant soil water storage and a better overall agreement between the observed and simulated runoff. It is recommended that adequate attention be given to the transferability of the parameter values to improve the simulation of subbasins hydrology.     

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.     

Transferability of hydrological model parameter spaces in the estimation of runoff in ungauged catchments

Abstract

In this study, transferability options of the Hydrologiska Byråns Vattenbalansavdelning (HBV) hydrological model parameter (MP) spaces were investigated to estimate ungauged catchment runoff. Three approaches were applied in the study: MP space transfer from single, neighbouring and all potential donor catchments. The model performance was evaluated by a jackknife procedure, where one catchment at a time was treated as if ungauged, and behavioural MP sets from candidate donor catchments were used to estimate the “ungauged” runoff. The results showed that ungauged catchment runoff estimation could not be guaranteed by transferring MP sets from a single physiographically nearest donor catchment. Integrating MP sets typically from one to six donor catchments supplemented the lack of effective MP sets and improved the model performance at the ungauged catchments. In addition, the analysis results revealed that the model performance converged to an average performance when the MP sets of all potential donor catchments were integrated.     

Synthetic design hydrographs for ungauged catchments: a comparison of regionalization methods

Design flood estimates for a given return period are required in both gauged and ungauged catchments for hydraulic design and risk assessments. Contrary to classical design estimates, synthetic design hydrographs provide not only information on the peak magnitude of events but also on the corresponding hydrograph volumes together with the hydrograph shapes. In this study, we tested different regionalization approaches to transfer parameters of synthetic design hydrographs from gauged to ungauged catchments. These approaches include classical regionalization methods such as linear regression techniques, spatial methods, and methods based on the formation of homogeneous regions. In addition to these classical approaches, we tested nonlinear regression models not commonly used in hydrological regionalization studies, such as random forest, bagging, and boosting. We found that parameters related to the magnitude of the design event can be regionalized well using both linear and nonlinear regression techniques using catchment area, length of the main channel, maximum precipitation intensity, and relief energy as explanatory variables. The hydrograph shape, however, was found to be more difficult to regionalize due to its high variability within a catchment. Such variability might be better represented by looking at flood-type specific synthetic design hydrographs.     

Observed hydrographs: on their ability to infer a time‐invariant hydrological transfer function for flow prediction in ungauged basins

Streamflow measurements provide information about the flow generation characteristics of land surfaces as well as the flow transferring nature of the channel network. In this study, such flow transferring properties of the channel network that were obtained from downstream flow observations were used for predicting flow in ungauged basins. A temporally averaged transfer function (ATF) of the channel segments of Kentucky River Basin (KRB) in Kentucky, USA, was extracted from observed hydrographs in a time‐invariant system as a function of drainage area. The ATF was regionalized through multiple regression analysis for 194 combinations of drainage areas that differ in topography, terrain, and geology. The application of ATF for flow prediction in ungauged basins was performed for Goose Creek, a subbasin of KRB by integrating ATF with the TOPMODEL. In addition, the ATF was shown to be capable of providing calibration and validation data for ungauged basins in a backward technique from a measured stream gauge downstream, with minimal data requirement of drainage area. The applicability of ATF was illustrated across a range of streamflow conditions from watersheds that varied greatly in their terrain and geology. Nash–Sutcliffe efficiency of the proposed method, as a function of drainage areas of the corresponding basins, to predict daily streamflow from ungauged basins ranged from 0.83 to 0.92. The results of the study concluded that the ATF obtained from measured streamflow thus proved to be a quick and simple tool for assessment of streamflow in both operational and modeling hydrology. Copyright © 2012 John Wiley & Sons, Ltd.     

A canonical correlation approach to the determination of homogeneous regions for regional flood estimation of ungauged basins

Abstract

A canonical correlation method for determining the homogeneous regions used for estimating flood characteristics of ungauged basins is described. The method emphasizes graphical and quantitative analysis of relationships between the basin and flood variables before the data of the gauged basins are used for estimating the flood variables of the ungauged basin. The method can be used for both homogeneous regions, determined a priori by clustering algorithms in the space of the flood-related canonical variables, as well as for “regions of influence” or “neighbourhoods” centred on the point representing the estimated location of the ungauged basin in that space.     

Analyzing uncertainties involved in estimating collapse risk with and without considering uncertainty probability distribution parameters

In the present study,modified Ibarra,Medina and Krawinkler moment-rotation parameters are used for modeling the uncertainties in concrete moment frame structures.Correlations of model parameters in a component and between two structural components were considered to analyze these uncertainties.In the first step,the structural collapse responses were obtained by producing 281 samples for the uncertainties using the Latin hypercube sampling(LHS)method,considering the probability distribution of the uncertainties and performing incremental dynamic analyses.In the second step,281 new samples were produced for the uncertainties by the central composite design(CCD)method without considering the probability distribution of the uncertainties and calculating the structural collapse responses.Then,using the response surface method(RSM)and artificial neural network(ANN)for the two simulation modes,structural collapse responses were predicted.The results indicated that the collapse responses at levels of 0 to 100%obtained from the two simulations have a high correlation coefficient of 98%.This suggests that random variables can be simulated without considering the probability distribution of uncertainties,by performing uncertainty analysis to determine structural collapse responses.     

Lag prediction in ungauged basins: an investigation through actual data of the upper Tiber River valley

A comparative analysis of a variety of relationships for prediction of basin lag is performed by applying them to 23 basins located in the same geographical area and characterized by a rather similar vegetative cover. The results of computations indicate that a lag–area relationship with two constant parameters is the best predictor for most basins; under different vegetative covers in the same basin only one parameter should be variable. For a few other basins characterized by an anomalous drainage channel network of low density, such a relationship can lead to unacceptable errors. Thus, there is a need for an additional relationship to overcome this difficulty, but a larger number of anomalous basins would be required for its determination. An alternative procedure, based on the use of the non‐linear kinematic wave, which at least allows singling out the cases where a specific lag–area relationship is not reliable, is proposed. This procedure, therefore, represents a partial but very useful solution to avoid considerable errors in hydrological practice. Copyright © 2002 John Wiley & Sons, Ltd.     

Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale

Abstract

A dynamic water quality model, HYPE, was applied to a large, data-sparse region to study whether reliable information on water quantity and water quality could be obtained for both gauged and ungauged waterbodies. The model (called S-HYPE) was set up for all of Sweden (～450 000 km²), divided into sub-basins with an average area of 28 km². Readily available national databases were used for physiographic data, emissions and agricultural practices, fixed values for representative years were used. Daily precipitation and temperature were used as the dynamic forcing of the model. Model evaluation was based on data from several hundred monitoring sites, of which approximately 90% had not been used in calibration on a daily scale. Results were evaluated using the Nash-Sutcliffe efficiency (NSE), correlation and relative errors: 92% of the spatial variation was explained for specific water discharge, and 88% and 59% for total nitrogen and total phosphorus concentrations, respectively. Day-to-day variations were modelled with satisfactory results for water discharge and the seasonal variation of nitrogen concentrations was also generally well captured. In 20 large, unregulated rivers the median NSE for water discharge was 0.84, and the corresponding number for 76 partly-regulated river basins was 0.52. In small basins, the NSE was typically above 0.6. These major achievements relative to previous similar experiments were ascribed to the step-wise calibration process using representative gauged basins and the use of a modelling concept, whereby coefficients are linked to physiographic variables rather than to specific sites.

Editor D. Koutsoyiannis

Citation Strömqvist, J., Arheimer, B., Dahné, J., Donnelly, C. and Lindström, G., 2012. Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale. Hydrological Sciences Journal, 57 (2), 229–247.     

Uncertainty quantization of meteorological input and model parameters for hydrological modelling using a Bayesian-based integrated approach

The traditional treatment of uncertainty in hydrological modelling primarily attributes it to model parameters, but rarely systematically considers meteorological input errors, especially in quantifying the impact of meteorological input errors on parameter uncertainty. This study developed a Bayesian-based integrated approach to quantitatively investigate uncertainties in meteorological inputs (precipitation and temperature) and model parameters as well as the variation in parameter uncertainty due to meteorological input errors. Additionally, we analysed the propagation from these uncertainties to runoff response in snowmelt and non-snowmelt periods. The applicability and advantages of this approach were presented by applying of the Soil and Water Assessment Tool to the Shitoukoumen Reservoir Catchment. Differential Evolution Adaptive Metropolis-Markov Chain Monte Carlo was applied for the straightforward Bayesian inference the uncertainties of meteorological inputs and model parameters. On this basis, multilevel factorial analysis technology was used to quantitatively investigate the specific impact of the model parameters' individual and interactive effects due to meteorological input errors. Finally, the impact of meteorological input errors and model parameter uncertainty on the model performance were analysed and quantified systematically. The results showed that the meteorological input errors could affect the random characteristics of multiple model parameters. Moreover, meteorological input errors could further affect the model parameters' effects on annual average runoff. Overall, the above results have significant implications in enhancing hydrological model to simulate/predict runoff and understanding hydrological processes during different periods.