Assessment of rainfall‐runoff models based upon wavelet analysis

A basic hypothesis is proposed: given that wavelet‐based analysis has been used to interpret runoff time‐series, it may be extended to evaluation of rainfall‐runoff model results. Conventional objective functions make certain assumptions about the data series to which they are applied (e.g. uncorrelated error, homoscedasticity). The difficulty that objective functions have in distinguishing between different realizations of the same model, or different models of the same system, is that they may have contributed in part to the occurrence of model equifinality. Of particular concern is the fact that the error present in a rainfall‐runoff model may be time dependent, requiring some form of time localization in both identification of error and derivation of global objective functions. We explore the use of a complex Gaussian (order 2) wavelet to describe: (1) a measured hydrograph; (2) the same hydrograph with different simulated errors introduced; and (3) model predictions of the same hydrograph based upon a modified form of TOPMODEL. The analysis of results was based upon: (a) differences in wavelet power (the wavelet power error) between the measured hydrograph and both the simulated error and modelled hydrographs; and (b) the wavelet phase. Power difference and wavelet phase were used to develop two objective functions, RMSE(power) and RMS(phase), which were shown to distinguish between simulated errors and model predictions with similar values of the commonly adopted Nash‐Sutcliffe efficiency index. These objective functions suffer because they do not retain time, frequency or time‐frequency localization. Consideration of wavelet power spectra and time‐ and frequency‐integrated power spectra shows that the impacts of different types of simulated error can be seen through retention of some localization, especially in relation to when and the scale over which error was manifest. Theoretical objections to the use of wavelet analysis for this type of application are noted, especially in relation to the dependence of findings upon the wavelet chosen. However, it is argued that the benefits of localization and the qualitatively low sensitivity of wavelet power and phase to wavelet choice are sufficient to warrant further exploration of wavelet‐based approaches to rainfall‐runoff model evaluation. Copyright © 2006 John Wiley & Sons, Ltd.     

RELATIONS BETWEEN PARAMETERS IN THE LINEAR RESERVOIR AND KINEMATIC WAVE MODELS

1 INTRODUCTION Since the traditional unit hydrograph method was proposed by Sherman (1932), it has been widely used in many studies, such as the works by Nash (1957), Linsley et al. (1958), Dooge (1959), Chow (1964), Mays and Taur (1982), and Jakeman et a…     

Rainfall–runoff model parameter estimation and uncertainty evaluation on small plots

Four seasonal rainfall simulations in 2009 and 2010 were applied to a field containing 36 plots (0.75 × 2 m each), resulting in 144 runoff events. In all simulations, a constant rate of rainfall was applied then halted 60 min after initiation of runoff, with plot‐scale monitoring of runoff every 5 min during that period. Runoff was simulated with the Kinematic Runoff and Erosion/Simulator of Transport with Infiltration and Runoff (KINEROS2/STWIR) field‐scale model, whose hydrodynamics are based on the kinematic wave equation. Because of the non‐linear nature of the model and a highly parameterized model with respect to the available data, several approaches were investigated to upscale nine runoff‐related parameters from a series of small monitored plots to the field scale. Inverse modeling was performed using the model‐independent Parameter ESTimation (PEST) algorithm to individually calibrate the nine KINEROS2/STWIR parameters on 36 plots. The parameters were averaged, and bootstrapping was used to assess uncertainty of the parameters via estimation of confidence intervals (CI). A Monte Carlo simulation using the bootstrap results showed reasonable field‐scale representation of flow rates. Median values of calibrated parameters were within the 95% CI obtained with bootstrapping. The simulated results for the median values associated with the 90% CI flow rates produced similar trends as those exhibited with the observed data, suggesting that median values of the calibrated parameters from the PEST inverse modeling could be used to represent the field scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling nitrogen dynamics for a mesoscale catchment using a minimum information requirement (MIR) concept / Modélisation des dynamiques de l'azote pour un bassin versant de taille moyenne,utilisant le concept de besoin minimum d'information

Abstract

Based on the water balance model LARSIM (Large Area Simulation Model), a model for the simulation of nitrogen transport was developed in a mesoscale catchment in southwest Germany. To meet the needs and constraints in river basin management, the nitrogen model was developed following the concept of minimum information requirement (MIR). The modelling concept uses only few calibration parameters and only easily accessible input data. Water balance, runoff generation and nitrogen transport were simulated on a 1-km² grid of sub-areas in which different land-use classes and soil characteristics were accounted. Temporal variability of the storage of mobile nitrogen were described using a monthly based mass balance. Nitrogen mobilization and transport was simulated using monthly values of different runoff components and data for soil properties, topography, hydrogeology and river network. The simulation was calibrated and validated using streamflow from two gauging stations and observed nitrogen concentrations at the catchment outlet, showing reasonable results for both streamflow and nitrogen dynamics. The results of the model application are discussed in the context of uncertainty problems and their implications for water management.     

Assessment of runoff and sediment yield in the Miyun Reservoir catchment by using SWAT model

The Soil and Water Assessment Tool (SWAT) was used to simulate the transport of runoff and sediment into the Miyun Reservoir, Beijing in this study. The main objective was to validate the performance of SWAT and the feasibility of using this model as a simulator of runoff and sediment transport processes at a catchment scale in arid and semi‐arid area in North China, and related processes affecting water quantity and soil erosion in the catchment were simulated. The investigation was conducted using a 6‐year historical streamflow and sediment record from 1986 to 1991; the data from 1986 to 1988 was used for calibration and that from 1989 to 1991 for validation. The SWAT generally performs well and could accurately simulate both daily and monthly runoff and sediment yield. The simulated daily and monthly runoff matched the observed values satisfactorily, with a Nash‐Sutcliffe coefficient of greater than 0·6, 0·9 and a coefficient of determination 0·75, 0·9 at two outlet stations (Xiahui and Zhangjiafen stations) during calibration. These values were 0·6, 0·85 and 0·6, 0·9 during validation. For sediment simulation, the efficiency is lower than that for runoff. Even so, the Nash‐Sutcliffe coefficient and coefficient of determination were greater than 0·48 and 0·6 for monthly sediment yield during calibration, and these values were greater than 0·84 and 0·95 during validation. Sensitivity analysis shows that sensitive parameters for the simulation of discharge and sediment yield include curve number, base flow alpha factor, soil evaporation compensation factor, soil available water capacity, soil profile depth, surface flow lag time and channel re‐entrained linear parameter, etc. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison of spectral and time domain calibration methods for precipitation‐discharge processes

Hydrological model parameter estimation is an important aspect in hydrologic modelling. Usually, parameters are estimated through an objective function minimization, quantifying the mismatch between the model results and the observations. The objective function choice has a large impact on the sensitivity analysis and calibration outcomes. In this study, it is assessed whether spectral objective functions can compete with an objective function in the time domain for optimization of the Soil and Water Assessment Tool (SWAT). Three empirical spectral objective functions were applied, based on matching (i) Fourier amplitude spectra, (ii) periodograms and (iii) Fourier series of simulated and observed discharge time series. It is shown that most sensitive parameters and their optimal values are distinct for different objective functions. The best results were found through calibration with an objective function based on the square difference between the simulated and observed discharge Fourier series coefficients. The potential strengths and weaknesses of using a spectral objective function as compared to utilising a time domain objective function are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Process‐based hydrological modelling: The potential of a bottom‐up approach for runoff predictions in ungauged catchments

Conceptual rainfall–runoff models are a valuable tool for predictions in ungauged catchments. However, most of them rely on calibration to determine parameter values. Improving the representation of runoff processes in models is an attractive alternative to calibration. Such an approach requires a straightforward, a priori parameter allocation procedure applicable on a wide range of spatial scales. However, such a procedure has not been developed yet. In this paper, we introduce a process‐based runoff generation module (RGM‐PRO) as a spin‐off of the traditional runoff generation module of the PREVAH hydrological modelling system. RGM‐PRO is able to exploit information from maps of runoff types, which are developed on the basis of field investigations and expert knowledge. It is grid based, and within each grid cell, the process heterogeneity is considered to avoid information loss due to grid resolution. The new module is event based, and initial conditions are assimilated and downscaled from continuous simulations of PREVAH, which are also available for real‐time applications. Four parameter allocation strategies were developed, on the basis of the results of sprinkling experiments on 60‐m² hillslope plots at several grassland locations in Switzerland, and were tested on five catchments on the Swiss Plateau and Prealps. For the same catchments, simulation results obtained with the best parameter allocation strategy were compared with those obtained with different configurations of the traditional runoff generation module of PREVAH, which was also applied as an event‐based module here. These configurations include a version that avoids calibration, one that transfers calibrated parameters, and one that uses regionalised parameter values. RGM‐PRO simulated heavy events in a more realistic way than the uncalibrated traditional runoff generation module of PREVAH, and, in some instances, it even exceeded the performance of the calibrated traditional one. The use of information on the spatial distribution of runoff types additionally proved to be valuable as a regionalisation technique and showed advantages over the other regionalisation approaches, also in terms of robustness and transferability.     

Evaluation of the PESERA model in two contrasting environments

The performance of the Pan‐European Soil Erosion Risk Assessment (PESERA) model was evaluated by comparison with existing soil erosion data collected in plots under different land uses and climate conditions in Europe. In order to identify the most important sources of error, the PESERA model was evaluated by comparing model output with measured values as well as by assessing the effect of the various model components on prediction accuracy through a multistep approach. First, the performance of the hydrological and erosion components of PESERA was evaluated separately by comparing both runoff and soil loss predictions with measured values. In order to assess the performance of the vegetation growth component of PESERA, the predictions of the model based on observed values of vegetation ground cover were also compared with predictions based on the simulated vegetation cover values. Finally, in order to evaluate the sediment transport model, predicted monthly erosion rates were also calculated using observed values of runoff and vegetation cover instead of simulated values. Moreover, in order to investigate the capability of PESERA to reproduce seasonal trends, the observed and simulated monthly runoff and erosion values were aggregated at different temporal scale and we investigated at what extend the model prediction error could be reduced by output aggregation. PESERA showed promise to predict annual average spatial variability quite well. In its present form, short‐term temporal variations are not well captured probably due to various reasons. The multistep approach showed that this is not only due to unrealistic simulation of cover and runoff, being erosion prediction also an important source of error. Although variability between the investigated land uses and climate conditions is well captured, absolute rates are strongly underestimated. A calibration procedure, focused on a soil erodibility factor, is proposed to reduce the significant underestimation of soil erosion rates. Copyright © 2009 John Wiley & Sons, Ltd.     

Studying the effect of different approaches to estimating model parameters on the accuracy of river runoff simulation by SWAP model

Different approaches to estimating the parameters of SWAP physically based model, which describes heat and water transfer processes in the soil-vegetaion (snow) cover-atmosphere system are examined. In particular, two methods of a priori estimation of parameter values and two variants of their calibration are discussed. The parameter sets obtained by different methods were used to simulate the runoff from 12 experimental catchments in the eastern USA. The calculations were conducted for a 39-year period (1960–1998) with a 3-hour step. The results of calculations were compared with each other and with measured river runoff values in order to identify the parameter set that is optimal for runoff evaluation. A strategy is proposed for a priori parameter estimation in the case of basins where observational data are too poor to enable parameter calibration.     

The application of the land surface model for calculating river runoff in high latitudes

The potentialities of the land surface model as applied to the calculation of river runoff in high latitudes were examined. Three approaches were used to specify input data based on meteorological data and land surface parameters. A method was developed for automated optimization of some model parameters by using direct search of minimum of root-mean-square deviation between the calculated and measured streamflow values. The global data sets are shown to be applicable in principle for hydrological calculations.     

Runoff sensitivity to snow depletion curve representation within a continental scale hydrologic model

The spatial variability of snow water equivalent (SWE) can exert a strong influence on the timing and magnitude of snowmelt delivery to a watershed. Therefore, the representation of sub-grid or sub-watershed snow variability in hydrologic models is important for accurately simulating snowmelt dynamics and runoff response. The U.S. Geological Survey National Hydrologic Model infrastructure with the precipitation-runoff modelling system (NHM-PRMS) represents the sub-grid variability of SWE with snow depletion curves (SDCs), which relate snow-covered area to watershed-mean SWE during the snowmelt period. The main objective of this research was to evaluate the sensitivity of simulated runoff to SDC representation within the NHM-PRMS across the continental United States (CONUS). SDCs for the model experiment were derived assuming a range of SWE coefficient of variation values and a lognormal probability distribution function. The NHM-PRMS was simulated at a daily time step for each SDC over a 14-year period. Results highlight that increasing the sub-grid snow variability (by changing the SDC) resulted in a consistently slower snowmelt rate and longer snowmelt duration when averaged across the hydrologic response unit scale. Simulated runoff was also found to be sensitive to SDC representation, as decreases in simulated snowmelt rate by 1 mm day⁻¹ resulted in decreases in runoff ratio by 1.8% on average in snow-dominated regions of the CONUS. Simulated decreases in runoff associated with slower snowmelt rates were approximately inversely proportional to increases in simulated evapotranspiration. High snow persistence and peak SWE:annual precipitation combined with a water-limited dryness index was associated with the greatest runoff sensitivity to changing snowmelt. Results from this study highlight the importance of carefully parameterizing SDCs for hydrologic modelling. Furthermore, improving model representation of snowmelt input variability and its relation to runoff generation processes is shown to be an important consideration for future modelling applications.     

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.     

A practical model to describe temporal variations in total suspended solids concentrations in highway runoff

Techniques to predict temporal variations in concentrations and loads of suspended solids from highway runoff are required to estimate impacts on receiving water ecology and to inform the design of interception/treatment devices. A recent UK study included the collection of rainfall, highway runoff rates and sediment load and quality data from six different sites where motorway runoff drained directly into a receiving watercourse. This data set is used to critically evaluate a previously-published model (Kim et al. 2005) aimed at predicting temporal variations in runoff quality. The comparisons, based on discrete samples collected during 21 storm events, suggest that a simplification of the model, requiring just two parameters, provides a robust estimate of temporal variations in total suspended solids (TSS). Generic parameter values are provided, and the model’s application is illustrated. The model captures first flush effects well, but the identified generic parameters fail to fullypredict the variation in absolute TSS values that are observed in practice.     

Investigating the use of spatial discretization of hydrological processes in conceptual rainfall runoff modelling: a case study for the meso‐scale

In this study a simple modelling approach was applied to identify the need for spatial complexity in representing hydrological processes and their variability over different scales. A data set of 18 basins was used, ranging between 8 and 4011 km² in area, located in the Nahe basin (Germany), with daily discharge values for over 30 years. Two different parsimoniously structured models were applied in lumped as well as in spatially distributed according to two distribution classifications: (1) a simple classification based on the lithology expressed in three permeability types and (2) a more complex classification based on seven dominating runoff production processes. The objective of the study was to compare the performances of the models on a local and on a regional scale as well as between the models with a view to identifying the accuracy in capturing the spatial variability of the rainfall‐runoff relationships. It was shown that the presence of a specific basin characteristic or process of the distribution classification was not related with higher model performance; only a larger basin size promoted higher model performance. The results of this study also indicated that the permeability generally contained more useful information on the spatial heterogeneity of the hydrological behaviour of the natural system than did a more detailed classification on dominating runoff generation processes. Although model performance was slightly lower for the model that used permeability as a distribution classification, consistency in its parameter values was found, which was lacking with the more complex distribution classification. The latter distribution classification had a higher flexibility to optimize towards the variability of the runoff, which resulted in higher performance, however, process representation was applied inconsistently. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation and modeling of runoff and sediment yield for different land covers under simulated rain in a semiarid region of Brazil

This paper quantifies the runoff and sediment yield for four different land covers in a semiarid region of Brazil. The WESP model, a distributed, event-oriented runoff-erosion model, was applied and its physical parameters, N_s and K_R, were adjusted based on observed runoff and sediment yield data using simulated rainfall with an average intensity of 53 mm h^-1. The sediment yield obtained was 53.02 kg ha^-1 (caatinga vegetation), 231.96 kg ha^-1 (bare soil), 309.75 kg ha^-1 (beans), and 847.38 kg ha^-1(corn). The results showed that caatinga cover yields the lowest erosion and runoff when compared to the other treatments. The results also show that the sediment yield and runoff values simulated with N_s, K_I, and K_R parameters were well calibrated, within acceptable deviations. The caatinga vegetation was more effective in protecting the soil, when compared to the other types of coverage. The beans and corn covers had the highest values of runoff and sediment yield, even higher than those observed for bare soil.     

Prediction uncertainty of conceptual rainfall-runoff models caused by problems in identifying model parameters and structure

Abstract

The uncertainties arising from the problem of identifying a representative model structure and model parameters in a conceptual rainfall-runoff model were investigated. A conceptual model, the HBV model, was applied to the mountainous Brugga basin (39.9 km”) in the Black Forest, southwestern Germany. In a first step, a Monte Carlo procedure with randomly generated parameter sets was used for calibration. For a ten-year calibration period, different parameter sets resulted in an equally good correspondence between observed and simulated runoff. A few parameters were well defined (i.e. best parameter values were within small ranges), but for most parameters good simulations were found with values varying over wide ranges. In a second step, model variants with different numbers of elevation and landuse zones and various runoff generation conceptualizations were tested. In some cases, representation of more spatial variability gave better simulations in terms of discharge. However, good results could be obtained with different and even unrealistic concepts. The computation of design floods and low flow predictions illustrated that the parameter uncertainty and the uncertainty of identifying a unique best model variant have implications for model predictions. The flow predictions varied considerably. The peak discharge of a flood with a probability of 0.01 year^?1, for instance, varied from 40 to almost 60 mm day^?1. It was concluded that model predictions, particularly in applied studies, should be given as ranges rather than as single values.     

Détermination des variations de la capacité d'absorption d'un sol en place sous averses simulées / Obtaining variations of field infiltration capacity from simulated rainstorm experiments

Abstract

By sprinkling an experimental plot with different intensities of simulated rainfall starting with different initial conditions of soil moisture, the variations of infiltration capacity and consequently the response of the soil surface to runoff are evaluated. The following values are successively determined from experimental data: the mean depth of surface storage; the mean depth of detention and the parameters of a chosen infiltration formula.     

Estimating source regions for snowmelt runoff in a Rocky Mountain basin: tests of a data‐based conceptual modeling approach

In many mountain basins, river discharge measurements are located far away from runoff source areas. This study tests whether a basic snowmelt runoff conceptual model can be used to estimate relative contributions of different elevation zones to basin‐scale discharge in the Cache la Poudre, a snowmelt‐dominated Rocky Mountain river. Model tests evaluate scenarios that vary model configuration, input variables, and parameter values to determine how these factors affect discharge simulation and the distribution of runoff generation with elevation. Results show that the model simulates basin discharge well (NSCE and R >0.90) when input precipitation and temperature are distributed with different lapse rates, with a rain‐snow threshold parameter between 0 and 3.3 °C, and with a melt rate parameter between 2 and 4 mm °C^?1 d^?1 because these variables and parameters can have compensating interactions with each other and with the runoff coefficient parameter. Only the hydrograph recession parameter can be uniquely defined with this model structure. These non‐unique model scenarios with different configurations, input variables, and parameter values all indicate that the majority of basin discharge comes from elevations above 2900 m, or less than 25% of the basin total area, with a steep increase in runoff generation above 2600 m. However, the simulations produce unrealistically low runoff ratios for elevations above 3000 m, highlighting the need for additional measurements of snow and discharge at under‐sampled elevations to evaluate the accuracy of simulated snow and runoff patterns. Copyright © 2013 John Wiley & Sons, Ltd.     

On the estimation of antecedent wetness conditions in rainfall–runoff modelling

The analysis of the physical processes involved in a conceptual model of soil water content balance is addressed with the objective of its application as a component of rainfall–runoff modelling. The model uses routinely measured meteorological variables (rainfall and air temperature) and incorporates a limited number of significant parameters. Its performance in estimating the soil moisture temporal pattern was tested through local measurements of volumetric water content carried out continuously on an experimental plot located in central Italy. The analysis was carried out for different periods in order to test both the representation of infiltration at the short time‐scale and drainage and evapotranspiration processes at the long time‐scale. A robust conceptual model was identified that incorporated the Green–Ampt approach for infiltration and a gravity‐driven approximation for drainage. A sensitivity analysis was performed for the selected model to assess the model robustness and to identify the more significant parameters involved in the principal processes that control the soil moisture temporal pattern. The usefulness of the selected model was tested for the estimation of the initial wetness conditions for rainfall–runoff modelling at the catchment scale. Specifically, the runoff characteristics (runoff depth and peak discharge) were found to be dependent on the pre‐event surface soil moisture. Both observed values and those estimated by the model gave good results. On the contrary, with the antecedent wetness conditions furnished by two versions of the antecedent precipitation index (API), large errors were obtained. Copyright © 2007 John Wiley & Sons, Ltd.