Calibration of conceptual models for rainfall-runoff simulation

Abstract

Conceptual mathematical models are a useful tool for rainfallrunoff modelling of a basin. The calibration of such models has attracted the attention of a number of hydrologists since unique and optimal parameters are difficult to obtain. The calibration of a conceptual model is discussed through a simple conceptual model whose parameters are determined using a search technique. It is shown that the optimization algorithm converges to a global optimum even when the errors in the initial parameters are quite significant and the input environment is noisy.     

Effects of streamflow isotope sampling strategies on the calibration of a tracer-aided rainfall-runoff model

Isotopes are increasingly used in rainfall-runoff models to constrain conceptualisations of internal catchment functioning and reduce model uncertainty. However, there is little guidance on how much tracer data is required to adequately do this, and different studies use data from different sampling strategies. Here, we used a 7-year time series of daily stable water isotope samples of precipitation and streamflow to derive a range of typical stream sampling regimes and investigate how this impacts calibration of a semi-distributed tracer-aided model in terms of flow, deuterium and flux age simulations. Over the 7 years weekly sampling facilitated an almost identical model performance as daily, and there were only slight deteriorations in performance for fortnightly sampling. Monthly sampling resulted in poorer deuterium simulations and greater uncertainty in the derived parameter sets ability to accurately represent catchment functioning, evidenced by unrealistic reductions in the volumes of water available for mixing in the saturation area causing simulated water age decreases. Reducing sampling effort and restricting data collection to 3 years caused reductions in the accuracy of deuterium simulation, though the deterioration did not occur if sampling continued for 5 years. Analysis was also undertaken to consider the effects of reduced sampling effort over the driest and wettest hydrological years to evaluate effects of more extreme conditions. This showed that the model was particularly sensitive to changes in sampling during dry conditions, when the catchment hydrological response is most non-linear. Across all dataset durations, sampling in relation to flow conditions, rather than time, revealed that samples collected at flows >Q50 could provide calibration results comparable to daily sampling. Targeting only extreme high flows resulted in poor deuterium and low flow simulations. This study suggests sufficient characterization of catchment functioning can be obtained through reduced sampling effort over longer timescales and the targeting of flows >Q50.     

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.     

A data-based regional scale autoregressive rainfall-runoff model: a study from the Odra River

This paper aims to compare the performances of multivariate autoregressive (MAR) techniques and univariate autoregressive (AR) methods applied to regional scale rainfall-runoff modelling. We focus on the case study from the upper and middle reaches of the Odra River with its main tributaries in SW Poland. The rivers drain both the mountains (the Sudetes) and the lowland (Nizina Śląska). The region is exposed to extreme hydrologic and meteorological events, especially rain-induced and snow-melt floods. For the analysis, four hydrologic and meteorological variables are chosen, i.e., discharge (17 locations), precipitation (7 locations), thickness of snow cover (7 locations) and groundwater level (1 location). The time period is November 1971–December 1981 and the temporal resolution of the time series is of 1 day. Both MAR and AR models of the same orders are fitted to various subsets of the data and subsequently forecasts of discharge are derived. In order to evaluate the predictions the stepwise procedure is applied to make the validation independent of the specific sample path of the stochastic process. It is shown that the model forecasts peak discharges even 2–4 days in advance in the case of both rain-induced and snow-melt peak flows. Furthermore, the accuracy of discharge predictions increases if one analyses the combined data on discharge, precipitation, snow cover, and groundwater level instead of the pure discharge multivariate time series. MAR-based discharge forecasts based on multivariate data on discharges are more accurate than AR-based univariate predictions for a year with a flood, however, this relation is reverse in the case of the free-of-flooding year. In contrast, independently of the occurrence of floods within a year, MAR-based discharge forecasts based on discharges, precipitation, snow cover, and groundwater level are more precise than AR-based predictions.     

A real-time combination method for the outputs of different rainfall-runoff models

Abstract

Application of the concept of combining the estimated forecast output of different rainfall-runoff models to yield an overall combined estimated output in the context of real-time river flow forecasting is explored. A Real-Time Model Output Combination Method (RTMOCM) is developed, based on the structure of the Linear Transfer Function Model (LTFM) and utilizing the concept of the Weighted Average Method (WAM) for model output combination. A multiple-input single-output form of the LTFM is utilized in the RTMOCM. This form of the LTFM model uses synchronously the daily simulation-mode model-estimated discharge time series of the rainfall-runoff models selected for combination, its inherent updating structure being used for providing updated combined discharge forecasts. The RTMOCM is applied to the daily data of five catchments, using the simulation-mode estimated discharges of three selected rainfall-runoff models, comprising one conceptual model (Soil Moisture Accounting and Routing Procedure—SMAR) and two black-box models (Linear Perturbation Model—LPM and Linearly-Varying Variable Gain Factor Model—LVGFM). In order to get an indication of the accuracy of the updated combined discharge forecasts relative to the updated discharge forecasts of the individual models, the LTFM is also used for updating the simulation-mode discharge time series of each of the three individual models. The results reveal that the updated combined discharge forecasts provided by the RTMOCM, with parameters obtained by linear regression, can improve on the updated discharge forecasts of the individual rainfall-runoff models.     

A comparative study of closed-form hydraulic conductivity prediction models

The Mualem and the Burdine hydraulic conductivity prediction models are considered in combination with the van Genuchten analytical retention curve, as well as the Brooks and Corey prediction model. An equivalence is presented between the retention curves of these models. A comparative study follows between hydraulic conductivities that are based on equivalent retention curves. A unified presentation of prediction models provides a framework for the whole analysis. The treatment of the equivalence problem consists in a minimization procedure characterized by uncoupling of the parameters and analytical evaluation of the objective function. Exact analytical equivalence relations are given for significant parts of the parameter ranges, and, for the remaining parts, analytical approximations are proposed. The comparisons between hydraulic conductivities are carried out via an inequality analysis. It is shown that the hydraulic conductivity of the Burdine model is less than that of the other models for extended ranges of equivalent parameters.     

A comparative study of seismic tomography models of Southwest China

The margin of the Tibetan Plateau of Southwest China is one of the most seismically active regions of China and is the location of the China Seismic Experimental Site (CSES). Many studies have developed seismic velocity models of Southwest China, but few have compared and evaluated these models which is important for further model improvement. Thus, we compared six published seismic shear-wave velocity models of Southwest China on absolute velocity and velocity perturbation patterns. The models are derived from different types of data (e.g., surface waves from ambient noise and earthquakes, body-wave travel times, receiver functions) and inversion methods. We interpolated the models into a uniform horizontal grid (0.5° × 0.5°) and vertically sampled them at 5, 10, 20, 30, 40, and 60 km depths. We found significant differences between the six models. Then, we selected three of them that showed greater consistency for further comparison. Our further comparisons revealed systematic biases between models in absolute velocity that may be related to different data types. The perturbation pattern of the model is especially divergent in the shallow part, but more consistent in the deep part. We conducted synthetic and inversion tests to explore possible causes and our results imply that systematic differences between the data, differences in methods, and other factors may directly affect the model. Therefore, the Southwest China velocity model still has considerable room for improvement, and the impact of inconsistency between different data types on the model needs further research. Finally, we proposed a new reference shear-wave velocity model of Southwest China (SwCM-S1.0) based on the three selected models with high consistency. We believe that this model is a better representation of more robust features of the models that are based on different data sets.     

Development of a fuzzy logic-based rainfall-runoff model

Abstract

Rainfall-runoff models are used to describe the hydrological behaviour of a river catchment. Many different models exist to simulate the physical processes of the relationship between precipitation and runoff. Some of them are based on simple and easy-to-handle concepts, others on highly sophisticated physical and mathematical approaches that require extreme effort in data input and handling. Recently, mathematical methods using linguistic variables, rather than conventional numerical variables applied extensively in other disciplines, are encroaching in hydrological studies. Among these is the application of a fuzzy rule-based modelling. In this paper an attempt was made to develop fuzzy rule-based routines to simulate the different processes involved in the generation of runoff from precipitation. These routines were implemented within a conceptual, modular, and semi-distributed model-the HBV model. The investigation involved determining which modules of this model could be replaced by the new approach and the necessary input data were identified. A fuzzy rule-based routine was then developed for each of the modules selected, and application and validation of the model was done on a rainfall-runoff analysis of the Neckar River catchment, in southwest Germany.     

Local spatial regression models: a comparative analysis on soil contamination

Spatial data analysis focuses on both attribute and locational information. Local analyses deal with differences across space whereas global analyses deal with similarities across space. This paper addresses an experimental comparative study to analyse the spatial data by some weighted local regression models. Five local regression models have been developed and their estimation capacities have been evaluated. The experimental studies showed that integration of objective function based fuzzy clustering to geostatistics provides some accurate and general models structures. In particular, the estimation performance of the model established by combining the extended fuzzy clustering algorithm and standard regional dependence function is higher than that of the other regression models. Finally, it could be suggested that the hybrid regression models developed by combining soft computing and geostatistics could be used in spatial data analysis.     

Using lumped conceptual rainfall-runoff models to simulate daily isotope variability with fractionation in a nested mesoscale catchment

This paper presents 19 months of stable isotope (δ²H and δ¹⁸O) data to enhance understanding of water and solute transport at two spatial scales (2.3 km² and 122 km²) in the agricultural Lunan catchment, Scotland. Daily precipitation and stream isotope data, weekly lake and spring isotope data and monthly groundwater isotope data revealed important insights into flow pathways and mixing of water at both scales. In particular, a deeper groundwater flow path significantly contributes to total streamflow (25-50%). Upstream lake isotope dynamics, susceptible to evaporative fractionation, also appeared to have an important influence on the downstream isotope composition. This unique tracer data set facilitated the conceptualization of a lumped catchment-scale flow-tracer model. The incorporation of hydrological, mixing and fractionation processes based on these data improved simulations of the stream δ²H isotope response at the catchment outlet from 0.37 to 0.56 for the Nash-Sutcliffe statistic. The stable isotope data successfully aided model conceptualization and calibration in the quest for a simple water and solute transport model with improved representation of process dynamics.     

Indoor imitation experimental study on driving factors of rainfall-runoff process

The driving actions are varied during the rain-fall-runoff process in a catchment. The impacts on therunoff process, caused by human activities or climatechange, can be attributed to two aspects: the charac-teristics of rainfall process and ground pad changes.To clarify their impacts on hydrological cycle is thefoundation of mechanism research of scientific hy-drology. So far, all of the research results, domestic andabroad, indicate that the advances on the understand-ing of hydrologica…     

A comparative study of seismic tomography models of the Chinese continental lithosphere

The Chinese mainland is subject to complicated plate interactions that give rise to its complex structure and tectonics. While several seismic velocity models have been developed for the Chinese mainland, apparent discrepancies exist and, so far, little effort has been made to evaluate their reliability and consistency. Such evaluations are important not only for the application and interpretation of model results but also for future model improvement. To address this problem, here we compare five published shear-wave velocity models with a focus on model consistency. The five models were derived from different datasets and methods (i.e., body waves, surface waves from earthquakes, surface waves from noise interferometry, and full waves) and interpolated into uniform horizontal grids (0.5° × 0.5°) with vertical sampling points at 5 km, 10 km, and then 20 km intervals to a depth of 160 km below the surface, from which we constructed an averaged model (AM) as a common reference for comparative study. We compare both the absolute velocity values and perturbation patterns of these models. Our comparisons show that the models have large (> 4%) differences in absolute values, and these differences are independent of data coverage and model resolution. The perturbation patterns of the models also show large differences, although some of the models show a high degree of consistency within certain depth ranges. The observed inconsistencies may reflect limited model resolution but, more importantly, systematic differences in the datasets and methods employed. Thus, despite several seismic models being published for this region, there is significant room for improvement. In particular, the inconsistencies in both data and methodologies need to be resolved in future research. Finally, we constructed a merged model (ChinaM-S1.0) that incorporates the more robust features of the five published models. As the existing models are constrained by different datasets and methods, the merged model serves as a new type of reference model that incorporates the common features from the joint datasets and methods for the shear-wave velocity structure of the Chinese mainland lithosphere.     

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.     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.     

Damage detection with image processing: a comparative study

Large structures, such as bridges, highways, etc., need to be inspected to evaluate their actual physical and functional condition, to predict future conditions, and to help decision makers allocating maintenance and rehabilitation resources. The assessment of civil infrastructure condition is carried out through information obtained by inspection and/or monitoring operations. Traditional techniques in structural health monitoring(SHM) involve visual inspection related to inspection standards th...     

A comparative study of concentrated plasticity models in dynamic analysis of building structures

Concentrated plasticity (CP) models are frequently used in static and dynamic building analysis and have been implemented in available commercial software. This investigation deals with three different CP‐models, a simplified macroelement model (SEM) for a complete building story, a frame element with elasto‐plastic interaction hinges (PH), and a frame element with fiber hinges (FB). The objectives of this work are to evaluate the quality of the earthquake responses predicted by these models and to identify important aspects of their implementation and limitations for their use in dynamic analysis. The three elements are tested in a single‐story asymmetric plan building and in a three‐story steel building. Results show that base shear and global response values are usually computed with better accuracy than interstory deformations and local responses. Besides, the main limitation of elasto‐plastic CP models is to control the displacement offsets that result from perfect elasto‐plastic behavior. On the other hand, calibration of the SEM‐model shows that global responses in steel structures may be computed within 20% error in the mean at a computational cost two orders of magnitude smaller than that of the other CP elements considered. However, the three element models considered lead to increasing levels of accuracy in the dynamic response and their use depends on the refinement of the analysis performed. Copyright © 2005 John Wiley & Sons, Ltd.     

ROC‐based calibration of flood inundation models

The use of spatial patterns of flood inundation (often obtained from remotely sensed imagery) to calibrate flood inundation models has been widespread over the last 15 years. Model calibration is most often achieved by employing one or even several performance measures derived from the well‐known confusion matrix based on a binary classification of flooding. However, relatively early on, it has been recognized that the use of commonly reported performance measures for calibrating flood inundation models (such as the F measure) is hampered because the calibration procedure commonly utilizes only one possible solution of a wet/dry classification of a remote sensing image [most often acquired by a synthetic aperture radar (SAR)] to calibrate or validate models and are biased towards either over‐prediction or under‐prediction of flooding. Despite the call in several studies for an alternative statistic, to this date, very few, if any, unbiased performance measure based on the confusion matrix has been proposed for flood model calibration/validation studies. In this paper, we employ a robust statistical measure that operates in the receiver operating characteristics (ROC) space and allows automated model calibration with high identifiability of the best model parameter set but without the need of a classification of the SAR image. The ROC‐based method for flood model calibration is demonstrated using two different flood event test cases with flood models of varying degree of complexity and boundary conditions with varying degree of accuracy. Verification of the calibration results and optional SAR classification is successfully performed with independent observations of the events. We believe that this proposed alternative approach to flood model calibration using spatial patterns of flood inundation should be employed instead of performance measures commonly used in conjunction with a binary flood map. © 2013 California Institute of Technology. Hydrological Processes © 2013 John Wiley & Sons, Ltd.     

Application of a rainfall-runoff model to three catchments in Iraq

Abstract

The capability of the Surface inFiltration Baseflow (SFB) conceptual rainfall-runoff model to simulate streamflow for three catchments selected from northern Iraq is investigated. These catchments differ in their climatic regimes and physical characteristics. Three versions of the model were tested: the original three-parameter model (SFB), the modified five-parameter model (SFB-5), and the modified six-parameter model (SFB-6). The available daily precipitation, potential evapotranspiration and runoff data were used in conjunction with a simulated annealing (SA) optimization technique to calibrate the various versions of the SFB model. A simple sensitivity analysis was then carried out to determine the relative importance of the model parameters. The study indicated that use of the original three parameter model was not adequate to simulate monthly streamflow in the selected catchments. The modified version (SFB-5) provided better runoff simulation than the original SFB model; overall a 19% increase was observed in the coefficient of determination (R²) between simulated and observed monthly runoff. The SFB-5 model performed with varying degrees of success among the catchments. The model performance in the validation stage was reasonable and comparable to that of the calibration stage. The sensitivity analysis of the SFB model for arid catchments revealed that the baseflow parameter (B) was the most sensitive one, while the S and F parameters were less sensitive than the B parameter.     

Comparative study of different wavelets for developing parsimonious Volterra model for rainfall-runoff simulation

Although the Volterra models are non-parsimonious ones, they are being used because they can mimic dynamics of complex systems. However, applying and identification of the Volterra models using data may result in overfitting problem and uncertainty. In this investigation we evaluate capability of different wavelet forms for decomposing and compressing the Volterra kernels in order to overcome this problem by reducing the number of the model coefficients to be estimated and generating smooth kernels. A simulation study on a rainfall?runoff process over the Cache River watershed showed that the method performance is successful due to multi-resolution capacity of the wavelet analysis and high capability of the Volterra model. The results also revealed that db2 and sym2 wavelets have the same high potential in improving the linear Volterra model performance. However, QS wavelet was more successful in yielding smooth kernels. Moreover, the probability of overfitting while identifying the nonlinear Volterra model may be less than the linear model.