Improved parameter estimation for hydrological models using weighted object functions

This paper discusses the sensitivity of calibration of hydrological model parameters to different objective functions. Several functions are defined with weights depending upon the hydrological background. These are compared with an objective function based upon kriging. Calibration is applied to piezometric readings from the Isle of Goeree in the Netherlands. For a study on the permeability of the first aquifer, the kriging predictor yields weights that differ from using prior knowledge, and emphasizes more strongly spatially isolated points than commonly applied objective functions. It reduces the range of differences between measurements and model simulations, but the mean absolute error increases. For a study on the resistance of the top layer and of the aquitard, use of prior information in the objective functions leads to a reduction in standard deviations of the differences between measured and calculated values by 40–80%. Copyright © 1999 John Wiley & Sons, Ltd.     

Development of an automatic calibration scheme for the HBV hydrological model

An automatic calibration scheme for the HBV model (ACSH) was developed. The ACSH was based on the physical significance of the model parameters and structure. The inference of hydrologists in the manual calibration was adopted as the guideline. A slight modification of the model structure of the soil routine was suggested to avoid interdependence of the parameters. In total nine parameters, except the snow routine, Fc and MAXBAS, were calibrated automatically in two stages; first the soil moisture routine and then the others. There are six sets in two stages in total. Using the Powell method, the parameters in each step were calibrated simultaneously with carefully selected objective functions, and in particular a powerful objective function for the soil moisture routine. The steps were in a fixed order in the ACSH according to the model structure. The optimal values of the model parameters were stable, with the different initial values varying in considerable ranges. The automatic calibration gave the same model performance as the manual calibration when the ACSH was tested in two basins. The automatic calibration can thus be used as a reference or as an alternative solution of the model. © 1997 John Wiley & Sons, Ltd.     

Automatic calibration of HEC‐HMS using single‐objective and multi‐objective PSO algorithms

This study presents single‐objective and multi‐objective particle swarm optimization (PSO) algorithms for automatic calibration of Hydrologic Engineering Center‐ Hydrologic Modeling Systems rainfall‐runoff model of Tamar Sub‐basin of Gorganroud River Basin in north of Iran. Three flood events were used for calibration and one for verification. Four performance criteria (objective functions) were considered in multi‐objective calibration where different combinations of objective functions were examined. For comparison purposes, a fuzzy set‐based approach was used to determine the best compromise solutions from the Pareto fronts obtained by multi‐objective PSO. The candidate parameter sets determined from different single‐objective and multi‐objective calibration scenarios were tested against the fourth event in the verification stage, where the initial abstraction parameters were recalibrated. A step‐by‐step screening procedure was used in this stage while evaluating and comparing the candidate parameter sets, which resulted in a few promising sets that performed well with respect to at least three of four performance criteria. The promising sets were all from the multi‐objective calibration scenarios which revealed the outperformance of the multi‐objective calibration on the single‐objective one. However, the results indicated that an increase of the number of objective functions did not necessarily lead to a better performance as the results of bi‐objective function calibration with a proper combination of objective functions performed as satisfactorily as those of triple‐objective function calibration. This is important because handling multi‐objective optimization with an increased number of objective functions is challenging especially from a computational point of view. Copyright © 2012 John Wiley & Sons, Ltd.     

Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models

Problem complexity for watershed model calibration is heavily dependent on the number of parameters that can be identified during model calibration. This study investigates the use of global sensitivity analysis as a screening tool to reduce the parametric dimensionality of multi-objective hydrological model calibration problems while maximizing the information extracted from hydrological response data. This study shows that by expanding calibration problem formulations beyond traditional, statistical error metrics to also include metrics that capture indices or signatures of hydrological function, it is possible to reduce the complexity of calibration while maintaining high quality model predictions. The sensitivity-guided calibration is demonstrated using the Sacramento Soil Moisture Accounting (SAC-SMA) conceptual rainfall–runoff model of moderate complexity (i.e., up to 14 freely varying parameters). Using both statistical and hydrological metrics, optimization results demonstrate that parameters controlling at least 20% of the model output variance (through individual effects and interactions) should be included in the calibration process. This threshold generally yields 30–40% reductions in the number of SAC-SMA parameters requiring calibration – setting the others to a priori values – while maintaining high quality predictions. Two parameters are recommended to be calibrated in all cases (percent impervious area and lower zone tension water storage), three parameters are needed in drier watersheds (additional impervious area, riparian zone vegetation, and percent of percolation going to tension storage), and the lower zone parameters are crucial unless the watershed is very dry. Overall, this study demonstrates that a coupled, multi-objective sensitivity and calibration analysis better captures differences between watersheds during model calibration and serves to maximize the value of available watershed response time series. These contributions are particularly important given the ongoing development of more complex integrated models, which will require new tools to address the growing discrepancy between the information content of hydrological data and the number of model parameters that have to be estimated.     

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.     

Estimating parameters of groundwater recharge model in frequency domain: Karst springs Jadro and Žrnovnica

The spectral method is based on the assumption of exponential forms of autocorrelation functions of the input and output time series. The results of practical applications of the spectral method on several karst springs in Croatia show that this assumption cannot always be reliably applied to the time series of rainfall and spring discharge, especially if short time periods are analysed. For this reason, the method is modified. The scale factor between the transfer function of total rainfall and the transfer function of groundwater recharge is considered as an additional model parameter which is determined in the optimization procedure. In addition to the theoretical background, this paper also presents the results of application of the modified spectral method on the springs Jadro and ?rnovnica located in the Dinaric karst area in Croatia. The parameters of groundwater recharge model are determined separately for both the springs and the obtained values are discussed and compared with the results of previous investigations. The values of the scale factors determined in the optimization procedure are compared to the values calculated using the theoretical equation. The comparison shows that the theoretical equation underestimates the optimal values of the scale factor. The underestimations are especially evident for periods of one year. Finally, the characteristics of rainfall–runoff relations of two springs are compared using the identified transfer functions and the results of simulations of the periodogram of observed discharge by the parametric periodogram. Copyright © 2008 John Wiley & Sons, Ltd.     

Temporal sampling strategies and uncertainty in calibrating a conceptual hydrological model for a small boreal catchment

How much data is needed for calibration of a hydrological catchment model? In this paper we address this question by evaluating the information contained in different subsets of discharge and groundwater time series for multi‐objective calibration of a conceptual hydrological model within the framework of an uncertainty analysis. The study site was a 5·6‐km² catchment within the Forsmark research site in central Sweden along the Baltic coast. Daily time series data were available for discharge and several groundwater wells within the catchment for a continuous 1065‐day period. The hydrological model was a site‐specific modification of the conceptual HBV model. The uncertainty analyses were based on a selective Monte Carlo procedure. Thirteen subsets of the complete time series data were investigated with the idea that these represent realistic intermittent sampling strategies. Data subsets included split‐samples and various combinations of weekly, monthly, and quarterly fixed interval subsets, as well as a 53‐day ‘informed observer’ subset that utilized once per month samples except during March and April—the months containing large and often dominant snow melt events—when sampling was once per week. Several of these subsets, including that of the informed observer, provided very similar constraints on model calibration and parameter identification as the full data record, in terms of credibility bands on simulated time series, posterior parameter distributions, and performance indices calculated to the full dataset. This result suggests that hydrological sampling designs can, at least in some cases, be optimized. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Calibration of the Hydrological Simulation Program Fortran (HSPF) model using automatic calibration and geographical information systems

Calibrating a comprehensive, multi‐parameter conceptual hydrological model, such as the Hydrological Simulation Program Fortran model, is a major challenge. This paper describes calibration procedures for water‐quantity parameters of the HSPF version 10·11 using the automatic‐calibration parameter estimator model coupled with a geographical information system (GIS) approach for spatially averaged properties. The study area was the Grand River watershed, located in southern Ontario, Canada, between 79° 30′ and 80° 57′W longitude and 42° 51′ and 44° 31′N latitude. The drainage area is 6965 km². Calibration efforts were directed to those model parameters that produced large changes in model response during sensitivity tests run prior to undertaking calibration. A GIS was used extensively in this study. It was first used in the watershed segmentation process. During calibration, the GIS data were used to establish realistic starting values for the surface and subsurface zone parameters LZSN, UZSN, COVER, and INFILT and physically reasonable ratios of these parameters among watersheds were preserved during calibration with the ratios based on the known properties of the subwatersheds determined using GIS. This calibration procedure produced very satisfactory results; the percentage difference between the simulated and the measured yearly discharge ranged between 4 to 16%, which is classified as good to very good calibration. The average simulated daily discharge for the watershed outlet at Brantford for the years 1981–85 was 67 m³ s^?1 and the average measured discharge at Brantford was 70 m³ s^?1. The coupling of a GIS with automatice calibration produced a realistic and accurate calibration for the HSPF model with much less effort and subjectivity than would be required for unassisted calibration. Copyright © 2002 John Wiley & Sons, Ltd.     

时频联合分析地震计正弦标定数据

介绍短时傅里叶变换,分析地震计正弦标定信号的特点,提出基于时间域和频率域联合分析正弦标定波形组起始点的方法,可以准确找出每组正弦标定信号的频率和振幅,计算地震计的速度响应灵敏度。     

Application of a land surface model for simulating rainfall streamflow hydrograph: 1. Model calibration

Different variants of parameters’ calibration of land surface model SWAP were examined with the aim to maximize the accuracy of reproducing rainfall runoff hydrograph. The optimization of parameter values was automated based on two different algorithms for the search of the global optimum of an objective function: a random search technique and a shuffled complex evolution method SCE-UA. In both cases, two objective functions, based on the mean systematic error and the Nash and Sutcliffe coefficient of efficiency, were used. The number of calibrated parameters varied from 10 to 15, and their values were within the reasonable range so as not to contradict the physical meaning and to ensure the best agreement between the simulated and observed daily river runoff. The streamflow hydrographs for some rivers in USA simulated with the use of different sets of optimized parameters were compared with observation data.     

基于AR模型模拟超高层建筑的脉动风速时程

风荷载是超高层建筑设计的主要荷载之一,而且通过风振时域分析可以更全面地了解超高层建筑风振响应特性,更直观地反映超高层建筑风致振动控制的有效性。因此,本文使用线性滤波法即白噪声滤波法(white noise filtration method,WNFM)中的自回归(auto-regressive,AR)模型模拟超高层建筑的风速时程。首先,考虑超高层建筑风速时程的时间和空间相关性,导出了四阶AR模型的参数表达式。接着,基于AR模型模拟了一幢高度为200 m超高层建筑的风速时程。最后,通过比较模拟风速功率谱、模拟自相关函数和互相关函数与目标风速功率谱、目标自相关函数和互相关函数的吻合程度,验证基于AR模型模拟超高层建筑风速时程的可行性。     

A spectral approach to estimation and smoothing of continuous spatial processes

This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems.A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters.We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data.     

Hydraulic Gradient Comparison Method to Estimate Aquifer Hydraulic Parameters Under Steady-State Conditions

The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity (or trans-missivity) and boundary conductance for a ground water flow model under steady-state conditions. This method, following formal optimization techniques, defines its objective function to minimize differences between interpreted (observed) and simulated hydraulic gradients, which results in minimization of differences between observed and simulated hydraulic heads. The key features of this method are that (1) the derived optimality conditions have an explicit form with a clear hydrology concept that is con-sistent with Darcy's law, and (2) the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient. This second feature allows a multidimensional optimization problem to be solved by many one-dimensional optimization procedures simultaneously, which results in a substantial reduction in computation time. The results of the numerical performance testing on a heterogeneous hypothetical case confirm that minimizing gradient residuals in the entire model domain leads to minimizing head residuals. Application of the method in real-world projects requires rigorous conceptual model development, use of a global calibration target, and an iterative calibration proess. The conceptual model development includes interpretation of a potentiometric surface and estimation of other hydrologic parameters. This method has been applied to a wide range of real-world modeling projects, including the Rocky Mountain Arsenal and Rocky Flats sites in Colorado, which demonstrates that the method is efficient and practical.     

Predicting floodplain inundation: raster‐based modelling versus the finite‐element approach

We compare two approaches to modelling floodplain inundation: a raster‐based approach, which uses a relatively simple process representation, with channel flows being resolved separately from the floodplain using either a kinematic or diffusive wave approximation, and a finite‐element hydraulic model aiming to solve the full two‐dimensional shallow‐water equations. A flood event on a short (c. 4 km) reach of the upper River Thames in the UK is simulated, the models being validated against inundation extent as determined from satellite synthetic aperture radar (SAR) imagery. The unconstrained friction parameters are found through a calibration procedure, where a measure of fit between predicted and observed shorelines is maximized. The raster and finite‐element models offer similar levels of performance, both classifying approximately 84% of the model domain correctly, compared with 65% for a simple planar prediction of water surface elevation. Further discrimination between models is not possible given the errors in the validation data. The simple raster‐based model is shown to have considerable advantages in terms of producing a straightforward calibration process, and being robust with respect to channel specification. Copyright © 2001 John Wiley & Sons, Ltd.     

Parameter estimation in semi‐distributed hydrological catchment modelling using a multi‐criteria objective function

Output generated by hydrologic simulation models is traditionally calibrated and validated using split‐samples of observed time series of total water flow, measured at the drainage outlet of the river basin. Although this approach might yield an optimal set of model parameters, capable of reproducing the total flow, it has been observed that the flow components making up the total flow are often poorly reproduced. Previous research suggests that notwithstanding the underlying physical processes are often poorly mimicked through calibration of a set of parameters hydrologic models most of the time acceptably estimates the total flow. The objective of this study was to calibrate and validate a computer‐based hydrologic model with respect to the total and slow flow. The quick flow component used in this study was taken as the difference between the total and slow flow. Model calibrations were pursued on the basis of comparing the simulated output with the observed total and slow flow using qualitative (graphical) assessments and quantitative (statistical) indicators. The study was conducted using the Soil and Water Assessment Tool (SWAT) model and a 10‐year historical record (1986–1995) of the daily flow components of the Grote Nete River basin (Belgium). The data of the period 1986–1989 were used for model calibration and data of the period 1990–1995 for model validation. The predicted daily average total flow matched the observed values with a Nash–Sutcliff coefficient of 0·67 during calibration and 0·66 during validation. The Nash–Sutcliff coefficient for slow flow was 0·72 during calibration and 0·61 during validation. Analysis of high and low flows indicated that the model is unbiased. A sensitivity analysis revealed that for the modelling of the daily total flow, accurate estimation of all 10 calibration parameters in the SWAT model is justified, while for the slow flow processes only 4 out of the set of 10 parameters were identified as most sensitive. Copyright © 2007 John Wiley & Sons, Ltd.     

基于阶跃响应在时域解析测定地震计参数

提出基于阶跃响应在时域解析测定地震计参数的方法，并对合理确定响应的时间零点提供了一种方法。对JC-V100 3D型便携式短周期地震计及与其配套的EDAS-3M型16位地震数据采集记录仪组成的系统进行了测试。结果表明：对JC-V1003D短周期地震计的传递函数进行测试是可行的，对地震计的阻尼系数Dc和自振周期Tc的测试结果是令人满意的。     

A parameter allocation approach for flow simulation using the WetSpa-Python model

Hydrologic models are simplified representations of natural hydrologic systems. Since these models rely on assumptions and simplifications to capture some aspects of hydrological processes, calibration of parameters is unavoidable. However, utilizing the philosophy of a recent modelling framework proposed by Bahremand (2016), we show how calibration of most model parameters can be avoided by allocating or presetting these parameters utilizing knowledge gained from sensitivity analyses, field observations and a priori specifications as a part of a parameter allocation procedure. This paper details the simulation of daily river flow of the Shemshak-Roudak watershed performed using the Python version of the WetSpa model. The WetSpa-Python model is a distributed model of hydrological processes applied at the watershed scale. The model was applied to the Shemshak-Roudak watershed of Iran with parameter allocation. Model calibration involved only two parameters. Straightforward methods were proposed for allocating model parameters, including three baseflow-related parameters and the determination of maximum active groundwater storage using a mass curve technique. Also, the Budyko curve was used to constrain a correction factor for potential evapotranspiration. The WetSpa-Python model was extended to include the influence of snowmelt. A failure to include snow in the hydrological processes of the WetSpa-Python model creates a significant discrepancy between the observed and simulated hydrographs during the spring. The results of daily simulations for 12 years (2002–2014) are in good agreement with observations of discharge (Kling-Gupta Efficiency = 0.84). These results demonstrate that it is feasible to simulate hydrographs with limited calibration given a knowledge of hydrological processes and an understanding of relationships between catchment characteristics and model parameters.     

Evaluation of a distributed model for urban catchments using a 7‐year continuous data series

The documentation existing on both land use and the delineation of pervious and impervious zones in urban areas tends to be rather complete. In addition, topographical information (altitudes, slopes) is generally available, although contours are not drawn in detail on urban‐area maps. The development of urban databases has provided a convenient means of accessing this information for the purpose of hydrological modelling. The objective of this paper is to evaluate a recent model, ‘SURF’ (semi‐urbanized runoff flow), specifically developed for coupling with a GIS based on a digital terrain representation. This model was evaluated by use of an original approach from the field of urban hydrology. A 7‐year continuous data series, which includes the dry periods, has been used as input to run the model. The principles behind the SURF model are briefly described herein. A sensitivity analysis is then performed in order to select the most influential parameters. Following the calibration stage, the model's validation is discussed. This validation is conducted not only by comparing observed and simulated hydrographs, but also by comparing the SURF model with a more conventional model in urban hydrology, called the URBAN model. It is demonstrated that the SURF model provides useful simulation results and does outperform the URBAN model. Copyright © 2000 John Wiley & Sons, Ltd.