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.     

River flow modelling: comparison of performance and evaluation of uncertainty using data-driven models and conceptual hydrological model

Hydrological and statistical models are playing an increasing role in hydrological forecasting, particularly for river basins with data of different temporal scales. In this study, statistical models, e.g. artificial neural networks, adaptive network-based fuzzy inference system, genetic programming, least squares support vector machine, multiple linear regression, were developed, based on parametric optimization methods such as particle swarm optimization (PSO), genetic algorithm (GA), and data-preprocessing techniques such as wavelet decomposition (WD) for river flow modelling using daily streamflow data from four hydrological stations for a period of 1954–2009. These models were used for 1-, 3- and 5-day streamflow forecasting and the better model was used for uncertainty evaluation using bootstrap resampling method. Meanwhile, a simple conceptual hydrological model GR4J was used to evaluate parametric uncertainty based on generalized likelihood uncertainty estimation method. Results indicated that: (1) GA and PSO did not help improve the forecast performance of the model. However, the hybrid model with WD significantly improved the forecast performance; (2) the hybrid model with WD as a data preprocessing procedure can clarify hydrological effects of water reservoirs and can capture peak high/low flow changes; (3) Forecast accuracy of data-driven models is significantly influenced by the availability of streamflow data. More human interferences from the upper to the lower East River basin can help to introduce greater uncertainty in streamflow forecasts; (4) The structure of GR4J may introduce larger parametric uncertainty at the Longchuan station than at the Boluo station in the East river basin. This study provides a theoretical background for data-driven model-based streamflow forecasting and a comprehensive view about data and parametric uncertainty in data-scarce river basins.     

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.     

Errors and uncertainty in physically-based rainfall-runoff modelling of catchment change effects

The error in physically-based rainfall-runoff modelling is broken into components, and these components are assigned to three groups: (1) model structure error, associated with the model’s equations; (2) parameter error, associated with the parameter values used in the equations; and (3) run time error, associated with rainfall and other forcing data. The error components all contribute to “integrated” errors, such as the difference between simulated and observed runoff, but their individual contributions cannot usually be isolated because the modelling process is complex and there is a lack of knowledge about the catchment and its hydrological responses. A simple model of the Slapton Wood Catchment is developed within a theoretical framework in which the catchment and its responses are assumed to be known perfectly. This makes it possible to analyse the contributions of the error components when predicting the effects of a physical change in the catchment. The standard approach to predicting change effects involves: (1) running “unchanged” simulations using current parameter sets; (2) making adjustments to the sets to allow for physical change; and (3) running “changed” simulations. Calibration or uncertainty-handling methods such as GLUE are used to obtain the current sets based on forcing and runoff data for a calibration period, by minimising or creating statistical bounds for the “integrated” errors in simulations of runoff. It is shown that current parameter sets derived in this fashion are unreliable for predicting change effects, because of model structure error and its interaction with parameter error, so caution is needed if the standard approach is to be used when making management decisions about change in catchments.     

Identifiability analysis: towards constrained equifinality and reduced uncertainty in a conceptual model

Abstract

Different sets of parameters and conceptualizations of a basin can give equally good results in terms of predefined objective functions. Therefore, a need exists to tackle equifinality and quantify the uncertainty bands of a model. In this paper we use the concepts of equifinality, identifiability and uncertainty to propose a simple method aimed at constraining the equifinal parameters and reducing the uncertainty bands of model outputs, and obtaining physically possible and reasonable models. Additionally, the uncertainty of equifinal solutions is quantified to estimate the amount by which output uncertainty can be reduced by knowing how to discard most of the equifinal solutions of a model. As a study case, a conceptual model of the Chillán basin in Chile is carried out. From the study it is concluded that using identifiability analysis makes it possible to constrain equifinal solutions with reduced uncertainty and realistic models, resulting in a framework that can be recommended to practitioners, especially due to the simplicity of the method.     

Assessing the relative importance of parameter and forcing uncertainty and their interactions in conceptual hydrological model simulations

Predictions of river flow dynamics provide vital information for many aspects of water management including water resource planning, climate adaptation, and flood and drought assessments. Many of the subjective choices that modellers make including model and criteria selection can have a significant impact on the magnitude and distribution of the output uncertainty. Hydrological modellers are tasked with understanding and minimising the uncertainty surrounding streamflow predictions before communicating the overall uncertainty to decision makers. Parameter uncertainty in conceptual rainfall-runoff models has been widely investigated, and model structural uncertainty and forcing data have been receiving increasing attention. This study aimed to assess uncertainties in streamflow predictions due to forcing data and the identification of behavioural parameter sets in 31 Irish catchments. By combining stochastic rainfall ensembles and multiple parameter sets for three conceptual rainfall-runoff models, an analysis of variance model was used to decompose the total uncertainty in streamflow simulations into contributions from (i) forcing data, (ii) identification of model parameters and (iii) interactions between the two. The analysis illustrates that, for our subjective choices, hydrological model selection had a greater contribution to overall uncertainty, while performance criteria selection influenced the relative intra-annual uncertainties in streamflow predictions. Uncertainties in streamflow predictions due to the method of determining parameters were relatively lower for wetter catchments, and more evenly distributed throughout the year when the Nash-Sutcliffe Efficiency of logarithmic values of flow (lnNSE) was the evaluation criterion.     

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.     

Investigating the uncertainty and transferability of parameters in SWAT model under climate change

ABSTRACT

There is an implicit assumption in most work that the parameters calibrated based on observations remain valid for future climatic conditions. However, this might not be true due to parameter instability. This paper investigates the uncertainty and transferability of parameters in a hydrological model under climate change. Parameter transferability is investigated with three parameter sets identified for different climatic conditions, which are: wet, intermediate and dry. A parameter set based on the baseline period (1961–1990) is also investigated for comparison. For uncertainty analysis, a k-simulation set approach is proposed instead of employing the traditional optimization method which uses a single best-fit parameter set. The results show that the parameter set from the wet sub-period performs the best when transferred into wet climate condition, while the parameter set from the baseline period is the most appropriate when transferred into dry climate condition. The largest uncertainty of simulated daily high flows for 2011–2040 is from the parameter set trained in the dry sub-period, while that of simulated daily medium and low flows lies in the parameter set from the intermediate calibration sub-period. For annual changes in the future period, the uncertainty with the parameter set from the intermediate sub-period is the largest, followed by the wet sub-period and dry sub-period. Compared with high and medium flows/runoffs, the uncertainty of low flows/runoffs is much smaller for both simulated daily flows and annual runoffs. For seasonal runoffs, the largest uncertainty is from the intermediate sub-period, while the smallest is from the dry sub-period. Apart from that, the largest uncertainty can be observed for spring runoffs and the lowest one for autumn runoffs. Compared with the traditional optimization method, the k-simulation set approach shows many more advantages, particularly being able to provide uncertainty information to decision support for watershed management under climate change.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR not assigned     

Sensitivity analysis of prior model probabilities and the value of prior knowledge in the assessment of conceptual model uncertainty in groundwater modelling

A key point in the application of multi‐model Bayesian averaging techniques to assess the predictive uncertainty in groundwater modelling applications is the definition of prior model probabilities, which reflect the prior perception about the plausibility of alternative models. In this work the influence of prior knowledge and prior model probabilities on posterior model probabilities, multi‐model predictions, and conceptual model uncertainty estimations is analysed. The sensitivity to prior model probabilities is assessed using an extensive numerical analysis in which the prior probability space of a set of plausible conceptualizations is discretized to obtain a large ensemble of possible combinations of prior model probabilities. Additionally, the value of prior knowledge about alternative models in reducing conceptual model uncertainty is assessed by considering three example knowledge states, expressed as quantitative relations among the alternative models. A constrained maximum entropy approach is used to find the set of prior model probabilities that correspond to the different prior knowledge states. For illustrative purposes, a three‐dimensional hypothetical setup approximated by seven alternative conceptual models is employed. Results show that posterior model probabilities, leading moments of the predictive distributions and estimations of conceptual model uncertainty are very sensitive to prior model probabilities, indicating the relevance of selecting proper prior probabilities. Additionally, including proper prior knowledge improves the predictive performance of the multi‐model approach, expressed by reductions of the multi‐model prediction variances by up to 60% compared with a non‐informative case. However, the ratio between‐model to total variance does not substantially decrease. This suggests that the contribution of conceptual model uncertainty to the total variance cannot be further reduced based only on prior knowledge about the plausibility of alternative models. These results advocate including proper prior knowledge about alternative conceptualizations in combination with extra conditioning data to further reduce conceptual model uncertainty in groundwater modelling predictions. Copyright © 2009 John Wiley & Sons, Ltd.     

Development of conceptual semi-distributed hydrological models and estimation of their parameters with the aid of GIS

Abstract

Conceptual semi-distributed hydrological models are developed for a limited consideration of spatial heterogeneity of hydrological characteristics within a river basin. This heterogeneity can be described by area distribution functions of hydrological characteristics which can be estimated in a most effective way by a Geographical Information System (GIS). It is shown how the application of a GIS can support the development and the calibration of a conceptual hydrological model. GIS information is used to establish the criteria for sub-division of the river basin and for estimation of model structures (especially for further horizontal divisions of each basin into more homogeneous parts). That information is also used for estimation of basin characteristics and their differences between sub-basins as a support for parameter calibration by optimization. The methodology presented can be used for the development of a model structure on an objective basis and for model calibration which considers the physical explanation of model parameters. The proposed method was successfully applied to a river basin within the Mosel basin (Germany).     

两种识别结构模态参数时域法的对比研究

模态参数是有效评估结构安全状况的关键参数,在结构抗震加固和健康诊断领域得到广泛应用。与频域法相比较,时域法直接利用实测的振动信号识别模态参数,不需要进行频域变换,减少数据处理带来的误差,并且可以实现大型结构的在线识别,真实地反应结构的现状。以同济大学12层钢筋混凝土标准框架振动台模型试验完整数据为对象,在详细介绍ITD法和复指数法2种时域法理论的基础上,通过编程选取结构不同测点的振动加速度时程数据,识别了小震和强震工况下12层钢筋混凝土框架模型振动台试验模型的模态频率和阻尼比,并结合移动谱识别结构模态参数的时变特性。结果表明:ITD法和复指数法可有效地识别结构的模态参数,自振频率的识别精度较高,而阻尼比的离散度较大;小震工况频率变化值不大,而强震工况频率值较初始时刻有明显的下降,这与试验现象是吻合的,进一步说明移动谱与这2种时域法相结合可以反应结构在塑性阶段的参数时变特性。     

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.     

Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models

This paper concerns efficient uncertainty quantification techniques in inverse problems for Richards’ equation which use coarse-scale simulation models. We consider the problem of determining saturated hydraulic conductivity fields conditioned to some integrated response. We use a stochastic parameterization of the saturated hydraulic conductivity and sample using Markov chain Monte Carlo methods (MCMC). The main advantage of the method presented in this paper is the use of multiscale methods within an MCMC method based on Langevin diffusion. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically sparse grid collocation methods. We show that the proposed algorithms dramatically reduce the computational cost associated with traditional Langevin MCMC methods while providing similar sampling performance.     

地震活动性参数全时空扫描动态寻优预报模型

选取10种物理意义清楚、独立性较好的地震活动性参数,以最大限度地提高预报效能为目标,采用全时空扫描方法建立动态寻优预报模型。研究表明,地震活动性参数动态寻优预报模型,在空间上,客观地反映了区域构造活动的差异性;在时间上,完整地反映了区域地震活动的涨落;可以有效地剔除背景干扰,提高地震异常识别率,避免预报的随机性和盲目性。     

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.     

Two conceptual models of displacement transfer and examples

The concept of displacement transfer[1] was initially utilized by Dahlstrom (1970) to explain the relation- ships of overlapping thrusts in the Canadian Rockies wherein the displacement on one thrust is transferred to another, but the total displacement is still held con- stant along trend. Displacement transfer, which may exist in compressional[2] as well as tensile environ-ments[3], is a familiar kinematic mechanism that keeps the magnitude of deformation steady along trend in the linear str…     

On the information content of forest transpiration measurements for identifying canopy conductance model parameters

Generally, forest transpiration models contain model parameters that cannot be measured independently and therefore are tuned to fit the model results to measurements. Only unique parameter estimates with high accuracy can be used for extrapolation in time or space. However, parameter identification problems may occur as a result of the properties of the data set. Time‐series of environmental conditions, which control the forest transpiration, may contain periods with redundant or coupled information, so called collinearity, and other combinations of conditions may be measured only with difficulty or incompletely. The aim of this study is to select environmental conditions that yield a unique parameter set of a canopy conductance model. The parameter identification method based on localization of information (PIMLI) was used to calculate the information content of every individual artificial transpiration measurement. It is concluded that every measurement has its own information with respect to a parameter. Independent criteria were assessed to localize the environmental conditions, which contain measurements with most information. These measurements were used in separate subdata sets to identify the parameters. The selected measurements do not overlap and the accuracies of the parameter estimates are maximized. Measurements that were not selected do not contain additional information that can be used to further maximize the parameter accuracy. Thereupon, the independent criteria were used to select eddy correlation measurements and parameters were identified with only the selected measurements. It is concluded that, for this forest and data set, PIMLI identifies a unique parameter set with high accuracy, whereas conventional calibrations on subdata sets give non‐unique parameter estimates. Copyright © 2001 John Wiley & Sons, Ltd.     

一种震相拾取误差的自动判别和计算方法

本文给出了一个主要用于深地震测深数据的震相识别误差（不确定性）的判别和计算方法.该方法集中讨论从记录截面拾取震相这一过程所引起的判别误差.以震相前后一定时窗内的地震记录振幅的均方根之比为判别依据,找出误差分布范围并给出走时误差与振幅比的分级相关函数.由此,当震相确定后,计算程序将根据记录数据自动算出识别误差.实践证明该方法不仅更加客观真实、方便快捷,而且为今后震相提取工作的进一步科学规范打下了基础.     

地震动强度参数估计的可解释性与不确定度机器学习模型

准确预测地震动强度参数(峰值加速度PGA、峰值速度PGV等)对于震后应急和地震危险性概率分析至关重要.作为地震动强度参数预测的新手段, 机器学习算法具有优势, 但也存在可解释性差和难给出预测结果不确定度的问题.本文提出采用自然梯度提升(NGBoost)算法在预测结果的同时提供其不确定度, 并结合SHAP值解释机器学习模型.基于NGA-WEST2强震动数据库, 本文训练出了适合预测活跃构造区地壳地震的PGA和PGV概率密度分布的机器学习模型.测试集数据PGA和PGV的预测值与真实值的相关系数可达0.972和0.984, 并可给出预测结果的合理概率密度分布.通过SHAP值, 我们从数据角度弄清了各输入特征(矩震级M_W、Joyner-Boore断层距R_jb、地下30 m平均S波速度V_S30、滑动角Rake、断层倾角Dip、断层顶部深度Z_TOR和V_S达到2.5 km·s^-1时的深度Z_2.5)对机器学习模型预测结果的影响机理.SHAP值显示, 基于NGBoost算法的机器学习模型的预测方式基本与物理原理相符, 说明了机器学习模型的合理性.SHAP值还揭示出一些以往研究忽视的现象: (1)对于活跃构造区地壳地震, 破裂深度较浅(Z_TOR＜~5 km)时, Z_TOR的SHAP值低于破裂深度较深(Z_TOR＞~5 km)时的值, 表明浅部破裂可能主要受速度强化控制, 地震动强度较弱.并且Z_TOR的SHAP值随Z_TOR值增大而减小, 表明地震动强度可能还受破裂深度变化引起的几何衰减变化影响; (2)破裂深度较深时, Z_TOR的SHAP值随Z_TOR值增大而增大, 表明深部破裂的地震动强度可能受和破裂深度变化相关的应力降或品质因子Q的变化影响; (3)Z_2.5较小(Z_2.5＜~1 km)时, Z_2.5的SHAP值的变化规律对于PGA和PGV预测是相反的, 表明加速度和速度频率不同, 受浅层沉积物厚度变化引起的共振频率变化影响不同.