scholarly journals Practical Experience of Sensitivity Analysis: Comparing Six Methods, on Three Hydrological Models, with Three Performance Criteria

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 1062 ◽  
Author(s):  
Anqi Wang ◽  
Dimitri P. Solomatine
Keyword(s):  
Sensitivity Analysis ◽  
Practical Experience ◽  
Distribution Functions ◽  
Ease Of Use ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Hydrological Models ◽  
Sensitivity Indices ◽  
Kolmogorov Smirnov

Currently, practically no modeling study is expected to be carried out without some form of Sensitivity Analysis (SA). At the same time, there is a large number of various methods and it is not always easy for practitioners to choose one. The aim of this paper is to briefly review main classes of SA methods, and to present the results of the practical comparative analysis of applying them. Six different global SA methods: Sobol, eFAST (extended Fourier Amplitude Sensitivity Test), Morris, LH-OAT, RSA (Regionalized Sensitivity Analysis), and PAWN are tested on three conceptual rainfall-runoff models with varying complexity: (GR4J, Hymod, and HBV) applied to the case study of Bagmati basin (Nepal). The methods are compared with respect to effectiveness, efficiency, and convergence. A practical framework of selecting and using the SA methods is presented. The result shows that, first of all, all the six SA methods are effective. Morris and LH-OAT methods are the most efficient methods in computing SI and ranking. eFAST performs better than Sobol, and thus it can be seen as its viable alternative for Sobol. PAWN and RSA methods have issues of instability, which we think are due to the ways Cumulative Distribution Functions (CDFs) are built, and using Kolmogorov–Smirnov statistics to compute Sensitivity Indices. All the methods require sufficient number of runs to reach convergence. Difference in efficiency of different methods is an inevitable consequence of the differences in the underlying principles. For SA of hydrological models, it is recommended to apply the presented practical framework assuming the use of several methods, and to explicitly take into account the constraints of effectiveness, efficiency (including convergence), ease of use, and availability of software.

scholarly journals Practical experience and framework for sensitivity analysis of hydrological models: six methods, three models, three criteria

2018 ◽  
Author(s):  
Anqi Wang ◽  
Dimitri P. Solomatine
Keyword(s):  
Sensitivity Analysis ◽  
Comparative Analysis ◽  
Practical Experience ◽  
Ease Of Use ◽  
Hydrological Models ◽  
Rainfall Runoff ◽  
Sensitivity Indices ◽  
Kolmogorov Smirnov ◽  
Better Than

Abstract. Sensitivity Analysis (SA) and Uncertainty Analysis (UA) are important steps for better understanding and evaluation of hydrological models. The aim of this paper is to briefly review main classes of SA methods, and to presents the results of the practical comparative analysis of applying them. Six different global SA methods: Sobol, eFAST, Morris, LH-OAT, RSA and PAWN are tested on three conceptual rainfall-runoff models with varying complexity: (GR4J, Hymod and HBV) applied to the case study of Bagmati basin (Nepal), and also initially tested on the case of Dapoling-Wangjiaba catchment in China. The methods are compared with respect to effectiveness, efficiency and convergence. A practical framework of selecting and using the SA methods is presented. The result shows that, first of all, all the six SA methods are effective. Morris and LH-OAT methods are the most efficient methods in computing SI and ranking. eFAST performs better than Sobol, thus can be seen as its viable alternative for Sobol. PAWN and RSA methods have issues of instability which we think are due to the ways CDFs are built, and using Kolmogorov-Smirnov statistics to compute Sensitivity Indices. All the methods require sufficient number of runs to reach convergence. Difference in efficiency of different methods is an inevitable consequence of the differences in the underlying principles. For SA of hydrological models, it is recommended to apply the presented practical framework assuming the use of several methods, and to explicitly take into account the constraints of effectiveness, efficiency (including convergence), ease of use, as well as availability of software.

SENSITIVITY ANALYSIS OF NONLINEAR MODELS TO PARAMETER PERTURBATIONS FOR SMALL SIZE ENSEMBLES OF MODEL OUTPUTS

2011 ◽  
Vol 21 (12) ◽  
pp. 3589-3609 ◽  
Author(s):  
L. M. IVANOV ◽  
R. T. TOKMAKIAN
Keyword(s):  
Sensitivity Analysis ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
A Priori ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
Model Sensitivity ◽  
Climate System Model ◽  
Sensitivity Indices

A new technique for nonlinear sensitivity analysis of geophysical models for small size ensembles of model outputs has been developed. Such an analysis utilizes the following metrics: (a) Sobol–Saltelli sensitivity indices and cumulative distribution functions if perturbations of model parameters are random, and (b) a Hartley-like measure if perturbations of model parameters are nonrandom and parametrized through fuzzy sets. The indices and the Hartley-like measure allow for ranging model parameters along their significance to the model output. Our calculations demonstrate that accurate estimates of the sensitivity indices are possible even if an ensemble of random perturbations contains considerably less than 100 members. Some calculations were successfully provided for random ensembles with 20–30 members only but, in general 50–100 member ensembles are required to get robust and significant estimations of model sensitivity. The fuzzy set concept allows for robust estimations for small size nonrandom ensembles of model outputs (50–100 members) and accounts for additional a priori information on model sensitivity coming from different sources. The Lorenz 63 model (a few degrees of freedom) and the ocean component (POP) of the Community Climate System Model (CCSM3) (several thousand degrees of freedom) are used to illustrate the sensitivity analysis based on this approach.

Sensitivity analysis of surface runoff parameters for hydrological modeling of periurban ungauged basin  

2021 ◽  
Author(s):  
Irene Di Cicco ◽  
Carlo Giudicianni ◽  
Armando Di Nardo ◽  
Roberto Greco
Keyword(s):  
Land Use ◽  
Sensitivity Analysis ◽  
Water Resources ◽  
Surface Runoff ◽  
Model Structure ◽  
Hydrological Models ◽  
Ungauged Basins ◽  
Model Simplification ◽  
Sensitivity Indices ◽  
Input Parameters

<p>Rapid human-induced changes, such as climate change, population growth and rapid urbanization, are putting enormous stress on water resources. An accurate estimate of available water resources is a prerequisite for sustainable water resources planning and management. For gauged basins, historical records of hydrological observations are available, but for ungauged basins, the assessment of water availability is a challenging task. Therefore, the major focus of studies in ungauged basins is the development of appropriate tools that can accurately quantify hydrologic responses under various land use and climatic conditions. The reduction of the number of unknown parameters to be estimated is a key aspect in the development of hydrological models for ungauged basins.</p><p>This work is part of these issues and proposes an approach to reduce the complexity of hydrological models that include substantial uncertainties about the input data, initial and boundary conditions, model structure and parameters, owing to lack of data (i.e. for ungauged basins) and poor knowledge of hydrological response mechanisms. The case study of a basin of the District of Licola, located in the territory of the municipality of Giugliano, a city near Naples (southern Italy) is analyzed. Originally devoted to agriculture and grazing, it has been affected in the last decades by intense urbanization, which caused an increase in the impermeability of the soil cover. The increase in residential, commercial and production buildings has changed the functioning of the drainage network canals, compared to the original conditions, causing an increase in the frequency of flooding in the area. The semi-distributed hydrological model SWMM is adopted, which allows the subdivision of the basin in sub-basins according to land use and soil data.</p><p>Sensitivity Analysis (SA) is an effective approach to model simplification, providing an assessment of how much each input / parameter contributes to the output uncertainty. In general, SA is an essential part of model development, reducing uncertainties that have negative effects on the accuracy and reliability of simulated results. Specifically, in this study the SA is carried out with a method based on the decomposition of the variance of the peak flow and runoff volume, to quantitatively evaluate the contributions of single uncertain inputs/parameters that characterize the surface runoff with respect to different rainfall events, for both pervious and impervious areas. To this aim, the Fourier Amplitude Sensitivity Test (FAST) is implemented. This method allows quantifying not only the “main effect” of variance, but also provides the Total Sensitivity Indices (TSI), defined as the sum of all the sensitivity indices for each parameter (including the effects of the interaction with other uncertain parameters).</p><p>The research objectives aims at: (i) increased understanding of the relationships between input and output variables in a complex hydrological system; (ii) reduction of model uncertainty, through the identification of input parameters mostly contributing to output variability and should therefore be the focus of sensitivity analysis; (iii) model simplification, fixing  the values of input parameters that have little effect on the output, and identifying and removing redundant parts of the model structure.</p>

scholarly journals From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1720 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Structural Reliability ◽  
Building Design ◽  
Design Standards ◽  
Average Value ◽  
Sensitivity Indices ◽  
Before And After ◽  
Input Variables ◽  
Total Sensitivity

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability Pf of a structure. Although the reliability is usually expressed via Pf, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as Pf-oriented SA or local SA based on Pf derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for Pf ranging from 9.35 × 10−8 to 1–1.51 × 10−8. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small Pf. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article.

scholarly journals Time-Series Mapping of PM10Concentration Using Multi-Gaussian Space-Time Kriging: A Case Study in the Seoul Metropolitan Area, Korea

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
No-Wook Park
Keyword(s):  
Time Series ◽  
Metropolitan Area ◽  
Space Time ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Elementary Functions ◽  
Seoul Metropolitan Area ◽  
Deterministic Trend ◽  
Gaussian Space

This paper presents space-time kriging within a multi-Gaussian framework for time-series mapping of particulate matter less than 10 μm in aerodynamic diameter (PM10) concentration. To account for the spatiotemporal autocorrelation structures of monitoring data and to model the uncertainties attached to the prediction, conventional multi-Gaussian kriging is extended to the space-time domain. Multi-Gaussian space-time kriging presented in this paper is based on decomposition of the PM10concentrations into deterministic trend and stochastic residual components. The deterministic trend component is modelled and regionalized using the temporal elementary functions. For the residual component which is the main target for space-time kriging, spatiotemporal autocorrelation information is modeled and used for space-time mapping of the residual. The conditional cumulative distribution functions (ccdfs) are constructed by using the trend and residual components and space-time kriging variance. Then, the PM10concentration estimate and conditional variance are empirically obtained from the ccdfs at all locations in the study area. A case study using the monthly PM10concentrations from 2007 to 2011 in the Seoul metropolitan area, Korea, illustrates the applicability of the presented method. The presented method generated time-series PM10concentration mapping results as well as supporting information for interpretations, and led to better prediction performance, compared to conventional spatial kriging.

scholarly journals Hierarchical Sensitivity Analysis for Large Scale Process-based Hydrological Modeling with Application in an Amazonian Watershed

2019 ◽  
Author(s):  
Haifan Liu ◽  
Heng Dai ◽  
Jie Niu ◽  
Bill X. Hu ◽  
Han Qiu ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Overland Flow ◽  
Global Sensitivity Analysis ◽  
Hydrologic Model ◽  
Model Parameters ◽  
Hydrological Models ◽  
Global Sensitivity ◽  
Uncertainty Sources ◽  
Sensitivity Indices

Abstract. Sensitivity analysis is an effective tool for identifying important uncertainty sources and improving model calibration and predictions, especially for integrated systems with heterogeneous parameter inputs and complex processes coevolution. In this work, an advanced hierarchical global sensitivity analysis framework, which integrates a hierarchical uncertainty framework and a variance-based global sensitivity analysis, was implemented to quantitatively analyze several uncertainties of a three-dimensional, process-based hydrologic model (PAWS). The uncertainty sources considered include model parameters, model structures (with/without overland flow module), and climate forcing. We apply the approach in a ~ 9000 km2 Amazon catchment modeled at 1 km resolution to provide a demonstration of multiple uncertainty source quantification using a large-scale process-based hydrologic model. The sensitivity indices are assessed based on three important hydrologic outputs: evapotranspiration (ET), ground evaporation (EG), and groundwater contribution to streamflow (QG). It is found that, in general, model parameters (especially those within the streamside model grid cells) are the most important uncertainty contributor for all sensitivity indices. In addition, the overland flow module significantly contributes to model predictive uncertainty. These results can assist model calibration and provide modelers a better understanding of the general sources of uncertainty in predictions of complex hydrological systems in Amazonia. We demonstrated a pilot example for comprehensive global sensitivity analysis of large-scale complex hydrological models in this research. The hierarchical sensitivity analysis methodology used is mathematically rigorous and can be applied to a wide range of large-scale hydrological models with various sources of uncertainty.

scholarly journals Analytical formulas of PFD and PFH calculation for systems with nonconstant failure rates

2017 ◽  
Vol 231 (4) ◽  
pp. 373-382 ◽  
Author(s):  
Elena Rogova ◽  
Gabriel Lodewijks ◽  
Mary Ann Lundteigen
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Failure Rates ◽  
Failure Rate Function ◽  
Analytical Formulas ◽  
Exact Calculations ◽  
Definition Of

Most analytical formulas developed for the PFD and PFH calculation assume a constant failure rate. This assumption does not necessarily hold for system components that are affected by wear. This article presents methods of analytical calculations of PFD and PFH for an M-out-of-N redundancy architecture with nonconstant failure rates and demonstrates its application in a simple case study. The method for PFD calculation is based on the ratio between cumulative distribution functions and includes forecasting of PFD values with a possibility of update of failure rate function. The approach for the PFH calculation is based on simplified formulas and the definition of PFH. In both methods, a Weibull distribution is used for characteristics of the system behavior. The PFD and PFH values are obtained for low, moderate and high degradation effects and compared with the results of exact calculations. Presented analytical formulas are a useful contribution to the reliability assessment of M-out-of-N systems.

scholarly journals Hierarchical sensitivity analysis for a large-scale process-based hydrological model applied to an Amazonian watershed

2020 ◽  
Vol 24 (10) ◽  
pp. 4971-4996
Author(s):  
Haifan Liu ◽  
Heng Dai ◽  
Jie Niu ◽  
Bill X. Hu ◽  
Dongwei Gui ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Global Sensitivity Analysis ◽  
Hydrological Models ◽  
Climate Scenarios ◽  
Analysis Method ◽  
Global Sensitivity ◽  
Uncertainty Sources ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method

Abstract. Sensitivity analysis methods have recently received much attention for identifying important uncertainty sources (or uncertain inputs) and improving model calibrations and predictions for hydrological models. However, it is still challenging to apply the quantitative and comprehensive global sensitivity analysis method to complex large-scale process-based hydrological models (PBHMs) because of its variant uncertainty sources and high computational cost. Therefore, a global sensitivity analysis method that is capable of simultaneously analyzing multiple uncertainty sources of PBHMs and providing quantitative sensitivity analysis results is still lacking. In an effort to develop a new tool for overcoming these weaknesses, we improved the hierarchical sensitivity analysis method by defining a new set of sensitivity indices for subdivided parameters. A new binning method and Latin hypercube sampling (LHS) were implemented for estimating these new sensitivity indices. For test and demonstration purposes, this improved global sensitivity analysis method was implemented to quantify three different uncertainty sources (parameters, models, and climate scenarios) of a three-dimensional large-scale process-based hydrologic model (Process-based Adaptive Watershed Simulator, PAWS) with an application case in an ∼ 9000 km2 Amazon catchment. The importance of different uncertainty sources was quantified by sensitivity indices for two hydrologic outputs of interest: evapotranspiration (ET) and groundwater contribution to streamflow (QG). The results show that the parameters, especially the vadose zone parameters, are the most important uncertainty contributors for both outputs. In addition, the influence of climate scenarios on ET predictions is also important. Furthermore, the thickness of the aquifers is important for QG predictions, especially in main stream areas. These sensitivity analysis results provide useful information for modelers, and our method is mathematically rigorous and can be applied to other large-scale hydrological models.

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