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ADVANCING HYDROLOGIC MODEL EVALUATION AND IDENTIFICATION USING MULTIOBJECTIVE CALIBRATION,SENSITIVITY ANALYSIS, AND PARALLEL COMPUTATION
Abstract
This thesis work has comprehensively compared, developed, and implemented tools for advancing the evaluation and identification of hydrologic models including the lumped conceptual Sacramento Soil Moisture Accounting (SAC-SMA) model coupled with a snow accumulation and ablation model (SNOW-17), the distributed conceptual Research Distributed Hydrologic Model (HL-RDHM), and a semi-distributed version of the physical Penn State Integrated Hydrologic Model (PIHM). The model evaluation and identification tools addressed in this thesis include evolutionary multiobjective optimization algorithms and several sensitivity analysis methods implemented for distributed parallel computing systems. This thesis work was partitioned into four component studies. Study 1 assesses the efficiency, effectiveness, reliability, and ease-of-use of state-of-the-art evolutionary multiobjective optimization (EMO) tools when calibrating the SAC-SMA and the PIHM. This research proposes and demonstrates a formal metrics-based methodology for algorithm evaluation that clearly demonstrates their relative strengths and weaknesses. Understanding the relative strengths and weaknesses of the currently available EMO algorithms was important for Study 2 in which two parallelization schemes were developed to improve EMO algorithms’ performance in terms of their computational cost, their ability to identify high quality solutions and their robustness on a variety of applications including computer science test functions, hydrologic model calibration, and long-term groundwater monitoring design.
Beyond EMO algorithmic improvements, model evaluation and identification also requires a detailed understanding of hydrologic simulations’ sensitivities to guide model improvement, advance calibration strategies, and enhance our understanding of the key observations and processes controlling model behavior. Study 3 compares the repeatability, robustness, efficiency, and ease-of-implementation of four sensitivity analysis (SA) methods ranging from local analysis using parameter estimation software (PEST) to global approaches including regional sensitivity
analysis (RSA), analysis of variance (ANOVA), and Sobol’s method. The four SA tools were applied to the fully lumped SAC-SMA coupled with SNOW-17 using different model time steps and watershed locations. The results show that lumped model parameter sensitivities are heavily impacted by the choice of analysis method, model time interval, and local watershed characteristics. Study 4 extends Study 3 to advance distributed hydrologic model evaluation and identification using Sobol’s variance decomposition method since it was shown to be more robust and interpretable relative to the other sensitivity analysis methods tested.
Study 4 demonstrates a methodology that balances the computational constraints posed by global sensitivity analysis with the need to fully characterize the HL-RDHM’s sensitivities. The model’s sensitivities were assessed for long-term (annual and monthly) as well as short-term (events) forecasting periods. Overall, the results reveal that storage variations, spatial trends in forcing, cell-connectivity, and cell proximity to the gauged outlet are the four primary factors that control the HL-RDHM’s behavior. This study suggests that operational forecasts would benefit from the joint use of a robust sensitivity analysis framework directly integrated into new calibration methodologies. Overall, this thesis advances the analysis, formulation, and solution of hydrologic model evaluation and identification problems using multiple performance objectives and state-of-the-art algorithms implemented to exploit high-performance computing.
Table of Contents
List of Figures x
List of Tables xvi
Acknowledgments xx
Chapter 1 Introduction 1
Chapter 2 Background 5
2.1 Multiobjective terminology and tools . . . . . . . . . . . . . . . . . 5
2.2 Multiobjective model calibration . . . . . . . . . . . . . . . . . . . . 7
2.3 Parallel evolutionary multiobjective algorithms . . . . . . . . . . . . 9
2.3.1 A brief introduction to parallel computing . . . . . . . . . . 9
2.3.2 Parallel EMO algorithms . . . . . . . . . . . . . . . . . . . . 11
2.3.2.1 Master-Slave model . . . . . . . . . . . . . . . . . . 11
2.3.2.2 Multi-Population model . . . . . . . . . . . . . . . 12
2.4 Parameter sensitivity analysis . . . . . . . . . . . . . . . . . . . . . 14
Chapter 3 Study 1: Assessing state-of-the-art multiobjective
tools for hydrologic model calibration 16
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Evolution-based multiobjective search . . . . . . . . . . . . . . . . . 18
3.2.1 Epsilon Dominance NSGAII (ε-NSGAII) . . . . . . . . . . . 18
3.2.2 Strength Pareto Evolutionary Algorithm 2 (SPEA2) . . . . . 19
3.2.3 Multiobjective Shuffled Complex Evolution Metropolis
(MOSCEM-UA) . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4 Similarities and difference between the algorithms . . . . . . 21
3.3 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Case study 1: The test function suite . . . . . . . . . . . . . 23
3.3.2 Case study 2: Leaf River watershed . . . . . . . . . . . . . 23
3.3.3 Case study 3: Shale Hills watershed . . . . . . . . . . . . . . 25
3.3.3.1 Integrated model description . . . . . . . . . . . . 25
3.3.3.2 Problem formulation . . . . . . . . . . . . . . . . . 26
3.4 Description of computational experiment . . . . . . . . . . . . . . . 29
3.4.1 Algorithm configurations and parameterizations . . . . . . . 29
3.4.2 Performance metrics . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.1 Optimization results for the test function suite . . . . . . . . 32
3.5.2 Optimization results for the Leaf River case study . . . . . . 36
3.5.3 Optimization results for the Shale Hills test case . . . . . . . 40
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6.1 Relative benefits and limitations of SPEA2 . . . . . . . . . . 44
3.6.2 Relative benefits and limitations of MOSCEM-UA . . . . . . 45
3.6.3 Relative benefits and limitations of ε-NSGAII . . . . . . . . 46
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Chapter 4 Study 2: Overcoming performance limits for multiob-
jective solution tools using parallelization strategies 49
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Evolutionary multi-objective optimization search . . . . . . 52
4.2.2 The ε-NSGAII . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.3 Parallelization strategies for the ε-NSGAII . . . . . . . . . . 56
4.2.3.1 The Master-Slave ε-NSGAII . . . . . . . . . . . . . 56
4.2.3.2 The Multi-Population ε-NSGAII . . . . . . . . . . 58
4.2.4 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.4.1 Case 1: Test problem DTLZ6 . . . . . . . . . . . . 62
4.2.4.2 Case 2: Model calibration in the Leaf River watershed 63
4.2.4.3 Case 3: Long-term groundwater monitoring design 65
4.2.5 Performance metrics . . . . . . . . . . . . . . . . . . . . . . 68
4.2.6 Description of computational experiment . . . . . . . . . . . 69
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.1 Optimization results for case study 1: DTLZ6 . . . . . . . . 71
4.3.2 Optimization results for case study 2: Leaf River calibration
application . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.3 Optimization results for case study 3: Long-term monitoring
application . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Chapter 5 Study 3: Assessing sensitivity analysis methods to ad-
vance lumped watershed model identification and eval-
uation 87
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Sensitivity analysis tools and sampling schemes . . . . . . . . . . . 89
5.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.2 Sensitivity analysis tools . . . . . . . . . . . . . . . . . . . . 91
5.2.2.1 PEST . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.2.2 Regional sensitivity analysis using Latin hypercube
sampling . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.2.3 Analysis of variance using iterated fractional facto-
rial design sampling . . . . . . . . . . . . . . . . . 93
5.2.2.4 Sobol’s method using quasi-random sequence sam-
pling . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Overview of the lumped hydrologic models . . . . . . . . . . . . . . 97
5.3.1 SNOW-17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.2 Sacramento soil moisture accounting model . . . . . . . . . 99
5.4 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4.1 Juniata watershed description . . . . . . . . . . . . . . . . . 100
5.4.2 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Computational experiment . . . . . . . . . . . . . . . . . . . . . . . 103
5.5.1 Model setup and parameterizations . . . . . . . . . . . . . . 103
5.5.2 Objective functions . . . . . . . . . . . . . . . . . . . . . . . 104
5.5.3 Bootstrap confidence intervals . . . . . . . . . . . . . . . . . 104
5.5.4 Evaluation of sensitivity analysis results . . . . . . . . . . . 105
5.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.6.1 Sensitivity results for PEST . . . . . . . . . . . . . . . . . . 106
5.6.2 RSA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.6.3 Sensitivity results for ANOVA . . . . . . . . . . . . . . . . . 111
5.6.4 Sensitivity results for Sobol’s method . . . . . . . . . . . . . 115
5.6.5 Comparative summary of sensitivity methods . . . . . . . . 118
5.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Chapter 6 Study 4: Advancing the identification and evaluation of distributed rainfall-Runoff models using Sobol’s
global sensitivity analysis 127
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2 Overview of the Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) . . . . . . . . . . . . . . . . . . . . . . 130
6.2.1 Model structure . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2.2 The components of HL-RDHM . . . . . . . . . . . . . . . . 131
6.2.2.1 SNOW-17 . . . . . . . . . . . . . . . . . . . . . . . 131
6.2.2.2 Sacramento Soil Moisture Accounting (SAC-SMA)
model . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.2.2.3 Hillslope and channel routing model . . . . . . . . 134
6.3 Sobol’s sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . 135
6.3.1 Sobol’s method . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.3.2 Latin Hypercube Sampling (LHS) . . . . . . . . . . . . . . . 137
6.4 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.4.1 Juniata watershed description . . . . . . . . . . . . . . . . . 138
6.4.2 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.5 Computational experiment . . . . . . . . . . . . . . . . . . . . . . . 139
6.5.1 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.5.2 Test cases and parameterization . . . . . . . . . . . . . . . . 140
6.5.3 Sensitivity analysis implementation . . . . . . . . . . . . . . 141
6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.6.1 Annual sensitivities based on distributed forcing and lumped
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.6.2 Monthly sensitivities based on distributed forcing and lumped parameters . . . . . . . . . . . . . . . . . . . . . . . 146
6.6.3 Event sensitivities based on distributed forcing and distributed parameters . . . . . . . . . . . . . . . . . . . . . . . 149
6.6.4 Verification of event analysis sensitivity rankings . . . . . . . 153
6.7 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . 156
Chapter 7 Overview of thesis conclusions and overall contributions 160
Chapter 8 Implications and future work 165
8.1 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Appendix A Source codes for sensitivity analysis tools 171
A.1 Public functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 A.2 Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . . . . 173 A.3 Iterated Fractional Factorial Design . . . . . . . . . . . . . . . . . . 174 A.4 Sobol’s random sequence . . . . . . . . . . . . . . . . . . . . . . . . 180 A.5 Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . 181
A.6 Sobol’s method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Bibliography 187
Chapter 1 Introduction
Over the past decade the increasing availability of spatially distributed hydrometeorlogical data (e.g., precipitation, air temperature and soil properties) coupled with advances in computational resources has resulted in increasing interest in the development of spatially distributed hydrological models [e.g. [3–7] ]. Developers of distributed models seek to better simulate watershed behavior by taking advantage of spatially distributed forcing as well as distributed watershed parameters for a broader array of processes such as surface flow, groundwater flow, sediment transport, solute transport, etc. The increasing complexity of distributed models poses several challenges in terms of (1) their severe computational demands relative to lumped watershed models [8, 9] , (2) their potential for over-parameterisation [10] , and (3) their high dimensional, nonlinear parametric spaces and structural uncertainties [11] .
Because of the uncertainties associated with the data, parameters, and model structure, there is no unique parameter set which is “optimal” for the model to yield simulations which best fit the observations [12] . This makes the problem of calibrating complex hydrologic models difficult since multiple parameter combinations could lead to equivalent model performance. Furthermore, the ill-posed inverse problem [12] could generate multiple optimal sets of parameters by using different model performance measures which evaluate the “goodness-of-fit” [13] . Manual calibration of complex hydrologic models is extremely challenging because of problem complexity as well as time constraints. Consequently, efforts should be made to calibrate hydrologic models using automatic tools that can identify multiple sets of parameters associated with multiple, conflicting performance metrics such as peak flow prediction accuracy and low flow prediction accuracy.
Multiobjective hydrologic model calibration problems are characterized by their non-linearity, high dimension, multi-modality, concavity, and discontinuity [14–20] . These properties make the problems extremely difficult to solve. These problem properties have motivated several prior studies to use heuristic-based optimization, and in particular evolutionary algorithms because they have been shown to work well on nonlinear, nonconvex, and multimodal problems [e.g., [14, 21] ]. Although a majority of prior studies have focused on highly simplified conceptual rainfallrunoff applications, there are an increasing number of recent studies focusing on developing automatic calibration strategies for distributed hydrologic models [19, 20, 22, 23] .
Given the increasing computational demands posed by automatic calibration methodologies, it is of paramount importance that optimal search strategies can identify high quality solutions efficiently. There is a need to advance our ability to solve multiobjective hydrologic model calibration problems by comprehensively assessing the relative efficiency, effectiveness, reliability, and ease-of-use of currently available evolutionary multiobjective optimization (EMO) tools. This thesis contributes a comprehensive methodology for assessing EMO tools. The EMO tool assessments were used to develop new multiobjective algorithms for distributed parallel computing environments. Parallel computing is used in this thesis to maximize the performance of EMO algorithms given time and computing constraints. The parallel multiobjective solution tools developed in this research were tested on hydrologic model calibration and groundwater monitoring design applications. These applications have a legacy of multiobjective work and encompass a broad range of problem properties (continuous unconstrained and discrete constrained spaces). This thesis contributes the first parallel EMO study in the water resources area that provides insights into the algorithm’s effectiveness, reliability as well as the impact of problem difficulty for parallelizing water resources applications.
There are two important challenges currently constraining hydrologic model calibration: (1) problem complexity and (2) computational demands. Parallelization helps to address the computational demands posed by hydrologic calibration by improving the efficiency, effectiveness, and robustness of the multiobjective so3
lution tools. In the context of problem complexity, sensitivity analysis is valuable for elucidating parameters’ impacts on a model’s response [24–30] . Sensitivity analysis results can be used to decide which parameters should be the focus of model calibration efforts, or even as an analysis tool to test if the model behaves according to its underlying assumptions [e.g., [31] ]. Ultimately, sensitivity methods should serve as diagnostic tools that help to improve mathematical models and potentially help us to identify where gaps in our knowledge are most severe and are most strongly affecting prediction uncertainty. Efforts should be made to fill the gaps in terms of data collection and understanding of the model. Therefore, this thesis research focuses both on the solution as well as the formulation of multiobjective calibration problems. Problem formulation was addressed by investigating effective sensitivity analysis tools that can be utilized to reduce the size and complexity of multiobjective calibration problems. The goal of sensitivity analysis is to reduce the search space by identifying the key parameters that control a hydrologic model’s responses.
Although there are a variety of sensitivity analysis approaches, very little guidance is available regarding sensitivity method selection. In addition, to date, the computational demands and spatial complexity of distributed hydrologic models have limited our ability to understand their parametric interactions and sensitivities. The limited body of recent literature applying sensitivity analysis to spatially distributed hydrologic models highlights the importance and significant challenges posed by this problem [9, 11, 30, 32–34] . Therefore, in this thesis, sensitivity analysis is conducted for both lumped hydrologic models and a distributed hydrologic model. The lumped hydrologic model analysis in this thesis seeks to comprehensively evaluate state-of-the-art sensitivity analysis tools with the goal of clarifying their relative advantages and drawbacks. The comparison study is implemented for lumped models due to their reduced computation demands relative to distributed models. The distributed model sensitivity analysis of this thesis utilizes the most effective sensitivity analysis tool identified via the lumped model sensitivity analysis to characterize the spatial and temporal trends of the Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM)’s parametric sensitivities and to identify the major factors that control the model’s behavior.
This thesis research has been divided into four studies. Study 1 aims at comprehensively assessing the efficiency, effectiveness, reliability, and ease-of-use of current evolutionary multiobjective optimization (EMO) tools for water resources engineering applications. Study 2 seeks to improve the EMO algorithms’ abilities in terms of their computational cost, their attained solution quality and robustness by using parallel computation. Study 3 focuses on identifying an effective sensitivity analysis tool that can be used to reduce the size of the parameter set that must be considered when evaluating and identifying lumped hydrologic models. Study 4 extends Study 3 by using the best performing global sensitivity analysis tool to analyze a computationally intensive distributed hydrologic model to elucidate its temporal and spatial parametric controls. The EMO and sensitivity analysis tools have been developed to exploit parallel computation.
In this thesis, Chapter 2 provides an overview of prior work in the areas of EMO algorithms, multiobjective calibrations, parallel EMO algorithms, and parametric sensitivity analysis. Chapters 3, 4, 5, and 6 discuss the details of studies 1, 2, 3, and 4 respectively. The contributions and overall conclusions of the thesis are presented in chapter 7. Chapter 8 proposes future work.
ADVANCING HYDROLOGIC MODEL EVALUATION AND IDENTIFICATION USING MULTIOBJECTIVE CALIBRATION,SENSITIVITY ANALYSIS, AND PARALLEL COMPUTATION
