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Sensitivity Analysis in Earth Observation Modelling

Sensitivity Analysis in Earth Observation Modelling

Copyright

Dedication

Contents

List of Contributors

Preface

ABOUT THE COVER

1 - INTRODUCTION TO SA IN EARTH OBSERVATION (EO)

1 - OVERVIEW OF SENSITIVITY ANALYSIS METHODS IN EARTH OBSERVATION MODELING

1. INTRODUCTION

1.1 DEFINING THE MODEL OUTPUTS AND INPUTS FOR SENSITIVITY ANALYSIS

1.1.1 Defining Factor (or Parametric) Uncertainty

2. LOCAL SENSITIVITY ANALYSIS

2.1 CORRELATION ANALYSIS

2.2 REGRESSION ANALYSIS

3. GLOBAL SENSITIVITY ANALYSIS

3.1 ONE-AT-A-TIME SENSITIVITY ANALYSIS METHODS

3.2 THE MORRIS METHOD FOR FACTOR SCREENING

3.3 VARIANCE-BASED SENSITIVITY ANALYSIS

3.4 SAMPLING METHODS FOR GLOBAL SENSITIVITY ANALYSIS

3.4.1 Random Sampling

3.4.2 Stratified Sampling and the Latin Hypercube

3.4.3 Sampling for Sensitivity Indices

3.5 SURROGATE MODELS FOR GLOBAL SENSITIVITY ANALYSIS

3.5.1 Generalized Linear Modeling

3.5.2 Neural Networks

3.5.3 Direct Sensitivity Analysis of Surrogate Models

3.6 POLYNOMIAL CHAOS

3.7 GAUSSIAN PROCESS AND BAYES LINEAR EMULATION

4. GRAPHICAL METHODS FOR GLOBAL SENSITIVITY ANALYSIS

4.1 SCATTER PLOTS

4.2 PLOTTING THE RESPONSE SURFACE

4.3 PLOTTING THE SENSITIVITY INDICES

5. CONCLUSIONS

REFERENCES

2 - MODEL INPUT DATA UNCERTAINTY AND ITS POTENTIAL IMPACT ON SOIL PROPERTIES

1. INTRODUCTION

2. A WORLD OF MODELS – HOW CAN THEY BE CLASSIFIED?

3. CAN WE TRUST MODELS? – MODEL ACCURACY AND THEIR SENSITIVITY TO INPUT DATA UNCERTAINTY

4. SELECTING THE MOST APPROPRIATE MODEL

5. WHY AND HOW TO ACCOUNT FOR MODELING UNCERTAINTIES CAUSED BY DIFFERENT INPUT DATA SOURCES

6. ASSESSING SENSITIVITY OF ENVIRONMENTAL MODELS

7. HOW SOIL TEXTURE MEASURED WITH VISIBLE-NEAR-INFRARED SPECTROSCOPY AFFECTS HYDROLOGICAL MODELING: A CASE STUDY

7.1 STUDY SITES AND INSTRUMENTS

7.2 SOIL SAMPLES

7.3 CHEMOMETRICS

7.4 IMPACT OF CHEMOMETRIC METHOD ON SOIL PREDICTION

7.5 DIFFERENT INSTRUMENTS, DIFFERENT SOIL PREDICTIONS? WHAT WAS FINALLY THE BEST SOIL PREDICTION ACCURACY?

7.6 WHAT DOES THIS FINALLY MEAN FOR OUR ENVIRONMENTAL MODELING?

8. WHAT DID WE LEARN?

REFERENCES

2 - LOCAL SA METHODS: CASE STUDIES

3 - LOCAL SENSITIVITY ANALYSIS OF THE LANDSOIL EROSION MODEL APPLIED TO A VIRTUAL CATCHMENT

1. INTRODUCTION

2. MATERIALS AND METHODS

2.1 MODEL DESCRIPTION

2.2 SENSITIVITY ANALYSIS

2.2.1 Parameters

2.2.2 Virtual Catchment

2.2.3 Sensitivity Calculation

3. RESULTS AND DISCUSSION

3.1 LINEAR HILLSLOPE

3.1.1 Aggregated Parameters

3.2 COMPLEX HILLSLOPES

4. CONCLUDING REMARKS

Acknowledgments

REFERENCES

4 - SENSITIVITY OF VEGETATION PHENOLOGICAL PARAMETERS: FROM SATELLITE SENSORS TO SPATIAL RESOLUTION AND TEMPORAL CO ...

1. INTRODUCTION

2. MONITORING VEGETATION PHENOLOGY

3. SENSITIVITY ANALYSIS

4. SENSITIVITY OF REMOTELY SENSED PHENOLOGICAL PARAMETERS

4.1 SATELLITE SENSOR

4.2 VEGETATION INDEX

4.3 SPATIAL RESOLUTION

4.4 COMPOSITE PERIOD, SMOOTHING, AND FILTERING

4.4.1 Composite Period

4.4.2 Smoothing Techniques

5. CASE STUDY

5.1 STUDY AREA

5.2 DATA AND METHODOLOGY

5.3 RESULTS AND DISCUSSION

6. CONCLUSION

REFERENCES

5 - RADAR RAINFALL SENSITIVITY ANALYSIS USING MULTIVARIATE DISTRIBUTED ENSEMBLE GENERATOR∗

1. INTRODUCTION

2. DATA AND METHODS

2.1 STUDY AREA AND DATA SOURCES

2.2 THE MULTIVARIATE DISTRIBUTED ENSEMBLE GENERATOR

2.3 THE XINANJIANG MODEL

3. METHODOLOGY

3.1 EXPERIMENTAL DESIGN

3.2 VERIFICATION METHOD

4. RESULTS AND DISCUSSION

4.1 IMPLEMENTATION OF ENSEMBLE FLOW GENERATION

4.2 IMPACT OF ERROR DISTRIBUTION ON MODEL OUTPUT

4.3 IMPACT OF SPATIOTEMPORAL DEPENDENCE ON MODEL OUTPUT

5. CONCLUSIONS

REFERENCES

6 - FIELD-SCALE SENSITIVITY OF VEGETATION DISCRIMINATION TO HYPERSPECTRAL REFLECTANCE AND COUPLED STATISTICS

1. INTRODUCTION

2. BACKGROUND ON SPECTRAL DISCRIMINATION OF VEGETATION

2.1 PARAMETRIC VERSUS NONPARAMETRIC STATISTICAL TESTS

2.1.1 Other Discrimination Methods

2.2 UNALTERED VERSUS PROCESSED HYPERSPECTRAL REFLECTANCE

2.3 CASE STUDIES FOR EFFECTS OF TYPE OF REFLECTANCE AND STATISTICAL TEST ON THE VEGETATION DISCRIMINATION RESULTS

3. SENSITIVITY OF SPECTRAL DISCRIMINATION OF VEGETATION TO THE TYPE OF REFLECTANCE AND STATISTICAL TEST

3.1 HYPERSPECTRAL DATA AND METHOD DESCRIPTION

3.2 SENSITIVITY OF VEGETATION SPECTRAL DISCRIMINATION TO REFLECTANCE TYPE AND STATISTICAL METHOD

3.3 SENSITIVITY OF VEGETATION SPECTRAL DISCRIMINATION TO THE NUMBER OF OBSERVATIONS

4. FINAL REMARKS

REFERENCES

3 - GLOBAL (OR VARIANCE)-BASED SA METHODS: CASE STUDIES

7 - A MULTIMETHOD GLOBAL SENSITIVITY ANALYSIS APPROACH TO SUPPORT THE CALIBRATION AND EVALUATION OF LAND SURFACE MODELS

1. INTRODUCTION

2. MODEL AND METHODS

2.1 REGIONAL SENSITIVITY ANALYSIS

2.2 VARIANCE-BASED SENSITIVITY ANALYSIS

2.3 THE PAWN DENSITY-BASED METHOD

2.4 THE JULES MODEL

2.5 THE SANTA RITA CREOSOTE STUDY SITE

2.6 EXPERIMENTAL SETUP: DEFINITION OF INPUT FACTORS AND OUTPUTS

2.7 DEFINITION OF THE RANGE OF VARIATION OF THE INPUT FACTORS

3. RESULTS

3.1 RESULTS OF REGIONAL SENSITIVITY ANALYSIS

3.2 RESULTS OF VARIANCE-BASED SENSITIVITY ANALYSIS

3.3 RESULTS OF PAWN

3.4 OVERALL SENSITIVITY ASSESSMENT FROM THE MULTIMETHOD APPROACH

4. CONCLUSIONS

Acknowledgments

REFERENCES

8 - GLOBAL SENSITIVITY ANALYSIS FOR SUPPORTING HISTORY MATCHING OF GEOMECHANICAL RESERVOIR MODELS USING SATELLITE I ...

1. INTRODUCTION

2. CASE STUDY

2.1 SURFACE DEFORMATION AT THE KB-501 WELL OF IN SALAH SITE

2.2 THREE-DIMENSIONAL HYDROMECHANICAL MODEL OF KB-501

3. METHODS

3.1 VARIANCE-BASED GLOBAL SENSITIVITY ANALYSIS

3.2 PRINCIPLES OF METAMODELING

3.3 INTRODUCTION TO KRIGING METAMODEL

3.4 DESCRIPTION OF THE WORKFLOW

4. APPLICATION

4.1 REDUCING THE NUMBER OF UNCERTAINTY INPUT PARAMETERS

4.2 CALIBRATION OF THE RESERVOIR YOUNG'S MODULUS

SUMMARY AND FUTURE WORK

Acknowledgments

REFERENCES

9 - ARTIFICIAL NEURAL NETWORKS FOR SPECTRAL SENSITIVITY ANALYSIS TO OPTIMIZE INVERSION ALGORITHMS FOR SATELLITE-BAS ...

1. INTRODUCTION

2. DATA AND METHODS

2.1 ARTIFICIAL NEURAL NETWORKS: OVERVIEW

2.1.1 Artificial Neural Networks for the Inversion of Satellite Measurements of Spectral Radiation for the Observation of the Ear ...

2.2 NEURAL NETWORK–BASED TECHNIQUES TO REDUCE THE INPUT VECTOR DIMENSIONALITY

2.2.1 Extended Pruning

2.2.2 Autoassociative Neural Networks

2.3 SAMPLE DATA SET

2.3.1 Sulfate Aerosols and Their Extinction Coefficient

2.3.2 Thermal Infrared Satellite Pseudo-Observations

3. RESULTS

3.1 TRAINING AND TESTING THE MAXIMUM DIMENSIONALITY NEURAL NETWORK

3.2 SELECTION OF THE INPUT WAVELENGTHS AND SPECTRAL SENSITIVITY ANALYSIS

3.3 COMPARING THE PERFORMANCES OF REDUCED DIMENSIONALITY NEURAL NETWORK

4. CONCLUSIONS

Acknowledgments

REFERENCES

10 - GLOBAL SENSITIVITY ANALYSIS FOR UNCERTAIN PARAMETERS, MODELS, AND SCENARIOS

1. INTRODUCTION

2. MORRIS METHOD

3. SOBOL' METHOD

3.1 FIRST-ORDER AND TOTAL-EFFECT SENSITIVITY INDICES

3.2 MONTE CARLO IMPLEMENTATION AND TWO APPROXIMATION METHODS

3.2.1 Sparse-Grid Collocation for Evaluating Mean and Variance

3.2.2 Distributed Evaluation of Local Sensitivity Analysis

4. SOBOL' METHOD FOR MULTIPLE MODELS AND SCENARIOS

4.1 HIERARCHICAL FRAMEWORK FOR UNCERTAINTY QUANTIFICATION

4.2 GLOBAL SENSITIVITY INDICES FOR SINGLE MODEL AND SINGLE SCENARIO

4.3 GLOBAL SENSITIVITY INDICES FOR MULTIPLE MODELS BUT SINGLE SCENARIO

4.4 GLOBAL SENSITIVITY INDICES FOR MULTIPLE MODELS AND MULTIPLE SCENARIOS

5. SYNTHETIC STUDY WITH MULTIPLE SCENARIOS AND MODELS

5.1 SYNTHETIC CASE OF GROUNDWATER REACTIVE TRANSPORT MODELING

5.2 UNCERTAIN SCENARIOS, MODELS, AND PARAMETERS

5.3 TOTAL SENSITIVITY INDEX FOR HEAD UNDER INDIVIDUAL MODELS AND SCENARIOS

5.4 TOTAL SENSITIVITY INDEX FOR HEAD UNDER MULTIPLE MODELS BUT INDIVIDUAL SCENARIOS

5.5 TOTAL SENSITIVITY INDEX FOR HEAD UNDER MULTIPLE MODELS AND MULTIPLE SCENARIOS

5.6 TOTAL SENSITIVITY INDEX FOR ETHENE CONCENTRATION

6. USING GLOBAL SENSITIVITY ANALYSIS FOR SATELLITE DATA AND MODELS

7. CONCLUSIONS AND PERSPECTIVES

Acknowledgments

REFERENCES

4 - OTHER SA METHODS: CASE STUDIES

11 - SENSITIVITY AND UNCERTAINTY ANALYSES FOR STOCHASTIC FLOOD HAZARD SIMULATION

1. INTRODUCTION

2. BASIC PRINCIPLES OF STOCHASTIC APPROACH TO FLOOD HAZARD

2.1 STOCHASTIC SIMULATION OF RESERVOIR INFLOWS

2.1.1 Storm Seasonality

2.1.2 Precipitation Magnitude–Frequency Relationship

2.1.3 Temporal and Spatial Distribution of Storms

2.1.4 Air Temperature and Freezing Level Temporal Patterns

2.1.5 The 1000-mb Air Temperature Simulation

2.1.6 Air Temperature Lapse Rates

2.1.7 Freezing Level

2.1.8 Watershed Model Antecedent Conditions Sampling

2.1.9 Initial Reservoir Level

2.2 SIMULATION OF RESERVOIR OPERATION–FLOOD ROUTING

2.3 SIMULATION PROCEDURE

3. UNCERTAINTY ASSOCIATED WITH STOCHASTICALLY DERIVED FLOOD QUANTILES

3.1 SENSITIVITY ANALYSIS

3.2 UNCERTAINTY ANALYSIS

3.3 CHARACTERIZATION OF UNCERTAINTIES FOR SELECTED MODEL COMPONENTS

3.3.1 The 48-hours Precipitation–Frequency Relationship for Bridge River System Watersheds

3.3.2 Watershed Response to Fast Runoff

3.3.3 The 1000-mb Air Temperature and Freezing Level

3.3.4 Storm Seasonality Where Precipitation Magnitudes Are Unrestricted

4. RESULTS

5. EFFECT OF EARTH OBSERVATIONS ON UNCERTAINTY IN PROBABILISTIC FLOOD ESTIMATES

6. CONCLUDING REMARKS

REFERENCES

12 - SENSITIVITY OF WELLS IN A LARGE GROUNDWATER MONITORING NETWORK AND ITS EVALUATION USING GRACE SATELLITE DERIVE ...

1. INTRODUCTION

2. METHODOLOGY

2.1 SATURATED THICKNESS: A FUNDAMENTAL MEASURE OF GROUNDWATER AVAILABILITY

2.2 INVERSE DISTANCE WEIGHTING APPROACH FOR OBTAINING REGIONAL GROUNDWATER AVAILABILITY FROM WELL MEASUREMENTS

2.3 ASSESSMENT OF INDIVIDUAL WELL SENSITIVITY USING THE JACKKNIFE APPROACH

2.4 GRACE SATELLITE AND GLOBAL HYDROLOGIC DATA

3. STUDY AREA

4. RESULTS AND DISCUSSION

4.1 MONITORING NETWORK AND ESTIMATION GRID CONFIGURATION ANALYSIS

4.2 PREDICTIONS OF SATURATED THICKNESS AND AVAILABLE GROUNDWATER RESOURCES

4.3 UNCERTAINTY IN ESTIMATED SATURATED THICKNESS AND WATER AVAILABILITY

4.4 SENSITIVITY OF INDIVIDUAL WELLS

4.5 EVALUATION OF SENSITIVITY MEASURES AGAINST GRACE-DERIVED DATA

5. SUMMARY AND CONCLUSIONS

REFERENCES

13 - MAKING THE MOST OF THE EARTH OBSERVATION DATA USING EFFECTIVE SAMPLING TECHNIQUES

1. INTRODUCTION: LOOKING FROM ABOVE

2. DATA ASSIMILATION

2.1 ERROR TRACKING

2.2 BUILDING A DATABASE

2.3 FROM DATA-RICH REGIONS TO DATA-POOR REGIONS

2.4 DECIDING FACTOR IN DESIGNING FUTURE SYSTEMS

3. SAMPLING SCHEMES

4. BOOTSTRAP SAMPLING

5. LATIN HYPERCUBE SAMPLING

6. CASE STUDY USING BOOTSTRAP SAMPLING

6.1 METHODOLOGY AND RESULTS

7. CONCLUSIONS

REFERENCES

14 - ENSEMBLE-BASED MULTIVARIATE SENSITIVITY ANALYSIS OF SATELLITE RAINFALL ESTIMATES USING COPULA MODEL

1. INTRODUCTION

2. SATELLITE RAINFALL ESTIMATES

3. METHODOLOGY OF ENSEMBLE-BASED MULTIVARIATE ANALYSIS

3.1 CALCULATING BIASES

3.2 FITTING MARGINAL DISTRIBUTION FUNCTION

3.3 JOINT DISTRIBUTION FUNCTION OF BIASES USING COPULA

3.3.1 Copulas

3.3.2 Gaussian Copula

3.3.3 t-Copula

3.4 ENSEMBLE BIAS SIMULATION

3.4.1 Generating an Ensemble of Satellite Rainfall Realizations

3.5 UNCERTAINTY ANALYSIS PROCEDURE

4. APPLICATION (CASE STUDY) AND RESULTS

4.1 EVALUATION OF BIAS-ADJUSTED SATELLITE RAINFALL ESTIMATES

4.2 COPULA-BASED BIAS SIMULATION

4.3 TESTING THE DEVELOPED MODEL AND UNCERTAINTY ANALYSIS

5. CONCLUSIONS AND FUTURE DIRECTIONS

REFERENCES

5 - SOFTWARE TOOLS IN SA FOR EO

15 - EFFICIENT TOOLS FOR GLOBAL SENSITIVITY ANALYSIS BASED ON HIGH-DIMENSIONAL MODEL REPRESENTATION

1. INTRODUCTION

2. HIGH-DIMENSIONAL MODEL REPRESENTATION

2.1 RANDOM SAMPLING—HIGH-DIMENSIONAL MODEL REPRESENTATION

2.2 GLOBAL SENSITIVITY ANALYSIS USING RANDOM SAMPLING–HIGH-DIMENSIONAL MODEL REPRESENTATION

2.3 VARIANCE REDUCTION METHODS

3. GRAPHICAL USER INTERFACE-HIGH-DIMENSIONAL MODEL REPRESENTATION SOFTWARE

3.1 OVERVIEW

3.2 EXTENSIONS TO STANDARD HIGH-DIMENSIONAL MODEL REPRESENTATION

3.3 SOFTWARE FEATURES

4. APPLICATIONS AND CASE STUDIES

4.1 GLOBAL LAND SURFACE MODELS

4.2 ATMOSPHERIC DISPERSION MODELS

4.3 APPLICATION FOR EARTH OBSERVATIONS

5. SUMMARY AND CONCLUSIONS

REFERENCES

16 - A GLOBAL SENSITIVITY ANALYSIS TOOLBOX TO QUANTIFY DRIVERS OF VEGETATION RADIATIVE TRANSFER MODELS

1. INTRODUCTION

2. VARIANCE-BASED GLOBAL SENSITIVITY ANALYSIS

3. RADIATIVE TRANSFER MODELS AND ARTMO

4. GLOBAL SENSITIVITY ANALYSIS TOOLBOX

4.1 GLOBAL SENSITIVITY ANALYSIS CONFIGURATION MODULE

4.2 GLOBAL SENSITIVITY ANALYSIS RESULTS VISUALIZATION MODULE

5. CASE STUDIES

5.1 EXPERIMENTAL SETUP

5.2 RESULTS

5.2.1 PROSPECT STi Results

5.2.2 PROSAIL STi Results

5.2.3 SCOPE STi Results

6. DISCUSSION

7. CONCLUSIONS

REFERENCES

17 - GEM-SA: THE GAUSSIAN EMULATION MACHINE FOR SENSITIVITY ANALYSIS

1. BAYESIAN ANALYSIS OF COMPUTER MODELS

2. GAUSSIAN PROCESS PRIOR DISTRIBUTION FOR A CODE OUTPUT

3. POSTERIOR DISTRIBUTION AFTER OBSERVING CODE RUNS

4. FUNCTIONALITY INCLUDED WITHIN GAUSSIAN EMULATION FOR SENSITIVITY ANALYSIS

4.1 STANDARDIZATION OF INPUTS

4.2 SENSITIVITY AND UNCERTAINTY ANALYSES OF THE MODEL PREDICTION

4.3 CROSS-VALIDATION

5. UNCERTAINTY IN EMULATOR ROUGHNESS PARAMETERS

6. USING THE GAUSSIAN EMULATION FOR SENSITIVITY ANALYSIS INTERFACE

7. SUMMARY OF INPUTS/OUTPUTS

7.1 INPUTS

7.2 OUTPUTS

7.2.1 Main Effect Realizations

7.2.2 Joint Effect Realizations

7.2.3 Prediction Realizations

7.2.4 Cross-Validation Results

8. CASE STUDY: SIMSPHERE

8.1 INTRODUCTION

8.2 SENSITIVITY ANALYSIS APPLIED TO SIMSPHERE

8.3 RESULTS

8.3.1 Emulator Validation

8.3.2 Results and Discussion

9. USING GAUSSIAN EMULATION FOR SENSITIVITY ANALYSIS EMULATORS WITH YOUR OWN SOFTWARE

10. CONCLUSIONS

Acknowledgments

REFERENCES

18 - AN INTRODUCTION TO THE SAFE MATLAB TOOLBOX WITH PRACTICAL EXAMPLES AND GUIDELINES

1. INTRODUCTION

2. STRUCTURE OF THE TOOLBOX

3. GLOBAL SENSITIVITY ANALYSIS METHODS AND EXAMPLES OF APPLICATION

3.1 VISUAL AND QUALITATIVE GLOBAL SENSITIVITY ANALYSIS METHODS

3.1.1 Scatter Plots

3.1.2 Regional Sensitivity Analysis Based on Grouping

3.1.3 Parallel Coordinate Plot

3.2 QUANTITATIVE GLOBAL SENSITIVITY ANALYSIS METHODS

4. GUIDELINES FOR THE IMPLEMENTATION OF GLOBAL SENSITIVITY ANALYSIS

5. OUTLOOK

Acknowledgments

REFERENCES

6 - CHALLENGES AND FUTURE OUTLOOK

19 - SENSITIVITY IN ECOLOGICAL MODELING: FROM LOCAL TO REGIONAL SCALES

1. INTRODUCTION

2. SENSITIVITY IN PROCESS-BASED ECOLOGICAL MODELS

3. TIME-DEPENDENT SENSITIVITY AND ITS IMPLICATIONS

4. GLOBAL SENSITIVITY ANALYSIS IN SOCIAL-ECOLOGICAL SYSTEMS

5. SENSITIVITY OF SOCIAL-ECOLOGICAL MODELS TO LAND USE MAPPING ERROR

6. COMPUTING STRATEGY

7. CONCLUDING REMARKS

Acknowledgments

REFERENCES

20 - CHALLENGES AND FUTURE OUTLOOK OF SENSITIVITY ANALYSIS

1. INTRODUCTION

2. BRIEF REVIEW OF SOME COMMONLY USED SENSITIVITY ANALYSIS METHODS

2.1 LOCAL ASSESSMENT OF PARAMETER SENSITIVITY

2.2 GLOBAL ASSESSMENT OF PARAMETER SENSITIVITY

2.2.1 The “One-Dimensional Cross Section” Strategy

2.2.2 The “Distribution of Derivatives” Strategy

2.2.3 The “Analysis of Variance” Strategy

2.2.4 The “Analysis of Cumulative Distributions” Strategy

2.2.5 The “Variogram Analysis of Response Surface” Strategy

3. CHALLENGES AND FUTURE OUTLOOK

3.1 COMPUTATIONAL EFFICIENCY

3.2 RELIABILITY (ACCURACY AND ROBUSTNESS)

3.3 AMBIGUITY IN THE DEFINITION OF “SENSITIVITY”

3.4 SPECIFICATION OF THE CRITERION REPRESENTING MODEL “RESPONSE”

4. CONCLUSIONS

Acknowledgments

REFERENCES

Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

R

S

T

U

V

W

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