Effective groundwater model calibration: with analysis of data, sensitivities, predictions, and uncertainty
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley-Interscience
2007
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| Subjects: | |
| Online Access: | Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 407-426) and index |
| Physical Description: | XVIII, 455 S. Ill., graph. Darst., Kt. 24 cm |
| ISBN: | 047177636X 9780471776369 |
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MARC
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| 084 | |a BAU 672f |2 stub | ||
| 100 | 1 | |a Hill, Mary C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Effective groundwater model calibration |b with analysis of data, sensitivities, predictions, and uncertainty |c Mary C. Hill ; Claire R. Tiedeman |
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c 2007 | |
| 300 | |a XVIII, 455 S. |b Ill., graph. Darst., Kt. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 407-426) and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Groundwater |x Mathematical models | |
| 650 | 4 | |a Hydrologic models | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grundwasser |0 (DE-588)4022369-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tiedeman, Claire R. |e Verfasser |4 aut | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip065/2005036657.html |3 Table of contents only | |
| 856 | 4 | 2 | |m OEBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015738347&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015738347 | ||
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| _version_ | 1804136641776844801 |
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| adam_text | IMAGE 1
CONTENTS
PREFACE
1 INTRODUCTION
1.1 BOOK AND ASSOCIATED CONTRIBUTIONS: METHODS, GUIDELINES, EXERCISES,
ANSWERS, SOFTWARE, AND POWERPOINT FILES, 1 1.2 MODEL CALIBRATION WITH
INVERSE MODELING, 3 1.2.1 PARAMETERIZATION, 5
1.2.2 OBJECTIVE FUNCTION, 6 1.2.3 UTILITY OF INVERSE MODELING AND
ASSOCIATED METHODS, 6 1.2.4 USING THE MODEL TO QUANTITATIVELY CONNECT
PARAMETERS, OBSERVATIONS, AND PREDICTIONS, 7 1.3 RELATION OF THIS BOOK
TO OTHER IDEAS AND PREVIOUS WORKS, 8
1.3.1 PREDICTIVE VERSUS CALIBRATED MODELS, 8 1.3.2 PREVIOUS WORK, 8
1.4 A FEW DEFINITIONS, 12 1.4.1 LINEAR AND NONLINEAR, 12 1.4.2
PRECISION, ACCURACY, RELIABILITY, AND UNCERTAINTY, 13 1.5 ADVANTAGEOUS
EXPERTISE AND SUGGESTED READINGS, 14
1.6 OVERVIEW OF CHAPTERS 2 THROUGH 15, 16
XVII
1
VII
IMAGE 2
VIII CONTENTS
2 COMPUTER SOFTWARE AND GROUNDWATER MANAGEMENT PROBLEM USED IN THE
EXERCISES 18
2.] COMPUTER PROGRAMS MODFLOW-2000, UCODE_2005, AND PEST, 18
2.2 GROUNDWATER MANAGEMENT PROBLEM USED FOR THE EXERCISES, 21
2.2.1 PURPOSE AND STRATEGY, 23
2.2.2 FLOW SYSTEM CHARACTERISTICS, 23
2.3 EXERCISES, 24 EXERCISE 2.1: SIMULATE STEADY-STATE HEADS AND PERFORM
PREPARATORY STEPS, 25
3 COMPARING OBSERVED AND SIMULATED VALUES USING OBJECTIVE FUNCTIONS
3.1 WEIGHTED LEAST-SQUARES OBJECTIVE FUNCTION, 26
3.1.] WITH A DIAGONAL WEIGHT MATRIX, 27
3.1.2 WITH A FUH WEIGHT MATRIX, 28
3.2 ALTERNATIVE OBJECTIVE FUNCTIONS, 28
3.2.1 MAXIMUM-LIKELIHOOD OBJECTIVE FUNCTION, 29
3.2.2 LI NORM OBJECTIVE FUNCTION, 29 3.2.3 MULTIOBJECTIVE FUNCTION, 29
3.3 REQUIRERNENTS FOR ACEURATE SIMU1ATED RESULTS, 30 3.3.1 ACEURATE
MODEL, 30
3.3.2 UNBIASED OBSERVATIONS AND PRIOR INFORMATION, 30 3.3.3 WEIGHTING
REFLECTS ERRORS, 31
3.4 ADDITIONAL ISSUES
3.4.] PRIOR INFORMATION, 32 3.4.2 WEIGHTING, 34
3.4.3 RESIDUALS AND WEIGHTED RESIDUALS, 35 3.5 LEAST-SQUARES
OBJECTIVE-FUNCTION SURFACES, 35
3.6 EXERCISES, 36 EXERCISE 3.]: STEADY-STATE PARAMETER DEFINITION, 36
EXERCISE 3.2: OBSERVATIONS FOR THE STEADY-STATE PROBLEM, 38
EXERCISE 3.3: EVALUATE MODEL FIT USING STARTING PARAMETER VALUCS, 40
4 DETERRNINING THE INFORMATION THAT OBSERVATIONS PROVIDE ON PARAMETER
VALUES USING FIT-INDEPENDENT STATISTICS
4.1 USING OBSERVATIONS, 42
4.1. I MODEL CONSLRUCTION AND PARAMETER DEFINITION, 42
4.1.2 PARAMETER VALUES, 43
26
41
IMAGE 3
CONTENTS IX
4.2 WHEN TO DETERMINE THE INFORMATION THAT OBSERVATIONS PROVIDE ABOUT
PARAMETER VALUES, 44 4.3 FIT-INDEPENDENT STATISTICS FOR SENSITIVITY
ANALYSIS, 46 4.3.1 SENSITIVITIES, 47
4.3.2 SCALING, 48 4.3.3 DIMENSIONLESS SCALED SENSITIVITIES (DSS), 48
4.3.4 COMPOSITE SCALED SENSITIVITIES (CSS), 50 4.3.5 PARAMETER
CORRELATION COEFFICIENTS (PCC), 51
4.3.6 LEVERAGE STATISTICS, 54 4.3.7 ONE-PERCENT SCALED SENSITIVITIES, 54
4.4 ADVANTAGES AND LIMITATIONS OF FIT-INDEPENDENT STATISTICS FOR
SENSITIVITY ANALYSIS, 56
4.4.1 SCALED SENSITIVITIES, 56 4.4.2 PARAMETER CORRELATION COEFFICIENTS,
58 4.4.3 LEVERAGE STATISTICS, 59 4.5 EXERCISES, 60
EXERCISE 4.1: SENSITIVITY ANALYSIS FOR THE STEADY-STATE MODEL WITH
STARTING PARAMETER VALUES, 60
5 ESTLMATING PARAMETER VALUES
5.1 THE MODIFIED GAUSS-NEWTON GRADIENT METHOD, 68 5.1.1 NORMAL
EQUATIONS, 68 5.1.2 AN EXAMPLE, 74 5.1.3 CONVERGENCE CRITERIA, 76 5.2
ALTERNATIVE OPTIMIZATION METHODS, 77
5.3 MULTIOBJECTIVE OPTIMIZATION, 78 5.4 LOG-TRANSFORMED PARAMETERS, 78
5.5 USE OF LIMITS ON ESTIMATED PARAMETER VALUES, 80 5.6 EXERCISES, 80
EXERCISE 5.1: MODIFIED GAUSS-NEWTON METHOD AND APPLICATION TO A
TWO-PARAMETER PROBLEM, 80 EXERCISE 5.2: ESTIMATE THE PARAMETERS OF THE
STEADY-STATE MODEL, 87
6 EVALUATING MODEL FIT
6.1 MAGNITUDE OF RESIDUALS AND WEIGHTED RESIDUALS, 93 6.2 IDENTIFY
SYSTEMATIC MISFIT, 94 6.3 MEASURES OF OVERALL MODEL FIT, 94 6.3.1
OBJECTIVE-FUNCTION VALUE, 95
67
93
IMAGE 4
X CONTENTS
6,3.2 CALCULATED ERROR VARIANCE AND STANDARD ERROR, 95
6.3.3 AIC, AIC C , AND EIC STATISTICS, 98 6.4 ANALYZING MODEL FIT
GRAPHICALLY AND RELATED STATISTICS, 99
6.4.] USING GRAPHICAL ANALYSIS OF WEIGHTED RESIDUALS 10 DETECT MODEL
ERROR, 100
6.4.2 WEIGHTED RESIDUALS VERSUS WEIGHTED OR UNWEIGHTED SIMULATED VALUES
AND MINIMUM, MAXIMUM, AND AVERAGE WEIGHTED RESIDUALS, 100
6.4.3 WEIGHTED OR UNWEIGHTED OBSERVATIONS VERSUS SIMULATED VALUES AND
CORRELATION COEFFICIENT R, 105
6.4.4 GRAPHS AND MAPS USING INDEPENDENT VARIABLES AND THE RUNS
STATISTIC, 106
6.4,5 NORMAL PROBABILITY GRAPHS AND CORRELATION COEFFICIENT R~, 108
6.4.6 ACCEPTABLE DEVIATIONS FROM RANDOM, NORRNALLY DISTRIBUTED WEIGHTED
RESIDUALS, 111 6.5 EXERCISES, 113 EXERCISE 6.1: STATISTICAL MEASURES OF
OVERALL FIT, 113
EXERCISE 6.2: EVALUATE GRAPH MODEL FIT AND RELATED STATISTICS, 115
7 EVALUATING ESTIMATED PARAMETER VALUES AND PARAMETER UNCERTAINTY
7.1 REEVALUATING COMPOSITE SCALED SENSITIVITIES, ]24
7.2 USING STATISTICS FROM THE PARAMETER VARIANCE-COVARIANCE MATRIX. 125
7.2, I FIVE VERSIONS OF THE VARIANCE-COVARIANCE MATRIX, 125
7.2.2 PARAMETER VARIANCES, COVARIANCES, STANDARD DEVIATIONS,
COEFFICIENTS OF VARIATION, AND CORRELATION COEFFICIENTS, 126
7.2.3 RELATION BETWEEN SAMPIE AND REGRESSION STATISTICS, 127
7,2.4 STATISTICS FOR LOG-TRANSFORRNED PARAMETERS, 130
7.2,5 WHEN TO USE THE FIVE VERSIONS OF THE PARAMETER VARIANCE-COVARIANCE
MATRIX, 130
7,2.6 SOME ALTERNATE METHODS: EIGENVECTORS, EIGENVALUES, AND SINGULAR
VALUE DECOMPOSITION, 132
7.3 IDENTIFYING OBSERVATIONS IMPORTANT TO ESTIMATED PARAMETER VAL LIES,
132
7.3.] LEVERAGE STATISTICS, 134
7,3,2 LNFLUENCE STATISTICS, 134
7.4 UNIQUCNESS AND OPTIMALITY OF THE ESTIMATED PARAMETER VALUES, ]37
7.5 QUANTIFYING PARAMETER VALUE UNCERTAINTY, 137
124
IMAGE 5
CONTENTS
7.5.1 INFERENTIAL STATISTICS, 137
7.5.2 MONTE CARLO METHODS, 140 7.6 CHECKING PARAMETER ESTIMATES AGAINST
REASONABLE VALUES, 140 7.7 TESTING LINEARITY, 142 7.8 EXERCISES, 145
EXERCISE 7.1: PARAMETER STATISTICS, 145 EXERCISE 7.2: CONSIDER ALL THE
DIFFERENT CORRELATION COEFFICIENTS PRESENTED, 155
EXERCISE 7.3: TEST FOR LINEARITY, 155
8 EVALUATING MODEL PREDICTIONS, DATA NEEDS, AND PREDICTION UNCERTAINTY
8.1 SIMULATING PREDICTIONS AND PREDICTION SENSITIVITIES AND STANDARD
DEVIATIONS, 158 8.2 USING PREDICTIONS TO GUIDE COLLECTION OF DATA THAT
DIRECTLY CHARACTERIZE SYSTEM PROPERTIES, 159
8.2.1 PREDICTION SCALED SENSITIVITIES (PSS) , 160 8.2.2 PREDICTION
SCALED SENSITIVITIES USED IN CONJUNCTION WITH COMPOSITE SCALED
SENSITIVITIES, 162 8.2.3 PARAMETER CORRELATION COEFFICIENTS WITHOUT AND
WITH PREDICTIONS, 162 8.2.4 CORNPOSITE AND PREDICTION SCALED
SENSITIVITIES USED WITH PARAMETER CERRELATION COEFFICIENTS, 165 8.2.5
PARAMETER-PREDICTION (PPR) STATISTIC, 166 8.3 USING PREDICTIONS TO GUIDE
COLLECTION OF OBSERVATION DATA, 170
8.3.1 USE OF PREDICTION, COMPOSITE, AND DIMENSIONLESS SCA1ED
SENSITIVITIES AND PARAMETER CORRELATION COEFFICIENTS, 170
8.3.2 OBSERVATION-PREDICTION (OPR) STATISTIC, 171
8.3.3 INSIGHTS ABOUT THE OPR STATISTIC FROM OTHER FIT-INDEPENDENT
STATISTICS, 173 8.3.4 IMPLICATIONS FOR MONITARING NETWORK DESIGN, 174
8.4 QUANTIFYING PREDICTION UNCERTAINTY USING INFERENTIAL STATISTICS, 174
8.4.1 DEFINITIONS, 175 8.4.2 LINEAR CONFIDENCE AND PREDICTION INTERVALS
ON PREDICTIONS, 176 8.4.3 NONLINEAR CONFIDENCE AND PREDICTION INTERVALS,
177 8.4.4 USING THE THEIS EXAMPLE TO UNDERSTAND LINEAR AND
NONLINEAR CONFIDENCE INTERVA1S, 181
8.4.5 DIFFERENCES AND THEIR STANDARD DEVIATIONS, CONFIDENCE INTERVALS,
AND PREDICTION INTERVALS, 182
XI
158
IMAGE 6
XII CONTENTS
8.4.6 USING CONFIDENCE INTERVALS TO SERVE THE PURPOSES OF TRADITIANAL
SENSITIVITY ANALYSIS, 184 8.5 QUANTIFYING PREDICTION UNCERTAINTY USING
MONTE CARLO ANALYSIS, 185
8.5.1 ELEMENTS OF A MONTE CAR10 ANALYSIS, 185
8.5.2 RELATION BETWEEN MONTE CARLO ANALYSIS AND LINEAR AND NONLINEAR
CONFIDENCE INTERVALS, 187
8.5.3 USING THE THEIS EXAMP1E TO UNDERSTAND MONTE CARLO METHODS, 188
8.6 QUANTIFYING PREDICTION UNCERTAINTY USING ALTERNATIVE MODELS, 189
8.7 TESTING MODEL NONLINEARITY WITH RESPECT TO THE PREDICTIONS, 189
8.8 EXERCISES, 193 EXERCISE 8.1: PREDICT ADVECTIVE TRANSPORT AND PERFARM
SENSITIVITY ANALYSIS, 195
EXERCISE 8.2: PREDICTION UNCERTAINTY MEASURED USING INFERENTIAL
STATISTICS, 207
9 CALIBRATING TRANSIENT AND TRANSPORT MODELS AND RECALIBRATING EXISTING
MODELS
9.1 STRATEGIES FOR CALIBRATING TRANSIENT MODELS, 213
9.1.1 INITIAL CONDITIONS, 213
9.1.2 TRANSIENT OBSERVATIONS, 214 9.1.3 ADDITIONAL MODEL INPUTS, 216
9.2 STRATEGIES FOR CALIBRATING TRANSPORT MODELS, 217 9.2.1 SELECTING
PROCESSES TO INCLUDE, 217 9.2.2 DEFINING SOURCE GEOMETRY AND
CONCENTRATIONS, 218
9.2.3 SCALE ISSUES, 219
9.2.4 NUMERICAL ISSUES: MODEL ACCURACY AND EXECUTION TIME, 220
9.2.5 TRANSPORT OBSERVATIONS, 223
9.2.6 ADDITIONAL MODEL INPUTS, 225
9.2.7 EXAMPLES OF OBTAINING A TRACTABLE, USEFUL MODEL, 226
9.3 STRATEGIES FOR RECALIBRATING EXISTING MODELS, 227
9.4 EXERCISES (OPTIONAL), 228
EXERCISES 9.1 AND 9.2: SIMULATE TRANSIENT HYDRAULIC HEADS UND PERFORM
PREPARATORY STEPS, 229
EXERCISE 9.3: TRANSIENT PARAMETER DEFINITION, 230
213
IMAGE 7
CONTENTS
EXERCISE 9.4: OBSERVATIONS FOR THE TRANSIENT PROBLEM, 231 EXERCISE 9.5:
EVALUATE TRANSIENT MODEL FIT USING STARTING PARAMETER VALUES, 235
EXERCISE 9.6: SENSITIVITY ANALYSIS FOR THE INITIAL MODEL, 235
EXERCISE 9.7: ESTIMATE PARAMETERS FOR THE TRANSIENT SYSTEM BY NONLINEAR
REGRESSION, 243 EXERCISE 9.8: EVALUATE MEASURES OF MODEL FIT, 244
EXERCISE 9.9: PERFARM GRAPHICAL ANALYSES OF MODEL FIT
AND EVALUATE RELATED STATISTICS, 246 EXERCISE 9.10: EVALUATE ESTIMATED
PARAMETERS, 250 EXERCISE 9.11: TEST FOR LINEARITY, 253 EXERCISE 9.12:
PREDICTIONS, 254
10 GUIDELINES FOR EFFECTIVE MODELING
10.1 PURPOSE OF THE GUIDELINES, 263 10.2 RELATION TO PREVIOUS WORK, 264
10.3 SUGGESTIONS TOR EFFECTIVE IMPLEMENTATION, 264
11 GUIDELINES 1 THROUGH 8-MODEL DEVELOPMENT
GUIDELINE 1: APPLY THE PRINCIPLE OF PARSIMONY, 268 G1.1 PROBLEM, 269
G1.2 CONSTRUCTIVE APPROACHES, 270 GUIDELINE 2: USE A BROAD RANGE OF
SYSTEM INFORMATION TO CONSTRAIN THE PROBLEM, 272
02.1 DATA ASSIMILATION, 273 02.2 USING SYSTEM INFORMATION, 273 02.3 DATA
MANAGEMENT, 274 02.4 APPLICATION: CHARACTERIZING A FRACTURED
DOLOMITE AQUIFER, 277
GUIDELINE 3: MAINTAIN A WELL-POSED, COMPREHENSIVE REGRESSION PROBLEM,
277 03.1 EXAMPLES, 278 03.2 EFFECTS OF NONLINEARITY ON THE CSS AND PEE,
281
GUIDELINE 4: INCLUDE MANY KINDS OF DATA AS OBSERVATIONS IN THE
REGRESSION, 284 04.1 INTERPOLATED OBSERVATIONS , 284 G4.2 CLUSTERED
OBSERVATIONS, 285
04.3 OBSERVATIONS THAT ARE INCONSISTENT WITH MODEL CONSTRUCTION, 286
XIII
260
268
IMAGE 8
XIV CONTENTS
04.4 APPLICATIONS: USING DIFFERENT TYPES OF OBSERVATIONS TO CALIBRATE
GROUNDWATER FLOW AND TRANSPORT MODELS, 287
GUIDELINE 5: USE PRIOR INFORMATION CAREFULLY, 288
05. I USE OF PRIOR INFORMATION COMPARED WITH OBSERVATIONS, 288 05.2
HIGHLY PARAMETERIZED MODELS, 290 05.3 APPLICATIONS: GEOPHYSICAL DATA,
291 GUIDELINE 6: ASSIGN WEIGHTS THAT REFLECT ERRORS, 291
G6.L DETERMINE WEIGHTS, 294 06.2 ISSUES OF WEIGHTING IN NONLINEAR
REGRESSION, 298 GUIDELINE 7: ENCOURAGE CONVERGENCE BY MAKING THE MODEL
MORE ACEURATE AND EVALUATING THE OBSERVATIONS, 306
GUIDELINE 8: CONSIDER ALTERNATIVE MODELS, 308
G8. I DEVELOP ALTERNATIVE MODELS, 309
08.2 DISCRIMINATE BETWEEN MODELS, 310 G8.3 SIMULATE PREDICTIONS WITH
ALTERNATIVE MODELS, 312
08.4 APPLICATION, 313
12 GUIDELINES 9 AND LO-MODEL TESTING
GUIDELINE 9: EVALUATE MODEL FIT, 316
G9.1 DETERMINE MODEL FIT,. 316
09.2 EXARNINE FIT FOR EXISTING OBSERVATIONS IMPORTANT TO THE PURPOSE OF
THE MODEL, 320
G9.3 DIAGNOSE THE CAUSE OF POOF MODEL FIT, 320
GUIDELINE 10: EVALUATE OPTIRNIZED PARAMETER VALUES, 323
GI O. I QUANTIFY PARAMETER-VALUE UNCERTAINTY, 323
G10.2 USE PARAMETER ESTIMATES TO DETECT MODEL ERROR, 323
G10.3 DIAGNOSE THE CAUSE OF UNREASONABLE OPTIMAL PARAMETER ESTIMATES,
326
GIO.4 IDENTIFY OBSERVATIONS IMPORTANT TO THE PARAMETER ESTIMATES, 327
GIO.5 REDUCE OR INCREASE THE NUMBER OF PARAMETERS, 328
13 CUIDELINES 11 AND 12- POTENTIAL NEW DATA
GUIDELINE 11: IDENTIFY NEW DATA TO IMPROVE SIMULATED PROCESSES,
FEATURES, UND PROPERTIES, 330
GUIDELINE LZ: IDENTIFY NEW DATA TO IMPROVE PREDICTIONS, 334
G 12.1 POTENTIAL NEW DATA TO IMPROVE FEATURES AND PROPERTIES GOVERNING
SYSTEM DYNARNICS, 334
G 12.2 POTENTIAL NEW DATA TO SUPPORT OBSERVATIONS, 335
315
329
IMAGE 9
CONTENTS
14 GUIDELINES 13 AND 14-PREDICTION UNCERTAINTY
GUIDELINE 13: EVALUATE PREDICTION UNCERTAINTY AND ACCURACY USING
DETERMINISTIC METHODS, 337 GL3.1 USE REGRESSION TO DETERMINE WHETHER
PREDICTED VALUES ARE CONTRADIETED BY THE CALIBRATED
MODEL, 337
G13.2 USE ORNITTED DATA AND POSTAUDITS, 338 GUIDELINE 14: QUANTIFY
PREDICTION UNCERTAINTY USING STATISTICAL METHODS, 339 G14.1 INFERENTIAL
STATISTICS, 341
G14.2 MONTE CARLO METHODS, 34]
15 USING AND TESTING THE METHODS AND GUIDELINES
15.1 EXECUTION TIME ISSUES, 345 15.2 FIE1D APPLICATIONS AND SYNTHETIC
TEST CASES, 347 15.2.1 THE DEATH VALLEY REGIONAL FLOW SYSTEM, CALIFORNIA
AND NEVADA, USA, 347
15.2.2 GRINDSTED LANDFILL, DENMARK, 370
APPENDIX A: OBJECTIVE FUNCTION ISSUES
A.1 DERIVATION OF THE MAXIMUM-LIKELIHOOD OBJECTIVE FUNCTION, 375 A2
RELATION OF THE MAXIMURN-LIKELIHOOD AND LEAST-SQUARES OBJECTIVE
FUNCTIONS, 376
A3 ASSUMPTIONS REQUIRED FOR DIAGONAL WEIGHTING TO BE CORRECT, 376 A4
REFERENCES, 381
APPENDIX B: CALCULATION DETAILS OF THE MODIFIED GAUSS-NEWTON METHOD
B.1 VECTORS AND MATRICES FOR NONLINEAR REGRESSION, 383 B.2 QUASI-NEWTON
UPDATING OF THE NORMAL EQUATIONS, 384 B.3 CALCULATING THE DAMPING
PARAMETER, 385 BA SOLVING THE NORMAL EQUATIONS, 389
B.5 REFERENCES, 390
APPENDIX C: TWO IMPORTANT PROPERTIES OF LINEAR REGRESSION AND THE
EFFECTS OF NONLINEARITY
C.] IDENTITIES NEEDED FOR THE PROOFS, 392 C.1.1 TRUE LINEAR MODEL, 392
C.1.2 TRUE NONLINEAR MODEL, 392
XV
337
345
374
383
391
IMAGE 10
XVI CONTENTS
CL.3 LINEARIZED TRUE NONLINEAR MODEL, 392 CIA APPROXIMATE LINEAR MODEL,
392 CI.5 APPROXIMATE NONLINEAR MODEL, 393 C.1.6 LINEARIZED APPROXIMATE
NONLINEAR MODEL, 393
C.L .7 THE IMPORTANCE OF X AND X, 394 CI .8 CONSIDERING MANY
OBSERVATIONS, 394 C.1.9 NORMAL EQUATIONS, 395
C.L. I0 RANDOM VARIABLES, 395 C.I. I I EXPECTED VALUE, 395 C.1.12
VARIANCE-COVARIANCE MATRIX OF A VECTOR, 395
C.2 PROOF OF PROPERTY 1: PARAMETERS ESTIMATED BY LINEAR REGRESSION ARE
UNBIASED, 395
C.3 PROOF OF PROPERTY 2: THE WEIGHT MATRIX NEEDS TO BE DEFINED IN A
PARTICULAR WAY FOR EQ. (7.1) TO APPLY AND FOR THE PARAMETER ESTIMATES TO
HAVE THE SMALLEST VARIANCE, 396
CA REFERENCES, 398
APPENDIX D: SELECTED STATISTICAL TABLES
0.1 REFERENCES, 406
REFERENCES
INDEX
399
407
427
|
| adam_txt |
IMAGE 1
CONTENTS
PREFACE
1 INTRODUCTION
1.1 BOOK AND ASSOCIATED CONTRIBUTIONS: METHODS, GUIDELINES, EXERCISES,
ANSWERS, SOFTWARE, AND POWERPOINT FILES, 1 1.2 MODEL CALIBRATION WITH
INVERSE MODELING, 3 1.2.1 PARAMETERIZATION, 5
1.2.2 OBJECTIVE FUNCTION, 6 1.2.3 UTILITY OF INVERSE MODELING AND
ASSOCIATED METHODS, 6 1.2.4 USING THE MODEL TO QUANTITATIVELY CONNECT
PARAMETERS, OBSERVATIONS, AND PREDICTIONS, 7 1.3 RELATION OF THIS BOOK
TO OTHER IDEAS AND PREVIOUS WORKS, 8
1.3.1 PREDICTIVE VERSUS CALIBRATED MODELS, 8 1.3.2 PREVIOUS WORK, 8
1.4 A FEW DEFINITIONS, 12 1.4.1 LINEAR AND NONLINEAR, 12 1.4.2
PRECISION, ACCURACY, RELIABILITY, AND UNCERTAINTY, 13 1.5 ADVANTAGEOUS
EXPERTISE AND SUGGESTED READINGS, 14
1.6 OVERVIEW OF CHAPTERS 2 THROUGH 15, 16
XVII
1
VII
IMAGE 2
VIII CONTENTS
2 COMPUTER SOFTWARE AND GROUNDWATER MANAGEMENT PROBLEM USED IN THE
EXERCISES 18
2.] COMPUTER PROGRAMS MODFLOW-2000, UCODE_2005, AND PEST, 18
2.2 GROUNDWATER MANAGEMENT PROBLEM USED FOR THE EXERCISES, 21
2.2.1 PURPOSE AND STRATEGY, 23
2.2.2 FLOW SYSTEM CHARACTERISTICS, 23
2.3 EXERCISES, 24 EXERCISE 2.1: SIMULATE STEADY-STATE HEADS AND PERFORM
PREPARATORY STEPS, 25
3 COMPARING OBSERVED AND SIMULATED VALUES USING OBJECTIVE FUNCTIONS
3.1 WEIGHTED LEAST-SQUARES OBJECTIVE FUNCTION, 26
3.1.] WITH A DIAGONAL WEIGHT MATRIX, 27
3.1.2 WITH A FUH WEIGHT MATRIX, 28
3.2 ALTERNATIVE OBJECTIVE FUNCTIONS, 28
3.2.1 MAXIMUM-LIKELIHOOD OBJECTIVE FUNCTION, 29
3.2.2 LI NORM OBJECTIVE FUNCTION, 29 3.2.3 MULTIOBJECTIVE FUNCTION, 29
3.3 REQUIRERNENTS FOR ACEURATE SIMU1ATED RESULTS, 30 3.3.1 ACEURATE
MODEL, 30
3.3.2 UNBIASED OBSERVATIONS AND PRIOR INFORMATION, 30 3.3.3 WEIGHTING
REFLECTS ERRORS, 31
3.4 ADDITIONAL ISSUES
3.4.] PRIOR INFORMATION, 32 3.4.2 WEIGHTING, 34
3.4.3 RESIDUALS AND WEIGHTED RESIDUALS, 35 3.5 LEAST-SQUARES
OBJECTIVE-FUNCTION SURFACES, 35
3.6 EXERCISES, 36 EXERCISE 3.]: STEADY-STATE PARAMETER DEFINITION, 36
EXERCISE 3.2: OBSERVATIONS FOR THE STEADY-STATE PROBLEM, 38
EXERCISE 3.3: EVALUATE MODEL FIT USING STARTING PARAMETER VALUCS, 40
4 DETERRNINING THE INFORMATION THAT OBSERVATIONS PROVIDE ON PARAMETER
VALUES USING FIT-INDEPENDENT STATISTICS
4.1 USING OBSERVATIONS, 42
4.1. I MODEL CONSLRUCTION AND PARAMETER DEFINITION, 42
4.1.2 PARAMETER VALUES, 43
26
41
IMAGE 3
CONTENTS IX
4.2 WHEN TO DETERMINE THE INFORMATION THAT OBSERVATIONS PROVIDE ABOUT
PARAMETER VALUES, 44 4.3 FIT-INDEPENDENT STATISTICS FOR SENSITIVITY
ANALYSIS, 46 4.3.1 SENSITIVITIES, 47
4.3.2 SCALING, 48 4.3.3 DIMENSIONLESS SCALED SENSITIVITIES (DSS), 48
4.3.4 COMPOSITE SCALED SENSITIVITIES (CSS), 50 4.3.5 PARAMETER
CORRELATION COEFFICIENTS (PCC), 51
4.3.6 LEVERAGE STATISTICS, 54 4.3.7 ONE-PERCENT SCALED SENSITIVITIES, 54
4.4 ADVANTAGES AND LIMITATIONS OF FIT-INDEPENDENT STATISTICS FOR
SENSITIVITY ANALYSIS, 56
4.4.1 SCALED SENSITIVITIES, 56 4.4.2 PARAMETER CORRELATION COEFFICIENTS,
58 4.4.3 LEVERAGE STATISTICS, 59 4.5 EXERCISES, 60
EXERCISE 4.1: SENSITIVITY ANALYSIS FOR THE STEADY-STATE MODEL WITH
STARTING PARAMETER VALUES, 60
5 ESTLMATING PARAMETER VALUES
5.1 THE MODIFIED GAUSS-NEWTON GRADIENT METHOD, 68 5.1.1 NORMAL
EQUATIONS, 68 5.1.2 AN EXAMPLE, 74 5.1.3 CONVERGENCE CRITERIA, 76 5.2
ALTERNATIVE OPTIMIZATION METHODS, 77
5.3 MULTIOBJECTIVE OPTIMIZATION, 78 5.4 LOG-TRANSFORMED PARAMETERS, 78
5.5 USE OF LIMITS ON ESTIMATED PARAMETER VALUES, 80 5.6 EXERCISES, 80
EXERCISE 5.1: MODIFIED GAUSS-NEWTON METHOD AND APPLICATION TO A
TWO-PARAMETER PROBLEM, 80 EXERCISE 5.2: ESTIMATE THE PARAMETERS OF THE
STEADY-STATE MODEL, 87
6 EVALUATING MODEL FIT
6.1 MAGNITUDE OF RESIDUALS AND WEIGHTED RESIDUALS, 93 6.2 IDENTIFY
SYSTEMATIC MISFIT, 94 6.3 MEASURES OF OVERALL MODEL FIT, 94 6.3.1
OBJECTIVE-FUNCTION VALUE, 95
67
93
IMAGE 4
X CONTENTS
6,3.2 CALCULATED ERROR VARIANCE AND STANDARD ERROR, 95
6.3.3 AIC, AIC C , AND EIC STATISTICS, 98 6.4 ANALYZING MODEL FIT
GRAPHICALLY AND RELATED STATISTICS, 99
6.4.] USING GRAPHICAL ANALYSIS OF WEIGHTED RESIDUALS 10 DETECT MODEL
ERROR, 100
6.4.2 WEIGHTED RESIDUALS VERSUS WEIGHTED OR UNWEIGHTED SIMULATED VALUES
AND MINIMUM, MAXIMUM, AND AVERAGE WEIGHTED RESIDUALS, 100
6.4.3 WEIGHTED OR UNWEIGHTED OBSERVATIONS VERSUS SIMULATED VALUES AND
CORRELATION COEFFICIENT R, 105
6.4.4 GRAPHS AND MAPS USING INDEPENDENT VARIABLES AND THE RUNS
STATISTIC, 106
6.4,5 NORMAL PROBABILITY GRAPHS AND CORRELATION COEFFICIENT R~, 108
6.4.6 ACCEPTABLE DEVIATIONS FROM RANDOM, NORRNALLY DISTRIBUTED WEIGHTED
RESIDUALS, 111 6.5 EXERCISES, 113 EXERCISE 6.1: STATISTICAL MEASURES OF
OVERALL FIT, 113
EXERCISE 6.2: EVALUATE GRAPH MODEL FIT AND RELATED STATISTICS, 115
7 EVALUATING ESTIMATED PARAMETER VALUES AND PARAMETER UNCERTAINTY
7.1 REEVALUATING COMPOSITE SCALED SENSITIVITIES, ]24
7.2 USING STATISTICS FROM THE PARAMETER VARIANCE-COVARIANCE MATRIX. 125
7.2, I FIVE VERSIONS OF THE VARIANCE-COVARIANCE MATRIX, 125
7.2.2 PARAMETER VARIANCES, COVARIANCES, STANDARD DEVIATIONS,
COEFFICIENTS OF VARIATION, AND CORRELATION COEFFICIENTS, 126
7.2.3 RELATION BETWEEN SAMPIE AND REGRESSION STATISTICS, 127
7,2.4 STATISTICS FOR LOG-TRANSFORRNED PARAMETERS, 130
7.2,5 WHEN TO USE THE FIVE VERSIONS OF THE PARAMETER VARIANCE-COVARIANCE
MATRIX, 130
7,2.6 SOME ALTERNATE METHODS: EIGENVECTORS, EIGENVALUES, AND SINGULAR
VALUE DECOMPOSITION, 132
7.3 IDENTIFYING OBSERVATIONS IMPORTANT TO ESTIMATED PARAMETER VAL LIES,
132
7.3.] LEVERAGE STATISTICS, 134
7,3,2 LNFLUENCE STATISTICS, 134
7.4 UNIQUCNESS AND OPTIMALITY OF THE ESTIMATED PARAMETER VALUES, ]37
7.5 QUANTIFYING PARAMETER VALUE UNCERTAINTY, 137
124
IMAGE 5
CONTENTS
7.5.1 INFERENTIAL STATISTICS, 137
7.5.2 MONTE CARLO METHODS, 140 7.6 CHECKING PARAMETER ESTIMATES AGAINST
REASONABLE VALUES, 140 7.7 TESTING LINEARITY, 142 7.8 EXERCISES, 145
EXERCISE 7.1: PARAMETER STATISTICS, 145 EXERCISE 7.2: CONSIDER ALL THE
DIFFERENT CORRELATION COEFFICIENTS PRESENTED, 155
EXERCISE 7.3: TEST FOR LINEARITY, 155
8 EVALUATING MODEL PREDICTIONS, DATA NEEDS, AND PREDICTION UNCERTAINTY
8.1 SIMULATING PREDICTIONS AND PREDICTION SENSITIVITIES AND STANDARD
DEVIATIONS, 158 8.2 USING PREDICTIONS TO GUIDE COLLECTION OF DATA THAT
DIRECTLY CHARACTERIZE SYSTEM PROPERTIES, 159
8.2.1 PREDICTION SCALED SENSITIVITIES (PSS) , 160 8.2.2 PREDICTION
SCALED SENSITIVITIES USED IN CONJUNCTION WITH COMPOSITE SCALED
SENSITIVITIES, 162 8.2.3 PARAMETER CORRELATION COEFFICIENTS WITHOUT AND
WITH PREDICTIONS, 162 8.2.4 CORNPOSITE AND PREDICTION SCALED
SENSITIVITIES USED WITH PARAMETER CERRELATION COEFFICIENTS, 165 8.2.5
PARAMETER-PREDICTION (PPR) STATISTIC, 166 8.3 USING PREDICTIONS TO GUIDE
COLLECTION OF OBSERVATION DATA, 170
8.3.1 USE OF PREDICTION, COMPOSITE, AND DIMENSIONLESS SCA1ED
SENSITIVITIES AND PARAMETER CORRELATION COEFFICIENTS, 170
8.3.2 OBSERVATION-PREDICTION (OPR) STATISTIC, 171
8.3.3 INSIGHTS ABOUT THE OPR STATISTIC FROM OTHER FIT-INDEPENDENT
STATISTICS, 173 8.3.4 IMPLICATIONS FOR MONITARING NETWORK DESIGN, 174
8.4 QUANTIFYING PREDICTION UNCERTAINTY USING INFERENTIAL STATISTICS, 174
8.4.1 DEFINITIONS, 175 8.4.2 LINEAR CONFIDENCE AND PREDICTION INTERVALS
ON PREDICTIONS, 176 8.4.3 NONLINEAR CONFIDENCE AND PREDICTION INTERVALS,
177 8.4.4 USING THE THEIS EXAMPLE TO UNDERSTAND LINEAR AND
NONLINEAR CONFIDENCE INTERVA1S, 181
8.4.5 DIFFERENCES AND THEIR STANDARD DEVIATIONS, CONFIDENCE INTERVALS,
AND PREDICTION INTERVALS, 182
XI
158
IMAGE 6
XII CONTENTS
8.4.6 USING CONFIDENCE INTERVALS TO SERVE THE PURPOSES OF TRADITIANAL
SENSITIVITY ANALYSIS, 184 8.5 QUANTIFYING PREDICTION UNCERTAINTY USING
MONTE CARLO ANALYSIS, 185
8.5.1 ELEMENTS OF A MONTE CAR10 ANALYSIS, 185
8.5.2 RELATION BETWEEN MONTE CARLO ANALYSIS AND LINEAR AND NONLINEAR
CONFIDENCE INTERVALS, 187
8.5.3 USING THE THEIS EXAMP1E TO UNDERSTAND MONTE CARLO METHODS, 188
8.6 QUANTIFYING PREDICTION UNCERTAINTY USING ALTERNATIVE MODELS, 189
8.7 TESTING MODEL NONLINEARITY WITH RESPECT TO THE PREDICTIONS, 189
8.8 EXERCISES, 193 EXERCISE 8.1: PREDICT ADVECTIVE TRANSPORT AND PERFARM
SENSITIVITY ANALYSIS, 195
EXERCISE 8.2: PREDICTION UNCERTAINTY MEASURED USING INFERENTIAL
STATISTICS, 207
9 CALIBRATING TRANSIENT AND TRANSPORT MODELS AND RECALIBRATING EXISTING
MODELS
9.1 STRATEGIES FOR CALIBRATING TRANSIENT MODELS, 213
9.1.1 INITIAL CONDITIONS, 213
9.1.2 TRANSIENT OBSERVATIONS, 214 9.1.3 ADDITIONAL MODEL INPUTS, 216
9.2 STRATEGIES FOR CALIBRATING TRANSPORT MODELS, 217 9.2.1 SELECTING
PROCESSES TO INCLUDE, 217 9.2.2 DEFINING SOURCE GEOMETRY AND
CONCENTRATIONS, 218
9.2.3 SCALE ISSUES, 219
9.2.4 NUMERICAL ISSUES: MODEL ACCURACY AND EXECUTION TIME, 220
9.2.5 TRANSPORT OBSERVATIONS, 223
9.2.6 ADDITIONAL MODEL INPUTS, 225
9.2.7 EXAMPLES OF OBTAINING A TRACTABLE, USEFUL MODEL, 226
9.3 STRATEGIES FOR RECALIBRATING EXISTING MODELS, 227
9.4 EXERCISES (OPTIONAL), 228
EXERCISES 9.1 AND 9.2: SIMULATE TRANSIENT HYDRAULIC HEADS UND PERFORM
PREPARATORY STEPS, 229
EXERCISE 9.3: TRANSIENT PARAMETER DEFINITION, 230
213
IMAGE 7
CONTENTS
EXERCISE 9.4: OBSERVATIONS FOR THE TRANSIENT PROBLEM, 231 EXERCISE 9.5:
EVALUATE TRANSIENT MODEL FIT USING STARTING PARAMETER VALUES, 235
EXERCISE 9.6: SENSITIVITY ANALYSIS FOR THE INITIAL MODEL, 235
EXERCISE 9.7: ESTIMATE PARAMETERS FOR THE TRANSIENT SYSTEM BY NONLINEAR
REGRESSION, 243 EXERCISE 9.8: EVALUATE MEASURES OF MODEL FIT, 244
EXERCISE 9.9: PERFARM GRAPHICAL ANALYSES OF MODEL FIT
AND EVALUATE RELATED STATISTICS, 246 EXERCISE 9.10: EVALUATE ESTIMATED
PARAMETERS, 250 EXERCISE 9.11: TEST FOR LINEARITY, 253 EXERCISE 9.12:
PREDICTIONS, 254
10 GUIDELINES FOR EFFECTIVE MODELING
10.1 PURPOSE OF THE GUIDELINES, 263 10.2 RELATION TO PREVIOUS WORK, 264
10.3 SUGGESTIONS TOR EFFECTIVE IMPLEMENTATION, 264
11 GUIDELINES 1 THROUGH 8-MODEL DEVELOPMENT
GUIDELINE 1: APPLY THE PRINCIPLE OF PARSIMONY, 268 G1.1 PROBLEM, 269
G1.2 CONSTRUCTIVE APPROACHES, 270 GUIDELINE 2: USE A BROAD RANGE OF
SYSTEM INFORMATION TO CONSTRAIN THE PROBLEM, 272
02.1 DATA ASSIMILATION, 273 02.2 USING SYSTEM INFORMATION, 273 02.3 DATA
MANAGEMENT, 274 02.4 APPLICATION: CHARACTERIZING A FRACTURED
DOLOMITE AQUIFER, 277
GUIDELINE 3: MAINTAIN A WELL-POSED, COMPREHENSIVE REGRESSION PROBLEM,
277 03.1 EXAMPLES, 278 03.2 EFFECTS OF NONLINEARITY ON THE CSS AND PEE,
281
GUIDELINE 4: INCLUDE MANY KINDS OF DATA AS OBSERVATIONS IN THE
REGRESSION, 284 04.1 INTERPOLATED "OBSERVATIONS", 284 G4.2 CLUSTERED
OBSERVATIONS, 285
04.3 OBSERVATIONS THAT ARE INCONSISTENT WITH MODEL CONSTRUCTION, 286
XIII
260
268
IMAGE 8
XIV CONTENTS
04.4 APPLICATIONS: USING DIFFERENT TYPES OF OBSERVATIONS TO CALIBRATE
GROUNDWATER FLOW AND TRANSPORT MODELS, 287
GUIDELINE 5: USE PRIOR INFORMATION CAREFULLY, 288
05. I USE OF PRIOR INFORMATION COMPARED WITH OBSERVATIONS, 288 05.2
HIGHLY PARAMETERIZED MODELS, 290 05.3 APPLICATIONS: GEOPHYSICAL DATA,
291 GUIDELINE 6: ASSIGN WEIGHTS THAT REFLECT ERRORS, 291
G6.L DETERMINE WEIGHTS, 294 06.2 ISSUES OF WEIGHTING IN NONLINEAR
REGRESSION, 298 GUIDELINE 7: ENCOURAGE CONVERGENCE BY MAKING THE MODEL
MORE ACEURATE AND EVALUATING THE OBSERVATIONS, 306
GUIDELINE 8: CONSIDER ALTERNATIVE MODELS, 308
G8. I DEVELOP ALTERNATIVE MODELS, 309
08.2 DISCRIMINATE BETWEEN MODELS, 310 G8.3 SIMULATE PREDICTIONS WITH
ALTERNATIVE MODELS, 312
08.4 APPLICATION, 313
12 GUIDELINES 9 AND LO-MODEL TESTING
GUIDELINE 9: EVALUATE MODEL FIT, 316
G9.1 DETERMINE MODEL FIT,. 316
09.2 EXARNINE FIT FOR EXISTING OBSERVATIONS IMPORTANT TO THE PURPOSE OF
THE MODEL, 320
G9.3 DIAGNOSE THE CAUSE OF POOF MODEL FIT, 320
GUIDELINE 10: EVALUATE OPTIRNIZED PARAMETER VALUES, 323
GI O. I QUANTIFY PARAMETER-VALUE UNCERTAINTY, 323
G10.2 USE PARAMETER ESTIMATES TO DETECT MODEL ERROR, 323
G10.3 DIAGNOSE THE CAUSE OF UNREASONABLE OPTIMAL PARAMETER ESTIMATES,
326
GIO.4 IDENTIFY OBSERVATIONS IMPORTANT TO THE PARAMETER ESTIMATES, 327
GIO.5 REDUCE OR INCREASE THE NUMBER OF PARAMETERS, 328
13 CUIDELINES 11 AND 12- POTENTIAL NEW DATA
GUIDELINE 11: IDENTIFY NEW DATA TO IMPROVE SIMULATED PROCESSES,
FEATURES, UND PROPERTIES, 330
GUIDELINE LZ: IDENTIFY NEW DATA TO IMPROVE PREDICTIONS, 334
G 12.1 POTENTIAL NEW DATA TO IMPROVE FEATURES AND PROPERTIES GOVERNING
SYSTEM DYNARNICS, 334
G 12.2 POTENTIAL NEW DATA TO SUPPORT OBSERVATIONS, 335
315
329
IMAGE 9
CONTENTS
14 GUIDELINES 13 AND 14-PREDICTION UNCERTAINTY
GUIDELINE 13: EVALUATE PREDICTION UNCERTAINTY AND ACCURACY USING
DETERMINISTIC METHODS, 337 GL3.1 USE REGRESSION TO DETERMINE WHETHER
PREDICTED VALUES ARE CONTRADIETED BY THE CALIBRATED
MODEL, 337
G13.2 USE ORNITTED DATA AND POSTAUDITS, 338 GUIDELINE 14: QUANTIFY
PREDICTION UNCERTAINTY USING STATISTICAL METHODS, 339 G14.1 INFERENTIAL
STATISTICS, 341
G14.2 MONTE CARLO METHODS, 34]
15 USING AND TESTING THE METHODS AND GUIDELINES
15.1 EXECUTION TIME ISSUES, 345 15.2 FIE1D APPLICATIONS AND SYNTHETIC
TEST CASES, 347 15.2.1 THE DEATH VALLEY REGIONAL FLOW SYSTEM, CALIFORNIA
AND NEVADA, USA, 347
15.2.2 GRINDSTED LANDFILL, DENMARK, 370
APPENDIX A: OBJECTIVE FUNCTION ISSUES
A.1 DERIVATION OF THE MAXIMUM-LIKELIHOOD OBJECTIVE FUNCTION, 375 A2
RELATION OF THE MAXIMURN-LIKELIHOOD AND LEAST-SQUARES OBJECTIVE
FUNCTIONS, 376
A3 ASSUMPTIONS REQUIRED FOR DIAGONAL WEIGHTING TO BE CORRECT, 376 A4
REFERENCES, 381
APPENDIX B: CALCULATION DETAILS OF THE MODIFIED GAUSS-NEWTON METHOD
B.1 VECTORS AND MATRICES FOR NONLINEAR REGRESSION, 383 B.2 QUASI-NEWTON
UPDATING OF THE NORMAL EQUATIONS, 384 B.3 CALCULATING THE DAMPING
PARAMETER, 385 BA SOLVING THE NORMAL EQUATIONS, 389
B.5 REFERENCES, 390
APPENDIX C: TWO IMPORTANT PROPERTIES OF LINEAR REGRESSION AND THE
EFFECTS OF NONLINEARITY
C.] IDENTITIES NEEDED FOR THE PROOFS, 392 C.1.1 TRUE LINEAR MODEL, 392
C.1.2 TRUE NONLINEAR MODEL, 392
XV
337
345
374
383
391
IMAGE 10
XVI CONTENTS
CL.3 LINEARIZED TRUE NONLINEAR MODEL, 392 CIA APPROXIMATE LINEAR MODEL,
392 CI.5 APPROXIMATE NONLINEAR MODEL, 393 C.1.6 LINEARIZED APPROXIMATE
NONLINEAR MODEL, 393
C.L .7 THE IMPORTANCE OF X AND X, 394 CI .8 CONSIDERING MANY
OBSERVATIONS, 394 C.1.9 NORMAL EQUATIONS, 395
C.L. I0 RANDOM VARIABLES, 395 C.I. I I EXPECTED VALUE, 395 C.1.12
VARIANCE-COVARIANCE MATRIX OF A VECTOR, 395
C.2 PROOF OF PROPERTY 1: PARAMETERS ESTIMATED BY LINEAR REGRESSION ARE
UNBIASED, 395
C.3 PROOF OF PROPERTY 2: THE WEIGHT MATRIX NEEDS TO BE DEFINED IN A
PARTICULAR WAY FOR EQ. (7.1) TO APPLY AND FOR THE PARAMETER ESTIMATES TO
HAVE THE SMALLEST VARIANCE, 396
CA REFERENCES, 398
APPENDIX D: SELECTED STATISTICAL TABLES
0.1 REFERENCES, 406
REFERENCES
INDEX
399
407
427 |
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| spelling | Hill, Mary C. Verfasser aut Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty Mary C. Hill ; Claire R. Tiedeman Hoboken, NJ Wiley-Interscience 2007 XVIII, 455 S. Ill., graph. Darst., Kt. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 407-426) and index Mathematisches Modell Groundwater Mathematical models Hydrologic models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Grundwasser (DE-588)4022369-3 gnd rswk-swf Grundwasser (DE-588)4022369-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Tiedeman, Claire R. Verfasser aut http://www.loc.gov/catdir/toc/ecip065/2005036657.html Table of contents only OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015738347&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hill, Mary C. Tiedeman, Claire R. Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty Mathematisches Modell Groundwater Mathematical models Hydrologic models Mathematisches Modell (DE-588)4114528-8 gnd Grundwasser (DE-588)4022369-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4022369-3 |
| title | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty |
| title_auth | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty |
| title_exact_search | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty |
| title_exact_search_txtP | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty |
| title_full | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty Mary C. Hill ; Claire R. Tiedeman |
| title_fullStr | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty Mary C. Hill ; Claire R. Tiedeman |
| title_full_unstemmed | Effective groundwater model calibration with analysis of data, sensitivities, predictions, and uncertainty Mary C. Hill ; Claire R. Tiedeman |
| title_short | Effective groundwater model calibration |
| title_sort | effective groundwater model calibration with analysis of data sensitivities predictions and uncertainty |
| title_sub | with analysis of data, sensitivities, predictions, and uncertainty |
| topic | Mathematisches Modell Groundwater Mathematical models Hydrologic models Mathematisches Modell (DE-588)4114528-8 gnd Grundwasser (DE-588)4022369-3 gnd |
| topic_facet | Mathematisches Modell Groundwater Mathematical models Hydrologic models Grundwasser |
| url | http://www.loc.gov/catdir/toc/ecip065/2005036657.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015738347&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hillmaryc effectivegroundwatermodelcalibrationwithanalysisofdatasensitivitiespredictionsanduncertainty AT tiedemanclairer effectivegroundwatermodelcalibrationwithanalysisofdatasensitivitiespredictionsanduncertainty |