Inverse methods in global biogeochemical cycles : [papers of a symposium workshop titled "Inverse modeling of global biogeochemical cycles", held in Crete, Greece in March 1998

Published by the American Geophysical Union as part of the __Geophysical Monograph Series__. Our understanding of biogeochemical cycles is directly related to the research and analyses we bring to them, and to our critical sense of the methods we use. Of primary importance here are the theories behind, and our use of, inverse methods and data assimilation techniques across a multidisciplinary context that includes atmosphere-biosphere and atmosphere-ocean interactions, atmospheric chemistry, physical oceanography, and ocean biogeochemistry. Certainly, researchers in many earth system science disciplines, whether novice or expert, will benefit from the breadth and depth we have brought to the topics discussed in this monograph. At the same time, we have provided readers with a unique opportunity to enhance their research acumen and their understanding of ways and means. Toward this end, this monograph consists of a tutorial section with problem sets for use by readers who wish to test and enhance their knowledge, and a research section that showcases some of the latest scientific results from use of the aforementioned methods in a variety of earth science disciplines.Content: Title Page ......Page 3 Copyright ......Page 4 CONTENTS......Page 5 PREFACE......Page 7 Introduction and Overview......Page 8 REFERENCES......Page 9 1. INTRODUCTION......Page 10 2. MEASUREMENT EQUATION......Page 12 3. CHEMICAL TRANSPORT MODEL ANDMODEL ERRORS......Page 14 4. INVERSE PROBLEM......Page 15 5. KALMAN FILTER......Page 16 6. SAMPILE APPLICATION......Page 18 7. CONCLUDING REMARKS......Page 20 REFERENCES......Page 24 1. INTRODUCTION......Page 26 2. ILL-CONDITIONING......Page 27 3. ERROR ANALYSIS......Page 28 4.1 Generic Relations......Page 29 4.3 State-Space Representations......Page 30 5.2 Statistics......Page 31 6. TIME-DEPENDENT INVERSIONS......Page 33 APPENDIX A: LEAST-SQUARES ESTIMATION......Page 34 APPENDIX B: ERROR ANALYSIS......Page 35 NOTATION......Page 36 REFERENCES......Page 37 1. INTRODUCTION......Page 39 2. MATHEMATICAL BACKGROUND......Page 40 3.3. Parameter Estimation......Page 42 4.1. Adjoint of Analytical Equations......Page 43 5.1. Passive Tracer in the Ocean......Page 44 5.2. Passive Tracer in the Atmosphere......Page 45 5.3. North Atlantic Meridional Heat Flux Sensitivity......Page 46 6. CONCLUSIONS......Page 48 APPENDIX A: TAMC EXAMPLE......Page 51 REFERENCES......Page 52 2. CONCEPTS OF PROBABILISTIC ESTIMATION......Page 55 2.2. Minimum Variance Estimation......Page 56 2.3. Maximum a Posteriori Probability Estimation......Page 57 3. EXAMPLE: ESTIMATION OF ACONSTANT VECTOR......Page 58 4.1. Estimation Problem in Linear Systems......Page 61 4.2. The Kalman Filter......Page 63 4.3. Minimum Variance and Conditional Mean......Page 64 4.4. The Fixed-Lag Kalman Smoother......Page 66 5. SUMMARY......Page 68 REFERENCES......Page 70 1. INTRODUCTION......Page 72 2. OBSERVATION EQUATION......Page 73 3.1. Analysis Method for Small Observation Vectors......Page 74 3.2. Analysis Methods for Large Observation Vectors......Page 75 4. COVARIANCE MODELING......Page 76 4.3. Homogeneity and Isotropy......Page 77 4.4. Spectral Representation......Page 78 5. COVARIANCE PARAMETER ESTIMATION......Page 79 6. EVOLUTION OF THE FORECAST ERROR COVARIANCE......Page 80 7. KALMAN FILTER ASSIMILATION ONISENTROPIC SURFACES......Page 81 REFERENCES......Page 83 1. INTRODUCTION......Page 85 2. BOX MODELS OF TRANSPORT......Page 86 3.2. TAMC and TAMLINK......Page 87 3.3. Sensitivities of Box Model......Page 88 4.1. Adjoint Methods Exercises......Page 94 4.2. Green's Function Methods......Page 96 4.3. Kalman Filtering......Page 97 5. SOLUTIONS......Page 103 APPENDIX- SYSTEM AND SOFTWAR EREQUIREMENTS......Page 108 REFERENCES......Page 109 1. INTRODUCTION......Page 111 2. DATA......Page 112 3.1. Model Grid......Page 115 3.2. Model Parameters and Equations......Page 116 3.3. Cost Function......Page 118 3.4. Adjoint Model......Page 119 4. RESULTS......Page 121 4.2. Export Production......Page 123 5. DISCUSSION......Page 125 REFERENCES......Page 127 1. INTRODUCTION......Page 129 2.1. Outline of the Formal Inverse Problem......Page 130 2.2. Issues and Opportunities......Page 132 3. USING REMOTE SENSING DATA TOCHARACTERIZE LAND SURFACES......Page 134 4. EVOLUTION OF EARTH OBSERVATION TECHNOLOGIES AND IMPLICATIONS......Page 137 NOTATION......Page 138 REFERENCES......Page 139 1. INTRODUCTION......Page 142 2. THE RRSQRT-FILTER ALGORITHM......Page 143 3.1. Ensemble Forecast......Page 144 3.2. Forecast Based on First Order Linearizations......Page 145 3.3. Forecasts Based on Second Order Linearizations......Page 146 4. COMPARISON OF FORECAST METHODS......Page 147 APPENDIX A' SETUP OF THE EXPERIMENTS......Page 148 REFERENCES......Page 149 1. INTRODUCTION......Page 150 3. SOLUTION OF THE INVERSE PROBLEM......Page 152 4. RESULTS......Page 154 5. CONCLUSIONS AND OUTLOOK......Page 155 NOTATION......Page 156 REFERENCES......Page 157 1. INTRODUCTION......Page 158 2.3. Local Thin Plate Fit......Page 160 3. THE ASSIMILATION METHOD......Page 161 3.2. Formulation of the JD Vat Algorithm......Page 162 4.1. Interpolation......Page 164 4.2. Assimilation......Page 166 5.1. Interpolation......Page 169 NOTATION......Page 170 REFERENCES......Page 172 1. INTRODUCTION......Page 173 2. MODEL......Page 174 3. DATA......Page 175 4.2. Adjoint Model......Page 176 4.3. Minimization Algorithm......Page 177 5.2. Estimated Circulation in the Atlantic During theLast Glacial Maximum......Page 178 6. CONCLUSION AND SUMMARY......Page 182 REFERENCES......Page 183 1.1. Background......Page 186 1.3. Southern Ocean......Page 187 2.2. Model Solution......Page 188 3.1. Optimal Solution......Page 190 3.2. Sensitivity Studies......Page 192 5.2. A Non-Steady-State Ocean......Page 194 REFERENCES......Page 195 1. INTRODUCTION......Page 197 2. METHOD......Page 198 3. APPLICATION TO THE INDIAN OCEAN......Page 199 4. RESULTS AND DISCUSSION......Page 200 APPENDIX I : MODEL EQUATIONS......Page 201 MODEL PARAMETERS I......Page 202 REFERENCES......Page 203 1. INTRODUCTION......Page 205 2.1. The PSyDyn Model......Page 207 3. INVERSIONS USING THE LINEAR LEAST SQUARES ALGORITHM......Page 209 3.1. The Linear Least Squares Algorithm......Page 210 3.2. Application of the Linear Least SquaresAlgorithm......Page 211 3.3. Results......Page 213 4.3. Results......Page 215 5. DISCUSSION......Page 217 NOTATION......Page 220 REFERENCES......Page 221 1. INTRODUCTION......Page 223 2. MODEL EQUATIONS AND DATA......Page 225 3. RECOVERY OF INITIAL CONDITIONS......Page 226 4. EXTRACTION OF MODEL PARAMETERS......Page 230 5. NONLINEAR GLOBAL OPTIMIZATION......Page 233 6. DISCUSSION......Page 234 NOTATION......Page 236 REFERENCES......Page 237 1. INTRODUCTION......Page 238 3. SOURCE ELEMENTS......Page 239 4. DATA SETS......Page 241 6. RESULTS OF INVERSE CALCULATIONS......Page 244 NOTATION......Page 251 REFERENCES......Page 252 1. INTRODUCTION......Page 253 3. MODELLING METHOD......Page 254 4.1. Surface C02 Fluxes......Page 256 4.2. Interannual Variability of Regional Source......Page 258 4.3. C02 Time Series......Page 259 REFERENCES......Page 261 1. INTRODUCTION......Page 263 2. METHOD......Page 264 3. EXPERIMENTAL DESIGN......Page 266 4.1. Response to Varying Observational NetworkConfiguration......Page 268 4.3. Uncertainty Due to Spatial Heterogeneity Sources......Page 270 4.4. Retrieval of Time-Dependent Sources......Page 273 REFERENCES......Page 274 1. INTRODUCTION......Page 276 2.1. Measurement Model......Page 277 2.2. Defining the Estimation Problem......Page 279 3. ERROR ANALYSIS......Page 280 3.1. Error Analysis Using Unbiased, GaussianMeasurement Errors......Page 281 3.2. Systematic Errors in the Measurement Model H......Page 286 3.3. Further Error Considerations......Page 287 NOTATION......Page 288 REFERENCES......Page 289 1. INTRODUCTION......Page 291 2.1. Components......Page 292 2.3. Time-Dependent Case......Page 295 3.1. Optimized Concentrations......Page 296 3.2. Net C02 Budget Over Large Regions......Page 298 3.4. Convergence Tests Between TD and TIInversions......Page 300 NOTATION......Page 303 REFERENCES......Page 304 1. INTRODUCTION......Page 306 2. RECTIFIER EFFECTS......Page 307 3. MEASUREMENT REQUIREMENTS......Page 308 4. HARVARD FOREST DATA......Page 310 5. AMAZON DATA......Page 312 6. A SIMPLE BOUNDARY-LAYER MODEL......Page 313 7. THE CO2 BUDGET AND RECTIFICATION AIRBORNE STUDY......Page 315 REFERENCES......Page 317 The Cd-rom Contains The Code And Data Files For The Exercises Outlined In The Paper By Rayner, Et At., (p. 81-106). Tutorial Section : Mathematical Tools And Techniques. Measurement Equation For Trace Chemicals In Fluids And Solution Of Its Inverse / Ronald G. Prinn ; Green's Function Methods Of Tracer Inversion / I.g. Enting ; Tangent Linear And Adjoint Biogeochemical Models / Ralf Giering ; Estimation Theory And Atmospheric Data Assimilation / Ricardo Todling ; Tracer Assimilation / Richard Ménard -- Tutorial Section : Exercises. Exercises / P.j. Rayner [and Others] -- Tutorial Section : Applications. Applying The Adjoint Method For Biogeochemical Modeling : Export Of Particulate Organic Matter In The World Ocean / Reiner Schlitzer ; Environmental Information Extraction From Satellite Remote Sensing Data / Michel M. Verstraete And Bernard Pinty -- Research Section. Nonlinear Kalman Filters For Atmospheric Chemistry Models / Arjo Segers [and Others] ; Inverse Modelling Of Sulfur Emissions In Europe Based On Trajectories / Petra Seibert ; A Comparison Between Interpolation And Assimilation As Cartography Methods For The Sage Ii Aerosol Product / Ghislain Franssens [and Others] ; Paleonutrient Data Analysis Of The Glacial Atlantic Using An Adjoint Ocean General Circulation Model / A.m.e. Winguth [and Others] ; Deep Water Formation Rates Inferred From Global Tracer Distributions : An Inverse Model / S. Peacock, M. Visbeck, And W. Broecker ; Comparisons Of Simulations Of A Marine Ecosystem Model With Czcs Data In The North Indian Ocean / M.k. Sharada And K.s. Yajnik ; Nonlinear Inversions Of A Model Of The Oceanic Dissolved-particulate Exchanges / Véronique Athias, Pierre Mazzega, And Catherine Jeandel ; On The Assimilation And Inversion Of Small Data Sets Under Chaotic Regimes / Pierre Mazzega ; Synthesis Inversion Of Atmospheric Co2 Using The Nire Chemical Transport Model / Shoichi Taguchi ; Calculating Co2 Fluxes By Data Assimilation Coupled To A Three Dimensional Mass Balance Inversion / R.j. Dargaville And I. Simmonds ; A Time-dependent Assimilation And Source Retrieval Technique For Atmospheric Tracers / Lori Bruhwiler, Pieter Tans, And Michel Ramonet ; An Inversion Method For Determining Time-dependent Surface Co2 Fluxes / David F. Baker ; Differences Of Co2 Flux Estimates Based On A Time-independent Versus A Time-dependent Inversion Method / Philippe Peylin [and Others] ; The Co2 Budget And Rectification Airborne Study : Strategies For Measuring Rectifiers And Regional Fluxes / Britton B. Stephens [and Others]. Prasad Kasibhatla ... [et Al.]. Includes Bibliographical References. System Requirements For Computer Disk: Requires Matlab And Fortran-77 Or Fortran-90. This monograph grew out of a March 1998 symposium on inverse modeling held in Crete, and is appropriate for advanced courses in biogeochemical cycle modeling. The 14 research papers on the latest developments in the theory and use of inverse methods and data assimilation complement the eight tutorials on adjoint, Green's function, and Kalman filtering methods. Topics covered include carbon dioxide source/sink estimation, atmospheric chemistry, physical oceanography, ocean biogeochemistry, and satellite data mapping. The CD-ROM of exercises requires MATLAB and Fortran- 77 or Fortran-90. No index. Annotation copyrighted by Book News, Inc., Portland, OR