Land Carbon Cycle Modeling: Matrix Approach, Data Assimilation, & Ecological Forecasting

Description

Carbon moves through the atmosphere, through the oceans, onto land, and into ecosystems. This cycling has a large effect on climate – changing geographic patterns of rainfall and the frequency of extreme weather – and is altered as the use of fossil fuels adds carbon to the cycle. The dynamics of this global carbon cycling are largely predicted over broad spatial scales and long periods of time by Earth system models. This book addresses the crucial question of how to assess, evaluate, and estimate the potential impact of the additional carbon to the land carbon cycle. The contributors describe a set of new approaches to land carbon cycle modeling for better exploring ecological questions regarding changes in carbon cycling; employing data assimilation techniques for model improvement; and doing real- or near-time ecological forecasting for decision support. This book strives to balance theoretical considerations, technical details, and applications of ecosystem modeling for research, assessment, and crucial decision making. Key Features Helps readers understand, implement, and criticize land carbon cycle models Offers a new theoretical framework to understand transient dynamics of land carbon cycle Describes a suite of modeling skills – matrix approach to represent land carbon, nitrogen, and phosphorus cycles; data assimilation and machine learning to improve parameterization; and workflow systems to facilitate ecological forecasting Introduces a new set of techniques, such as semi-analytic spin-up (SASU), unified diagnostic system with a 1-3-5 scheme, traceability analysis, and benchmark analysis, for model evaluation and improvement Related Titles Isabel Ferrera, ed. Climate Change and the Oceanic Carbon Cycle: Variables and Consequences (ISBN 978-1-774-63669-5) Lal, R. et al., eds. Soil Processes and the Carbon Cycle (ISBN 978-0-8493-7441-8) Windham-Myers, L., et al., eds. A Blue Carbon Primer: The State of Coastal Wetland Carbon Science, Practice and Policy (ISBN 978-0-367-89352-1) Cover Half Title Title Page Copyright Page Table of Contents Preface Notes on the Editors Contributors Unit I: Fundamentals of Carbon Cycle Modeling Chapter 1: Theoretical Foundation of the Land Carbon Cycle and Matrix Approach Convergence of the Land Carbon Cycle Donor Pool-Dominant Transfer and Other Properties That Govern the Land Carbon Cycle The Matrix Approach to Model Representation of the Land Carbon Cycle The Paradox of the Matrix Equation and Nonautonomous Systems Predictability of the Land Carbon Cycle Dynamic Disequilibrium of Land Carbon Cycle Suggested Reading Quizzes Chapter 2: Introduction to Modeling What is a Model? Models in Research Ways of Using Models System Dynamics Types of Land Carbon Cycle Models Modeling Workflow Specify the Question or Hypothesis and Identify How Modeling Can Help Choose a Model Verify that the Model Works Calibrate the Model Validate the Model Design the Model Experiment Summary Suggested Reading Quizzes Chapter 3: Flow Diagrams and Balance Equations of Land Carbon Models Carbon Flow Diagram Carbon Balance Equations From Flow Diagram to Carbon Balance Equations Suggested Reading Quizzes Chapter 4: Practice 1: Carbon Flow Diagram and Carbon Balance Equations Introduction Unit II: Matrix Representation of Carbon Balance Chapter 5: Developing Matrix Models for Land Carbon Models What is the Matrix Version of the Carbon Balance Equation? How to Derive the Matrix Equation? Suggested Reading Quizzes Chapter 6: Coupled Carbon-Nitrogen Matrix Models Introduction Matrix Representation of C-N Coupling in Terrestrial Ecosystem (TECO) Model Application of Matrix Representation of C-N Coupled Model Matrix Representation of C-N Coupling in CLM5 Global Validation of the CLM5 Matrix Model for C and N Simulations Suggested Reading Quizzes Chapter 7: Compartmental Dynamical Systems and Carbon Cycle Models Introduction Definition of Compartmental Systems Classification of Compartmental Systems Autonomous Versus Nonautonomous Systems Linear Versus Nonlinear Systems Properties and Long-Term Behavior of Autonomous Compartmental Systems Linear Systems Nonlinear Systems Stability Analysis Near Equilibria Linear Systems Nonlinear Systems Properties and Long-Term Behavior of nonautonomous Systems Linear Systems Nonlinear Systems Final Remarks Suggested Reading Quizzes Chapter 8: Practice 2: Matrix Representation of Carbon Balance Equations and Coding Introduction Unit III: Carbon Cycle Diagnostics for Uncertainty Analysis Chapter 9: Unified Diagnostic System for Uncertainty Analysis Uncertainty in Land Carbon Cycle Modeling One Formula to Represent Land Carbon Cycle Models A Three-dimensional (3D) Space to Describe Model Outputs Five Traceable Components for Traceability Analysis Suggested Reading Quizzes Chapter 10: Sensitivity Analysis with Matrix Equations: A Case Study with ORCHIDEE What is Sensitivity Analysis? Sobol Sensitivity Analysis One-at-a-time Sensitivity Analysis Spatial Pattern Suggested Reading Quizzes Chapter 11: Matrix Phosphorus Model and Data Assimilation Introduction A Brief Overview of Soil P Dynamics Models Matrix Approach to Soil P Modeling and Data Assimilation An Example of Applying a Matrix Model and Data Assimilation to Soil P Data Selection and Description Construction of the P Matrix Model Model Validation and Data Assimilation New Knowledge Emerging From Data Assimilation with the Matrix Model Soil P Dynamics Quantified by Data Assimilation Soil P Dynamics in Relation to Other Ecosystem Properties Summary Suggested Reading Quizzes Chapter 12: Practice 3: Diagnostic Variables in Matrix Models Motivation of the Uncertainty Diagnostics The Mathematical Foundation of the Diagnostics of Land Carbon Cycle Models Carbon Storage Capacity and Carbon Storage Potential Residence Time and Carbon Input Suggested Reading Unit IV: Semi-Analytic Spin-Up (SASU) Chapter 13: Nonautonomous ODE System Solver and Stability Analysis Introduction Analytical Solution First Order Non-homogeneous Scalar Equation One-Pool Model Homogeneous Nonautonomous ODEs System Non-homogeneous Nonautonomous ODEs System N- Pool Model Mathematica Calculation For the Analytical Solution of a 3-pool Model Stability Instantaneous Steady State Instantaneous Steady State for a 3-pool Model Global Attractor The Global Attractor of the N-Pool Model General Stability Statements Suggested Reading Quizzes Chapter 14: Semi-Analytic Spin-Up (SASU) of Coupled Carbon-Nitrogen Cycle Models What Is Spin-Up? Development of Spin-Up Approaches Semi-Analytic Spin-Up The Procedure of Semi-Analytic Spin-Up in CABLE Computational Efficiency Suggested Reading Quizzes Select one option from the given answers Chapter 15: Time Characteristics of Compartmental Systems Introduction Age and Transit Time Distributions for Autonomous Systems in Equilibrium Age and Transit Time Distributions for Nonautonomous Systems Age Distributions Transit Time Distributions Final Remarks Suggested Reading Quizzes Chapter 16: Practice 4: Efficiency and Convergence of Semi-Analytic Spin-Up (SASU) in TECO SASU to Improve Computational Efficiency of Spin-up of Biogeochemical Models Spin-up in the Simplified TECO Model Spin-up with Different Model Parameters Spin-up in a Weak Nonlinear System Unit V: Traceability and Benchmark Analysis Chapter 17: Overview of Traceability Analysis A Key Challenge for Earth System Models: Identification of Uncertainty Sources Traceability Framework: Design and Key Components Benefits of Traceability Analysis for Identifying Model Uncertainty Sources Summary Suggested Reading Quizzes Chapter 18: Applications of the Transient Traceability Framework Introduction A Traceability Framework for Transient Land Carbon Storage Dynamics Transient Traceability Analysis of Carbon Storage at Duke Forest and Harvard Forest Transient Traceability Analysis of Land Carbon Storage in Model Intercomparison Projects Summary Suggested Reading Quizzes Chapter 19: Benchmark Analysis Introduction Aspects of Land Models to be Evaluated Reference Data Sets as Benchmarks Benchmarking Metrics Performance of Three CLM Versions and Future Improvements Conclusions Suggested Reading Quizzes Chapter 20: Practice 5: Traceability Analysis for Evaluating Terrestrial Carbon Cycle Models Introduction Unit VI: Introduction to Data Assimilation Chapter 21: Data Assimilation: Introduction, Procedure, and Applications Introduction of Data Assimilation The Need for Data Assimilation SEVEN-STEP Procedure of Data Assimilation Scientific Values of Data Assimilation Suggested Reading Quizzes Chapter 22: Bayesian Statistics and Markov Chain Monte Carlo Method in Data Assimilation Introduction Bayes’ Theorem Markov Chain Monte Carlo Method Convergence of MCMC Results Suggested Reading Quizzes Chapter 23: Application of Data Assimilation to Soil Incubation Data Soil Incubation Experiments Soil Carbon Models Application of Data Assimilation to Soil Incubation Data Summary Suggested Reading Quizzes Chapter 24: Practice 6: The Seven-step Procedure for Data Assimilation Introduction Step 1: Defining an Objective Step 2: Preparing Data Step 3: Model Step 4: Cost Function Step 5: Optimization Method Step 6: Estimate Parameters Step 7: Prediction Exercises with CarboTrain Toolbox Suggested Reading Unit VII: Data Assimilation with Field Measurements and Satellite Data Chapter 25: Model-Data Integration at the SPRUCE Experiment Introduction Site Description Modeling for the SPRUCE Experiment Model Validation and Uncertainty Quantification Suggested Reading Quizzes Chapter 26: Application of Data Assimilation to a Peatland Methane Study Uncertainty in Methane Modeling Assimilation of Methane Emissions Data into the TECO Model Suggested Reading Quizzes Chapter 27: Global Carbon Cycle Data Assimilation Using Earth Observation: The CARDAMOM Approach Introduction Challenges for Modeling Model Complexity Model Error Data-Model Integration CARDAMOM and DALEC – An Example Framework for C Cycle Diagnostics The Data Assimilation Linked Ecosystem Carbon (DALEC) Model The Carbon Data Model Framework (CARDAMOM) Innovations in the CARDAMOM Approach An Example of CARDAMOM Key Challenges and Opportunities for Data Assimilation Suggested Reading Quizzes Chapter 28: Practice 7: Data Assimilation at the SPRUCE Site Practice design Unit VIII: Value of Data to Constrain Models and Their Predictions Chapter 29: Information Contents of Different Types of Data Sets to Constrain Parameters and Predictions Introduction An Overview of the Information Contents of Model and Data A Method to Quantify the Information Contents of Model and Data Short- and Long-term Information Contents of Model and Data The Information Contents of Data Depend on the Amount and Type of Data Model Equifinality Prediction of Land Carbon Dynamics After Data Assimilation Summary Suggested Reading Quizzes Chapter 30: Using Data Assimilation to Identify Mechanisms Controlling Lake Carbon Dynamics Models and Data-Model Fusion Processes That May Control Epilimnetic C Dynamics Model Calibration and Selection Processes That Control Epilimnetic C Dynamics Suggested Reading Quizzes Chapter 31: Data-Constrained Uncertainty Analysis in Global Soil Carbon Models Introduction Alternative Model Structures Datasets and Data-Model Fusion Posterior Distribution of Model Parameters Uncertainties in Soil Carbon Projections Under RCP 8.5 Sensitivity to Initial Conditions and Model Parameters Suggested Reading Quizzes Chapter 32: Practice 8: Information Contents of Land Carbon Pool and Flux Measurements to Constrain a Land Carbon Model Introduction Summary Unit IX: Ecological Forecasting with EcoPAD Chapter 33: Introduction to Ecological Forecasting Introduction Weather Forecasting Models and Predictability of the Terrestrial Carbon Cycle Data Availability to Constrain Forecast Via Data Assimilation Workflow System to Facilitate Ecological Forecasting Suggested Reading Quizzes Chapter 34: Ecological Platform for Assimilating Data (EcoPAD) for Ecological Forecasting Why Do We Need EcoPAD? General Structure of EcoPAD Applications of EcoPAD: The Example of SPRUCE Suggested Reading Quizzes Chapter 35: Practice 9: Ecological Forecasting at the SPRUCE Site Introduction Dataset Preparation for EcoPAD Accessing and Working With EcoPAD-SPRUCE Unit X: Process-based Machine Learning and Data-driven Modeling (PRODA) Chapter 36: Introduction to Machine Learning and Neural Networks Introduction and Applications of Machine Learning K-fold Cross-Validation For Evaluating Prediction/Test Accuracy Other Applications Avoiding Under/Overfitting in a Neural Network For Regression Comparing Neural Networks For Image Classification Cross-Validation For Evaluating Predictions of Earth System Model Parameters Suggested Reading Quizzes Chapter 37: PROcess-Guided Deep Learning and DAta-Driven Modelling (PRODA) The Need for Optimizing Parameterization of Earth System Models The Workflow of PRODA Model Representation of SOC Content Across Observation Sites Spatial Distribution of SOC Across the Conterminous U.S. Vertical Distribution of SOC Across the Conterminous U.S. Toward More Realistic Representations of SOC Distribution Suggested Reading Quizzes Chapter 38: Practice 10: Deep Learning to Optimize Parameterization of CLM5 Rationale of Estimating Parameter Values by a Deep Learning Model What Is a Neural Network? Hyperparameters in the Neural Network Tuning the Neural Network for Better Performance PRODA Versus Data Assimilation Alone for Optimized SOC Distributions in CLM5 Appendices Appendix 1: Matrix Algebra in Land Carbon Cycle Modeling Motivations Matrix Operations Basic Operations Matrix Multiplication Quiz 1 Matrix Equations Identity Matrix, Inverse Matrix Solving Matrix Equations Quiz 2 Linear System Eigenvalues and Eigenvectors Quiz 3 Suggested Reading Appendix 2: Introduction to Programming in Python What is Python and How Does It Run? The First Python Program Variables and Operators Advanced Variables and Operators The List Variable The Function Operator The Class Operator The Module Operator Summary Suggested Reading QuizZES Appendix 3: CarboTrain User Guide Introduction Download CarboTrain Prerequisite Software Installation on Windows Install Python 3.7.9 Fortran Complier Install R 3.6.3 Installation on macOS Install Python 3.7.9 Fortran Compiler Install R 4.0.5 Uses of CarboTrain References Index