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

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