Theoretical Foundation of the Land Carbon Cycle and Matrix Approach

The land carbon cycle has been extensively studied yet its fundamental properties have not been fully understood. This chapter offers empirical evidence to demonstrate a general dynamic pattern that the land carbon cycle changes in a direction toward a moving attractor in response to global change. This general pattern is captured by a matrix equation. The relatively simple matrix equation can unify land carbon cycle models, accelerate computational efficiency for spin-up, diagnose model performance with new analytics, enable data assimilation with complex models to improve their predictive skills, and guide carbon cycle research with a new theoretical framework of dynamic disequilibrium.