Understanding how the terrestrial biomass will respond to perturbations is currently a large source of uncertainty within ESMs. Cohort-based demographic models have been a recent development of DGVMs that can improve the representation of size-dependent interactions between the environment and species normally seen in individual-based models while removing stochastic characteristics within global runs. RED partitions the population of a PFT into size classes, of an appropriate variable (biomass, basal diameter) across the physiological range. Using a biomass/basal-diameter spaced advection equation that accounts for size-dependent scaling of the structural growth and mortality across the classes, we are able to model how the population evolves over time. By assuming a power scaling size-growth relationship with constant mortality, RED derives a quasi-Weibull distribution for the forest steady state. When compared to forest inventory data the solution provides a realistic fit. By applying a boundary condition limiting seedlings to open space, RED can derive solutions for the total vegetation fraction, biomass, and other variables by only knowing two parameters - the background ratio of mortality and growth and the fraction of NPP going into seedling production. From this, we have shown that RED can obtain realistic global outputs for biomass densities and evaluatory metrics.The analytical solutions derived from the foundational equations and assumptions of RED suggests an inherent simplicity of the forest structure, with low competition between trees, strong competition for seedlings, and size-independent mortality. Divergence from the analytical solution could indicate a historic disturbance. As RED allows for the representation of asymmetrical mortality and growth, disturbances in which size is important can be dynamically simulated. The theory and model allows for potential insights into how ecosystems will respond to future increases in CO2 and disturbances.

Relationships between climate variability and climate sensitivity are to be expected where the damping of a climatic anomaly is due to a change in the energy balance of the planet, such that the Fluctuation-Dissipation theorem heuristically applies [Leith, 1975]. A recent attempt to relate Equilibrium Climate Sensitivity (ECS) to global temperature variability over the historical period suggested a surprisingly tight emergent constraint on ECS [Cox et al., 2018]. However, the sensitivity-variability relationship in that study was partially hidden by anthropogenic forcing over the historical period. Here we examine instead CMIP5 control runs. These runs have no external forcing and therefore provide a much cleaner test of proposed links between internal variability and sensitivity. It has been noted before that there is a positive correlation between decadal temperature variability and climate sensitivity across climate models [Colman & Power, 2018]. Questions remained however as to how robust this relationship is across different model ensembles, what mechanisms are responsible for it, and whether it can be used as an emergent constraint on climate sensitivity. We examine the relationship between decadal variability and ECS using models of varying complexity, including CMIP5 control runs and a range of conceptual energy balance models for which analytical solutions are presented. Based on these results, a general mechanism becomes apparent and the shape of the relationship is determined to be more quadratic than linear. The nonlinearity has implications for using this relationship as an emergent constraint, where an incorrect assumption of linearity might lead to biased estimates. A further surprising implication of the study is that a slowdown in global warming does not necessarily imply that climate sensitivity is lower than previously estimated. Models with a higher sensitivity, but which broadly reproduce the long-term record of global warming, are actually more likely to have slow-down periods than models with lower sensitivity.