A significant proportion of the uncertainty in climate projections arises from uncertainty in the representation of land carbon uptake. Dynamic global vegetation models (DGVMs) vary in their representations of regrowth and competition for resources, which results in differing responses to changes in atmospheric

A key requirement of Earth system science is to estimate how much carbon the land surface will take up in the decades ahead

Within the context of modelling vegetation at a global level, there is a trade-off between the complexity of ecological process representation and the necessity of parsimony at scale

In a similar vein other models have limited the number of cohort dimensions. The POP model

This paper presents a simplified cohort model –

A full list of variables, parameters, and units are given in Table

Model variables, parameters, and units.

The underlying theoretical model for RED is a continuity equation, for each PFT and spatial location, which describes the time evolution of the number density

We wish to produce a model of vegetation demography that can be updated numerically and which explicitly conserves vegetation carbon, providing a constraint on the number of plants moving between mass classes in the discrete form. In order to do this we integrate Eq. (

To solve Eq. (

Schematic depicting the hierarchical PFT functional group regime within RED. Trees shade trees, shrubs, and grasses. Shrubs shade shrubs and grasses, while grasses only shade grasses.

The space available to the seedlings of the

Competition coefficients assumed for different plant functional groups. A more detailed example of this is given for specific PFTs in Table

Schematic of RED coupled to an ESM or land carbon cycle model. RED is driven by a time series of net carbon assimilate,

RED updates plant size distributions, biomass, and fractional areal coverage for an arbitrary number of PFTs at each spatial location and can be driven by variables provided by a land carbon cycle model, an Earth system model, or observations (see Fig.

List of PFT names and assumed allometric scaling parameters (

The input values of net assimilate for each PFT (

The steady state of the continuum model defined by Eqs. (

The total equilibrium stand density,

The total equilibrium structural growth,

The total equilibrium coverage,

The total equilibrium carbon mass,

Observation-based dataset of the PFT area fractions for the nine JULES PFTs

Mean net assimilate

The equations above therefore define the equilibrium state of the discrete system for given values of

For these runs, the numerical RED model is set up to use the nine PFTs which are currently used in JULES

Here we use the analytical forms for the equilibrium state (Sect.

We use the procedure outlined in Sect.

Maps of dominant PFT for

Goodness of fits for the RED equilibrium coverages to the coverages from ESA LC_CCI dataset across PFTs.

The fit of the RED equilibrium vegetation coverage to the ESA observations is generally very good (Table

Diagnosed maps of mortality rates

The mortality rate derived is dependent on the assumed areal coverage and the total assimilate. A high coverage with a low growth rate will result in a compensating low diagnosed mortality rate (and vice versa). Furthermore, the choice of

The area-weighted median values of observed coverage and driving net assimilate against

Site-level assessments of the rates of stand mortality within pantropical forests conclude a range of background rates

There is a need to better understand the influence of mortality arising from disturbance events such as droughts and fire in order to constrain model projections

Diagnosed mortality rates for

Another key issue is anthropogenic land use and land-use change

In Fig.

Comparison of observation-based estimates of tropical tree mortality

Analysis of the RED equilibrium is an indirect approach to estimating tree mortality based on simple yet mechanistic principles of demography and relying on few inputs (vegetation cover and assimilate). It is however conditional on the assumed estimates of vegetation coverage and net rates of assimilation.

Comparison of diagnosed mortality rates, with observation-based maps of fire and land use.

In this subsection we demonstrate the vegetation successional dynamics simulated by RED in an idealized spin-up from bare soil, for a grid box at the edge of the Amazonian rainforest (Fig.

Dynamical runs of RED for a grid box at the edge of the Amazonian rainforest, starting from bare soil (solid lines) and the diagnosed equilibrium state (dashed lines).

Faster-growing grass PFTs dominate the grid box within the first 12 years, before being replaced by evergreen shrubs which shade the grass seedlings. Eventually, broadleaf evergreen tropical trees replace much of the shrub and grass, on a timescale determined in large part by the parameter

The modelled evolution of number density versus mass distribution for each PFT is shown in panel (c) (after 6 years), panel (d) (after 13 years), and panel (e) (after 100 years), with the eventual demographic equilibrium profiles shown by the dashed lines. It is clear that grass PFTs are close to their demographic equilibrium after only 6 years, but tree PFTs need more than 100 years to reach equilibrium.

The dashed lines in Fig.

Transient simulations of global vegetation will be the subject of a future paper, but in the final subsection of this paper we wish to demonstrate the utility of the semi-analytical equilibrium for initialization of global model runs. Figure

Global model spin-up from bare soil. As for Fig.

The response of the land surface to climate change is a key uncertainty in climate projections. Ambitious climate targets also rely on land management practices such as reforestation and afforestation to increase the storage of carbon on land. First-generation dynamic global vegetation models (DGVMs) attempted to model the land surface in terms of bulk properties such as mean vegetation cover, vegetation carbon and leaf area index. These models lack information about the plant size distribution, which compromised their ability to represent recovery from disturbance and the impact of land management. Providing useful guidance on these issues requires improved DGVMs, which can represent changes in tree-size distributions within forests (so called “demography”). A number of much more sophisticated second-generation DGVMs are now under development. These models often explicitly simulate the number of plants within different size or mass classes and on different patches of land, which are defined by the time since a disturbance event. Such second-generation models are therefore in principle able to simulate variations in plant number density as both a function of patch age and plant size. However, this completeness is at the expense of much computational and parameter complexity.

Our previous work in evaluating demographic equilibrium theory for regional forest inventory datasets in North America

Internally within the model we make a number of simplifications. Firstly, the number density for each PFT is treated as a function of plant mass alone. This immediately eliminates the need to explicitly represent patches and, therefore, removes age as an independent dimension. This is a distinct approach relative to cohort DGVMs which are based on patches defined by time since disturbance, such as the POP or ORCHIDEE-MICT models

Finally, we assume that competition is only significant for the lowest “seedling” mass class. This enables us to represent gap dynamics among plants and resultant stages in succession. This represents a significant simplification compared to other approaches involving the perfect plasticity assumption (PPA), as used within DGVMs such as LM3-PPA or CLM(ED)

These simplifications allow RED to be solved analytically for the steady-state vegetation cover given information on the mortality and growth rates per unit area for each PFT. Such analytical steady-state solutions mean that RED can be easily initialized in drift-free preindustrial states, which is vital to avoid spurious sources and sinks in climate–carbon cycle projections. The analytical solutions also enable RED to be calibrated to the observed vegetation cover, via a single parameter (

Aside from the existence of analytical steady-state solutions, RED is attractive for large-scale applications because it is both parameter sparse (“parsimonious”) and requires very few driving variables. The main driving variable is the time-varying net plant growth rate for each PFT, which is defined as net primary production minus the local litterfall. These driving data can be provided by a land-surface scheme, as we do in this study, or from observations. The only other driving variable for RED is the mortality rate, which we treat in this study as a geographically varying PFT-specific constant that is independent of mass. However, in principle RED could utilize mortality rates that depend on plant mass and time to represent individual disturbance events (e.g. forest fires, disease outbreaks). Despite its simplicity, the RED model is able to fit the global distribution of vegetation types (Fig.

There are inevitably weaknesses with any particular modelling approach. For RED, a current limitation is for competition to lead to a single PFT at each location within each co-competing vegetation class (i.e. tree, shrub, grass). The PFT with the highest equilibrium fraction will end up excluding subdominant PFTs within the same vegetation class. It was necessary for us to account for this eventual competitive exclusion to derive zero-drift steady states for the global runs presented in Sect.

RED is currently being coupled to the JULES land-surface model, replacing TRIFFID as the default DGVM within that framework. In parallel, significant improvements are being made to the representation of physiological processes in JULES, most notably through the representation of nonstructural carbohydrate (“SUGAR”;

In this paper we have presented a new intermediate complexity second-generation dynamic global vegetation model (DGVM), which captures important changes in forest demography. The

For large-scale application in ESMs, a primary concern is to ensure that the total vegetation carbon obeys carbon balance (i.e. only changes due to the net impact of total growth minus total mortality). Here we use that requirement to derive the functional form for

The total vegetation carbon in each mass class is

Equation (

The quasi-Weibull number density solution to DET (Eq.

Integrating Eq. (

The lowest population flux,

To solve for the discrete model equilibrium, we start from the flow equation from Eq. (

An expression for the total stand density at equilibrium,

In equilibrium, the rate of the recruitment of seedlings (Eq.

Inevitably discretized models will not exactly reproduce exact continuum analytical solutions, as a result of numerical inaccuracies that arise from using a finite number of mass classes. However, where exact analytical solutions exist they can be used to benchmark numerical models and optimize discretization schemes, which is what we set out to do in this appendix. We compare the continuum analytical solution for the equilibrium coverage (Eq.

Comparison of the discretized model to the continuum analytical solution, showing convergence for higher numbers of mass classes. This example uses parameters for broadleaf evergreen tropical trees (BET-Tr PFT) with

The numerical versions of RED shown in Fig.

For geometric scaling any mass can be expressed in terms of

From Fig.

The diagnosed mortality rates in Fig.

The sensitivity of the mortality rate to assumed input variables:

The red lines in Fig.

The RED model Python code is archived at

Originally the model framework was in JRM's thesis

The authors declare that they have no conflict of interest.

We are grateful to the Met Office for considering implementation in JULES, via a ticket 1034 within a branch of the code repository.

This research has been supported by the Newton Fund (CSSP-Brazil), the European Research Council (ECCLES), the University of Exeter/Met Office (CASE Studentship), Joint UK BEIS/Defra Met Office Hadley Centre Climate Programme (GA01101), and the European Commission Horizon 2020 research and innovation programme (grant agreement no. 641816).

This paper was edited by Carlos Sierra and reviewed by three anonymous referees.