Vegetation demographic models (VDMs) are advanced tools for simulating forest responses to climate and land-use changes, and are essential for projecting carbon cycling and large-scale forest management strategies. Despite their increasing incorporation into Earth System Models, VDMs differ in their demographic assumptions, with no prior quantitative comparison of their performance. We benchmarked nine VDMs against observational data from boreal, temperate and tropical sites, assessing their accuracy in predicting tree growth, carbon turnover, biomass stocks and size distributions. Models were simulated under consistent climate conditions with postdisturbance recovery monitored for at least 420 yr. Postdisturbance carbon recovery trajectories showed significant variability while remaining within observational ranges. Initial regrowth rates varied substantially (0.03-0.60, 0.18-0.70 and 0.35-1.10 kgCm-2 yr-1 for boreal, temperate and tropical sites, respectively), influenced by each model's initial forest state. Models captured mature forest carbon content but showed compensating effects between overestimated growth and underestimated mortality rates. This first multi-model benchmarking identifies growth and mortality rates as critical calibration targets and highlights the need to refine postdisturbance establishment conditions for model development. We outline specific benchmarking variables needed to improve predictions of forest responses to environmental change.

Vegetation is subject to multiple pressures in the 21st century, including changes in climate, atmospheric composition and human land-use. Changes in vegetation type, structure, and function also feed back to the climate through their impact on the surface-atmosphere fluxes of carbon and water. Dynamic Global Vegetation Models (DGVMs), are therefore key component of the latest Earth System Models (ESMs). Model projections for the future land carbon sink still span a wide range, in part due to the difficulty of representing complex ecosystem and biogeochemical processes at large scales (i.e. grid lengths ≈ 100km). The challenge for developers of DGVMs is therefore to find an optimal balance between detailed process representation and the ability to scale-up. We categorise DGVMs into four groups; Individual, Average Area, Two Dimensional Cohort and One Dimensional Cohort models. From this we review popular methods used to represent dynamic vegetation within the context of Earth System modelling. We argue that the minimum level of complexity required to effectively model changes in carbon storage under changing climate and disturbance regimes, requires a representation of tree size distributions within forests. Furthermore, we find that observed size distributions are consistent with Demographic Equilibrium Theory, suggesting that One Dimensional Cohort models with a focus on tree size, offer the best balance between computational tractability and realism for ESM applications.

The modelled global vegetation for the end of the 21st century is currently is insufficiently constrainedby climate models. A significant proportion of that uncertainty has been attributed to the limitationsof current Dynamic Global Vegetation Models (DGVMs), and the misrepresentation of mortality, dis-turbance and regrowth within forests. Improving the simulation of the underlying processes of de-mographic change is of primary importance in the development of predictors of future climate.Here we present the Robust Ecosystem Demography (RED), a new dynamical vegetation model whichsimulates the size-structure of forests by partitioning the population of a Plant Functional Type (PFT)into mass classes. Allometric scaling of mortality and growth across mass classes allows for a varietyof complex demographic processes to be captured, such as disturbances and regrowth. Competitionamong PFTs is done purely through restricting the recruitment of new vegetation to unshaded space.RED represents a reduction of complexity from more numerically unwieldy cohort DGVMs whichsimulate both size and patch dimensions. The limited number of dimensions and simple competitiveregime allows the equilibrium state to be solved for analytically, providing two potential functions - (i)Avoiding-spinning up by providing an equilibrium state for intilisation. (ii) Insights into the demog-raphy of vegetated areas, arising from parameter tuning to fit observation, such as coverage or carbonmass. When paired with a rate of mortality or carbon assimilate rate gives, respectfully, required as-similate or mortality rates.We demonstrate the model functionality using offline UKESM PFT carbon assimilate rates, pairedwith observed vegetation cover from the ESA LC_CCI datasets for the 9 different PFTs. From thisdataset we calibrate a novel global equilibrium mortality map for each PFT and show the competitiveand successional behaviour of dynamical runs with convergence to the fitted equilibrium. Finally, weexplore underlying ecological questions that emerge from the equilibrium solutions.

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 CO2 and climate. More advanced cohort-based patch models are now becoming established in the latest DGVMs. These models typically attempt to simulate the size distribution of trees as a function of both tree size (mass or trunk diameter) and age (time since disturbance). This approach can capture the overall impact of stochastic disturbance events on the forest structure and biomass – but at the cost of increasing the number of parameters and ambiguity when updating the probability density function (pdf) in two dimensions. Here we present the Robust Ecosystem Demography (RED), in which the pdf is collapsed onto the single dimension of tree mass. RED is designed to retain the ability of more complex cohort DGVMs to represent forest demography, while also being parameter sparse and analytically solvable for the steady state. The population of each plant functional type (PFT) is partitioned into mass classes with a fixed baseline mortality along with an assumed power-law scaling of growth rate with mass. The analytical equilibrium solutions of RED allow the model to be calibrated against observed forest cover using a single parameter – the ratio of mortality to growth for a tree of a reference mass (μ0). We show that RED can thus be calibrated to the ESA LC_CCI (European Space Agency Land Cover Climate Change Initiative) coverage dataset for nine PFTs. Using net primary productivity and litter outputs from the UK Earth System Model (UKESM), we are able to diagnose the spatially varying disturbance rates consistent with this observed vegetation map. The analytical form for RED circumnavigates the need to spin up the numerical model, making it attractive for application in Earth system models (ESMs). This is especially so given that the model is also highly parameter sparse.

Reviewer: In this paper, Argles and co-authors introduce the ‘Robust Ecosystem Demographic’ (RED) model. RED is introduced as an alternative to cohort-based vegetation demographics models, and its justifications are largely presented as being in opposition to more complex approaches that discretize tree size and age since disturbance. Instead of discretizing age since disturbance and tracking individual cohorts performance, RED makes several simplifying assumptions including:

Predicting the response of forests to climate and land-use change depends on models that can simulate the time-varying distribution of different tree sizes within a forest – so-called forest demography models. A necessary condition for such models to be trustworthy is that they can reproduce the tree-size distributions that are observed within existing forests worldwide. In a previous study, we showed that demographic equilibrium theory (DET) is able to fit tree-diameter distributions for forests across North America, using a single site-specific fitting parameter (μ) which represents the ratio of the rate of mortality to growth for a tree of a reference size. We use a form of DET that assumes tree-size profiles are in a steady state resulting from the balance between a size-independent rate of tree mortality and tree growth rates that vary as a power law of tree size (as measured by either trunk diameter or biomass). In this study, we test DET against ForestPlots data for 124 sites across Amazonia, fitting, using maximum likelihood estimation, to both directly measured trunk diameter data and also biomass estimates derived from published allometric relationships. Again, we find that DET fits the observed tree-size distributions well, with best-fit values of the exponent relating growth rate to tree mass giving a mean of ϕ=0.71 (0.31 for trunk diameter). This finding is broadly consistent with exponents of ϕ=0.75 (ϕ=1/3 for trunk diameter) predicted by metabolic scaling theory (MST) allometry. The fitted ϕ and μ parameters also show a clear relationship that is suggestive of life-history trade-offs. When we fix to the MST value of ϕ=0.75, we find that best-fit values of μ cluster around 0.25 for trunk diameter, which is similar to the best-fit value we found for North America of 0.22. This suggests an as yet unexplained preferred ratio of mortality to growth across forests of very different types and locations.

The authors present a model development work on vegetation demography, and seek to incorporate it into an earth system model. The framework provides a simplified solution to model the global vegetation distribution based on the “Metabolic Scaling theory". Both the topic and the model concept are very interesting. However, there are numerous errors and ambiguous expressions throughout the current manuscript. The model descriptions are not clear enough, especially for the equations and units. At some points, I have to stop to calculate the units of each term. I’m also not fully convinced by the model outputs and validations. Extra information are necessary to be provided for a proper judgement, e.g., how the NPP data was created, which climate forcing and vegetation map were used. I suggest an overall revision and reorgniza-tion of themanuscript. My major question about this approach is how it can be used in transit-time simulations, especially for the future projections. From a modelling aspect, the model simply ignored many factors that can be modfied due to climate change. Nevertheless, it would be very exciting if enough evid-ences support that some important emergent properties from land ecosystems would remain constant in a fast changing world.

Abstract. Understanding the relative abundance of trees of different sizes is an important part of predicting the response of forests to changes in climate, land-use and disturbance events. Two competing theories of forest size-distributions are demographic equilibrium theory (DET), based on scaling of mortality and growth with size, and metabolic scaling theory (MST), based scaling size with metabolic rates and how trees fill space. Recently, it was shown that for US forests DET is a much better model than MST, even using the same growth scaling with size. Studies comparing DET and MST have so far focused on trunk diameter, but tree mass and the associated forest mass per unit area (biomass density) are much more relevant to climate. In this study, we extend by fitting both DET and MST to mass data for the Amazon rainforest. The conversion via allometry from trunk diameter data to mass leads to an artefact in the mass distribution, which can be corrected by excluding smaller trees. We derive equations to calculate the total forest biomass density from the mass distribution equation, for both models, and these can be used as an indicator of goodness of model fit to the data. The models were fitted to the data, using Maximum Likelihood Estimation, at the forest plot, regional and continental scale. The fits for both diameter and mass demonstrate that MST is rarely a good fit for Amazon size-distributions and that DET is much better and can estimate biomass density, at the forest plot scale, with a mean error of 6 % (10 % if DET allometry fixed to MST) of its true value, compared to 139 % for MST. The median of the fitted growth scaling power for all the 124 plots is very close to the MST allometry values, implying MST allometry is a mean scaling, around which smaller forest plots cluster. At the larger regional scale, the error in the biomass density estimate of DET reduces to 2 % or less and it is less than 1 % for the whole continent. This suggests that models based on DET, such as the relatively simple Robust Ecosystem Demography model (RED), are a good basis for a next-generation dynamic global vegetation model, and that Amazonian forests remain close to demographic equilibrium on large-scales, despite climate change and significant anthropogenic disturbance.

Abstract. Understanding the relative abundance of trees of different sizes is an important part of predicting the response of forests to changes in climate, land-use and disturbance events. Two competing theories of forest size-distributions are demographic equilibrium theory (DET), based on scaling of mortality and growth with size, and metabolic scaling theory (MST), based scaling size with metabolic rates and how trees fill space. Recently, it was shown that for US forests DET is a much better model than MST, even using the same growth scaling with size. Studies comparing DET and MST have so far focused on trunk diameter, but tree mass and the associated forest mass per unit area (biomass density) are much more relevant to climate. In this study, we extend by fitting both DET and MST to mass data for the Amazon rainforest. The conversion via allometry from trunk diameter data to mass leads to an artefact in the mass distribution, which can be corrected by excluding smaller trees. We derive equations to calculate the total forest biomass density from the mass distribution equation, for both models, and these can be used as an indicator of goodness of model fit to the data. The models were fitted to the data, using Maximum Likelihood Estimation, at the forest plot, regional and continental scale. The fits for both diameter and mass demonstrate that MST is rarely a good fit for Amazon size-distributions and that DET is much better and can estimate biomass density, at the forest plot scale, with a mean error of 6 % (10 % if DET allometry fixed to MST) of its true value, compared to 139 % for MST. The median of the fitted growth scaling power for all the 124 plots is very close to the MST allometry values, implying MST allometry is a mean scaling, around which smaller forest plots cluster. At the larger regional scale, the error in the biomass density estimate of DET reduces to 2 % or less and it is less than 1 % for the whole continent. This suggests that models based on DET, such as the relatively simple Robust Ecosystem Demography model (RED), are a good basis for a next-generation dynamic global vegetation model, and that Amazonian forests remain close to demographic equilibrium on large-scales, despite climate change and significant anthropogenic disturbance.

The distribution of tree sizes within a forest strongly influences how it will respond to disturbances and environmental changes such as future climate change and increases in atmospheric CO2. This means that global vegetation models must include variation in tree size to accurately represent carbon sinks, such as that seen in North America. Here we use an analytical model of large-scale forest demography which assumes tree growth varies as a power of tree diameter whilst tree mortality is independent of size. The equilibrium solutions of this model are able to accurately reproduce the tree-size distributions, for 61 species and four plant functional types, measured across North America, using just a single species-specific fitting parameter, mu, which determines the ratio of mortality to growth. The predictions of metabolic scaling theory for tree-size distributions are also tested and found to deviate significantly from observations and that maybe explained by the assumptions made about how individual trees fill the available space. We show that equilibrium forest demography implies a single curve that relates mean tree diameter to mu, and that this can be used to make reasonable estimates of the whole dataset mean trunk diameter by fitting only to the larger trees. Our analysis suggests that analytical solutions such as those in this paper may have a role in aiding the understanding and development of next-generation Dynamic Global Vegetation Models based on ecosystem demography.

Large angle picosecond reorientation of the magnetization has been studied in circular Ni81Fe19 thin-film elements of 30 μm diameter and 500 Å thickness by means of an optical pump–probe technique. The sample was pumped by an optically triggered magnetic field pulse and probed by a time resolved magneto-optical Kerr effect measurement. The temporal profile of the pulsed field and the in-plane uniaxial anisotropy of the element were first determined from measurements made in large static fields where the magnetization exhibited small amplitude ferromagnetic resonance oscillations. Measurements of large amplitude oscillations were then made in a smaller static field that was still larger than the in-plane uniaxial anisotropy field and sufficient to saturate the sample. Using the measured temporal profile of the pulsed field, the Landau–Lifshitz–Gilbert equation was used to model the motion of the magnetization as a coherent rotation process. The same values of the anisotropy and damping constants provided an adequate simulation of both the high and low field data. The magnetization was found to move through an angle of up to about 30° on subnanosecond time scales. The dependence of the reorientation upon the direction of the static applied field and observed deviations from the coherent precession model are discussed.

We describe how magneto-optical pump-probe spectroscopy may be used to study magnetisation dynamics with femtosecond temporal resolution. Optically triggered magnetic field pulses have been used to induce large amplitude picosecond precessional motion of the spontaneous magnetisation while direct optical stimulation has been used to manipulate the magnitude of the spontaneous magnetisation on femtosecond time scales.

We present the results of optical pump-probe measurements made on Ni81Fe19 films of thickness d=50, 500 and 5000Å. We show that the rise time of the pulsed field within the sample may be determined, and that when d is sufficiently small, the value of the Gilbert damping parameter may be obtained from the decay of the magneto-optical signal. The pulsed field was found to rise more slowly when applied perpendicular to the plane of the sample and as the thickness of the sample was increased. By changing the orientation of the pulsed field relative to the static magnetisation we were able to alter the ellipticity of the trajectory of the precessing magnetisation and observe variations in the decay of the precession. We discuss these effects in terms of eddy current shielding of the rising field, eddy current damping of the motion of the magnetisation, and propagation of spin waves from the point at which the sample response is probed. For the thinnest sample studied (d=50Å) we found the value of the Gilbert damping parameter to be strongly field dependent, so that, contrary to our expectations, the calculated Ferromagnetic Resonance (FMR) line width increased as the field was reduced. Under certain circumstances a second mode of higher frequency was observed in the thickest film. We believe this to be a magnetostatic surface mode that has not previously been observed by means of the optical pump-probe technique.

The rise and damping of spin excitations in three Ni81Fe19 films of thickness 50, 500, and 5000 Å have been studied with an optical pump–probe technique in which the sample is pumped with an optically triggered magnetic field pulse. The motion of the magnetization was described by the uniform mode solution of the Landau–Lifshitz–Gilbert equation. The rise time of the pulsed field within the film was smallest in the 50 Å sample and was generally greater when the pulsed field was perpendicular to the film plane. The damping constant was smallest in the 500 Å sample. The variations in the rise time and damping are attributed to the presence of eddy currents and structural disorder in the films. Under certain excitation conditions a second mode was observed in the 5000 Å sample which we believe to be a magnetostatic surface mode.

Small-amplitude ferromagnetic resonance (FMR) oscillations have been studied in a thin Fe film by means of an optical pump-probe technique in which the sample magnetisation is pumped by an optically triggered magnetic field pulse and probed by means of the magneto-optical Kerr effect. The magnetic field pulse is generated by a current pulse in a coplanar transmission line on which the sample is overlaid. The sample was probed at different positions above the transmission line, to study the effect of pump fields applied at different angles to the sample plane, and the static field was applied in different directions relative to the plane of incidence. The Landau–Lifshitz–Gilbert equation has been used to model the response of the sample magnetisation and the experimental and theoretical curves are found to be in reasonable agreement. From the phase and decay of the FMR oscillations the rise time of the pump field inside the sample and the value of the Gilbert damping constant have been determined. The rise time of the pumping field within the sample is found to depend upon the orientation of the pumping field relative to the plane of the sample. The value of the damping constant is found to depend upon the orientation of the static field relative to the transmission line. We suggest that the observed behaviour results from the generation of eddy currents.