a stand-alone tree demography and landscape structure ......savanna transect in northern australia,...

Biogeosciences 11 4039ndash4055 2014wwwbiogeosciencesnet1140392014doi105194bg-11-4039-2014copy Author(s) 2014 CC Attribution 30 License

A stand-alone tree demography and landscape structure module forEarth system models integration with inventory data fromtemperate and boreal forests

V Haverd1 B Smith12 L P Nieradzik1 and P R Briggs1

1CSIRO Marine and Atmospheric Research PO Box 3023 Canberra ACT 2601 Australia2Dept of Physical Geography and Ecosystem Science Lund University Soumllvegatan 12 22362 Lund Sweden

Correspondence toV Haverd (vanessahaverdcsiroau)

Received 17 January 2014 ndash Published in Biogeosciences Discuss 11 February 2014Revised 16 June 2014 ndash Accepted 16 June 2014 ndash Published 1 August 2014

Abstract Poorly constrained rates of biomass turnover area key limitation of Earth system models (ESMs) In lightof this we recently proposed a new approach encoded in amodel called Populations-Order-Physiology (POP) for thesimulation of woody ecosystem stand dynamics demogra-phy and disturbance-mediated heterogeneity POP is suitablefor continental to global applications and designed for cou-pling to the terrestrial ecosystem component of any ESMPOP bridges the gap between first-generation dynamic veg-etation models (DVMs) with simple large-area parameteri-sations of woody biomass (typically used in current ESMs)and complex second-generation DVMs that explicitly simu-late demographic processes and landscape heterogeneity offorests The key simplification in the POP approach com-pared with second-generation DVMs is to compute physio-logical processes such as assimilation at grid-scale (with CA-BLE (Community Atmosphere Biosphere Land Exchange)or a similar land surface model) but to partition the grid-scale biomass increment among age classes defined at sub-grid-scale each subject to its own dynamics POP was suc-cessfully demonstrated along a savanna transect in north-ern Australia replicating the effects of strong rainfall andfire disturbance gradients on observed stand productivity andstructure

Here we extend the application of POP to wide-rangingtemporal and boreal forests employing paired observationsof stem biomass and density from forest inventory data tocalibrate model parameters governing stand demography andbiomass evolution The calibrated POP model is then cou-pled to the CABLE land surface model and the combined

model (CABLE-POP) is evaluated against leafndashstem allom-etry observations from forest stands ranging in age from 3 to200 year Results indicate that simulated biomass pools con-form well with observed allometry We conclude that POPrepresents an ecologically plausible and efficient alternativeto large-area parameterisations of woody biomass turnovertypically used in current ESMs

1 Introduction

Changes in woody biomass storage in forest and savannaecosystems including woody ecosystems regenerating onabandoned agricultural lands are the major driver of theterrestrial carbon sink which currently amounts to arounda quarter of anthropogenic emissions mitigating climatechange (Ahlstroumlm et al 2012 Pan et al 2011 Le Queacutereacuteet al 2013) Such ecosystem dynamics and their feedbacksto atmospheric carbon content and radiative forcing are rep-resented in Earth system models (ESMs) by incorporatingdynamic vegetation models (DVMs) These attempt to de-scribe changes in vegetation biomass components over timeas the net effect of the allocation of net primary production(NPP) which increases or decreases biomass pools throughphenological (seasonal) cycles of foliage and roots mortal-ity of plant individuals and disturbances such as wildfiresand storms The first-generation DVMs adopted by most cur-rent ESMs (Arora et al 2013) employ large-area param-eterisations designed for application on the scales of gridcells 10s to 100s of kilometres on a side Typically these

Published by Copernicus Publications on behalf of the European Geosciences Union

4040 V Haverd et al A stand-alone tree demography and landscape structure module for ESM

parameterisations treat carbon flows associated with respi-ration and mortality as first-order decay processes expressedas products of pool biomasses and bulk rate parameters in-dependent of age structure (the ldquobig woodrdquo approximationWolf et al 2011) These are computationally efficient ndash animportant consideration for global-scale applications ndash buthave the disadvantage of not resolving underlying popula-tion and community processes such as recruitment mortalityand competition between individuals and species for limitingresources (eg Sitch et al 2003) This lack of mechanisticdetail means that the models are unable to directly exploitthe wealth of information on forest stand structure and dy-namics available from forest inventories These have beenused to develop individual-based height-structured modelsthat have been successfully used to simulate forest dynamicsat the stand scale since the 1970s (eg Botkin et al 1972Bugmann 2001 Smith et al 2001) Different DVMs havealso been shown to simulate widely different patterns andtime evolution of biomass pools especially under future cli-mate projections (Cramer et al 2001 Friedlingstein et al2006 Sitch et al 2008 Friend et al 2014) where modelswith a conservative response of biomass turnover to climaticforcing tend to retain a net biomass sink over the comingcentury whereas others simulate a source or reduced sink bylate 21st century (Ahlstroumlm et al 2012) In ESM simula-tions with an active carbon cycle feedback to climate suchdifferences translate into divergence in the simulated globalclimate (Friedlingstein et al 2006) It has been suggestedthat the representation of forest dynamics in ESMs may beone of the greatest sources of uncertainty in future climateprojections (Purves and Pacala 2008)

A handful of offline (not coupled to the atmosphere)second-generation DVMs exist that simulate demographicprocesses and landscape heterogeneity of forests using moreexplicit approaches that have been demonstrated to accu-rately replicate forest size structure and successional dynam-ics as predicted by community ecological theory Examplesinclude LPJ-GUESS (Smith et al 2001) and ED (Moorcroftet al 2001 Fisher et al 2010) Such approaches are per-ceived as offering promise as an improved second genera-tion of DVMs (Purves and Pacala 2008 Fisher et al 2010)These models include stochastic representations of processessuch as recruitment mortality and large-scale disturbancewhich requires replication of dynamic objects such as treeindividuals and patches and repeated computations of thesame processes as applied to different objects in order to ob-tain a representative average for the ecosystem as a wholeFor studies of global and continental carbon balance and forcoupling to ESMs however this is a potential disadvantagebecause of their demand in terms of both of memory andprocessing power and the additional complication that theresults are not strictly deterministic which complicates theanalysis of results In addition the intricate internal represen-tation of stand structure and its integration with plant physio-logical processes such as carbon assimilation allocation and

phenology implies that the enhancement of existing land sur-face models (LSMs) lacking or employing simpler parame-terisations of vegetation dynamics may be a time-consumingtechnically challenging task

Wolf et al (2011) recently used global forest inventorydata to assess forest biomass allometry in eight global landsurface models including two second-generation DVMsSimulated relationships between stem and foliage biomasspools generally conformed poorly with observed allome-try indicative of model failure to consistently reproduceboth structural and functional characteristics of vegetationBest overall performance was noted for the models ED andORCHIDEE-FM (Bellassen et al 2010) which include anexplicit parameterisation of self-thinning which stronglycontrols biomass turnover rates in closed-forest ecosystems(Westoby 1984) The study recommended the use of biomassallometry data from forest inventories as a simple approachto improving the characteristic behaviour of global land sur-face models with respect to structural dynamics

To simultaneously overcome the limited ecological real-ism of simulated wood turnover in many first-generationDVMs and the technical limitations of current second-generation DVMs Haverd et al (2013) proposed a new ap-proach for the simulation of woody ecosystem stand dy-namics demography and disturbance-mediated heterogene-ity The approach encoded in a model called Populations-Order-Physiology (POP) is designed to be modular deter-ministic computationally efficient and based on sufficientecological realism for application at the grid scales typicallyemployed by DVMs and ESMs for continental to global ap-plications Coupled to the CABLE (Community AtmosphereBiosphere Land Exchange Wang et al 2011) LSM POP re-ceives woody biomass increment from CABLE and returnsan updated biomass state (an approach conceptually simi-lar to that of ORCHIDEE-FM but with key differences dis-cussed in Sect 42) CABLE-POP was demonstrated along asavanna transect in northern Australia successfully replicat-ing the effects of strong rainfall and fire disturbance gradi-ents on observed stand productivity and structure (Haverd etal 2013) The key simplification in the POP approach com-pared with second-generation DVMs is to compute physi-ological processes such as carbon assimilation at grid-scale(with CABLE or a similar land surface model) but to par-tition the grid-scale biomass increment among age classesdefined at sub-grid-scale each subject to its own dynam-ics POP is not a new DVM but a scheme for dynamicallyestimating size structure and turnover of woody vegetationforced by productivity information from an external LSM

In the present study we extend the application of POP toglobally distributed forests heeding the recommendation ofWolf et al (2011) to constrain and improve the performanceof the model by using allometric scaling relationships fromforest inventory data Thus calibrated the combined model(CABLE-POP) is evaluated against leafndashstem allometry andtotal biomass observations from forest stands

Biogeosciences 11 4039ndash4055 2014 wwwbiogeosciencesnet1140392014

V Haverd et al A stand-alone tree demography and landscape structure module for ESM 4041

2 Methods

21 Models

211 POP (Populations-Order-Physiology)

POP is described in Appendix 1 of Haverd et al (2013) andthe detailed description (Appendix A) and summary beloware largely reproduced from that paper For the purpose ofthe present application which includes closed-forest ecosys-tems we extended tree mortality in POP to include a crowd-ing component as described below A Fortran 90 version ofthe POP computer code is included in the supplementary ma-terial to this paper

POP is designed to be modular deterministic computa-tionally efficient and based on defensible ecological princi-ples Parameterisations of tree growth and allometry recruit-ment and mortality are broadly based on the approach of theLPJ-GUESS DVM (Smith et al 2001) The time step (1t)

is 1 yearPOP is designed to be coupled to a land surface

model (LSM) or the land surface component of an ESM(Sect 212) which provides forcing in terms of the an-nual grid-scale stem biomass increment (1C (kg C mminus2)) forwoody vegetation as an average across a simulated tile orgrid cell In LSMs such as the CABLE model employed inthe present study (see below) each tile represents the propor-tion of a grid cell dominated by one major vegetation typesuch as evergreen or deciduous forest For scaling to the land-scape (tile or grid cell) scale POP also requires mean re-turn times of exogenous (large-scale) disturbances For thepresent study where we focus on the patch-scale size struc-tural dynamics we adopt a mean ldquocatastrophicrdquo disturbancereturn time of 100 years which kills all individuals (cohorts)and removes all biomass in a given patch POP can also ac-count for ldquopartialrdquo disturbance such as fire which resultsin the loss of a size-dependent fraction of individuals andbiomass preferentially affecting smaller (younger) cohortsHowever this feature is not used here Stem biomass incre-ment is provided by the host LSM (here CABLE) or pre-scribed for stand-alone calibration

State variables are the density of tree stems partitionedamong age classes (cohorts) of trees and representativeneighbourhoods (patches) of different age since last distur-bance across a simulated landscape representing a spatialunit (tile or grid cell) of an LSM Hereinafter we use the termldquogrid cellrdquo to refer to the spatial unit at which POP is cou-pled to the host LSM in our study a vegetation tile compris-ing either evergreen needleleaved or deciduous broadleavedforest A patch thus represents a stand of vegetation of suf-ficient extent to encompass a neighbourhood of individualwoody plants competing with one another in the uptake andutilisation of light soil resources and space Patches are notspatially referenced but represent a statistical sample of lo-cal stand structure within the overall landscape of the grid

cell Trees are assumed to belong to the plant functional type(PFT) defined for the tile or grid cell in the host LSM Indi-viduals are not distinguished within a cohort but each cohorthas a diagnostically varying mean individual stem biomass(see below) from which other size metrics (height stem di-ameter and crown area) can be derived (see Appendix A4)

POP thus simulates allometric growth of cohorts of treesthat compete for light and soil resources within a patch Theannual stem biomass increment is partitioned among cohortsaccording to a power function of their current aggregate stembiomass (size) on the assumption that larger individuals pre-empt resources owing to a larger surface area and explo-ration volume of their resource-uptake surfaces (leaves andfine roots) and due to the advantage conferred on taller in-dividuals by the shading of shorter ones in crowded stands(Westoby 1984) A cohortrsquos share of the total annual biomassincrement is divided equally among individuals Thus be-tween cohorts there is shading implicit in the weighting ofthe biomass partitioning towards larger treescohorts

The mortality parameterisation was specifically updatedfor this study and is therefore described here in detail Keymodel parameters are listed in Table 1

Population dynamics are governed by

dNy

dt= minus

(mRy + mCy

)Ny (1)

whereNy is the stem density of the cohort established in yeary andmRy andmCy are cohort mortalities (yrminus1) due to re-source limitation and crowding respectivelyNy is initialisedas recruitment density and is reset (according to disturbanceintensity) when the patch experiences disturbance

The mortality rate for a cohort depends on the growth ef-ficiency (GE) closely related to the concept of the relativegrowth rate (RGR) given by

GEy = 1CyCsy (2)

whereCy (kg C mminus2) is the stem biomass and1Cy is theannual stem biomass increment of theyth cohorts is set to075 which is the power governing the mean proportional-ity between plant resource-uptake surfaces (leaves and roots)and stem biomass for a wide range of plant taxa and veg-etation types according to Enquist and Niklas (2001) GEthus represents annual growth relative to the estimated areaof resource-uptake surfaces for trees of a particular size Wecharacterise the response of resource-limitation mortality toGE by a logistic curve with the inflection point at GEmin

mRy =mRy

1+ (GEyGEmin)p (3)

wherey is the index for a particular cohort andmRmax (yrminus1)

is the upper asymptote for mortality as GE declines a proxyfor the resilience of plants to extended periods of resourcestress and is set to the value of 03 adopted in the LPJ-GUESS DVM (Smith et al 2001) The exponentp assigned

wwwbiogeosciencesnet1140392014 Biogeosciences 11 4039ndash4055 2014


Table 1POP model parameters

Symbol units description value source Eq

s [ ] Power governing the mean proportion-ality between plant resource-uptake sur-faces and stem biomass

075 (Enquist and Niklas2001)

24

GEmin [kg mminus2](1-s) Parameter in resource-limitation mortalityformulation

0015 CalibratedHaverd et al (2013)

3

p [ ] Parameter in resource-limitation mortalityformulation

5 LPJ-GUESS DVMSmith et al (2001)

3

mRmax [yrminus1] Parameter in resource-limitation mortalityformulation


3

αC [ ] determines the onset of crowding mortal-ity with respect to crown projective cover

100 This work 5

fc [ ] Scaling factor in formulation for crowd-ing mortality

0013 CalibratedThis work

5

kallom [ ] Parameter in relationship between crownarea and trunk diameter at breast height

200 Widlowski et al (2003) 6

krp [ ] Parameter in relationship between crownarea and trunk diameter at breast height


a default value of 5 governs the steepness of the response ofmR to GE around GE = GEmin For this study GEmin was setto its calibration value of 0015 as determined previously byoptimisation against northern Australian tree basal area data(Haverd et al 2013)

The partitioning of the grid-cell-level annual biomass in-crement among cohorts in a patch is governed by

1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t(4)

where 1C is the grid-cell annual biomass increment (as-sumed to be partitioned equally among patches)1t is thetime step of 1 year and the summation is over all co-horts in the patch Individuals within a patch are thus as-sumed to capture resources in proportion to the area of theirresource-uptake surfaces estimated as thes power of stembiomass following the allometric scaling theory of Enquistand Niklas (2001)

The additional crowding mortality component (mCy) wasincluded to allow for self-thinning in forest canopies Self-thinning is dependent on the assumption that some trees(within a cohort) have a slight advantage in pre-empting re-sources creating a positive feedback to their growth and ulti-mately resulting in death of the most suppressed individualsIn contrast in POP the total stem biomass increment for acohort is equally partitioned amongst all members To com-pensate for this simplification we use the following param-eterisation which emulates the contribution to self-thinningassociated with within-cohort competition

mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](5)

Equation (5) implies that crowding mortality never exceedsgrowth Herecpcy is crown projective cover (Appendix A5)

Acy crown projected area (mminus2 mminus2) of all crowns in theyth and taller cohortsαC a coefficient which determines theonset of crowding mortality with respect tocpc andfc is atunable scaling factorαC was set to 100 corresponding toan onset of crowding mortality atcpc sim 08 This value im-plies that crowding mortality is insignificant in the Australiansavanna simulations thus retaining the validity of the param-eters relating tomRy in Eq (5) as used in the earlier study ofHaverd et al (2013) Crown projected area is evaluated as

Acy = NykallomDkrpy (6)

whereNy is stem density (mminus2) Dy is stem diameter atbreast height (m) (Appendix A Eq A6ndashA9) andkallom andkrp are parameters set to respective values of 200 and 167 re-spectively based on literature values compiled by Widlowskiet al (2003)

Additional mortality occurs as a result of disturbancesReplicate patches representing stands of differing age sincelast disturbance are simulated for each grid cell It is assumedthat each grid cell is large enough to accommodate a land-scape in which the frequency of patches of different ages fol-lows a negative exponential distribution with an expectationrelated to the current disturbance interval This assumptionis valid if grid cells are large relative to the average area af-fected by a single disturbance event and disturbances are aPoisson process occurring randomly with the same expecta-tion at any point across the landscape independent of pre-vious disturbance events To account for disturbances andthe resulting landscape structure state variables of patchesof different ages are averaged and weighted by probabilityintervals from the negative exponential distribution The re-sultant weighted average of for example total stem biomassor annual stem biomass turnover is taken to be representative



NPP

stem biomass amppopulation density

times cohort amp patch

stembiomassturnover

stembiomass

increment

disturbancereturn time

temperatureprecipitation

incoming radiationhumidity

windspeedCO2

forestLAI

leaf amp rootbiomass

crownprojective

cover

Figure 1 Coupling of CABLE and POP along with key inputs andoutputs

for the grid cell as a whole Strictly the Poisson assump-tion demands that the mean disturbance interval is invari-able over time a difficult assumption to uphold in practiceas disturbance agents such as wildfires windthrow and pestor pathogen attacks may increase or decrease depending onvariations in climate and other drivers A constant past dis-turbance regime was assumed in the present study

212 CABLE-POP

CABLE is a global land surface model consisting of fivecomponents (Wang et al 2011) (1) the radiation module de-scribes direct and diffuse radiation transfer and absorption bysunlit and shaded leaves (2) the canopy micrometeorologymodule describes the surface roughness length zero-planedisplacement height and aerodynamic conductance from thereference height to the air within canopy or to the soil sur-face (3) the canopy module includes the coupled energy bal-ance transpiration stomatal conductance and photosynthesisof sunlit and shaded leaves (4) the soil module describes heatand water fluxes within soil and snow at their respective sur-faces and (5) the CASA-CNP biogeochemical model (Wanget al 2010) In this study we used CABLE-20 with the de-fault the soil module replaced by the SoilndashLitterndashIso (SLI)model (Haverd and Cuntz 2010)

As illustrated in Fig 1 coupling between CABLE andPOP is achieved by exchange of two variables CABLE sup-plies annual stem biomass increment to POP and POP returnsan annual stem biomass loss to CABLE To convert betweenstem biomass (POP) and tree biomass (CABLE) we assumea ratio of 07 a representative average for forest and wood-land ecosystems globally (Poorter et al 2012) The result-ing tree biomass turnover is applied as an annual decrease inthe CABLE tree biomass pool and replaces the default fixedbiomass turnover rate

The model set-up in this study was designed to permitevaluation of CABLE-POP predictions of leafndashstem allom-etry CABLE-POP was run offline at 1

times 1 spatial resolu-tion for grid cells containing the locations of forests in theCannellndashUsoltsev (CndashU) database (see Sect 22 on data be-low) Simulations were forced using GSWP-2 (Globa SoilWetness Project) 3-hourly meteorology for the 1986ndash1995period (Dirmeyer et al 2006) Leaf area index (LAI) wasprescribed using a monthly climatology from the MODIS(Moderate Resolution Imaging Spectroradiometer) Collec-tion 5 product (Ganguly et al 2008) Vegetation cover wasprescribed as one of three of the CABLE PFTs evergreenneedleleaf evergreen broadleaf or deciduous broadleaf eachwith its own set of physiological parameters Note thatCABLE does not distinguish between cold- and drought-deciduous broadleaved vegetation Needleleaf and broadleafwere distinguished based on the classification in the CndashUdatabase All needleleaf forests were assumed evergreen andbroadleaf forests were classified as deciduous or evergreenaccording to the larger area fraction specified in the vegeta-tion distribution data set by Lawrence et al (2012) In caseswith no information on either a distinction was made by thelocation with broadleaf forests north of 17 N assumed de-ciduous

The modelling protocol was as follows (i) CABLE soilmoisture and temperature were initialised by running CA-BLE (without CASA-CNP) once for 10 years (using the10 year meteorological data record) (ii) CABLE (withoutCASA-CNP) was run a second time for 10 years from thisinitial state this time with daily forcing inputs to CASA-CNPbeing saved namely gross primary production soil moistureand soil temperature and (iii) CASA-CNP was run for 400year (40times 10 year of repeated forcing) at daily time stepwith POP being called annually and initial biomass stores setto zero

22 Data

Forest inventory data for total biomass stem biomass foliagebiomass and stem density were sourced from the BiomassCompartments Database (Teobaldelli 2008) This databasecontains data from around 5790 plots and represents a har-monised collection of existing data sets (Cannell 1982Usoltsev 2001) covering the temperate and boreal forestregion globally The data include the following compart-ments stem bark branches foliage roots fruits dead woodand understorey Latitudes and longitudes were rounded tothe nearest degree centred on the half-degree and the datawere separated into broadleaf and needleleaf groups withldquomixed forestrdquo sites removed Latitudelongitude duplicateswere then removed separately for each of the needleleaf andbroadleaf subsets leaving all but one randomly selected oc-currence in each 1 times 1 grid cell This resulted in a 3 reduction in data Data for a small number of tropical sitesin the database were omitted as they did not contain all



Figure 2 Locations of forest stands used for CABLE-POP calibra-tion and evaluation

data required for our analysis For comparison with modeloutput the data were further filtered such that only plots withdata for stem biomass foliar biomass stem density and agewere retained leaving 178 broadleaf plots and 304 needle-leaf plots Hereafter we refer to the data for these plots asthe ldquoCndashU datardquo Their locations are denoted in Fig 2 Aver-age stem biomassMstem(kg treeminus1) and foliar biomassMfol(kg treeminus1) per tree were obtained by dividing the bulk quan-tities by stem density (N) Total biomass per tree (M) wasestimated as the sum of woody foliar and fine root biomassassuming allometric ratios of stem biomass to total woodybiomass (07) (Widlowski et al 2003) and fine root to foliarbiomass (10) (Luyssaert et al 2007)

In this study we use the CndashU data in three ways (i) toconstruct a biomassndashdensity (log(M) vs log(N)) plot for thepurpose of calibrating the crowding mortality component ofPOP (Sect 23 below) (ii) to construct leafndashstem allometryplots (log(Mfol) vs log(Mstem)) for the purpose of evaluatingthe CABLE-POP scaling exponent (slope) relatingMfol toMstem and for tuning the CABLE allocation coefficients toleaves and stems to which the intercept is sensitive (Sect 3below) and (iii) to evaluate CABLE-POP predictions of stembiomass directly against data (Sect 3 below)

23 Calibration

The crowding mortality component of the POP model wascalibrated using average biomass per tree (M) (kg dry matterper tree) and stem density (N) (trees haminus1) data from thecombined broadleaf and needleleaf data sets These variablescan be plotted in the form of the self-thinning ldquolawrdquo (egWestoby 1984)

log10(M) = α + β log10(N) (7)

which describes the ageing trajectory of forest stands afterthey exit the initial density-independent growth phase andbefore the stand is sufficiently self-thinned that mortality be-

1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)

CminusU DataPOP simulation of upper boundfit to CminusU datafit to CminusU upper bound

Figure 3 POP calibration Biomassndashdensity plot showing all thepoints in the CndashU data a linear fit to all the CndashU data a linear fitto 30 data points lying along the upper bound POP simulations ofpatches with the same age and StemNPP as the 30 data points lyingalong the upper bound

comes density-independent (Hereafter all log functions re-fer to log10) The self-thinning part of the trajectory formsthe upper bound of a plot of log(M) vs log(N) (Fig 3)with points below this upper bound resulting from youngstands in the density-independent growth phase and addi-tional disturbance-related mortality beyond that describedby self-thinning Thirty-three points along this upper boundwere selected for POP calibration This was done by bin-ning the data in Fig 3 into 39 evenly spaced bins span-ning a log(N) range of 23ndash45 and selecting the observa-tion corresponding to the maximum value in each non-emptybin The coefficients in Eq (7) were estimated from thesepoints using reduced major axis (rma) regression (eg Sokaland Rohlf 1995 Sect 1413) and treated as observationsThe corresponding model observables were constructed fromstand-alone POP simulations of stands with the same age andCABLE-estimated annual stem increment (hereafter Stem-NPP) as the observations and with a high initial stem den-sity (3 individuals mminus2) to accelerate the progress of youngstands towards self-thinning behaviour The residuals be-tween modelled and observed coefficients of Eq (7) wereminimised by optimising thefc parameter (Eq A11) us-ing the PEST parameter estimation software (Doherty 2004)which implements the LevenbergndashMarquardt down-gradientsearch algorithm This returned a value offc = 0013plusmn 0007(1σ) All other POP parameters were held fixed at their priorvalues (Haverd et al 2013) to ensure that the model param-eter set is equally valid for the savanna landscape (to whichthe model was initially applied) as for simulation of foreststands in the present study

Data points not lying on the upper bound were not selectedfor calibration because these observations are not expected to



be influenced by crowding mortality The key indicator of thecalibrated modelrsquos skill is its representation of the leafndashstemallometry plots (log(Mfol) vs log(Mstem)) (Sect 31 Figs 4(ii) and (iv)) of which none of the observation points wereused directly in calibration

Calibration results are shown in Fig 3 This biomassndashdensity plot reveals excellent agreement between the regres-sion line fit to the POP simulation points (β = minus144plusmn 008(1σ) andα = 69plusmn 02 (1σ) R2

= 097) and the regressionline fit to the upper bound data points (β = minus145 plusmn 006(1σ) andα = 69plusmn 02 (1σ) R2

= 097) Note that the fit tothe CndashU data set as a whole yields very different parameters(β = minus167 plusmn005 (1σ) andα = 71plusmn02 (1σ) R2

= 067)which do not reflect the self-thinning trajectory underliningthe importance of selecting upper-bound data for the purposeof calibrating the self-thinning description in POP (Eq4)

CABLE parameters were held fixed at their default PFT-specific values except for allocation coefficients of evergreenneedleleaf forests and deciduous broadleaf forests whichwere manually tuned to match the intercept of the leafndashstem allometry plots Resulting proportions of NPP allo-cated to leaf wood and fine roots respectively are [021 029050] (evergreen needleleaf) and [033 037 030] (deciduousbroadleaf) Corresponding values for evergreen broadleafforests were held fixed at their default values of [020035 045] because this PFT is underrepresented in the data(Fig 2)

3 Results

31 Comparison with observations

Figure 4 shows results of CABLE-POP simulations Eachsimulation point represents a single patch with age matchedto the age of the corresponding CndashU data point POP param-eters were kept the same as for the POP calibration run withno distinction between PFTs The initial stem density was setto 2 stems mminus2 to approximately match the upper limit ofN

in the observationsThe CABLE-POP simulations in the density-biomass

plots (i and ii) lie along the upper bound of the observationsIt is not expected that the model should capture the distribu-tion of the scattered observations below this bound these ob-servations are likely to correspond to (i) young stands in thedensity-independent growth phase (with density highly de-pendent on initial stem density the variability of which is notcaptured in POP) (ii) very old stands of declining biomassin whichN is decreasing whileM is approximately constant(the total biomass of a very old stand ultimately declinesin part due to reduced productivity arising from physiologi-cal decline and nutrient limitations (Dewar 1993 Gower etal 1996) In a global context this effect will be importantmainly in the few global regions in which natural disturbanceregimes and human management scarcely limit mean stand

age For this reason and in the interest of model parsimonywe do not attempt to represent a declining biomass trend invery old stands here) and (iii) stands which have undergonemanaged thinning particularly prevalent amongst needleleafstands Hence the discrepancy between linear fits to the pre-dictions and observations (Table 2) is expected

In contrast the linear fits to the CABLE-POP predictionsand observations in the leafndashstem allometry plots (iii and iv)(see also Table 1) agree very well and generally better thanthe corresponding fits derived for other LSMs by Wolf etal (2011) Note here thatMfol andMstemare average foliageand stem biomass per tree (kg DM treeminus1)

As noted by Wolf et al (2011) a major impediment to val-idating models directly against measured biomass is the needto consider the many idiosyncrasies of each forest stand (egspecies mix climate waternutrient limitations timing ofdisturbances management) Nonetheless CABLE-POP sim-ulations of biomass in broadleaf forest stands (Fig 3v) arelargely unbiased (slope = 094plusmn 004 when intercept set tozero) and capture a high proportion of the variance (r2

=

057) Total biomass in needleleaf stands (Fig 3vi) is lesswell predicted (slope = 094plusmn 03 when intercept set to zeror2

= 023) a likely consequence of intensive managementparticularly deliberate thinning Thinning is performed foreconomic reasons (eg Aruga et al 2013) or to promotestand health (eg Ronnberg et al 2013) and would reducetree density while leaving the average stem biomass initiallyunaffected resulting in a shift to the right for affected standsin Fig 3iv (consistent with the high density of outliers) Thiswould also explain the overestimation of low-biomass standsby CABLE-POP in Fig 3vi because biomass would be re-moved in the early stages of a stand Furthermore as statedby Law et al (2013) multi-stage thinning can also lead to anenhanced storage of long-term biomass which explains whyCABLE-POP overestimates the younger standsrsquo biomass butdoes not reach the maximum values of the needleleaf standsin the CndashU data Uncertainties in woody increment predic-tion may also contribute to poor predictions of total biomassin needleleaf stands

Figure 5 shows biomass component fractions extractedfrom CABLE-POP patch-scale simulations and comparedwith estimates derived from the Cannell and Usoltsevdatabases by Wolf et al (2011) The CABLE-POP simula-tions reproduce the major features of the data particularly thesharp decline in the fraction of foliage biomass and the rela-tively large foliage biomass fraction associated with needle-leaf stands compared to broadleaf stands In contrast de-fault CABLE simulations fail to capture the sharp decline inthe fraction of foliage biomass because they assume a fixedturnover time for biomass turnover (40 year for broadleaf and70 year for needleleaf) The root component is dominatedby the coarse-root fraction which in our simulations was aconstant proportion of woody biomass Therefore we do notexpect CABLE-POP or default CABLE to reproduce the ob-served decline in root shoot ratio with total biomass



0 100 200 300 400 5000

100

200

300

400

500

CminusU stem biomass [t DM haminus1]

CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf

(i) CminusU dataCABLEminusPOP

minus1 0 1 2 3 4minus2

minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)

CminusU dataCABLEminusPOPother LSMs

0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf

(ii) CminusU dataCABLEminusPOP


minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)


Figure 4Evaluation of CABLE-POP predictions against CannellndashUsoltsev data separated into broadleaf and needleleaf classes respectively(i) and(ii) biomassndashdensity plot(iii) and(iv) leafndashstem allometry plot (Mfol and Mstemare average foliage and stem biomass per tree (kgDM treeminus1)) including results derived for other LSMs by Wolf et al (2011) and(v) and(vi) total biomass predictions vs observations In(indashiv) lines denote linear fits to the observations and predictions Solid lines denote linear regression fits to the data points (see Table 1 forregression coefficients)

32 POP mortality dynamics

Figure 6 illustrates the dynamic behaviour of POP mortalityvia stand-alone POP simulations of two undisturbed patcheswith low and high extremes of annual stem biomass incre-ment StemNPP= 005 kg C mminus2yrminus1 (low production) andStemNPP= 020 kg C mminus2yrminus1 (high production) For refer-ence CABLE simulations of the CndashU stands give average an-nual stem biomass increments of (017plusmn006 1σ ) (broadleaf)and (016plusmn 005 1σ ) (needleleaf) kg C mminus2yearminus1 Figure

6i shows the ageing trajectory of each patch in biomassndashdensity space with points representing every fifth year Thelow-production patch exhibits an initial increase in densityas recruitment augments the population during initial years(Fig 6vii) before rapidly transitioning to a regime of declin-ing stem density characterised by a slope ofminus1 as resource-mediated stress induces mortality cancelling any net increasein stand biomass (Fig 6v) The ageing trajectory of the low-production patch never reaches the upper bound of the CndashUdata (representing self-thinning due to crowding mortality)



Table 2Reduced major axis regression coefficients associated with biomassndashdensity leafndashstem allometry and stem biomass plots of Fig 4

Slope Intercept R2 N

log(M) vs log(N ) CndashU (BL) minus163plusmn 007 695plusmn 024 070 178log(M) vs log(N ) CABLE-POP (BL) minus191plusmn 005 847plusmn 017 090 178log(M) vs log(N ) CndashU (NL) minus157plusmn 006 67plusmn 018 066 304log(M) vs log(N ) CABLE-POP (NL) minus152plusmn 002 699plusmn 009 092 304log(Mfol ) vs log(Mstem) CndashU (BL) 069plusmn 002 minus089plusmn 004 084 178log(Mfol ) vs log(Mstem) CABLE-POP (BL) 064plusmn 002 minus096plusmn 002 085 178log(Mfol ) vs log(Mstem) CndashU (NL) 074plusmn 002 minus060plusmn 004 079 304log(Mfol ) vs log(Mstem) CABLE-POP (NL) 068plusmn 001 minus059plusmn 002 094 304lowastCABLE-POP stem biomass vs CndashU stem biomass (BL) 094plusmn 004 0 057 178lowastCABLE-POP stem biomass vs CndashU stem biomass (NL) 099plusmn 004 0 024 304

lowast Standard linear regression with intercept forced through zero

because the stand is relatively sparse (Fig 6ii) and resource-stress mortality prevents crowding (Fig 6iii) In contrast thehigh-production patch (Fig 6i) experiences only a brief in-crease in density (Fig 6viii) before transitioning to a regimeof declining stem density following a trajectory analogousto the upper bound of the CndashU data (slopeminus145) corre-sponding to domination of crowding mortality (Fig 6iv) dueto high crown projective cover (Fig 6ii) and initially lowresource limitation mortality (Fig 6iv) Resource-limitationmortality governs the level and rate of approach to equilib-rium biomass at which mortality (population level) cancelsthe aggregate effects of individual tree growth ie a slopeof minus1 on the ageing trajectory (Fig 6i) Resource-limitationmortality rises more slowly initially than crowding mortal-ity (Fig 6iii iv) responding to declining growth efficiencywith size (trees investing more in maintenance costs of grow-ing tall) while crowding occurs relatively rapidly as indi-viduals spread horizontally to maximise their light uptakeand growth Turnover rate coefficients (Fig 6iii iv) sim-ulated by POP increase with age in contrast to the time-invariant turnover rate coefficients assumed by default CA-BLE and other LSMs employing the big wood assumptionThe big wood assumption leads to relative higher mortality inyounger stands particularly in the low-productivity example(Fig 6iii) The big wood assumption also leads to turnoverrate coefficients being invariant with productivity One con-sequence of this is illustrated in Figs 5 and 6 which showthat for the fixed rate coefficient chosen here (002 yearminus1)

the biomass of the low-productivity patch is adequately sim-ulated but that of the higher productivity patch is signifi-cantly underestimated compared with the POP simulations

Figure 6vii and viii show that there are fewer size (age)classes at higher NPP reflecting stronger dominance by thetallest cohort in high-production stands where deep shadingbeneath the upper canopy promotes high resource-limitationmortality for all but the dominant cohort as expected fromEqs (3ndash4)

4 Discussion

41 Limitations of big wood models

The term ldquobig wood approximationrdquo was coined by Wolfet al (2011) to describe the representation of woody veg-etation biomass dynamics in the majority of LSMs consid-ered in their review These effectively treat woody biomass(Mwood) as a single carbon pool obeying first-order kinet-ics with a rate coefficient (k) linearly scaling a single woodybiomass pool dMwooddt = minuskMwood+ αwoodNPP whereαwood is the fraction of NPP allocated to wood The big woodapproach is unrealistic as it compounds the differential re-sponses to environmental drivers and system state of treegrowth (generally positive) and population growth (positiveor negative depending on the balance between recruitmentand mortality) Cohorts of different age will face differentmortality rates depending on the microenvironment imposedby realised stand structure and this in turn will vary amongpatches in a landscape depending on the disturbance historyThis suggests that it is important to specifically simulate thesize distribution of trees in forest vegetation and account forhow changes in this distribution may alter the response ofecosystem functions like biomass carbon turnover to forcingvariables

As plotted in Fig 6iii and iv modelled biomass turnoverrate ndash an emergent property in POP ndash increases with standage (as commonly observed in real forest stands Franklin etal 1987) before reaching an equilibrium value which differsbetween stands of differing productivity In accordance withthe discussion of Wolf et al (2011) this suggests that bigwood models cannot be expected to perform well for globallyimportant young forest stands instead being more applicableto relatively rare older stands at equilibrium biomass

A second limitation of big wood models also emphasisedby Wolf et al (2011) is that they are not readily amenableto validation against forest inventory data such as those usedin this study This is because they do not carry informationabout tree density Wolf et al (2011) attempted to circumvent



0 200 4000

05

1

Fra

ctio

n B

iom

ass

CABLEminusPOP Broadleaf

rootstemleaf

0 200 4000

05

1CABLEminusDefault Broadleaf

0 200 4000

05

1CABLEminusPOP Needleleaf

0 200 4000

05

1CABLEminusDefault Needleleaf

0 200 4000

05

1CannellminusBroadleaf

Fra

ctio

n B

iom

ass

0 200 4000

05

1CannellminusNeedleleaf

0 200 4000

05

1UsoltsevminusBroadleaf

Biomass [t DM haminus1]

Fra

ctio

n B

iom

ass

0 200 4000

05

1UsoltsevminusNeedleleaf


Figure 5 Biomass component fractions as a function of totalbiomass top CABLE-POP patches second row default CABLEthird and bottom rows data-derived estimates reproduced fromWolf et al (2011)

this problem by applying a fit to biomassndashdensity (log(M)

vs log(N)) as a post hoc estimate of density which was thenused to evaluate component biomass per tree as required egfor the leafndashstem allometry plots (Fig 4iii iv) (Results aredenoted ldquoother LSMsrdquo in these plots)N was thus estimatedusing

log(N) = minusα(β + 1) + log(M times N)(β + 1) (8)

whereM times N is total biomass andβ andα are respectivelythe slope and intercept of a reduced major axis regressionfit to log(M) vs log(N) observations for the whole (global)data set (Fig 4) As an approach for estimatingN at a grid-cell level this assumes that forests throughout the world arefollowing the same log densityndashlog biomass trajectory Wesuggest this is unlikely as individual stands may be expected

to follow different trajectories depending on productivity andage as illustrated in Fig 6 and discussed above We appliedEq (8) to CABLE-POP grid cell estimates of total biomassto derive a post hoc prediction of stem density and henceaverage foliage and stem biomass per tree analogous to theapproach of Wolf et al (2011) Results are shown in Fig 7and indicate that the grid-cell results (deduced via Eq (8)with α = 622 andβ = minus132 (Wolf et al 2011 Table 5))lie on a significantly different line to the patch-level CABLE-POP simulations (individual points shown in Fig 4iii iv) forwhich the internal model stem density was used to deduceaverage foliage and stem biomass per tree The same wastrue when values ofα = 69 andβ = minus144 were used cor-responding to a fit to log(M) vs log(N) used in the presentstudy (Fig 3) Allometric data from global forest invento-ries are thus of limited value for evaluatingconstraining bigwood models which do not carry number-density informa-tion

Predicted global carbon fluxes diverge markedly betweenEarth system models both in the magnitude and shape (signtiming of change) of the subsequent trajectory (Ahlstroumlm etal 2012 Anav et al 2013) One cause of such divergenceis that models many employing a big wood simplificationfor biomass dynamics differ markedly in terms of woodybiomass turnover and its response to future climate and CO2forcing In projections with ESMs that account for carbon cy-cle feedbacks this translates into divergence in the simulatedclimate (Friedlingstein et al 2006 2013) We concur withWolf et al (2011) and argue that big wood models lack eco-logical realism and cannot be expected to simulate woodybiomass turnover in a realistic manner under changing cli-mate forcing They should be phased out from use in carboncycle studies

42 Limitations of the POP approach

The approach presented and demonstrated in this paper offersa potential alternative suitable as a replacement for the bigwood approximation for the representation of biomass struc-tural dynamics for woody vegetation in large-scale modelsPOP is not a replacement for a full-featured DVM It does notrepresent biogeochemical processes nor in its current formcompetitive interactions among PFTs nor biophysical feed-backs associated with age-structured vegetation Further ageeffects on LAI and NPP are not accounted for because of thesimplifying assumption that NPP (and therefore LAI) is uni-form among patches while structure is assumed to vary

POP is designed to be readily coupled to a biogeochemi-cal LSM as implemented in many current climate and Earthsystem models Such LSMs generally do not feature compet-ing plant types but may have fixed tiles representing grid-cell fractions dominated by different types of vegetationPOP simulates size structure dynamics separately for each(woody) vegetation tile based on the principle of asymmet-ric (ie size-dependent) competition between co-occurring



15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing

StemNPP = 005 kg C mminus2yminus1


fit to CminusU Data

fit to CminusU upper bound

0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]

(iii) StemNPP = 005 kg C mminus2yminus1

total mortality

resource limitation mortality

crowding mortality

turnover rate coefficient

0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]

(iv) StemNPP = 020 kg C mminus2yminus1

total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3

(v) StemNPP = 005 kg C mminus2yminus1

time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15

(vi) StemNPP = 020 kg C mminus2yminus1

time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3

(vii) StemNPP = 005 kg C mminus2yminus1

time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12

(viii) StemNPP = 02 kg C mminus2yminus1

time [y]

stem

den

sity

[ind

iv m

minus2 ]

Figure 6 POP dynamics as illustrated by undisturbed patch simulations at low and high extremes of annual stem increment (StemNPP= 005 kg Cmminus2 yearminus1 and StemNPP= 020 kg Cmminus2 yearminus1) (i) Biomassndashdensity plot showing the ageing trajectories of each patch(every 5th year plotted) Linear fits to the CndashU data and their upper bound are shown for reference(ii) time course of crown projective coverfor each patch and(iii) and(iv) time course of mortality its components and turnover rate coefficient for patches with low(iii) and high(iv) annual stem increments Dotted lines (blue) represent mortality based on a fixed turnover rate (dotted black line) of 002 yearminus1 and(v)and(vi) time course of stem biomass for patches with low(v) and high(vi) annual stem increments Solid lines indicate contributions formdifferent cohorts Dotted lines represent biomass accumulation assuming a fixed turnover rate of 002 yearminus1 and(vii) and(viii) time courseof stem density for patches with low(vii) and high(viii) annual stem increments Solid lines indicate contributions from different cohorts

individuals but with no competition among PFTs (tiles)Competition between trees and grasses deciduous and ever-green vegetation and C3 and C4 plants provides an importantexplanation for global biome distributions and may modulatethe responses of vegetation to future climate and [CO2] forc-

ing (Smith et al 2014) We plan to introduce PFTs and todistinguish canopy and understorey strata in a later develop-ment of the approach

In its current form vegetation structure represented in POPonly feeds back on woody biomass turnover represented in




minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)

CminusU dataCABLEminusPOP GridminusCellCABLEminusPOP patch

CminusU dataCABLEminusPOP GridminusCellCABLEminusPOP Patch

Figure 7 LeafndashStem allometry plots for(i) broadleaf and(ii) needleleaf PFTs CndashU data and CABLE-POP patch results are the same asin Fig 3 (iii) and (iv) CABLE-POP grid-cell results are from deducing stem density from total grid-cell biomass (average over multiplepatches weighted by probability of time since last disturbance with a mean disturbance interval of 100 year) via Eq (8) and using this tocomputeMfol andMstemfrom grid-cell foliage and stem biomass components

the host LSM Other feedbacks such as the acclimation ofallocation with agesize (Lloyd 1999) and age-related de-cline in forest growth (eg Zaehle et al 2006) could alsobe implemented using the modular approach presented hereIndeed such feedbacks are represented in the ORCHIDEE-FM model (Bellassen et al 2010) which adopts a simi-larly modular approach the forest management module (FM)in ORCHIDEE-FM is supplied with stem biomass incre-ment from the host LSM (ORCHIDEE) and returns biomassturnover In other respects FM and POP are different In par-ticular POP is distinguished by its representation of sub-grid-scale disturbance-mediated heterogeneity Further thestand dynamics of POP are applicable from sparse woodysavannas to closed forest In contrast FM was developedspecifically for forests it represents management effects andnatural mortality is based exclusively on stand self-thinning

The parameterisation of crowding mortality Eq (5) is in-dependent of growth rates and assumes only that the propor-tionality between log biomass and log density revealed by theobserved data continues to hold true in a future simulationThis assumption is reasonable if mortality depends more onbiomass than on growth rate The robustness of this propor-tionality across wide climatic gradients is clear from the ob-served data as plotted in Fig 3

The present paper is concerned with the patch-scale dy-namics ndash not the landscape scaling component of POP whichwas presented and applied in Haverd et al (2013) Howeverwe expect that the equilibrium assumption implicit in thePoisson-based method of weighting patches of different timesince last disturbance will be robust to a gradually changingdisturbance regime (typical for most climate change studies)though the approach will break down in the case of a stepchange in mean disturbance interval

5 Conclusions

By discriminating individual and population growth and ex-plicitly representing asymmetric competition among agesizeclasses of trees co-occurring within forest stands POP over-comes a key limitation of the big wood approach and provedable to reproduce allometric relationships reflecting link-ages between productivity biomass and density in widelydistributed temperate and boreal forests Coupled to a bio-geochemical land surface model able to prognose woodybiomass productivity at stand (or grid cell) level POP maybe calibrated and evaluated against forest inventory dataas demonstrated in this study This is achieved without amarked increase in model complexity or computational de-mand thanks to a modular design that separates the role ofthe parent land surface model (prognosing whole-ecosystemproduction) and the population dynamics model (partitioningthe production among cohorts computing mortality for eachand returning the stand-level integral as whole-ecosystembiomass turnover to the parent model) (Fig 1)

The present paper focuses on stand-level demographicsand its influence on the accumulation and turnover of stemcarbon biomass At the landscape level the incidence and in-tensity of disturbance events ndash such as wildfires storms oranthropogenic interventions such as forest harvest or landuse conversions ndash provide an additional regionally importantcontrol on biomass accumulation and turnover (Shevliakovaet al 2009) Such landscape-level effects are accounted forby our model for example along a rainfall-mediated wild-fire and biomass gradient in savannah vegetation of northernAustralia (Haverd et al 2013)



Appendix A Detailed description of POP

A1 State variables and governing equation

In POP state variables are the sub-grid-scale (patch-specific)densities of woody plant individualsNy (mminus2) in agesizeclasses with an arbitrary number of agesize cohorts wherey is the simulation year in which the cohort was created


dNy

dt= minus

(mRy + mCy

)Ny (A1)

wheremRy andmCy are cohort mortalities (yrminus1) due to re-source limitation and crowding respectivelyNy is initialisedas recruitment density and is episodically reset (accordingto disturbance intensity) when the patch experiences distur-bance Below we describe the formulations of recruitmentbiomass accumulation (partitioning of grid-scale stem incre-ment amongst cohorts) cohort structure and mortality dis-turbance and landscape heterogeneity The model time step(1t) is 1 year

A2 Recruitment

A new cohort is created each year with density (may be zero)given by

Ny(y) = Nmaxmicro(F) (A2)

whereNmax is the maximum establishment density expectedunder optimal conditions for seedling growth with assumedvalue of 02 mminus2 F is a proxy for growth conditions in theseedling layer expressed as a fraction of optimum set here asa function of (patch-dependent) stem biomassC (kg C mminus2)with an exponent of 23 accounting for the proportional in-crease in resource-uptake surfaces (leaves and fine roots) rel-ative to stem biomass assuming no change in linear propor-tions with size

F = exp(minus06C23

) (A3)

The functionmicro(F) is a non-rectangular hyperbola modifiedfollowing Fulton (1991) to account for the reduction of re-cruitment to the adult population under conditions of growthsuppression in the seedling population (essentially enhancedseedling mortality due to resource stress)

micro(F) = exp

[α

(1minus

2θ

F + 1minus

radic(F + 1)2 minus 4θF

)] (A4)

whereθ is a shape parameter set to 095 andα is a shape pa-rameter in the range 01ndash10 with higher values correspond-ing to a greater suppression of recruitment (eg in shade-intolerant tree species) A value of 35 fitted to data for Nor-way spruce (a shade-tolerant boreal tree) (Fulton 1991) isadopted as a default value

A3 Biomass partitioning

Stem biomass increment for each patch1C (kg C mminus2) isassumed equal to the grid-scale value accumulated over thePOP model time step1t (y) It is partitioned among cohortsas a basis for the characterisation of structure in turn affect-ing survivorship and growth An assumption may be madethat individuals capture resources in a varying proportion totheir size following a power relationship to biomass with anexponent (s) As resource uptake and therefore productiv-ity is essentially linked to surface area (of leaves and roots)and assuming no change in linear proportions with growththen an exponent of 34 may be assumed based on allomet-ric scaling theory (Enquist and Niklas 2001)

On this basis annual stem biomass increment may bepartitioned among cohorts in proportion to the population-weighted current biomass of individuals within each cohort

1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)

whereCy is the stem biomass summed across individuals ofcohortNy

A4 Cohort structure

Cohort structure is characterised by height and canopy coverHeight (Hy m) is determined from stem biomass by the al-lometric relations (Huang et al 1992 Smith et al 2001)

Hy = kD23y (A6)

whereDy is mean tree stem diameter (m) A default valueof 50 is chosen for the scaling coefficientk based on fittingEq (A6) to height-diameter data for European tree speciessynthesised in Widlowski et al (2003)

Vy = Hy

π

4D2

y (A7)

(volumeVy of a cylinder m3 π the ratio of the circumfer-ence to the radius of a circle) and

CyNminus1y = Vy middot ρw (A8)

(absolute stem biomass for an individual in cohortNywithwood densityρw set here to 300 kg mminus3)

Combining Eqs (A6ndashA8)

Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality

Mortality is defined as a proportional reduction in cohortdensity (Eq A1) Adapting and simplifying the approach



of the LPJ-GUESS DVM (Smith et al 2001) we aggregatemultiple causes of mortality in real tree stands within a gen-eralised resource-limitation mortality that increases with size(and therefore age) and under conditions of declining pro-ductivity whether caused by interference in resource uptakeamong neighbours (Westoby 1984) abiotic factors such asdrought or secondary biotic factors (eg pathogen attacks)(Franklin et al 1987) Resource limitation leads to a declinein growth efficiency (GE ie growth rate as a function ofsize) characterised by the ratio of stem biomass incrementto current stem biomass for a given cohort Below a certainthreshold GEmin mortality increases markedly (Pacala et al1993) We characterise the response of resource-limitationmortality to growth efficiency by a logistic curve with theinflection point at this threshold

mRy =mRmax

1+ (GEyGEmin)p (A10)

where GEy = 1CyCsy s takes the same value as in Eq (A5)

andmRmax is the upper asymptote for mortality as GE de-clines set to 03 yearminus1 following Smith et al (2001) Theexponentp assigned a default value of 5 governs the steep-ness of response around GE = GEmin which may be regardedas a calibration parameter

An additional crowding mortality component (mCy) is in-cluded to allow for self-thinning in forest canopies Self-thinning is dependent on the assumption that some trees(within a cohort) have a slight advantage in pre-emptingresources creating a positive feedback to growth and ulti-mately resulting in death of the most suppressed individualsIn contrast in POP the total stem biomass increment for a co-hort is equally partitioned amongst all members Thereforewe require the following new parameterisation which emu-lates the contribution to self-thinning associated with within-cohort competition

Crowding mortality is expressed as

mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)

such that it never exceeds growth Herecpcy =(1minus exp

(minusAcy

))is crown projective coverAcy crown

projected area (mminus2 mminus2) of all crowns in theyth and tallercohorts αC a coefficient which determines the onset ofcrowding mortality with respect tocpc andfc is a tunablescaling factorαC was set to 100 corresponding to anonset of crowding mortality atcpcsim 08 This value waschosen to be sufficiently high such that crowding mortality isinsignificant in the Australian savanna simulations (Haverdet al 2013) thus retaining the validity of the parametersrelating tomR in Eq (A10) as used in this earlier studyCrown projected area is evaluated as

Acy = NykallomDkrpy (A12)

whereNy is stem density (mminus2) Dy is stem diameter atbreast height (m) andkallom and krp are parameters set to

respective values of 200 and 167 based on literature valuescompiled by Widlowski et al (2003)

Additional mortality occurs as a result of disturbances seebelow

A6 Disturbance and landscape heterogeneity

Landscape heterogeneity is accounted for by simulating anumber of patches (within a grid cell) which differ by age(time since last disturbance) Each grid-cell state variable(eg stem biomass) is computed as a weighted mean of thepatch state variables with patch weight corresponding tothe probability (p) of the patch occurring in the landscapeDisturbance is treated as a Poisson process with time (x)

since last disturbance distributed exponentially amongst thepatches according to the grid-cell mean disturbance interval(λ)

p(x) = λexp(minusλx) (A13)

In this work we heldλ fixed in time but it could also beprescribed a time-dependent variable

Disturbances (periodic events that recur randomly at thelocal scale destroying all (catastrophic disturbance) or afraction of biomass (partial disturbance) in a patch) signif-icantly affect biomass residence time vegetation structureand thereby resource use and productivity at a large spatialscale At the level of a grid cell or large landscape patches ofdifferent ages (years since last disturbance) should occur atfrequencies corresponding to the expected likelihood of a lo-cal disturbance sometime in the corresponding period givena known expected disturbance return time The latter is pre-scribed in this work but could be computed prognosticallyeg by a wildfire module incorporated within CABLE

A partial disturbance event in an affected patch is simu-lated by removing a size-dependent fraction of the biomass(and hence stems) in each cohort In this work this fractionis specified using an observation-based relationship betweentree size and the probability of tree survival following a fire ofspecified intensity (see Appendix A3) Following either typeof disturbance event (catastrophic or partial) recruitment oc-curs and the patch persists in the landscape and its age sincethe particular type of disturbance is set to zero

Importantly patch weightings by age are evaluated aftergrowth recruitment non-disturbance-related mortality anddisturbance It is particularly important that the weightingsbe calculated after disturbance otherwise patches of age zerowould not be represented

Vegetation structure changes more from year to year earlyin vegetation development following a disturbance than laterAfter a period corresponding to a few average tree generationtimes a steady state is reached with no further net changesin vegetation structure (provided there are no trends in forc-ing data) To strike a balance between computational effi-ciency and ldquoaccuracyrdquo in characterising landscape structurewe simulate patches with a sequence of (nage_max= 5minus 7)



maximum ages with equally spaced cumulative probabilities(assuming an exponential distribution of patch ages with ex-pected value equal to the mean disturbance interval) To en-sure a wide spread of ages in any given year we additionallysimulate (npatch_reps= 4minus7) replicate patches for each max-imum age with the first disturbance occurring in year 1a2a 3anpatch_repsa and thereafter every ldquonpatch_repsardquo years(where ldquonpatch_repsardquo is the maximum age of the patch)

A7 Patch weightings

Each patch is characterised by time since last disturbanceand its weighting in the landscape is given by the probabil-ity of this age occurring in an exponential distribution Whentwo disturbance types (catastrophic and partial) are consid-ered each patch is characterised by two ages correspondingto times since each disturbance type and two weights onefor each age The patch weighting is then the product of theweights for each age divided by the number of patches withthe same combination of two ages and normalised such thatpatch weights sum to one

We evaluate weights for each unique time since each dis-turbance as follows first we construct an ordered list ofnageunique ages since last disturbance Each unique ageai is as-sociated with lower and upper integer bounds (bli andbui)spanning the range of ages to be represented byai Thesebounds are set as follows

bli =

0 i = 1

ai i gt 1aiminus1 = ai minus 1

buiminus1 + 1 i gt 1aiminus1 6= ai minus 1

(A14)

bui =

0 ai = 0

ai (i = 1ai gt 0) or

(i gt 1aiminus1 = ai minus 1)

int[(ai + ai+1)2] 1 lt i lt nage

ai i = nage

The weighting for each ageai is evaluated as the sum of theexponential frequenciesw = λexp(minusλx) (whereλ is the ex-pectation value of the time since disturbance andx the inte-gral age) of integral ages frombli to buI inclusive

A8 Tree foliage projective cover

Tree foliage projective cover is calculated following (Haverdet al 2012) as 1minusPgap wherePgap is defined here the proba-bility of radiation penetrating the entire canopy from directlyabove (ie zero zenith angle)

Pgap= eminusλAc(1minusPwc) (A15)

In Equation (A15)λ is the number density of crownsAc isthe projected area of a crown envelope (ie an opaque crown)and Pwc is the mean expected gap (or porosity) through asingle crown or partial crown The overbar denotes a meanover the distribution of crown heights and dimensions thusAc (1minus Pwc) is the mean area of the projected objects that fillthe crown volume Crowns are approximated as spheroidsWe assume that crown horizontal and vertical diameters aremonotonic functions of tree height (h) such that the meanprojected area is

Ac (1minus Pwc) =

hmaxinthmin

Ac(h)(1minus Pwc(h))p(h)dh (A16)

wherep(h) is the tree height probability distribution andhmin andhmax are the lower and upper extremes of the treeheights respectively The crown porosityPwc is approxi-mated as

Pwc asymp eminusGFasmean (A17)

HereG is the projection of the leaf area in the direction ofthe beam (assumed here to be 05 corresponding to a spheri-cal leaf angle distribution) andsmeanis the mean path lengththrough the crown approximated as

smean= VAC (A18)

with V the crown volume andFa the foliage area volumedensity equated here with the ratio of tree LAI to total crownvolume We assumed a vertical-to-horizontal-crown-radiusratio of 15



The Supplement related to this article is available onlineat doi105194bg-11-4039-2014-supplement

AcknowledgementsV Haverd and P Briggs acknowledge theAustralian Climate Change Science Program for enabling theircontributions to this work Benjamin Smith acknowledges fundingas an Ernest Frohlich Visiting Fellow to the CSIRO Division ofMarine and Atmospheric Research Canberra This study is acontribution to the strategic research area Modelling the Regionaland Global Earth System (MERGE) The authors thank JosepCanadell and Michael Raupach for helpful suggestions to improvethe manuscript

Edited by S Zaehle

References

Ahlstroumlm A Schurgers G Arneth A and Smith B Robust-ness and uncertainty in terrestrial ecosystem carbon responseto CMIP5 climate change projections Environ Res Lett 7044008 doi1010881748-932674044008 2012

Arora V K Boer G J Friedlingstein P Eby M Jones C DChristian J R Bonan G Bopp L Brovkin V Cadule PHajima T Ilyina T Lindsay K Tjiputra J F and Wu TCarbon-concentration and carbon-climate feedbacks in CMIP5earth system models J Climate 26 5289ndash5314 2013

Aruga K Murakami A Nakahata C Yamaguchi R Saito Mand Kanetsuki K A model to estimate available timber and for-est biomass and reforestation expenses in a mountainous regionin Japan J Forest Res 24 345ndash356 2013

Bellassen V Le Maire G Dhote J F Ciais P and Viovy NModelling forest management within a global vegetation modelPart 1 Model structure and general behaviour Ecol Modell221 2458ndash2474 doi101016jecolmodel201007008 2010

Botkin D B Wallis J R and Janak J F Some ecological con-sequences of a computer model of forest growth J Ecol 60849ndash872 1972

Bugmann H A review of forest gap models Climatic Change 51259ndash305 2001

Cramer W Bondeau A Woodward F I Prentice I CBetts R A Brovkin V Cox P M Fisher V Foley J AFriend A D Kucharik C Lomas M R Ramankutty NSitch S Smith B White A and Young-Molling C Globalresponse of terrestrial ecosystem structure and function to CO2and climate change results from six dynamic global vegetationmodels Glob Change Biol 7 357ndash373 2001

Dewar R C A mechanistic analysis of self-thinning in terms of thecarbon balance of trees Ann Bot-London 71 147ndash159 1993

Dirmeyer P A Gao X A Zhao M Guo Z C Oki T K andHanasaki N GSWP-2 ndash multimodel anlysis and implicationsfor our perception of the land surface B Am Meteorol Soc87 1381ndash1397 2006

Enquist B J and Niklas K J Invariant scaling relations acrosstree-dominated communities Nature 410 655ndash660 2001

Fisher R McDowell N Purves D Moorcroft P Sitch SCox P Huntingford C Meir P and Woodward F I As-sessing uncertainties in a second-generation dynamic vegetationmodel caused by ecological scale limitations New Phytol 187666ndash681 2010

Franklin J F Shugart H H and Harmon M E Treedeath as an ecological process Bioscience 37 550ndash556doi1023071310665 1987

Friedlingstein P Cox P Betts R Bopp L Von Bloh WBrovkin V Cadule P Doney S Eby M Fung I Bala GJohn J Jones C Joos F Kato T Kawamiya M Knorr WLindsay K Matthews H D Raddatz T Rayner P Reick CRoeckner E Schnitzler K G Schnur R Strassmann KWeaver A J Yoshikawa C and Zeng N Climate-carbon cy-cle feedback analysis results from the (CMIP)-M-4 model inter-comparison J Climate 19 3337ndash3353 2006

Friedlingstein P Meinshausen M Arora V K Jones C DAnav A Liddicoat S K and Knutti R Uncertainties inCMIP5 climate projections due to carbon cycle feedbacks J Cli-mate 27 511ndash526 doi101175JCLI-D-12-005791 2013

Friend A D Lucht W Rademacher T T Keribin R Betts RCadule P Ciais P Clark D B Dankers R Falloon P D ItoA Kahana R Kleidon A Lomas M R Nishina K OstbergS Pavlick R Peylin P Schaphoff S Vuichard N Warsza-wski L Wiltshire A and Woodward F I Carbon residencetime dominates uncertainty in terrestrial vegetation responses tofuture climate and atmospheric CO2 P Natl Acad Sci USA111 3280ndash3285 doi101073pnas1222477110 2014

Ganguly S Samanta A Schull M A Shabanov N VMilesi C Nemani R R Knyazikhin Y and Myneni RB Generating vegetation leaf area index Earth system datarecord from multiple sensors Part 2 Implementation analy-sis and validation Remote Sens Environ 112 4318ndash4332doi101016jrse200807013 2008

Gower S T McMurtrie R E and Murty D Aboveground netprimary production decline with stand age potential causesTrends Ecol Evol 11 378ndash382 1996

Haverd V and Cuntz M Soil-Litter-Iso a one-dimensional modelfor coupled transport of heat water and stable isotopes in soilwith a litter layer and root extraction J Hydrol 388 438ndash4552010

Haverd V Lovell J L Cuntz M Jupp D L B Newnham G Jand Sea W The Canopy Semi-analytic P-gap And RadiativeTransfer (CanSPART) model formulation and application AgrForest Meteorol 160 14ndash35 2012

Haverd V Smith B Cook G Briggs P R Nieradzik L Rox-burgh S R Liedloff A Meyer C P and Canadell J GA stand-alone tree demography and landscape structure modulefor Earth system models Geophys Res Lett 40 1ndash6 2013

Law B E Hudiburg T W and Luyssaert S Thinning effects onforest productivity consequences of preserving old forests andmitigating impacts of fire and drought Plant Ecol 6 73ndash852013

Lawrence P J Feddema J J Bonan G B Meehl G AOrsquoNeill B C Oleson K W Levis S Lawrence D MKluzek E Lindsay K and Thornton P E Simulating the bio-geochemical and biogeophysical impacts of transient land coverchange and wood harvest in the Community Climate System



Model (CCSM4) from 1850 to 2100 J Climate 25 3071ndash30952012

Le Queacutereacute C Andres R J Boden T Conway THoughton R A House J I Marland G Peters G Pvan der Werf G R Ahlstroumlm A Andrew R M Bopp LCanadell J G Ciais P Doney S C Enright C Friedling-stein P Huntingford C Jain A K Jourdain C Kato EKeeling R F Klein Goldewijk K Levis S Levy P Lo-mas M Poulter B Raupach M R Schwinger J Sitch SStocker B D Viovy N Zaehle S and Zeng N The globalcarbon budget 1959ndash2011 Earth Syst Sci Data 5 165ndash185doi105194essd-5-165-2013 2013

Lloyd J The CO2 dependence of photosynthesis plant growth re-sponses to elevated CO2 concentrations and their interaction withsoil nutrient status II Temperate and boreal forest productivityand the combined effects of increasing CO2 concentrations andincreased nitrogen deposition at a global scale Funct Ecol 13439ndash459 doi101046j1365-2435199900350x 1999

Luyssaert S Inglima I Jung M Richardson A D Reich-stein M Papale D Piao S L Schulzes E D Wingate LMatteucci G Aragao L Aubinet M Beers C Bernhofer CBlack K G Bonal D Bonnefond J M Chambers JCiais P Cook B Davis K J Dolman A J Gielen BGoulden M Grace J Granier A Grelle A Griffis TGrunwald T Guidolotti G Hanson P J Harding RHollinger D Y Hutyra L R Kolar P Kruijt B Kutsch WLagergren F Laurila T Law B E Le Maire G Lindroth ALoustau D Malhi Y Mateus J Migliavacca M Misson LMontagnani L Moncrieff J Moors E Munger J W Nikin-maa E Ollinger S V Pita G Rebmann C Roupsard OSaigusa N Sanz M J Seufert G Sierra C Smith M LTang J Valentini R Vesala T and Janssens I A CO2balance of boreal temperate and tropical forests derived froma global database Glob Change Biol 13 2509ndash2537 2007

Moorcroft P R Hurtt G C and Pacala S W A method forscaling vegetation dynamics the ecosystem demography model(ED) Ecol Monogr 71 557ndash585 2001

Pan Y D Birdsey R A Fang J Y Houghton R Kauppi P EKurz W A Phillips O L Shvidenko A Lewis S LCanadell J G Ciais P Jackson R B Pacala S WMcGuire A D Piao S L Rautiainen A Sitch S andHayes D A large and persistent carbon sink in the worldrsquosforests Science 333 988ndash993 2011

Poorter H Niklas K J Reich P B Oleksyn J Poot P andMommer L Biomass allocation to leaves stems and rootsmeta-analyses of interspecific variation and environmental con-trol New Phytol 193 30ndash50 2012

Purves D and Pacala S Predictive models of forest dynamicsScience 320 1452ndash1453 2008

Ronnberg J Berglund M Johansson U and Cleary M In-cidence of Heterobasidion spp following different thinningregimes in Norway spruce in southern Sweden Forest EcolManag 289 409ndash415 2013

Shevliakova E Pacala S W Malyshev S Hurtt G CMilly P C D Caspersen J P Sentman L T Fisk J PWirth C and Crevoisier C Carbon cycling under 300 yearsof land use change importance of the secondary vegetation sinkGlobal Biogeochem Cy 23 2009

Sitch S Smith B Prentice I C Arneth A Bondeau ACramer W Kaplan J O Levis S Lucht W Sykes M TThonicke K and Venevsky S Evaluation of ecosystem dynam-ics plant geography and terrestrial carbon cycling in the LPJ dy-namic global vegetation model Glob Change Biol 9 161ndash1852003

Sitch S Huntingford C Gedney N Levy P E Lomas MPiao S L Betts R Ciais P Cox P Friedlingstein PJones C D Prentice I C and Woodward F I Evaluation ofthe terrestrial carbon cycle future plant geography and climate-carbon cycle feedbacks using five Dynamic Global VegetationModels (DGVMs) Glob Change Biol 14 2015ndash2039 2008

Smith B Prentice I C and Sykes M T Representation ofvegetation dynamics in the modelling of terrestrial ecosystemscomparing two contrasting approaches within European climatespace Global Ecol Biogeogr 10 621ndash637 2001

Smith B Warlind D Arneth A Hickler T Leadley P Silt-berg J and Zaehle S Implications of incorporating N cy-cling and N limitations on primary production in an individual-based dynamic vegetation model Biogeosciences 11 2027ndash2054 doi105194bg-11-2027-2014 2014

Sokal R R and Rohlf F J Biometry W H Freeman and Com-pany New York 887 pp 1995

Wang Y P Law R M and Pak B A global model of carbonnitrogen and phosphorus cycles for the terrestrial biosphere Bio-geosciences 7 2261ndash2282 doi105194bg-7-2261-2010 2010

Wang Y P Kowalczyk E Leuning R Abramowitz G Rau-pach M R Pak B van Gorsel E and Luhar A Diagnos-ing errors in a land surface model (CABLE) in the time andfrequency domains J Geophys Res-Biogeo 116 G01034doi1010292010jg001385 2011

Westoby M The self-thinning rule Adv Ecol Res 14 167ndash2251984

Widlowski J L Verstraete M M Pinty B and Gobron NAllometeric relationships of selected European tree species ECJoint Research Centre Ispra Italy 2003

Wolf A Ciais P Bellassen V Delbart N Field C Band Berry J A Forest biomass allometry in globalland surface models Global Biogeochem Cy 25 Gb3015doi1010292010gb003917 2011

Zaehle S Sitch S Prentice I C Liski J Cramer WErhard M Hickler T and Smith B The importance ofage-related decline in forest NPP for modeling regional car-bon balances Ecol Appl 16 1555ndash1574 doi1018901051-0761(2006)016[1555tioadi]20co2 2006



parameterisations treat carbon flows associated with respi-ration and mortality as first-order decay processes expressedas products of pool biomasses and bulk rate parameters in-dependent of age structure (the ldquobig woodrdquo approximationWolf et al 2011) These are computationally efficient ndash animportant consideration for global-scale applications ndash buthave the disadvantage of not resolving underlying popula-tion and community processes such as recruitment mortalityand competition between individuals and species for limitingresources (eg Sitch et al 2003) This lack of mechanisticdetail means that the models are unable to directly exploitthe wealth of information on forest stand structure and dy-namics available from forest inventories These have beenused to develop individual-based height-structured modelsthat have been successfully used to simulate forest dynamicsat the stand scale since the 1970s (eg Botkin et al 1972Bugmann 2001 Smith et al 2001) Different DVMs havealso been shown to simulate widely different patterns andtime evolution of biomass pools especially under future cli-mate projections (Cramer et al 2001 Friedlingstein et al2006 Sitch et al 2008 Friend et al 2014) where modelswith a conservative response of biomass turnover to climaticforcing tend to retain a net biomass sink over the comingcentury whereas others simulate a source or reduced sink bylate 21st century (Ahlstroumlm et al 2012) In ESM simula-tions with an active carbon cycle feedback to climate suchdifferences translate into divergence in the simulated globalclimate (Friedlingstein et al 2006) It has been suggestedthat the representation of forest dynamics in ESMs may beone of the greatest sources of uncertainty in future climateprojections (Purves and Pacala 2008)

A handful of offline (not coupled to the atmosphere)second-generation DVMs exist that simulate demographicprocesses and landscape heterogeneity of forests using moreexplicit approaches that have been demonstrated to accu-rately replicate forest size structure and successional dynam-ics as predicted by community ecological theory Examplesinclude LPJ-GUESS (Smith et al 2001) and ED (Moorcroftet al 2001 Fisher et al 2010) Such approaches are per-ceived as offering promise as an improved second genera-tion of DVMs (Purves and Pacala 2008 Fisher et al 2010)These models include stochastic representations of processessuch as recruitment mortality and large-scale disturbancewhich requires replication of dynamic objects such as treeindividuals and patches and repeated computations of thesame processes as applied to different objects in order to ob-tain a representative average for the ecosystem as a wholeFor studies of global and continental carbon balance and forcoupling to ESMs however this is a potential disadvantagebecause of their demand in terms of both of memory andprocessing power and the additional complication that theresults are not strictly deterministic which complicates theanalysis of results In addition the intricate internal represen-tation of stand structure and its integration with plant physio-logical processes such as carbon assimilation allocation and

phenology implies that the enhancement of existing land sur-face models (LSMs) lacking or employing simpler parame-terisations of vegetation dynamics may be a time-consumingtechnically challenging task

Wolf et al (2011) recently used global forest inventorydata to assess forest biomass allometry in eight global landsurface models including two second-generation DVMsSimulated relationships between stem and foliage biomasspools generally conformed poorly with observed allome-try indicative of model failure to consistently reproduceboth structural and functional characteristics of vegetationBest overall performance was noted for the models ED andORCHIDEE-FM (Bellassen et al 2010) which include anexplicit parameterisation of self-thinning which stronglycontrols biomass turnover rates in closed-forest ecosystems(Westoby 1984) The study recommended the use of biomassallometry data from forest inventories as a simple approachto improving the characteristic behaviour of global land sur-face models with respect to structural dynamics

To simultaneously overcome the limited ecological real-ism of simulated wood turnover in many first-generationDVMs and the technical limitations of current second-generation DVMs Haverd et al (2013) proposed a new ap-proach for the simulation of woody ecosystem stand dy-namics demography and disturbance-mediated heterogene-ity The approach encoded in a model called Populations-Order-Physiology (POP) is designed to be modular deter-ministic computationally efficient and based on sufficientecological realism for application at the grid scales typicallyemployed by DVMs and ESMs for continental to global ap-plications Coupled to the CABLE (Community AtmosphereBiosphere Land Exchange Wang et al 2011) LSM POP re-ceives woody biomass increment from CABLE and returnsan updated biomass state (an approach conceptually simi-lar to that of ORCHIDEE-FM but with key differences dis-cussed in Sect 42) CABLE-POP was demonstrated along asavanna transect in northern Australia successfully replicat-ing the effects of strong rainfall and fire disturbance gradi-ents on observed stand productivity and structure (Haverd etal 2013) The key simplification in the POP approach com-pared with second-generation DVMs is to compute physi-ological processes such as carbon assimilation at grid-scale(with CABLE or a similar land surface model) but to par-tition the grid-scale biomass increment among age classesdefined at sub-grid-scale each subject to its own dynam-ics POP is not a new DVM but a scheme for dynamicallyestimating size structure and turnover of woody vegetationforced by productivity information from an external LSM

In the present study we extend the application of POP toglobally distributed forests heeding the recommendation ofWolf et al (2011) to constrain and improve the performanceof the model by using allometric scaling relationships fromforest inventory data Thus calibrated the combined model(CABLE-POP) is evaluated against leafndashstem allometry andtotal biomass observations from forest stands



2 Methods

21 Models











dNy

dt= minus

(mRy + mCy

)Ny (1)



GEy = 1CyCsy (2)


mRy =mRy

1+ (GEyGEmin)p (3)









24



3



3



3


100 This work 5



5







1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t(4)



mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](5)








NPP



stembiomassturnover

stembiomass

increment




windspeedCO2

forestLAI


crownprojective

cover



212 CABLE-POP






22 Data







23 Calibration


log10(M) = α + β log10(N) (7)


1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)













3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References
















































2 Methods

21 Models











dNy

dt= minus

(mRy + mCy

)Ny (1)



GEy = 1CyCsy (2)


mRy =mRy

1+ (GEyGEmin)p (3)









24



3



3



3


100 This work 5



5







1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t(4)



mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](5)








NPP



stembiomassturnover

stembiomass

increment




windspeedCO2

forestLAI


crownprojective

cover



212 CABLE-POP






22 Data







23 Calibration


log10(M) = α + β log10(N) (7)


1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)













3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References




















































24



3



3



3


100 This work 5



5







1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t(4)



mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](5)








NPP



stembiomassturnover

stembiomass

increment




windspeedCO2

forestLAI


crownprojective

cover



212 CABLE-POP






22 Data







23 Calibration


log10(M) = α + β log10(N) (7)


1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)













3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References
















































NPP



stembiomassturnover

stembiomass

increment




windspeedCO2

forestLAI


crownprojective

cover



212 CABLE-POP






22 Data







23 Calibration


log10(M) = α + β log10(N) (7)


1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)













3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References



















































23 Calibration


log10(M) = α + β log10(N) (7)


1 15 2 25 3 35 4 45 5 55 6minus2

minus1

0

1

2

3

4

log(N)

log(

M)













3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References






















































3 Results








=






0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References
















































0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(v)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Broadleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iii)


0 100 200 300 400 5000

100

200

300

400

500


CA

BLE

minusP

OP

ste

m b

iom

ass

[t D

M h

aminus1 ]

(vi)

1 2 3 4 5minus2

minus1

0

1

2

3

4

log(N)

log(

M)

Needleleaf



minus15

minus1

minus05

0

05

1

15

2

log(Mstem

)

log(

Mfo

l)

(iv)















4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References























































4 Discussion







0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References
















































0 200 4000

05

1

Fra

ctio

n B

iom

ass


rootstemleaf

0 200 4000

05


0 200 4000

05


0 200 4000

05


0 200 4000

05


Fra

ctio

n B

iom

ass

0 200 4000

05


0 200 4000

05



Fra

ctio

n B

iom

ass

0 200 4000

05















15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References
















































15 2 25 3 35 4 45 5

minus1

0

1

2

3

4

log(N)

log(

M)

(i)stand ageing



fit to CminusU Data


0 50 100 150 200 2500

02

04

06

08

1

time [y]

crow

n pr

ojec

ted

cove

r

(ii)



0 50 100 150 200 2500

002

004

006

008

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]0 50 100 150 200 250

0

01

02

03

04

time [y]

mor

talit

y [k

g C

mminus

2 yminus

1 ]


total mortality


crowding mortality


0

001

002

003

004

turn

over

rat

e co

effic

ient

[yminus

1 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

5

10

15


time [y]

stem

bio

mas

s [k

g C

mminus

2 ]

0 50 100 150 200 2500

05

1

15

2

25

3


time [y]

stem

den

sity

[ind

iv m

minus2 ]

0 50 100 150 200 2500

02

04

06

08

1

12


time [y]

stem

den

sity

[ind

iv m

minus2 ]








minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References

















































minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Broadleaf

(i)(i)(i)


minus15

minus1

minus05

0

05

1

15

2

log(Mstem)

log(

Mfo

l)

Needleleaf

(ii)







5 Conclusions









dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References




















































dNy

dt= minus

(mRy + mCy

)Ny (A1)


A2 Recruitment




F = exp(minus06C23

) (A3)


micro(F) = exp

[α

(1minus

2θ

F + 1minus


)] (A4)





1Cy

1t=

(CyNy)sNysum

(CiNi)sNi

1C

1t (A5)


A4 Cohort structure


Hy = kD23y (A6)


Vy = Hy

π

4D2

y (A7)





Hy = k34(

4Cy

π middot Nyρw

)14

(A9)

A5 Mortality





mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References

















































mRy =mRmax






mCy = min

[1

1texp

(αC(1minus 1cpcy

))fc

1Cy

Cy1t

](A11)


(minusAcy



















A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References

















































A7 Patch weightings



bli =

0 i = 1



(A14)

bui =

0 ai = 0




ai i = nage






Ac (1minus Pwc) =

hmaxinthmin





smean= VAC (A18)






Edited by S Zaehle

References


















































Edited by S Zaehle

References















































a stand-alone tree demography and landscape structure ......savanna transect in northern australia,...

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