Forest dynamics
Miquel De Caceres
2025-07-14
Source:vignettes/runmodels/ForestDynamics.Rmd
ForestDynamics.RmdAbout this vignette
This document describes how to run the forest dynamics model of
medfate, described in De Cáceres et al. (2023) and
implemented in function fordyn(). This document is meant to
teach users to run the simulation model with function
fordyn(). Details of the model design and formulation can
be found at the corresponding chapters of the medfate
book.
Because the model builds on the growth and water balance models, the
reader is assumed here to be familiarized with spwb() and
growth() (otherwise read vignettes Basic
water balance and Forest
growth).
Preparing model inputs
Any forest dynamics model needs information on climate, vegetation
and soils of the forest stand to be simulated. Moreover, since models in
medfate differentiate between species, information on
species-specific model parameters is also needed. In this subsection we
explain the different steps to prepare the data needed to run function
fordyn().
Model inputs are explained in greater detail in vignettes Understanding
model inputs and Preparing
model inputs. Here we only review the different steps required
to run function fordyn().
Soil, vegetation, meteorology and species data
Soil information needs to be entered as a data frame
with soil layers in rows and physical attributes in columns. Soil
physical attributes can be initialized to default values, for a given
number of layers, using function defaultSoilParams():
examplesoil <- defaultSoilParams(4)
examplesoil## widths clay sand om nitrogen bd rfc
## 1 300 25 25 NA NA 1.5 25
## 2 700 25 25 NA NA 1.5 45
## 3 1000 25 25 NA NA 1.5 75
## 4 2000 25 25 NA NA 1.5 95As explained in the package overview, models included in
medfate were primarily designed to be ran on forest
inventory plots. Here we use the example object provided with
the package:
data(exampleforest)
exampleforest## $treeData
## Species N DBH Height Z50 Z95
## 1 Pinus halepensis 168 37.55 800 100 600
## 2 Quercus ilex 384 14.60 660 300 1000
##
## $shrubData
## Species Cover Height Z50 Z95
## 1 Quercus coccifera 3.75 80 200 1000
##
## $herbCover
## [1] 10
##
## $herbHeight
## [1] 20
##
## $seedBank
## [1] Species Percent
## <0 rows> (or 0-length row.names)
##
## attr(,"class")
## [1] "forest" "list"Importantly, a data frame with daily weather for the period to be simulated is required. Here we use the default data frame included with the package:
## dates MinTemperature MaxTemperature Precipitation MinRelativeHumidity
## 1 2001-01-01 -0.5934215 6.287950 4.869109 65.15411
## 2 2001-01-02 -2.3662458 4.569737 2.498292 57.43761
## 3 2001-01-03 -3.8541036 2.661951 0.000000 58.77432
## 4 2001-01-04 -1.8744860 3.097705 5.796973 66.84256
## 5 2001-01-05 0.3288287 7.551532 1.884401 62.97656
## 6 2001-01-06 0.5461322 7.186784 13.359801 74.25754
## MaxRelativeHumidity Radiation WindSpeed
## 1 100.00000 12.89251 2.000000
## 2 94.71780 13.03079 7.662544
## 3 94.66823 16.90722 2.000000
## 4 95.80950 11.07275 2.000000
## 5 100.00000 13.45205 7.581347
## 6 100.00000 12.84841 6.570501Finally, simulations in medfate require a data frame
with species parameter values, which we load using defaults for
Catalonia (NE Spain):
data("SpParamsMED")Simulation control
Apart from data inputs, the behaviour of simulation models can be
controlled using a set of global parameters. The default
parameterization is obtained using function
defaultControl():
control <- defaultControl("Granier")Here we will run simulations of forest dynamics using the basic water
balance model (i.e. transpirationMode = "Granier"). The
complexity of the soil water balance calculations can be changed by
using "Sperry" as input to defaultControl().
However, when running fordyn() sub-daily output will never
be stored (i.e. setting subdailyResults = TRUE is
useless).
Executing the forest dynamics model
In this vignette we will fake a ten-year weather input by repeating the example weather data frame ten times.
meteo <- rbind(examplemeteo, examplemeteo, examplemeteo, examplemeteo,
examplemeteo, examplemeteo, examplemeteo, examplemeteo,
examplemeteo, examplemeteo)
meteo$dates <- as.character(seq(as.Date("2001-01-01"),
as.Date("2010-12-29"), by="day"))Now we run the forest dynamics model using all inputs (note that no
intermediate input object is needed, as in spwb() or
growth()):
fd<-fordyn(exampleforest, examplesoil, SpParamsMED, meteo, control,
latitude = 41.82592, elevation = 100)## Simulating year 2001 (1/10): (a) Growth/mortality## Package 'meteoland' [ver. 2.2.4]## , (b) Regeneration nT = 2 nS = 1
## Simulating year 2002 (2/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2003 (3/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2004 (4/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2005 (5/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2006 (6/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2007 (7/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2008 (8/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2009 (9/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1
## Simulating year 2010 (10/10): (a) Growth/mortality, (b) Regeneration nT = 2 nS = 1It is worth noting that, while fordyn() calls function
growth() internally for each simulated year, the
verbose option of the control parameters only affects
function fordyn() (i.e. all console output from
growth() is hidden). Recruitment and summaries are done
only once a year at the level of function fordyn().
Inspecting model outputs
Stand, species and cohort summaries and plots
Among other outputs, function fordyn() calculates
standard summary statistics that describe the structural and
compositional state of the forest at each time step. For example, we can
access stand-level statistics using:
fd$StandSummary## Step NumTreeSpecies NumTreeCohorts NumShrubSpecies NumShrubCohorts
## 1 0 2 2 1 1
## 2 1 2 2 1 1
## 3 2 2 2 1 1
## 4 3 2 2 1 1
## 5 4 2 2 1 1
## 6 5 2 2 1 1
## 7 6 2 2 1 1
## 8 7 2 2 1 1
## 9 8 2 2 1 1
## 10 9 2 2 1 1
## 11 10 2 2 1 1
## TreeDensityLive TreeBasalAreaLive DominantTreeHeight DominantTreeDiameter
## 1 552.0000 25.03330 800.0000 37.55000
## 2 551.3664 25.20608 806.1349 37.66427
## 3 550.7271 25.37989 812.2899 37.77951
## 4 550.0821 25.55415 818.4331 37.89512
## 5 549.4296 25.72834 824.5462 38.01077
## 6 548.7731 25.90235 830.6199 38.12627
## 7 548.1108 26.07559 836.6488 38.24152
## 8 547.4429 26.24825 842.6316 38.35648
## 9 546.7673 26.42015 848.5666 38.47111
## 10 546.0879 26.59163 854.4529 38.58540
## 11 545.4065 26.76272 860.2918 38.69934
## QuadraticMeanTreeDiameter HartBeckingIndex ShrubCoverLive BasalAreaDead
## 1 24.02949 53.20353 3.750000 0.00000000
## 2 24.12613 52.82897 3.092002 0.03916800
## 3 24.22321 52.45909 3.139797 0.03982577
## 4 24.32047 52.09584 3.188166 0.04049381
## 5 24.41771 51.74031 3.237209 0.04128376
## 6 24.51479 51.39268 3.286750 0.04185502
## 7 24.61149 51.05316 3.336758 0.04254409
## 8 24.70790 50.72159 3.387258 0.04323843
## 9 24.80398 50.39794 3.438823 0.04405903
## 10 24.89983 50.08188 3.489709 0.04464407
## 11 24.99540 49.77303 3.541118 0.04510441
## ShrubCoverDead BasalAreaCut ShrubCoverCut
## 1 0.000000000 0 0
## 2 0.005308865 0 0
## 3 0.004784382 0 0
## 4 0.004858242 0 0
## 5 0.004946666 0 0
## 6 0.005008892 0 0
## 7 0.005085376 0 0
## 8 0.005162595 0 0
## 9 0.005255268 0 0
## 10 0.005319858 0 0
## 11 0.005368566 0 0Species-level analogous statistics are shown using:
fd$SpeciesSummary## Step Species NumCohorts TreeDensityLive TreeBasalAreaLive
## 1 0 Pinus halepensis 1 168.0000 18.604547
## 2 0 Quercus coccifera 1 NA NA
## 3 0 Quercus ilex 1 384.0000 6.428755
## 4 1 Pinus halepensis 1 167.6992 18.684443
## 5 1 Quercus coccifera 1 NA NA
## 6 1 Quercus ilex 1 383.6671 6.521640
## 7 2 Pinus halepensis 1 167.3956 18.764917
## 8 2 Quercus coccifera 1 NA NA
## 9 2 Quercus ilex 1 383.3314 6.614976
## 10 3 Pinus halepensis 1 167.0892 18.845381
## 11 3 Quercus coccifera 1 NA NA
## 12 3 Quercus ilex 1 382.9929 6.708766
## 13 4 Pinus halepensis 1 166.7790 18.925384
## 14 4 Quercus coccifera 1 NA NA
## 15 4 Quercus ilex 1 382.6506 6.802954
## 16 5 Pinus halepensis 1 166.4668 19.004930
## 17 5 Quercus coccifera 1 NA NA
## 18 5 Quercus ilex 1 382.3063 6.897421
## 19 6 Pinus halepensis 1 166.1517 19.083809
## 20 6 Quercus coccifera 1 NA NA
## 21 6 Quercus ilex 1 381.9591 6.991777
## 22 7 Pinus halepensis 1 165.8338 19.161980
## 23 7 Quercus coccifera 1 NA NA
## 24 7 Quercus ilex 1 381.6091 7.086272
## 25 8 Pinus halepensis 1 165.5121 19.239294
## 26 8 Quercus coccifera 1 NA NA
## 27 8 Quercus ilex 1 381.2552 7.180852
## 28 9 Pinus halepensis 1 165.1884 19.315922
## 29 9 Quercus coccifera 1 NA NA
## 30 9 Quercus ilex 1 380.8995 7.275712
## 31 10 Pinus halepensis 1 164.8637 19.391978
## 32 10 Quercus coccifera 1 NA NA
## 33 10 Quercus ilex 1 380.5428 7.370741
## ShrubCoverLive BasalAreaDead ShrubCoverDead BasalAreaCut ShrubCoverCut
## 1 NA 0.000000000 NA 0 NA
## 2 3.750000 NA 0.000000000 NA 0
## 3 NA 0.000000000 NA 0 NA
## 4 NA 0.033509817 NA 0 NA
## 5 3.092002 NA 0.005308865 NA 0
## 6 NA 0.005658184 NA 0 NA
## 7 NA 0.034032852 NA 0 NA
## 8 3.139797 NA 0.004784382 NA 0
## 9 NA 0.005792915 NA 0 NA
## 10 NA 0.034563686 NA 0 NA
## 11 3.188166 NA 0.004858242 NA 0
## 12 NA 0.005930120 NA 0 NA
## 13 NA 0.035197398 NA 0 NA
## 14 3.237209 NA 0.004946666 NA 0
## 15 NA 0.006086359 NA 0 NA
## 16 NA 0.035643612 NA 0 NA
## 17 3.286750 NA 0.005008892 NA 0
## 18 NA 0.006211407 NA 0 NA
## 19 NA 0.036189436 NA 0 NA
## 20 3.336758 NA 0.005085376 NA 0
## 21 NA 0.006354650 NA 0 NA
## 22 NA 0.036738721 NA 0 NA
## 23 3.387258 NA 0.005162595 NA 0
## 24 NA 0.006499713 NA 0 NA
## 25 NA 0.037394149 NA 0 NA
## 26 3.438823 NA 0.005255268 NA 0
## 27 NA 0.006664884 NA 0 NA
## 28 NA 0.037848485 NA 0 NA
## 29 3.489709 NA 0.005319858 NA 0
## 30 NA 0.006795587 NA 0 NA
## 31 NA 0.038196361 NA 0 NA
## 32 3.541118 NA 0.005368566 NA 0
## 33 NA 0.006908048 NA 0 NAPackage medfate provides a simple plot
function for objects of class fordyn. For example, we can
show the interannual variation in stand-level basal area using:
plot(fd, type = "StandBasalArea")
Tree/shrub tables
Another useful output of fordyn() are tables in long
format with cohort structural information (i.e. DBH, height, density,
etc) for each time step:
fd$TreeTable## Step Year Cohort Species DBH Height N Z50 Z95 ObsID
## 1 0 NA T1_148 Pinus halepensis 37.55000 800.0000 168.0000 100 600 <NA>
## 2 0 NA T2_168 Quercus ilex 14.60000 660.0000 384.0000 300 1000 <NA>
## 3 1 2001 T1_148 Pinus halepensis 37.66427 806.1349 167.6992 100 600 <NA>
## 4 1 2001 T2_168 Quercus ilex 14.71147 663.4696 383.6671 300 1000 <NA>
## 5 2 2002 T1_148 Pinus halepensis 37.77951 812.2899 167.3956 100 600 <NA>
## 6 2 2002 T2_168 Quercus ilex 14.82286 666.9265 383.3314 300 1000 <NA>
## 7 3 2003 T1_148 Pinus halepensis 37.89512 818.4331 167.0892 100 600 <NA>
## 8 3 2003 T2_168 Quercus ilex 14.93417 670.3712 382.9929 300 1000 <NA>
## 9 4 2004 T1_148 Pinus halepensis 38.01077 824.5462 166.7790 100 600 <NA>
## 10 4 2004 T2_168 Quercus ilex 15.04536 673.8025 382.6506 300 1000 <NA>
## 11 5 2005 T1_148 Pinus halepensis 38.12627 830.6199 166.4668 100 600 <NA>
## 12 5 2005 T2_168 Quercus ilex 15.15628 677.2155 382.3063 300 1000 <NA>
## 13 6 2006 T1_148 Pinus halepensis 38.24152 836.6488 166.1517 100 600 <NA>
## 14 6 2006 T2_168 Quercus ilex 15.26653 680.5977 381.9591 300 1000 <NA>
## 15 7 2007 T1_148 Pinus halepensis 38.35648 842.6316 165.8338 100 600 <NA>
## 16 7 2007 T2_168 Quercus ilex 15.37640 683.9581 381.6091 300 1000 <NA>
## 17 8 2008 T1_148 Pinus halepensis 38.47111 848.5666 165.5121 100 600 <NA>
## 18 8 2008 T2_168 Quercus ilex 15.48585 687.2959 381.2552 300 1000 <NA>
## 19 9 2009 T1_148 Pinus halepensis 38.58540 854.4529 165.1884 100 600 <NA>
## 20 9 2009 T2_168 Quercus ilex 15.59508 690.6164 380.8995 300 1000 <NA>
## 21 10 2010 T1_148 Pinus halepensis 38.69934 860.2918 164.8637 100 600 <NA>
## 22 10 2010 T2_168 Quercus ilex 15.70395 693.9158 380.5428 300 1000 <NA>The same can be shown for dead trees:
fd$DeadTreeTable## Step Year Cohort Species DBH Height N N_starvation
## 1 1 2001 T1_148 Pinus halepensis 37.66427 806.1349 0.3007620 0
## 2 1 2001 T2_168 Quercus ilex 14.71147 663.4696 0.3328701 0
## 3 2 2002 T1_148 Pinus halepensis 37.77951 812.2899 0.3035959 0
## 4 2 2002 T2_168 Quercus ilex 14.82286 666.9265 0.3356938 0
## 5 3 2003 T1_148 Pinus halepensis 37.89512 818.4331 0.3064527 0
## 6 3 2003 T2_168 Quercus ilex 14.93417 670.3712 0.3385412 0
## 7 4 2004 T1_148 Pinus halepensis 38.01077 824.5462 0.3101753 0
## 8 4 2004 T2_168 Quercus ilex 15.04536 673.8025 0.3423437 0
## 9 5 2005 T1_148 Pinus halepensis 38.12627 830.6199 0.3122073 0
## 10 5 2005 T2_168 Quercus ilex 15.15628 677.2155 0.3442822 0
## 11 6 2006 T1_148 Pinus halepensis 38.24152 836.6488 0.3150806 0
## 12 6 2006 T2_168 Quercus ilex 15.26653 680.5977 0.3471530 0
## 13 7 2007 T1_148 Pinus halepensis 38.35648 842.6316 0.3179484 0
## 14 7 2007 T2_168 Quercus ilex 15.37640 683.9581 0.3500218 0
## 15 8 2008 T1_148 Pinus halepensis 38.47111 848.5666 0.3216949 0
## 16 8 2008 T2_168 Quercus ilex 15.48585 687.2959 0.3538608 0
## 17 9 2009 T1_148 Pinus halepensis 38.58540 854.4529 0.3236776 0
## 18 9 2009 T2_168 Quercus ilex 15.59508 690.6164 0.3557639 0
## 19 10 2010 T1_148 Pinus halepensis 38.69934 860.2918 0.3247318 0
## 20 10 2010 T2_168 Quercus ilex 15.70395 693.9158 0.3566545 0
## N_dessication N_burnt Z50 Z95 ObsID
## 1 0 0 100 600 <NA>
## 2 0 0 300 1000 <NA>
## 3 0 0 100 600 <NA>
## 4 0 0 300 1000 <NA>
## 5 0 0 100 600 <NA>
## 6 0 0 300 1000 <NA>
## 7 0 0 100 600 <NA>
## 8 0 0 300 1000 <NA>
## 9 0 0 100 600 <NA>
## 10 0 0 300 1000 <NA>
## 11 0 0 100 600 <NA>
## 12 0 0 300 1000 <NA>
## 13 0 0 100 600 <NA>
## 14 0 0 300 1000 <NA>
## 15 0 0 100 600 <NA>
## 16 0 0 300 1000 <NA>
## 17 0 0 100 600 <NA>
## 18 0 0 300 1000 <NA>
## 19 0 0 100 600 <NA>
## 20 0 0 300 1000 <NA>Accessing the output from function growth()
Since function fordyn() makes internal calls to function
growth(), it stores the result in a vector called
GrowthResults, which we can use to inspect intra-annual
patterns of desired variables. For example, the following shows the leaf
area for individuals of the three cohorts during the second year:
plot(fd$GrowthResults[[2]], "LeafArea", bySpecies = T)
Instead of examining year by year, it is possible to plot the whole
series of results by passing a fordyn object to the
plot() function:
plot(fd, "LeafArea")
Finally, we can create interactive plots for particular steps using
function shinyplot(), e.g.:
shinyplot(fd$GrowthResults[[1]])Forest dynamics including management
The package allows including forest management in simulations of
forest dynamics. This is done in a very flexible manner, in the sense
that fordyn() allows the user to supply an arbitrary
function implementing a desired management strategy for the stand whose
dynamics are to be simulated. The package includes, however, an in-built
default function called defaultManagementFunction() along
with a flexible parameterization, a list with defaults provided by
function defaultManagementArguments().
Here we provide an example of simulations including forest management:
# Default arguments
args <- defaultManagementArguments()
# Here one can modify defaults before calling fordyn()
#
# Simulation
fd<-fordyn(exampleforest, examplesoil, SpParamsMED, meteo, control,
latitude = 41.82592, elevation = 100,
management_function = defaultManagementFunction,
management_args = args)## Simulating year 2001 (1/10): (a) Growth/mortality & management [thinning], (b) Regeneration nT = 2 nS = 2
## Simulating year 2002 (2/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2003 (3/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2004 (4/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2005 (5/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2006 (6/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2007 (7/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2008 (8/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2009 (9/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2
## Simulating year 2010 (10/10): (a) Growth/mortality & management [none], (b) Regeneration nT = 2 nS = 2When management is included in simulations, two additional tables are produced, corresponding to the trees and shrubs that were cut, e.g.:
fd$CutTreeTable## Step Year Cohort Species DBH Height N Z50 Z95 ObsID
## 1 1 2001 T1_148 Pinus halepensis 37.66427 806.1349 9.336019 100 600 <NA>
## 2 1 2001 T2_168 Quercus ilex 14.71147 663.4696 383.667130 300 1000 <NA>Management parameters were those of an irregular model with thinning interventions from ‘below’, indicating that smaller trees were to be cut earlier:
args$type## [1] "irregular"
args$thinning## [1] "below"Note that in this example, there is resprouting of Quercus ilex after the thinning intervention, evidenced by the new cohort (T3_168) appearing in year 2001:
fd$TreeTable## Step Year Cohort Species DBH Height N Z50
## 1 0 NA T1_148 Pinus halepensis 37.550000 800.00000 168.0000 100.0000
## 2 0 NA T2_168 Quercus ilex 14.600000 660.00000 384.0000 300.0000
## 3 1 2001 T1_148 Pinus halepensis 37.664271 806.13493 158.3632 100.0000
## 4 1 2001 T3_168 Quercus ilex 1.000000 47.23629 3000.0000 300.0000
## 5 2 2002 T1_148 Pinus halepensis 37.781093 812.32085 158.1918 100.0000
## 6 2 2002 T3_168 Quercus ilex 1.138024 55.69980 2614.7351 300.0000
## 7 3 2003 T1_148 Pinus halepensis 37.900789 818.61986 158.0190 100.0000
## 8 3 2003 T3_168 Quercus ilex 1.253654 62.74529 2359.1259 300.0000
## 9 4 2004 T1_148 Pinus halepensis 38.020666 824.89477 157.8443 100.0000
## 10 4 2004 T3_168 Quercus ilex 1.369318 69.79045 2147.8635 300.0000
## 11 5 2005 T1_148 Pinus halepensis 38.140533 831.13577 157.6687 100.0000
## 12 5 2005 T2_168 Quercus ilex 1.412651 74.28409 2389.9033 282.3452
## 13 6 2006 T1_148 Pinus halepensis 38.257946 837.21650 157.4920 100.0000
## 14 6 2006 T2_168 Quercus ilex 1.528913 81.36774 1910.3305 282.3452
## 15 7 2007 T1_148 Pinus halepensis 38.376094 843.30313 157.3139 100.0000
## 16 7 2007 T2_168 Quercus ilex 1.645496 88.47031 1766.7767 282.3452
## 17 8 2008 T1_148 Pinus halepensis 38.494588 849.37529 157.1340 100.0000
## 18 8 2008 T2_168 Quercus ilex 1.763384 95.65826 1641.4803 282.3452
## 19 9 2009 T1_148 Pinus halepensis 38.613206 855.42160 156.9532 100.0000
## 20 9 2009 T2_168 Quercus ilex 1.882011 102.89694 1531.7118 282.3452
## 21 10 2010 T1_148 Pinus halepensis 38.731810 861.43514 156.7719 100.0000
## 22 10 2010 T2_168 Quercus ilex 2.001189 110.17479 1434.9302 282.3452
## Z95 ObsID
## 1 600 <NA>
## 2 1000 <NA>
## 3 600 <NA>
## 4 1000 <NA>
## 5 600 <NA>
## 6 1000 <NA>
## 7 600 <NA>
## 8 1000 <NA>
## 9 600 <NA>
## 10 1000 <NA>
## 11 600 <NA>
## 12 1000 <NA>
## 13 600 <NA>
## 14 1000 <NA>
## 15 600 <NA>
## 16 1000 <NA>
## 17 600 <NA>
## 18 1000 <NA>
## 19 600 <NA>
## 20 1000 <NA>
## 21 600 <NA>
## 22 1000 <NA>References
- De Cáceres M, Molowny-Horas R, Cabon A, Martínez-Vilalta J, Mencuccini M, García-Valdés R, Nadal-Sala D, Sabaté S, Martin-StPaul N, Morin X, D’Adamo F, Batllori E, Améztegui A (2023) MEDFATE 2.9.3: A trait-enabled model to simulate Mediterranean forest function and dynamics at regional scales. Geoscientific Model Development 16: 3165-3201 (https://doi.org/10.5194/gmd-16-3165-2023).