Forest dynamics
Miquel De Caceres
2025-08-27
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$StandSummary## Step NumTreeSpecies NumTreeCohorts NumShrubSpecies NumShrubCohorts
## 1 0 2 2 1 1
## 2 1 2 2 1 1
## 3 2 2 2 1 1
## 4 3 2 2 1 1
## 5 4 2 2 1 1
## 6 5 2 2 1 1
## 7 6 2 2 1 1
## 8 7 2 2 1 1
## 9 8 2 2 1 1
## 10 9 2 2 1 1
## 11 10 2 2 1 1
## TreeDensityLive TreeBasalAreaLive DominantTreeHeight DominantTreeDiameter
## 1 552.0000 25.03330 800.0000 37.55000
## 2 551.3664 25.20608 806.1349 37.66427
## 3 550.7271 25.37991 812.2899 37.77951
## 4 550.0821 25.55420 818.4330 37.89512
## 5 549.4296 25.72846 824.5461 38.01077
## 6 548.7731 25.90244 830.6197 38.12627
## 7 548.1108 26.07567 836.6486 38.24151
## 8 547.4429 26.24831 842.6313 38.35647
## 9 546.7673 26.42020 848.5662 38.47111
## 10 546.0879 26.59156 854.4526 38.58539
## 11 545.4065 26.76259 860.2914 38.69934
## QuadraticMeanTreeDiameter HartBeckingIndex ShrubCoverLive BasalAreaDead
## 1 24.02949 53.20353 3.750000 0.00000000
## 2 24.12613 52.82897 3.092002 0.03916800
## 3 24.22322 52.45909 3.139798 0.03982580
## 4 24.32050 52.09585 3.188170 0.04049396
## 5 24.41777 51.74031 3.237219 0.04128410
## 6 24.51483 51.39269 3.286758 0.04185535
## 7 24.61153 51.05317 3.336766 0.04254437
## 8 24.70793 50.72161 3.387265 0.04323866
## 9 24.80401 50.39796 3.438831 0.04405921
## 10 24.89979 50.08190 3.489708 0.04464393
## 11 24.99534 49.77305 3.541115 0.04510400
## ShrubCoverDead BasalAreaCut ShrubCoverCut
## 1 0.000000000 0 0
## 2 0.005308865 0 0
## 3 0.004784383 0 0
## 4 0.004858246 0 0
## 5 0.004946676 0 0
## 6 0.005008905 0 0
## 7 0.005085388 0 0
## 8 0.005162607 0 0
## 9 0.005255279 0 0
## 10 0.005319864 0 0
## 11 0.005368564 0 0Species-level analogous statistics are shown using:
fd$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 6.614992
## 10 3 Pinus halepensis 1 167.0892 18.845380
## 11 3 Quercus coccifera 1 NA NA
## 12 3 Quercus ilex 1 382.9929 6.708824
## 13 4 Pinus halepensis 1 166.7790 18.925382
## 14 4 Quercus coccifera 1 NA NA
## 15 4 Quercus ilex 1 382.6505 6.803075
## 16 5 Pinus halepensis 1 166.4668 19.004926
## 17 5 Quercus coccifera 1 NA NA
## 18 5 Quercus ilex 1 382.3063 6.897510
## 19 6 Pinus halepensis 1 166.1517 19.083803
## 20 6 Quercus coccifera 1 NA NA
## 21 6 Quercus ilex 1 381.9591 6.991865
## 22 7 Pinus halepensis 1 165.8338 19.161973
## 23 7 Quercus coccifera 1 NA NA
## 24 7 Quercus ilex 1 381.6091 7.086334
## 25 8 Pinus halepensis 1 165.5121 19.239286
## 26 8 Quercus coccifera 1 NA NA
## 27 8 Quercus ilex 1 381.2552 7.180910
## 28 9 Pinus halepensis 1 165.1884 19.315913
## 29 9 Quercus coccifera 1 NA NA
## 30 9 Quercus ilex 1 380.8995 7.275647
## 31 10 Pinus halepensis 1 164.8637 19.391970
## 32 10 Quercus coccifera 1 NA NA
## 33 10 Quercus ilex 1 380.5428 7.370624
## 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 0.034032872 NA 0 NA
## 8 3.139798 NA 0.004784383 NA 0
## 9 NA 0.005792932 NA 0 NA
## 10 NA 0.034563773 NA 0 NA
## 11 3.188170 NA 0.004858246 NA 0
## 12 NA 0.005930183 NA 0 NA
## 13 NA 0.035197604 NA 0 NA
## 14 3.237219 NA 0.004946676 NA 0
## 15 NA 0.006086497 NA 0 NA
## 16 NA 0.035643831 NA 0 NA
## 17 3.286758 NA 0.005008905 NA 0
## 18 NA 0.006211519 NA 0 NA
## 19 NA 0.036189616 NA 0 NA
## 20 3.336766 NA 0.005085388 NA 0
## 21 NA 0.006354757 NA 0 NA
## 22 NA 0.036738863 NA 0 NA
## 23 3.387265 NA 0.005162607 NA 0
## 24 NA 0.006499793 NA 0 NA
## 25 NA 0.037394259 NA 0 NA
## 26 3.438831 NA 0.005255279 NA 0
## 27 NA 0.006664956 NA 0 NA
## 28 NA 0.037848416 NA 0 NA
## 29 3.489708 NA 0.005319864 NA 0
## 30 NA 0.006795519 NA 0 NA
## 31 NA 0.038196097 NA 0 NA
## 32 3.541115 NA 0.005368564 NA 0
## 33 NA 0.006907901 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$TreeTable## Step Year Cohort Species DBH Height N Z50 Z95 ObsID
## 1 0 NA T1_148 Pinus halepensis 37.55000 800.0000 168.0000 100 600 <NA>
## 2 0 NA T2_168 Quercus ilex 14.60000 660.0000 384.0000 300 1000 <NA>
## 3 1 2001 T1_148 Pinus halepensis 37.66427 806.1349 167.6992 100 600 <NA>
## 4 1 2001 T2_168 Quercus ilex 14.71147 663.4696 383.6671 300 1000 <NA>
## 5 2 2002 T1_148 Pinus halepensis 37.77951 812.2899 167.3956 100 600 <NA>
## 6 2 2002 T2_168 Quercus ilex 14.82288 666.9271 383.3314 300 1000 <NA>
## 7 3 2003 T1_148 Pinus halepensis 37.89512 818.4330 167.0892 100 600 <NA>
## 8 3 2003 T2_168 Quercus ilex 14.93423 670.3732 382.9929 300 1000 <NA>
## 9 4 2004 T1_148 Pinus halepensis 38.01077 824.5461 166.7790 100 600 <NA>
## 10 4 2004 T2_168 Quercus ilex 15.04550 673.8066 382.6505 300 1000 <NA>
## 11 5 2005 T1_148 Pinus halepensis 38.12627 830.6197 166.4668 100 600 <NA>
## 12 5 2005 T2_168 Quercus ilex 15.15638 677.2185 382.3063 300 1000 <NA>
## 13 6 2006 T1_148 Pinus halepensis 38.24151 836.6486 166.1517 100 600 <NA>
## 14 6 2006 T2_168 Quercus ilex 15.26663 680.6006 381.9591 300 1000 <NA>
## 15 7 2007 T1_148 Pinus halepensis 38.35647 842.6313 165.8338 100 600 <NA>
## 16 7 2007 T2_168 Quercus ilex 15.37646 683.9602 381.6091 300 1000 <NA>
## 17 8 2008 T1_148 Pinus halepensis 38.47111 848.5662 165.5121 100 600 <NA>
## 18 8 2008 T2_168 Quercus ilex 15.48592 687.2977 381.2552 300 1000 <NA>
## 19 9 2009 T1_148 Pinus halepensis 38.58539 854.4526 165.1884 100 600 <NA>
## 20 9 2009 T2_168 Quercus ilex 15.59501 690.6143 380.8995 300 1000 <NA>
## 21 10 2010 T1_148 Pinus halepensis 38.69934 860.2914 164.8637 100 600 <NA>
## 22 10 2010 T2_168 Quercus ilex 15.70382 693.9120 380.5428 300 1000 <NA>The same can be shown for dead trees:
fd$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 0.3035960 0
## 4 2 2002 T2_168 Quercus ilex 14.82288 666.9271 0.3356940 0
## 5 3 2003 T1_148 Pinus halepensis 37.89512 818.4330 0.3064535 0
## 6 3 2003 T2_168 Quercus ilex 14.93423 670.3732 0.3385419 0
## 7 4 2004 T1_148 Pinus halepensis 38.01077 824.5461 0.3101772 0
## 8 4 2004 T2_168 Quercus ilex 15.04550 673.8066 0.3423454 0
## 9 5 2005 T1_148 Pinus halepensis 38.12627 830.6197 0.3122093 0
## 10 5 2005 T2_168 Quercus ilex 15.15638 677.2185 0.3442841 0
## 11 6 2006 T1_148 Pinus halepensis 38.24151 836.6486 0.3150822 0
## 12 6 2006 T2_168 Quercus ilex 15.26663 680.6006 0.3471545 0
## 13 7 2007 T1_148 Pinus halepensis 38.35647 842.6313 0.3179497 0
## 14 7 2007 T2_168 Quercus ilex 15.37646 683.9602 0.3500230 0
## 15 8 2008 T1_148 Pinus halepensis 38.47111 848.5662 0.3216960 0
## 16 8 2008 T2_168 Quercus ilex 15.48592 687.2977 0.3538617 0
## 17 9 2009 T1_148 Pinus halepensis 38.58539 854.4526 0.3236771 0
## 18 9 2009 T2_168 Quercus ilex 15.59501 690.6143 0.3557634 0
## 19 10 2010 T1_148 Pinus halepensis 38.69934 860.2914 0.3247297 0
## 20 10 2010 T2_168 Quercus ilex 15.70382 693.9120 0.3566526 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 37.781094 812.32091 158.1918 100.0000
## 6 2 2002 T3_168 Quercus ilex 1.138025 55.69984 2614.7333 300.0000
## 7 3 2003 T1_148 Pinus halepensis 37.900792 818.62002 158.0190 100.0000
## 8 3 2003 T3_168 Quercus ilex 1.253656 62.74543 2359.1212 300.0000
## 9 4 2004 T1_148 Pinus halepensis 38.020670 824.89498 157.8443 100.0000
## 10 4 2004 T3_168 Quercus ilex 1.369321 69.79064 2147.8583 300.0000
## 11 5 2005 T1_148 Pinus halepensis 38.140537 831.13600 157.6687 100.0000
## 12 5 2005 T2_168 Quercus ilex 1.412760 74.29166 2389.7162 282.3466
## 13 6 2006 T1_148 Pinus halepensis 38.257950 837.21672 157.4920 100.0000
## 14 6 2006 T2_168 Quercus ilex 1.529022 81.37533 1910.1852 282.3466
## 15 7 2007 T1_148 Pinus halepensis 38.376098 843.30336 157.3139 100.0000
## 16 7 2007 T2_168 Quercus ilex 1.645689 88.48298 1766.5566 282.3466
## 17 8 2008 T1_148 Pinus halepensis 38.494595 849.37566 157.1340 100.0000
## 18 8 2008 T2_168 Quercus ilex 1.763580 95.67111 1641.2866 282.3466
## 19 9 2009 T1_148 Pinus halepensis 38.613214 855.42201 156.9531 100.0000
## 20 9 2009 T2_168 Quercus ilex 1.882208 102.90984 1531.5418 282.3466
## 21 10 2010 T1_148 Pinus halepensis 38.731818 861.43553 156.7719 100.0000
## 22 10 2010 T2_168 Quercus ilex 2.001386 110.18771 1434.7802 282.3466
## 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).