Process-based forest growth models with spatially explicit representation
are relevant tools to investigate innovative silviculture practices and/or
climate change effects because they are based on key ecophysiological
processes and account for the effects of local competition for resources on
tree growth. Such models are rare and are often calibrated for a very limited
number of species and rarely for mixed and/or uneven-aged stands, and none
are suitable for the temperate forests of Québec. The aim of this study
was to calibrate and evaluate HETEROFOR (HETEROgeneous FORest), a process-based and spatially
explicit model based on resource sharing, for 23 functionally diverse tree
species in forest stands with contrasting species compositions and
environmental conditions in southern Quebec. Using data from the forest
inventory of Quebec, we evaluated the ability of HETEROFOR to predict
the short-term growth (5–16 years) of these species at the tree and stand
levels and the long-term dynamics (120 years) of red and sugar maple
stands. The comparison between the prediction quality of the calibration
and evaluation datasets showed the robustness of the model performance in
predicting individual-tree growth. The model reproduced correctly the individual
basal area increment (BAI) of the validation dataset, with a mean Pearson's
correlation coefficient of 0.56 and a mean bias of 18 %. Our results also highlighted that considering tree position is of importance for predicting individual-tree growth most accurately in complex stands with both vertically and horizontally heterogeneous structures. The model also showed a good ability
to reproduce BAI at the stand level, both for monospecific (bias of
-3.7 %; Pearson's r=0.55) and multi-species stands (bias of -9.1 %;
Pearson's r=0.62). Long-term simulations of red maple and sugar maple
showed that HETEROFOR was able to accurately predict the growth (basal area
and height) and mortality processes from the seedling stage to the mature
stand. Our results suggest that HETEROFOR is a reliable option to simulate
forest growth in southern Quebec and to test new forestry practices under
future climate scenarios.
Fonds de recherche du QuébecPINT-BILAT-P – R.P00419Fonds De La Recherche Scientifique - FNRSPINT-BILAT-P – R.P00419Service Public de Wallonien/aIntroduction
Forest ecosystems are subject to an increased disturbance frequency and
intensity caused by global changes, leading to large-scale mortalities and
jeopardizing the ability of forests to sustain the provision of crucial
ecosystem services
(Trumbore
et al., 2015; Seidl et al., 2017; McDowell et al., 2020). It is therefore
necessary to account for the high level of uncertainty related to these
ongoing and future changes by considering flexible management strategies
that increase forest resilience and multifunctionality, particularly those that
promote multi-species and uneven-aged stands
(Messier
et al., 2021; Jactel et al., 2021; Brockerhoff et al., 2017). However, there
is still a lack of knowledge about the ecology of mixed stands, as well as of
guidelines for their long-term management
(del Río et al., 2021; Forrester,
2019).
Performing experiments to test the effects of various management strategies
and/or future environmental conditions on forests is complicated due to the
longevity and slow growth of tree species. Modelling approaches are
therefore a useful tool for studying these issues on a long timescale
(Pretzsch
et al., 2015; Maréchaux et al., 2021; Ruiz-Benito et al., 2020). Of the
many different types of models used in forest management, which differ in their
structure and complexity depending on the initial objectives
(Makela et
al., 2000; Porté and Bartelink, 2002), there are three main types:
empirical models, process-based models, and hybrid models (i.e., using both
empirical and process-based approaches; Fontes et al., 2010). Empirical
models are usually calibrated from descriptive relationships derived from
inventory data and are only suitable for extrapolation to systems and
environmental conditions for which they have been parameterized
(Fontes et al., 2010). On the
contrary, process-based models (PBMs) are more appropriate for investigating
innovative silviculture and/or climate change effects, as they rely on key
ecophysiological processes (e.g., photosynthesis, light interception, and respiration) to simulate forest growth using a set of interdependent
sub-models
(Bohn et
al., 2014; Makela et al., 2000). These PBMs can spatially represent the
forest in several ways
(Pretzsch et al., 2015): at
the stand scale by considering an average tree of the stand, at the cohort
scale by handling the forest as horizontally homogeneous layers, or at the individual-tree scale by considering each tree in the stand. Furthermore, these PBMs may be
spatially explicit (e.g., BALANCE; Grote and Pretzsch, 2002)
or not
(e.g.,
PPA; Purves et al., 2008; Strigul et al., 2008). Spatially explicit models
allow one to account for the effects of local competition for resources on tree
growth and for the disturbance dynamics and their effects on
regeneration (light heterogeneity in the understorey); they are therefore the
most relevant model type for studying forest management strategies in changing
environments for uneven-aged and mixed stands
(Seidl et al., 2005; Pretzsch,
2022). Individual-based and spatially explicit models are particularly well
suited to testing silvicultural approaches that conduct to
structurally complex stands such as the continuous-cover forestry.
The present study is the first step toward the development of a stand-level
modelling project that aims to test how contrasting management strategies
affect the resilience and multifunctionality of eastern North American
forests. Long-term simulations will be carried out by crossing future
climate scenarios and disturbances (e.g., windstorms, droughts, and biotic
outbreaks) with current and alternative management strategies: (i) business
as usual, i.e., the same management as that practised in the last decades; (ii) enriching forests with drought-tolerant species adapted to the expected
climate change; and (iii) enriching forests with species based on the
functional-level approach
(Aubin
et al., 2016; Messier et al., 2021; Aquilué et al., 2021). This latter
approach promotes both the functional diversity (i.e., the diversity of
traits represented in the stand) as a means of increasing adaptation to
disturbances through the partitioning of ecological niches and also the
functional redundancy (i.e., when multiple species share similar traits) to
ensure the continuity of a function if one species is lost
(Messier
et al., 2019; Oliver et al., 2015; Mori et al., 2013). To do so, we require
a spatially explicit individual- and process-based model in which the main
processes, such as light interception, carbon allocation, phenology, and
water balance, are included. Several forest growth models already exist and
have been calibrated for temperate species in eastern North America,
including empirical models, e.g., Artémis (Power, 2016) and
MGM (Bokalo et al., 2013); hybrid models such
as TRIPLEX (Peng et al., 2002) and ZELIG-CFS
(Larocque et al., 2011); and
process-based models, e.g., SORTIE/BC
(Coates et al., 2003) and Forest v5.1
(Schwalm and Ek, 2004). However,
neither of these two PBMs, which are the only two PBMs in this region that
consider individual-tree growth
(Pretzsch et al., 2015),
correspond to our expectations. Forest v5.1, although very exhaustive
regarding the processes integrated, does not consider the spatial
representation of each tree. In contrast, SORTIE/BC is spatially explicit
but does not integrate water and phenological processes and/or climate
change.
Here, we describe the parameterization and validation of the HETEROFOR (HETEROgeneous FORest) model in structurally and compositionally
complex stands in eastern North America. HETEROFOR is a spatially explicit and process-based model that describes individual-tree growth based on
resource sharing (light and water), and it was specifically developed to simulate complex uneven-aged and mixed stands
under various disturbance scenarios (de Wergifosse et al., 2020; Jonard et al., 2020). More specifically, we (i) calibrated the model for 23 tree species that represent a wide range of functional groups and that are already present in Quebec or are from southern provenances which could be
suitable for planting in the future; (ii) evaluated the ability of HETEROFOR
to predict the short-term growth (5–16 years) of these species at the tree
and stand levels using data from the forest inventory of Quebec; and
(iii) tested if the model could reproduce growth and mortality processes in
the long-term (120 years) with a focus on red maple and sugar maple, the two
major species of Quebec's temperate forests.
Materials and methodsHETEROFOR
HETEROFOR is a tree-scale and spatially explicit process-based model
designed to investigate the response of structurally complex stands (i.e.,
uneven-aged and/or mixed stands) to changing environmental conditions and
management options (Jonard et al., 2020; de Wergifosse
et al., 2020). It is implemented and freely available on Capsis
(Dufour-Kowalski et al., 2012), a collaborative
simulation platform for forest growth and dynamics modelling. An overview of
the functioning of the model, as well as the description of the
carbon-related processes (photosynthesis, respiration, carbon allocation, and
tree dimensional growth), can be found in Jonard et al. (2020),
while the phenology and water balance modules are described by de Wergifosse
et al. (2020), the light interception module is described by André et al. (2021), and the regeneration module is described by Ryelandt (2019).
In short, HETEROFOR starts by running the phenology routine from
meteorological data. It determines for each species the budburst, yellowing,
and falling dates, as well as the daily foliage stage (foliage development
stage and green leaf proportion). Furthermore, for the deciduous species,
phenology is calculated at the tree scale to account for the extended
vegetation period of understorey trees (de Wergifosse et al.,
2020). The solar radiation intercepted by the trunk and the crown of each
tree is then calculated using a ray-tracing approach with the SAMSARALIGHT
library of Capsis
(Courbaud et al., 2003;
André et al., 2021). The gross primary production (GPP) is calculated
hourly from the photosynthetically active radiation absorbed per unit of
leaf area and from the soil water potential using the photosynthesis model
CASTANEA, also available on Capsis
(Dufrêne
et al., 2005; Farquhar et al., 1980). The net primary production (NPP) is
estimated as a fraction of the GPP, depending on the tree dimensions,
neighbour competition, and air temperature. This approach implicitly accounts
for carbon losses due to maintenance and growth respiration. The NPP is
first allocated to foliage and fine roots and, for trees over a given size,
to fruits. The remaining NPP is then allocated to structural components (trunk,
branches, and structural roots) using allometric equations, which derive
tree dimensional growth (primarily for growth in height, with the remainder
for growth in diameter) while considering competition with neighbouring
trees (Jonard et al., 2020). A distance-dependent approach
was used to estimate the changes in crown dimensions in the four cardinal
directions based on the competition with the neighbouring trees (for more details, see Jonard
et al., 2020). When a tree does not have
enough NPP to support its growth (due to light competition, water stress, or
ageing), the leaf biomass is reduced, inducing a defoliation, which will
ultimately lead to the death of the tree when the defoliation reaches a
given threshold (90 % by default; Jonard et al., 2020).
HETEROFOR also includes a regeneration module based on the regeneration
library of Capsis. Considering the large number of seedlings that may be
present in the understorey, explicitly locating all of them would be too time
consuming and unrealistic. Instead, the stand is divided into square cells
of a given size (10 m × 10 m by default), and seedlings are managed as
cohorts of species structured vertically in several size classes, with all
individuals within a size class having the same dendrometric
characteristics. From the tallest size class to the shortest, the radiation
absorbed by each one and transmitted to the next one is computed following the
Beer–Lambert law. The individual growth increment is calculated from the
transmittance, and other morphological attributes (crown radius, woody
biomass, leaf biomass) are derived from the height or the diameter using
allometric relationships. GPP and NPP are calculated for the whole size
class using CASTANEA and are compared to the individual biomass increment
(i.e., individual NPP, based on annual height increment) to deduce the
number of seedlings able to survive with the available radiation
(Ryelandt, 2019). Saplings are recruited and spatialized once they
reach the recruitment height (10 m by default).
Species
The calibration and evaluation of HETEROFOR were completed for 23 North
American tree species – 14 broadleaved and 9 coniferous species (Table 1) –
including all the major species of managed forests in the Quebec
temperate forests (Abies balsamea, Acer rubrum, Acer saccharum, Betula alleghaniensis, Picea glauca, Pinus strobus, Populus tremuloides, and Tsuga canadensis). We also selected species that are present to a
limited extent in Quebec but which could be suitable for planting in the
coming years, mainly northern US species currently at their northern range
limit in Quebec (e.g., Acer saccharinum, Prunus serotina, Quercus rubra, and Tilia americana; Fig. S1 in the Supplement). These 23 species belong to seven
functional groups (Table 1; Fig. S2) according to the clustering of Mina et
al. (2022), which considers 77 North American tree
species and is based on nine functional traits identified as essential for
ecosystem functioning and resilience to disturbances
(Aquilué et al., 2021; Kühn et al., 2021).
Thus, this set of species will allow us to study various types of species
mixtures and management scenarios, particularly those based on
functional diversity and redundancy. Mean tree diameter at breast height
(DBH) in the selected sites from the Quebec forest inventory (see
Sect. 2.3) varied from 11.7 cm for Betula populifolia to 21.3 cm for Tilia americana (15.9 cm on average for
all species), and the range of diameter for a single species varied from 11.6 cm for Betula populifolia to 57.4 cm for Pinus strobus (34.6 cm on average for all species; Table 1).
Sites
We selected 200 plots from the permanent sample plots (PSPs) of the forest
inventory of Quebec (MFFP, 2021) to calibrate and evaluate
the model. The plot size was 400 m2, and the time span between two
inventories for a given plot ranged between 5 and 16 years (Table S1). In
each survey, the diameter at breast height was measured on every tree larger
than 9.1 cm DBH (some smaller ones are still present in the dataset – they were
considered to be recruited trees and were kept for calibration and evaluation; see
Table 1), whereas tree height was only measured on a subsample of trees
(about 15 % of the trees). Social status (dominant, co-dominant,
intermediate, and oppressed) and sun exposure class (from 1, where a tree grows
in full light, to 4, where it grows in the absence of light) of each recorded tree were also
indicated in only a few plots.
All plots were selected within the temperate deciduous forest area (latitude < 47∘; Fig. 1) and based on their species composition to
ensure a sufficient number of individuals of each species of interest. They
were also selected to be evenly distributed among the three physiographic
regions characterizing this part of Quebec (Appalachians, Canadian
Shield, and Saint Lawrence Lowlands; Fig. 1), which can be distinguished by
soil parent material, topography, distribution of permafrost, and tree line
location (Acton et al., 2015). The plots covered a wide
variety of environmental conditions and stand characteristics: mean annual
temperature ranged from 0.6 to 7.1 ∘C, mean annual
precipitation comprised of rain and snow from 919 to 1446 mm (average
over the 1970–2019 period), mean DBH from 10.3 to 27.7 cm, tree density
from 325 to 2725 trees ha-1, and basal area from 3.5 to 60.6 m2 ha-1 (Table S1 in the Supplement). There were also large variations in
soil properties. Soil coarse fraction varied between 0 % and 80 %; soil
depth varied between 0.12 and 1 m; and 10 different soil textures derived from
the USDA textural triangle (Schoeneberger et al., 2012)
were represented among all sites, with four types dominating (sandy loam,
loamy sand, sand, and loam accounted for 85 % of the sites; Table S1).
Selected characteristics of the 23 tree species sampled from 200
permanent plots of the Quebec forest inventory.
1 From budburst date to falling starting date.
2 See Fig. S2 for more details about functional group
characteristics.
The 200 stands were classified into five forest types based on their species
composition: monospecific broadleaved and monospecific coniferous when a
single species accounted for more than 75 % of the total basal area of the
stand; multi-species broadleaved and multi-species coniferous when,
respectively, broadleaved or coniferous trees represented at least 75 % of
the total basal area of the stand with two species representing at least
25 %; and mixed when both coniferous and broadleaved species
accounted for more than 25 % of the total basal area. In total, there were
32 monospecific broadleaved stands, 26 monospecific coniferous stands, 71
multi-species broadleaved stands, 26 multi-species coniferous stands, and 45 mixed stands.
In addition, species richness ranged from 2 to 12 species per stand, and
functional richness ranged from 1 to 6, illustrating a high diversity of the
selected stands. This provided an adequate dataset to evaluate the ability
of the model to simulate growth in structurally complex stands.
To perform an evaluation with a dataset independent from the one used to
calibrate the model (see Sect. 2.4), the 200 sites were split into two
datasets of 100 sites (Fig. 1). Therefore, sites numbered 1–100 (Table S1;
total n trees = 3754) were used for calibration, and sites numbered
101–200 (Table S1; total n trees = 3511) were dedicated to model
evaluation, with both datasets being similar in terms of environmental
conditions and stand characteristics. This splitting of the sites was also
made based on species composition to have at least 100 individuals for each
species in each dataset. However, five species were sparsely represented in
the forest inventory plots (Acer saccharinum, Fraxinus americana, Prunus serotina, Tilia americana, and Ulmus americana). For those species, we chose to use a greater
number of individuals for the calibration (for a minimum of around 100 trees
for each species), resulting in around 40 trees per species remaining to
perform the evaluation. Therefore, these five species were calibrated
independently but were grouped together as “other broadleaved” for the
evaluation.
Location of the 200 selected permanent sample plots of the forest
inventory of Quebec. The red square in the insert locates the study area
within Quebec (in blue) and Canada.
Model calibration
Most of the parameters needed by HETEROFOR are species-specific and are
described in Table 2. Values were either retrieved from the literature or were
fitted with available data when dealing with empirical relationships (see
the “source” column in Table 2). Phenological parameters were calibrated
using the Phenological Modelling Platform (Chuine et al.,
2013). All values for each species are given in Table S2. Some other
parameters are generic for all species or by species type (broadleaved vs.
coniferous, deciduous vs. evergreen) and are presented in Table S3. The
regeneration module has been fully calibrated for only six species so far.
Parameters and values for these species are presented in Table S4.
The carbon use efficiency (CUE, kgC kgC-1 – corresponding to the NPP-to-GPP ratio) is a crucial parameter and the only one for which running the
model is necessary for the calibration. The CUE was determined for each tree
using an empirical relationship based on tree diameter, a light competition
index, and temperature and was computed following de Wergifosse et al. (2022):
CUE=α+βdbh+γdbh2+δlnLCI+εTair+error,
where dbh (cm) is the diameter at breast height; LCI is the light competition
index; Tair (∘C) is the mean annual temperature; and α, β, γ, δ and ε are species-specific
parameters. The LCI corresponds to the ratio between the absorbed radiation
with and without neighbouring trees and ranges from 0 (no light reaching
the tree) to 1 (no light competition; Jonard et al., 2020).
This equation was fitted with data from our first dataset of inventory plots
dedicated to calibration (sites numbered from 1 to 100 in Table S1). The NPP
was obtained from the two inventories for each tree using the reconstruction
mode in HETEROFOR (for detailed
information, see Jonard et al., 2020) and then divided by the predicted GPP to estimate CUE.
Model evaluationShort-term evaluation: individual-tree growth incrementsModel initialization
HETEROFOR requires three different files to be initialized: stand
characteristics, soil properties, and meteorological data.
The stand characteristics file contains the position of each tree (x,y,z)
and its main dendrological characteristics: girth at breast height (cm),
total height (m), crown base height (m), height of the maximum crown
extension (m), and crown radii in the four cardinal directions (m). The
initial observations on each monitoring plot were used for stand input data.
However, only the diameter was available for every tree, and total height was available
for only a small subset of the trees. Thus, crown dimensions and total height
(when not measured) were estimated using previously calibrated
species-specific allometric equations (see Jonard et al., 2020,
for the equations and Table S2 for parameters). Tree positions were randomly
generated considering the social status of the tree and/or the sun exposure
class when available, as well as the size of the trees. The procedure starts
by randomly positioning the dominant trees and/or those with a maximum sun
exposure class (the tree receives direct sunlight both on the top and on its
four sides), without any crown overlapping between them. When this
information was not available, the 15 % tallest trees and the 15 % with
the largest diameters were considered to be dominant. The position of the
remaining trees is randomly assigned but constrained by the position of the
dominant trees: a tree cannot be positioned close to a dominant one if its
total height exceeds the height of the largest crown extension of the
dominant tree nearby. Crown overlapping is possible for non-dominant trees
and is bounded by a maximum value. Finally, the stand file also includes the
longitude, latitude, slope, and aspect of the site.
The model also needs a description of the soil horizons. For each horizon,
this file includes the upper and lower limits (m); the coarse fraction
(m3 m-3); the bulk density (kg m-3); sand, silt, and clay
contents (g g-1); organic carbon content (mg g-1); soil pH
(H2O); and fine-root proportion (%). All of these data were collected
from various sources. The organic horizon thickness; sand, silt, and clay
contents; coarse fraction; and soil pH of the horizons were recorded in the
forest permanent-inventory database. The description of the soil profile was
found in the ecological inventory of Quebec, conducted by the Ministry of
Natural Resources, le point d'observation ecologique (POE; Saucier, 1994). For each inventory
plot, we selected the closest POE that had the same soil type. Bulk density and
organic carbon content for each soil type were retrieved from the National
Soil Database of the Canadian Soil Information Service
(NSDB, 2021).
Lastly, meteorological inputs were obtained from the ERA5 global reanalysis
(Bell et al., 2021; Hersbach et al., 2020) and
provided hourly data of air temperature (∘C), soil surface
temperature (∘C), solar radiation (W m-2), rainfall (mm),
relative humidity (%), wind speed (m s-1), and wind direction
(∘).
Description of the species-specific parameters used in HETEROFOR
(see Table S3 for the generic parameters).
SymbolDescriptionUnitsSourceLight interceptionkExtinction coefficientm-1Aubin et al. (2000), Bolstad and Gower (1990), Bréda (2003), Raulier et al. (1999)SLAminMinimum specific leaf aream2 kg-1Kattge et al. (2020)SLAmaxMaximum specific leaf aream2 kg-1Kattge et al. (2020)Tree dimensionshcb %Crown base heightm m-1Calculated with data from USDA – Forest Service (1999) and Power et al. (2012)DdCrown-to-stem diameter function (α, b, γ, δ in Eq. 10 in Jonard et al., 2020)m m-1Fitted with data from USDA – Forest Service (1999) and Power et al. (2012)shCoefficient to shift the mean crown-to-stem diameter ratio to its maximumDimensionlessEstimated with data from USDA – Forest Service (1999) and Power et al. (2012)ΔdbhDefault dbh incrementcm yr-1Calculated from the Quebec forest inventory data (MFFP, 2021)ΔhcbmaxMaximum annual change in the crown base heightm yr-1Calculated from the Quebec forest inventory data (MFFP, 2021)ΔhHeight growth function (α, b, γ, δ, ε, ζ, η in Eq. 2 in de Wergifosse et al., 2022)m yr-1Fitted from the Quebec forest inventory data (MFFP, 2021)VtotTree total-volume function (a, b, c in Eq. 5 in Deleuze et al., 2014b)m3Fitted from biomass data and wood densityVstemTree stem fraction function (d, e, f, g in Eq. 5 in Deleuze et al., 2014a)m3 m-3Fitted from biomass data and wood densityCarbon allocationbleafLeaf biomass function (α, b, γ in Eq. 15 in Jonard et al., 2020)g OMFitted with data from Falster et al. (2015), Ung et al. (2017), and Schepaschenko et al. (2017)bstructural_aboveAboveground structural biomass (α, b, γ in Eq. 26 in Jonard et al., 2020)kg OMFitted with data from Falster et al. (2015), Ung et al. (2017), and Schepaschenko et al. (2017)ρstemStem volumetric masskgC m-3Zanne et al. (2009)δleafLeaf relative loss ratekgC kgC-1 yr-1Ameztegui et al. (2017), Wright et al. (2004)δfrFine-root relative loss ratekgC kgC-1 yr-1Coleman et al. (2000), Krasowski et al. (2018), McCormack et al. (2012, 2013)RespirationasapwoodSapwood area function (a, b, c in Eq. 12 in Jonard et al., 2020)cm2Fitted or retrieved from the literatureaCUECarbon use efficiency (α, b, γ, δ, ε in Eq. 1 in this paper)kgC kgC-1Calibrated using the Quebec forest inventory data (MFFP, 2021)
Continued.
SymbolDescriptionUnitsSourceWater balancebark %Bark proportionPercentageMiles and Smith (2009)ρbarkBark volumetric masskg m-3Miles and Smith (2009)cbark_llBark storage capacity in the leafless period (c, d, Rmin in Eq. 16 in de Wergifosse et al., 2020)L mm-1André et al. (2008)cbark_ldBark storage capacity in the leaved period (c, d, Rmin in Eq. 16 in de Wergifosse et al., 2020)L mm-1André et al. (2008)p1sw, p2swStomatal response to soil water potential (Eq. 55 in de Wergifosse et al., 2020)AdimensionalDetermined from drought tolerance index of Niinemets and Valladares (2006)Phenologyt0Chilling starting dateDay of yearMorin et al. (2009)Tmin, Tmax, ToptMinimum, maximum, and optimal chilling temperatures (optimum chilling model, Eq. 1 in de Wergifosse et al., 2020)∘CCalibrated with data from Crimmins and Crimmins (2017)Ca, Cb, CcChilling parameters (sigmoid chilling model, Eq. 2 in de Wergifosse et al., 2020)AdimensionalCalibrated with data from Crimmins and Crimmins (2017)C*Chilling threshold∘CCalibrated with data from Crimmins and Crimmins (2017)Fb, FcForcing parameters (Eq. 3 in de Wergifosse et al., 2020)AdimensionalCalibrated with data from Crimmins and Crimmins (2017)Tb_forBase temperature for forcing∘CChuine (2000)F*Forcing threshold∘CCalibrated with data from Crimmins and Crimmins (2017)
a Anderson-Teixeira et al. (2015), Bond-Lamberty et al. (2002), Bovard et al. (2005), Falster et al. (2015), Hadiwijaya et al. (2020), Hernandez-Hernandez (2014), Hernandez-Santana et al. (2015), Kenefic and Seymour (1999), McIntire (2018), Penner and Deblonde (1996), Quiñonez-Piñón and Valeo (2017), Thurner et al. (2019), and Wullschleger et al. (2001)
Simulations
Stand structure is known to influence light interception and tree growth
and needs to be integrated when modelling structurally complex stands by
considering the precise tree position and spatial configuration of crowns
(Forrester, 2014; Pretzsch,
2022). To investigate the importance of the spatially explicit
representation to the prediction accuracy of tree growth increments, we
carried out 10 simulations per plot, each simulation having a new spatial
arrangement of trees. To do this, we ran the semi-random procedure used to
locate the trees 10 times per plot, resulting in 10 stands that were
different in terms of spatial arrangement but had the same species
composition, tree density, and basal area.
Model performances
The evaluation of the model outputs was performed at the individual-tree
level, focusing on the basal area increment (BAI, cm2 yr-1) and height increment (m yr-1) following a two-step
procedure: (i) comparison of the mean predicted increment (basal area or
height) from the 10 simulations to those observed from the forest
inventories and (ii) comparison, for each tree, of the best prediction
within the 10 simulations with the observed value. This evaluation was done
using the hundred plots dedicated to evaluation (plot IDs from 101 to 200;
Table S1) to perform an independent evaluation, using 3511 trees with BAI
measurements and 508 trees with height measurements.
The evaluation of BAI was carried out for 18 species individually, and the
other five (Acer saccharinum, Fraxinus americana, Prunus serotina, Tilia americana, and Ulmus americana) were evaluated together as “other broadleaved” (but calibrated
independently; see Sect. 2.3). Regarding tree height increment, sample
size for each species was not sufficient to perform a species-specific
evaluation. Therefore, we evaluated height increment by grouping all trees
as either broadleaved (n=247) or coniferous trees (n=259).
We assessed the accuracy of the model using several metrics. The relative
bias identifies underestimated (negative bias) or overestimated (positive
bias) overall model predictions and is calculated as follows:
Bias%=Pred‾-Obs‾Obs‾×100,
where Pred‾ and Obs‾ are the means of the predictions and
observations, respectively. A paired t test was performed to test bias
significance. The root-mean-square error (RMSE) quantifies the quadratic
mean of the differences between predictions and observations and is computed
as follows:
RMSE=∑i=1nPredi-Obsi2n,
where Obsi are the observed values, Predi are the predicted
values, and n is the number of observations.
The strength of the relationship between observations and predictions was
investigated with the Pearson's correlation coefficient (r) and with a
Deming regression (mcr package; Manuilova et al., 2021),
which considered errors for both observations and predictions. All the
above-mentioned procedures were carried out with the R software version
4.1.0. (R Core Team, 2021).
Long-term evaluation: growth and mortality processes starting from
regeneration
To evaluate the ability of HETEROFOR to predict growth and mortality
processes in the long term, we conducted 120-year simulations starting with
a cohort of 1-year-old seedlings. We focused this evaluation on stands
dominated by the two major species of Quebec's temperate forests, sugar
maple (Acer saccharum) and red maple (Acer rubrum).
The inventory files used to initialize the simulations contained only a
regeneration cohort of 20 000 1-year-old seedlings of 20 cm in height per
hectare, with no overstorey trees. For each stand type (red maple or sugar
maple), we compared four different compositions of regeneration: (i) 100 %
maple (either red or sugar maple); (ii) 75 % maple (either red or sugar
maple) and 25 % species A; (iii) 75 % maple (either red or sugar maple) and
25 % species B; and (iv) 50 % maple (either red or sugar maple), 25 %
species A, and 25 % species B. Species A and B associated with red maple were
yellow birch (Betula alleghaniensis) and black cherry (Prunus serotina), and those associated with sugar maple
were American beech (Fagus grandifolia) and white ash (Fraxinus americana). Average values for southern
Quebec were used for soil and meteorological inputs required by the
model.
We used data from the PSPs to compare predicted total stand basal area
(m2 ha-1) and mean stand height to observed field data.
The selected PSPs were located in the temperate forest area (latitude
< 47∘), had a regular structure, had not been disturbed,
and were composed of at least 50 % red or sugar maple in terms of basal
area. The PSPs considered in this sampling may include some PSPs used for the
calibration or the short-term evaluation. Tree height was only measured on a
subsample of trees in the PSPs, where selected trees were chosen to represent
three size classes of the dominant species (largest diameters, around quadratic
mean diameters, and small diameters). This implies that the heights measured in
our sampling plots are almost exclusively those of maple trees. To be consistent with
these characteristics of the PSP dataset, we therefore considered the mean
height of maple trees instead of the dominant height in this long-term
evaluation. For sugar maple, we also compared the simulations to a dataset
from a study by Nolet et al. (2010) about the productivity of
even-aged sugar maple stands established following a clear cut or fire. We
used self-thinning relationships to evaluate the ability of HETEROFOR to
reproduce the mortality process. Also known as maximum size density, this
relationship describes at maximum stand density the natural process in which
tree density per area decreases over time as the average tree size increases
(Reineke, 1933). The self-thinning lines from our simulations
were compared to those of Andrews et al. (2018) and those of Lhotka and
Loewenstein (2008), which
were obtained from data in eastern North America, and to the dataset of
Nolet et al. (2010).
ResultsShort-term evaluationTree basal area increment
We found that HETEROFOR was able to predict the basal area increment of the
various species (Fig. 2), but prediction accuracy strongly varied between
species. The Pearson's correlation coefficient was highly significant
(p<0.001) for almost all species, ranging from 0.328 for Q. rubra to 0.759
for P. glauca, except in the case of B. populifolia (r=0.23; p<0.05). The bias was less than 25 %
for 15 of the 19 species, and the RMSE was 5.25 cm2 yr-1
on average. BAI was weakly predicted for the trees with the largest BAI of a
few species (A. saccharum, B. papyrifera, and P. resinosa), but the slope of the regression of observations vs.
predictions was close to 1 on average (averaged slope = 1.12), and the 1:1
line was within the confidence interval of the regression for 10 of the 19
species (Fig. 2).
Observed versus mean predicted basal area increment for each
species (or group of species) using the evaluation dataset. Each dot
represents the mean of the 10 predictions for a single tree, with the error
bars indicating the standard deviation. The blue line represents the Deming
regression between observed and predicted values, the light-blue area is the
confidence interval at 95 %, and the dashed red line corresponds to the
1:1 line. Model performance is indicated using Pearson's r (p value: ***<0.001; *<0.05), the relative bias (paired t test – p value: ***<0.001; **<0.01), and the RMSE.
Compared to the mean predictions of BAI performed with the calibration
dataset, we observed that modelling performance with the evaluation dataset
was slightly less reliable (Fig. 3). With the evaluation dataset,
correlations were lower for all species except A. saccharum, and predictions were more
biased for all species except Q. rubra (Fig. 3). On average, the correlation
coefficient between observed and predicted BAI values decreased from 0.678
with calibration plots to 0.568 with evaluation plots, and the bias (in
absolute values) increased from 8.8 % to 18 %. Only a limited number of
species showed a strong difference between the two datasets for some of the
performance metrics considered (i.e., B. populifolia and Q. rubra with regards to the Pearson's
coefficient; P. resinosa with regards to the RMSE; and B. populifolia, P. mariana, and P. rubens with regards to the bias).
Regressions between observations and predictions were very similar between
both datasets (average slope of 1.15 and 1.12, average intercept of -0.94
and -0.55), and predictions with the evaluation dataset showed an even
better relationship for five species, with a slope closer to 1 and an
intercept closer to 0 (A. balsamea, L. laricina, P. mariana, P. rubens, and P. strobus; Fig. 3).
Statistical parameters (from left to right: Pearson's correlation
coefficient, root-mean-square error, relative bias, intercept, and slope of
the Deming regression) assessing the performance of the model for each
species using the calibration (black dots) or the evaluation (yellow dots)
dataset. The dotted blue line indicates the best agreement between
observations and predictions for each parameter.
With the random selection of tree positions (10 replicates), we observed a
large variation in predictions for a single tree, as illustrated by the error
bars in Fig. 2. The relative difference between the minimum and maximum
predicted basal area for a single tree ranged from 0 to 138 %, with 94 %
of the trees having a difference of less than 10 %. This relative difference
was related to initial tree size, with the largest differences being
associated with smaller trees (Fig. S3). Predictions were greatly improved
for all species when focusing solely on the best prediction for each tree
(Fig. 4). Pearson's coefficient was always highly significant and
ranged from 0.696 (Q. rubra) to 0.958 (P. glauca). Differences between observations and
predictions were less biased for all species, with a maximum bias of 24.1 %
(A. saccharum) and a bias < 15 % for 16 of the 19 species (Fig. 4). The confidence
intervals of the regressions were smaller than those obtained from the mean
predictions: the slopes were, on average, similar, although the slopes furthest
from 1 were much improved (e.g., P. glauca and P. resinosa).
Observed versus best predicted basal area increment for each
species (or group of species) using the evaluation dataset. Each dot
represents the best prediction within the 10 simulations for a single tree.
The blue line represents the Deming regression between observed and
predicted values, the light-blue area is the confidence interval at 95 %,
and the dashed red line corresponds to the 1:1 line. Model performance is
indicated using Pearson's r (p value: ***<0.001), the relative
bias (paired t test – p value: ***<0.001; **<0.01), and
the RMSE.
Height growth increment
Predictions of height increment for the two groups of species were less
accurate than the predictions of basal area increment (Fig. S4). Considering
the mean predictions, the correlation coefficient was 0.304 (p<0.001) for broadleaved species and 0.123 (p<0.05) for coniferous
species, and predictions were significantly underestimated in both cases
(biases of -33.3 % and -31.7 %; Fig. S4). We observed a large variation
in predictions for a single tree, with a relative difference between the
minimum and maximum predicted height ranging from 0.3 % to 5.7 %. As for
BAI, this difference increased as initial tree size decreased (Fig. S3).
Focusing on the correlation coefficient, modelling performances of height
increment were strongly improved when only considering the best prediction
for each tree: Pearson's r increased from 0.304 to 0.729 for broadleaved
trees and from 0.123 to 0.718 for coniferous species (Fig. S4). However, the
slopes were similar, and the biases, which decreased to around -20 %,
remained significant.
Stand basal area increment
The model showed a good ability to reproduce observed mean BAI at the stand
level, both for monospecific and multi-species stands, as shown by the
regression tests, with a slope very close to 1, and the 1:1 line was within
the confidence interval (Fig. 5). Moreover, the correlations were strong
between observations and predictions (r=0.547 and 0.624), and predictions
were slightly underestimated in both cases.
Observed versus predicted basal area increment at the stand level
for the 100 stands of the evaluation dataset, grouped by forest type:
monospecific stands (left panel) vs. multi-species stands (right panel). The
blue line represents the Deming regression between observed and predicted
values, the light-blue area is the confidence interval at 95 %, and the dashed red line corresponds to the 1:1 line. Model performance is indicated
using Pearson's r (p value: ***<0.001; p value: **<0.01), the relative bias (paired t test – p value: *<0.05) and the
RMSE.
Long-term evaluationBasal area
The simulated total stand basal area over 120 years is shown in Fig. 6a–b in comparison with forest inventories. For the six species used in the
simulations, recruitment height was reached between 26 and 36 years. Our
results showed that values of basal area for all the different regeneration
combinations matched the PSP data at 30 years, suggesting that the
regeneration module simulated seedling growth efficiently. Growth from
regeneration module outputs to 120 years were similar for the four
simulations of red-maple-dominated stands. Simulations reached a value of
basal area around 35 m2 ha-1 at 120 years and agreed
with the PSP data over the whole period (Fig. 6a). For sugar maple stands,
simulations starting with 100 % maple or 75 % maple + 25 % American
beech showed similar basal area and were closely related to the PSP data
but were at the lower range of the values from Nolet et al. (2010). The other two simulations showing a higher growth after
50 years had stands containing 25 % white ash. Both of these
simulations were more consistent with the basal area recorded by Nolet et
al. (2010) between 70 and 90 years and reached 36–39 m2 ha-1 at 120 years, which is still within the upper
range of the PSP data.
Height
The simulated evolution of mean height demonstrated a good fit with the PSP
data for both maples (Fig. 6c–d). The height was slightly lower than the
average PSP value around 30 years for both species and increased in
agreement with the main range of the PSP values over time until the height
reached 22.1 and 24.6 m for sugar maple and red maple stands, respectively.
Regarding the red maple simulations, mean height was similar among the three
stand compositions until 60 years. By the end of the 120 years, height
growth was highest in the pure stands (25.6 m) followed by the stimulations
with 75 % maple (24.8 m) and 50 % maple (23.8 m; Fig. 6c). The four
simulations were quite similar over time for the sugar maple stands, with
final mean heights between 21.2 and 22.6 m (Fig. 6d). Mean height values from
Nolet et al. (2010) range from 13.1 to 24.8 m (mean 18.6 m) but
did not show any consistent trend. As a result, the curves simulated for
sugar maple stands did not match their values over the whole time period but
were consistent with the overall range (Fig. 6d).
Mortality
A visual assessment of the predicted self-thinning lines vs. the
self-thinning lines of Andrews et al. (2018) and of Lhotka and
Loewenstein (2008) confirmed
the adequacy of the model in reproducing mortality over time for both species,
regardless of the initial regeneration composition (Fig. 6e–f). Compared to
the theoretical lines, the predicted density–size relationships at 120 years
were excellent for both species, while tree density started to decrease a
bit earlier with our simulations than what was reported by Andrews et al. (2018), especially for
sugar maple (Fig. 6f). Our predictions also match the values of Nolet et al. (2010) very well, as the predicted curve passes through the
scatterplot (Fig. 6f).
Evaluation of stand basal area (a, b), mean height of
maple species (c, d), and stand density (e, f) over 120 years for stands dominated by Acer rubrum(a, c, e) or Acer saccharum(b, d, f). The red line represents the self-thinning
curves of Andrews et al. (2018), and the dashed red
line represents the self-thinning line of Lhotka and Loewenstein (2008). PSP refers to
permanent sample plot of the forest inventory of Quebec. Stand ages in
the PSP dataset are grouped into 20-year classes (e.g., age class 30 refers to
stands between 21 and 40 years), except for age class 120 (stands > 100 years). The green dots in panels (b), (d), and (f) are from Nolet et al. (2010). Acer proportion corresponds to the initial proportion of
maple in the regeneration used in the four different simulations: (i) 100 %
maple, (ii) 75 % maple – 25 % species A, (iii) 75 % maple – 25 %
species B, (iv) 50 % maple – 25 % species A – 25 % species B.
DiscussionAbility of HETEROFOR to reproduce individual-tree growth
Short-term model evaluation (i.e., 5–16 years) was conducted using forest
inventory data from monospecific and multi-species stands, focusing on basal
area increment for each species and height increment at the
broadleaf and conifer levels. Our results regarding basal area increment are
consistent with previous studies that evaluated HETEROFOR in Europe for a
more limited number of tree species (European beech and sessile and pedunculate
oaks). Compared to Jonard et al. (2020), we found a lower RMSE
for all species except Pinus strobus, as well as a lower correlation between observations
and predictions (Pearson's r between 0.23 and 0.76 here versus 0.63 and
0.83 in Jonard et al., 2020). In another study dealing with
the same two species from 36 sites in Europe, de Wergifosse et al. (2022) evaluated individual-tree growth
based on girth increment and found a correlation of 0.58 for
sessile and pedunculate oaks and of 0.75 for European beech and found a bias lower than
14 %. Biases are higher in our study, ranging from -42 % to 38 %
depending on the species, with half of the species showing a bias lower than
-14 % or of 14 %. Although our predictions are overall less accurate with
respect to most indicators, some species are still predicted more accurately
than oak and as well as beech (e.g., Pinus strobus, Thuja occidentalis, and Picea glauca). It should also be noted that these
two European studies used many more characteristics (i.e., tree positions,
crown dimensions, soil profile, etc.) to calibrate the CUE and to evaluate the
model, which definitely increased the accuracy of their model predictions.
Comparing our results with other process-based models is difficult, as there
are only a few spatially explicit PBMs accounting for light-, water-, and
phenology-related processes
(Pretzsch et al., 2015) and
where the evaluation of the model performance, when available, is not
performed on individual-tree growth but mostly on stand level predictions.
However, our results are in the same range of biases as the process-based
model BALANCE (18 % to 47 %; Grote and Pretzsch, 2002), as
well as those of two hybrid models evaluated at the individual-tree level,
SILVA (-47 % to
70 %; Schmid et al., 2006; Pretzsch, 2002) and ForCEEPS
(-7.3 % to 89.9 %; Morin et
al., 2021). Looking at the stand level, predictions of basal area increment
were in good agreement with observed values in both monospecific and
multi-species stands. BAI was slightly underestimated in multi-species
stands compared to in the monospecific stands, but the prediction errors were
smaller, and the correlation between predictions and observations was higher.
The values of the different evaluation metrics at the stand level were
consistent with those of other process-based modelling studies
(Schwalm
and Ek, 2004; Forrester et al., 2021; Gonzalez-Benecke et al., 2014, 2016).
Height growth was predicted less accurately than BAI and was underestimated
for both conifers and broadleaved species (negative bias of 31.7 % and
33.3 %), particularly for trees with the highest height increment. This
lower accuracy in height predictions is common in forest growth models
(Schwalm
and Ek, 2004; de Wergifosse et al., 2022; Korol et al., 1995; Strimbu et
al., 2017), notably due to the higher potential measurement errors of height than of diameter. These inaccuracies in height measurements, which can be estimated
within 1 m (Jurjević et al.,
2020), are present during both initial and final inventories and have a
greater impact on predictions in areas like Quebec, where tree height
growth is limited. Nevertheless, although tree height predictions were not
perfectly accurate, the height growth over the long term in both sugar and
red maple stands was consistent with observed data. Compared to the study of
de Wergifosse et al. (2022) using
HETEROFOR, our results are aligned regarding Pearson's r and the RMSE;
however, although our results also reported an underestimation of height growth
predictions, the bias was higher in our study (31 %–33 % versus 10 %–20 %).
Considering the large range of stand compositions and environmental
conditions covered by the plots for most of the 23 species, our evaluation
of HETEROFOR demonstrated its ability to accurately predict individual-tree
growth for these species. The comparison between the prediction strength for
the calibration and evaluation datasets illustrates that our model is robust
and can be confidently used to capture the variations in individual-tree
growth in the temperate forests of Quebec. Very few species showed a
clear difference in more than one indicator between the two datasets (Pinus resinosa,
Betula populifolia, and Quercus rubra). A recalibration of the CUE by combining the two datasets could bring about
more accuracy in the tree growth prediction for these species, especially
for red pine, which is only present in a few sites (three for the calibration and
five for the evaluation) with a lack of large trees (> 25 cm in DBH)
in the calibration sites that could explain the poor prediction related to the trees
with the largest BAIs.
With more detailed inventory data, two key functions of HETEROFOR involved
in carbon allocation processes could also be refined, allowing for a better
consideration of competition and tree dimension when predicting tree growth.
The first key function is the CUE, for which a simplified version based on
DBH, LCI, and air temperature was used in our study (see Eq. 1 in Sect. 2.4). However, other predictors based on tree height, crown base height, and
crown diameter could be added to this equation to account for the effect of
tree size and tree shape (slenderness and/or crown extension) on the CUE (see Eq. 1 in de Wergifosse et al., 2022). The second key function is the
height growth function, which predicts the annual height growth based on
DBH, height, the potential height growth (i.e., potential height increment
if all the growth potential is allocated to the primary growth in height and
nothing is left for the secondary growth in DBH), the light competition
index (LCI), and an error term (standard error of the residuals). As tree
positions and most tree height measurements were not available in our
dataset, the LCI was not considered when fitting this equation in our study
(b=0 in Δh; see Table S2). However, including the LCI in this
function would allow us to consider the fact that understorey trees experiencing high
levels of competition for light would generally invest more carbon for
height growth than diameter growth
(Trouvé et al., 2015).
Influence of tree position on model predictions
Changing tree positions within the stand had a strong effect on tree growth
predictions, particularly for smaller trees. This seems logical because the
more dominant a tree is, the less it will be affected by the neighbouring
trees and therefore by the change in its position. When focusing on the best
prediction for each tree, we showed that the model predictions were greatly
improved for all species. This illustrates that considering tree position in process-based tree-level models is necessary to predict individual-tree growth most accurately in complex stands with both vertically and horizontally heterogeneous structures
(Pretzsch et al., 2015).
However, this does not mean that our predictions would match the best
predictions if we had the initial tree positions, but we can assume that the
predictions would probably be between the mean and the best predictions.
The variation in the position of a tree and the modification of its local
environment influence HETEROFOR through three variables: (i) the amount of
absorbed photosynthetically active radiation, determined from a ray-tracing
approach and consequently impacted by the crowns of neighbouring trees; (ii) the specific leaf area, which varies according to the local position of the
crown within the canopy; and (iii) a defoliation factor – i.e., the leaf
biomass of a tree is reduced by defoliation when the available carbon is not
sufficient to ensure normal leaf development (Jonard et
al., 2020). However, a random term in the height growth function (hereafter
referred to as height effect) can also have an influence on tree growth
between each simulation and may be confounded by the position effect. To
disentangle the importance of these two factors (position effect vs. height
effect) in the simulations, we performed additional simulations on 10
sites, considering five different positions per site and five repetitions
per position within each site. The five repetitions of each position within each
site allowed us to account for only the height effect. We then determined
the variation explained by the position and height effects using a linear
mixed model that uses the girth increment as the response variable and the site
and the tree as random factors. The variation explained by the position
accounted for 95.05 % compared to the 4.95 % explained by the height effect,
which confirmed that the position was the most important factor for explaining
the variations in the predictions among the simulations.
Simulation of maple stand dynamics
The results of the long-term simulations for even-aged stands dominated by
red maple or sugar maple showed that HETEROFOR was able to accurately
predict the growth and mortality processes from the seedling stage to the
mature stand. Indeed, the evolution of basal area and height growth over
time corresponds to the data from the Quebec forest inventory, and the
self-thinning curves correspond to those previously reported in the same
area
(Lhotka
and Loewenstein, 2008; Andrews et al., 2018).
The calibration and performance of the regeneration module were satisfactory
for both maple stand types. The basal area at the time of recruitment
(around 30 years old), i.e., when the saplings are individualized in the
model, was very close to that observed in the PSPs. However, the seedling
height growth was slightly underestimated for the two species, and the
mortality was initiated somewhat early for the sugar maple, depending on the
self-thinning curve considered. These discrepancies could be due to the type
of data used to calibrate the seedling height growth function, which
determined annual height growth and is also used to estimate seedling
mortality within the cohorts. As the height increment in the seedling
calibration dataset was not measured directly, it was deduced from the
collar diameter using allometric relationships.
Our results are thus promising regarding the suitability of the model for
simulating seedling growth and mortality processes and thereby for testing the
introduction of new species during the regeneration phase, which is a
crucial step of forest dynamics and presents the greatest potential for
adapting to future environmental conditions and unknown disturbance events
(König et
al., 2022; Kitajima and Fenner, 2000). Further evaluation of seedling growth
using long-term regeneration data for maples and other species, as well as
considering a variety of light conditions in the understorey, will be of great
importance.
Regarding the dynamic of basal area once the trees are recruited, our
predictions for the pure maple stands of the two species were very close to the
middle range of the PSPs. This may be somewhat surprising for sugar maple given
the results presented in the short-term evaluation section, where the model
tended to underestimate basal area increment at the individual-tree level.
However, by looking further into the evaluation site by site, it is evident
that the predictions for some sites are very good, while others are not, with
biases between 1.5 % and 62 % and Pearson's r between 0.04 and 0.87. The
purpose of these long-term simulations was to observe whether the model was
able to plausibly reproduce the whole of the stand dynamics. We only did one
simulation with an average soil and climate, which seem to correspond to
the mean environmental conditions for the observations. In addition, our
results regarding sugar maple growth are quite different from those of Nolet
et al. (2010), who observed higher basal areas and mean height,
particularly for younger stands. Sugar maples can establish themselves in a wide
variety of sites more or less favourable to their growth (Nolet and
Boureima, 2009), and several studies and yield tables in Quebec, Ontario,
and the northeastern United States have shown basal area increments similar to
ours (Carpentier, 1987; Eyre, 1980; Reed et
al., 1994), while others are more in agreement with the values observed by
Nolet et al. (2010; Nolet
et al., 2008; Nyland et al., 2004). In the Nolet et al. (2010)
dataset, older stands are characterized by poorer and thinner soils compared to
younger ones, which may explain the same productivity of their sites
regardless of age. Therefore, HETEROFOR appears to be more adequate for simulating
sugar maple growth on sites with thin and/or poor soils, as well as on mixed
stands, as shown by the short-term evaluation, but it may be less suitable when
growing in full light in nutrient-rich soils. Finally, the results of the
simulations with two or three species were consistent with the diameter
growth increment of the different associated species. The white ash is the
species with the highest diameter growth increment (0.45 cm yr-1) compared to the other five species that are within a similar range
(0.26–0.34 cm yr-1; MFFP, 2021), clearly showing
that the basal area of the stands containing white ash was significantly
higher.
Conclusions
The purpose of this study was to calibrate and evaluate the performance of
the spatially explicit process-based model HETEROFOR for southern Quebec
using the plots of the Quebec forest inventory, representing a large
range of environmental conditions and stand structures. Despite the lack of
some information needed to initialize the model (tree position, tree height,
and crown dimensions), our evaluation demonstrated the ability of HETEROFOR
to predict both the individual-tree growth of 23 species of eastern
North America over the short term and the stand dynamics of the two major
species in southern Quebec over the long term. The continuation of this
study will include a more detailed assessment of the regeneration module
using long-term regeneration surveys, the calibration of the regeneration
parameters for all 23 species, and a refinement of the CUE for a few
species. However, HETEROFOR can now be considered an appropriate option
to simulate forest growth in Quebec's temperate forests and to test
innovative management strategies under future climate scenarios.
Code and data availability
The source codes of Capsis and HETEROFOR are accessible to all of the
members of the Capsis co-development community. Those who want to join this
community are welcome, but they must contact François de Coligny
(francois.decoligny@inrae.fr) and sign the Capsis charter
(Dufour-Kowalski et al., 2012). This
charter grants access to all the models to the modellers of the Capsis
community. The modellers may distribute the Capsis platform with their own
model but not with the models of others without their agreement. Capsis4
is a free software (LGPL licence) which includes the kernel, the generic
pilots, the extensions, and the libraries. For HETEROFOR, we also chose an
LGPL licence and decided to freely distribute it through an installer
containing the Capsis4 kernel, and the latest version (or any previous one)
of HETEROFOR is available upon request from Mathieu Jonard (mathieu.jonard@uclouvain.be).
The end users can install Capsis from an installer containing only the
HETEROFOR model, while the modellers who signed the Capsis charter can
access the complete version of Capsis with all of the models. Depending
on your status (end user vs. modeller or developer), the instructions to
install Capsis are given on the Capsis website
(http://capsis.cirad.fr/capsis/documentation, last access: 4 November 2022). The source code for the modules published in Geoscientific Model Development (Jonard et al., 2020; de Wergifosse et
al., 2020) can be downloaded from 10.5281/zenodo.3591348
(Jonard et al., 2019).
The version of HETEROFOR used for this paper, a user guide of the model, and the data and scripts used for this study are available from
10.5281/zenodo.7225303 (Guignabert et
al., 2022).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-16-1661-2023-supplement.
Author contributions
AG carried out the calibration, performed the simulations, and analyzed the
model outputs with support from MJ and FA. AG, MJ, and QP
interpreted the results. FA and MJ developed the model code. CM and
PN provided data. QP, CM, and MJ acquired financial support for the
project. AG led the writing of the paper with contributions from all the
authors.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We are grateful
to Bert Van Schaeybroeck for the meteorological data acquisition and processing, to
Louis de Wergifosse for sharing the R script about random tree location, and to
Lana Ruddick for revising the English of this paper.
Financial support
This study was supported by the Fonds de Recherche du Québec (FRQ) and the Fonds de la Recherche Scientifique (FNRS) through the project “Forests in an uncertain context: comparing contrasting strategies of risk management at the local and regional scales” (contract PINT-BILAT-P – R.P00419). Arthur Guignabert is funded by a postdoctoral grant from the FNRS in the framework of this project. Mathieu Jonard was supported through the 5-year forest research program “Accord-cadre de recherche et de vulgarisation forestières” funded by the Public Service of Wallonia/Regional Forest Service (SPW-DNF).
Review statement
This paper was edited by Christian Folberth and reviewed by Mats Mahnken and one anonymous referee.
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