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Citation: Boukhris, I.; Lahssini, S.;
Collalti, A.; Moukrim, S.; Santini, M.;
Chiti, T.; Valentini, R. Calibrating a
Process-Based Model to Enhance
Robustness in Carbon Sequestration
Simulations: The Case of Cedrus
atlantica (Endl.) Manetti ex Carrière.
Forests 2023,14, 401. https://
doi.org/10.3390/f14020401
Academic Editor: Mark Vanderwel
Received: 18 December 2022
Revised: 8 February 2023
Accepted: 12 February 2023
Published: 16 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Calibrating a Process-Based Model to Enhance Robustness in
Carbon Sequestration Simulations: The Case of Cedrus
atlantica (Endl.) Manetti ex Carrière
Issam Boukhris 1,2,* , Said Lahssini 3,* , Alessio Collalti 4,5,6 , Said Moukrim 7, Monia Santini 2,
Tommaso Chiti 1,2 and Riccardo Valentini 1,2
1Department for Innovation in Biological, Agri-Food and Forest Systems (DIBAF), University of Tuscia,
01100 Viterbo, Italy
2Division Impacts on Agriculture, Forests and Ecosystem Services (IAFES), Fondazione Centro
Euro-Mediterraneo sui Cambiamenti Climatici, 01100 Viterbo, Italy
3Department of Forest Development, National School of Forest Engineers, Salé 11000, Morocco
4Forest Modelling Lab., Institute for Agriculture and Forestry Systems in the Mediterranean,
National Research Council of Italy (CNR-ISAFOM), Via Madonna Alta 128, 06128 Perugia, Italy
5Department of Agriculture and Forest Sciences (DAFNAE), University of Tuscia, 01100 Viterbo, Italy
6National Biodiversity Future Center (NBFC), 90133 Palermo, Italy
7BioBio Research Center, Faculty of Sciences, Mohammed V University, Rabat 10000, Morocco
*Correspondence: issam.boukhris@unitus.it (I.B.); marghadi@gmail.com (S.L.)
Abstract:
To assess the degree to which it has met its commitments under the Paris Agreement,
Morocco is called upon to carry out carbon assessments and transparent evaluations. Within the
forestry sector, little is known about the role of Morocco’s forests in contributing to carbon uptake.
With this aim, we applied for the first time in the literature the 3-PG model to Cedrus atlantica ((Endl.)
Manetti ex Carrière, 1855), which represents about 131,800 ha of Morocco’s forest area (i.e., Azrou
forest). Through the Differential Evolution-Markov Chains (DE-MC) we tested and assessed the
sensitivity and calibrated the 3-PG model. This process-based model provided significant results
regarding the carbon sequestration capacity. The results showed the following: i. Parameters related
to stand properties, canopy structure, and processes, as well as biomass partitioning, are the most
important or sensitive for the performance of the model; ii. The DE-MC method optimized the values
of the 3-PG parameters which was confirmed by the means of the Gelman–Rubin convergence test;
iii. According to the predictions of the calibrated 3-PG, the Net Primary Production in the pure Azrou
forest varies between 0.35 and 8.82
tC.ha−1.yr−1
, it is equal in average to 5.48
tC.ha−1.yr−1
, which
given the total area corresponds to 7918 tC.ha−1.
Keywords:
Atlas cedar; 3-PG; carbon sequestration; DE-MC (Differential Evolution-Markov chains);
parameter optimization
1. Introduction
Forest ecosystems have the capacity to produce goods and services that are essential for
human well-being [
1
,
2
]. These services range from providing wood products and drinking
water to cultural and supporting services [
3
]. Forests have been affected by humans
more rapidly than ever in recent years [
4
]. Climate change brings novel severity and
timing of multiple stresses, which may significantly affect the provision of these Ecosystem
Services (ES) [
5
,
6
]. Consequently, these changes introduce considerable uncertainty into
the management of forest resources in order to sustain the provision of ES [7].
The Intergovernmental Panel on Climate Change (IPCC) reported a requirement for
large-scale carbon dioxide (CO
2
) removal in most scenarios that limit global warming
to 1.5
◦
C or well below 2
◦
C [
8
]. Net-zero emissions and global decarbonization targets
recognize the important role of forest ecosystems in contributing to these ambitions [
8
,
9
].
Forests 2023,14, 401. https://doi.org/10.3390/f14020401 https://www.mdpi.com/journal/forests
Forests 2023,14, 401 2 of 18
Forests currently absorb around 30% of CO
2
emissions each year and play a central role in
the terrestrial ecosystem and carbon cycles [10].
Methods for carbon storage assessment can be divided into four main categories:
i. inventory-based estimation which is a collection of methods generally applied to estimate
carbon storage on the basis of regional forest inventory data; ii. Satellite-based estimation
which makes use of active, or passive remote sensing or both in order to quantify above-
ground carbon; iii. estimation through modelling which can rely on simulating the main
ecophysiological processes governing forest evolution; and, iv. the combination of the three
aforementioned categories [11].
The complexity of forest ecosystems and the multiple interactions between differ-
ent compartments, impose major difficulties for researchers to predict accurately their
systemic responses based on simple statistical relationships. Constantly updated tools
to describe vegetation dynamics in an evolving context of climate change have emerged,
including process-based models (PBMs) [
12
]. These models are built around the main eco-
physiological processes underlying productivity and can include detailed representations
of competition, population dynamics, and forest succession [13,14].
PBMs can perform better than the empirical growth models and showed to be more
accurate for long-term projections [
15
–
18
]. Among the most widely used PBMs in forestry
literature, the Physiological Principles Predicting Growth (3-PG) model [
19
], uses simple
equations to simulate physiological processes controlling carbon balance such as solar radi-
ation absorption, carbon sequestration and allocation, mortality, as well as water balance
such as canopy interception and evapotranspiration [
20
]. In addition, 3-PG is parsimo-
nious in the requirement of parameters to calibrate if compared to other models from
the same class [
21
], and it incorporates modules that convert biological outputs, based
on allometric equations, into operational data of immediate interest to forest managers
such as diameter at breast height (DBH), tree height and biomass stocks which makes it
appropriate for forest management purposes [
13
]. This model has been successfully tested
in the last twenty-five years in many regions of the world and provided interesting results
for a variety of tree species: Cunningamia lanceolata (Lamb.) Hook [
22
], Eucalyptus grandis
W. Hill and Eucalyptus urophylla S.T.Blake [
23
], Eucalyptus grandis W.Hill and Eucalyptus
camaldulensis Dehnham [
20
,
24
,
25
], Eucalyptus globulus Labill. [
15
,
25
], Pinus ponderosa Dou-
glas ex C.Lawson [
26
,
27
], Pinus patula Seem. [
28
], Pinus sylvestris L. [
29
,
30
], Picea sitchensis
(Bong.) Carrière [
31
] and Mediterranean maquis (e.g., Quercus ilex L.) [
32
] but, to our
knowledge, never for Cedrus atlantica ((Endl) Manetti ex Carrière, 1855), which represents
about 131,800 ha of Morocco’s forest area.
Morocco is among the most committed countries on climate and sustainable develop-
ment issues. As a ratifier of the Paris agreement, this country has agreed to periodically
present its Nationally Determined Contributions (NDCs) while being consistent with the
enhanced transparency framework (ETF). Concerning the forestry sector, the lack of growth
models for different species and growth conditions limits the tier assessment approach
adopted. PBMs, if properly calibrated, could be interesting prospects and valuable tools,
and this is the purpose of the present work.
Specifically, in the present work we will: i. try to define the most sensitive parameters
which are going to describe the evolution of Cedrus atlantica at the level of the Azrou forest
(Morocco); ii. try to optimize the 3-PG model parameters as to provide, for the first time in
the literature, a calibration set for Cedrus atlantica, and iii. we will simulate the quantity
of carbon sequestered in terms of Net Primary Productivity (NPP) by the cedar forest of
Azrou during the period 2016–2021 using the calibrated model.
2. Materials and Methods
2.1. Study Area
The study was conducted in Azrou forest, Morocco. It is a large forest massif covering
178 km
2
in the central part of the Middle Atlas (between 5.00
°
to 5.29
°
W and 33.28
°
to
33.52° N) (Figure 1).
Forests 2023,14, 401 3 of 18
The Middle Atlas is famous for its magnificent Atlas cedar and holds about 70.4%
of the total area of this species in Morocco which corresponds to 93,500 ha [
33
]. Cedrus
atlantica (Endl.) Manetti ex Carrière, endemic species of Morocco and Algeria [
34
], occurs
at elevations between 1500 and 2400 m a.s.l [
35
]. Middle Atlas cedar forests contain
several deciduous and evergreen tree species (e.g., Quercus rotundifolia, Quercus canariensis,
Pinus pinaster, Ilex aquifolium), shrub species, short meadowlands, and other aromatic and
medicinal plants.
Cedrus atlantica, which represents the main species of Azrou forest, forms pure or mixed
stands with Quercus rotundifolia,Quercus canariensis, and secondary species depending on
the nature of the substrate. The Cedrus atlantica stands occupy 1491.41 ha in a pure state,
7182 ha in mixture with Quercus canariensis representing 48.74% of the total area of the
forest; the Quercus canariensis stands extend over an area of 4419.77 ha representing 25%
of the forest [
36
]. In the present work, only pure cedar stands will be considered and
discussed. Figure 1illustrates the spatial extent of these stands.
Cedar ecosystem fulfils important functions and provides several services for the
local population and human well-being (e.g., recreation, cultural inspiration, habitat for
wildlife, place of grazing, Carbon and water regulation). However, these ecosystems suffer
from recent climatic variations [
37
] which are amplified by anthropogenic pressures and
disturbances (e.g., overgrazing, excessive clearance of woodlands, overexploitation) [
38
].
Besides the anthropogenic disturbance, an increase in drought occurrence and severity
has been documented over a large part of the Azrou forest. This established fact was
a predisposing factor in the dieback of the cedar, particularly on sites characterized by
the absence of silviculture supposed to adapt stand density and structure to soil water
availability [
39
]. In recent years, disturbance regimes in many forest ecosystems have
profoundly changed with the climate being an important driver of this dynamic. Thus,
given the causal relationship between climate and drought with an expected decrease in
precipitations at the level of the Mediterranean region, drought events are projected to
increase in frequencies, sizes, and severities within the Azrou forest [40].
Figure 1.
Map of the administrative situation of the Azrou forest and the location of pure cedar
stands in this forest.
2.2. Overall Approach
In order to deal with the calibration of 3-PG for C. atlantica, various data has been
collected which was used to analyze model sensitivity and then to calibrate the model.
Figure 2shows the flowchart of the overall methodology used here. Data was collected
Forests 2023,14, 401 4 of 18
from various sources: i. field data (forest resources); ii. data extracted from remotely
sensed earth observations (GEE database); and, iii. data collected from other databases
(the European Soil Database) [
41
]. Sensitivity analysis was conducted to define the most
important parameters for the 3-PG model. The 20 most sensitive parameters out of 55
which represent the total of parameters in 3-PG were retained from sensitivity analysis
and used for optimization according to the Differential Evolution-Markov Chains (DE-MC)
approach described below. The calibrated model was then used to predict the NPP over
the entire study area and compared to the observed MODIS NPP of reference for the
period 2016–2021.
Figure 2. Flowchart of the global methodology.
2.3. Used Data
The 3-PG model requires a set of input data for its initialization which includes: (1) model
species parameters (species-specific eco-physiological and allometric characteristics that
can be partially derived from forest inventories and literature), (2) site data (e.g., latitude,
altitude, information about physics of the soil), (3) initial stand structural data (e.g., DBH,
tree height, stand density), (4) climatic data (meteorological data at a monthly time step,
e.g., mean daily incident solar radiation, mean monthly air temperature). Such data could
be classified as in situ and ex-situ data according to their way of collection. In addition,
the calibration process of this model requires observational data (5) for model validation.
2.3.1. In-Situ Data
As tree growth depends on stand density, and climate conditions, the study area
was stratified according to stand density, exposure, and soil type. Due to the absence of
permanent plots, the sampling design was based on temporary circular plots of 0.05 ha
with their borders set by means of a Haglöf Vertex IV and its transporter including any tree
whose distance from the plot center is less than or equal to 12.6 m. In total, 24 plots were
randomly selected within 4 sampling strata according to an optimal allocation (considering
stratification criteria: stands density and exposure). The variance of the estimate was
reduced according to the Cochran formula [
42
] and the relative sampling error (RSE),
which was found to be equal to 14.5%, was computed according to the equation presented
below (Equation (1)).
RSE(¯
Y) = 1
¯
Y
v
u
u
t1
N2
k
∑
i=1
(Nt(Nt−nt)s2
t
nt
)(1)
Forests 2023,14, 401 5 of 18
with ¯
Yrepresenting the estimate of the population mean annual carbon increment, Nand
Nt
correspond to the total number of units within the population and within each stratum,
respectively.
nt
and
st
represent the number of sampling units and the standard deviation
of the annual increase in carbomass, respectively, in each stratum from the kensemble strata
(Table 1).
Due to the large scale of the soil map, substrate representativeness was verified during
the fieldwork. Indeed, 9 plots are based on a limestone bedrock while 15 plots are based on
a basaltic bedrock, which implies the representativeness of samples with regard to the type
of bedrock.
Table 1. Characteristics of the selected sampling strata.
Stratum Area (ha) The Standard Deviation of the Annual
Increase in Carbomass (tC.ha−1.yr−1)Number of Selected Plots
Cool exposure/Low density 368 0.55 6
Warm exposure/Low density 675 0.24 5
Cool exposure/High density 145 1.05 5
Warm exposure/High density 258 1.18 8
Total 1446 24
To derive the stand’s current and previous (2016, the start year of the simulations)
characteristics, plots were inventoried. Data related to the site and tree parameters were
collected. At each sample plot, the stem circumferences of all trees with a circumference
greater than the pre-countable circumference of 20 cm were measured using a Tricle tape
measure. Setting such a threshold for the tree measurement is justified by the fact that:
i- biomass equations used here were developed on the basis of trees of medium to large
dimensions, thus it is statistically inappropriate to apply them to small dimensions, ii- the
sampling plots in our study have not been subject to recent disturbances which imply that
the proportion of small trees in those plots is too low to impact the overall plot biomass.
Furthermore, among the trees in the plot, three representative trees were measured for
height (using a Haglöf Vertex IV), and their radial increments over the last five years were
measured using a Haglöf Pressler corer used for core extraction and a BORLETTI calliper
for measuring the thickness of the last five rings.
2.3.2. Ex-Situ Data
Other categories of data, specifically (2), (4), and (6), were derived using remotely
sensed data using the cloud computing platform Google Earth Engine (GEE) [
43
]. Data for
the available soil water variable from site parameters category (2) was extracted from the
European Soil Database [
41
]. Below is a summary table of the data used in this study along
with their metadata (Table 2).
Table 2. Summary of data collected ex-situ.
Category Variable Collection Name Band Name Spatial/Temporal
Resolution
Climate (4)
tmp_min “ECMWF/ERA5/DAILY” minimum_2m_air_temperature 0.25°/1 day
tmp_max “ECMWF/ERA5/DAILY” maximum_2m_air_temperature 0.25°/1 day
tmp_mean “MODIS_006_MOD11A2” LST_Day_1km 1000 m/8 days
prcp “ECMWF/ERA5/MONTHLY” total_precipitation 0.25°/1 month
srad “ECMWF/ERA5_LAND/MONTHLY” surface_solar_radiation_downwards 0.1°/1 month
frost_days “MODIS/006/MOD11A1” LST_Day_1km 1000 m/1 day
Site (2) ASW European Soil Database [41] SMU_EU_S_TAWC 1000 m/-
NPP (6) Npp “MODIS/006/MOD17A2H” PsnNet 500 m/8 days
Forests 2023,14, 401 6 of 18
2.4. Data Preparation and Preprocessing
2.4.1. Model Initialization
To assess the initial biomass carbon stock, the use of carbomass models developed
at the level of Azrou forest [
44
] was relevant instead of taking into account the default
parameters of the IPCC. These models with an associated error (RMSE) varying between
0.9 and 1.65 according to the tree compartment, were used to estimate the amount of carbon
per compartment (i.e., aboveground part, stem, and foliage) per tree on each plot (Table 3).
The conversion factors that emerged from the previous study were used to ensure the
transition from biomass to carbomass in each tree compartment (Table 4). However, since
root biomass was not the subject of the aforementioned study, the ratio of root biomass to
aboveground biomass (0.29) proposed in [45] was used in the present work.
Table 3. Carbomass models used in this study.
Component Model
Tree (Aboveground part) SCOT(C,H) = 53.05C2.09897 H0.4063 (2)
Stem SCOTr(C,H) = 53.624C2.19062 H0.36418 (3)
Foliage SCOF(C,H) = 0.671045 +0.024967CH (4)
C: Circumference at breast height, H: Total height, SCOT: Aboveground carbomass, SCOTr: Stem carbomass,
SCOF: Foliage carbomass.
Table 4. Conversion factor for each compartment of the tree.
Compartment Stem Foliage Branches Mean
%Carbon 57.41 57.30 54.30 56.43
The average diameter increment was computed at each plot level and was used to
generate the 2016 biomass stock for each compartment namely: stem biomass, root biomass,
and foliage biomass.
2.4.2. Climate Data
The data preprocessing was conducted through the GEE platform using the Web
programming interface to ensure work efficiency [
43
]. Image collections were loaded in the
working environment, and then they were filtered by the area of interest and further by
date to include only the images related to the study period. Then, all images were multi-
plied by their corresponding scale factor. Some collections did not require any additional
preprocessing, solar radiation (srad) whose temporal resolution equals the simulation step
of the 3-PG model (1 month), while the other collections required an additive preprocessing
to bring their temporal resolution to one month.
2.5. Sensitivity Analysis
Accurate predictions and simulations depend on the accuracy of model parameter
setting, climate data, and site information [
46
,
47
]. Sensitivity analysis defines the sensitivity
as well as the importance of each model parameter and provides a sufficient basis for
selection during model calibration. Optimizing parameters with low sensitivity increases
the computation time without significantly improving the accuracy of the model [48].
The revised Morris method was chosen [
49
,
50
]. It is a one-step-at-time (OAT) method,
which means that for each iteration of the algorithm, only one parameter assigns itself a
new value, and the others remain unchanged [
51
,
52
]. The reason for choosing this approach
is that it is well suited for models containing dozens of factors without depending on strict
assumptions about the model such as additivity and monotonicity of the input-output
Forests 2023,14, 401 7 of 18
relationship of the model. Moreover, this method is easy to understand and implement,
and its results are easy to interpret [53].
The Morris algorithm starts at a randomly chosen in a k- dimensional space, where
k represents the number of model parameters for which the sensitivity will be evaluated,
and creates a trajectory through the k- dimensional space. Two neighbouring points differ
by a distance called a “step” in only one direction. For each trajectory, a given variable can
be assigned a discrete number of values called “levels” sampled evenly within the factor
range of variation. This process of trajectory construction is iterated a number of times
in such a way as to explore all the possible factor levels. Then, for each “repetition” and
parameter, the difference in the response of the target variable considering two adjacent
points is calculated, which conventionally represents the elementary effect. Based on this
difference, it is possible to compute for each parameter two metrics namely
µ
* which refers
to the mean of the absolute elementary effect, and
σ
which refers to the standard deviation
of the elementary effect. Thereafter, considering the different level values of those metrics,
model parameters could be classified into three main groups, namely parameters with a
negligible effect, parameters with linear effect without interaction, and parameters with a
non-linear or interaction effect, respectively.
The parameters of the Morris algorithm have been assigned the following values:
(Number of levels: 20, number of repetitions: 500, step: 3). For the output variable of
the Morris method, which is used for the computation of the elementary effect, it was
assimilated to the fit to the observed variable (NPP observed) and expressed by its log-
likelihood with normal error assumption for NPP.
The choice of the range of variation for the parameters of the present model was based
on literature analysis. In the absence of a reference value specific to the genus Cedrus sp.,
a default value general for coniferous species was used, and the minimum and maximum
values of the variation intervals were set given those considerations [
17
]. The sensitivity
analysis was performed on all of the 55 parameters of the 3-PG model [13].
2.6. Model Calibration
The DE-MC (Differential Evolution-Markov Chains) method, which is a combination
of Markov Chain Monte Carlo (MCMC) and genetic algorithms (GA), has been used for
the calibration and optimization of the 3-PG model parameters. This method that com-
bines a priori knowledge about parameters with observations is widely used in ecological
research [
54
–
56
]. The a posteriori values of the parameters can be used as a result of the
calibration, and the optimized parameter set of the model can be compared to the initial
parametrization set, which seems to be extremely useful in identifying parameters that
estimate the observed evolution of a given species.
The Bayesian theory combines a priori knowledge about the parameters of the model
with observations of the variables that will be predicted by the model to perform a posterior
estimation of these parameters [
57
]. The MCMC method involves the construction of a
Markov chain with the parameters of the posterior distribution to obtain posterior samples
of these parameters and subsequently infer the numerical characteristics of these parameters
based on these samples. Bayesian theory is expressed by the following formula:
P(θ/y) = f(y/θ)g(θ)
Rf(y/θ)g(θ)d(θ)(5)
with
θ
and yrepresent the parameters and output values simulated by the 3-PG model (e.g.,
NPP), respectively; P(
θ
/y) is the posterior probability density function of the parameters,
and f(y/
θ
) refers to the observations. The conditional probability density knowing the
parameters a priori is called the likelihood function, g(
θ
) being the a priori distribution
of the parameters, and d(
θ
) corresponds to the differential of the model parameters. To
solve the scaling and orientation problem of the jumping distribution, Braak [
58
] proposed
a method combining MCMC and DE which inherits GA thereby giving DE-MC. For the
DE-MC case, which is defined as the distance between the current parameters vector
Forests 2023,14, 401 8 of 18
and the candidate vector, is calculated in DE-MC as a multiple of the difference between
two parameter vectors of the current population. The selection process of DE-MC is
based on the Metropolis ratio defining the probability for which a candidate could be
successful [
59
]. Based on the results of the sensitivity analysis, the 20 most influential
parameters were selected to reduce the computational time and improve the efficiency
of the optimization as in Trotsiuk et al. [
60
]. Bayesian calibration was performed using
differential evolution [
58
], and the MCMC algorithm from the BayesianTools library [
61
]
with 3 chains and 4 × 106iterations (see Figure 3).
Figure 3. Flowchart of the DE-MC method (Differential Evolution-Markov chains).
3. Results
3.1. Stands Characterization
3.1.1. Adjustment of the Height-Circumference Relationship
Considering that the estimation of biomass for Cedrus altlantica is based on a two inputs
model (stem circumference at 1.30 m (C in meters) and tree height (H in meters)) and that
the only parameter that was measured for all the tree individuals is the circumference, (see
Methods), the development of Height-Circumference model was necessary. For this specific
purpose, a second-degree polynomial model was fitted using the ordinary least square
method (OLS). As a result of the fitting, we obtained the following Equation (
R2= 0.80
,
p≤0.0001).
H=1.052 +17.548C−2.606C2(6)
3.1.2. Results of Stands’ Characterization
Based on the aggregation of data collected at the sampling plot level, it is possible
to characterize the forest by homogeneous strata. Table 5, presents by stratum level,
the average of all dendrometric descriptors collected in the field and biomass in different
tree compartments presented as tonnes of dry matter per hectare (tDM.ha−1).
Forests 2023,14, 401 9 of 18
Table 5. Forest inventory results by sampling stratum.
Stratum N (trees.ha−1)D (cm) Age
(yr)
SB±SD
(tDM.ha−1)
FB±SD
(tDM.ha−1)
RB±SD
(tDM.ha−1)
CAI
(cm.yr−1)
Cool exposure/High density 466 49 174 89.25 ±19.3 0.50 ±0.12 48.88 ±15.3 1.1
Cool exposure/Low density 180 35 107 49.78 ±10.6 0.19 ±0.05 17.62 ±6.6 1.13
Warm exposure/High density
792 46 159 268.08 ±52 0.92 ±0.20 93.95 ±13.4 0.93
Warm exposure/Low density
140 71 149 66.68 ±16.2 0.16 ±0.13 22.68 ±9.3 1.96
N: Density, D: Mean diameter, Age: Mean age, SB: Mean stem biomass, FB: Mean foliage biomass, RB: Mean
root biomass, CAI: Mean increment in circumference.
Results show that low-density stands had the highest increment in circumference, 1.96
and 1.13
cm.yr−1
, respectively, for warm and cool exposures, while the lowest values were
observed in highly dense stands, 1.1 and 0.93
cm.yr−1
, respectively, for cool and warm
exposures. The results obtained, concerning the density of the stand and the biomass of
different tree compartments, were used to initialize the model.
3.2. Sensitivity Results
The results from the Morris sensitivity analysis highlight that the parameters related
to stand properties, canopy structure and physiological processes, as well as biomass
partitioning are particularly the most important or sensitive for the model’s performance
More explicitly, the parameters with an important overall influence on the NPP, having
the highest value of
µ
*, were in order: alphaCx (Canopy quantum efficiency), fN0 (Value
of fN fertility ratio (FR) equals to 0), rAge (relative age to give an age growth-modifier
value (fAge) of 0.5), MaxCond (Maximum canopy conductance), fNn (power in the fertility
equation), Topt (Optimum temperature for growth), SLA1 (Specific leaf area for mature
leaves), pFS20 (Foliage-Stem partitioning ratio at B = 20 cm). It was also found that
those same parameters tend to produce larger
σ
, which could indicate non-linearities or
interactions with other parameters (Figure 4).
Figure 4.
Results of the Morris sensitivity analysis. The 55 parameters are listed on the x-axis. A high
value of
µ
* indicates a large influence of the parameter on the output variable while a high value of
σ
indicates a nonlinear or interaction effect.
Forests 2023,14, 401 10 of 18
3.3. Calibration
Based on the Morris analysis, the 20 most influential parameters were used for calibra-
tion purposes using the Differential Evolution Markov Chain Monte Carlo algorithm (DEzs
MCMC) [
62
]. The calibration of the model converged to parameter values close to the values
used to generate the reference data. This was verified by means of the Gelman–Rubin con-
vergence test in which the potential scale reduction factor (psrf) is equal to 1.01. The value
of psrf is lower than 1.1, which confirms the convergence of the calibration [
63
,
64
]. It also
emerges from this study that the posterior distribution is well-defined. In the bayesian
calibration, the posterior probability for the model parameters should have a prominent
peak without being bimodal. This is generally achieved with a high number of iterations
(e.g., 10
6
in the case of our study) to narrow the parameter space. The normal distribution
or pseudo-normal (skewed) validates all those criteria (Figure 5).
Furthermore, to evaluate the performance of the model, the predictive posterior
distribution was calculated by running the model with 500 random samples from the
parameters’ global posterior distribution. Then, the NPP was simulated over time for
each combination of parameters. The best parameter set was then assimilated to the
maximum posterior probability which corresponds to the mode of the posterior probability
distribution. To verify the superiority of our parametrization dataset, the comparison of
the results provided by the three parametrization sets, namely the default, the median,
and the calibrated set of parameters was done using the mean squared error metric (MSE)
with reference to the MODIS observations on NPP (
NPPMODIS
) with nbeing the number
of observation on NPP (Equation
(7)
). The results show that the proposed parameterization
dataset is indeed more accurate than the default one and that MSE was reduced by about
18% (Table 6).
MSE =1
n
n
∑
i=1
(NPPpredicted −NPPMOD IS)2(7)
Figure 5.
The posterior distributions of the reduced parameters of the 3-PG model developed in the
present work.
Table 6. Prediction error of the three candidate parametrization datasets for selection.
Default Model Median Model Calibrated Model
MSE 0.32068 0.26213 0.26210
Forests 2023,14, 401 11 of 18
Given these results, the obtained parametrization dataset will be used for future
estimates of carbon sequestration by the Azrou cedar forest. Below is an explicit description
of the 3-PG model parameters optimized in the present study (Table 7).
Table 7.
Initial values, ranges, and posterior distributions of the 20 optimized 3-PG model parameters.
Parameter Unit Initial Value Range Mode Mean ±Standard
Deviation Description
pFS20 - 0.6 [0.05, 0.8] 0.29 0.39 ±0.21 Foliage stem partitioning at D = 20 cm
aWS - 0.05 [0, 0.4] 0.117 0.201 ±0.109
Constant in stem mass v. diameter relationship
pRn - 0.2 [0.0001, 0.5] 0.466 0.267 ±0.141 Minimum fraction of NPP to roots
gammaF1 1/month 0.049 [0.0001, 0.04] 0.0126 0.0198 ±0.0117 Maximum litterfall rate
Tmin Degree °C 0 [−1, 8] −0.82 3.25 ±2.45 Minimum temperature for growth
Topt Degree °C 19.5 [10, 30] 23.87 23.98 ±4.06 Optimum temperature for growth
Tmax Degree °C 35 [30, 40] 38.57 36.11 ±2.59 Maximum temperature for growth
fN0 - 0.6 [0.0001, 1] 0.1300 0.3943 ±0.2648 Value of fN when FR = 0
fNn - 1 [0, 1] 0.87 0.47 ±0.28 Power of (1-FR) in fN
MaxAge Years 500 [350, 550] 461 452 ±57 Maximum stand age used in age modifier
nAge - 4 [1, 4.325] 2.477 2.537 ±0.970 Power of relative age in function for fAge
rAge - 0.95 [0.0001, 1.4] 0.2436 0.6980 ±0.3510 Relative age to give fAge = 0.5
SLA1 m2/kg 5.5 [5, 30] 22.33 16.62 ±7.15 Specific leaf area for mature leaves
K - 0.2921 [0.4, 0.6] 0.40 0.49 ±0.06 Extinction coefficient for absorption of PAR by
the canopy
MaxIntrcptn - 0.25 [0.1, 0.4] 0.36 0.25 ±0.087 Maximum proportion of rainfall evaporated
from canopy
alphaCx molC/molPAR 0.04212129 [0.02, 0.09] 0.0493 0.0468 ±0.0188 Canopy quantum efficiency
Y - 0.47 [0.44, 0.51] 0.48 0.47 ±0.02 Ratio NPP/GPP
MaxCond m/s 0.02 [0.001, 0.03] 0.022 0.016 ±0.008 Maximum canopy conductance
CoeffCond 1/mBar 0.05 [0.0001, 0.07] 0.0030 0.0367 ±0.0196 Defines stomatal response to VPD
BLcond m/s 0.2 [0.0001, 0.3] 0.1105 0.1479 ±0.0861 Canopy boundary layer conductance
Sources for optimized parameters ranges: [22,29,30,65–71].
3.4. NPP Simulation
In order to provide an overall estimate of carbon sequestration capacity by the pure
cedar forest of Azrou (we ran the 3-PG for the period 2016–2021), the estimation of se-
questration by each sampling unit was performed using the calibrated 3-PG model. First,
a simulation of NPP was carried out by sample plot, then these results were aggregated by
stratum and their respective averages were calculated. Subsequently, in order to provide
an overview of the carbon sequestered in the Azrou forest, the average annual amount of
sequestrated carbon per unit area was multiplied by the area occupied by each stratum.
Later, a conversion factor of 0.56 was used to convert biomass (dry weight) to carbon
equivalent (C) (tonnes). These results are represented in the table below (Table 8).
Table 8. Carbon increment per stratum unit.
Statum Area (ha) Unit Carbon Increase ±SD
(tC.ha−1.yr−1)
Stratum Carbon Increase
(tC.yr −1)
Cool exposure/Low density 368 5.20 ±0.34 1913
Warm exposure/Low density 675 5.08 ±0.46 3429
Cool exposure/High density 145 7.24 ±0.77 1049
Warm exposure/High density 258 5.92 ±0.41 1527
Pure cedar forest 1446 5.47 7918
Results show that dense stands have an important carbon uptake dynamic in compari-
son to stands with lower densities. It also emerges that for stands belonging to the same
density category, cool exposures always sequestrate annually more carbon than warm expo-
sures. In fact, for the high-density category, stands with cool exposure annually sequestrate
7.24
tC.ha−1.yr−1
while those with warm exposure sequestrate 5.92
tC.ha−1.yr−1
. Regard-
ing low-density stands, those with cool exposure annually sequestrate 5.20
tC.ha−1.yr−1
,
while those with warm exposure annually sequestrate 5.08 tC.ha−1.yr−1.
Forests 2023,14, 401 12 of 18
Moreover, although it has been demonstrated in the present work that stands with
cool exposure hold the highest sequestrating capacity, warm exposed stands within the
forest of Azrou contribute to 67% of the annual carbon uptake while cool exposed stand
contributes only to 33% of the annual carbon uptake. However, stands with warm exposure
occupy 72% of the total area of the forest, while those with cool exposure occupy only 28%
of the total area of the forest.
4. Discussion
4.1. Parameter Sensitivity and Optimization
In the present study, the overall sensitivity of 55 parameters of the 3-PG model in
simulating NPP was analyzed using Morris’ sensitivity. As a result, it was found that
NPP simulated by the 3-PG model is particularly sensitive to some parameters related
to canopy structure and processes (e.g., alphaCx, SLA1, MaxCond), and conductance
modifiers (e.g., fN0, rAge, fNn, Topt), as well as carbon partitioning (e.g., pFS20). While
there are three possible approaches to assigning values to parameters in a model namely:
i. direct measurement, ii analogy with other species and iii. parameter estimation [
13
].
The present work exclusively used the last two approaches given the unavailability of
direct measurement for this species. It is in that sense that the results of the sensitivity
analysis were leveraged and allowed to assign generic values derived from a benchmark-
ing that included conifer species to parameters with a low ranking in sensitivity, while
20 parameters with a high ranking in sensitivity were fitted to the observations on NPP.
To illustrate the importance of sensitivity analysis in understanding the behaviour of the
model, some examples will be discussed in the following.
4.1.1. NPP and Canopy Processes and Structure
The maximum quantum efficiency (alphaCx; i.e., the maximum attainable efficiency
when no environmental or structural modifiers limit the maximum potential photosynthesis)
is directly used for the calculation of NPP. NPP results from the multiplication of ‘alphaCx’
by the absorbed photosynthetically active radiation (APAR), canopy cover, and a series of
environmental and structural modifiers for the computation of the Gross Primary produc-
tivity (GPP) and then reduced through the NPP/GPP ratio (Y; i.e.,
NPP = GPP ∗Y
)
[72,73]
which represents one of the twenty most influential parameters. Similarly, other models
(e.g., 3D-CMCC-FEM and CLM4.5-FATES) which simulate NPP mechanistically as the net
result from GPP less Autotrophic Respiration [
52
,
74
] have shown that the number of live
biomass controls mostly NPP [
75
]. In addition, the non-trivial role of Y is something that
has been discussed by Collalti et al. [
76
], and represents a large source of uncertainty for
models who apply the “NPP = GPP
∗
Y” given that it has been found to range from 0.22
to 0.79 [
72
]. GPP (and then NPP) was also found to be sensitive to ‘SLA1’, this parameter
refers to the specific leaf area for mature trees which varies between stands of different
ages and is necessary for the computation of Leaf Area Index (LAI) and GPP, subsequently.
GPP was also found to be sensitive to the maximum canopy conductance (MaxCond),
given that canopy conductance is central to calculations of canopy photosynthesis and
thus NPP [
77
]. Similarly to our results, Almeida et al. [
20
] found that biomass-related
outputs for Eucalyptus grandis W.Hill (root, stem, and foliage biomass) were sensitive in
3-PG to alphaCx and Maxcond. In Keryn I. et al. [
78
], NPP has been found to be sensitive
for Eucalyptus grandis W.Hill and Pinus radiata D.Don to alphaCx and Maxcond. Those find-
ings agree with our results showing that independently from species considered, the NPP
simulated by the 3-PG model is sensitive mostly to these parameters. Moreover, results
obtained from different studies using various PBMs were in good agreement with our
findings. Typically, in a study conducted by Zaehle et al. [
79
], using the LPJ-DGVM model,
both the intrinsic quantum efficiency and maximum canopy conductance were among the
four most important parameters controlling NPP. In Pappas et al. [
80
], intrinsic quantum
efficiency was of utmost importance in LPJ-GUESS parameterization, explaining most of
the variability in carbon fluxes. In a different study led by Tatarinov et al. [
81
], using the
Forests 2023,14, 401 13 of 18
BIOME-BGC model, the effect of ’SLA’ on NPP was strong for both Fagus sylvatica L. and
Picea abies L.
4.1.2. NPP and Conductance Modifiers
In addition to parameters of the canopy structure and processes, ‘fN0’ and ‘fNn’,
representing the coefficients of the relationship between the fertility index and the fertility
growth modifier were found to be important for the model, which is consistent with
other studies that demonstrated the relevance of the relation between the fertility indexes
and the stand productivity [
82
]. Moreover, ‘rage’ was also found to be important for the
performance of the model, this parameter intervenes in the definition of the age-related
growth modifier which in turn modifies canopy conductance and quantum efficiency which
are accounted for in the calculations of GPP and NPP [
20
]. The optimum temperature
for growth (Topt) had also a high sensitivity ranking for GPP and NPP, this could be
attributed to its contribution to the calculation of the effective quantum canopy efficiency
and thus to the NPP [
19
]. In Trotsiuk et al. [
60
], which applied 3-PG to examine the growth
of Pinus sylvestris L. and Fagus sylvatica L. mixtures along site and climatic gradients,
biomass-related outputs (Wr, Wf, and Ws) were found to be sensitive to fN0, fNn, and rAge,
which is consistent with our findings. In addition, our results were in good agreement
with Xenakis et al. [
30
], who applied 3-PG on commercial plantations of Pinus sylvestris L.,
found that fN0 was important for foliage and root biomass while both fN0 and Topt were
important for stem biomass.
4.1.3. NPP and Carbon Partitioning
In addition to parameters belonging to the canopy structure and processes as well as
the conductance modifiers classes, ‘pFS20’, which refers to the partitioning ratio between
foliage and stem for a representative tree of DBH = 20 cm, has been found to be important
for the performance of the model. The high sensitivity of NPP to this parameter could
be explained by the fact that pFS20 is a determining factor in the updating of the foliage
biomass pool and thus of the Leaf Area Index (LAI) which intervenes in the calculation of
the NPP through the absorbed active radiations. In a study conducted by Ulrich et al. [
83
],
who applied the 3-PG model on Pinus ponderosa L., GPP was found to be sensitive to
‘PFS20’. In fact, it was shown that an increase of about 40% in the value of ‘PFS20’ induces
an increase of about 22.5% in GPP, thus in NPP as well given the fixed proportionality
between GPP and NPP. Results from other studies, e.g., the one by Massoud et al. [
74
] that
made use of the CLM4.5(FATES) model, show the importance of leaf and stem allometry
parameters controlling dynamic carbon allocation and thus the general vegetative state and
size structure of the forest.
4.2. Implications, Future Perspectives, and Limitations
Results show that the calibrated model decreased the error by about 18% compared
to the default parametrization dataset. The 3-PG model was calibrated using time series,
and different sites since NPP is inherently dynamic in contrast to slowly varying state
variables (e.g., DBH). To our knowledge, the present study is the only one in the literature
to have calibrated the 3-PG model for the Atlas cedar species. The present calibration
set for 3-PG will enable a better assessment of the carbon sequestration by a cedar forest
instead of using the default increment as suggested by the IPCC. The calibrated model
also offers the possibility of predicting the impact of climate change on forest productivity
under different management options, which is of paramount importance in the context of
forest disturbances being more pronounced in recent years and likely to be of the same
magnitude in the coming decades [
84
]. Specifically, in the context of our study area, drought
which is defined as a sporadic disturbance of the water cycle, is becoming more frequent
in recent years. As a response, plants deploy water-use strategies to avoid excessive
water consumption which are mainly translated into physiological and structural changes.
Physiological responses include a decrease in stomatal conductance through stomatal
Forests 2023,14, 401 14 of 18
closure to control the water flux. This may also induce a reduction in CO
2
diffusion and
thus a short-term reduction in GPP. From a structural perspective, for example, a reduction
in leaf area due to early senescence could be responsible for the reduction of photosynthetic
activity (GPP). Besides the carbon fluxes change, drought could also induce vegetation
mortality, e.g., due to cavitation when the demand for water exceeds the supply, and the
air is aspirated into the xylem or carbon starvation when autotrophic respiration exceeds
photosynthesis. However, from a technical perspective, 3-PG is only able to represent the
effect of drought on GPP, while density-independent mortality in general and drought-
induced mortality in specific is not conceived as part of the 3-PG scheme.
The model calibrated in this study simulates the evolution of NPP over time in a pure
forest of Cedrus atlantica. Forest stand dynamics are not only dependent on the ecological
and physiological characteristics of the species but also on the human interventions that may
prevail by station [
57
]. This last element has not been considered due to the unavailability
of permanent plots with recorded monitoring, however, this lack has been compensated by
a choice of temporary plots that were recently intact. Ideally, a network of monitoring plots
should be set up in the Azrou forest to properly follow the evolution of its stands. The data
thus obtained could help calibrate the 3-PG model considering its various components.
Additionally, given the importance of the quality of observations for the performance of the
model, using the method of Eddy Covariance could be a prominent tool to meet the quality
standards enabling the monitoring of GPP with relatively a high certainty [
85
] instead of
using NPP of MODIS having a spatial resolution of 500 m, generally exceeding the plot
size, we can lead to spatial error in the case of very heterogeneous forests. It should also be
mentioned that in the Azrou forest, the Atlas cedar is found either in a pure state, mixed
with the holm oak or to a less degree with the Mirbeck’s oak. Owing to this species mixture,
the evaluation of carbon sequestration in the whole forest of Azrou using 3-PG requires the
calibration of the holm oak model for which the literature is quite rich [32,86].
From another perspective, it should be noted that the amount of carbon in soil repre-
sents a substantial portion of the carbon found in terrestrial ecosystems. In a recent study
conducted at the level of the Azrou forest, soil carbon has been found to constitute between
46.4% and 59.1% of the total carbon stock [
87
]. The 3-PG model used for the frame of
our study is only able to follow the evolution of carbon in the biomass pools, however,
an upgraded version of this same model (i.e., 3PGN) couples 3PG with ICBM/2N which
is a soil model and provide a way to account for the soil carbon balance [
30
]. Moreover,
in the context of the present study, the root-to-shoot ratio provided by the IPCC has been
used given the non-availability of accurate vegetation-specific values. For the purpose of
better accuracy in the estimation of biomass, it will be advantageous to calibrate/develop
specific allometric equations in the future.
The results obtained in this work show that the annual carbon update in the pure cedar
forest of Azrou varies from 0.35 and 8.82
tC.ha−1.yr−1
(inter-plot variability). In compliance
with our results, previous studies have demonstrated the ability of the Atlas cedar to achieve
high levels of the annual increment in volume ranging from 8 to
12 m3.ha−1.yr−1[88,89]
.
However, the comparison of these findings with the generic increment suggested by
the IPCC, and adopted by the National Forest Inventory services (NFIs) which is about
0.47 tC.ha−1.yr−1
highly underestimates Cedar forest carbon sequestration capacity and
should raise questions about the relevance of the methodology used.
5. Conclusions
In this study, the sensitivity of 55 parameters of the 3-PG to the NPP was analyzed
during the period 2016–2021. The 20 parameters with a high influence on NPP have been
selected and optimized according to the DE-MC method. The conclusions of this study are
as follows:
(1)
Parameters related to stand properties, canopy structure, and processes, as well as
biomass partitioning, are the most important or sensitive for the performance of
the model.
Forests 2023,14, 401 15 of 18
(2)
DE-MC method optimized the values of the 3-PG parameters which was confirmed
by the means of Gelman–Rubin convergence test.
(3)
According to the predictions of 3-PG, the annual carbon sequestration in the pure
Azrou forest varies between 0.35 and 8.82
tC.ha−1.yr−1
, it is equal in average to
5.48 tC.ha−1.yr−1, which given the total area corresponds to 7918 tC.yr−1.
Author Contributions:
Conceptualization, S.L. and I.B.; methodology, S.L. and I.B.; resources, S.L.
and R.V.; writing—original draft preparation, S.L., I.B., S.M. and A.C. All authors contributed to the
writing and reviewed the manuscript. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Data Availability Statement:
A zip file containing the data and scripts used in the frame of the
present study can be requested from issam.boukhris@unitus.it or marghadi@gmail.com.
Acknowledgments:
We thank Anass Legdou, and through him the Moroccan Department of Waters
and Forests (Regional Directorate of the Middle Atlas) and the National School of Forest Engineers
(Salé, Morocco) for providing logistical and intellectual support. We would like also to thank
the reviewers for taking the necessary time and effort to review the manuscript. We sincerely
appreciate all your valuable comments and suggestions, which helped us in improving the quality of
the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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