Climate change affects forest growth in numerous and sometimes opposite ways, and the resulting trend is often difficult to predict for a given site. Integrating and structuring the knowledge gained from the monitoring and experimental studies into process-based models is an interesting approach to predict the response of forest ecosystems to climate change. While the first generation of models operates at stand level, one now needs spatially explicit individual-based approaches in order to account for individual variability, local environment modification and tree adaptive behaviour in mixed and uneven-aged forests that are supposed to be more resilient under stressful conditions. The local environment of a tree is strongly influenced by the neighbouring trees, which modify the resource level through positive and negative interactions with the target tree. Among other things, drought stress and vegetation period length vary with tree size and crown position within the canopy.
In this paper, we describe the phenology and water balance modules integrated in the tree growth model HETEROFOR (HETEROgenous FORest) and evaluate them on six heterogeneous sessile oak and European beech stands with different levels of mixing and development stages and installed on various soil types. More precisely, we assess the ability of the model to reproduce key phenological processes (budburst, leaf development, yellowing and fall) as well as water fluxes.
Two two-phase models differing regarding their response function to
temperature during the chilling period (optimum and sigmoid functions) and a simplified one-phase model are used to predict budburst date. The two-phase model with the optimum function is the least biased (overestimation of 2.46 d),
while the one-phase model best accounts for the interannual variability
(Pearson's
Climate projections for the future indicate a substantial increase in air
temperature all over Europe (between 1.0 and 5.5
Since climate change affects some tree growth processes positively and others negatively and given the interactions among factors as well as the feedback and acclimation mechanisms, it is not easy to predict the resulting effect on tree growth at a given site (Lindner et al., 2014; Herr et al., 2016). Knowledge about climate change has been acquired based on long-term monitoring studies that are limited to the observed changes (Bussotti and Pollastrini, 2017; Etzold et al., 2019) and on experiments of environment manipulation generally analysing one or two factors at a time for a limited period (Ainsworth and Long, 2005; Norby et al., 2010; Wolkovich et al., 2012; Meir et al., 2015). In order to apprehend the complex functioning of forest ecosystems, the use of process-based modelling is a complementary approach that allows the integration and structuring of the existing knowledge and extrapolations to be made for unprecedented conditions like those projected for the coming decades.
Process-based models were originally built to predict forest growth response to environmental changes at stand level without accounting for management operations and canopy heterogeneity. Such models were therefore suitable for pure even-aged stands but hardly manage to simulate mixed and structurally complex stands (Dufrêne et al., 2005; Pretzsch et al., 2007). Yet, nowadays, a promising way to adapt forests to climate change is to progressively turn them into uneven-aged and mixed stands using continuous cover forestry and natural-disturbance-based management to improve their stress resistance and resilience (DeRose and Long, 2014; Messier et al., 2015; Anderegg et al., 2018). To account for the spatial heterogeneity, some process-based models were designed or adapted to simulate various tree cohorts (Collalti et al., 2016). However, this approach only considers the vertical dimension of spatial heterogeneity while implementing innovative forestry practices in structurally complex stands requires the horizontal dimension to be accounted for through a spatially explicit approach at tree level (Pacala and Deutschman, 1995; Pretzsch et al., 2007; Berger et al., 2008; Bravo et al., 2019).
To reproduce the complexity of forest ecosystem functioning in mixed and structured forests, models must take individual variability, local environment and tree adaptive behaviour into account (Berger et al., 2008). Tree size and species influence physiological and morphological properties that in turn affect the main growth processes (Binkley et al., 2013). Considering average individuals is therefore a rough approximation and does not allow for all the variability within a heterogeneous forest to be accounted (Berger et al., 2008). Even in cohort-based approaches, tree grouping can only be done for a limited number of criteria that are not necessarily representative of the whole tree diversity. The local environment of a tree is strongly influenced by the neighbouring trees, which modify the resource level through positive and negative interactions with the target tree (Grossiord et al., 2014). As trees compete for limited resources, neighbouring trees can decrease light, water and nutrient availability. Tree species can however develop strategies to avoid competition by using different temporal and spatial niches (complementarity; Grossiord, 2018). Positive interactions may also occur when the neighbouring trees improve the growing conditions of the target trees (facilitation; Pretzsch et al., 2013). Finally, trees adapt their morphology and physiological behaviour to the local environmental conditions by optimizing carbon allocation in order to maximize the acquisition of the limiting resource (Petritan et al., 2009; Yuang et al., 2019).
As this study focus on phenology and water cycling, we briefly review how these processes are influenced by tree characteristics and local environment. Phenology timing varies among tree species, which favours early-leafing species but can also expose them to late frosts (Lopez et al., 2008; Liu et al., 2018). Many studies report that leaf development starts earlier and leaf senescence occurs later in the understory compared to the overstorey (Gill et al., 1998; Seiwa, 1999a; Augspurger and Bartlett, 2003; Schieber, 2006; Vitasse, 2013; Gressler et al., 2015), which allows the understory trees to benefit from a longer growing period and consequently, to increase their productivity (Jolly et al., 2004). The presence of warmer temperatures in the understory is one of the hypotheses advanced to explain this difference in budburst between under- and overstorey (Augspurger and Bartlett, 2003; Schieber, 2006). Using a construction crane, Vitasse (2013) tested this hypothesis by transplanting seedlings of five tree species at 30 and 35 m height in the canopy. He observed that the budburst of the seedling growing at these heights was much earlier than that of the dominant trees. He concluded that the main factor to explain this difference in budburst is driven by ontogeny (tree age and height) as stated by Seiwa (1999b) and that the vertical profile in temperature within the canopy only plays a secondary role. To capture the differences in budburst between understorey and dominant trees, ontogeny must be taken into account in priority.
Drought stress occurs when trees can no longer adjust their water use to soil water availability, which reduces growth and can even lead to mortality in the short or medium term due to hydraulic failure or progressive carbon starvation (McDowell and Allen, 2015; Meir et al., 2015; Greenwood et al., 2017). The stomatal control of water use varies among tree species and depends on tree size (Martínez-Vilalta and Lloret, 2016). In general, stomatal conductance decreases with tree height, which can be related to the fact that taller trees experience higher hydraulic resistance, higher soil-to-leaf water potential differences and are more vulnerable to cavitation (Grote et al., 2016). For the same climate conditions above the forest canopy, water demand varies with the degree of crown shading (local microclimate), which depends on the crown position within the canopy (Bennett et al., 2015). All in all, dominant trees are more susceptible to drought stress and mortality since they are more exposed to stressful conditions (excessive radiation, high vapour pressure deficit and elevated temperature) and present a higher risk of cavitation (Grote et al., 2016; Rötzer et al., 2017). In addition, as dominant trees have higher evapotranspiration rates, the soil water reserves in their surroundings are more rapidly depleted, which is however partly compensated by deeper rooting and horizontal water redistribution. These dominant trees reduce water availability for suppressed trees but, at the same time, decrease their evaporation demand. Complementarity in water use can occur when trees of different size and species take up water from different soil layers (Schwendenmann et al., 2015). This can also result in facilitation through hydraulic lift (Zapater et al., 2011). Mixed and structured stands promote facilitation and complementarity in water use but can also lead to faster exploitation of soil water reserves (Schäfer et al., 2018).
Modelling the complex functioning of heterogeneous forests is rather challenging. A more detailed representation of tree interactions comes at the price of a higher complexity, eventually lower robustness and longer computing times. One needs however spatially explicit individual-based models for gaining a mechanistic and comprehensive understanding of tree interactions and for comparing various spatial representations of stand structure in order to select the best one for the considered function (Berger et al., 2008; Bravo et al., 2019). Among other things, such models allow tree spatial configuration to be taken into account and stands composed of the same trees but with a contrasted spatial aggregation to be distinguished between (e.g. intimate vs. patch-wise mixture). However, very few models of this type currently exist. For all of these reasons, we decided therefore to develop a spatially explicit individual-based model called HETEROFOR for HETEROgeneous FOrest.
The processes regulating the carbon fluxes and the dimensional growth constitute the core of the HETEROFOR model and are described in Jonard et al. (2020a). Here, we focus on the description of two modules essential for predicting the impact of climate change on tree growth: phenology and water balance (Park et al., 2016; Choat et al., 2018). Phenology is described at the species level, with the possibility to make it dependent on tree size. Water balance can be achieved at the tree level or at the stand level by aggregation of individual tree properties. We used data from long-term forest monitoring to evaluate the capacity of the model to reproduce key phenological phases (budburst, leaf development, yellowing and fall) and the soil water content dynamics, as well as to estimate individual transpiration, stand throughfall and deep drainage. Evaluating each module separately is necessary to ensure the consistency of the whole model (Soares et al., 1995).
HETEROFOR is a model hosted in Capsis (Computer-Aided Projections of Strategies In Silviculture), a software platform for forest growth simulations (Dufour-Kowalski et al., 2012) that provides the execution system and procedures to run simulations and display the outputs. Still, apart from these data structures and operative methods, all initialization and evolution procedures are specific to HETEROFOR. The initialization phase of the model consists in loading different files (tree species parameters, tree and stand characteristics, chemical and physical soil properties, meteorological data, and fruit production data) in order to create trees and soil horizons. Then, tree growth is calculated yearly according to the HETEROFOR methods presented in Jonard et al. (2020a). So far, HETEROFOR is adapted and calibrated only for deciduous species, but the adaptation to evergreen species is under progress.
Once the initialization is completed, the first routine called is the calculation of phenological periods from meteorological data, which is described is Sect. 2.1.2. This function provides key phenological dates and the daily foliage state (foliage development stage and green vs. discoloured leaf proportion) during the year. These phenological outputs are notably used for the radiation budget carried out using the SamsaraLight library coupled to HETEROFOR (Courbaud et al., 2003). According to a ray tracing approach and based on the solar radiation from the meteorological file, this library differentiates the direct and the diffuse components of the global radiation and determines, for both, the part of energy absorbed by the crown and the trunk of each tree and the part transmitted to the forest floor. The intercepted radiation is required to estimate evapotranspiration and tree photosynthesis. All aboveground and belowground water fluxes are calculated according to the processes described in Sect. 2.1.3, which allows the performance of an hourly water balance for each soil horizon at the tree or stand scale.
For each tree, gross primary production (gpp) is estimated either annually with a radiation use efficiency approach or daily using the photosynthesis method implemented in
the model CASTANEA of Capsis (Dufrêne et al., 2005). In the latter case,
the daily gpp is cumulated over the year. At the end of the year, a part of
the annual gpp is used for growth and maintenance respiration, the remaining
part constituting the net primary production (npp). Maintenance respiration can be estimated as a
fraction of the gpp or calculated for each tree compartment by a method
accounting for the living biomass, its nitrogen concentration and a
The phenological module aims at predicting the temporal variation in the foliage status during the vegetation period. From budburst, leaf biomass progressively increases until a maximum value, then remains constant and finally decreases during leaf fall. This temporal evolution is characterized by the proportion of leaf biomass relative to its maximum value at full leaf development. In addition, two types of leaves are distinguished: green and discoloured leaves. The green leaf proportion is the ratio between the green leaf and the maximum leaf biomass. These two foliage properties are key variables used to simulate energy, water and carbon fluxes within the forest ecosystem. Photosynthesis and tree transpiration are dependent on the proportion of green leaves, since they are not active anymore on discoloured leaves. When leaves start yellowing, they still intercept rainfall, while their photosynthetic activity and transpiration are progressively reduced.
The following phenological phases are distinguished, in chronological order:
chilling period or endodormancy: accumulation of coldness that breaks the bud dormancy; it is initiated at the chilling starting date ( forcing period or ecodormancy: accumulation of heat that initiates the leaf development in the bud and leads to the budburst (budburst date is leaf development: progressive growth of the leaves from budburst to the complete leaf development (leaf development date is ageing: accumulation of coldness that is initiated at the ageing starting date ( yellowing: loss of photosynthetic activity linked to the decrease in day length; this phase ends at the yellowing ending date ( falling: the fall of the dead leaves starts (
Since the phenological timing can vary considerably between species, the phenology dates are calculated for each tree species separately. Intra-specific differences are also likely to occur according to the size or social status (Cole and Sheldon, 2017) and can be optionally accounted for as described later.
The phenological module is optional in HETEROFOR. Activating the phenology requires an hourly meteorological file. If not activated, the model uses the budburst and leaf fall dates provided by the user, which are identical for all years and tree species.
The principle behind the whole phenology module is similar for each phase. A
A two-phase model considering chilling and forcing is implemented to
calculate the average budburst date (
The second response function to temperature uses a sigmoid function (Chuine,
2000) as follows:
This rate is summed each day until reaching the chilling threshold (
The budburst is activated when the sum of the daily forcing rates reaches
the forcing threshold (
A simplified one-phase version is implemented as well, which only considers
forcing similarly to the two-phase model (Eq. 3). In this case, the forcing
starting date (
As the module was calibrated based on observations carried out on trees
representative of the stand, the predicted budburst starting date is
expected to be that of an average tree. Since, at this date, the leaf
expansion of some trees has already started in real conditions, the model
shifts the budburst date to correspond to that of the earliest trees. This
budburst shift,
Once the budburst starting date (
The leaf proportion (leafProp; in grams per gram) is calculated daily for each tree species
(sp) according to
As many studies have shown that budburst in the understory occurs earlier
than in the overstorey and ascribed this primarily to ontogeny (Gill et al.,
1998; Seiwa 1999a, b; Augspurger and Bartlett, 2003; Schieber,
2006; Vitasse, 2013), we implemented an option to make the phenology
size-dependent (
With the option phenology at tree level, the leaf proportion of each tree
(
A fixed date, defined according to Dufrêne et al. (2005), is considered
for the start of the ageing process (
The leaf yellowing calculation gives the green leaf proportion, greenProp (in grams per gram), which provides the fraction of remaining green leaves compared to the maximum amount of green leaves for each tree species. It is set to 1 before
the start of yellowing and then decreases with day length according to the
following equation:
The day length (in hours) is calculated according to Teh (2006):
The yellowing phase ends when the green leaf proportion drops below a
threshold, called yellowing threshold,
The falling rate (
According to Eq. (10), leafProp
Similarly to leaf development but with a reverse order, the option phenology at tree level first
triggers the leaf yellowing and fall in the taller trees and then in the
smaller ones in order to reproduce the observations reported by Gressler et
al. (2015). This options updates daily the green leaf and leaf proportions
of each tree (
The option phenology at tree level provides the opportunity to compare two contrasted hypotheses regarding individual tree phenology and to evaluate to what extent it has an impact on tree growth.
The water balance module operates at an hourly time step and simulates the partitioning of incident rainfall into the main forest water fluxes and pools, namely interception (i.e. water storage on foliage and bark and evaporation), throughfall, stemflow, water movements between soil horizons and deep drainage, transpiration and soil water uptake in the different soil horizons, and soil evaporation (Fig. 1). Surface runoff and groundwater level rise are not yet considered in the current HETEROFOR version. Instead, when saturation is reached in a soil layer, the water surplus is transferred to the horizon below or is lost when it occurs in the last horizon.
Schematic representation of the water fluxes and pools in
the water balance module. Rainfall is divided into throughfall directly reaching
the forest floor and a pre-stemflow component intercepted by the
foliage and the bark. Once the foliage and bark are saturated, the water
surplus increases the throughfall flux and flows along the branches and the
trunk to generate stemflow. The throughfall and stemflow fluxes enter in the
upper part of the soil and then, move from one horizon to the other
according to the Darcy's law. For a soil horizon, hr, the water input fluxes can be the drainage
from the upper horizon (
In a first step, the parameters considered as constant during the leaved and leafless periods are estimated. Then, the various water fluxes are calculated at an hourly time step. The default option for the water balance module calculates the water fluxes at the stand level by summing properties estimated at the tree level (maximum foliage and bark storage capacities and throughfall and stemflow proportions). For this option, tree transpiration is calculated at the tree level and summed at the stand scale. Stand transpiration is then used to estimate root water uptake in the different soil horizons, assuming that all trees are taking up water in the same reservoirs in which soil water is redistributed homogeneously between two hourly time steps. This hypothesis can be justified by soil anisotropy, which induces a higher horizontal than vertical soil conductance. This is justified since water movements through the same horizon depend only on its own hydrological properties, while the presence of one horizon with a low conductance can slow down vertical water movement in the upper horizons (Todd and Mays, 2005). Moreover, as sediments are preferentially deposited on their longest side, the vertical conductance is decreased with regard to the horizontal one (Cristiano et al., 2016) so that the ratio of the horizontal vs. vertical conductance ranges between 2 and 10 in alluvial soils and amounts to 100 in clay soils (Todd and Mays, 2005).
The user can select an alternative option
The pedon area (
In sparse stands, all the stand area is not allocated to the trees, and the remaining area is considered as a pedon without any associated tree. With the fine spatial resolution, the model performs a water balance for each tree pedon and also for the remaining pedons (without tree). Contrary to the default option, the alternative option supposes no water redistribution among pedons. This hypothesis could become more appropriate than the perfect-redistribution hypothesis when soil dries (Friedman and Jones, 2001), at least beyond the air entry value (Assouline and Or, 2006). The two options allow the user to test two contrasting hypotheses regarding soil water redistribution in the horizontal dimension. In the following description, variables calculated at the stand scale are represented with capital letters, while lowercase letters are used for variables at the tree level. In some cases, when the equation is the same at the tree and the stand level, the variables are represented only with capital letters to avoid unnecessary duplications.
The maximum foliage storage capacity of a tree (
To obtain it at the stand level (
Bark storage capacity depends on season (i.e. leaved and leafless periods)
and on tree species. It is derived from a linear model proposed by André
et al. (2008a) predicting the individual stemflow (sf; in litres) produced during a
rain event as a function of tree girth (C130; in centimetres) and rainfall amount (
As it is multiplied by the rainfall amount in Eq. (15), the term “
For a given tree, the proportion of stand rainfall reaching the ground at
the base of the trunk as stemflow may be calculated by dividing the stemflow
rate (see above) by the pedon or stand area (
During the leaved period, the radiation absorbed by the trees is provided by
the SamsaraLight library for either the whole period (simplified radiation
balance, the default option) or every hour of key phenological dates
(detailed radiation balance, an alternative option). It may be determined
by either considering absorption by tree crowns as a function of leaf area
density and ray path length through the crown by applying the Beer–Lambert
law or specifying relative crown radiation absorption coefficients for
each species. At the tree scale, the proportion of incident radiation
absorbed per unit of leaf area during the vegetation period (
In the following sections, all of these proportions are used to estimate the hourly absorbed or transmitted radiations based on the hourly incident radiation.
For the leafless period, the proportions of incident radiation intercepted
by the trunks and the branches and transmitted to the understory are
obtained based on the Beer–Lambert law using the bark area index (i.e. bark
surface divided by the stand or pedon area, BAI, in square metres per square metre) calculated
from the bark biomass, density and thickness as follows:
Based on the preceding calculations, the water balance module starts
updating the different water fluxes and pools for every hourly time step.
First water evaporation from foliage and from bark is computed using the
Penman–Monteith (P–M) equation (Monteith, 1965) at the tree or stand scale.
The latent heat flux density is calculated as follows:
The radiation absorbed hourly per unit of leaf area (
According to Teh (2006) and depending on the scale considered (tree or
stand), the mean canopy air resistance may be obtained by integrating the
canopy air conductance (
The mid-canopy height is determined as the mid-height between the dominant
height of the stand (
WS is estimated at the different heights (
While no surface resistance is considered for the foliage evaporation
(infinite conductance), the bark conductance (in metres per second) depends on the
bark storage at the previous time step (
Hourly tree or stand foliage evaporation (EV
Evaporation from foliage and from bark cannot be larger than the
corresponding amounts of water stored on these surfaces, namely
Rainfall passing through the canopy can be intercepted by the foliage, the
branches and the stems of the tree(s). These reservoirs saturate
progressively, and the water then flows along the trunks to the tree base(s)
to produce stemflow or drips from the canopy to the ground as throughfall.
For some of the parameters (i.e. storage capacities, stemflow proportions)
showing contrasting values depending on the season, the leaved and the
leafless periods are distinguished to describe these processes. In addition,
several intermediate state variables are considered, namely
tree or stand rainfall foliage storage ( previous stand foliage storage (prevS remaining foliage storage capacity (
For the
For the
Throughfall and stemflow fluxes are then calculated separately for the
leaved and leafless periods. For both periods, tree or stand throughfall and
pre-stemflow (preSF; in litres) are considered as complementary
fractions of the non-intercepted rainfall. Pre-stemflow is the amount of
rain deviated towards the branches and the trunk but not necessarily
reaching the base of the trunk due to storage and evaporation losses. At the
stand level, pre-stemflow is estimated separately for each tree species.
the tree or species bark storage ( the previous tree or species bark storage (prevS the remaining bark storage capacity of a given tree or species (RemC
At the stand scale, stemflow is obtained by summing stemflow fluxes over the
tree species as follows:
As for evaporation from foliage and bark, the Penman–Monteith equation (see
Eq. 27) is used to estimate hourly tree transpiration during the vegetation
period. In this case, the radiation absorbed per unit of leaf area by each
tree (
The latent heat flux density (in watts per square metre) determined by
applying this parametrization to Eq. (27) is then converted to tree
transpiration (TR
The Penman–Monteith equation is also used to estimate ground vegetation
transpiration and soil evaporation at the tree and stand scale. For this
purpose, the radiation transmitted to the understory is subdivided for each
time step into the radiation absorbed by per unit of leaf area of the ground
vegetation (
The energy effectively available for soil evaporation is obtained by
subtracting the soil heat flux density (
For ground vegetation transpiration and soil evaporation, the aerodynamic resistance is computed by applying Eqs. (36)–(38) between the ground level and the dominant height.
The surface resistances of the ground vegetation (
The modelling of water uptake distribution among soil horizons and of water
transfer from a horizon to another requires estimates of the hydraulic
properties for all soil horizons. The relationship between the soil water
content (
The Mualem–van Genuchten function allows for the estimation of the soil hydraulic
conductivity based on the relative water content and the saturated
conductivity.
These two functions (Eqs. 63 and 64) partly share the same parameters, which
are estimated based on soil horizon properties (i.e. organic carbon
content,
For mineral horizons, pedotransfer equations elaborated by Weynants et al. (2009) are used as follows:
Once tree and ground vegetation hourly transpiration has been calculated,
the module sums the transpiration of all trees for the stand approach and adds
the ground vegetation transpiration to obtain the hourly stand
transpiration, corresponding to the stand water uptake. Then, tree or stand
water uptake is distributed among the horizons according to a method
described in Couvreur et al. (2012). This method assumes that water
absorption occurs preferentially in horizons where the water potential
(matric potential,
The second term of the sum of Eq. (70) is null when integrated on all the horizons. Then, it does not change the total amount of water uptake, but it refines its distribution. Moreover, this method can generate water uplift that can occur when the top horizons are much drier than the deep ones.
At the tree and stand scale, the module performs an hourly water balance for each soil horizon hr (numbered from the topsoil) and updates its water content (
The input fluxes are the drainage (
To ensure the mass conservation, a variable time step (
For the top horizon,
Soil evaporation occurs only in organic horizons. The amount of water
evaporated from the horizon hr (
The absolute extractable water (EW; in millimetres) is defined as the amount of water
stored in the soil that can be used by the plants:
Description of the different module parameters for sessile oak and European beech and origin of their value.
The relative extractable water (REW; in millimetres) corresponds to the ratio between
this value of extractable water and the reference extractable water at the
field capacity (
Most of the model parameters were taken directly from the literature. In addition, an adjustment of some relationships was conducted using available data, which are described hereafter, but no overall calibration of the model was performed. The model parameters for sessile oak and European beech are presented in Table 1. Regarding common hornbeam, less information is available. For this tree species, we used specific parameters for light interception, photosynthesis, respiration and carbon allocation (Appendix A) but the same parameters as European beech for water balance and phenology given their similar morphology.
For the hydrological module, the parameters of Eq. (53) determining the stomatal conductance were determined based on data from Jonard et al. (2011) using a nonlinear fitting procedure.
For the soil hydraulic properties, the saturation
The parameters of the phenological module used to calculate the start of
budburst were determined using observations from the Pan European Phenology
dataset (PEP725), which provides data about phenological observations across
different European countries, though not in Belgium. We selected 129 sites
on the western border of Germany covering the latitudes of our six study plots
(49.5–51.0
Six sessile oak (
The experimental site of Baileux was installed to study the impact of species mixture on forest ecosystem functioning (Jonard et al., 2006, 2007, 2008; André et al., 2008a, b) and consisted of three plots. Two plots were located in stands dominated by either sessile oak or European beech, and the third one presents a mixture of both species. In these plots, sessile oak trees originated from a massive regeneration in 1880 and displayed the typical Gaussian distribution of even-aged stands, while European beech trees appeared to be progressively giving rise to an uneven-aged structure with all diameter classes represented. The stand in Chimay was an ancient coppice with standards, presently composed of mature sessile oak trees with an important hornbeam understorey. The stands in Louvain-la-Neuve and Virton were both more or less even-aged stands dominated by European beech but differed in their age, with much older trees in Louvain-la-Neuve than in Virton (130 vs. 60 years old in 2009). All stand characteristics are provided in Table 2.
Initial stand characteristics for the main tree species and for the whole stands.
Soil and meteorological characteristics of the different study sites (2001–2016 period).
The Baileux, Chimay and Virton stands were all located on Cambisol but with some nuances, ranging from Dystric to the Calcaric variants in Chimay and Virton, respectively, while an Abruptic Luvisol was found in Louvain-la-Neuve (FAO soil taxonomy). All sites presented a moder humus, except Virton for which mull was observed. In Baileux, Chimay and Louvain-la-Neuve, the soil developed from the parent bedrock mixed with aeolian loess deposition that occurred at the interglacial period. In Virton, the soil originated only from the bedrock weathering. The parent materials were sandstone and shales, clayey sandstone, and hard limestone bedrocks in Baileux, Chimay and Virton, respectively. In Louvain-la-Neuve, the soil was almost exclusively built from the loess deposits. These differences in parent material generated contrasting physical and chemical soil properties (Table 3).
The soil textures also varied significantly among sites. Based on the USDA taxonomy, the soil texture was silty clayey loam and silty loam in Baileux and Louvain-la-Neuve, respectively. In Chimay and Virton, finer soil textures were observed, with a clayey loam and a clay texture, respectively. In relation to the texture, drainage was good in Baileux and Louvain-la-Neuve, while the presence of inflating clay triggered the appearance of a shallow water table during the wet period and drought cracks during summer in Chimay. In Virton, despite the high clay content in the lower horizons, drainage was good due to the existence of faults in the bedrock (Table 3).
Finally, stoniness and drainage influenced the estimate of the maximum extractable water reserve. While the beech-dominated and mixed stands in Baileux and in Virton showed the lowest water reserve, the highest value was found in Louvain-la-Neuve, with intermediate values for the oak stand in Baileux and in Chimay (Table 3).
Even if the same type of climate occurred all over Belgium (temperate
oceanic), the study sites were located in different bioclimatic zones (Van
der Perre et al., 2015). Louvain-la-Neuve was in the Hesbino-Brabançon zone with the highest
average temperatures (11.0
For Chimay, Louvain-la-Neuve and Virton, we used data from the meteorological stations of the Pameseb network. The records covered the 1999–2018 period. A tipping bucket located at 1 m height was used to monitor rainfall. Global radiation was registered with a pyranometer; air temperature was registered with a resistance sensor thermistor; relative humidity was registered with a psychrometer; wind speed was registered with an anemometer. All of these devices were placed at 1.5 m height. Data were collected at 12 min intervals and were then averaged hourly. For Baileux, an independent meteorological station managed by our laboratory has been used to collect meteorological data since 2002. The devices were identical to those described before. Air temperature, relative humidity and rainfall were monitored at 1.5 m. Wind speed and global radiation were taken at 2.5 m above the ground.
The various routines to calculate the budburst starting date were tested, and the two-phase model with the optimum response function for chilling was retained for the evaluation of the water balance module, as this approach performed better (see Sect. 3.1.1).
The phenological observations available on the level II sites of Chimay, Louvain-la-Neuve and Virton were used to evaluate the model predictions. These phenological observations were carried out on 20 dominant and co-dominant sessile oaks in Chimay (2012–2014) and 20 dominant and co-dominant European beeches in Louvain-la-Neuve and Virton (2012–2016) according to the ICP Forests manual (Beuker et al., 2016). They consisted of weekly observations of the percentage of budburst, yellowing and leaf fall, depending on the season. As the model predicted the budburst for an average tree, we evaluated it with the budburst observations of the median tree. In addition, we visually assessed the agreement between the predicted and observed increase in leaf biomass proportion (leafProp) during the leaf development period and between the predicted and observed decrease in green leaf proportion (greenProp) and in leafProp during leaf yellowing and leaf fall, respectively. We did not perform a statistical evaluation for these latter variables as the corresponding processes were not calibrated independently in the model. Finally, as there were no data available for trees of different social status, we could not directly evaluate the option Phenology at tree level. We evaluated however its impact on tree growth predictions for the three stands in Baileux.
Regarding the water balance module, the evaluation was conducted using variables integrating most of the processes described in the model. The observed throughfall, extractable water dynamics, individual transpiration and deep drainage (considered in the next section) were compared to model predictions. For the evaluation of the throughfall, extractable water and drainage predictions, we used simulations carried out at the stand scale since the corresponding observations cannot be related to a particular tree. Regarding individual tree transpiration, the approaches at the two scales were compared (tree vs. stand).
For the evaluation of throughfall predictions, only independent throughfall data collected in Chimay, Louvain-la-Neuve and Virton between 2000 and 2016 were used, as the rainfall partitioning routine was calibrated based on data from the Baileux forest (André et al., 2008a, b). The collecting devices consisted of three long gutters connected to plastic barrels. The throughfall volume was measured weekly based on the height of water in the barrels. A log transformation of both the observations and the predictions was necessary to remove the heteroscedasticity.
Individual tree transpiration predictions were evaluated against observations derived from sap flux measurements. These measurements were taken on 16 sessile oak and 16 European beech trees of different sizes in the three stands of Baileux between April and September 2003 (Jonard et al., 2011).
Extractable water was estimated based on Eq. (80) using soil water content measurements taken between 2005 and 2017 in Baileux and for the 2015–2018 period in the other sites. Soil water content was measured hourly using a thermo-time domain reflectometer (TDR) inserted in some horizons (measurements at three to five different soil depths depending on the site). In order to decrease the influence of the soil disturbance due to the instrument installation, the first year of records was discarded. Indeed, Walker et al. (2004) showed that inserting a moisture sensor in a soil disturbed its hydraulic properties and water content during at least 9 months. The electrical signal from the TDR was transformed into relative dielectric permittivity and then converted into soil volumetric water content (in cubic metres per cubic metre) using the equation of Topp et al. (1980) for Baileux and resorting to our own calibration for the other sites (established based on gravimetric measurements of soil water content).
Deep drainage can represent a large water output but is difficult to measure
directly. Among the existing indirect approaches to estimate this component,
we retained the mass-balance method using chloride ion (
To test the quality of the predictions, different statistical tests and
indices were used. The absolute bias, defined as the difference between the
mean observation and prediction, and the relative bias, corresponding to the
ratio between the absolute bias and the mean observation, were calculated to
detect any over- or underestimation. To assess the precision of the
predictions, the root mean square error (RMSE) was used and calculated as
follows:
When the range of values differed considerably for one variable between the different sites, the RMSE was divided by the range, i.e. the difference between the maximum and the minimum values. This normalized root-mean-square error (NRMSE) is much more adapted for comparisons in these situations.
The agreement between observations and predictions was also evaluated with
the Pearson's correlation coefficient (
On average, the budburst was best predicted with the two-phase model with
the optimum response function for chilling (bias
Comparison of the observed and predicted budburst of the
median tree in Chimay, Virton and Louvain-la-Neuve for the three
phenological variants implemented. The quality of the predictions is
indicated by the RMSE, the absolute bias and the
Pearson's correlation coefficient (
Observed and predicted increase in leaf proportion in Chimay, Louvain-la-Neuve and Virton during the budburst and leaf development phase (data from 2012 to 2016). Observations are missing in Chimay for 2013, in Louvain-la-Neuve for 2012 and 2013, and in Virton for 2013.
Simulated leaf yellowing and leaf fall were also evaluated by comparison with observations. While the leaf ageing threshold was taken from Dufrêne et al. (2005), the yellowing parameter determining the length of the yellowing period was adjusted with the 5 years of data from Chimay (sessile oak), Louvain-la-Neuve and Virton (European beech). Therefore, only the yellowing start was independently evaluated. The prediction of the start of the yellowing displayed a low absolute bias (2.7 d) and RMSE (7.0 d). However, a weak correlation (0.056) was found between predictions and observations (data not shown).
For the temporal dynamics of leaf yellowing and leaf fall, the agreement between model predictions and observations was just assessed visually since the parameter regulating these processes (yellowing, falling rate and falling frost amplifier) were adjusted with the same data. The overall agreement was good. The simulated decrease in green leaf proportion was similar for all sites as the photoperiod reduction is identical for each site and year (Fig. 4a, c and e). The only noticeable difference came from the yellowing starting date, which depended on air temperature. For Chimay (sessile oak), a close agreement was found between predictions and observations. For Louvain-la-Neuve (European beech), predictions were correctly centred, but the predicted trend was more abrupt, and the start of the decrease displayed some delay, except in 2012. For Virton (European beech), the decreasing trend was correctly displayed, but the decrease start was less precise in 2016 (Fig. 4e).
Observed and predicted temporal dynamics in leaf yellowing
and in leaf fall in Chimay, Louvain-la-Neuve and Virton (data from
2012–2016). Yellowing is represented by the decrease in green leaf
proportion
Concerning the leaf fall, the temporal dynamics were correctly represented in Chimay (sessile oak). In Louvain-la-Neuve (European beech), the model predicted a slightly too slow decrease in leaf proportion in 2012 and 2015. For the other years, the observed and predicted leaf proportion matched well even if the predicted start of the fall appeared later than in the observations for some years. In Virton (European beech), the predictions were well centred with regard to the observations, but the decrease in leaf proportion was a bit too fast in 2012 (Fig. 4b, d and f).
The option phenology at tree level was used to test if the agreement between predicted and observed basal area increment could be improved. With the default phenology option, HETEROFOR tended to overestimate the growth of dominant trees and underestimate that of suppressed trees (Jonard et al., 2020a). With the option phenology at tree level, this bias was partially resorbed. The slope of the Deming regression went from 0.74 to 0.84 for sessile oak and from 0.79 to 0.88 for European beech, being much closer to the identity line (Appendix D). This was however at the price of slightly lower Pearson's correlation coefficients.
For each site, the main water fluxes affecting the water balance were calculated daily, summed up and the annual values were averaged for the 2002–2016 period (Table 4). Depending on the site, 65 % to 78 % of the rainfall reached the floor as throughfall and 6 % to 13 % as stemflow. The remaining 16 % to 22 % was intercepted by the tree foliage and the bark and evaporated. Then, 31 % to 45 % of the water received as rainfall returned in the atmosphere through tree transpiration. The remaining 26 % to 44 % was lost from the ecosystem through drainage.
Rainfall partitioning was correctly reproduced by the HETEROFOR model.
Across all considered sites (Virton, Chimay and Louvain-la-Neuve), the mean
bias of throughfall predictions was very limited (
Comparison of the observed and predicted daily
transpiration of sessile oak and European beech in 2003, considering the tree
and the stand scale for the water balance calculation. The quality of
predictions is indicated by the RMSE, the
relative bias and the Pearson's correlation coefficient
(
Temporal dynamics of observed and predicted extractable
water amount (in millimetres) in the various stands. The prediction quality is indicated
by the NRMSE, the relative bias and the Pearson's
correlation coefficient (
The model reproduced well the individual transpiration for sessile oak and
European beech in the Baileux site (in 2003), with similar performances at
the tree and stand scale (Pearson's
As the temporal variation in the extractable water was affected by all the
water fluxes, it was used to check the performances of the water balance
module (Fig. 7). A clear seasonal pattern appeared. At the beginning of the
vegetation period, the extractable water (EW) values were highest. Then, tree
and ground vegetation transpiration progressively depleted the water reserve,
which was partly recharged with rainfall events. Depending on their
frequency, duration and intensity, the decline in EW was more or less
pronounced, and available water could reach levels close to zero. For all the
sites, the Pearson's correlation between observed and predicted relative
extractable water ranged from 0.893 to 0.950. These high correlation values
and the graph inspection show that the seasonal pattern was precisely
reproduced by the HETEROFOR model. NRMSE values range from 10.54 to 13.96 %, while relative bias values were around
The predicted deep drainage was compared with estimates calculated on a
yearly basis using Cl as a tracer. The RMSE (100.6 mm) and the bias (
In order to predict the impact of global changes on forests, it is crucial to integrate and structure the existing knowledge in process-based models. However, this first step is not sufficient. A detailed documentation of the models and an evaluation of their performances are also needed in order to use them while knowing exactly their strengths and limits. While most models were described in scientific articles or reports, their evaluation was often limited to one or two sites used to illustrate the model functioning and were generally based on integrative response variables such as radial tree growth (Vanclay and Skovsgaard, 1997; Schmidt et al., 2006). Yet, to provide robust predictions of tree growth under changing conditions, the model must be able to accurately reproduce not only the observed tree growth but also the intermediate processes describing resource availability (light, water and nutrients) (Soares et al., 1995). In the following section, we discuss the quality of the predictions for two main drivers of tree growth (phenology and water balance) in relation with the concepts used to describe them.
The two-phase model with the optimum response function for chilling was the least-biased variant for predicting budburst. However, the one-phase model including only the forcing period better captured the interannual variability. While the bias is likely to originate from the model calibration (data used for calibration were observations from western Germany) and could be corrected, the ability of the model to predict temporal variability is more representative of its structural quality. It is common that models accounting only for the forcing period better represent the observations of budburst temporal variability (Leinonen and Kramer, 2002; Fu et al., 2014; Basler, 2016). Two reasons can explain this. First, in areas where the chilling requirements are always met as in western Europe, the chilling parameters are not constrained enough by the observations and therefore are more difficult to calibrate. When few phenological observations are available, taking the chilling into account increases the model complexity without improving the accuracy of the predictions (Leinonen and Kramer, 2002; Fu et al., 2014). Secondly, two-phase models predict the break of endodormancy (end of chilling) and the start of budburst, while they are only calibrated from budburst observations. When endodormancy break observations are used for the calibration, the chilling parameters are estimated more accurately (Chuine et al., 2016), but these data are difficult to obtain and consequently very scarce (Jones et al., 2013).
Similarly to Chuine et al. (2016), we advise using a two-phase model (with the optimum response function for chilling) when endodormancy break observations are available or for long-term simulations with climate conditions beyond the range used for the model calibration. For example, for trees located at the southern margins of their species distribution area, the expected rise in winter temperature could prevent the fulfilling of their chilling requirements and inhibit budburst (Clark et al., 2014). This phenomenon would only be captured by a two-phase model. When few phenological data are available for calibration, the one-phase model should be preferred, especially for simulations with climate conditions similar to those used for the calibration. This highlights the importance of having both one and two-phase options to describe budburst. Most process-based models listed in Table 5 had however only one phenological variant except 4C.
Predicted annual water fluxes and the corresponding
percentage of rainfall in brackets for the different study sites during the
period 2002–2016. The minimum, maximum and mean values from literature are
indicated with the number of studies (
Papers included in the literature review: Cepel (1967), Aussenac (1968, 1970), Lemée (1974); Nagy (1974); Szabo (1975); Aussenac and Boulangeat (1980); Matzner and Ulrich (1981); Rowe (1983); Bücking and Krebs (1986); Gerke (1987); Giacomin and Trucchin (1992); Neal et al. (1993); Leuschner (1994); Ulrich et al. (1995); Heil (1996); Tarazona et al. (1996); Bellot and Escarre (1998); Didon-Lescot (1998); Herbst et al. (1998); Nizinski and Saugier (1998); Forgeard et al. (1980); Granier et al. (2000); Bent (2001); Michopoulos et al. (2001); Knoche et al. (2002); Mosello et al. (2002); Dripps (2003); Bastrup-Birk and Gundersen (2004); Hanson et al. (2004); Ladekarl et al. (2005); Schipka et al. (2005); Vincke et al. (2005); Carlyle-Moses and Price (2006); Christiansen et al. (2006); Roberts and Rosier (2006); Schmidt (2007); Herbst et al. (2008); Staelens et al. (2008); Ahmadi et al. (2009); Müller and Bolte (2009); Risser et al. (2009); and Gebauer et al. (2012).
A possible improvement of the two-phase phenological models would be to integrate the photoperiod effect on budburst. Indeed, some recent studies have shown evidence that photoperiod can compensate for a lack of chilling temperature that would prevent the buds from opening and for an early frost episode that would trigger budburst before winter (Vitasse and Basler, 2013; Pletsers et al., 2015). This mechanism is particularly present for late-successional species like beech and oak trees and is regularly cited as a key element used to simulate the phenology under climate change (Basler and Körner, 2012). Some models tried to account for the photoperiod effect simply by replacing chilling by photoperiod (Kramer, 1994; Schaber and Badeck, 2003) but, in this way, failed to represent the combined effect of these variables. Recently, a few models integrating the compensatory effect of photoperiod on chilling have appeared. However, these models include more phenological parameters for similar predictive ability (Gauzere et al., 2017). It remains indeed difficult to disentangle the co-varying effect of chilling and day length with in situ measurements (Flynn and Wolkovich, 2018) since photoperiod variations only occur for sites with different latitudes where other confusing factors play a role as well (Primack et al., 2009). Therefore, a large quantity of data are necessary to calibrate these models. Therefore, we decided to favour the accuracy of our phenological model with a more process-based approach, but we are looking forward for improvements in these kinds of models and a more consensual body of literature.
The better growth predictions obtained for the small trees when the phenology was calculated at the individual scale highlight the importance of the “phenological avoidance strategy” displayed by understory trees. This had already been mentioned by Lopez et al. (2008) who observed that early-leafing species received between 45 % and 80 % of their photon flux during the budburst period. Moreover, a simulation study showed that a 1-week (2-week) lengthening of the understory vegetation period with regard to the overstorey in both spring and autumn generated a productivity increase of 32 % (55 %) on such a short period (Jolly et al., 2004).
In a first step, the annual water fluxes predicted by HETEROFOR were compared to measurements and predictions of other studies (Table 4). Then, some water fluxes were individually evaluated when data were available. Finally, some potential improvement of the water balance module were discussed.
Various studies were taken from the literature to compare our water module predictions with observations. They cover a range of annual rainfall comprised of between 425 and 1476 mm (Table 4), which is comparable to what can be found in Belgium. The proportions of rainfall converted to stemflow obtained with HETEROFOR (6.1 % to 13.1 %) are within the range reported in the literature (0.6 % to 20.4 %). This large observation spectrum comes from the important seasonal (higher stemflow proportion in winter than during the vegetation period) and species differences (stemflow importance is higher for beech than oak trees), which are accounted for in HETEROFOR. However, the mean value from the literature (7.3 % of rainfall) is close to the average value for the six study sites (10.3 %). The proportions of intercepted rainfall (15.9 % to 22.0 %) and throughfall (64.8 % to 78.0 %) are also consistent with the ranges reported in other studies (1.9 % to 31.0 % and 59.8 % to 83.1 %). Moreover, we observed a good matching between the average values (respectively 19.5 % and 73.8 % from literature and 19.4 % and 70.2 % for our study sites). For transpiration, the range found in the literature is large (14.8 % to 52.3 %, with an average value of 31.9 %), which is not surprising since interannual and intersite variabilities are high for this variable (Schipka et al., 2005; Vincke et al., 2005). The predicted transpiration proportions are less variable (31.2 % to 44.9 %) and their average value of 36.0 % is slightly above to the mean observed transpiration (31.9 %). Regarding drainage, no direct measurements can be made; all the estimates from the literature come from indirect methods or modelling also subject to uncertainties. The range of drainage values reported in the literature (13 % to 70 %) is very large and contains the range obtained with HETEROFOR (26.3 % to 44.2 %). The mean predicted drainage (39.7 %) is close to the mean value of the literature (37.5 %). By this comparison with the water fluxes reported in the literature, we show that HETEROFOR provides plausible estimates of the various components of the water cycle.
Comparing predicted and observed throughfall is interesting for the evaluation of the
water balance module since throughfall is an integrative variable depending
on the water storage capacity of foliage, on evaporation and on the
proportion of stemflow. The good agreement between observations and
predictions indicates that the partitioning of rainfall when passing through
the canopy and the evaporation of the water intercepted by foliage and bark
are described well. Among the different models of Table 5, no one
accounts separately for stemflow and throughfall, but other models not
included in the list consider the two fluxes separately (e.g. Gotilwa
HETEROFOR satisfyingly reproduced individual tree transpiration with similar prediction quality for the tree and stand approach regarding the water balance calculation. For European beech, the water balance calculation at the tree scale allowed even the correction of the small bias which appeared with the stand approach (Fig. 6). The year selected for the simulation (2003) was particularly dry and hot during summer, which allowed a large range of meteorological and soil water conditions to be covered. It is indeed interesting to test the tree approach under dry conditions since horizontal water redistribution is much less efficient in this case.
Twenty to thirty percent of the transpiration variability remained unexplained by the model, which can be partly ascribed to model inaccuracies but also to the large uncertainty associated with the sap flux measurements. Among other things, the measurements made by Jonard et al. (2011) did not take the azimuthal variation in the sap flux into account since only one sensor per tree was installed.
This first evaluation of tree transpiration predictions indicates that no loss of precision occurred with the tree scale approach, while this detailed spatial representation could have increased the variability in transpiration predictions since it generated some heterogeneity in soil water availability (Appendix C). These good results show that the water balance calculation at the tree scale provides a promising tool to better understand the individual variability and local environment effects on tree water use and sensitivity to drought. This must be considered in a dynamics of continuous improvement of the model and will require more transpiration measurements and in-depth comparisons of predictions and observations.
The amount of extractable water (EW), directly influenced by tree transpiration and soil evaporation, is also a key element of the water cycle, driving, among other things, the drought resistance of a stand. The temporal dynamics of EW was captured well by HETEROFOR, as evidenced by the high correlations (Pearson's coefficient was between 0.893 and 0.950) between observed and predicted EW for the various study sites (Fig. 7). These correlations are within the high end of the range reported for similar models. With the BALANCE model, Grote and Pretzsch (2002) obtained a Pearson's correlation of 0.85 between the observed and predicted soil water content of the upper soil (0–20 cm horizon) in a beech forest in Germany (Freising). Applying BALANCE on three broadleaved stands of oak or beech in Germany, Rötzer et al. (2005) were also able to correctly reproduce soil water content dynamics but mentioned a significant decrease in the quality of predictions during the 2003 drought due to an overestimation of the soil drying, which was not observed with HETEROFOR in 2018. Comparing the observed soil water content at various soil depths with that predicted by the 4C model in mixed oak and pine forest (Brandenburg, Germany), Gutsch et al. (2015) obtained Pearson's correlations ranging from 0.59 to 0.74. In an oak stand in Tennessee (USA), Hanson et al. (2004) compared the ability of nine process-based forest models to reproduce soil water dynamics in the 0–35 cm horizon of the soil and obtained correlations ranging from 0.81 to 0.96.
In the study of Hanson et al. (2004), relative bias was evaluated as well
for soil water content and ranged between
Comparison of the spatial scale (S: stand;
C: cohort; I: individual; and I
Simplifications and errors in the model conception may also generate divergence between observations and predictions. However, this structural uncertainty can be limited by selecting the most appropriate concepts. HETEROFOR predicts water transfer between soil horizons using the Darcy law. We tried to implement an approach of intermediate complexity between simple bucket models and the Richards equations. From a theoretical point of view, the Richards approach is the most state-of-the-art but requires very long calculation times (Fatichi et al., 2016) and is usually implemented in models specifically dedicated to water flow simulations (in Table 5, only one of the models, MAESPA, uses them). Forest ecosystem models generally use simpler approaches such as the bucket model declined in a large variety of forms (Table 5). These models consider one or several buckets with a specified water storage capacity that is filled with rainfall and is emptied by evapotranspiration. If the soil water content is at field capacity, water is transferred to the underlying layer and finally lost by drainage. Improved versions can account for transfer between buckets in unsaturated conditions using the Darcy law (leaky bucket model).
Our water transfer routine discretizes the soil in horizons whose thickness varies from a few centimetres (upper horizons) to half a metre (deeper horizons). Compared to the numerical resolution of Richards equation, which requires thin soil layers (1 to 2 cm), our vertical discretization of the soil profile is quite coarse and inaccurately predicts the advance of the wetting front. As the tree transpiration and photosynthesis depend on the soil water conditions of the whole soil profile, this inaccuracy has very limited implications on the simulated tree growth. In our approach, water transfer during a time step is calculated based on the horizon water potentials estimated at the end of the previous time step. As such, the model makes the hypothesis that the water content does not change significantly during the time step, which is certainly not the case close to the wetting front and cannot ensure mass conservation. In order to limit this problem, the model uses an adaptive time step estimated based on the Peclet number described in Eq. (77). This allows mass conservation to be ensured.
Finally, another reason that could explain the discrepancy between predictions and observations is the presence of macropores that cause preferential flows. These water fluxes defined as water movements in the soil along preferred pathways that bypass the soil matrix (Hardie et al., 2011) can be generated by soil shrinkage, root growth, chemical weathering, cycles of freezing and thawing or bioturbation (Aubertin, 1971). These macropores are more frequent in forest soils than in agricultural soils as the latter are often ploughed and homogenized. They are however difficult to characterize given their strong spatial heterogeneity in both vertical and horizontal directions (Aubertin, 1971). Adaptations of the Richards equations can be used to account for the preferential flows (dual porosity and dual permeability) but require a good characterization of soil macropores (not possible to achieve routinely in forest soils given their heterogeneity) and are still more complicated to solve than the classical Richards equations. We implemented in the model the transfer of the soil water surplus (when water saturation is reached) to the underlying horizon and the possibility to redirect part of this surplus as deep drainage to account empirically for preferential flows. Indeed, preferential flows in macropores become significant only when rainfall exceeds the water infiltration rate in the soil matrix and accumulates in the soil surface. The fraction of the water surplus considered as preferential flows is an empirical parameter reflecting the macroporosity of the site.
The performances of the soil water transfer routine can also be checked
based on the deep drainage flux. In this study, we compared the deep
drainage estimated with HETEROFOR and with the chloride mass balance
approach. The mean drainage predicted with HETEROFOR was 379 mm yr
On the other hand, modelling errors could explain the bias presence. One of them could be the overestimation of the transpired water amount. However, deep drainage tends to produce during winter, while transpiration only takes place during the vegetation period (spring and summer). Therefore, if transpiration was overestimated we should observe an underestimation of the EW during spring and summer (low values), which is not the case (Fig. 7).
Hanson et al. (2004) measured deep drainage at the watershed level by
accounting for rainfall and stream flow outputs and compared their
measurements with the predictions of several models. Their multimodel
comparison displayed similar RMSE (65.5 to 225.6 mm) and relative bias (
Increasing the functional trait diversity and promoting uneven-aged stands are among the management strategies that foresters can use to make their forests more resistant to stressful conditions and more resilient after a disturbance (Pedro et al., 2015; Jactel et al., 2017; Anderegg et al., 2018). With the growing interest for mixed and uneven-aged stands, various attempts have been made to better account for stand structure in process-based forest models. Some of these models present very detailed 3D representations of individual tree structure but describe generally only specific physiological processes (e.g. LIGNUM, EMILION and MAESPA). Such models are very useful tools for analysing outcomes of ecophysiological experiments and obtaining a better understanding of specific ecophysiological processes (e.g. drought sensitivity) in structurally complex stands. Since they are generally computationally expensive and applied to one or a limited number of individuals, they can however not be used for simulating long-term forest dynamics according to various climate and forest management scenarios. Other individual-based models can be applied on all the trees of a stand in long-term simulations but at the cost of a coarse representation of physiological processes (e.g. SORTIE/BC). These models are interesting for the analysis of tree growth dynamics in heterogeneous forests but are less suitable for taking into account the changing environment. Since they simplify stand structure representation, cohort-based models can afford a detailed process-based description of the main processes involved in tree growth (e.g. 4C, ANAFORE, PSIM-DNDC and 3D-CMCC; see Table 5 for model characteristics). Here, the compromise is made on the spatial representation, which accounts for the vertical gradient in growing conditions but not for the horizontal heterogeneity. Such models can indeed not distinguish between stands composed of the same trees but with various degrees of spatial aggregation (e.g. intimate vs. patch-wise mixture). Similarly, some individual-based models choose to sacrifice the horizontal heterogeneity of some processes (e.g. iLand and Hybrid, which calculate most of the water balance at stand scale; see Table 5 for model characteristics).
To simulate the impact of management in heterogeneous forests under changing conditions, we developed a spatially explicit individual-based approach designed to account for individual variability, local environment and adaptive behaviour of trees (Berger et al., 2008). The compromise was not achieved by strongly reducing the complexity of a particular aspect (spatial representation, process description or spatial or temporal coverage), but instead we tried to develop a balanced approach in which each aspect is described with the same level of complexity.
Among the existing individual-based models, BALANCE and NOTG-3D are close to HETEROFOR since they were designed according to the same philosophy. They present however some substantial conceptual differences (Table 5). Except BALANCE for leaf yellowing, HETEROFOR is the only model determining budburst, leaf yellowing and fall at the tree level. While rainfall partitioning is only calculated in HETEROFOR, the spatial representation of local climate conditions in the canopy is finer in BALANCE and NOTG-3D, which consider different canopy layers or voxels. Regarding transpiration, HETEROFOR and BALANCE implement the widely used Penman–Monteith equation, while it is determined as part of detailed energy budget in NOTG-3D. Finally, they all describe soil water dynamics at the individual scale, but HETEROFOR displays a more mechanistic approach for describing soil water transfer among horizons (bucket vs. Darcy model).
In HETEROFOR, some processes were described at two spatial scales (tree or stand level) in order to have the opportunity to compare the two approaches and choose the most appropriate one depending on the pursued objective. The phenological timing is species dependent and can optionally vary with tree size. This option (phenology at tree level) is very interesting since it accounts for both the ontogeny effect and the vertical gradient in climate conditions. With this option, a longer vegetation period is assigned to the understory compared to the overstorey, which allows for the improvement of radial growth predictions by correcting the growth underestimation in small trees and the overestimation in bigger ones (Appendix D). This first attempt to describe phenology at tree scale is quite empirical and could be adapted in the future as knowledge on inter-individual phenology differences improves. Individual phenology observations for trees of all social status will be necessary to better calibrate and evaluate this module in an iterative cycle of model improvement.
For the water balance, HETEROFOR accounts for a direct tree size effect on stomatal conductance (stomatal conductance is inversely proportional to the height of largest crow extension) and for an indirect effect on the sapwood to leaf area ratio whose components both depend on tree size (Jonard et al., 2020a). In addition, individual transpiration is a function of the radiation intercepted by the tree, the local wind speed and the soil water availability. Finally, the tree adaptive behaviour to the local environment is described by an adaptation of the foliage biomass to local competition conditions and by specific leaf area varying with crown position within the canopy (Jonard et al., 2020a). Whatever the considered scale (tree or stand), HETEROFOR was able to correctly reproduce individual tree transpiration. Additional sap flux measurements as well as a characterization of the horizontal soil water content heterogeneity (using ground-penetrating radar tomography – GPR – technique for example) would be very useful to further evaluate the model performances and still enhance its ability to describe the complex hydrological functioning of heterogeneous forest. Among the possible improvements, mortality representation could be enhanced by considering hydraulic failure during severe droughts (Martin-StPaul et al., 2017). Another model improvement would be to take the interaction between the water cycle and the phenology into account by integrating a drought effect on budburst, leaf yellowing and fall as reported in some observation studies (Sanz-Pérez and Castro-Díez, 2010; Xie et al., 2018).
In this paper, two key modules of HETEROFOR are described in detail and evaluated in four sites/six stands. The phenological module correctly predicts the leaved period, which is essential to simulating light interception by trees, evapotranspiration, photosynthesis and respiration. With the hydrological module, HETEROFOR properly estimates rainfall interception, individual transpiration, soil water and deep drainage. Reproducing correctly the soil water dynamics is necessary to adequately predict photosynthesis since stomatal conductance closely depends on it. In addition, the description of the nutrient cycling requires accurate estimates of the water fluxes since water is the main vehicle for nutrient transport.
Our spatially explicit individual-based approach allows for a description of the phenology and water balance in structurally complex stands by partly accounting for the tree size effect on phenology and on tree transpiration, for the local environment modification (radiation and water availability) and for the adaptive behaviour of trees to local conditions (e.g. tree leaf area). Given the complexity of the functioning of heterogeneous forests, there are still a lot of ways to explore for improving the model, which will be done progressively as part of an iterative approach based on the comparison of predictions with observations. Our model will also be used to compare various spatial representation scales (tree, cohort, stand) and to determine the most appropriate one depending on the considered process and the pursued objective.
Simulating resource availability properly is necessary to produce robust predictions of tree growth under changing climate conditions. The next steps will be to extend the model validation to other European sites in order to cover a larger range of ecological conditions and to use HETEROFOR to simulate stands dynamics under various management options and climate scenarios.
Description of some model parameters for European hornbeam (regarding light interception, respiration, carbon allocation and tree dimension increment) and origin of their value.
Comparison of the log-transformed observed and predicted monthly throughfall in Chimay (sessile oak), Louvain-la-Neuve (European beech) and Virton (European beech) between 2000 and 2016. The shaded area represents the confidence interval of the Deming regression (95 %) of observations on predictions, and the solid line corresponds to the identity line.
Temporal dynamics of soil-extractable water simulated with the tree approach in the three stands of Baileux for 2003. The shaded area represents the 80 % confidence interval of the values obtained for the various pedons. For comparison, the mean extractable water calculated with the stand approach is represented with a dashed line.
Comparison of observed and predicted basal
area increments for sessile oak and European beech considering the two
phenology modalities (tree vs. stand scale). The quality of predictions is
indicated by the Pearson's correlation coefficient (
The source codes of Capsis and HETEROFOR are accessible to all the members of
the Capsis co-development community. Those who want to join this community
are welcome but must contact François de Coligny (coligny@cirad.fr) or
Nicolas Beudez (nicolas.beudez@inra.fr) and sign the Capsis charter
(
The end users who do not need access to the source code can install Capsis
from an installer containing only the HETEROFOR model, while the modellers
who signed the Capsis charter can have access to the complete version of Capsis with all the models. Depending on your status (end user vs. modeller or
developer), the instructions to install Capsis are given on the Capsis
website (
The data used in this paper are available through the input files for HETEROFOR which are embedded in the installer (see Sect. 6).
LdW, MJ, FA, NB and FdC developed the model code. LdW performed the simulation and analysed the model outputs. LdW and MJ prepared the paper with contributions from all coauthors.
The authors declare that they have no conflict of interest.
We are grateful to the two anonymous reviewers whose suggestions and comments help us to significantly improve the quality of this paper. We also would like to thank Mathieu Javaux for his sound advice on modelling water flows in the soil.
This research has been supported by the Fonds De La Recherche Scientifique – FNRS, Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (grant no. 1.E005.18), the Service Public de Wallonie (SPW/DGO 3/DNF) (Accord-Cadre de Recherche et Vulgarisation Forestières 2014–2019) and the Fonds De La Recherche Scientifique – FNRS (PDR-WISD; SustainFor project).
This paper was edited by Min-Hui Lo and reviewed by Rüdiger Grote and one anonymous referee.