Mathieu Jonard, Frédéric André, Louis de Wergifosse Université Catholique de Louvain, ELI-e

HETEROFOR is a spatially-explicit and process-based model describing individual tree growth based on resource sharing (light, water and nutrients) in uneven-aged and mixed stands. HETEROFOR was progressively elaborated through the integration of various modules (light interception, phenology, water cycling, photosynthesis and respiration, carbon allocation, mineral nutrition and nutrient cycling).

HETEROFOR was developped to account for interactions between individuals of different tree species and of different size and to take global change (especially climate change) into account. In addition, HETEROFOR allows to better understand tree response to water and nutritional stresses. The spatial scale considered is the stand (0.5 to 5ha) and the time scale ranges from a decade to a century.

For example, it is used to predict change in tree species composition in pure and mixed stands of oak and beech in the Belgian Ardennes and to analyze how competition between the two tree species will evolve according to different climate and sylvicultural scenarios.

For the initialization, HETEROFOR downloads a series of files containing tree species parameters and input data on tree location, dimensions and chemistry, chemical and physical soil properties and open field meteorological conditions (hourly time step). These data are used to create trees and soil horizons at the initial step. Then, HETEROFOR predicts tree growth at a yearly time step.

At the end of the initial step and of the next ones (after tree dimensions have been updated), the phenological periods (leaf development, leaf colouring and shedding) are defined for the next step from meteorological data. When no meteorological measurements are available, the vegetation period is defined by the user who provides the budburst and the leaf shedding dates. Knowing the key phenological dates and the rates of leaf expansion, colouring and falling, the foliage state is predicted at any time during the year, which is used to carry out a simplified or detailed radiation budget with the SAMSARALIGHT library of CAPSIS.

Based on a ray tracing approach, SAMSARALIGHT calculates the solar radiation absorbed by the trunk and crown of each individual tree and the radiation transmitted to the ground. This allows HETEROFOR to estimate the proportions of incident radiation absorbed by the trunk and the crown of each tree and the part transmitted to the ground (simplified budget: average values for the vegetation period, detailed budget: hourly values for several key phenological dates). These proportions and the incident radiation measured in the meteorological station are used during the next step to compute the hourly global, direct and diffuse radiation absorbed per unit bark or leaf area. Predicting how solar energy is distributed within the forest ecosystem is necessary to estimate foliage, bark and soil evaporation, tree transpiration and leaf photosynthesis.

Every hour, HETEROFOR performs a water balance and updates the water content of each horizon. Rainfall is partitioned in throughfall, stemflow and interception (Andre et al., 2008a; 2008b and 2011). Part of the rainfall reaches directly the ground (throughfall) while the rest is intercepted by foliage and bark. These two tree compartments both have a certain water storage capacity which is regenerated by evaporation. When the foliage is saturated, the overflow joins the throughfall flux whose proportion increases. When the bark is saturated, water starts to flow along the trunk (stemflow). Throughfall and stemflow supply the first soil horizon (forest floor) with water while soil evaporation and root uptake deplete it. The water evaporation from the soil (as well as from the foliage and the bark) is calculated at stand scale with the Penman-Monteith equation. Using the same equation, individual tree transpiration is estimated by determining the stomatal conductance from tree characteristics and soil extractable water. The distribution of root water uptake among the soil horizons is done according to the water accessibility (evaluated based on the water potential and the vertical distribution of fine roots). Water exchanges between soil horizons are considered as water inputs (capillary rise) or outputs (drainage). This soil water transfers are calculated based on the water potential gradients according to the Darcy law and using pedotransfer functions to determined soil hydraulic properties. ).

The gross primary production of each tree (gpp) is computed with the photosynthesis method of CASTANEA that requires the proportions of sunlit and shaded leaves, the direct and diffuse PAR absorbed per unit leaf area and the relative extractable water reserve. Alternatively, gpp can be predicted based on a PAR use efficiency approach, (eventually also distinguishing sunlit and shaded leaves). This gpp is then converted to net primary production (npp) after subtraction of growth and maintenance respiration. Maintenance respiration is either considered as a fixed proportion of gpp or calculated for each tree compartment by considering the living biomass, the nitrogen concentration and a Q10 function for the temperature dependency. Carbon allocation is made in priority to functional organs (foliage and fine roots) by ensuring a functional balance between carbon fixation and nutrient uptake. The fine root to leaf biomass ratio is a function of the tree nutritional status. Allometric relationships are then used to describe carbon allocation to structural components (trunk, branches and coarse roots) and to derive the growth of the main tree dimensions (diameter at breast height, total height, crown base height, height of largest crown extension, crown radii in 4 directions) while considering competition with neighbouring trees.

Knowing the chemical composition of the tree compartments for a given tree nutrient status, HETEROFOR computes the individual tree nutrient requirements based on the estimated growth rate and deduces the tree nutrient demand after subtraction of the amount of nutrient re-translocated. On another hand, the potential nutrient uptake is obtained by calculating the maximum rate of ion transport towards the roots (by diffusion and mass flow). The actual uptake is then determined by adjusting the tree nutrient demand and growth rate so that tree nutrient demand matches soil nutrient supply. The nutrient limitation of tree growth is achieved through the regulation of maintenance respiration and though the effect of the tree nutrient status on fine root allocation.

The central compartment of the nutrient cycling is the soil solution whose chemical composition is in equilibrium with the exchange complex and the secondary minerals. This compartment receives the nutrient coming from atmospheric deposition, organic matter mineralization and primary mineral weathering, and is depleted by root uptake and immobilization in micro-organisms. The chemical equilibrium within the soil solution, with the exchange complex or the minerals is updated yearly with the geochemical model PHREEQC (coupled to HETEROFOR through a dynamic link library).

This model description is largerly inspired from Jonard et al. (2019) published for interactive discussion in Geoscientifc Model Development.

Jonard, M., André, F., de Coligny, F., de Wergifosse, L., Beudez N., Davi, H., Ligot, G., Ponette, Q., Vincke, C. Submitted to GMD. HETEROFOR1.0: an individual-based and spatially-explicit model for exploring the response of structurally-complex forests to uncertain future conditions. I. Carbon fluxes and tree dimensional growth.