Above-ground modules in Hi-SAFE (Tree phenology, tree C allocation, tree light interception, microclimate) Deliverable D.4.1 (SAFE European Research contract QLK5-CT-2001-00560) Silvoarable Agroforestry For Europe (SAFE) Christian Dupraz, Grégoire Vincent, Isabelle Lecomte, François Bussière, Hervé Sinoquet August 2004 Foreword Hi-SAFE is the detailed 3D process-based biophysical model of the SAFE project. It includes the main tree functions with regard to major resources (carbon, water, nitrogen) and responses to the major climate variables (light, air temperature and humidity). The present text shows how light and carbon acquisition by the trees has been taken into account in the Hi-SAFE module. Requirements of the Hi-SAFE model include sensitivity to a number of environmental and biological factors, and short computation time. THE TREE PHENOLOGY MODULE This module should trigger other modules to give a fair representation of temperate trees phenology. BUDBREAK We suggest to model budbreak date as a function of accumulated temperatures above a threshold. Accumulation start after a starting date. Budbreak module Parameters Date to start accumulation of temperatures Threshold temperature of acronym Value suggested for Hybrid Walnut Unit Ph_Date_Start_Acc_T (Ph_BB_DSAT) 01 January DOY 10°C °C 210 °C-day effective Ph_Budburst_Effective_ T (Ph_BB_ET) Threshold of temperatures Budburst accumulated to trigger Ph_Budburst_Acc_T (Ph_BB_AT) This module triggers the Tree C photosynthesis, Tree water extraction, Tree C allocation, tree growth modules. Related questions : This budbreak module initialises the Carbon pool of the leaves to a starting value. What value? Has this absolute value an impact on the speed of leaf expansion right after budbreak? At the start of the growing season, tree leaf area is mostly formed with C reserves (C labile pool). This is not accounted for by the C allocation module. In what module is tree respiration accounted for? Tree respiration should be activated all the year round, and should therefore not be triggered by the phenology module. END OF LEAF AREA EXPANSION This is a key phenology stage. According to our field observations, the end of leaf extension is strongly dependent on water/nitrogen stress. Even in non limiting conditions for water, nitrogen light and temperature, most temperate tree species exhibit a limited period of leaf expansion. We describe here the end of the first flush of leaf expansion, including preformated and neoformated phytomeres. The C allocation module allocates every day some Carbon to the leaf pool, and will apparently never predict the end of leaf expansion. This was already a poor feature of HyPAR. This should be modified by the phenology module. This phenology module should be able to fairly describe the following situations : A tree with no stress stops expanding leaves anyway at some date A tree with some stress stops earlier to expand leaves It is not possible to use a simple date for stopping leaf expansion (even if this date is predicted from tree stress indexes). Leaf expansion ceases gradually. The phenology module, combined with the C allocation module should result in a sigmoid shape for leaf expansion. We suggest a module using 3 parameters : A fixed date of end of the leaf expansion in non limiting conditions (potential expansion with no water stress, no nitrogen stress). This can be documented by monitoring well cared trees (irrigated, fertilised…). Some tree species may never stop (Eucalypts, Paulownia), but most temperate tree species will stop. Some trees, after a pause, will resume a second flush, but this is beyond the scope of HySAFE, as this is very unlikely in real conditions of AF plantations. A fixed delay between the beginning of the leaf expansion rate decrease until the leaf expansion stop. This is necessary to avoid a sudden stop of leaf expansion. A threshold for accumulated water and/or nitrogen stress to trigger the slow down of leaf expansion. Parameters End of leaf expansion module acronym Date of end of leaf area expansion in no stress conditions Delay for leaf expansion slowing Ph_Leaf expansion_unstressed (Ph_LE_U) Ph_Leaf expansion_delay (Ph_LE_D) Threshold of accumulated Ph_Leaf water stress to trigger leaf expansion_Threshold expansion slowing down (Ph_LE_T) Value suggested for Hybrid Walnut 30 July Unit DOY 15 days To be discussed To be discussed If no stress occur, at a date given by Ph_LE_D - Ph_LE_T, leaf expansion slows down. The rate of leaf expansion can then be linearly decreasing until Ph_LE_U. It must be discussed with Marcel van Oijen where in the C allocation module we should include this impact. The sum of all C allocation coefficient must remain 1. Related questions: Most temperate trees have short shoots and long shoots. The leaf area of a single tree is the sum of the leaf area of short and long shoots. Short shoots end expanding in a short delay (usually less than a month, often about a week as in Wild Cherry). Long shoots expand much more longer. The leaf area of a single tree can be decomposed in two sigmoid curves describing short and long shoot area respectively. A possible strong impact of competitive stress is the demography of short shoots, as was hypothesised in the MODELO approach. Should we include this approach in HySAFE? LEAF-FALL A very simple module could be triggered by the average temperature of the last 15 days. When this temperature falls below a threshold, leafall starts. Using an average temperature over a 15 days period is useful to avoid taking into account short periods of cold days. Leafall is assumed to occur during a fixed maximum time lapse, but a faster leafall will occur if some climatic events occur : high winds, frost. Leafall module (temperature driven) acronym Value Unit suggested for Hybrid Walnut Threshold of temperature Ph_Leafall_Threshold_T 15 °C (average of air temperature (Ph_LF_TT) over the last 15 days) Usual duration of leafall Ph_LF_Duration 15 days (Ph_LF_D) Sensibility to frost or high Ph_LF_Sensibility If frost or Y/N switch winds (Ph_LF_S) winds>10 m.s-1 occur, full leaf fall Parameters Related question However, it must be noticed that our field observations show clearly that leafall is much earlier for trees that experienced high water stress during the growing season. This could be modelled by an accumulated stress index. But how to interfere with the temperature signal? An other approach would be to consider a life expectancy for leaves. This life expectancy would be diminished by accumulated stress. Leaf-fall would occur at the earliest date predicted from the temperature driven module and from the life-expectancy module. Leafall module (life-expectancy driven) Parameters acronym Value suggested for Hybrid Walnut Life expectancy of leaves Ph_Leafall_Life_expectan 210 cy (Ph_LF_LE) Factor to convert Ph_Leaf To be accumulated water stress in expansion_Stress factor discussed a decrease of the life (Ph_LF_SF) expectancy of leaves Unit DOY Day. Stress-1 ROOT PHENOLOGY A similar approach could be developed for root phenology. The current C allocation module will allow root growth all over the growing season, and will prevent any root growth when the trees have no leaves (is that right?). This could be done in a similar pattern as for the leaves phenology modules. For trees that display root growth before budburst or after leaf-fall, C should be allocated from the C labile pool? FRUIT PHENOLOGY It was decided in Clermont-Ferrand to include a simple fruit sink for Carbon and Nitrogen as a forcing variable. Fruit sink volume is a forcing variable and should be provided as a time-series (one value per year), or as a function of tree growth/vigour. It could include an alternate bearing pattern. Fruit sink inception date could be fixed in a first approach, or could depending on climate. Fruit sink end of filling date could also be fixed, or depend on accumulated stress indexes. Fruit phenology (forcing variable) forcing acronym Value suggested for Hybrid Walnut Fruit sink volume C Ph_Fruits_C (Ph_F_C) Depends on tree age Fruit sink volume N Ph_Fruits_N (Ph_F_N) Depends on tree age Fruit sink inception date Ph_Fruits_Start_date 150 (Ph_F_SD) Parameters variable or Unit Kg C Kg N DOY Fruit sink end of filling date Ph_Fruits_End_date (Ph_F_ED) 270 DOY A high priority for fruits may be assumed, or may not be assumed. This has to be decided within the C allocation module, and may involve other parameters. CONCLUSION Several phenology modules require accumulated stress indexes. Stress indexes are a key component of the HySAFE model, but were not discussed up to now. They are essential tools to introduce controls in the integrated model. They should be now defined and agreed. TREE RADIATION INTERCEPTION 1. OBJECTIVES: The radiation interception module is aimed at computing: Incident radiation available to the crop canopy: This is the spatial distribution of the transmitted radiation below the tree canopy. The crop canopy is likely to be divided into strips parallel and perpendicular to the row direction, and the radiation model should compute incident radiation above each crop area. Radiation intercepted by each individual tree defined in the scene: Note that the scene could include only one tree. The radiation model provides inputs for the carbon acquisition module, the water consumption and the canopy microclimate modules. 2. THE HYPAR SOLUTION: In the HyPAR model, radiation interception is computed from the turbid medium analogy, i.e. the model is based on Beer’s law. For computation of available light to the crop canopy, the trees are modelled as simple shapes filled with leaf area turbid medium, while the canopy is divided in cells (max. number 20 x 20). A transmission coefficient of the tree canopy is computed for each canopy cell. Surprisingly, computation of light interception by the trees is made by assuming that trees make a multilayer canopy, i.e. not a discontinuous canopy. Input parameters / variables include: Incident radiation: The sky is assumed to be overcast, so that computations can be made by using the only daily incident radiation (MJ m-2 day-1). Note however that simulated radiation exchanges are insensitive to row direction, day of year nor latitude. Canopy structure: tree dimensions with regard to geometry used to abstract tree shape, tree leaf area, extinction coefficient. Note that the extinction coefficient globally accounts for the effect of leaf angle, foliage clumping and optical properties of leaves. Note also that canopy dimensions must be simulated by the model, namely tree growth and development modules, but I am unsure that any model is able to cope with dynamics of tree dimensions. 3. STATE OF THE ART: The only two ways to simulate radiation exchanges in vegetation canopies are the turbid medium analogy – as used in HyPAR – and ray-tracing and/or projection techniques based on simulated 3D plants. None of the tree models proposed in the literature is able to properly simulate dynamics of the 3D architecture in response to environmental factors; and time needed for light computations on simulated 3D plants is incompatible to the time requirements for Hi-SAFE simulations. The only way is thus to adopt a turbid medium model, although projection models for 3D plants could be used to derive parameters of the turbid medium model. Improvement of the light HyPAR module could be: 1. To use discontinuous tree canopies for both the computations of available light to the crop, and light interception by the trees. 2. To improve the flexibility of the scene definition, i.e. number and location of trees on the scene, and discretisation of the crop canopy. 3. To better take into account the directional components of incident radiation: at least direct radiation coming from the sun direction, and diffuse radiation obeying a classical sky radiance distribution (e.g. Uniform or Standard OverCast distributions). 4. To better define the extinction coefficient, as a function of leaf angle distribution, foliage clumping and optical properties. The rationale to explicit the extinction coefficient is well known, and Goudriaan’s expression (1977) accounting for both leaf angle and optical properties could be used. 4. LIGHT MODEL IN HI-SAFE: Courbaud’s light model (MOUNTAIN, 2003) meets most of the above requirements (namely requirements #1, #2, #3). Moreover, it is written in Java, has been incorporated in the CAPSIS system, and the author was available to help us for code adaptations. The model MOUNTAIN has been therefore chosen to be included in the Hi-SAFE model. As mentioned by its author, this model was developed for spatially heterogeneous coniferous forest canopies. Based on the interception of light rays by parabolic crowns, it calculates simultaneously the energy intercepted by each tree and the distribution of light reaching the ground. Slope and exposure are taken into account as a function of the distribution of incident light rays. An optimisation process that reduces the computing time needed to find trees which intercept a ray and to manage plot boundaries was developed. A detailed description of the model is given in Courbaud et al. (2003). Small modifications to Courbaud’s model have included: o the use of Goudriaan’s expression (1977) for the extinction coefficient. For a given beam direction , the transmission T of light within a crown is computed from Beer’s law as: T exp( K D L) (1) Where the extinction coefficient K is modelled as: K G (2) D is leaf area density within the tree crown (m 2 m-3). L is length on the beam path within the tree crown (m). L is computed from geometry principles, from the intersection points between the crown envelope and the beam line. G is the projection coefficient of leaf area, which depends on both foliage inclination distribution and direction . is the leaf absorptance in the PAR (Photosynthetically Active Radiation) waveband (400-700 nm). Note that beams are regularly spaced, so that a given beam represents a small area Ab. Average light interception I by a tree is therefore expressed in square-meter, i.e. as interception area of the tree I 1 T A b (3) Beams o The sky discretisation according to the turtle concept (Den Dulk, 1989) in order to shorten the number of computed directions and then time computation. The sky vault was characterised by a set of 46 directions. o The computation of both sunlit and shaded leaf area: This is useful since the photosynthesis response to light is not linear. Computation is based on the following equation (see e.g. Sinoquet et al., 1993) I sun K Dsun L (4) Equation (4) simply means that leaf area intercepting light in the sun direction is the sunlit leaf area. Since leaf photosynthesis response is not linear, light interception in Hi-SAFE is computed five times a day, according to the Gaussian integration proposed by Goudriaan. This is a compromise between: o A single simulation run at day scale, which has been shown to overestimate by 20% carbon acquisition by the trees (Fig. 1). o Simulation runs at hourly scale, which would multiply computing time in a way incompatible with simulation time requirements in Hi-SAFE. In order to save more time, light computations are run only when (see Balandier et al., 2000): Trees are leafy. The daily sun course significantly changes, i.e. every 2-3 days near the equinox and every 10 days near solstices. Sensitivity analyses could be performed in order to fit the time interval between light computations. Tree structure shows significant changes, in terms of tree dimension and leaf area. Finally the model outputs are PAR interception by each tree in the vegetation scene and PAR transmission to each crop zone, both for diffuse radiation and direct radiation at the 5 time steps. As radiation variables are proportional to incident radiation, only relative values (i.e. assuming that incident diffuse and direct radiation is equal to 1) are stored in memory. They can therefore be used several days showing different conditions of incident radiation, as long as the sun course or the canopy structure does not significantly change. For each time step, sunlit and shaded area of each tree are also computed (see equation 4). 5. INPUT PARAMETERS REQUESTED: Input parameters for the radiation model are: Incident radiation: This includes at least the daily amount of global radiation (MJ m -2 day-1), and possibly the amount of diffuse radiation (MJ m-2 day-1). If not available, daily diffuse radiation is computed from empirical relationships, given that data of both global and diffuse radiation are available from a weather station. Incident solar radiation is partitioned into PAR (400-700 nm) and NIR (Near Infra Red, 700-1200 nm) components according to coefficients found in the literature (e.g. Varlet-Grancher, 1975). The sun course is computed from astronomical formulae involving site location (latitude) and date in the year. Canopy structure: Canopy structure includes: Dimensions and leaf area of the trees. These parameters must be computed by the tree growth and development modules. Leaf angle distribution, which could be surveyed from measurements in the field. Data are already available for walnut (UMR PIAF, Clermont-Ferrand) and poplar trees (Casella, Forestry Commission, UK). Foliage dispersion parameters, which account for clumping. The dispersion parameters should be derived from a comparison between simulated values of the Hi-SAFE light model and a projection model applied to the 3D mock-ups of the SAFE tree species (UMR AMAP, Montpellier). Optical properties of the leaves: They include leaf reflectance and transmittance. They usually do not show large intra- and inter-species differences. They could however be surveyed in case of the SAFE tree species by using a Li-cor 1800 spectrophotometer equipped with an integrating sphere. Such a device is available in UEPF (INRA Lusignan, contact: C. Varlet-Grancher). Daily climate input : day D Tmin, Tmax (°) - Rhmin, RHMax (%) Global radiation (KW m-2) - PAR (moles m-2) Rain (mm) - ETP (mm) Wind Speed (m s-1) Co2pressure (pa) Daily climate input : day D + 1 Climate generator (using D and D+1) Sun Declination (°) - Day Length (hours) For each time step (X default =5) : - Hour of each time steps - Sun elevation and azimuth (°) - Global PAR (µmol m-2) – Diffuse PAR (µmol m-2) - Temperature (°) Relative Humidity (%) VPD (pa) - Wind Speed (m s-1) First execution YES NO Any leaf in trees ? NO YES leaf NO area > threshold sun declination > threshold YES YES Direct beams set position (X time steps) Direct lighting computation (at each X time step) - direct energy intercepted by each tree (unit?) - direct energy remaining on each cell (%) Diffuse lighting computation (once) - diffuse energy intercepted by each tree (unit) - diffuse energy remaining on each cell (%) Result agregation to have : - % of energy intercepted by each tree (direct+diffuse) - % of energy on each cell (direct+diffuse) NO For X time steps : Tree photosynthesis (µmol m-2 s-1) calculated for shaded leaves (energy used is ....in which unit ?) Aggregation of X results to have a total daily photosynthesis for each tree in µmol m-2 d-1 C allocation module For X time steps : Tree photosynthesis (µmol m-2 s-1) calculated for shaded leaves (energy used is .... in which unit ?) THE CARBON ACQUISITION BY THE TREE 1. OBJECTIVES: The carbon acquisition module is aimed at computing the whole net photosynthesis of the tree at daily scale (gC tree-1 day-1). This module provides inputs to the carbon partitioning module. 2. THE HYPAR SOLUTION Photosynthesis in HyPAR is computed by scaling gas exchange from leaf to canopy. The leaf photosynthesis model is Farquhar’s (1980), combined with Jarvis’ for stomatal conductance. Farquhar’s and Jarvis’ models involve (e.g. see equations in Le Roux et al., 1999): Biochemical parameters which primarily varies with species and nitrogen content, namely the maximal rate of carboxylation (Vcmax), the maximal rate of electron transfert (Jmax) and dark respiration (Rd). The maximal stomatal conductance (gsmax) could be included in this group. Biochemical photosynthesis parameters which may vary with species, but are usually assumed to be constant as their measurement is difficult. They include activation and deactivation energy, Michaelis constants and specificity factors. Values proposed by Jordan and Ogren (1984) are usually used, although Bernacchi’s values (2001) are becoming more popular. Environmental variables which influence both assimilation rates and stomatal conductance, namely PAR irradiance, leaf temperature and vapour pressure deficit at leaf surface. Simulation of carbon acquisition by the whole tree at daily scale needs both space and time integration of the leaf model, i.e. from leaf to tree and from minute to day, respectively. In HyPAR, space integration follows Sellers et al. (1992), who assumes full acclimation of leaf nitrogen content and then leaf physiological traits to timeaveraged light – i.e. relative variation in leaf physiological parameter scales with relative variation in time-averaged light. In these conditions, carbon gain by the whole tree is proportional to net assimilation and then physiological parameters of leaves in a given location, mostly chosen at the top of canopy. Such a way shows two major advantages: Leaf models must be parameterised for the only top leaves, rather than assessing variations within the canopy. This shortens the amount of field measurements needed to parameterise the model. Computing time can be saved. This approach has been further tested in case of isolated tree crowns (Kruijt et al., 1997) and has proved successful. Moreover, in case of a isolated walnut tree, simulation with the RATP model (Sinoquet et al., 2001) have shown that carbon gain is weakly sensitive to the nitrogen distribution within the crown, and that the observed nitrogen distribution is close to the theoretical distribution leading to maximal carbon gain (Le Roux and Sinoquet, unpublished data). This means that formalism adopted in HyPAR is probably satisfactorily. On contrast, the way the leaf scale model is integrated over the daytime is unsatisfactory. HyPAR documentation implicitly suggests that the model runs with the mean daily leaf irradiance. As shown in Fig. 1 from a simulation study with the RATP model (Sinoquet et al. 2001) on a 20-year walnut tree, the single daily run results in a 20% overestimation of daily carbon gain, in comparison with a daily integration of hourly simulation outputs. 3. ALTERNATIvES: Photosynthesis modules for tree growth models have been recently reviewed by Le Roux et al. (2001). Approaches used at the daily time step are the RUE concept (Radiation Use Efficiency, Monteith, 1972) and empirical models, where the effect of environmental factors (leaf irradiance, temperature, CO2 concentration, water stress, N supply) is taken into account by empirical functions. Note that Le Roux et al.’s review – which does not include the HyPAR model – does not report any model using Farquhar’s model at time steps larger than one hour. The approach used in HyPAR is good, because Farquhar’s model use physiologically-sound parameters and the spatial integration process (after Sellers, 1992) avoids to parameterise the whole variations of leaf photosynthesis and stomatal parameters within tree crowns. The only questionable point in HyPAR tree photosynthesis is time integration at daily scale. Farquhar’s model usually runs at short time steps. Because photosynthesis responses to light and temperature are not linear, running the model with the mean daily leaf irradiance provides a biased estimation of the daily carbon acquisition. 4. PHOTOSYNTHESIS MODEL IN HI-SAFE Like in HyPAR, tree photosynthesis in Hi-SAFE is computed from Farquhar’s model associated with Jarvis’ to take stomatal responses into account. In Jarvis’s model, responses to leaf PAR irradiance, vapour pressure deficit, leaf temperature, CO2 concentration in the air are modelled from empirical relationships (see e.g. Le Roux et al. 1999 for application to walnut trees). The environmental factors are assumed not to interact, so that the empirical functions are multiplied to account for the overall effect of climatic factors. The maximum stomatal conductance gs max is assumed to depend on leaf nitrogen content. While there is no direct link between nitrogen content and stomatal capacity of leaves, this way allows to take into account differences in gsmax between sun and shade leaves (see e.g. Leroux et al. 1999). Since the HyPAR model does not include a complete leaf energy budget which could allow to compute leaf temperature, leaf temperature is assumed to be equal to air temperature (as in Wang & Jarvis, 1990). This assumption is correct as long as water stress keeps moderate. Otherwise coupling between leaf boundary layer, vapour pressure deficit and stomatal conductance is analytically solved in a new elegant way (see code lines XXX to YYY). The effect of water stress on gsmax is also taken into account by introducing an additional response to the soil water content. As soil water content shows spatial variations in the Hi-SAFE model, the average soil water content of 50% of soil volume occupied by the tree root system is used in the relationship. Note also that this effect is computed once per day, and from soil water content of the previous day in order to avoid to take into account interactions between soil water content and transpiration. The Harley et al. (1992) version of the Farquhar model (Farquhar et al. 1980) has been used. It computes assimilation rate as limited by drak and light photosynthesis responses, using a biochemical framework. All equations used are given in Le Roux et al. (1999). The model outputs are thus: o Leaf boundary layer conductance, computed from wind speed in the canopy. o Leaf stomatal conductance, computed from Jarvis’ model o Leaf photosynthesis rate, computed from Farquhar’s model. Computations are performed 5 times a day. For each time step, photosynthesis rate is computed separately for sunlit and shaded area. This allows to satisfactorily take into account the non-linear responses to environmental parameters (de Pury and Farquhar, 1997). 5. INPUT PARAMETERS REQUESTED: Input parameters for the carbon acquisition model are: Microclimatic variables sensed by the leaves: Leaf irradiance: as computed from the radiation interception model. Leaf temperature assumed to be equal to air temperature. Leaf nitrogen content: as computed from the tree model. Note that the spatial distribution of leaf nitrogen within the tree crown is not taken into account. Indeed RATP simulations on a 20-year walnut tree have shown that the daily carbon gain at tree scale is weakly influenced by the spatial distribution of leaf nitrogen (see Fig. 2). Leaf physiological parameters: As previously mentioned, they include i) a set of parameters available in the literature (Bernacchi et al. 2001), which are commonly used for any plant species, and ii) leaf parameters – namely, Vcmax, Jmax, Rd and gsmax -, the values of which mainly depends on leaf nitrogen content on an area basis. The best way should therefore be to parameterise relationships between these parameters and N content for the SAFE tree species. Such relationships have already be established for walnut trees (Le Roux et al., 1999) Stomatal responses of leaves to microclimatic variables: Namely, responses to PAR irradiance, vapour pressure deficit, temperature and water stress. Such responses exist for walnut trees (Le Roux et al., 1999), and should parameterised for the other SAFE tree species. INTRA-DAY WEATHER DATA GENERATOR 1. Objectives: The Hi-SAFE model is fed from microclimate variables at daily scale, i.e. as commonly available from standard weather stations. As the carbon acquisition model is run 5 times a day, it needs meteorological data at intra-day scale. The intra-day weather data generator was therefore developed to feed the light and carbon acquisition modules with climatic data, namely air temperature, air humidity, global and diffuse incident radiation. 2. Intra-day data computation: Astronomical formulae dealing with the sun direction (namely sun elevation and azimuth) have been included in the data generator, in order to compute the day length, and sunrise and sunset times, as a function of latitude and day of the year. This allows one to define the time for the 5 carbon gain computations, which are regularly spaced during the day. As a consequence, time step #3 is TST midday. Air temperature and humidity are computed from minimum and maximum daily values which are supposed to be available from the weather station. Minimum temperature and maximum air humidity are assumed to occur at sunrise, while maximum temperature and minimum humidity are supposed to occur at midday. Interpolation is made from a sine function, the amplitude of which is given by the difference between two successive extremum values. As daily diffuse incident radiation D is rarely measured in weather stations, estimation from daily global (G) and extra-terrestrial (G0) radiations has been included in the weather generator: D / G aG / G0 b (5) where a et b are empirical coefficients. Extra-terrestrial radiation G0 is computed from astronomical formulae, as a function of latitude and day of the year. Intra-day global and diffuse incident radiation (i.e. for 5 time steps in the day) is computed by assuming that instantaneous radiation is proportional to the sine of sun elevation (Perrin de Brichambault 1976). The data generator checks for conservation of daily incident radiation. Model structure For each day If trees are leafy Generate the climatic data for the 5 time steps: Weather generator Astronomical formulae Air temperature and humidity Global and diffuse radiation: Gi and Di If canopy structure has changed Update diffuse PAR variables (tree and crops): Light model If sun course OR canopy structure has changed For each time step Update direct PAR variables (tree and crops): Light model For each tree For each time step Compute leaf irradiance of sunlit and shaded area For shaded and sunlit foliage area Compute assimilation rate: Photosynthesis model Leaf boundary conductance Leaf stomatal conductance Net photosynthesis rate Sum up contributions of shaded and sunlit area Sum up contributions of 5 time steps THE TREE GROWTH MODULE 1. INTRODUCTION STATEMENT OF OBJECTIVES This module is part of the tree growth model (which as a whole also includes simulation of water and N uptake mediated through a spatially explicit root growth model and C uptake via a light interception and photosynthesis module). The present module more specifically covers C and N allocation to (and from) the different compartments identified, and provides a spatially explicit above ground tree representation. The tree growth model itself is part of the Hi-SAFE agroforestry biophysical model which is designed to describe a 3-5 years growth period of the tree + crop agro system in a temperate (seasonal) climate on a daily time step. It should be capable of simulating early years of tree development as well as the functioning of large mature trees. It should address pruning or root trenching which are considered to be important management practices to orient the productive outcome of such systems. 2. PRELIMINARY REMARKS (based on bibliographical review and discussions with Christian Dupraz, Marcel van Oijen, Andre Lacointe, Martina Mayus, Nick Jackson and other members of the HiSAFE consortium) 2.1. Is carbon supply limiting tree growth? Recent evidence based on repeated measurements of above ground tree nonstructural-carbohydrates stocks which have been conducted in a variety of climates, suggest that growth of mature trees in natural stands may never be limited by carbon availability (Hoch et al. 2003; Korner 2003). This may reflect the fact that trees have not yet adapted to the elevated ambient CO2 levels and that the limiting step is integration of carbon into functional tissues rather than carbon uptake per se. For example at high elevations, it has been argued that temperature may limit growth more than C uptake (Korner 1998) as “growth as such, rather than photosynthesis or the carbon balance, is limited. In shoots coupled to a cold atmosphere, meristem activity is suggested to be limited for much of the time, especially at night”. The same type of restriction may play a substantial role at high northern latitude. This idea that tree growth is not intrinsically limited by C-uptake is apparently contradictory with the extensive experimental data that prove that access to light is of paramount importance in determining relative competitive success of individual trees in a forest stand. More probably in most environments tree growth is co-limited by a number of factors. The most limiting step may indeed not be C-uptake rate but biosynthesis rate of new tissues, particularly so under cold climates or low nitrogen fertility. In any case, in low-density tree stands as those we are dealing with, light availability is unlikely to limit C uptake as severely as in denser forest stands. Hence it is suggested that emphasis be put on N and H2O limitations to growth, be it at the Cuptake step or the biosynthesis of new functional tissues step. 2.2. Internal C flows and wood anatomy Internal C flows are tightly linked to wood anatomy. There are four basic types of wood, ring porous, diffuse porous, (semi diffuse), conifer without resin ducts and conifers with resin ducts. In the SAFE project we are concerned with the first two types only (Oak and walnut having ring porous wood and poplar and wild cherry diffuse porous wood) In a recent study (Barbaroux and Bréda 2002), NSC concentrations in ten outer rings of sessile oak (sap wood only) were found to be about 4% of the total dry weight (vs 2% in beech) with a much more pronounced radial gradient as well as stronger seasonal pattern in oak than in beech. In the latter study there was also circumstantial evidence suggesting that radial growth was more sensitive than photosynthesis to moderate water stress in both species as NSC accumulation was not reduced when growth was, supposedly due to water shortage. Growth temporal pattern of the various tree compartments is also related to wood anatomy. Diffuse-porous trees have vessels of about equal size and diameter arranged at about equal distances from each other throughout the growth increment. These vessels are produced regularly during the growing season. Such vessel anatomy permits moderate loading throughout the entire growing season, i.e., loading of free water and essential elements dissolved in it. There is no or negligible heartwood in those species. Ring porous trees such as, oak, elm, chestnut and black locust, have large diameter vessels in the first portion of the growth increment and vessels of smaller diameter later in the growth increment. Vessels are produced early in the season before leaf expansion in spring. Ring-porous tree have no or little over-wintering functional xylem. (See Shigo 1994). 2.3. Tree response to pruning The few reviews found on the subject (Geisler and Ferree 1984; Stiles 1984; Richards 1986) focus on fruit trees and are not recent. A quick Internet search was also conducted to complement the information reported in the above-mentioned horticultural reviews. Overall, the literature consulted supports the view that response to pruning depends on the timing of pruning and that the general response will be towards a redistribution of growth to the pruned compartment. The extent to which remobilisation of NSC is involved in fuelling compensatory growth and how this may relate to pruning severity is unclear. Root pruning and defoliation experiments in a broad range of species (Richards 1986) tend to support the interpretation that “in a constant environment the S/R ratio tends to constancy and is restored following manipulative treatments that may initially disrupt it”. This may imply an increased RGR of the severed compartment and a reduced growth of the intact compartment as well as an extended growth period of the pruned compartment. For example effect of root pruning in peach seedling was quickly overcome by a “redistribution of growth” in favour of roots. Similarly root pruning of trees have been shown to induce reduced growth rate of above ground in many tree species (Geisler and Ferree 1984). In one experiment conducted with 2 clones of coppiced 4 year old poplar there was no evidence of root dye back after the above part was severed during the dormant period (Dickmann et al. 1996). Growth rate of roots has been sometimes observed to remain unaffected (noble fir, Monterrey pine) or to increase (apple, peach) or to decrease in case root pruning was extremely severe. Restoration of shoot:root ratio after pruning may take several months (as in the case of 22-year old trees of white pine). Timing of pruning is also known to affect significantly the tree response. Pruning in winter (dormant pruning) produces the most new growth, pruning has the greatest dwarfing effect in June and early July, “It first dwarfs the root system, and then the whole tree”. Mid summer pruning has little or no effect on stimulating new vegetative growth (http://www.gov.on.ca/OMAFRA/english/crops/facts/00-005.htm). Also stressed in (Stiles 1984): pruning after terminal buds have formed minimizes the possibility of stimulating renewed shoot growth during the same season. Sprouting in poplars was also observed to be substantially less for trees pruned in May than in March. (http://www.cropinfo.net/AnnualReports/2002/popprune2002.htm). Timing of root pruning notably in apple also influences the response: pruning in July reduced shoot growth but not if done in late summer (Stiles 1984). Tree pruning is also known to affect the diameter/height relationship (height growth being less affected than radial increment) and the tapering of the trunk (http://www.for.gov.bc.ca/hfp/forsite/training/growth-and-yield/gy-07.htm). 2.4. C-uptake modelling It was finally decided to replace the initially preferred Farquard type infra-daily time step photosynthetic module a by a simple Radiation Use efficiency approach ((Bartelink et al. 1997). A number of reasons can be put forward to justify this simplification So much uncertainty exists in terms of C-allocation patterns that it would not make much sense to use a lot of computer resources to – try and - estimate C uptake to a great level of detail if further accounting of C the various pools is so grossly done. The candidate photosynthesis model (which includes a Jarvis model of stomata functioning) - which was developed for plants growing without water limitation - would be relevant if the evaporative demand were to be computed on a infra-daily time step. This again would imply a significant additional cost in term of computer time (and would not be consistent with the crop daily time step yielding a number of additional complications). No human resources were available to calibrate this photosynthetic model for the tree species under consideration. RUE approach to simulate C-uptake and daily time step are congruent with the STICS crop model At this stage maximum RUE is a species-specific constant (g/MJ of intercepted PAR) which is reduced through dimensionless modifiers to take into account water stresses, nutritional stresses and possibly temperature effect. 2.5. Should respiration processes be explicit in the tree model? There was considerable discussion about whether respiration should be explicitly computed in the model. The model is meant to run under a variety of climate types. The contribution of respiration fluxes to total C budget is considerable (as much as half of the integrated daily net foliage carbon gain can be lost to respiration by the whole plant) and largely influenced by temperature. Therefore it seemed justified to consider including respiration in the model (as done in Hypar). However as a Radiation Use Efficiency approach to C-uptake modelling implicitly includes the growth and maintenance respiration costs by relating intercepted radiation with net Carbon accumulation no explicit respiration modelling seemed warranted. However it should be stressed that doing so, NSC accounting is done on a 'Structural carbon unit' base as no conversion cost from NSC to SC is considered. In addition to the above reason some more technical obstacles to incorporating respiration in the model exist. Dependence of growth and maintenance respiration rates on temperature in trees appear to be highly variable between sites and species as illustrated for example in (Coleman et al. 1996; Lavigne and Ryan 1997). For a given air temperature respiration rates further vary with tissue composition. Differing organ thermal mass and organ location will also complicate the relation between ambient air temperature and respiration rates. Seasonal variation has been reported to occur (Desrochers et al. 2002) as well as rapid acclimation to temperature (Bostad et al. 2003). Hence calibration of respiration parameters may be an extremely time consuming and largely fruitless exercise as no site nor species- specific data will be available from the project. It should be stressed that, in the absence of strict NSC accounting, a number of situations won’t be correctly predicted as for example mortality related to NSC exhaustion in seedlings or saplings following defoliation (Canham et al. 1999). If respiration is incorporated in a later version, it is suggested to implement a mechanistic approach to C allocation based on the transportresistance paradigm as proposed by (Thornley 1998). 2.6. Root phenology Root and shoot growth are highly coordinated and patterns of root vs. shoot growth appear to vary among species. Generally fine root production is halted during winter resumes with leaf expansion in spring and stops with leaf fall (Pregitzer et al. 2000; Cote et al. 2003). (Friend and Coleman 1994) distinguish three fundamental C allocation patterns between root and shoot in woody plants. The first one is associated with determinate shoot growth limited to late spring and early summer during which most of the assimilates are directed upward during the flushing episode and then downwards to the lower stem and roots (eg Picea). The second pattern is associated with indeterminate shoot growth which extends over most of the growing season (e.g. Populus) where allocation to root and shoot largely overlap over the whole growing season. The third pattern (e.g. Quercus) is associated with recurrent leaf flushing and root and shoot growth peaks alternate. However this view is not entirely supported by the data presented in Kramer and Kozlowski 1989 (from Lyr and Hoffmann 1967) showing that root growth precedes shoot growth in Picea abies and Populus trichocarpa by c. 3 weeks for example and that peak of root and shoot growth are roughly concomitant in Quercus borealis… In most fruit trees species examined in (Atkinson 1980) root growth in spring precedes bud burst. Peak of root growth normally occur in early summer but sometimes in spring or in autumn depending on species or cultivar. Some observation of non-synchronous root and shoot maximum growth (notably in apple trees) have been interpreted as a result of competition between both sinks for assimilates. Noticeably in one-year-old apple one major peak of root growth coincided with shoot growth while when the same trees where three years old the main peak of root growth was delayed until the rate of extension shoot growth was decreased. Suberized (brown) roots seem to be active in water absorption in apple. Root longevity also appears to vary significantly with species and a number of biotic and abiotic factors (Black et al. 1998). 3. THE POINT OF VIEW CHOSEN FOR THE C ALLOCATION MODULE C allocation is governed by two types of rules teleonomic (or goal driven) allocation rules based on allometric equations defining the relative sizes of aboveground sub-compartments and below ground subcompartments. Allometric relationships are supposed to capture internal constraints not explicitly dealt with in the model (e.g. architectural model and structural stability constraints or hydraulic constraints) in relation to the tree dimensions. an optimal allocation assumption (‘functional equilibrium’) between above ground and below ground mediated through stress indices, which basically assumes that plant allocates its biomass so as to maximise it’s growth rate under the given environmental conditions. Various tree phenological stages are considered, which govern the application of different sets of rules for C allocation by switching on and off C sinks. Phenological stage notably determines when NSC pool will act as a sink or a source of C. Differences/similarities of some important features with some other models that were considered are reviewed in appendix 1 (Hypar, Walnucas, Simplified SuperTree) 4. DESCRIPTION OF THE MAIN ALGORITHMS AND COMPONENTS 4.1. Tree parts considered Stem Branches (distinction between stem and branches is necessary because of alteration of the branch / stem allometry following pruning) Foliage Coarse (structural) roots Fine roots (feeder roots) C partitioning between fine roots and coarse roots is controlled by the root development module and is not dependent on a fixed allometric relation but depends on the tree root geometry, which is adaptive. No distinction between sapwood and heartwood is considered. This distinction would notably be important to include if maintenance respiration was to be estimated correctly. It may also be important for the nutrient budget through locking-up of nutrient in heartwood (cf Hypar). 4.2. C and N compartments C and N pools are divided into structural and non-structural pools. N is allocated to the tree parts according to target (structural) N contents. a) Management of C reserves Location NSC is considered to be homogeneously spread and entirely located in woody tissues (stem, branch and coarse roots) and reserve pool will consequently be affected by branch pruning or root trenching in proportion to the severed woody biomass. Note: reserve pools are not affected by senescence of woody biomass but could be made so. Flows to and from NSC pool C flows from NSC pool to fuel growth may occur only if the following conditions are simultaneously met There is significant imbalance in tree structure Phenological stage allows (from early spring to end of foliage expansion) Only imbalance within aboveground compartments is considered here. A possible extension of a similar concept to root:shoot imbalance following pruning is discussed under section 4.8. Imbalance is here defined as the departure from the allometric rules of the foraging organs (leaves in this case). ImbThreshold= |1- (LF/LFtarget )| (i) where LF is the current Leaf carbon mass Fraction of the aboveground compartment LFtarget is the predicted carbon mass fraction of leaf according to allometric equations If ImbThreshold is more than a given threshold, (to be calibrated later and which may be considered a parameter common to all species at first), then remobilisation of NSC will occur at a fixed daily rate. This amount of daily mobilisation of NSC (maxDailyNSC) can be set equal to a fixed percentage of the total structural C pool in first approximation and will need to be adjusted per species based on observed dynamics of growth on favourable sites. Note that it is possible that not all the C potentially remobilised a given day is converted into structural biomass as growth stresses may limit the actual conversion rate. Hence even in the period when remobilisation is possible NSC pool may actually increase if C-uptake is significant and growth much constrained. The sensitivity of this maximum rate of NSC remobilisation (a parameter which will not be measured…) will need to be assessed carefully. However C-uptake and stress levels rather than NSC remobilisation rate will rapidly take over in governing the overall growth dynamics, and this rate may not be very sensitive in fine. Outside periods of possible remobilisation of NSC, the NSC pool acts as a sink. This sink is set proportional to the total tree woody biomass (targetNSCFraction) and has priority over growth of woody tissues. Alternatively allocation to NSC could set to be proportional to the newly formed long-lived structural C (see paragraph on future improvements). Even though reserves accumulation and woody tissue growth may be non-overlapping in time (with more accumulation than growth towards the end of the growing season) and differently affected by environmental stress they are functionally and structurally linked and allocation of C to reserves as a fixed fraction of (new) wood (and coarse root) tissue seems to be an acceptable simplification (Barbaroux and Bréda 2002). In addition to this minimum amount of daily C-uptake allocated to reserves, if growth is limited more than C-uptake the surplus of C not incorporated into new biomass is diverted to the NSC reserve pool. In this regard it seems important to include an explicit dependence of growth rate on temperature, which is likely to be a significant limiting factor at northern latitudes. The calibration of such a function remains however problematic. b) N uptake and allocation dynamics. Within tree N recycling is quantitatively important as exemplified by the fact that 60% of annual N demand in mature walnuts was shown to be derived from N redistribution from internal pools (Weinbaum and Kessel 1998). In certain species up to 90% of the leaf N may be derived from storage N (Millard 1996). In deciduous trees, N is predominantly stored as protein in the bark and roots during the winter and remobilized in the spring when the buds break. During the summer, N is stored in the leaves and a proportion is withdrawn during senescence.(Millard et al. 1995). N uptake does not necessarily cease with dormancy and can amount for as much as 50% of total annual N uptake in Nothofagus fusca (Stephens et al. 2001) and substantial amounts were reported to be absorbed between leaf fall and bud break in Pecan tree (Acuna et al. 2003). This suggests that including active N absorption mechanisms and diffusion processes may be crucial to correctly estimate year-round N balance in the system. Due to lack of quantitative data for the various tree species under consideration and consistent with the crude N repartition in the foliage adopted (supposedly homogeneous), a simplistic N balance module is proposed. Overall N demand is defined by the sum of the product of the various compartments size with the N/C optimum ratios in each compartment multiplied by targetNcoefficent (which defines the total tree demand). N absorption may occur even when demand is 0 as defined by the luxuryNCoefficient. If total tree N concentration falls below the overall optimal N/C ratio (defined by the weighted sum of all structural compartments) N stress occurs. Above the overall optimal ratio N is assumed to be non-limiting. N is freely remobilised from the NSN pool in case N uptake is insufficient to maintain N/C ratios in the different structural compartments at target N/C levels, as is the case in particular in spring. NSN is considered to be located entirely in and proportionally to the woody biomass (and is affected by pruning proportionally to the woody biomass severed). Based on the general observation that under low nutrient supply starch accumulates (Poorter and Villar 1997 in (Poorter 2001)) N stress is considered to affect both C uptake and C conversion rate (in the latter case inducing higher rates of NSC accumulation). Partial N recovery by translocation from dying leaves is included (to be measured, set to 50% at this stage (cf Kramer and Kozlowski 1979). 4.3. Above-ground allometric and geometric equations Relative dimensions of the aboveground part of the tree are forcing functions in the model (except for crown volume which may be altered by pruning) which serve as guides to the distribution of biomass between compartments and in space within compartments. Diameter-height relations, stem profile and crown diameter A first allometric equation links total tree height (H) to diameter at breast height (D) H=cD^d (i) This relation is known to be altered by tree density (Cabanettes et al. 1998) and pruning (http://www.for.gov.bc.ca/hfp/forsite/training/growth-and-yield/gy-07.htm). Those parameters are therefore characteristic of a given context i.e. a combination of a tree species, a tree spacing and a tree management regime. Those parameters are not dynamically altered by pruning or thinning in the model. Data from the French Inventaire Forestier National were used to calibrate those relation for wild cherry, black walnut and poplar. Only poplar data were adequate to assess impact of planting density on the heightdbh relation, as illustrated below. For the other two species data of tree growing in 55 50 45 density classes range from <100 trees per ha (lower most line) to > 500 trees per ha (upper most line) 40 height (m) 35 30 25 20 15 10 5 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 dbh (m) hedges were used. Figure 43-1: Height-dbh relationship adjusted for planting density (Poplar I214 clone) Stem profile is known to be altered by pruning, planting density and age (Niklas 1995). However we considered a single equation per species to relate stem volume to tree height and diameter, following the model proposed by (Pryor 1988) in which log transformed values of stem volume are regressed against log transformed values of D & H. A linear relationship between crown width and dbh is assumed and parameterised for each species (this relation is extremely stable and may be assumed to be independent of planting density in first approximation). 900 800 CROWNDIAM 700 600 Fig 43-2: DBH and crown diameter relation in walnut (data courtesy of AMAP) 500 400 300 200 100 0 5 10 DBH 15 20 Crown length is derived from total tree height and crown base height. Crown base height is set at initialisation and only altered by pruning (no natural branch shedding considered) In addition to the above “outer dimensions” description, it is necessary to estimate the biomass relationships between the different compartments. The driving variable in biomass allocation in the above ground tree part is the stem biomass. Biomass of stem is fully determined from stem volume and wood density. From the stem size and crown base height the crown volume is determined. However the biomass of branches and leaves per unit crown volume is likely to depend on the tree architectural characteristics and may vary with tree size and this will need to be estimated. The ratio of foliage biomass to wood biomass in beech has been to decrease significantly with increasing tree size (Bartelink 1997). To assess the variations in the relative size of the various compartments in relation to crown volume, species and planting density, it was proposed to use AMAP mock-ups to simulate typical trees of various sizes growing under various planting densities. For the time being a common allometric relation is used for all species to relate branch volume to crown volume. Parameters are based on data published by Bartelink (1997). BranchVolumeRatio= aBranchVolume * crownVolume^bBranchVolume Leaf biomass is set to a fixed proportion of the crown volume (through a species specific Leaf Area Density parameter which is also used in the light interception module). Alternatively a simple model could be derived from the pipe model theory if the proportion of over-wintering functional xylem can be ascertained for each species (see paragraph on future improvements) Assuming a fixed “triaxial ellipsoid” to describe crown shape, the crown volume V is related to the three half-axis values a, b and c by V = 4/3*Pi*a*b*c (ii) (or V= 4/6*Pi*a*b*c (ii’) in case of a half ellipsoid) Parameters a and b (horizontal axes) are constrained respectively by inter-tree distances on the line and inter line distances. Figure 43-3: View from above illustrating constraints applied to lateral crown expansion by inter-tree planting distance Crown deformation as a function of planting pattern is only applicable to regular planting patterns and assumes equivalent development of all trees. Maximum values for a and b (horizontal radii) are defined respectively as on the line inter-tree distance and inter-row distance (possibly adjusted during growth if stand thinning occurs). In other words each tree is allocated a vital surface of a * b (m^2). We assume that the allometric relationship linking dbh to crown width reflects the relationship between crown projection and stem section for symmetric crowns. Hence from dbh we infer the expected equivalent radius r if r > amax then b is defined as r^2/amax. If b exceeds bmax lateral canopy expansion is halted. Growth in diameter and growth in height will however continue based on diameter-height allometry hence violating the dbh-crown_width relationship. Another possibility considered would be to relax this spatial constraint by allowing additional crown expansion to mimic the fact that as trees come into contact the interstitial space between crowns will continue to be gradually filled until the full projection of the space is saturated (completely closed canopy). Hence we could tolerate further growth of horizontal axes until the equivalent section reaches the surface = amax*bmax. This however may be difficult to reconcile with the light model which does not consider crown intersection and hence this option is not implemented at this stage. 4.4 Crown shape and crown volume alteration by pruning Two types of crow shapes are considered: complete triaxial ellipsoid and half triaxial ellipsoids (truncated on the vertical axis). The first type would apply to poplar (upward general orientation of branches). The second type would be preferred for oak, wild cherry and walnut. Pruning is defined by a reduction of canopy length expressed a fraction of initial length removed. Let a and b be the horizontal radii and c be the vertical radius before pruning. And a’, b’ and c’ the radii values after pruning. Pruning will reduce vertical axis by a certain fraction X (between 0 and 1) and the new vertical radius is simply computed as c’ = (1-X) c The new horizontal radii are computed as half the width of the ellipsoid before pruning measured at the height of new centre of ellipsoid (see 2D diagram below) a’ = a * sin(acos(X)) and b’=b * sin(acos(X)) Fig: 44-1: Sketch of pruning effect c’ a’ a Fig. 44-2: fraction of volume removed V(x) as a fraction of canopy length removed (x) c 1 1 0.5 V( x) 0 0 0 0.5 1 0 x 1 Canopy thinning is also possible and will alter the leaf area density and branch volume without changing canopy shape. 4.5 Belowground allometric relationship Coarse root-to fine root allocation ratios are governed by the root module and are not discussed here. Locally driven senescence (water logging), or root growth cessation may need to be considered and fed back from the tree root growth model to the C allocation module. 4.6. Phenology Phenology remains fairly crude. In particular no tree flowering or fruiting is yet implemented. Change from one phenological stage to the next is based on accumulated degree-days, or average minimum temperature over a time window. Developmental stages considered are based on (Dupraz and Lecomte 2003) Dormancy End of dormancy is triggered when a threshold temperature sum has been reached. Start of dormancy is concomitant to end of leaf fall Growth Growth starts with bud-burst and ceases with leaf fall. Leaf fall occurs at a given date at a given location and may be hastened by lower than usual temperatures (but this function has not yet been calibrated). Stem growth is known to precede budburst in ring porous trees in relation to the lack of over wintering functional xylem. This is neglected here and should not have major impacts on overall growth of the various plant components as this growth is fuelled by internal remobilisation of C and N resources. Probably more important to predict the outcome of competition between tree and the crop would be to assess whether root growth is indeed synchronous (as implemented by default) or rather precedes leaf flush by a significant period of time. Active foliage expansion period During the leaf expansion phase, almost all assimilates are allocated to non-woody tissues, i.e., leaves and fines roots as those sink forces are much stronger since those compartments start from zero (or much reduced values for fine roots) each spring. Length of period of active foliage development is likely to depend on current trophic conditions (see note mentioned above). This could be explicitly included provided that we have a clear understanding of what kind of physiological stress maybe used to trigger cessation of foliage expansion. Growth without additional leaf growth Once initial leaf flush has ceased all additional C will be allocated to roots, woody biomass and NSC. During the wood production phase, only leaf sink is switched off (by default fine roots sink is not but it may need to be adjusted as well). 4.7. Implementation of the optimal allocation assumption The degree of “reactivity” in root:shoot equilibrium is species-specific and governed by three parameters RSNoStressResponsiveness, NdesatResponsiveness, WstressResponsiveness. N and H20 limitations affect overall daily growth rate (conversion rate of available NSC to new organs), C uptake rate per unit leaf area (negative impact of both water stress and sub-optimal nitrogen content), and the relative allocation to above vs. below ground. An index of global N status is introduced which will affect relative allocation to aboveand belowground compartments. If N content is above the target overall nitrogen content, C allocation to the aerial part is increased, whereas if N content falls below this level allocation to roots is increased. Preliminary tests suggest that due to the annual loss of N following leaf and root senescence and the fluctuating size of these compartments, this target level should be set slightly above the N level defined by the optimum N concentrations otherwise every other year the tree faces severe N shortage once N starts becoming limiting. This is level of N content is controlled by the targetNcontent parameter. A Nitrogen saturation index (Nsat) is defined which may affect biomass allocation in the absence of water (or nitrogen) limitations. Let Ntot be the current total N pool size Let Nmax be the maximum N pool size (defined as Nopti * targetNcontent *NluxuryCoeff) Let Ntarget be the base level of the N pool above which saturation is measured (defined as Nopti * NtargetCoeff) Then Nsat = 1- ((Ntot-Ntarget)/(NMax-Ntarget)) if Ntot>Ntarget and 0 otherwise. When saturation is above 0 the fraction of the structural biomass increment allocated to roots β’ is computed as ' 1 N sat NoStress (iii) where β is the default allocation fraction of C to roots Nsat saturation of the maximum admissible NSN pool δNoStress a parameter governing the capacity of the plant to reallocate growth to aerial fraction in case of nitrogen saturation (RSNoStressResponsiveness) Note that in case of full saturation root growth is altogether stopped. Hence this function is inactivated in early spring (during the first growth flush as initial root growth will occur whatever the level of internal N reserves) i.e. when aboveground imbalance is above 90%. Similarly Ndesat measures the deficit of N (relative to the target level) and is defined as Ndesat = Ntot/NTarget if Ntot<NTarget and 1 otherwise N-demand (an input to the belowground competition module) is defined as max(Ntarget-Ntot,0) Daily water deficit is defined as (1-ETR/ETP). See below how water demand is computed. RUE is affected proportionally to this water deficit. The same water stress index is used to modify growth rate (C conversion rate) and RUE. The rational for this being that there are strong evidences that water may limit growth directly (in addition to C uptake limitation) i.e. affecting the relative fraction of C allocated to NSC. However contrary to the case of low nutrient availability, starch does not seem accumulate in leaves at low water supply (Chaves 1991 in (Poorter 2001), but see (Barbaroux and Bréda 2002) and also (Chaves et al. 2002)) suggesting that a C conversion rate reducer based on water stress may not be necessary or could at least be downplayed. At present the modifier used to decrease growth rate (in addition to RUE) is a power of the daily water stress index (default power coefficient = 0.2) that ensures that only strong stresses have a significant impact on NSC conversion rate. Root:shoot allocation is also considered to be affected by water availability (see this section below) but a time-averaged value (over the last 10 days) is used instead of the daily water stress. Time-averaged water stress and N status index (referred to as TimeAveragedWstress and Ndesat) may be compound (default implementation) or alternatively only the maximum of both stresses may be applied when computing the modification in the root:shoot grozth partitioning. Both (Canham et al. 1996) working with tree seedlings and (Poorter and Nagel 2000) in their quantitative review for plants observed that C allocation to roots was affected more strongly by variation in soil nitrogen availability than it was by soil moisture availability. Hence the general implementation proposed is the following: ' Ndesat Nstress TimeAveragedWstress Wstress (iv) or ' Max( Ndesat where Nstress , TimeAveragedWstress Wstress ) (iv’) α’ is the new fraction of total C allocated to growth which is allocated to the aboveground compartment α is the default fraction of C allocated to shoot, which is equal to current shoot fraction N-desat and W-stress stand respectively for Nitrogen saturation deficit and Water stress indices (both between 0 and 1). N desat is similar to a stress index in that it is equal to 1 in the absence of deficit and decreases as deficit increases. δNstress , δWstress are parameters characterising the species specific "responsiveness" to N-stress or W-stress, which control the amplitude of the functional response to stress Introduction of the δNstress , δWstress parameters called NitrogenDesatResponsiveness and WaterStressResponsiveness will allow simulating different plant strategies. For example seedlings of Quercus rubra appeared more conservative than Acer rubrum seedlings in terms of there allocation of C in response to limited N availability (Canham et al. 1996). It is also a way of explicitly introducing the greater responsiveness of root:shoot allocation pattern to N shortage than water shortage. Calibration of these parameters may however prove uneasy. 4.8. Senescence Within growing season turnover rates of coarse roots, branches and leaves (by default set to 0.0005) are considered and determine daily senescence rate of both compartments. Fine root senescence rate is computed in the root growth module. Accelerated end of growing season mortality of leaves is triggered by phenology (as described in (Dupraz and Lecomte 2003). Exceptional senescence induced by pruning in the unprunned compartment is not considered in the model due to lack of clear evidence and quantitative estimates, but could be implemented if need be (see section below). Neither is accelerated leaf fall triggered by prolonged stress included at this stage. A default small turnover rate of stem compartment (to account for bark fall) could be added. 4.9. C flow alteration following severe pruning If frequency and severity of pruning remains moderate it is likely that the optimal allocation paradigm governing above and belowground C apportioning will suffice to describe tree response to pruning. If pruning becomes very intense (like in the case of coppicing for example) and compensatory growth is expected to be largely fuelled by NSC remobilisation (rather than by mere reorientation of steady state C flows) then this would need to be included in the model. It would then be necessary to introduce a new teleonomic assumption by which the tree would seek to recover the root:shoot equilibrium prevailing before pruning, and to define what level of pruning severity would determine dye-back of the overdeveloped compartment. Such additional complexity is not deemed necessary or even desirable at this stage. 4.10. Tree water demand The following notations are used throughout the present paragraph ∆ rate of change of saturating water vapour pressure with temperature evaluated at ambient temperature A energy available above canopy (Rn –S), with Rn net radiation above surface, S subsurface heat flow (W. m-2 ) Rn net radiation = (1-a) Rs-Rl a albedo (0.05 for water surface, 0.23 for green leaves) Rl long-wave heat radiation (W m-2) computed as 5.67 10-8 (Ta+273,16)4 (0.56-0.08ea0.5) (0.1+0.9n/N) with n duration of the number of sunshine hours (h) n day length (h) ea actual water vapor pressure in the air (hPa) Ta temperature of the air (° Celsius) γ psychometric constant ( = 0.67 hPa. K-1) Lv Latent heat of vaporization for water (L=2.454 MJ. kg-1 at 20 °C) ρw, density of water ρ , density of air (1.2047 kg. m-3) . cp specific heat of the unit mass of the air (cp = 1004 J. kg-1. K-1) E evaporation rate (volume of water per unit land area per unit time); 1 W. m -2 ≈ 0.0352 mm. d-1 Da water vapour pressure deficit in the air surrounding the plot (weather input) rat tree canopy aerodynamic resistance, dependent on wind speed s.m-1 rst tree canopy stomatal conductance, s.m-1 Ts (tree) leaf temperature (° Celsius) In the first version of the Hi-SAFE model tree and crop water demand are uncoupled (the scene is treated as a patchy environment) and tree water demand is simply computed based on Penman-Monteith formula Lv ρw ETranspitree = (∆ Atree + cp ρ Da / rat)/ (∆ + γ + γ (rst/rat )) (3) In case the foliage is wet the potential transpiration is simply decreased by the amount of water stored on foliage Finally using actual transpiration rate (once competition has occurred) the tree foliage temperature can be recomputed as Ts = Ta + ra .(Rn - Lv ρw ETtree)/( . cp) (10) Note: There exist numerous equations for calculating ra as a function of wind speed u (m. s-1) and crop height Hc (m). One of them is ra = [ln(z-dc)/z0]2/[k2 .uz] where dc = 0.63. Hc z0 = 0.13. Hc (14) (15) (16) z is the reference height (m), usually 2 m taken here as being equal to tree height + 1 m, dc is a so called zero plane displacement (m), z0 the roughness length (m), k is von Karman's constant (k=0.41) and uz is wind speed (m. s-1) measured at height z (supposed to be equal to measured wind speed at standard height) and Hc is the tree height. 5. FUTURE IMPROVEMENTS AND POTENTIAL ISSUES 5.1. Suggested future improvements to the C allocation Temperature effects Calibrating impact of temperature on RUE and partitioning to reserve pool (reflecting change in rate of C incorporation into functional or structural C) and remobilisation rate will be uneasy though it may be important in explaining between site and between year variations in tree growth. Both the rate of conversion of NSC to new tissues, and the RUE are temperature dependent. The latter may be roughly estimated from bibliographic search. The former (much like the respiration parameters) is more elusive but should have marginal effects on overall growth and may be neglected in first approximation. After (Jones 1993) the following shape of temperature response may be used (were k is the reduction in the rate under concern at a given temperature) 1.0 Fig 51-1: Proposed temperature response curve reducer 0.8 0.6 K(t) = max( 0.4 (2*(t+Tmin)^2 *(Tmax+Tmin)^2 -(t+Tmin)^4)/(Tmax+Tmin)^4,0) 0.2 0.0 0 10 20 30 40 temperature (deg C) 50 (e.g. Tmin=0, Tmax=30) Branch volume calculations – Pipe model application Allometric relations between leaf surface (and crown volume) and branch biomass may be derived by application of the pipe model theory. Next version may include this functional constraint in the model allowing parameterising this allocation fraction to woody biomass according to the type of wood (diffuse porous, semi-diffuse or ring porous) Long term non-stomatal water stress We may also need to introduce a water stress index to take into account the nonstomatal limitation of photosynthesis during drought. According to Kozlowski and Pallardy (Kozlowski and Pallardy 1996), the relative importance of stomatal and non-stomatal inhibition of photosynthesis during drought varies with the drought tolerance of the species, increasing in xeric plants under drought but decreasing in mesic plants. Non-stomatal inhibition of photosynthesis are considered by those authors to be especially important in the long term and under severe water deficit. Some species show after-effects of water deficits on photosynthesis that may last for weeks or months after irrigation resumes. This calls for the introduction of a water stress index which could be used to reduce further photosynthesis under severe drought and which recovery could be made time dependent. Such an index could be based on accumulated days of water deficit above a certain threshold. An explicit time recovery function could be introduced (based on a daily recovery fraction for example as done in (Noordwijk and Lusiana 2000)). 5.2. Potential issues Even though we have tried to keep the number of parameters to a minimum some calibration problems will undoubtedly arise. The root:shoot equilibrium assumption combined with fixed allometric ratios within above ground and below-ground compartment may prove awkward. If there is solid evidence in support of the functional equilibrium assumption, it seems that this is best expressed when dissociating foraging organs from structural organs. E.g. stem and branch fraction are affected differently by limiting light availability (Korner 1994; Poorter and Nagel 2000). Linking phenology to extreme events e.g. early frost impact on N remobilisation and leaf shedding, leaf fall triggered by water stress (a common reaction in black walnut and poplar according to (Kozlowski and Pallardy 1996). N balance is based on average values per compartment. However nitrogen content in woody tree parts decreases with age and therefore the N balance as it is computed presently is biased. STELLA IMPLEMENTATION AND TESTING Introduction The model was first implemented under Stella (see full set of equations in Appendix) to test the internal consistency of the proposed approach and explore the general behaviour of the model. A full assessment of this module cannot be conducted while it is disconnected from the other modules. To conduct sensitivity analysis tests fixed resource capture efficiencies were used as forcing variables LUE = 3 g x m-1 x d-1 for light capture (0.003) A default rate of 0.001 kg N per kg of C of fine roots was used for N absorption efficiency Water deficit was simulated by imposing a particular stress level throughout one (or more) growing seasons or on a series of days of the growing season. Nuptake was reduced by a factor equal to the water stress value. In addition, a simple allometric relation was used to link fine roots biomass to total below ground biomass and a fixed fine root mortality rate was used to simulate root development (as substitute of the input from the root growth module in the full model). Extensive tests were conducted leading to the conclusion that the models prediction are sensible and that all parameter tested are sensitive at least under a particular set of values of the other parameters. A few examples are given below to illustrate the general behaviour of the model. Sensitivity Analysis Test Runs Example 1: Nresponsiveness – 20 year run Input variables NResponsiveness Run # 0.5 1 1 2 1.5 3 2 4 Output variables: DBH, root:shoot allocation; Nstress 1: TreeDBH 1: 2: TreeDBH 3: TreeDBH 4: TreeDBH 0,65 3 4 2 1: 0,40 3 4 2 2 3 4 1 1 1 1: 0,15 1 0.00 2 3 4 1825.00 Graph 1: p2 (Untitled) 3650.00 5475.00 Time 18:32 7300.00 mer 8 sep 2004 Figure SA1-1: Tree diameter at breast height 1-4: Root:Shoot ratio v . TotalStructuralC 0,30 Figure SA1-2: Root:shoot ratio 0,15 0,00 0,00 1000,00 2000,00 Graph 1: p1 (Untitl… TotalStructuralC 1: NStress 1: 2: NStress 18:32 3: NStress mer 8 sep 2004 4: NStress 1,05 1 2 3 4 1 2 3 4 3 4 3 4 Figure SA1-3 : Nstress 2 2 1: 0,95 1 1 1: 0,85 0.00 1825.00 Graph 1: p3 (Untitled) 3650.00 5475.00 Time 18:32 7300.00 mer 8 sep 2004 Discussion With the parameter values and initial state variable values used in this series of test runs, tree dbh is severely constrained by an NResponsiveness value of 0.5. At this level of the parameter, the tree fails to alter its root:shoot allocation fraction sufficiently (figure 2) and suffers systematic nitrogen stress throughout the growing season (figure 3) leading to a gradually decreasing annual growth after year 5 Example 2: LUE – 20 year runs LUE (g. m-2. d-1) # run 0.0015 1 0.002 2 0.0025 3 0.003 4 Output variables: DBH, total structural C, root:shoot ratio 1: TreeDBH 1: 2: TreeDBH 3: TreeDBH 4: TreeDBH 0.65 4 4 1: Fig. SA2-1: Tree diameter 3 0.40 3 4 2 3 2 4 1: 0.15 1 0.00 2 3 1 1825.00 Graph 1: p2 (Untitled) 2 1 3650.00 Time 1 5475.00 7300.00 11:17 PM Wed, Sep 08, 2004 1: TotalStructuralC 1: 2: TotalStructuralC 3: TotalStructuralC 4: TotalStructuralC 2000.00 4 1: 1000.00 4 Fig. SA2-2: Total Structural C accumulation 3 3 4 1 1: 3 2 4 1 2 3 1 2 2 1 0.00 0.00 1825.00 3650.00 Graph 1: p4 (Untitled) 5475.00 Time 7300.00 11:17 PM Wed, Sep 08, 2004 1-4: Root:Shoot ratio v . TotalStructuralC 0.30 Figure SA2-3: root:shoot ratio 0.15 0.00 0.00 1000.00 Graph 1: p1 (Untitl… TotalStructuralC 2000.00 11:17 PM Wed, Sep 08, 2004 Discussion Effect of LUE on tree dbh is almost linear resulting in an additional increment in dbh of ca. 12 cm after 20 years per 0.0005 unit increment in LUE (fig 1) whereas the effect on total structural C is exponential (figure 2) as expected. Faster growing trees invest more C into roots (figure 2) as they experience earlier and stronger N stresses (data not shown). Slow growing trees (runs # 1 & 2) actually show a gradual decrease in annual dbh increment. This decreasing return is associated with a steady decrease of the root:shoot ratio. Slow growing trees experience later and milder N stress (data not shown) and fail to increase significantly their below-ground C allocation fraction (N responsiveness was set to 1 for this series of run, but qualitatively similar results are obtained by setting Nresponsiveness to 2). Trees simply dry out of carbon when LUE is set to 0.0015 or lower. Example 3: Canopy pruning intensity Canopy pruning is set to occur on year 3. Runs are made for five years. Three pruning intensities are compared 1-9: TreeDBH 1: 0.23 1: 0.20 1: 0.16 Fig. SA3-1: impact of canopy pruning (0%, 25% and 50 % intensity on tree dbh) 0.00 456.25 Graph 1: p2 (Untitled) 912.50 Time 1368.75 1825.00 12:20 AM Thu, Sep 09, 2004 1-9: AGAllocFrac 1: 0.90 1: 0.70 1: 0.50 Fig SA3-2: alteration of Above ground allocation fraction following canopy pruning 0.00 456.25 Graph 1: p5 (Untitled) 912.50 Time 1368.75 1825.00 12:20 AM Thu, Sep 09, 2004 Discussion Canopy pruning of 50% intensity reduces dbh increment on year 3 clearly less than 50% (fig 1) due to an increase in the above ground allocation fraction (fig 2) as determined by the functional equilibrium implemented. Appendix 1 : List of the main parameters used in C allocation module PARAMETER DEFINITION Def Value Range (wild cherry) NSC pool management targetCLabilePoolSize (kg) steadyStateSavingFraction imbalanceThreshold controls growth rate when growth is fuelled by reserve remobilisation 0.005 fraction of C allocated to NSC pool under normal (autotrophic) growth conditions 0.05 Level of relative imbalance in C partitioning between foraging and structural organs above which growth becomes strictly autotrophic (no more C remobilisation from NSC reserves) 0.7 Root:shoot ratio waterStressResponsiveness power coefficient nitrogenStressResponsiveness power coefficient RSNoStressResponsiveness power coefficient 0.0010.05 0.01-0.10 0.1-0.9 1 2 0-2 0-2 Nitrogen balance OptiNCBranch optiNCCoarseRoot OptiNCFineRoot OptiNCFoliage OptiNCStem targetNCoefficient functional optimum N/C concentration functional optimum N/C concentration functional optimum N/C concentration functional optimum N/C concentration functional optimum N/C concentration coefficient applied to optimum to define target concentration 0.01 0.01 0.02 0.04 0.01 1.2 1-1.3 luxuryNCoefficient Coefficient applied to optimum to define maximum concentration 2 1.5-3 leafNRemobilisationFraction fraction of LeafN remobilised before leaf fall fineRootNRemobilisationFraction fraction of fineRootN remobilised before root death 0.5 0.5 Tree size and allometries aTree bTree aCrownVolume bCrownVolume AStemVolume BStemVolume cStemVolume allometric coefficient linking diameter to height allometric coefficient linking diameter to height allometric coefficient linking diameter to crown width allometric coefficient linking diameter to crown width allometric coeff. linking stem volume to height and dbh -1.984 (P) allometric coeff. linking stem volume to height and dbh 1.846 (P) allometric coeff. linking stem volume to height and dbh 1.2148 (P) 126 0.692 15.8 1.19 -8.821 2.131 0.4723 aBranchVolume bBranchVolume Allometric coeff. Linking branch volume ratio to crown volume Allometric coeff. Linking branch volume ratio to crown volume 0.0005 0.2 Carbon content leafCarbonContent (g/g) specificLeafMass (kg/m2) woodDensity (g/dm3) Leaf carbon content (g C g total dry biomass) Leaf dry mass per unit leaf area Dry wood density 0.6 0.05 500 Default senescence rates LeafSenescenceRate Daily leaf senescence rate 0.0005 0.0005 (?) 0.0005 branchSenescenceRate coarseRootSenescenceRate fastSenescenceRate FineRootSenescenceRate MISCELLANEOUS Daily branch senescence rate Daily coarse root senescence rate leaf senescence rate once leaf fall has started (see phenology module) 0.1 Daily fine root senescence rate 0.005 0-1 0-1 Radiation Use Efficiency (g/MJ solar radiation) Maximum RUE (no stress) 2 Maximum daily NSC remobilisation rate (expressed per unit maxDailyNSC structural C) 0.001 1-3 Appendix 2 Table comparing selected features of different tree growth modules in different models: Wanulcas version 2.0 (Noordwijk and Lusiana 2000); Hypar version 3.0 (Mobbs et al. 1999); "Simple SuperTree" (van Oijen 2003) Features Aboveground geometry Hi-SAFE (this draft) Tree Triaxial ellipsoid Tree organs Phenological stages Foliage, stem, branches, coarse roots and fine roots (Fruits to be added later on) Dormancy, foliage expansion, tree growth without additional foliage growth Walnucas Cylinder + Ellipsoid Hypar Truncated Ellipsoid Leaves+twigs, bare stem, branches, coarse roots and fine roots (+ fruit, latex…) SimpleSuperTree None Foliage (multilayered), Foliage, stem, coarse sapwood +bark, heart roots and fine roots wood, coarse roots and fine roots (Sexual immaturity), Dormancy, growth Flowering, fruiting None Non Structural Carbon Explicit NSC pool, size Explicit « carbohydrate Implicit NSC pool (C Explicit C labile pool pool linked to tree size reserve pool » in stem remobilisation from sapwood) Non Structural Explicit NSN pool, Implicit (limited luxury Implicit (limited luxury Explicit NSN pool, Nitrogen pool maximum size of which consumption allowed) consumption allowed) (unbound N uptake); is controlled by tree size C allocation Above and belowground Above and belowground partitioning based on partitioning based on dynamic functional dynamic functional equilibrium (an explicit equilibrium (an explicit Allometric relation between tree diameter and total woody biomass; Fixed ratio Above and belowground partitioning based on dynamic functional equilibrium mediated response to sub-optimal water and nitrogen availability); Separate allometric rules drive partitioning between AG sub compartments and BG sub compartments; response to sub-optimal water and nitrogen availability); Separate allometric rules drive partitioning between AG sub compartments and BG sub compartments N flows Follow C flows; Saturation levels of nitrogen in all organs vary in parallel; Remobilisation occurs from senescing leaves and fine roots Follow C flows; Saturation levels of nitrogen in all organs vary in parallel; No remobilisation from senescing organs Maintenance Respiration None None Growth respiration None None between aboveground and below ground woody biomass; Fixed C ratio between fine root and foliage biomass; Fixed ratio between sap wood area and subtended leaf area Follow C flows ; Saturation levels of nitrogen in all organs vary in parallel; Optimal allocation of N in the foliage; Rubiscobound, chlrorophyllbound and other “structural” N distinguished; Remobilisation from senescing leaves and fine roots through relative size of labile C & N pools; Allometry driven in AG and BG sub compartments (?) Follow C flows; Leaf N dynamics largely independent from other organs N content via a routine simulating dynamics of leaf protein synthesis and break down; Organs N content unbound; Depends on organ size, None N content and temperature Explicit (single value for None all organ types) REFERENCE CITED Acuna, M. L. E., M. W. Smith, N. O. Maness, B. S. Cheary, B. L. Carroll and G. V. Johnson (2003). "Influence of nitrogen application time on nitrogen absorption, partitioning, and yield of pecan." Journal of the American Society for Horticultural Science 128(2): 155162. Atkinson, D. (1980). "The distribution and effectiveness of the roots of tree crops." Horticultural Reviews 1: 424490. Barbaroux, C. and N. Bréda (2002). "Contrasting distribution and seasonal dynamics of carbohydrate reserves in stem wood of adult ring-porous sessile oak and diffuse-porous beech trees." Tree Physiology 22: 1201-1210. Bartelink, H. H. (1997). "Allometric relationships for biomass and leaf area of beech (Fagus sylvatica L)." Annales des Sciences Forestieres 54(1): 39-50. Bartelink, H. H., K. Kramer and G. M. J. Mohren (1997). "Applicability of the radiation-use efficiency concept for simulating growth of forest stands." Agricultural and Forest Meteorology 88(1-4): 169-179. Black, K. E., C. G. Harbron, M. Franklin, D. Atkinson and J. E. Hooker (1998). "Differences in root longevity of some tree species." Tree Physiology 18(4): 259-264. Bostad, P. V., P. Reich and T. Lee (2003). "Rapid temperature acclimation of leaf respiration rates in Quercus alba and Quercus rubra." Tree Physiology 23: 969–976. Cabanettes, A., D. Auclair, W. Imam and C. Dupraz (1998). "Diameter and height growth curves for widely-spaced trees in European agroforestry." Agroforestry Systems 43(1-3): 169-181. Canham, C. D., A. R. Berkowitz, V. R. Kelly, Lovett, G.M. , S. V. Ollinger and J. Schnurr (1996). "Biomass allocation and multiple resource limitation in tree seedlings." Canadian Journal of Forest Research - Revue Canadienne de Recherche Forestiere 26(9): 1521-1530. Canham, C. D., R. K. Kobe, E. F. Latty and R. L. Chazdon (1999). "Interspecific and intraspecific variation in tree seedling survival: effects of allocation to roots versus carbohydrate reserves." Oecologia 121(1): 1-11. Chaves, M. M., J. S. Pereira, J. Maroco, M. L. Rodrigues, C. P. P. Ricardo, M. L. Osorio, I. Carvalho, T. Faria and C. Pinheiro (2002). "How plants cope with water stress in the field. Photosynthesis and growth." Annals of Botany 89(Special Issue): 907-916. Coleman, M. D., R. E. Dickson, J. G. Isebrands, D. F. Karnosky, D. Whitehead and F. M. Kelliher (1996). "Root growth and physiology of potted and field-grown trembling aspen exposed to tropospheric ozone." Tree Physiology 16(1-2): 145-152. Cote, B., N. Belanger, F. Courchesne, J. W. Fyles and W. H. Hendershot (2003). "A cyclical but asynchronous pattern of fine root and woody biomass production in a hardwood forest of southern Quebec and its relationships with annual variation of temperature and nutrient availability." Plant and Soil 250(1): 49-57. Desrochers, A., S. M. Landhausser and V. J. Lieffers (2002). "Coarse and fine root respiration in aspen (Populus tremuloides)." Tree Physiology 22(10): 725-732. Dickmann, D. I., P. V. Nguyen and K. S. Pregitzer (1996). "Effects of irrigation and coppicing on above-ground growth, physiology, and fine-root dynamics of two fieldgrown hybrid poplar clones." Forest Ecology and Management 80(1-3): 163-174. Dupraz, C. and I. Lecomte (2003). Proposal for a simple phenology module in Hi-SAFE. Montpellier, INRA: 4. Friend, A. L. and M. D. Coleman (1994). Carbon allocation to root and shoot systems in woody plants. Biology of adventitious root Formation. T. D. D. a. B. E. Haissig. New-York, Plenum Press: 245-273. Geisler, D. and D. C. Ferree (1984). "Response of plants to root pruning." Horticultural Reviews 6: 155-188. Hoch, G., A. Richter and C. Korner (2003). "Non-structural carbon compounds in temperate forest trees." Plant Cell and Environment 26(7): 1067-1081. Jones, M. B. (1993). Plant microclimate. Photosynthesis and production in a changing environment. D. O. Hall, J. M. O. Scurlock, H. R. Bolhar-Nordenkampf, R. C. Leegood and S. P. Long. London, Chapman & Hall: 47-64. Korner, C. (1994). Biomass fractionation in plants: a reconsideration based on plant functions. A whole plant perspective on carbon-nitrogen interactions. J. R. E. Garier. The Hague, SPB Accademic Publishing: 173-185. Korner, C. (1998). "A re-assessment of high elevation treeline positions and their explanation." Oecologia 115(4): 445459. Korner, C. (2003). "Carbon limitation in trees." Journal of Ecology 91(1): 4-17. Kozlowski, T. T. and G. S. Pallardy (1996). Physiology of woody plants, Academic Press. Lavigne, M. B. and M. G. Ryan (1997). "Growth and maintenance respiration rates of aspen, black spruce and jack pine stems at northern and southern BOREAS sites." Tree Physiology 17: 543-551. Millard, P. (1996). "Ecophysiology of the internal cycling of nitrogen for tree growth." Zeitschrift fur Pflanzenernahrung und Bodenkunde 159(1): 1-10. Millard, P., M. Tagliavini and G. H. Neilsen (1995). Internal cycling of nitrogen in trees. Mineral nutrition of deciduous fruit plants. Mobbs, D. C., G. Lawson, A. D. Friend, N. M. J. Crout, J. R. M. Arah and M. G. Hodnet (1999). HYPAR Model for agroforestry systems, v 3.0, Institute of Terrestrial Ecology: 113. Niklas, K. J. (1995). "Size-dependent Allometry of Tree Height, Diameter and Trunk-taper." Annals of Botany 75(3): 217-227. Noordwijk, M. v. and B. Lusiana (2000). WaNulCAS v2.0, Background on a model of water, nutrient and light capture in agroforestry systems. Bogor, ICRAF. Poorter, H. and O. Nagel (2000). "The role of biomass allocation in the growth response of plants to different levels of light, CO2, nutrients and water: a quantitative review." Australian Journal of Plant Physiology 27(6): 595-607. Poorter, L. (2001). "Light-dependent changes in biomass allocation and their importance for growth of rain forest tree species." Functional Ecology 15: 113-123. Pregitzer, K. S., J. S. King, A. J. Burton, S. E. Brown, R. Norby, A. Fitter and R. Jackson (2000). "Responses of tree fine roots to temperature." New phytologist 147(1 (Special issue: Root dynamics and global change: An ecosystem perspective)): 105-115. Pryor, S. N. (1988). The silviculture and yield of wild cherry. Forestry Commission Bulletin: No. 75, 23 pp. Richards, D. (1986). Tree growth and productivity - the role of roots. Acta Horticulturae. Stephens, D. W., P. Millard, M. H. Turnbull and D. Whitehead (2001). "The influence of nitrogen supply on growth and internal recycling of nitrogen in young Nothofagus fusca trees." Australian Journal of Plant Physiology 28(3): 249-255. Stiles, W. C. (1984). "Effects of pruning on growth and size of trees." Acta Horticulturae 146: 225-229. Thornley, J. H. M. (1998). "Modelling shoot: root relations: the only way forward?" Annals of Botany 81: 165-171. van Oijen, M. (2003). An allocation module for simulation of trees in SAFE. Edimburgh, CEH: 14. Weinbaum, S. and C. v. Kessel (1998). "Quantitative estimates of uptake and internal cycling of 14N-labeled fertilizer in mature walnut trees." Tree Physiology 18(12): 795-801. THE MICROCLIMATE MODULE CONCEPT RAINFALL INTERCEPTION MODULE Experimental data on stemflow for several species showed that the stemflow depends on tree crown architecture and is somehow proportional to the tree leaf area index. This provide a relationship that was implemented in the crop model STICS (Brisson et al., 2004). The same relationships were proposed for the HiSAFE model. The rain interception is governed by two equations: Stemflow ratio: First, for each tree, a part of the incident rainfall is diverted as stemflow: Stemflow Rain KstemflowM axTree 1- exp - KstemflowT ree LAI Eq. 1 Were Rain is the incident rainfall (mm), Stemflow is the part of the incident rainfall that reached the soil as stemflow (mm) and LAI is the Leaf Area Index of the tree. Therefore, the stemflow is governed by 2 parameters : KstemflowMaxTree : represents the upper limit of the stemflow which means that over a given crown size, the stemflow no longer increased KstemflowTree : that represents the proportionality between stemflow and tree leaf. Crown water storage : A part of the remaining rainfall is stored in tree crowns. This water contributed to so called “interception loss” in hydrological models. The volume of water stored per tree crown depended on surface storage properties of the different organs of the tree : crown, leaves, branches, bark and on the arrangement between these surfaces depending on tree architecture. The storage of water in tree crowns was simply expressed as : Storage Capacity Wettabilit yTree LAI Eq. 2 Where WettabilityTree expressed the storage capacity of the tree crown per unit of leaf area (mm). In the model, the water volume stored in the crown is considered as a tank with a storage capacity that is daily filled with available rainfall (i.e. rainfall that reached the crown and was not diverted as stemflow) and emptied by direct evaporation calculated in the microclimate module. Once the tank is full the additional rainfall is transmitted to the cells below the tree as throughfall. Parameters estimation : For some species stemflow parameters were calculated from published data. For other species, not studied until now, parameters were calculated using data for morphologically similar species. A protocole was proposed for the estimation of storage capacity of the tree crowns. (see “Rainfall interception parameterisation.doc” for details). NEW MICROCLIMATE MODULE Theoretical background The new microclimate module was implemented in the HiSAFE daily loop, in Java language under CAPSIS environment. As the previous one, this module used the Shuttleworth and Wallace formalism (Shuttleworth and Wallace 1985)(see previous reports for more details). Each water vapour flux is then expressed as : E i sR ni C p D o / rai Eq. 3 s (rci / rai ) Were Ei is the water vapour flux (MJ day-1 m-2), D0 is the saturation deficit of the air within the canopy (mbar) and Rni is the net radiation of the canopy (MJ day-1 m-2), rci and rai are canopy and aerodynamic resistances, respectively (s m -1). The other symbols representing thermodynamic constants Reciprocally, D0 depends on the actual air saturation deficit (Da) and the sum of all the radiation and water vapour fluxes (Rn=∑Rni, E=∑Ei) : D 0 D a sR n (s )E raa C p Eq. 4 As a consequence of that coupling between E fluxes and D 0, a first estimate of D0 must be implemented at the beginning of the daily loop according to the available information from weather data of the day and actual evapotranspirations of the previous day. Then, as the fluxes and interactions between trees and crop were calculated, more accurate estimation of D0 can be provided. Finally the actual value can be calculated at the end of the daily loop accounting for all the stresses. (full details of The C++ code skeleton developed for those purpose were in “MicroclimatHiSAFE.doc”). Initial D0 estimate At the beginning of the daily loop, after the radiative transfer module, the first implementation of Eq. 4 needs estimates of Rni and Ei for each components of the system, namely trees, crop transpirations, water stored on trees an crops direct evaporation and soil evaporation. Each Rni, (one per tree , crop and soil ) was calculated from weather data, solar radiation absorbed by trees and transmitted to cells. We used, as in STRICS standard Brutsaert (1975) estimate for long wave radiation. When the canopy temperature is not available, air temperature is used. These R ni represent the total available energy per component i. Rni = Rvi + εi(Ra-σTs4) Eq. 5 where Rvi is the visible available radiation, calculated by the radiative transfer module for trees and estimated for cells by (1-ai)Rgi Eq. 6 with Rgi , the visible radiation received by the cell calculated by radiative transfer module and ai, the cell albedo (implemented). Ra is the atmospheric radiation following Brutsaert (1975) currently implemented in STICS, εi is the emmissivity of the component i, σ the Stephen-Boltzman constant and Ts the canopy temperature replaced by Ta , mean daily air temperature from the weather data. The available energy is first used for direct evaporation of water present on vegetation according to Prestley-Taylor equation (1972), hence E i sR n i s Eq. 7 Were α is a coefficient calculated by Brisson et al. (1998). The remaining energy, if any, is then used for trees and crops transpiration according the rates of the previous day following : E id E i ( d 1) R n id R n i ( d 1) Eq. 8 were subscripts d and d-1 means “of the day” and “of the day before” respectively. Then the water vapour fluxes, E=∑Eid is used for D0 estimation in Eq; 4. In order to account for tree canopy effects on crop microclimate, D0 is used as Da in the following STICS instances. Second D0 and fluxes calculation after the STICS runs As STICS provide for each cell, crop an soil water vapour fluxes and canopy temperature estimates. These variables are then used, for providing new estimates of Rni and Ei that are both used for a D0 calculation : actual Ts replaced Ta in Eq. 5 and actual crop and soil evaporation and transpiration from STICS are used in Eq. 4 for an updated D0 estimation. Then trees direct evaporations and potential transpirations are calculated by Eq. 3 with the updated values of the other variables. The potential transpiration of trees (from here) and crop (from STICS) are now all available for the water competition module. Final canopies energy budget and canopy temperatures estimates The trees canopy temperatures are calculated using the same formalism as in STICS to be consistent with crop temperature estimates. In that formalism, the average tree canopy temperature (TS) is the average of the minimum tree canopy temperature occurring in the morning before sunrise (T Smin) and the maximum tree canopy temperature occurring at midday (TSmax). In both cases, the canopy temperature TS come from the canopy energy budget equation. H + E + Rn = 0 Eq. 9 with H C p ra (T Ts ) Eq. 10 soit Ts T (R n E) ra C p Eq. 11 For TSmin : T = Tm (Tm = Minimum temperature of the day from weather data) ; E = 0; Rn calculated by Eq. 5 with Rvi = 0 For TSmax : T = Tx(Tx Maximum daily temperature from weather data); E = Emax.