GOTILWA+ An integrated model of forest growth

Transcription

1 GOTILWA+ An integrated model of forest growth Carlos Gracia Santi Sabaté Anabel Sánchez Model documentation and User s guide Updated March, 2003 (draft document, version 5) 1

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3 CONTENTS PART I: Model description...5 MODEL DESCRIPTION (OVERVIEW)...7 What s Gotilwa?...7 Aims And Purposes Of Gotilwa...8 What Is A Tree In Gotilwa...9 What Is A Forest In Gotilwa...10 What Can And What Can Not Be Simulated By Gotilwa...10 What can be simulated...10 What can not be simulated...11 CLIMATE...11 Incoming radiation...12 Temperature...14 Atmospheric CO Vapour Pressure Deficit, VPD...16 Precipitation...17 Evapotranspiration...18 Wind speed...18 SOIL...19 Soil Moisture...19 Soil Organic Matter Decomposition...22 Leaf Shedding/Litterfall...23 Fine Roots Mortality...26 TREE and STAND STRUCTURE...27 The Pipe Model...27 UNDERSTOREY...28 PHYSIOLOGICAL PROCESSES...29 Light Interception And Extinction...29 Leaf Energy Balance...30 Conductance...34 Photosynthesis...35 Canopy Structure And Hydrology...38 Autotrophic Respiration...39 Phenology...40 NET PRIMARY PRODUCTION AND CARBON ALLOCATION...41 CLIMATE CHANGE...42 MANAGEMENT REGIMES...43 MODEL VALIDATION...44 PART II : GOTILWA+ User s guide...47 Starting GOTILWA The simulation Controller...50 Forest System...50 The Input Data...52 The Input Data...53 Help on line...55 Modifying the Input data files...56 Photosynthesis...57 Stomatal conductance...59 Forest Structure...60 Tree density...61 Understorey...62 Soil definition...63 Canopy...64 Climate...65 Plot daily climate values...65 Plot monthly climate values...66 Analyze climate data

4 Convert ASCII to RANDOM climate files...68 Climate Change...69 Management...69 Management...70 Weather generator...71 Weather generator...72 Using the batch...72 Plotting and mapping results...73 Generating growth and yield tables...74 The Constant values...75 The output variables...81 The output variables...82 Plotting selected output variables...83 Focusing a zooming a given time period...83 Daily, Monthly and annual plots...84 Comparing plots...85 Basic statistics of plotting variables...86 PART III: Simulating the growth of Aleppo pine in Catalonia...87 List of main publication involving GOTILWA Main publications describing some field experiments related to GOTILWA Publications describing the estimation of parameters used in GOTILWA

5 PART I: Model description 5

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7 MODEL DESCRIPTION (OVERVIEW) What s Gotilwa? GOTILWA+ is a mechanistic deterministic forest growth model that has been implemented to simulate the forest growth processes and to explore how these processes are influenced by climate, tree stand structure, management techniques, soil properties and climate change. The name, GOTILWA, is an acronym for Growth Of Trees Is Limited by WAter. The name itself defines the main characteristic of the model. Water is, very often, the limiting factor for plant growth (Piñol et al., 1991; Sala, 1992) and thus it constitutes a key factor in the model (Tello et al., 1994). In a standard simulation climatic data are daily analyzed. From the interaction between daily rainfall and the forest structure the amount of intercepted water by the canopy layer, throughfall and stemflow are also estimated. This effective rainfall increases the water stored in the soil which is used by the trees. The proportion of sapwood to heartwood, the leaf area of each tree and, consequently, the leaf area index (LAI) of the forest are all highly dependent on water availability in the model. Figure 1. Schematic representation of the climate, physiological processes, soil traits, tree and stand structure and management regimes in the GOTILWA+ model. 7

8 GOTILWA+ has been used to explore: the responses of different forest types to water availability, especially in the Mediterranean and other arid or sub arid zones, the effects of Global Change on the forest dynamics, production and Carbon fluxes, as well as the effects of different forest management techniques on the Carbon stocks and fluxes. Nevertheless, the model is general enough to be applied to other forest types. Some applications to Loobos (The Netherlands, temperate Scots pine forest), Hyytiala (Finland, boreal Scots pine forest), Bray (France, temperate Maritime pine forest) have been made. It can be applied to all tree species, deciduous or evergreen, in all regions, boreal, temperate or Mediterranean. With mono-specific tree communities. The carbon uptake by the trees is computed by using the Farquhard model of photosynthesis. The pool of carbon gained leads to an increase, primarily, in the mobile carbon stored in the plant. A fraction of this carbon compensates the maintenance respiration, while the remaining carbon, if any, constitutes the net primary production (NPP). Associated to the formation of new biomass components there is a metabolic cost which constitutes the growth respiration. The balance between the maintenance respiration, the NPP and the metabolic cost associated to the formation of new biomass, determines the processes of leaf formation and leaf fall, tree ring formation, the rate of change of sapwood into heartwood and, consequently, the changes in tree structure within each size class. These changes will affect in turn the hydrological fluxes which will subsequently take place in what might be described as a feed-back process (Sala and Tenhunen, 1994). Aims And Purposes Of Gotilwa GOTILWA is a forest growth model that has been implemented to simulate the forest growth processes and to explore how these processes are influenced by climate, tree and stand structure, management techniques, soil properties and climate change. GOTILWA has been used to explore: the responses of different forest types to water availability, especially in the mediterranean and other arid or sub arid zones, the effects of Global Change on the forest dynamics, production and Carbon fluxes, the effects of different forest management techniques on the Carbon stocks and fluxes. The time resolution used in the model is: a) for physiological processes (Photosynthesis, Stomatal Conductance, Respiration, ) 1 hour time step. Integrated to produce daily values and b) for structural values (tree ring formation, biomass, ) 1 day time step. The output of the model is produced at three levels: daily, monthly and yearly. The forest is described as a population of individuals each of them having its particular size (DBH). The total population density (trees/ha) and the distribution of trees in DBH classes are used to define the initial structure of the population. In GOTILWA+, all the trees belonging to a given DBH class are considered as identical and all of them experience the same processes. Results of GOTILWA+ are computed for each DBH class and they are integrated at the stand level. Mixed species forests can not be simulated, that is, interaction between different tree species growing in a particular stand are out of the scope of the model. GOTILWA+ can simulate the understorey structure, biomass and evolution and its interaction with the tree layer. 8

9 What Is A Tree In Gotilwa A single tree is, in the context of GOTILWA, a complex individual formed by two main parts: the above and below-ground components the structure of which are summarised in table 1. The aerial part is formed by three main components: leaves, branches and stem while coarse roots (including lignotubers if it is the case) and fine roots are the two components of the belowground biomass. Six main variables are used to characterise the leaves at the tree level: leaf area of a tree (m 2 ), leaf biomass of a tree (g) both linked by the leaf specific mass (mg/c m 2 ), the mobile carbon stored in leaves in a given moment (g) and the maximum mobile carbon that can be stored in leaves. LSM changes according to the variations in the mobile carbon but there is a maximum value of LSM that never can be surpassed. In addition to the structural variables the physiological characterization of the leaves of a species has several parameters involved. These leaves can be amphistomatous or hypostomatous and obviously, deciduous or evergreen. Addenda: resprouter or seedler. Table 1. Components of the above and below-ground tree structure in the GOTILWA model. leaf area AF m 2 AF=αLAI SA leaf biomass BF g BF=AF LSM mobile carbon CMH g CM=BF PC PC=CM/BF maximum mobile carbon CMHo g Input constant leaf specific mass LSM m 2 LSM=LSMo (1-(CMHo- CMH)) maximum leaf specific mass LSMo m 2 Input constant diameter at breast height DBH cm Basal area AB cm 2 AB=0.25 π DBH 2 Sapwood area AA cm 2 AA=AB VGA vigor VGA % VGA=AA/AB wood biomass BMA kg BMA=αBM DBH β branches biomass BR kg BR=BMA PBR mobile carbon CMM kg maximum mobile carbon CMMo kg Input constant Fraction of respiring FAR % Input constant sapwood biomass BMS kg BMS/BMA=k vigor VGS % VGS=VGA mobile carbon CMM kg maximum mobile carbon CMMo kg ABOVE- GROUND BIOMASS BELOW- GROUND BIOMASS FRACTION VARIABLE SIMBOL UNITS STRUCTURAL RELATIONS LEAVES BRANCHES AND STEM COARSE ROOTS FINE ROOTS biomass BRF g BRF=αRF AA 9

10 Tree Structure Parameter Units α-biomass B=a*DBH^b --- β-biomass B=a*DBH^b --- belowground/aboveground biomass kg/kg α-lai m 2 /cm 2 m 2 of leaves per cm 2 of sapwood α-vigor cm 2 /cm 2 cm 2 of sapwood per cm 2 of total wood cross-sectional area α-fine roots g/cm 2 g of fine roots per cm 2 of sapwood Leaf Specific Mass mg/cm 2 Max. mobile Carbon in Leaves % Max. mobile Carbon in Wood % Fraction of respiring sapwood % Leaf Shedding (base line) day -1 Fine roots mortality (base line) day -1 Gross /fine literfall g/g Branches /aboveground biomass kg/kg Wood density g/cm 3 Cumulated sapflow kg/cm 2 /t Seedler/Resprouter bolean What Is A Forest In Gotilwa The forest is described as a population of individuals each of them having its particular size (DBH). The total population density (trees/ha) and the distribution of trees in DBH classes are used to define the initial structure of the population. In GOTILWA, all the trees belonging to a given DBH class are considered as identical and all of them experience the same processes. DBH class is defined by the user with the condition that the total number of classes do not exceed 50. Narrower classes increase the precission of the results but also increase the simulation time. The disk space required to save the results is not affected by this parameter. No particular position in space of each single tree is taken into account. What Can And What Can Not Be Simulated By Gotilwa What can be simulated The growth of any one single species forest (young or mature, plantation or natural forest) provided that the initial density (trees/ha) and DBH distribution is defined. The evolution in time of the structure of the forest growing under different climates. The running length is only limited by the available space in the hard disk to store the results. The effect of given changes in a particular climate on the forest. Typical situations are: increase gradually the atmospheric CO 2 concentration, temperature and increase or decrease of rainfall according to a given pattern normally obtained from the GCM models to express the effects of global change on the forest growth and stand structure. 10

11 The consequences of different management scenarios on the forest. The combination of some or all of these scenarios that is, forest structure, climate change and management techniques, to provide any particular forest scenario. -The possibility to simulate, the growth of any one single species forest (young or mature, plantation or natural forest) provided that the initial density (trees/ha) and DBH distribution is defined. With the possibility of including the growth of an understorey cover. - The possibility to simulate the effect of given changes in a particular climate on the forest. Typical situations are: increase gradually the atmospheric CO 2 concentration, temperature and increase or decrease of rainfall according to a given pattern normally obtained from the GCM models to express the effects of global change on the forest growth and stand structure. - The possibility to simulate the consequences of different management scenarios on the forest. And the combination of some or all of these scenarios that is, forest structure, climate change and management techniques, to provide any particular forest scenario. -Its ability to simulate water stressed situations, which is crucial in Mediterranean-type climates. What can not be simulated Mixed species forests: Interaction between different tree species growing in a particular stand are out of the scope of GOTILWA. -It can only simulate one single species forest. -Nutrient cycle is not included in the model. -It does not distinguish horizontal spatial heterogeneity. -Tree height, which can be interesting for some applications, is not included as an explicit variable. -Some of the processes included in the model need empirical relations. -It does not include processes such as herbivory or insect attacks. -It needs a good knowledge of the forest. CLIMATE Climate is defined as the characteristic patterns, means and extremes of weather (local, short-term atmospheric conditions). It affects all the physiological mechanisms of trees and determines the soil processes. Microclimate, or local variation in climate, is the climate near the surface of the Earth and it is really what influences vegetation and soil processes to the extent that plants are coupled to their microclimate. Daily values of the incoming radiation, maximum and minimum air temperature, rainfall, wind speed, vapour pressure deficit and atmospheric CO 2 concentration are the climatic variables used by GOTILWA. When daily values are not available, the GOTILWA Weather Generator (GWG) can be used to generate daily values from monthly records which are much more common in most weather stations. The basics of GWG are described in Apendix *. Photosynthesis and other physiological processes are simulated at one hour 11

12 time step so, hourly values of solar radiation, air temperature, precipitation are estimated from the daily values provided as input data. The way these hourly values are generated are described in the next paragraphs. Table 3. Climate variables CLIMATE Variables Symbol Units Solar radiation Q MJ/m 2 /day Max. Daily temperature Max T ºC Min. Daily temperature Min T ºC Rainfall P mm/day Wind speed m/s CO 2 ppm Vapour Pressure Deficit VPD kpa Incoming radiation Solar radiation is the ultimate source of energy for photosynthesis. When solar radiation reaches the atmosphere and arrives to the Earth s surface it can be divided into two different components: direct radiation, if it comes directly from the sun, and diffuse radiation, if it is reflected or scattered by clouds and dust particles. Table 2. The ecosystem components in GOTILWA. CLIMATE TREES SOIL Process Variables Units Solar radiation MJ/m 2 /day Max. Daily temperature ºC Min. Daily temperature ºC Rainfall mm/day Wind speed m/s CO 2 ppm Vapour Pressure Deficit kpa Photosynthesis Stomatal Conductance Tree Structure Canopy structure Density Organic layers Mineral layers Plants are only able to use for photosynthesis 50% of total solar radiation (direct and diffuse), within the band nm, it is called the Photosynthetic Active Radiation (PAR). From the meteorological data set we obtain total daily global radiation at the Earth s surface. As our photosynthesis calculations are performed on hourly basis, we need to estimate hour by hour the diurnal course of this measured value of surface global radiation. To do so, we first calculate global extra-terrestrial radiation for each hour of 12

13 the day considering clear sky conditions and constant atmospheric transmissivity. Summing up this hourly values we obtain the daily global extra-terrestrial radiation value Q ex for that day. Then the ratio Q sur /Q ex is calculated being Q sur the radiation measured at the surface of the earth. This ratio is used as a correction factor for cloudiness and atmospheric conditions of that particular day. Applying this correction factor to each hourly value of Figure X. Estimation of the incident solar radiation using the relative position of the sun and earth for a particular date and time. extra-terrestrial radiation we can obtain the hourly values of surface radiation. Q ex is computed using the position of the forest plot on the Earth s surface (latitude and longitude), the day of the year and the time of the day. The solar elevation angle β (figure X) can be calculated as: sinβ = cosα = sinφ sinδ + cosφ cosδ cosω The solar zenith angle α, is α = 90 β being φ, the latitude (GG.mm) and δ the solar declination (radians) calculated using the Lokmanhekim method: δ = cos x cos 2x cos3x sinx sin2x sin3x where ( ) 365 x = 360 d d = Julian date of the day (1 to 365) ω, is the time angle: (( ) 15 ) cos β sin ωγ= = hcos 12δ sinω γ, is the solar azimuth angle: [ 1 cos β ] ( sinφ cosδ cosω φ sinδ ) cosγ = cos and, is the day length. To calculate the day length that is, the hours of sun for a particular day we first obtain the hour of sunrise, H srise, and the hour of sunset, H sset, and then the day length as follows: 13

14 H srise arctg = 12 1 [ tgφ tgδ ] 2 ( tgφ tgδ ) 15 = H sset H srise H sset arctg = [ tgφ tgδ ] ( tgφ tgδ ) 15 2 The incident direct radiation on a horizontal surface, I dh (MJ/m2/min) for each hour of the day can be estimated as: 2 1 sin β I dh = I k r τ sin β the incident diffuse radiation on a horizontal surface, I fs (MJ/m2/min), for clear sky conditions as: and for cloud covered sky conditions, I fn (MJ/m2/min), as: Generalizing this equations, the incident direct radiation for each hour of the day, I dir (MJ/m2/min) on a given surface that forms an angle ϕ with the sun rays, can be I fn = I k r cos 2 ( 2 n e 1 ϕ 1 sinβ 1 sinβ 2 τ I fs = 0.35 I k τ e 2 1 sin β I dir = I k r τ cosϕ estimated as: and the diffuse radiation for each hour of the day, I s for clear sky conditions, I n for cloud covered sky conditions and I dif for partially covered sky conditions, (MJ/m2/min), as: / 2) I I s ndif 1 sin β 2 τ = 0.35 Ik τ e = 2 I r n e = I + I * n * cos ( ϕ/ / 2) 2 k where I k, is the solar constant, MJ/m 2 /min, τ is the atmospheric transmissivity, usually 0.7 for clear skies, r is the relative distance earth-sun in a given day: r 2 (( 360 ) day) = cos 365 and ϕ, is the angle formed by the sun rays and a surface of inclination ψ and azimuth θ, sin cosϕ = ( sinδ sinφ cosψ ) ( sinδ cosφ sinψ cosθ ) ( cosδ cosφ cosψ cosω ) + ( cosδ sinψ sinθ sinω ) ( cosδ sinφ sinψ cosθ cosω ) β 1 2 [( ) ( )* e ] + [ I * cos ( ϕ / 2) * ( 1 n) ] dh fs fs Temperature Air temperature directly controls leaf carbon gain by influencing rates of photosynthesis and respiration. The daily temperature pattern follows a sinusoidal curve with maximum 14

15 an minimum temperatures lagging the corresponding incident radiation curve by a few hours (depending on latitude). From the meteorological data set we obtain daily maximum and minimum temperatures. To build up the daytime pattern of air temperature GOTILWA uses the empirical sinusoidal function; T air hour ( T + T (( T T ) cos( 1.5 π ( hour H ) ) )) = 0.5 min max max min srise where T min is the minimum temperature (ºC) of the day, T max is the maximum daily temperature (ºC) and is the day length (hours) calculated as: = 24cos 1 ( tan[ φ π 180] tanδ ) π The figure X represent the daytime pattern of air temperature of a day with maximum temperature of 31ºC and minimum temperature of 18ºC. 40 Figure X. Example of daytime pattern of air temperature of a day with maximum temperature of 31ºC and minimum temperature of 18ºC. temperature (ºC) hours Atmospheric CO 2 The pre-industrial (until year 1840) atmospheric CO 2 concentration is 280 ppm. From this base-line pre-industrial concentration the model calculates the CO 2 concentration value that corresponds to every determinate year of simulation applying two different constants of climate change for the periods 1840 to 1990 and 1990 onwards. Besides this, the initial CO 2 concentration can be any value defined by the user which will remain constant all along the simulation unless a change in that value is determined in the climate change file. 15

16 Vapour Pressure Deficit, VPD Water vapour pressure contributes to the total measured atmospheric pressure and its partial pressure is called water vapour pressure. When air above water has no extra capacity for holding water vapour the partial pressure is termed the saturation vapour pressure. The saturation vapour pressure increases with temperature. VPD is the difference between the saturation vapour pressure and the actual vapour pressure at the same temperature. It is an index of the drying power of the air, the higher the deficit the greater the evaporation rate (Photosynthesis and production in a changing environment, Hall D.O. et. al. 199_) From the meteorological data set we obtain the vapour pressure of the day, VP which we consider measured at dawn and thus VPD is considered to be equal to 0. This consideration is not exactly true for dry atmospheric condition and thus a correction factor should be applied (Waring and Schlesinger). GRAFICA WARING AND SCHLESINGER The saturation vapour pressure for each hour of the day is calculated as, (( T ( ( T 254.4) )) ( ) ) esat = exp T + being T the air temperature at a determined hour of the day. We then calculate the VPD for each hour of the day as, 16

17 VPD = esat VP Precipitation Water enters terrestrial ecosystems from the atmosphere as precipitation. The amount of water available for transpiration plays an important role in determining the productivity of the plants in the system. Water is especially important in Mediterranean ecosystems as it is very often the limiting factor. From the meteorological data set we obtain total daily precipitation from which we estimate the rainy periods of the day. This estimation is carried out as follows: rain (mm) hour Figure X. Example of rain distribution in a particular day using the random approach of GOTILWA. First of all we know the total amount of rain fallen in a day, for instance 6 mm. Then we generate a random number that determines the hour of the day in which the rainy episode starts, for instance 9:00 a.m. We have that maximum intensity of rain is 1 mm/hour and minimum intensity of rain 0.2 mm/hour. After that we generate successive random numbers (between 0.2 and 1) that determine the intensity of rain for each hour in the rainy episode. Depending on this aleatory rain intensities in each hour a determined amount, from the daily total rain, falls. For instance intensities of 0.9, 0.3, 1, 0.6, 0.7, 0.2, 0.8, 1, 0.5 mm/hour from 9:00 (starts to rain) to 10:00, from 10:00 to 11:00, from 11:00 to 12:00 and so on until 18:00 (rain ends). -in that way total daily rain is distributed into consecutive hours of rain with determined intensities of rain and the rainy episode ends when the total amount has been distributed = 6 mm distributed in 9 hours from 9 in the morning to 6 in the afternoon. -if we get to the hour 24:00 we start again in the first hour of the day. -in days of heavy rain it is possible to arrive again to the initial hour when rain started, 9:00 in the example, with still some rain to be distributed. In this case we proceed in the same way determining another random intensity for that hour, for instance 0.5 mm/hour, and continue to do so for the following hours until the total amount is distributed. Note that for this hour the sum of the two assigned intensities ( = 1.4 mm/hour) is higher than the defined maximum intensity (1 mm/hour). 17

18 Evapotranspiration Evapotranspiration is the water lost to the atmosphere from the soil surface (evaporation) and through plants (transpiration). Evaporation and transpiration are functions of water availability and temperature. If they are not available, it can be calculated/estimated by GOTILWA through the Penman and Monteith equation: S I dir ETP = 1.08 ( S + γ )λ where I dir is the incoming solar radiation (see...), λ the evaporation latent heat (MJ/mol): T the hourly air temperature and γ, the psicrometric constant (kpa/ºc) estimated as: being Po the normal pressure (Po=101.3 kpa) and Cp the specific heat of air at constant pressure (Cp = J/g/ºK). The saturation vapour pressure deficit for each hour of the day S, is: S = e esat esat the saturation vapour pressure, is estimated as: and the vapour pressure, e as: ( ( 42.9) ) λ = T P o C p γ = λ being T the temperature (ºC) at that time of the day. (( T ( ( T 254.4) )) ( ) ) esat = exp T + ((( T + 1) ( (( T + 1) 254.4) )) (( + 1) ) ) e = exp T + Wind speed Wind is the large-scale transport of air masses resulting from differences in air pressure. It is directly involved in heat and mass transfer by forced convection, so it is very important in influencing heat and gas exchange across the boundary layers of plants. Increase in wind speed decreases leaf boundary layer resistance which tends to increase evaporation and bring leaf temperature closer to air temperature. (Photosynthesis and production in a changing environment, Hall D.O. et. al. 199_). From the meteorological data set we obtain the mean daily wind speed. If it is not available a number between 1 and 5 is assigned randomly by GOTILWA. 18

19 SOIL Table 2. Components of the SOIL hydraulic conductivity and SOIL organic matter. Process Parameter Symbol Units Initial SOC in organic horizons g/cm 2 Initial SOC in mineral horizons % of dry weight Bulk density g/cm 3 Decomposition rate of OM in LF h. k(lf) day -1 Soil Carbon Fluxes Decomposition rate of OM in AB h. k(ab) day -1 Soil temperature effect factor Q LF to AB transfer rate t o m --- W min mm W max mm Hydraulic gradient m/m Soil Hydraulic Conductivity m/day Soil Hydraulic Conductivity Mean Soil Depth m Minimum Water Usable mm/m Stones volume % Soil Moisture Water availability can limit growth and production. The rainfall water that arrives to the soil, effective precipitation, is stored within soil pores to be absorbed later by plant roots and finally returns to the atmosphere through transpiration from leaf surfaces. This system is termed the soil-plant-atmosphere continuum and water moves though it along gradients of water potential. Soil water content is a measure of the amount of soil water present in the soil at a determinate moment. It can be express as a weight fraction (grams of water/grams of soil) or as a volume fraction (cm3 of water/cm3 of soil). In order to estimate soil moisture content, some aspects of soil characteristics have to be defined and taken into account: -Soil particle density, D p, is the mean density, mass per unit volume, of soil solids (Mg/m3). Weight.. of. solids D s = Volume. of. solids Soil particle density is practically constant for a given horizon as it does not depend on soil structure or soil particle size. A mean value of particle density that can be assumed for most mineral surface soils is 2.65 Mg/m3. As organic matter (or organic carbon) has low values of particle density, this mean value should be adjusted taking into account the soil organic matter content. In the model this adjustment is done as follows, ( ) D s = SOC 19

20 -Soil bulk density, D b, is the mass per unit volume (Mg/m3) of dry soil (includes soil solids and soil pores). Weight.. of. dry. soil D b = Volume. of. soil( solids + pores) The bulk density value of a determinate soil gives information about soil compaction and thus about soil pore spaces. All the factors that affect soil pore space influence bulk density, for instance, organic matter increases total macro-porosity consequently decreasing bulk density. Calculations of bulk density can be done by several approaches, some obtained by correlation studies, whereas others come from theoretical considerations. In all of them it is necessary to take into account some factors such as organic carbon (or organic matter) content and texture (clay content, sand content). In the model bulk density is estimated using the equation of Honeysett & Ratkowsky, 1989 modified assuming that, in mean, the ratio OM/C is (Jackson, 1961), [ log ( 1. )] D b = SOC Porosity, percentage of pore space in total soil volume. Values of porosity vary widely for different soil types. Porosity can be calculated from the values of particle density and bulk density, Bd P = D s s Water-filled porosity, WFP and water-holding capacity, WHC are similar terms both of which can be used to express values of soil water content available for plants. In the model, WFP is estimated from, 20

21 WFP = 100 WFP as a percentage of water in relation to soil weight In GOTILWA, we calculate soil moisture, M, as a percentage of maximum water-filled porosity: -We first estimate soil particle density and soil bulk density as function of soil organic carbon. -Then we calculate soil porosity from soil particle density and soil bulk density. -From soil porosity and soil particle density we obtain water-filled porosity -We calculate water in the soil from the consideration of the amount of water that the soil can hold and from the water balance between inputs as precipitation and outputs as evapotranspiration, runoff and drainage. -Finally we obtain soil moisture, M = % soil water / maximum soil WFP P ( 100 P) D s 21

22 Soil Organic Matter Decomposition Organic Matter, OM, incorporated to the soil, proceeds from two different sources of plant litter, aboveground litter (leaves, branches, stems and reproductive organs) and belowground litter (coarse and fine roots). The fraction of OM in the soil is quite small in relation to other soil components. In spite of this, it plays a critical role due to its determinant effect on soil properties and structure. Furthermore Soil Organic Matter, SOM, is the substrate for soil microbial activity. The process of decomposition and mineralization of SOM by micro-organisms produces the release of nitrogen and other nutrients making them again available for plant use (recycling of nutrients), and the release of carbon to the atmosphere as CO 2, constituting a basic step in the global carbon balance. The OM decomposition rate depends on different factors such as the quality of the plant material that is decomposing and the environmental conditions in the soil, basically soil moisture and soil temperature, although good aeration and almost neutral ph are also important. The study of CO 2 efflux has to include both the effect of temperature and water. Microbial activity is very sensitive to changes in soil water content. Empirical observations show that soil respiration activity reaches its maximum value at about 60% of the maximum water-filled porosity. Below this value, the microbial activity becomes limited by water; above this value, the lack of oxygen becomes limiting, and features typical of anaerobic conditions, such as denitrification, are likely to occur. In both directions (above and below) CO 2 efflux decreases strongly. The activity of micro-organisms is also very sensitive to temperature. Microbial decomposition increases with increasing temperature. Usually the effect of temperature is expressed as Q10 effect, that is, Q = k t k t the ratio of increase in metabolic activity as a consequence of an increase of 10 ºC in temperature: in which kt is the velocity constant of a given metabolic process at a temperature t, and kt +10, the same constant, but at a temperature t +10. In the Van t Hoff law, (for chemical reactions), Q10 is of the order of 2 or 3. For living systems it is not so easy, because in practice Q10 is not constant in the range of biotic temperatures (0-30ºC). For soils, Q10 tend to increase with increasing temperature (Schleser, 1982), and for a given pair of temperatures ( t and t+10) also depends on the water content of the sample (Howard & Howard, 1993). Microbial decomposition of plant OM can be described with the equation, k t OM t = OM o e in which, the amount of OM at a determinate time OM t during its decomposition is proportional to the initial OM, OM o and to its first-order decomposition rate, k In GOTILWA, soil is divided in two layers; an organic layer and a mineral layer with an organic matter transfer rate between them. To determine the amount of OM present in each soil layer GOTILWA takes into account the OM entering the soil from litterfall, dead trees and slash material for the organic layer and the OM entering the soil from the amount of dead fine roots, dead trees, slash material and OM coming from the upper layer, for the mineral one. 22

23 The OM transfer from the organic layer to the mineral layer is function of the transfer rate and of the amount of OM that has been decomposed in the organic layer. Each one of the layers has a different OM decomposition rate. Both rates are function of soil temperature (Q10) and water. Estimation of soil temperature is calculated from air temperature using a moving average of 11 days. Estimation of soil water for organic layers is calculated taking into account the cumulated rainfall of the previous 30 days and estimation of soil water for mineral layers depends on the percentage soil water filled porosity. The model calculates the amount of OM that is decomposed in each of the two soil layers and that is consequently lost into the atmosphere as CO 2 efflux and also the OM remaining in the soil layers. LF LF t 0 = Ω(1 e k ) Q t Ω 1 AB AB t 0 = Ψ(1 e k ) Q t S S 1 2 Soil moisture Leaf Shedding/Litterfall Leaf shedding is mainly related to carbon balance, during unfavourable periods in which GPP and mobile carbon stored cannot compensate the respiratory cost the trees can lose a supplementary fraction of leaf biomass to reduce their respiratory cost. The fraction of leaf mass loss is the amount necessary to allow GPP and mobile carbon to compensate tree respiration. Nevertheless there is also a temperature dependent leaf shedding, Q10. The production of woody material litter in the model is accounted for as a proportion relative to leaf litter. In GOTILWA+, a base line fine root mortality rate is defined, η, and apart from it, mortality can be induced by three factors that enhance fine root decay, 23

24 -soil temperature: expressed as Q10 effect. Soil temperature has a rapid effect of increasing fine root mortality when it is different from the temperature optimal, 25ºC. µ = η + Q 1 10 t being, µ 1 the mortality rate induced by temperature, and t the soil temperature. -soil water content: for a determinate range of soil water content, which is the optimal for processes that take place in the soil, fine root mortality is not enhanced, but, below and above this range, water becomes a factor that increases fine roots mortality either because water is limiting or because is too abundant and then oxygen becomes limiting. Being, µ 2 the mortality rate induced by water in the soil (see figure 4). -length of the growth period: the beginning and end of the growth period are determined as functions of temperature. During the time before and after the growth period fine root mortality increases quite drastically following the equation, µ 3 = η + f day t day µ 3 is the mortality rate induced by phenology, and t the daily temperature. Each factor inducing mortality, determines a mortality rate and the model takes into account as mortality rate for fine roots the maximum of these three rates, µ = max [ µ, µ µ ] 1 2, 3 Figure 4. The mortality of fine roots is assumed to be the higher of the three components induced by soil temperature, soil water content and phenology. 24

25 Leaf litter production in forest ecosystems is strongly related to climate. It is low at high latitudes due to shorter growing seasons and it increases with decreasing latitude. However, for a determinate latitude quite a wide range of variation can occur resulting from the influence of particular/local conditions (disturbances, water stress, low nutrient availability,...). In GOTILWA, leaf shedding is basically a temperature dependent process, Q10. Nevertheless during unfavourable periods in which GPP and mobile carbon stored cannot compensate the respiratory cost the trees can lose a supplementary fraction of leaf biomass to reduce their respiratory cost. The fraction of leaf mass loss is the amount necessary to allow GPP and mobile carbon to compensate tree respiration. Translocation of mobile carbon from leaves into nearby branches and the tree stem, takes place prior to leaf abscission. The amount of carbon retranslocated depends on the amount of mobile carbon stored in leaves. Leaf specific mass (LSM) of shed leaves decreases according to this translocation (Sabaté 1993). The production of woody material litter in the model is accounted for as a proportion relative to leaf litter. Soil is divided in two layers, organic and inorganic horizons. Soil organic matter (OM) is originated by plant litter: leaves, branches, stems and reproductive organs aboveground and coarse and fine roots belowground. Each one of the layers has a different OM decomposition rate. Both rates are function of soil temperature (Q10) and water. The model calculates the amount of OM that is decomposed in each of the two soil layers and that is consequently lost into the atmosphere as CO 2 efflux. 25

26 Fine Roots Mortality Fine roots are the fraction of tree roots of diameter less than 2.5 mm. They are very dynamic with turnover times of between a few weeks and more than 8 years (Hendrick and Pregitzer, 1992). Knowledge of fine root production and decay is not yet fully complete, however it is clear that they represent an important proportion of the whole plant production and that fine root litter involves a significant transfer of carbon and nutrients from the plants into the soil. In GOTILWA, a base line fine root mortality rate is defined, η, and apart from it, mortality can be induced by three factors that enhance fine root decay, -soil temperature: expressed as Q10 effect. Soil temperature has a rapid effect of increasing fine root mortality when it is different from the temperature optimum, 25ºC. µ = η + Q 1 10 t being, µ 1 the mortality rate induced by temperature, and t the soil temperature. -soil water content: for a determinate range of soil water content, which is the optimal for processes that take place in the soil, fine root mortality is not enhanced, but, below and above this range, water becomes a factor that increases fine roots mortality 26

27 either because water is limiting or because is too abundant and then oxygen becomes limiting. Being, µ 2 the mortality rate induced by water in the soil. -length of the growth period: the beginning and end of the growth period are determined as functions of temperature. During the time before and after the growth period fine root mortality increases quite drastically following the equation, µ 3 = η + f day t day µ 3 is the mortality rate induced by phenology, and t the daily temperature. Each factor inducing mortality, determines a mortality rate and the model takes into account as mortality rate for fine roots the maximum of this three rates, µ = max [ µ, µ µ ] 1 2, New amount of fine root biomass, is calculated after mortality has occurred, Bfr t = Bfr t 1 1 ( µ ) being, Bfr t-1 and Bfr t fine root biomass before and after fine root mortality respectively. 3 TREE and STAND STRUCTURE The Pipe Model 27

28 Interception is estimated for each rainfall event as a function of the Leaf Area Index and the rainfall intensity. The intensity of precipitation is simulated distributing the daily rainfall into a number of hours of rain which are randomly assigned. The stream runoff, leaving a stand can be estimated as a function of rainfall and Water Filled Porosity, WFP, that is a measure of how saturated the soil is, h 24 Runoff = = h= 0 ( R I )* ( W WFP ) hour soil max where R hour is the hourly rainfall (mm), I is the interception, W soil is the amount of water in the soil (mm) and WFP max is the maximum WFP. Actual evaporation and transpiration are functions of water availability and temperature. Figure 6. Main water fluxes simulated by GOTILWA+ UNDERSTOREY 28

29 PHYSIOLOGICAL PROCESSES Light Interception And Extinction Light interception and extinction is defined by the properties and characteristics of canopy structure. Canopy structure, the way leaves are displayed within the canopy, determines directly the amount of leaf area that is intercepting the incident radiation and in what conditions and also how this intercepted radiation is attenuated on its way down through the canopy. Furthermore, radiation, specifically the photosynthetic photon flux = photons with wavelengths between 400 and 700 nm =PAR, at each level of the canopy is the major factor determining leaf photosynthesis. In the process of estimating canopy photosynthesis it is then essential to determine canopy structure and light interception at each level in the canopy and to take into account solar position. As canopy structure is very complex it is necessary to approximate its description. In order to do so we use methods that only take into account the most important aspects of canopy structure: leaf area index ( area of leaves m 2 per unit of ground area m 2 ) which determines the amount of intercepting surface and leaf angle which changes the amount of light that the leaf absorbs and thus it is the most influential factor involved in the different rates of light extinction through canopy. Light intensity decreases exponentially with increasing canopy depth, which is characterised by an extinction coefficient. In this model, we use the method proposed by Campbell (1986) to determine the extinction coefficient. In it the radiation extinction coefficient within a canopy is calculated using an ellipsoidal leaf angle distribution. The leaf angle distribution of a canopy is represented by the distribution of the area on the surface of an ellipsoid of revolution. Being a the vertical axis length of the ellipse and b the horizontal axis length, a single parameter x can be defined as x = b/a. This parameter, x, representing the ratio of vertical to horizontal projections of a volume foliage determines the shape of the distribution. An spherical distribution would have a value of x = 1. The extinction coefficient,µ, is calculated by x µ = 2 π + tan β ( x ( x ) ) 2 Once we obtain this distribution and its extinction coefficient we can apply it to divide the canopy in two fractions, sun and shade and so we obtain the leaf area that is in the sun or in the shade, the corresponding amount of radiation (direct and diffuse) that is absorbed by each fraction and thus the photosynthesis that this sunlit or shaded leaves are able to perform. We calculate the fraction of total LAI that is sunlit, 0.5 sinβ LAIsun 1 e µ LAI = sinβ sinβ µ 29

30 the total radiation (MJ/m2/min) scattered, Q scat, incident on sunlit leaves, Q sun, and incident on shaded leaves, Q shade, Q scat = 0.07 I 1 d sinβ ( LAI ) e LAI Q shade = I fs e + Q scat µ sinβ Q sun = I d e + Q shade from which we obtain the mean photosynthetic photon flux density (µe/m2/s) for sun leaves, PPFD sun, and shade leaves PPFD shade, taking into account that 42% of global radiation is PAR and considering 4.6 µeinsteins per Watt in solar radiation: 4.6 PPFD sun Q 6 10 = 7 sun 4.6 PPFD shade Q 6 10 = 7 shade Leaf Energy Balance The process of photosynthesis is only able to use a very small portion of all the solar energy that arrives to the canopy. Most of it, in the form of heat, has the effect of increasing leaf temperature. Leaf temperature controls all the physiological processes that take place in leaves. A simplified approach is needed to explain leaf energy exchange with the environment (early studies by Gates, 1962). In it we accept the condition that a leaf must be energetically balanced. This means that, at a determined leaf temperature, the energy inputs must be equal to the energy outputs as expressed by the equation, Q i + L = α Q + R + C + λ E i v and in that sense, if any of the components of this equation changes, leaf temperature will change until a new balance is met. 30

31 The inputs in the leaf energy balance equation are: incident short-wave radiation, Q i (MJ/m 2 /min) and incident long-wave radiation, L (MJ/m 2 /min) and the outputs are: reflectance, α.q i (MJ/m 2 /min), long-wave radiation emitted by the leaf, R (MJ/m 2 /min), convection, C v (MJ/m 2 /min) and transpiration, E (mols/m 2 leaf/min). Q i: It is function of latitude, longitude, hour of day, year,... L : Infrared radiation is calculated by the Stefan-Boltzmann equation, L = ξ σ 4 a T a ξ = a T ( VP 1000) 1 7 a where ξ a is the atmospheric emissivity, σ is the Stefan-Boltzman constant σ = 5.67 * 10-8 W/m 2 /ºK and T a is the air temperature (ºK). α.q i : It represents the fraction of radiation arriving to the leaf that is reflected. Some leaf surface characteristics such as pubescence or waxes can increment this term. α is the leaf surface albedo. R : Re-radiation of long-wave radiation emitted by the leaf surface (MJ/m 2 /min) is also calculated by the Stefan-Boltzmann equation. Emissivity in leaves is quite high. Temperature is the factor that affects more this re-radiation. 31

32 In the model, only the re-radiation from one side of sun leaves is taken into account as it is assumed that re-radiation from the other leaf side is balanced with re-radiation from other leaves. For the same reason, the re-radiation component of the balance is not taken into account for shade leaves. R = σ ' 4 F a ξ l Tl where ξ l is the leaf emissivity, σ is the Stefan-Boltzman constant σ = 5.67 * 10-8 W/m 2 /ºK and T l is the leaf temperature (ºK). C v : Sensible energy transfer between leaf and air. Part of the leaf energy in form of heat warms the air adjacent to the surface of the leaf. This warm air is removed by turbulent air flow. The rate at which this warm air is removed is basically determined by the temperature gradient between air and leaf and by the thickness of an air layer of slower non-turbulent movement that surrounds leaf surfaces, the boundary layer. The boundary layer thickness is very variable and it is affected by leaf structure, size, thickness, degree of lobbing and roughness of its surface. It determines, together with wind speed, the resistance of this layer to the diffusion of water vapour, CO 2 and energy. Its inverse is boundary layer conductance which is proportional to the fluxes of water vapour and CO 2 through the boundary layer. C v = k a V D ( T T ) l a where V is the air speed (m/s) and D is the leaf characteristic dimension. C v 6 = 100 g BLH Θ C p ( T T ) l a where Θ is the air density (kg/m3) and g BLH the boundary layer conductance for heat (m/s) calculated as follows, g BLH ' = F a V D in a similar way the boundary layer conductance for water vapour (m/s) is, g BLW = F a V D F a and F a are factors used to describe conductances taking into account if the leaves are amphistomatous or hypostomatous. For amphistomatous leaves they are equal to 2, that 32

33 is, conductances have to be doubled, and for hypostomatous leaves, F a is equal to 2 and F a is equal to 1. E: Latent energy exchange occurring when water evaporates. When water is converted into water vapour and it is evaporated, an important amount of energy in the form of heat is lost from the leaf to the atmosphere. The water that is transpired in this way has to be replaced. Thus, transpiration imposes a constant movement of water within the plant, from the soil, where it is absorbed, to the leaves, where it is lost as a consequence of the water concentration gradient between leaf and atmosphere. In the direction opposite to the water concentration gradient another gradient occurs: the CO 2 concentration gradient, that determines the movement of CO 2 from the atmosphere into the plant to be used for photosynthesis. Both of these processes occur through openings at the leaf surface called stomata, the regulation of which determines the balance of carbon gain and water loss. If there is not enough water in the soil to maintain transpiration, stomata close and thus water loss and carbon uptake are restricted. The resistance of stomata to the diffusion of water vapour and CO 2 is a determinant factor in the rates of transpiration and photosynthesis. This resistance is function of the aperture and density of stomatal pores in the leaf. Transpiration depends on stomatal conductance, boundary layer conductance, incident radiation, temperature, vapour pressure deficit, and wind speed. In the model we estimate transpiration with the Penman-Monteith equation coupled to the atmosphere as in Jarvis, EXPLICAR LAS FORMULAS DE JARVIS??? Transpiration, E, has different components, one that depends on net radiation, Eq (mols/m 2 leaf/min), and another that depends on vapour pressure deficit, Ei (mols/m 2 leaf/min). ( Ω) i E = Ω E q + 1 E E q Fa S Q = S a ( + γ ) λ E i F = a C p g s λ γ 1.6 VPD Ω = ( S + γ ) + γ g BL, W S + γ R gas g o ( T ) s P leaf 33

34 R gas is the universal gas constant J/mol/K In GOTILWA, leaf energy balance is coupled to the processes of photosynthesis and stomatal conductance through leaf temperature. In this sense, leaf temperature is calculated by and iterative computing procedure that involves the Leaf Energy Balance equation and that is connected to the processes of Photosynthesis and Stomatal conductance: -to start this iterative procedure, the initial leaf temperature for a determinate hour of the day is made equal to the air temperature for that hour. - each term of the balance equation is calculated and we proceed to the comparison between the inputs and the outputs. -depending on this comparison the leaf temperature value is raised or lowered by an increment. -this process is repeated until the equation is balanced, moment when the definitive leaf temperature for that hour is achieved. The leaf temperature estimates are used in the photosynthesis and conductance processes from where estimated values of assimilation and boundary layer and stomatal conductance are calculated which are in turn used in the calculations of the terms in the leaf energy balance equation. Conductance To reach the leaf, CO 2 must diffuse through the boundary layer and through the stomata. The restriction of the stomata to the diffusion of water vapour and CO 2 is termed stomatal resistance and it plays a basic role in controlling the rates of transpiration and photosynthesis. Stomata have physiological control mechanisms that optimise carbon gain with respect to water loss. The inverse of stomatal resistance is stomatal conductance which is proportional to the fluxes of water vapour and CO 2. Many environmental and physiological factors influence stomatal conductance: temperature, light, vapour pressure deficit, intracellular CO 2 concentration, leaf surface CO 2 concentration, leaf water potential, assimilation... In GOTILWA we calculate stomatal conductance, g s, using Leuning s version (1995) of the Ball-Berry semi-empirical model. This model includes, directly or indirectly, the main factors that influence stomatal conductance but it was developed for well-watered plants and so plant water stress is not accounted for in it. g s = g 0 + A VPD ( C Γ ) 1 + a g 1 n g sdo where, A n is the net assimilation rate (µmol CO 2 /m 2 /s), g 0 is the stomatal conductance when leaf irradiance tends to zero (mol CO 2 /m 2 /s), g 1 is an empirical constant in the Leuning model, Ca is the air CO 2 concentration (µmol/mol), Γ is the CO 2 compensation point (µmol/mol) and g sdo is an empirical constant in the Leuning model (kpa). 34

35 As soil dries there is a reduction in water uptake, stomatal conductance diminishes and thus there is a decrease in photosynthesis and in transpiration. In order to take into account the effect of water stress on conductance we include, in GOTILWA, a factor, Wfac, that gives an idea of soil relative water content and ranges between 0 and 1. Wfac relates existing water in the soil to the maximum and minimum water that provokes maximum and minimum stomatal conductance. This factor modifies the final value of stomatal conductance in the equation by Leuning, 1995 determining its dependence on soil water content. W fac W = W soil gsmax + W gs0 W gs0 where W soil is the volume of water in the soil (m 3 /m 3 ), W gs0 is the soil water content below which g s is minimum in Leuning model and W gsmax is the soil water content above which g s is maximum in Leuning model. Taking this into account we have, g s = g 0 + W VPD ( C Γ ) 1 + a g 1 fac A g n sdo Photosynthesis Through photosynthesis, plants use radiation to synthesise organic compounds from CO 2 and water. These compounds are then used to maintain plant tissues, to form new tissues and grow, or to create stores. The photosynthetic carbon gain is controlled by temperature and radiation and limited by the availability of water and nutrients. Temperature directly controls rates of gross photosynthesis and respiration because it affects the activity of the enzymes involved in these processes. Temperature, therefore, determines the rate of net photosynthesis (balance between the carbon fixed from the atmosphere by plants, gross photosynthesis, and the carbon released by leaves during dark respiration). From the incident radiation on a leaf only photons with wavelengths between 400 and 700 nm can be used for photosynthesis, it is the photosynthetic photon flux (PPF). Photosynthetic photon flux is absorbed by leaves and determines the rate of CO 2 assimilation as it is the source of the energy used in photosynthesis. Water loss from leaf transpiration is an inevitable consequence of photosynthesis. In this sense, there is a close relation between stomatal conductance and assimilation. The fixation of CO 2 by the leaf influences stomatal conductance and as stated before, the control of stomatal opening allows the plant to meet the compromise of maximising CO 2 uptake while minimising water vapour loss. 35

36 Many nutrients are required by plants in order to have a normal functioning. Different plant tissues have different concentration of nutrients. In terrestrial ecosystems nitrogen is the most important nutrient to take into account as it is the most limiting one. In GOTILWA, photosynthetic assimilation rates are estimated using the biochemical model of photosynthesis in leaves of C3 plants by Farquhar et al., 1980 and Farquhar and von Caemmerer, In it two different rates of CO 2 assimilation are calculated: the assimilation rate limited by Rubisco activity/by carboxylation efficiency, A c A c = V cmax C i C + K i c Γ O + i 1 K o in which Vcmax is the potential rate of whole maximum catalytic activity of Rubisco in the presence of saturating levels of RuP2 and CO 2 (µmol/m 2 /s), Γ * is the CO 2 compensation point in the absence of mitochondrial respiration (Pa), Oi and Ci are the intercellular oxygen and carbon concentrations respectively, Kc (Pa) is the Michaelis- Menten constant of Rubisco for CO 2 and Ko (Pa) is the Michaelis-Menten constant of Rubisco for O 2. and the assimilation rate limited by photosynthetic electron transport, A j A j = J Ci Γ* 4 C + 2Γ i * being, θ J 2 ( PPFD Q + J ) J + PPFD Q J = 0 max max where J is the electron transport rate for a given absorbed photon irradiance, Jmax is the potential rate of whole-chain electron transport, θ determines the curvature of response of electron transport to irradiance. net assimilation rate would be, A = min, { Ac A j } Rd where Ac is the gross rate of photosynthesis limited by Ribulose Biphosphate Carboxylase-Oxygenase (Rubisco) activity, Aj is the gross rate of Ribulose Biphosphate (RuP2) regeneration though electron transport and Rd is daytime respiration. All this terms are c i and temperature dependent and Aj is also dependent of absorbed radiation. The main determinant of A at low c i will be Vcmax which will be directly dependent on the quantity of active Rubisco. At higher c i values, A is constrained by the capacity of the leaf to regenerate RuBP for carboxylation, it is therefore limited by RuBP 36

37 concentration and more precisely by the regeneration of RuBP determined by the regeneration of the potential rate of non-cyclic electron transport. Intercellular CO 2 concentration, c i depends on the rate of CO 2 diffusion through stomata and on the amount of CO 2 that is used for photosynthesis. c i = c a A g s Dependencies of leaf temperature on all the processes, components and enzymes of the leaf biochemistry and physiology are of major importance. To represent the temperature dependencies of the kinetic parameters Kc and Ko we use the Arrhenius function normalised with respect to 25ºC, K c = K c E akc 298 R gas e 25 ( T 25) l ( T + 273) l K o E ako 298 R gas = K e o25 ( T 25) l ( T + 273) l where Kc (Pa) is the Michaelis-Menten constant of Rubisco for CO 2 and Ko (Pa) is the Michaelis-Menten constant of Rubisco for O 2, K c25 and K o25 are the same constants at 25 ºC, R gas is the universal gas constant J/mol/K and E akc and E ako are activation energies (J/mol). To describe the temperature dependence of the CO 2 compensation point we use a second-order polynomial equation (Brooks and Farquhar 1985), Γ ( T 25) ( 25) 2 l T = Γ * being the CO 2 compensation point in the absence of mitochondrial respiration (Pa). l The temperature dependence of Vcmax and Jmax are calculated according to Farquhar et al. (1980) and Harley et al. (1992), V cmax = V e cmax25 E avcmax 298 R gas ( T ) l ( T + 273) l V omax = V e omax25 E avomax 298 R gas ( T ) l ( T + 273) l 37

38 J max = E ajmax 298 R gas J e max25 ( T ) l ( T + 273) S Jmax R 1 + gas e l 1 + e S Jmax ( T + 273) E ( ) l djmax T l 298 R 298 gas E djmax where Ea are the activation energies (J/mol) for the different parameters and S Jmax is the electron-transport temperature response parameter (J/mol/K). Dark respiration or day time respiration is the process of respiration that continues during the light in the mitochondria and that represents an important part of carbon lost by the plant. It is very much dependent on temperature. In the model it is calculated hourly and separately for sunlit leaves and shade leaves, as it is done for photosynthesis. A rate of dark respiration for a determinate temperature, R d (µmol/m 2 /s), is calculated and taken into account to obtain the final values of assimilation. R d T l 25 = R 10 d Q10 Canopy Structure And Hydrology As we explained previously, plant canopy structure determines how incident radiation is intercepted. Similarly, plant canopy structure determines water fluxes, how much of the incoming water from precipitation that reaches the canopy is intercepted and therefore evaporated and consequently how much arrives to the soil. The amount of rainfall that is carried off an area by streams and rivers is the stream flow or runoff. In GOTILWA, interception is estimated as a constant percentage of the amount of rainfall. The stream flow/runoff, leaving a catchment or a stand can be estimated as a function of rainfall and Water Filled Porosity, WFP, that is a measure of how saturated the soil is, ( R I ) ( W WFP ) Runoff = * hour where R hour is the hourly rainfall (mm), I is the interception, W soil is the amount of water in the soil (mm) and WFP max is the maximum WFP. soil max 38

39 Autotrophic Respiration Plants need to spend carbon and energy, that are obtained from photosynthesis, in maintaining the function of their tissues: leaves, branches, roots, stem and reproductive structures and also in the construction of new ones. The respiration used to maintain existing living tissues is termed maintenance respiration. Associated to the formation of new biomass components there is a metabolic cost which constitutes the growth respiration. The respiration that occurs when assimilates are converted into new tissues is called growth respiration. In the model day respiration is calculated hourly and separately for sunlit leaves and shade leaves, as it is done for photosynthesis. A rate of day respiration (respiration during light conditions) for a given temperature, R d (µmol/m 2 /s), is calculated and taken into account to obtain the final values of assimilation. R d T l 25 = R 10 d Q10 A part of the GPP (Gross Primary Production) is used to compensate the respiratory cost of all the living tissues and the remaining primary production is used in the formation of new biomass which involves a growth respiratory cost. Through these respiration processes carbon, previously fixed in photosynthesis, is returned to the atmosphere in the form of CO 2. In GOTILWA, concerning maintenance respiration and taking into account the different plant tissues we have: Leaf respiration The respiration of any component of the plant is temperature dependent. The role of temperature is introduced using the Q 10 function estimated as: Q 10,t = Q 10,25 T air where T air is the air temperature. The final respiration rate depends on the fraction of mobile carbon present in the leaf. This fraction has a base respiration rate of 55.5 cal g -1 DM day -1 while the structural components have a base respiration rate of 33.3 cal g -1 DM day -1 so, the respiration of the leaf tissues is: Rl = 55.5 C m Q 10,t (1- C ) Q where R l is the leaf respiration rate, C m is the fraction of mobile carbon in leaves and Q 10,t is the value of Q 10 at temperature t. m 10, t 39

40 Wood respiration Similarly, the living woody tissues depend on the Q 10 value and the base respiration rate which has been estimated as 35 cal g -1 DM year -1. The fraction of living xylem is a constant fraction of sapwood. Fine root respiration Fine root respiration is calculated depending on the Q 10 value and taking into account that 10% of carbon in fine roots is in structural components (base respiration rate of 33.3 cal g -1 DM day -1) and 90% is in non-structural components (base respiration rate of 55.5 cal g -1 DM day -1 ). R fr = B fr (( 0.1* 33.3) +(1-0.1 *55.5) * Q * ) 10, t where R fr is the fine root respiration rate, B fr is fine root biomass and Q 10,t is the value of Q 10 at temperature t. Concerning growth respiration, in GOTILWA we assume that due to the transport of carbon between organs and across cell membranes, the formation of new biomass in plants from net carbon uptake has a respiration cost. On average, 1 g of carbohydrates gives about 0.68 g of new tissues and the difference is consumed during the process of growth respiration. Phenology Phenology, i.e. seasonal plant activity driven by environmental factors, results from a combination of two components. The first is the stage of annual development, which is modulated by the effect of the increase in temperatures on frost dehardening (according to the temperature sum approach, (Leinonen 1997), and the decrease in temperatures on hardening, i.e. assuming that frost temperatures reduce or reverse the development. In addition, seasonal photosynthetic capacity incorporates the Pelkonen and Hari (1980) approach, which introduces a factor K (ranging from 0 to 1 depending of the stage of annual development). This factor multiplies the value of V cmax and J max used in Farquhar s equations (Leinonen 1997). The second component acts under drought conditions: when water availability is lower, which in Mediterranean conditions usually coincides with a rise in temperatures. Under such circumstances stomatal conductance is reduced according to Leuning s equation, and consequently gas exchange. At this point, when leaf respiration is higher than photosynthesis and mobile carbon exhausted, a number of leaves are shed until the negative value of the carbon balance is offset. Both deciduous and evergreen trees have the two components. Evergreen trees produce new leaves when photosynthesis has recharged mobile carbon expended in winter to maintain the living biomass. Deciduous trees unfold leaves when the stage of development imposes conditions for photosynthesis at 90% of optimal (i.e K>0.9), then leaf unfolding occurs in 10 days (arbitrary value, but matching observed time for unfolding). Then stored mobile carbon is, as in evergreens, used to build up new leaves. As in evergreens, new flushes may occur when mobile carbon pools are replenished. 40

41 Leaf fall occurs gradually when day length is decreasing and the stage of development imposes values of photosynthesis lower than 95% of optimal conditions (K<0.95). As the stage of development decreases, leaf fall rate is increased NET PRIMARY PRODUCTION AND CARBON ALLOCATION It is assumed that the amount of carbon allocated to different plant tissues varies with species, stages of growth, season and environment characteristics. Although these allocation patterns are not clearly determined. In GOTILWA, the balance between maintenance respiration, NPP and the metabolic cost associated to the formation of new biomass, determines the processes of leaf formation and leaf fall, tree ring formation, the rate of change of sapwood into heartwood and, consequently, the changes in tree structure within each size class. These changes will affect in turn the hydrological fluxes which will subsequently take place in what might be described as a feed-back process (Sala and Tenhunen 1994). To calculate gross production the model uses the photosynthesis equations based on Farquhar and co-workers approach (Farquhar and Von Caemmerer 1982). Stomatal conductance uses Leuning s approach that modifies Ball, Woodrow and Berry model (Leuning 1995). Leaf temperature is determined based on leaf energy balance (Gates 1962, 1980) and transpiration is estimated according to the Penman-Monteith equation (Monteith 1965, Jarvis and Mcnaughton 1986). NPP is allocated to the different parts of the plant following a set of allocation rules. The plant uses a fraction of this NPP to form new leaves and fine roots to compensate their turnover. The remaining NPP is allocated to the pool of mobile carbon in leaves and woody tissues. If the NPP exceeds the carbon storage demand it is used in the formation of leaves and fine roots, in the case that leaf area and fine root biomass are lower than the leaf area and fine root biomass that can be supported by the existing sapwood area. The remaining NPP, if any, is invested in the production of new leaves, new fine roots and new wood in such a proportion that the new sapwood area and the new leaf area and new fine root biomass fit the constant ratio. 41

42 Figure 3. Diagramatic representation of the carbon allocated to maintenance and formation of the different new tissues. The basic assumptions and priority allocation rules that are followed in GOTILWA are, -Leaf area supported by an individual tree is proportional to the sapwood cross-sectional area in a constant value. Changes in the sapwood cross sectional area are translated into changes in leaf area and vice versa. -Fine root biomass supported by an individual tree is proportional to the sapwood crosssectional area in a constant value. Changes in the sapwood cross sectional area are translated into changes in fine root biomass. -If the fixed carbon/gpp exceeds the cost of respiration, it is used to increase the pool of mobile carbon stored, first of all, in leaves and after that, in woody tissues. The remaining carbon/npp, if any, is used to renew biomass and build new biomass. -During periods in which GPP does not compensate the maintenance respiration, the carbon stored in leaves and in stem sapwood is used to compensate the leaf and stem respiration while carbon stored in coarse roots is used to compensate the respiration of fine roots. -If the mobile carbon stored does not compensate the respiratory cost, leaf shedding reduces the amount of leaf tissue and thus, reduce respiration until both values, respiration and carbon availability, compensate each other. -If this compensation point cannot be reached, even when all the leaves are shed, the tree metabolism is unbalanced and it dies. CLIMATE CHANGE 42

43 MANAGEMENT REGIMES 43

44 MODEL VALIDATION The model has been validated against different data sets. In the frame of the LTEEF project (ENV4-CT ), it has been validated against 1997 daily eddy flux data from sites of the EUROFLUX project and against data from growth and yield tables from the same sites GOTILWA HESSE 8 4 Y = * X r 2 = 0.56 NEE 0-5 HESSE GOTILWA 5 4 GOTILWA HESSE 5 4 Y = * X r 2 = 0.64 E 3 2 HESSE GOTILWA Figure 7. Comparison of GOTILWA+ daily results for Hesse with EUROFLUX data for the variables E (mm) and NEE (gc m -2 d 1 ). 44

45 HYYTIALA GOT ILWA HYYTIALA GOT ILW A HYYTIALA DBH (cm) CAI (m3/ha/year) Age (years) Age (years) LOOBOS 30 GOT ILWA LOOBOS 14 GOT ILWA LOOBOS DBH (cm) CAI (m3/ha/year) Age (years) Age (years) Figure 8. Comparison of GOTILWA+ results for Hyytiala and Loobos with Growth and Yield tables for the variables DBH (cm) and CAI ( m 3 ha -1 y 1 MODEL ). VALIDATION MONTHLY LITTERFALL LITTERFALL (g DM m -2 month -1 ) TIME (months, ) OBSERVED SIMULATION OF CONTROL PLOT 1 SIMULATION OF CONTROL PLOT 2 SIMULATED OBSERVED Sim = * Obs r 2 = TREE RING WIDTH (mm), Sim = * Obs r 2 = SIMULATED 4 2 CONTROL PLOT MINIMUM THINNING MAXIMUM THINNING OBSERVED Figure 9. Top: comparison of measured monthly litterfall in the Quercus ilex forest of Prades from 1982 to 1989 with the values simulated by GOTILWA+ in two control plots. Bottom: tree rings observed between 1992 and 1994 in a thinning experiment on the same forest compared with the values produced by GOTILWA+. 45

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47 PART II : GOTILWA+ User s guide 47

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49 Starting GOTILWA+ 49

50 The simulation Controller Forest System Figure X. Forest file. You can choose and define here which file to use for each of the processes and simulation conditions, the years from the climate file you want to simulate and the path where the results of your simulation are going to be saved in. From this window you can also have access to all the model data windows and charts. This information is saved in a file with extension.for. 50

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53 The Input Data Table XX. Input parameters from the GOTILWA+ model. Process Parameter Symbol Units Latitude Lat GG.mm Altitude Alt M a.s.l. Stand position Deciduous/Evergreen Leaf Photosynthesis Stomatal Conductance Tree Structure Maximum rate of carboxylation Vc max at µmols/m 2 /s 25ºC Activation energy of Vc max Ea J/mol Intercellular partial pressure of CO2 C ppmv Maximum rate of oxygenation Vo max at µmols/m 2 /s 25ºC Activation energy of Vo max Ea J/mol Intercellular partial pressure of O2 C ppmv Potential electron transport rate J max at 25ºC µmols/m 2 /s Activation energy of J max Ea J/mol Curvature parameter of J max Ed J/mol Electron-transport temperature S J/mol/ºK response parameter Curvature of response of electron Θ An/PPFD transport to irradiance Michaelis-Menten constant of Kc at 25ºC Pa Rubisco for CO2 Activation energy of Kc max Ea J/mol Intercellular partial pressure of CO2 C ppmv Michaelis-Menten constant of Ko at 25ºC Pa Rubisco for O2 Activation energy of Ko max Ea J/mol Intercellular partial pressure of O2 C ppmv Dark respiration rate Rd at 25ºC µmols/m 2 /s Temperature effect factor Q10 at 25ºC -- Residual (Cuticular) conductance µmols/m 2 /s Leuning Constant g1 -- Factor of gs vs VPD responses gsdo kpa SWC at which gs=0 Sgso m 3 /m 3 SWC at which gs=gsmax Sgsmax m 3 /m 3 Leaf characteristical dimension D m All sided area/projected area --- X parameter (ellipsoidal distribution) X v/h Hypostomatous/Amphistomatous --- α-biomass --- β-biomass --- belowground/aboveground biomass kg/kg α-lai m 2 /cm 2 α-vigor cm 2 /cm 2 α-fine roots g/cm 2 Leaf Specific Mass mg/cm 2 Max. mobile Carbon in Leaves % Max. mobile Carbon in Wood % Fraction of respiring sapwood % Leaf Shedding (base line) day -1 53

54 Soil Carbon Fluxes Soil Hydraulic Conductivity Constant values Fine roots mortality (base line) day -1 Gross /fine literfall g/g Branches /aboveground biomass kg/kg Wood density g/cm 3 Cumulated sapflow kg/cm 2 Seedler/Resprouter Initial SOC in organic horizons g/cm 2 Initial SOC in mineral horizons % of dry weight Bulk density g/cm 3 Decomposition rate of OM in LF h. k(lf) day -1 Decomposition rate of OM in AB h. k(ab) day -1 P(LF) mm Soil temperature effect factor Q LF to AB transfer rate t o m --- W min mm W max mm Foliage Projective Cover % Hydraulic gradient M/m Soil Hydraulic Conductivity M/day Mean Soil Depth M Minimum Water Usable mm/m Stones volume % PAR to Global radiation ratio joule/joule µeinsteins per Watt µe/watts Atmospheric CO2 (pre-industrial) ppm Energetic equivalent of OM cal/g Organic Matter/Carbon g/g N per 100 g of OM g/100 g Respiration rate of structural cal/g/day components Respiration rate of non-structural cal/g/day components Respiration rate of live components cal/g/day of wood Efficiency of Carbon in OM formation g/g 54

55 Help on line 55

56 Modifying the Input data files 56

57 Photosynthesis Figure X. Photosynthesis parameter file. This data window groups all the variables involved in the process of photosynthesis necessary for model calculations. This values are saved in a file with extension.pho. -Vc max at 25ºC, (mmols/m2/s) is the maximum rate of carboxylation at 25 ºC. -Vo max at 25ºC, (mmols/m2/s) is the maximum rate of oxygenation. -J max at 25ºC (mmols/m2/s) is the potential electron transport rate. -Phi, is the curvature of response of electron transport to irradiance. -S, (J/mol/ºK) is the electron-transport temperature response parameter. -Q (An/PPFD) is the curvature of response of electron transport to irradiance. -Kc at 25ºC, (Pa) is the Michaelis-Menten constant of Rubisco for CO 2. -Ko at 25ºC, (Pa) is the Michaelis-Menten constant of Rubisco for O 2. -Rd at 25ºC, (mmols/m2/s) is the dark respiration rate. -Q10 at 25ºC, is the temperature effect factor. -Ea, (J/mol) are the activation energies of each of the corresponding parameters: Vc max, Vo max, J max, Kc and Ko. - Ed, (J/mol) is the deactivation energy of Jmax. -C, (ppmv) are the intercellular partial pressures of CO 2 and O 2 depending on the variable they are referred to. 57

58 Table 4: Leaf Photosynthesis and Stomatal Conductance parameters. Process Parameter Symbol Units Maximum rate of carboxylation Vc max at 25ºC µmols/m 2 /s Activation energy of Vc max Ea J/mol Intercellular partial pressure of CO2 C ppmv Maximum rate of oxygenation Vo max at 25ºC µmols/m 2 /s Activation energy of Vo max Ea J/mol Intercellular partial pressure of O2 C ppmv Potential electron transport rate J max at 25ºC µmols/m 2 /s Activation energy of J max Ea J/mol LEAF PHOTOSYNTHESIS STOMATAL CONDUCTANCE Curvature parameter of J max Ed J/mol Electron-transport temperature response parameter S J/mol/ºK Curvature of response of electron transport to irradiance Θ An/PPFD Michaelis-Menten constant of Rubisco for CO2 Kc at 25ºC Pa Activation energy of Kc max Ea J/mol Intercellular partial pressure of CO2 C ppmv Michaelis-Menten constant of Rubisco for O2 Ko at 25ºC Pa Activation energy of Ko max Ea J/mol Intercellular partial pressure of O2 C ppmv Dark respiration rate Rd at 25ºC µmols/m 2 /s Temperature effect factor Q10 at 25ºC -- Residual (Cuticular) conductance µmols/m 2 /s Leuning Constant g1 -- Factor of gs vs VPD responses gsdo kpa SWC at which gs=0 Sgso m 3 /m 3 SWC at which gs=gsmax Sgsmax m 3 /m 3 Leaf characteristical dimension D m All sided area/projected area unitless X parameter (ellipsoidal distribution) X v/h Hypostomatous/Amphistomatous Bolean 58

59 Stomatal conductance Figure X. Stomatal conductance parameter file. This data window groups all the variables involved in the process of stomatal conductance necessary for model calculations. This values are saved in a file with extension.stc. -Residual (Cuticular) conductance (mmols/m2/s) -g1, is the Leuning Constant -gsdo, (kpa) is the factor of gs vs VPD responses -Sgso, (m3/m3) is the soil water content at which gs=0 -Sgsmax, (m3/m3) is the soil water content at which gs=gsmax -D, (m) is the leaf characteristical dimension -All sided area/projected area -X, (v/h) is the X parameter (ellipsoidal distribution) -Hypostomatous/Amphistomatous, depending if the leaves of the species simulated has stomata in just one side of the leaf or in both sides. 59

60 Forest Structure Figure X. Structural variables file. This data window groups the variables related to location of the forest, and structural and physiological variables of the species of the stand. This values are saved in a file with extension.phy. -Latitude, (GG.mm). -Altitude, (m a.s.l.). -alpha-biomass, coefficient a for the allometric relation Biomass (aboveground) vs diameter B=a*DBH^b. -beta-biomass, coefficient b for the allometric relation Biomass (aboveground) vs diameter B=a*DBH^b. -belowground/aboveground biomass, (kg/kg). -alpha-lai, (m2/cm2) index that relates leaf area to cross-sectional sapwood area. -alpha-vigor, (cm2/cm2) index that relates sapwood area to total wood area. -alpha-fine roots, (g/cm2) index that relates fine root biomass to sapwood area. -Leaf Specific Mass, (mg/cm2) -Maximum mobile Carbon stored in Leaves, (%) is the maximum percentage quantity of carbon that can be stored in the leaves in the form of starch or other storage carbohydrates. -Maximum mobile Carbon stored in Wood, (%) is the maximum percentage quantity of carbon that can be stored in wood in the form of starch or other storage carbohydrates. -Fraction of respiring sapwood, (%) is the part of sapwood formed by living cells and that consequently perform all the life processes in this case respiration. -Leaf shedding rate under optimal conditions, (day -1 ) is the base line rate of leaf shedding. -Fine roots mortality rate under optimal conditions, (day -1 ) is the base line rate of fine root mortality. -Gross /fine literfall, (g/g) relation between the branches litter and the leaf litter. -Branches/aboveground biomass, (kg/kg) relation between branches biomass and total aboveground biomass. -Wood density, (g/cm3) -Cumulated sapflow, (kg/cm2) for a determinate species and climatic conditions the quantity of water that is transported through a xylem tube before it collapses and becomes heartwood. -Seedler/Resprouter, depending of the tipe of reproduction of the species, be it by seeds or by resprouts 60

61 Tree density Figure X. Tree density file. This data window shows the density distribution per DBH classes of the trees in the stand. Both the number of trees per DBH class and the amplitude of the DBH classes can be modified. Also the type of forest in relation to tree age (one or several stand ages) can be specified here. This values are saved in a file with extension.est. 61

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63 Soil definition Figure X. Soil carbon fluxes parameter file. This data window groups the variables related to soil organic matter decomposition and carbon fluxes necessary for model calculations. This values are saved in a file with extension.sol. -Initial SOC in organic (LF) horizons, (g/cm2) -Initial SOC in mineral (AB) horizons, (% of dry weight) -Bd, (g/cm3) Bulk density is the mass per unit volume of dry soil (includes soil solids and soil pores). -k(lf), (day -1 ) is the decomposition rate of OM in LF horizons. -k(ab), (day -1 ) is the decomposition rate of OM in AB horizons. -P(LF), (mm) is the parameter that includes the effect of water in the soil on the decomposition rate of organic matter in organic layers, it is calculated taking into account the cumulated rainfall of the previous 30 days. -Soil Q10, is the soil temperature effect factor. -T LF to AB, is the organic matter transfer rate from organic to mineral layers. -W min, (mm)and W max (mm) are the parameters that include the effect of water in the soil on the decomposition rate of organic matter in mineral layers, it depends on the percentage soil water filled porosity. Figure X. Hydrological properties parameter file. This data window groups the variables related to soil water content. This values are saved in a file with extension SOL. -Foliage Projective Cover, (%) is the percentage of soil covered by the projection of tree canopies. -Hydraulic gradient, (M/m) is a topographic parameter that represents the slope of the site ((max. height min height )/distance between max. height and min height). -Soil Hydraulic Conductivity, (m/day) is a measure of the soil capacity of conducting /transporting the water flux. -Mean Soil Depth, (m) -Minimum Soil Water Usable, (mm/m) is the amount of water that remains attached to the soil particles and thus it can t drain and plants can t use it. -Relative volume of stones, (%) 63

64 Canopy Figure X. Canopy hydrology parameter file. This data window groups the variables related to watercanopy relationships. This values are saved in a file with extension CPY. In this data window the type of species, evergreen or deciduous, is defined. 64

65 Climate Plot daily climate values Figure X. Daily climate data file. This data window shows numerically and graphically all the daily climate data of the chosen file. The data can be explored year by year or several years at the same time. These values are taken from a file with extension CLM (binary file). 65

66 Plot monthly climate values Figure X. Monthly climate data file. This data window shows numerically and graphically all the monthly climate data of the chosen file. The data can be explored year by year or several years at the same time. These values are monthly averages taken from a daily climate data file with extension CLM (binary file). 66

67 Analyze climate data Figure X. Analysing climate file. This data window shows mean values and standard deviations for the climatic variables: -radiation (MJ/m 2 /day), Q: average daily value for each month. -precipitation (mm/day), P: average daily value for each month. -days of precipitation, DP: amount of days of rainfall in the month. -potential evapotranspiration (mm/day), ETP: average daily value for each month. -minimum temperature (ºC), min T: average daily value for each month. -maximum temperature (ºC), max T: average daily value for each month. -vapour pressure (kpa), VP: average daily value for each month. -wind (m/s), Wind: average daily value for each month. For each window, the last column is the average monthly value of the whole series of years in the file and the last row is the sum of the values for each year. These values are taken from a daily climate data file with extension CLM (binary file). 67

68 Convert ASCII to RANDOM climate files Figure X. Transforming climate data file. This window allows to transform either climate files in ASCII format (.txt,.prn) to climate files in binary format (.clm) or the other way around just by selecting the chosen file and providing the latitude of the place. 68

69 Climate Change Figure X. Climate Change scenario data file. In this data window, different scenarios of atmospheric CO 2, temperature and rainfall changes can be defined. The changes in these variables can be undertaken either by defining new absolute values to be used as a fix value in the simulation or by defining increments to be introduced annually all along the simulation. These values of climate change are taken from a file with extension GCH. 69

70 Management Figure X. Forest management data file. In this data window the management regime to be applied to the forest can be defined. For each year of thinning, it is necessary to determine: 1- the type of thinning to be applied that is, if the thinning is going to be performed by acting over the number of trees, the amount of basal area, the amount of biomass or the amount of stem volume, 2- if it is going to be applied to the smaller trees, to the bigger trees or to trees of diverse DBH classes (in this case a new window will come out where a table representing the DBH classes and the years of simulation can be filled in), 3- if the thinning is going to be carried out as an absolute value as a relative value or defining a minimum and a maximum value between which range the forest is going to be. 4- the intensity of thinning, that is the number of trees or the amount of basal area, biomass or stem volume that it is going to be cut (the number in positive, eg. 90) or that it is going to be left in the forest (the number in negative, eg. -90). It is also possible to define a regime of regeneration either in resprouting species (the value to put is the percentage of carbon stored in the stump that is assigned to resprouting) or in seedling planting (the value to put is the number of seedlings). These values are taken from a file with extension MNG. 70

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72 Weather generator Figure X. Weather generator data file. In this data window, it is possible to generate randomly daily values from a source climate file of monthly values. These climatic data is saved in a file with extension CLM. Using the batch 72

73 Plotting and mapping results 73

74 Generating growth and yield tables Figure X. Growth and Yield table. This data window shows the model simulation results in the form of a growth and yield table. Figure X. Growth and Yield table. The Growth and Yield table data window also allows to represent the variables Current Annual Increment and Mean Annual Increment. 74

75 The Constant values Figure X. Constant values file. This data window groups the constants used by the model. This values are saved in a file with extension KON. -PAR to Global radiation ratio, (joule/joule)is the fraction of global radiation that plants are able to use for photosynthesis, Photosynthetic Active Radiation. -µeinsteins per Watt, (me/watts) is theequivalence between µeinsteins to Watts. -Atmospheric CO2, (ppm) is the atmospheric CO2 pre-industrial concentration used as the base-line concentration from which the model calculates the CO 2 concentration value that corresponds to every determinate year of simulation. -Energetic equivalent of Organic Matter, (cal/g) -Organic Matter to Carbon ratio, (g/g) -Nitrogen per 100 g of Organic Matter, (g/100 g) -Respiration rate of structural components, 25ºC, (cal/g/day) -Respiration rate of non-structural components, 25ºC, (cal/g/day) -Respiration rate of live components of wood, 25ºC, (cal/g/day) -Plant tissues formed by 1 g of invested Carbon, (g/g) is the efficiency of Carbon in Organic Matter formation. 75

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82 The output variables 82

83 Plotting selected output variables Focusing a zooming a given time period 83

84 Daily, Monthly and annual plots 84

85 Comparing plots 85

86 Basic statistics of plotting variables 86

87 PART III: Simulating the growth of Aleppo pine in Catalonia 87

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