B Symbols

The following tables list all symbols used in this document, along with their units and definition. When symbols are input for medfate model functions, the R name of those parameters in the package (either in data frame SpParamsMED, soil input data frame, or the output of functions such as spwbInput()) is also indicated.

B.1 Dimensions

Symbol Units R Description
\(\Delta t_{step}\) \(s\) 86400/ndailysteps Subdaily temporal step
\(\Delta t_{substep}\) \(s\) 86400/(ndailysteps*nsubsteps) Subdaily temporal substep
\(c\) (count) Number of plant cohorts
\(l\) (count) Number of vertical layers
\(\Delta z\) \(m\) verticalLayerSize/100 Width of vertical layers
\(S\) (count) Number of soil layers
\(d_{s}\) mm widths Width of soil layer \(s\)
\(Z_{s}\) mm widths Depth of soil layer \(s\)
\(Z_{soil}\) mm Overall soil depth

B.2 Soils

Symbol Units R Description
\(P_{clay,s}\) % clay Percent of clay in soil layer \(s\)
\(P_{sand,s}\) % sand Percent of sand in soil layer \(s\)
\(OM_s\) % om Percentage of organic mater per dry weight in soil layer \(s\)
\(BD_{s}\) \(g\cdot cm^{-3}\) bd Bulk density in soil layer \(s\)
\(P_{rocks,s}\) % rfc Percentage of rock fragment content in soil layer \(s\)
\(\theta_s\) \(m^3 \cdot m^{-3}\) Volumetric moisture in soil layer \(s\)
\(\Psi_s\) MPa Water potential in soil layer \(s\)
\(\Psi_{fc}\) MPa Water potential at field capacity
\(A_s\), \(B_s\) Parameters of the Saxton pedotransfer functions for soil layer \(s\)
\(\theta_{sat, s}\) \(m^3 \cdot m^{-3}\) VG_theta_sat Volumetric moisture at saturation for soil layer \(s\)
\(\theta_{fc, s}\) \(m^3 \cdot m^{-3}\) Volumetric moisture at field capacity (-0.033 MPa) for soil layer \(s\)
\(\theta_{wp,s}\) \(m^3 \cdot m^{-3}\) Volumetric moisture at wilting point (-1.5 MPa) for soil layer \(s\)
\(\theta_{res,s}\) \(m^3 \cdot m^{-3}\) VG_theta_res Residual volumetric moisture for soil layer \(s\)
\(n_s\) VG_n Parameter \(n\) of the Van Genuchten (1980) model for soil layer \(s\)
\(\alpha_s\) VG_alpha Parameter \(\alpha\) of the Van Genuchten (1980) model for soil layer \(s\)
\(K_{sat,s}\) \(mmol \cdot s^{-1} \cdot m^{-1} \cdot MPa^{-1}\) Ksat Saturated soil conductivity for soil layer \(s\).
\(K_{unsat,s}\) \(mmol \cdot s^{-1} \cdot m^{-1} \cdot MPa^{-1}\) Kunsat Unsaturated soil conductivity for soil layer \(s\).
\(P_{macro, s}\) % macro Percentage of macroporosity corresponding to soil layer \(s\).
\(\gamma_{soil}\) \(mm \cdot day^{-1}\) Gsoil The maximum daily evaporation from soil
\(Z_{wt}\) mm Water table depth
\(V_{s}\) mm Water volume in soil layer \(s\)
\(V_{soil}\) mm Overall water volume in the soil
\(V_{fc, soil}\) mm Water retention capacity of the whole soil
\(W_{s}\) [0-1] W Proportion of moisture in relation to field capacity in soil layer \(s\)
\(W_{i,s}\) [0-1] W Proportion of moisture in relation to field capacity in soil layer \(s\) within fraction of stand area covered by cohort \(i\)
\(W_{rhizo, i,s}\) [0-1] Proportion of moisture in relation to field capacity in soil layer \(s\) within the rhizosphere of cohort \(i\)
\(S_{snow}\) mm SWE Snow water equivalent of the snow pack storage over the soil surface

B.3 Plant/leaf classification

Symbol Units R Description
\(GF\) Categorical GrowthForm “Tree”, “Shrub” or “Tree/Shrub”
\(LF\) Categorical LifeForm Raunkiaer life form
\(L_{shape}\) Categorical LeafShape Leaf shape: “Broad”, “Needle”, “Linear”, “Scale”, “Spines” or “Succulent”
\(L_{size}\) Categorical LeafSize Leaf size: “Small” (< 225 mm), “Medium” (> 225 mm & < 2025 mm) or “Large” (> 2025 mm)
\(L_{pheno}\) Categorical PhenologyType Leaf phenology type

B.4 Vegetation

Symbol Units R Description
\(SP_i\) (count) Species Species identity of cohort \(i\)
\(A_{sh,i}\) \(cm^2\) Area occupied by an average shrub individual of cohort \(i\)
\(B_{sh,i}\) \(kg\) Fine-fuel biomass of an average shrub individual of cohort \(i\)
\(H_i\) \(cm\) Height Average tree or shrub height of cohort \(i\)
\(H_{crown,i}\) \(cm\) Crown base height (i.e. the height corresponding to the first living branch) of cohort \(i\)
\(CCF_i\) Crown competition factor of cohort \(i\)
\(CW_i\) \(m\) Crown width that a tree of cohort \(i\) would have in open-ground conditions
\(CR_i\) [0-1] CR Crown ratio (i.e. ratio between crown length and plant height) of cohort \(i\)
\(N_i\) \(ind · ha^{-1}\) N Density of tree individuals of cohort \(i\)
\(DBH_i\) \(cm\) DBH Diameter at breast height of trees in cohort \(i\)
\(Cover_i\) % Cover Percent cover of shrubs in cohort \(i\)
\(H_{herb}\) % herbHeight Average height (in cm) of herbaceous vegetation
\(Cover_{herb}\) % herbCover Percent cover of herbaceous vegetation
\(FB_{i}\) \(kg \cdot m^{-2}\) Foliar biomass of cohort \(i\)
\(FB_{tree,i}\) \(kg\) Foliar biomass of a single tree of cohort \(i\)
\(\phi_i\) [0-1] Fraction of maximum leaf area currently expanded for cohort \(i\)
\(LAI^{live}_i\) \(m^2 \cdot m^{-2}\) LAI_live (Maximum) leaf area index (one-side leaf area per surface area of the stand) of woody cohort \(i\)
\(LAI^{dead}_i\) \(m^2 \cdot m^{-2}\) LAI_dead Dead leaf area index (one-side dead leaf area per surface area of the stand) of woody cohort \(i\)
\(LAI^{\phi}_i\) \(m^2 \cdot m^{-2}\) LAI_expanded Current expanded leaf area index (one-side expanded leaf area per surface area of the stand) of woody cohort \(i\)
\(LAI^{all}_{i}\) \(m^2 \cdot m^{-2}\) Total leaf area index (live or dead) of woody cohort \(i\)
\(LAI^{live}_{woody}\) \(m^2 \cdot m^{-2}\) Maximum leaf area index of living leaves of woody vegetation in the stand
\(LAI^{dead}_{woody}\) \(m^2 \cdot m^{-2}\) Leaf area index of dead leaves of woody vegetation in the stand
\(LAI^{\phi}_{woody}\) \(m^2 \cdot m^{-2}\) Current expanded leaf area index of live leaves of woody vegetation in the stand
\(LAI_{woody}\) \(m^2 \cdot m^{-2}\) Total leaf area index (live or dead) of woody vegetation in the stand
\(LAI_{herb}\) \(m^2 \cdot m^{-2}\) Leaf area index of herbaceous vegetation in the stand
\(LAI_{stand}\) \(m^2 \cdot m^{-2}\) Total leaf area index of the stand
\(LA_{i}\) \(m^{2}\) Leaf area of an individual of cohort \(i\)
\(FRP_{i,s}\) [0-1] V[i,s] The proportion of fine roots of cohort \(i\) in soil layer \(s\)
\(FRA_{i,s}\) \(m^2\) Fine root area of cohort \(i\) in soil layer \(s\)
\(L_{radial,i,s}\) m Radial length of coarse roots of cohort \(i\) in soil layer \(s\)
\(W_{i}\) \(kg \cdot m^{-2}\) Fine fuel biomass of cohort \(i\)
\(Z_{50,i}\) mm Z50 Depth above which 50% of the fine root mass of cohort \(i\) is located
\(Z_{95,i}\) mm Z95 Depth above which 95% of the fine root mass of cohort \(i\) is located

B.5 Meteorology

Symbol Units R Description
\(DOY\) DOY Day of the year
\(T_{mean}\) \(^{\circ} \mathrm{C}\) MeanTemperature Mean daily temperature
\(T_{min}\) \(^{\circ} \mathrm{C}\) MinTemperature Minimum daily temperature
\(T_{max}\) \(^{\circ} \mathrm{C}\) MaxTemperature Maximum daily temperature
\(T_{base}\) \(^{\circ} \mathrm{C}\) Base temperature for calculation of \(GDD\)
\(RH_{min}\) % MinRelativeHumidity Minimum daily relative humidity
\(RH_{max}\) % MaxRelativeHumidity Maximum daily relative humidity
\(P\) \(L \cdot m^{-2} = mm\) Precipitation Precipitation (including rainfall and snow)
\(Pr\) \(L \cdot m^{-2} = mm\) Rainfall Liquid water precipitation (rainfall)
\(Ps\) \(L \cdot m^{-2} = mm\) Snow Snow precipitation
\(PET\) \(L \cdot m^{-2} = mm\) PET Potential evapotranspiration, preferably calculated using Penman’s equation
\(Rad\) \(MJ \cdot m^{-2}\) Radiation Solar radiation after accounting for clouds
\(u\) \(m \cdot s^{-1}\) WindSpeed Wind speed
\(P_{atm}\) kPa Atmospheric pressure
\(\rho_{air}\) \(kg \cdot m^{-3}\) Air density
\(T_{atm}\) \(^{\circ} \mathrm{C}\) Tatm Atmospheric (above-canopy) air temperature
\(T_{can}\) \(^\circ \mathrm{C}\) Tcan Canopy air temperature
\(T_{air,j}\) \(^\circ \mathrm{C}\) Tair Air temperature in canopy layer \(j\)
\(T_{soil,s}\) \(^\circ \mathrm{C}\) Tsoil.s Temperature of soil layer \(s\)
\(e_{atm}\) kPa Atmospheric (above-canopy) water vapor pressure
\(e_{air,j}\) kPa VPair Water vapor pressure in canopy layer \(j\)
\(C_{atm}\) kPa Catm Atmospheric (above-canopy) \(CO_2\) concentration
\(C_{air,j}\) kPa VPair \(CO_2\) concentration in canopy layer \(j\)
\(u_j\) \(m \cdot s^{-1}\) Wind speed at canopy layer \(j\)

B.6 Anatomy

Symbol Units R Description
\(H_v\) \(m^2 \cdot m^{-2}\) 1/Al2As Huber value (ratio of sapwood area to leaf area)
\(LW\) \(cm\) LeafWidth Leaf width
\(SLA\) \(m^2 \cdot kg^{-1}\) SLA Specific leaf area
\(\rho_{leaf}\) \(g \cdot cm^{-3}\) LeafDensity Leaf tissue density
\(\rho_{wood}\) \(g \cdot cm^{-3}\) WoodDensity Wood tissue density
\(\rho_{fineroot}\) \(g \cdot cm^{-3}\) FineRootDensity Fine root tissue density
\(\Theta_{sapwood}\) \(m^3 \cdot m^{-3}\) Sapwood porosity (volume of empty spaces over total volume)
\(\Theta_{leaf}\) \(m^3 \cdot m^{-3}\) Leaf porosity (volume of empty spaces over total volume)
\(SRL\) \(cm \cdot g^{-1}\) SRL Specific root length
\(RLD\) \(cm \cdot cm^{-3}\) RLD Fine root length density (i.e. density of root length per soil volume)
\(r_{6.35}\) r635 Ratio between the weight of leaves plus branches and the weight of leaves alone for branches of 6.35 mm

B.7 Radiation

Symbol Units R Description
\(k_{PAR,i}\) (unitless) kPAR PAR extinction coefficient for cohort \(i\)
\(k_{SWR,i}\) (unitless) SWR extinction coefficient for cohort \(i\)
\(k_{LWR}\) (unitless) LWR extinction coefficient
\(k_{b}\) (unitless) Extinction coefficient for direct light for cohort \(i\)
\(k_{d,i}\) (unitless) Extinction coefficient for diffuse light for cohort \(i\) (equal to \(k_{PAR,i}\) or \(k_{SWR,i}\))
\(\alpha_{SWR,i}\) [0-1] alphaSWR Short-wave radiation absorbance coefficient for cohort \(i\)
\(\alpha_{PAR,i}\) [0-1] PAR absorbance coefficient for cohort \(i\)
\(\gamma_{SWR,i}\) [0-1] gammaSWR Short-wave radiation leaf reflectance (albedo) for cohort \(i\)
\(\gamma_{SWR,soil}\) [0-1] Short-wave radiation soil reflectance
\(\gamma_{PAR,i}\) [0-1] PAR leaf reflectance for cohort \(i\)
\(L^{PAR}_{ground}\) [0-1] LgroundPAR Fraction of PAR reaching the ground
\(L^{SWR}_{ground}\) [0-1] LgroundSWR Fraction of SWR reaching the ground
\(I_{beam}\) \(W·m^{-2}\) Instantaneous direct shortwave irrradiance from the atmosphere
\(I_{dif}\) \(W·m^{-2}\) Instantaneous diffuse shortwave irrradiance from the atmosphere
\(L_{atm}\) \(W·m^{-2}\) Instantaneous longwave radiation from the atmosphere
\(I_{beam,j}\) \(W·m^{-2}\) Instantaneous direct shortwave irrradiance at the top of canopy layer \(j\)
\(I_{dif,j}\) \(W·m^{-2}\) Instantaneous diffuse shortwave irrradiance at the top of canopy layer \(j\)
\(I_{beam,soil}\) \(W·m^{-2}\) Instantaneous direct shortwave irrradiance reaching the soil
\(I_{dif,soil}\) \(W·m^{-2}\) Instantaneous diffuse shortwave irrradiance reaching the soil
\(LAI^{sunlit}_{i,j}\) \(m^2·m^{-2}\) Leaf area index of sunlit leaves of cohort \(i\) in layer \(j\).
\(LAI^{shade}_{i,j}\) \(m^2·m^{-2}\) Leaf area index of shade leaves of cohort \(i\) in layer \(j\).
\(\Phi^{sunlit}_{i,j}\) \(W·m^{-2}\) Short-wave radiation absorbed by sunlit leaves of cohort \(i\) in layer \(j\), per leaf area unit.
\(\Phi^{shade}_{i,j}\) \(W·m^{-2}\) Short-wave radiation absorbed by sunlit leaves of cohort \(i\) in layer \(j\), per leaf area unit.
\(K^{sunlit}_{abs,i,j}\) \(W·m^{-2}\) Short-wave radiation absorbed by sunlit foliage of cohort \(i\) in layer \(j\), per ground area unit.
\(K^{shade}_{abs,i,j}\) \(W·m^{-2}\) Short-wave radiation absorbed by sunlit foliage of cohort \(i\) in layer \(j\), per ground area unit.

B.8 Water balance

Symbol Units R Description
\(Ps\) mm Snow Precipitation as snow
\(Pr\) mm Rain Precipitation as rainfall
\(Sm\) mm Snowmelt Snowmelt
\(Pr_{net}\) mm NetRain Net rainfall
\(In\) mm Interception Interception loss
\(Ru\) mm Runoff Water exported from the stand as runoff
\(Ro\) mm Runon Water imported to the stand as runon
\(Dd\) mm DeepDrainage Water exported from the stand as deep drainage
\(Es\) mm SoilEvaporation Evaporation from the soil surface
\(Tr_{woody}\) mm Transpiration Woody plant transpiration
\(Tr_{herb}\) mm HerbTranspiration Herbaceous plant transpiration
\(Tr_{i}\) mm Transpiration of woody plant cohort \(i\)

B.9 Energy balance

Symbol Units R Description
\(K_{abs,can}\) \(W \cdot m^{-2}\) SWRcan Atmosphere shortwave radiation absorbed by the canopy
\(K_{abs,j}\) \(W \cdot m^{-2}\) Atmosphere shortwave radiation absorbed by canopy layer \(j\)
\(K_{abs,soil}\) \(W \cdot m^{-2}\) SWRsoil Atmosphere shortwave radiation absorbed by the soil
\(L_{net,can}\) \(W \cdot m^{-2}\) LWRcan Canopy net longwave radiation
\(L_{net,j}\) \(W \cdot m^{-2}\) Net long-wave radiation of canopy layer \(j\)
\(L_{net,soil}\) \(W \cdot m^{-2}\) LWRsoil Soil net longwave radiation
\(H_{can,atm}\) \(W \cdot m^{-2}\) Hcan Turbulent heat exchange between the canopy and the atmosphere
\(H_{can,soil}\) \(W \cdot m^{-2}\) Hcansoil Turbulent heat exchange between the canopy and the soil
\(H_{j}\) \(W \cdot m^{-2}\) Sensible heat flux between canopy layer \(j\) and the leaves it contains
\(LE_{can}\) \(W \cdot m^{-2}\) LEcan Energy released as latent heat from the canopy towards the atmosphere
\(LE_{j}\) \(W \cdot m^{-2}\) Energy released as latent heat by canopy layer \(j\)
\(LE_{soil}\) \(W \cdot m^{-2}\) LEsoil Energy released as latent heat from the soil
\(TC_{LAI}\) \(J \cdot m^{-2} \cdot K^{-1}\) thermalcapacityLAI Canopy thermal capacitance per LAI unit
\(TC_{can}\) \(J \cdot m^{-2} \cdot K^{-1}\) Canopy thermal capacitance
\(TC_{j}\) \(J \cdot m^{-2} \cdot K^{-1}\) Thermal capacitance of canopy layer \(j\)
\(TC_{soil,s}\) \(J \cdot m^{-2} \cdot K^{-1}\) Thermal capacitance of soil layer \(s\)
\(VHC_{soil,s}\) \(J \cdot m^{-3} \cdot K^{-1}\) Volumetric heat capacity of soil in layer \(s\)

B.10 Forest hydrology

Symbol Units R Description
\(P_G\) mm Amount of rainfall needed to saturate the canopy for a given event
\(S_{canopy}\) mm Cm Canopy water storage capacity
\(ER_{ratio}\) (unitless) Ratio between evaporation rate and rainfall rate
\(C_{canopy}\) [0-1] Canopy cover
\(PE_{soil}\) mm Evaporation demand from the soil
\(SE_{soil}\) mm Evaporation supply from the soil
\(t_{soil}\) \(day\) Time needed to evaporate the current water deficit in the first soil layer
\(PET_{herb}\) mm Potential evapotranspiration in the herb layer

B.11 Plant hydraulics

Symbol Units R Description
\(K_{stem,max,ref}\) \(kg \cdot s^{-1} \cdot m^{-1} \cdot MPa^{-1}\) Kmax_stemxylem Maximum stem sapwood reference conductivity per leaf area unit
\(K_{root,max,ref}\) \(kg \cdot s^{-1} \cdot m^{-1} \cdot MPa^{-1}\) Kmax_rootxylem Maximum root sapwood reference conductivity per leaf area unit
\(k_{stem, \max}\) \(mmol \cdot s^{-1} \cdot m^{-2} \cdot MPa^{-1}\) VCstem_kmax Maximum whole-stem conductance (per leaf area unit)
\(k_{root, \max}\) \(mmol \cdot s^{-1} \cdot m^{-2} \cdot MPa^{-1}\) VCroot_kmax Maximum root conductance (per leaf area unit)
\(k_{rhizo, \max}\) \(mmol \cdot s^{-1} \cdot m^{-2} \cdot MPa^{-1}\) Maximum rhizosphere conductance (per leaf area unit)
\(k_{leaf, \max}\) \(mmol \cdot s^{-1} \cdot m^{-2} \cdot MPa^{-1}\) VCleaf_kmax Maximum leaf conductance (per leaf area unit)
\(c_{leaf}\), \(d_{leaf}\) (unitless), MPa VCleaf_c, VCleaf_d Parameters of the vulnerability curve for leaves
\(c_{root}\), \(d_{root}\) (unitless), MPa VCroot_c, VCroot_d Parameters of the vulnerability curve for root xylem
\(c_{stem}\), \(d_{stem}\) (unitless), MPa VCstem_c, VCstem_d Parameters of the vulnerability curve for stem xylem
\(\Psi\) MPa Water potential in a given water compartment/segment
\(\Psi_P\) MPa Turgor water potential in a given water compartment/segment
\(\Psi_S\) MPa Osmotic (solute) water potential in a given water compartment
\(\Psi_{cav}\) MPa Minimum water potential experienced by xylem in previous steps (cavitation)
\(\Psi_{canopy}\) MPa Canopy water potential
\(\Psi_{leaf}\) MPa Leaf water potential
\(\Psi_{rootcrown}\) MPa Water potential at the root crown
\(\Psi_{stem}\) MPa Water potential at the end (highest part) of the stem
\(PLC\) [0-1] Proportion of conductance loss
\(PLC_{stem}\) [0-1] Proportion of conductance loss in stem xylem tissue
\(p_{root}\) [0-1] pRootDisc Relative root conductance leading to hydraulic disconnection from a soil layer
\(E_i\) \(mmol \cdot s^{-1} \cdot m^{-2}\) Steady-state water flow through a hydraulic segment \(i\)
\(k_i\) \(mmol \cdot s^{-1} \cdot m^{-2} \cdot MPa^{-1}\) Hydraulic conductance function for segment \(i\)
\(\Psi_{up}\) MPa Upstream water potential
\(\Psi_{down}\) MPa Downstream water potential

B.12 Photosynthesis

Symbol Units R Description
\(WUE_{\max}\) \(g\, C \cdot mm^{-1}\) WUE Water use efficiency at VPD = 1kPa and without light or CO2 limitations
\(WUE_{PAR}\) WUE_par Coefficient describing the progressive decay of WUE with lower light levels
\(WUE_{CO2}\) WUE_co2 Coefficient for WUE dependency on atmospheric CO2 concentration
\(WUE_{VPD}\) WUE_vpd Coefficient for WUE dependency on vapor pressure deficit
\(J_{max}\) \(\mu mol\,e \cdot m^{-2} \cdot s^{-1}\) Jmax Maximum rate of electron transport at current leaf temperature
\(V_{max, 298}\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Vmax Rubisco’s maximum carboxylation rate at current leaf temperature
\(J_{max, 298}\) \(\mu mol\,e \cdot m^{-2} \cdot s^{-1}\) Jmax298 Maximum rate of electron transport at 298K
\(V_{max, 298}\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Vmax298 Rubisco’s maximum carboxylation rate at 298K
\(T_{leaf}\) \(^\circ C\) Leaf temperature.
\(u_{leaf}\) \(m \cdot s^{-1}\) Leaf-level wind speed.
\(VPD_{leaf}\) kPa Leaf vapour pressure deficit.
\(g_{w}\) \(mol\, H_2O \cdot s^{-1} \cdot m^{-2}\) Leaf diffusive conductance to water vapor
\(g_{c}\) \(mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Leaf diffusive conductance to carbon dioxide
\(g_{sw}\) \(mol\, H_2O \cdot s^{-1} \cdot m^{-2}\) Leaf stomatal conductance to water vapour
\(g_{sw,\min}\) \(mol\, H_2O \cdot s^{-1} \cdot m^{-2}\) Gswmin Minimum stomatal conductance to water vapour
\(g_{sw,\max}\) \(mol\, H_2O \cdot s^{-1} \cdot m^{-2}\) Gswmax Maximum stomatal conductance to water vapour
\(\Phi^{leaf}_{PAR}\) \(W \cdot m^{-2}\) Photosynthetically active radiation absorbed per leaf area
\(Q^{leaf}_{PAR}\) \(\mu mol\,photon \cdot m^{-2} \cdot s^{-1}\) PAR photon flux density per leaf area
\(A_c\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Rubisco-limited photosynthesis rate
\(A_e\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Electron transport-limited photosynthesis rate
\(A\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Leaf gross photosynthesis rate
\(A_n\) \(\mu mol\, CO_2 \cdot s^{-1} \cdot m^{-2}\) Leaf net photosynthesis rate

B.13 Plant water content

Symbol Units R Description
\(LFMC_{\max}\) % maxFMC Maximum live fuel moisture content, corresponding to fine fuels (< 6.35 mm twigs and leaves).
\(\epsilon_{leaf}\) MPa LeafEPS Modulus of elasticity of leaves
\(\epsilon_{stem}\) MPa StemEPS Modulus of elasticity of symplastic xylem tissue
\(\pi_{0,leaf}\) MPa LeafPI0 Osmotic potential at full turgor of leaves
\(\pi_{0,stem}\) MPa StemPI0 Osmotic potential at full turgor of symplastic xylem tissue
\(RWC\) [0-1] Relative water content
\(RWC_{sym}\) [0-1] Relative water content in the symplasm fraction of a tissue
\(RWC_{apo}\) [0-1] Relative water content in the apoplasm fraction of a tissue
\(V_{segment}\) \(l \cdot m^{-2}\) Water capacity of a segment (leaf or stem)
\(V_{leaf}\) \(l \cdot m^{-2}\) Vleaf Leaf water capacity per leaf area unit
\(V_{sapwood}\) \(l \cdot m^{-2}\) Vsapwood Sapwood water capacity per leaf area unit

B.14 Stomatal regulation

Symbol Units R Description
\(\theta_1(\Psi_{leaf})\), \(\theta_2(\Psi_{leaf})\) [0-1] Cost functions 1 and 2
\(\beta(\Psi_{leaf})\) [0-1] Gain function
\(Profit_1(\Psi_{leaf})\), \(Profit_2(\Psi_{leaf})\) [0-1] Profit functions 1 and 2
\(E_{sunlit}\) \(mmol \cdot s^{-1} \cdot m^{-2}\) Instantaneous transpiration flow rate for sunlit leaves
\(E_{shade}\) \(mmol \cdot s^{-1} \cdot m^{-2}\) Instantaneous transpiration flow rate for shade leaves

B.15 Carbon pools

Symbol Units R Description
\(V_{storage,leaf, i}\) \(L \cdot ind^{-1}\) Leaf (carbon) storage volume for an individual of cohort \(i\)
\(V_{storage,sapwood, i}\) \(L \cdot ind^{-1}\) Sapwood (carbon) storage volume for an individual of cohort \(i\)
\(SS_{leaf,i}\) \(mol\,gluc\cdot L^{-1}\) SugarLeaf Sugar concentration in leaves of cohort \(i\)
\(SS_{sapwood,i}\) \(mol\,gluc\cdot L^{-1}\) SugarSapwood Sugar concentration in sapwood of cohort \(i\)
\(ST_{leaf,i}\) \(mol\,gluc\cdot L^{-1}\) StarchLeaf Starch concentration in leaves of cohort \(i\)
\(ST_{sapwood,i}\) \(mol\,gluc\cdot L^{-1}\) StarchSapwood Starch concentration in sapwood of cohort \(i\)
\(S_{plant}\) \(mol\,gluc\cdot ind^{-1}\) Total labile carbon storage in a plant individual
\(B_{leaf}\) \(g\,dry\cdot ind^{-1}\) Leaf dry biomass in a plant individual (for respiration costs)
\(B_{sapwood}\) \(g\,dry\cdot ind^{-1}\) Sapwood dry biomass in a plant individual
\(B_{living, sapwood}\) \(g\,dry\cdot ind^{-1}\) Sapwood dry biomass corresponding to (living) parenchymatic tissues in a plant individual (for respiration costs)
\(B_{fineroot}\) \(g\,dry\cdot ind^{-1}\) Fine root dry biomass in a plant individual (for respiration costs)

B.16 Carbon balance

Symbol Units R Description
\(M_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Leaf daily maintenance respiration in a plant individual
\(M_{sapwood}\) \(mol\,gluc\cdot day^{-1}\) Sapwood daily maintenance respiration in a plant individual
\(M_{fineroot}\) \(mol\,gluc\cdot day^{-1}\) Fine root daily maintenance respiration in a plant individual
\(MR_{leaf}\) \(g\,gluc\cdot g\,dry^{-1}\cdot day^{-1}\) RERleaf Leaf respiration rate at 20 ºC
\(MR_{sapwood}\) \(g\,gluc\cdot g\,dry^{-1}\cdot day^{-1}\) RERsapwood Living sapwood (parenchymatic tissue) respiration rate at 20 ºC
\(MR_{fineroot}\) \(g\,gluc\cdot g\,dry^{-1}\cdot day^{-1}\) RERfineroot Fine root respiration rate at 20 ºC
\(G_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Leaf daily growth respiration in a plant individual
\(G_{sapwood}\) \(mol\,gluc\cdot day^{-1}\) Sapwood daily growth respiration in a plant individual
\(G_{fineroot}\) \(mol\,gluc\cdot day^{-1}\) Fine root daily growth respiration in a plant individual
\(F_{phloem}\) \(mol\,gluc\cdot day^{-1}\) Daily phloem transport of sugars from leaves to sapwood
\(SC_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Daily conversion from leaf sugar to leaf starch
\(SC_{sapwood}\) \(mol\,gluc\cdot day^{-1}\) Daily conversion from sapwood sugar to sapwood starch
\(TS_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Daily translocation of leaf sugars (prior to senescence)
\(TS_{sapwood}\) \(mol\,gluc\cdot day^{-1}\) Daily translocation of sapwood sugars (prior to senescence)
\(TT_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Daily translocation of leaf starch (prior to senescence)
\(RE_{leaf}\) \(mol\,gluc\cdot day^{-1}\) Daily root exudation of leaf carbon
\(RE_{sapwood}\) \(mol\,gluc\cdot day^{-1}\) Daily root exudation of sapwood carbon

B.17 Growth, senescence and mortality

Symbol Units R Description
\(RGR_{leaf, max}\) \(m^2 \cdot cm^{-2} \cdot day^{-1}\) RGRleafmax Maximum leaf area daily growth rate, relative to sapwood area
\(RGR_{sapwood, max}\) \(cm^2 \cdot cm^{-2} \cdot day^{-1}\) RGRsapwoodmax Maximum daily sapwood relative growth rate (in sapwood area basis)
\(RGR_{fineroot, max}\) \(g\,dry \cdot g\,dry^{-1} \cdot day^{-1}\) RGRfinerootmax Maximum daily fine root relative growth rate
\(LA^{target}\) \(m^2\) Leaf area allocation target
\(\Delta LA_{alloc}\) \(m^2\) Leaf area increase dictated by the difference between leaf area allocation target and current leaf area
\(\Delta LA_{source}\) \(m^2\) Leaf area increase according to leaf metabolic carbon availability
\(\Delta LA_{sink}\) \(m^2\) Leaf area increase dictated by sink limitations (leaf relative growth rate and relative cell expansion rate)
\(\Delta LA\) \(m^2\) Actual leaf area increase
\(\Delta SA_{source}\) \(cm^2\) Sapwood area increase according to sapwood storage carbon availability
\(\Delta SA_{sink}\) \(cm^2\) Sapwood area increase dictated by sink limitations
\(\Delta SA\) \(cm^2\) Actual sapwood area increase
\(B_{fineroot,target}\) \(g\, dry\) Fine root biomass allocation target
\(\Delta B_{fineroot,alloc}\) \(g\, dry\) Fine root biomass increase dictated by the difference between fine root biomass allocation target and current fine root biomass
\(\Delta B_{fineroot,source}\) \(g\, dry\) Fine root biomass increase according to sapwood metabolic carbon availability
\(\Delta B_{fineroot,sink}\) \(g\, dry\) Fine root biomass increase dictated by sink limitations (fine root relative growth rate and relative cell expansion rate)
\(\Delta B_{fineroot}\) \(g\, dry\) Actual fine root biomass increase

Bibliography

Genuchten, M.V. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil science society of America journal, 44, 892–898.