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 |
| \(Z_{sat}\) | mm | Depth to saturation | |
| \(V_{s}\) | 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.