- Generated on Mon Feb 3 2020 19:58:04 for CLASSIC by
1.8.13
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CLASSIC
Canadian Land Surface Scheme including Biogeochemical Cycles
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Net Photosynthesis and canopy conductance. More...
Functions/Subroutines | |
| subroutine | photosyncanopyconduct (AILCG, FCANC, TCAN, CO2CONC, PRESSG, FC, CFLUX, QA, QSWV, IC, THLIQ, ISAND, TA, RMAT, COSZS, XDIFFUS, ILG, IL1, IL2, IG, ICC, ISNOW, SLAI, THFC, THLW, FCANCMX, L2MAX, NOL2PFTS, CO2I1, CO2I2, RC, AN_VEG, RML_VEG, DAYL, DAYL_MAX) |
Net Photosynthesis and canopy conductance.
All biogeochemical processes in CLASSIC are simulated at a daily time step except gross photosynthetic uptake and associated calculation of canopy conductance, which are simulated on a half hour time step with CLASS (physics). The photosynthesis module of CLASSIC calculates the net canopy photosynthesis rate, which, together with atmospheric \(CO_2\) concentration and vapour pressure or relative humidity, is used to calculate canopy conductance. This canopy conductance is then used by CLASSIC in its energy and water balance calculations.
The photosynthesis parametrization is based upon the approach of Farquhar et al. (1980) [35] and Collatz et al. (1991, 1992) [23] [24] as implemented in SiB2 (Sellers et al. 1996) [81] and MOSES (Cox et al. 1999) [28] with some minor modifications as described in Arora (2003)[12]. Arora (2003) [12] outlines four possible configurations for the model based on choice of a \(\textit{big-leaf}\) or \(\textit{two-leaf}\) (sunlight and shaded leaves) mode and stomatal conductance formulations based on either Ball et a. (1987) [14] or Leuning (1995) [59]. The Ball et al. (1987) [14] formulation uses relative humidity while Leuning (1995) [59] uses vapour pressure deficit in calculation of canopy conductance. While the model remains capable of all four possible configurations, in practice, the model is usually run using the big-leaf parametrization with the stomatal conductance formulation of [59], which is the configuration described here. The original description of the CLASSIC photosynthesis parametrization in Arora (2003) [12] did not include discussion of all the PFTs simulated by CLASSIC, which we expand upon here.
The gross leaf photosynthesis rate, \(G_\mathrm{o}\), depends upon the maximum assimilation rate allowed by the light ( \(J_\mathrm{e}\)), Rubisco ( \(J_\mathrm{c}\)) and transport capacity ( \(J_\mathrm{s}\)). The limitation placed on \(G_\mathrm{o}\) by the amount of available light is calculated as ( \(mol\, CO_2\, m^{-2}\, s^{-1}\))
\[ J_\mathrm{e} = \left\{\begin{array}{l l}\varepsilon\, (1-{\nu})I \left[\frac{c_{i} - \Gamma}{c_{i} + 2\Gamma}\right], \qquad C_3 plants\\ J_\mathrm{e} = \varepsilon\, (1-{\nu})I, \qquad C_4 plants \end{array} \right. \qquad (Eqn 1) \]
where \(I\) is the incident photosynthetically active radiation ( \(PAR\); \(mol\, photons\, m^{-2}\, s^{-1}\)), \({\nu}\) is the leaf scattering coefficient, with values of 0.15 and 0.17 for \(C_3\) and \(C_4\) plants, respectively, and \(\varepsilon\) is the quantum efficiency ( \(mol\, {CO_2}\, (mol\, photons)^{-1}\); values of 0.08 and 0.04 are used for \(C_3\) and \(C_4\) plants, respectively). \(c_\mathrm{i}\) is the partial pressure of \(CO_2\) in the leaf interior ( \(Pa\)) and \(\Gamma\) is the \(CO_2\) compensation point ( \(Pa\)) (described below).
The Rubisco enzyme limited photosynthesis rate, \(J_\mathrm{c}\), is given by
\[ J_\mathrm{c} = \left\{\begin{array}{l l} V_\mathrm{m} \left[\frac{c_\mathrm{i} - \Gamma}{c_\mathrm{i} + K_\mathrm{c}(1 + O_\mathrm{a}/K_\mathrm{o})}\right], \qquad C_3 plants\\ J_\mathrm{c} = V_\mathrm{m}, \qquad C_4 plants \end{array} \right. \qquad(Eqn 2) \]
where \(V_\mathrm{m}\) is the maximum catalytic capacity of Rubisco ( \(mol\, CO_2\, m^{-2}\, s^{-1}\)), adjusted for temperature and soil moisture, as described below. \(K_\mathrm{o}\) and \(K_\mathrm{c}\) are the Michaelis–Menten constants for \(O_2\) and \(CO_2\), respectively. \(O_\mathrm{a}\) is the partial pressure ( \(Pa\)) of oxygen.
The transport capacity ( \(J_\mathrm{s}\)) limitation determines the maximum capacity to transport the products of photosynthesis for \(C_3\) plants, while for \(C_4\) plants it represents \(CO_2\) limitation
\[ J_\mathrm{s} = \left\{\begin{array}{l l} 0.5 V_\mathrm{m}, \qquad C_3 plants\\ 2 \times 10^4\, V_\mathrm{m} \frac{c_\mathrm{i}}{p}, \qquad C_4 plants \end{array} \right. \qquad (Eqn 3)\]
where \(p\) is surface atmospheric pressure ( \(Pa\)).
\(V_\mathrm{m}\) is calculated as
\[ V_\mathrm{m} = \frac{V_{max}f_{25}(2.0)S_{root}(\theta) \times 10^{-6}} {[1+ \exp{0.3(T_\mathrm{c} - T_{high})}][1 + \exp{0.3(T_{low} - T_\mathrm{c})}]}, \label{V_m} \qquad (Eqn 4)\]
where \(T_\mathrm{c}\) is the canopy temperature ( \(C\)) and \(T_{low}\) and \(T_{high}\) are PFT-dependent lower and upper temperature limits for photosynthesis (see also classicParams.f90). \(f_{25}\) is the standard \(Q_{10}\) function at \(25\, C\) ( \((f_{25}(Q_{10}) = Q^{(0.1(T_\mathrm{c}-25))}_{10}\)) and \(V_{max}\) is the PFT-dependent maximum rate of carboxylation by the enzyme Rubisco ( \(mol\, CO_2\, m^{-2}\, s^{-1}\); see also classicParams.f90). The constant \(10^{-6}\) converts \(V_{max}\) from units of \({\mu}mol\, CO_2\, m^{-2}\, s^{-1}\) to \(mol\, CO_2\, m^{-2}\, s^{-1}\).
The influence of soil moisture stress is simulated via \(S_{root}(\theta)\), which represents a soil moisture stress term formulated as
\[ S_{root}(\theta) = \sum_{i=1}^g S(\theta_i) r_{i}, \qquad (Eqn 5)\]
\[ \label{soilmoist_str} S(\theta_i) = \left[1 - \left\{1 - \phi_i \right\}\right]^\varrho, \qquad (Eqn 6)\]
where \(S_{root}(\theta)\) is calculated by weighting \(S(\theta_i)\) with the fraction of roots, \(r_{i}\), in each soil layer \(i\) and \(\varrho\) is a PFT-specific sensitivity to soil moisture stress (unitless; see also classicParams.f90). \(\phi_i\) is the degree of soil saturation (soil wetness) given by
\[ \label{phitheta} \phi_{i}(\theta_{i}) = \max \left[0, \min \left(1, \frac{\theta_{i} - \theta_{i, wilt}}{\theta_{i, field} - \theta_{i, wilt}} \right) \right], \qquad (Eqn 7)\]
where \(\theta_{i}\) is the volumetric soil moisture ( \(m^{3} water\, (m^{3} soil)^{-1}\)) of the \(i\)th soil layer and \(\theta_{i, field}\) and \(\theta_{i, wilt}\) the soil moisture at field capacity and wilting point, respectively.
The \(CO_2\) compensation point ( \(\Gamma\)) is the \(CO_2\) partial pressure where photosynthetic uptake equals the leaf respiratory losses (used in Eqs. 1 and 2). \(\Gamma\) is zero for \(C_4\) plants but is sensitive to oxygen partial pressure for \(C_3\) plants as
\[ \label{co2comp} \Gamma = \left\{\begin{array}{l l} \frac{O_\mathrm{a}}{2 \sigma}, C_3 plants\\ 0, C_4 plants, \end{array} \right.\qquad (Eqn 8) \]
where \(\sigma\) is the selectivity of Rubisco for \(CO_2\) over \(O_2\) (unitless), estimated by \(\sigma = 2600f_{25}(0.57)\). The \(CO_2\) ( \(K_\mathrm{c}\)) and \(O_2\) ( \(K_\mathrm{o}\)) Michaelis–Menten constants used in Eq. 2 are determined via
\[ \label{K_c} K_\mathrm{c} = 30f_{25}(2.1), \qquad (Eqn 9) \]
\[ \label{K_o} K_o = 3 \times 10^4 f_{25}(1.2).\qquad (Eqn 9) \]
Given the light ( \(J_\mathrm{e}\)), Rubsico ( \(J_\mathrm{c}\)) and transportation capacity ( \(J_\mathrm{s}\)) limiting rates, the leaf-level gross photosynthesis rate, \(G_\mathrm{o}\) ( \(mol\, CO_2\, m^{-2}\, s^{-1}\)), is then determined following a minimization based upon smallest roots of the following two quadratic equations
\[ J_\mathrm{p} = \frac{(J_\mathrm{c} + J_\mathrm{e}) \pm \sqrt{(J_\mathrm{c} + J_\mathrm{e})^2 - 4\beta_1 (J_\mathrm{c} + J_\mathrm{e})}}{2\beta_1} , \qquad (Eqn 10) \]
\[ \label{G_o}G_\mathrm{o} = \frac{(J_\mathrm{p} + J_\mathrm{s}) \pm \sqrt{(J_\mathrm{p} + J_\mathrm{s})^2 - 4\beta_2 (J_\mathrm{p} + J_\mathrm{s})}}{2\beta_2}, \qquad (Eqn 10) \]
where \(\beta_1\) is 0.95 and \(\beta_2\) is 0.99. When soil moisture stress is occurring, both the \(J_\mathrm{s}\) and \(J_\mathrm{c}\) terms are reduced since the \(V_\mathrm{m}\) term (Eq. 4) includes the effect of soil moisture stress through the \(S(\theta)\) term and this reduces the leaf-level gross photosynthesis rate.
The current version of CLASSIC does not include nutrient constraints on photosynthesis and, as a result, increasing atmospheric \(CO_2\) concentration leads to unconstrained increase in photosynthesis. In natural ecosystems, however, down regulation of photosynthesis occurs due to constraints imposed by availability of nitrogen, as well as phosphorus. To capture this effect, CTEM uses a nutrient limitation term, based on experimental plant growth studies, to down regulate the photosynthetic response to elevated \(CO_2\) concentrations (Arora et al., 2009)[10]. The parametrization, and its rationale, are fully described in Arora et al. (2009) [10] but the basic relations are summarized here. The leaf-level gross photosynthetic rate is scaled by the down-regulation term, \(\Xi_\mathrm{N}\), to yield the nutrient limited leaf level gross photosynthetic rate as
\[ G_{\mathrm{o}, N-limited} = \Xi_\mathrm{N} G_\mathrm{o}, \\ \Xi_\mathrm{N} = \frac{1 + \gamma_{gd} \ln(c_\mathrm{a}/c_{0})}{1 + \gamma_g \ln(c_\mathrm{a}/c_{0})}, \qquad (Eqn 11)\]
where \(c_\mathrm{a}\) is the atmospheric \(CO_2\) concentration in ppm, \(c_{0}\) is the pre-industrial \(CO_2\) concentration ( \(285.0\, ppm\)), \(\gamma_g\) is 0.95 (Arora et al. 2009) [10]. A value of \(\gamma_{gd}\) lower than \(\gamma_g\) ensures that \(\Xi_\mathrm{N}\) gradually decreases from its pre-industrial value of one as \(c_\mathrm{a}\) increases to constrain the rate of increase of photosynthesis with rising atmospheric \(CO_2\) concentrations.
Finally, the leaf-level gross photosynthesis rate, \(G_{\mathrm{o}, N-limited}\) is scaled up to the canopy-level, \(G_{canopy}\), by considering the exponential vertical profile of radiation along the depth of the canopy as
\[ G_{canopy} = G_{\mathrm{o}, N-limited} f_{PAR}, \\ \label{fpar} f_{PAR} = \frac{1}{k_\mathrm{n}}(1-\exp^{-k_\mathrm{n}LAI}), \qquad (Eqn 12) \]
which yields the gross primary productivity ( \(G_{canopy}\), GPP). \(k_\mathrm{n}\) is the extinction coefficient that describes the nitrogen and time-mean photosynthetically absorbed radiation ( \(PAR\)) profile along the depth of the canopy (see also classicParams.f90) (Ingestad and Lund, 1986; [45] Field and Mooney, 1986 [37]), and \(LAI\) ( \(m^{2}\, leaf\, (m^{2}\, ground)^{-1}\)) is the leaf area index.
The net canopy photosynthetic rate, \(G_{canopy, net}\) ( \(mol\, CO_2\, m^{-2}\, s^{-1}\)), is calculated by subtracting canopy leaf maintenance respiration costs ( \(R_{mL}\); see mainres.f) as
\[ \label{Gnet} G_{canopy, net} = G_{canopy} - R_{mL}.\qquad (Eqn 13) \]
Coupling of photosynthesis and canopy conductance
When using the Leuning (1995) [59] approach for photosynthesis–canopy conductance coupling, canopy conductance ( \(g_\mathrm{c}\); \(mol\, m^{-2}\, s^{-1}\)) is expressed as a function of the net canopy photosynthesis rate, \(G_{canopy, net}\), as
\[ \label{canopy_cond} g_\mathrm{c} = m \frac{G_{canopy, net} p}{(c_\mathrm{s} - \Gamma)}\frac{1}{(1+V/V_\mathrm{o})} + b {LAI}\qquad (Eqn 14) \]
where \(p\) is the surface atmospheric pressure ( \(Pa\)), the parameter \(m\) is set to 9.0 for needle-leaved trees, 12.0 for other \(C_3\) plants and 6.0 for \(C_4\) plants, parameter \(b\) is assigned the values of 0.01 and 0.04 for \(C_3\) and \(C_4\) plants, respectively. \(V\) is the vapour pressure deficit ( \(Pa\)) and the parameter \(V_\mathrm{o}\) is set to \(2000\, Pa\) for trees and \(1500\, Pa\) for crops and grasses. The partial pressure of \(CO_2\) at the leaf surface, \(c_\mathrm{s}\), is found via
\[ \label{c_s} c_\mathrm{s} = c_{ap} - \frac{1.37 G_{canopy, net} p}{g_b}.\qquad (Eqn 15) \]
Here, \(c_{ap}\) is the atmospheric \(CO_2\) partial pressure ( \(Pa\)) and \(g_b\) is the aerodynamic conductance estimated by CLASS ( \(mol\, m^{-2}\, s^{-1}\)). The intra-cellular \(CO_2\) concentration required in Eqs. 1–3 is calculated as
\[ \label{c_i} c_\mathrm{i} = c_\mathrm{s} - \frac{1.65 G_{canopy, net} p}{g_\mathrm{c}}.\qquad (Eqn 16) \]
Since calculations of \(G_{canopy, net}\) and \(c_\mathrm{i}\) depend on each other, the photosynthesis-canopy conductance equations need to be solved iteratively. The initial value of \(c_\mathrm{i}\) used in calculation of \(G_{canopy, net}\) is the value from the previous time step or, in its absence, \(c_\mathrm{i}\) is assumed to be \(0.7c_{ap}\).
Canopy ( \(g_\mathrm{c}\)) and aerodynamic ( \(g_b\)) conductance used in above calculations are expressed in units of \(mol\, CO_2\, m^{-2}\, s^{-1}\) but can be converted to the traditional units of \(m\, s^{-1}\) as follows
\[ g_\mathrm{c} (m\, s^{-1}) = 0.0224\, \frac{T_\mathrm{c}}{T_\mathrm{f}}\, \frac{p_0}{p}\, g_\mathrm{c} (mol\, m^{-2}\, s^{-1}), \qquad (Eqn 17) \]
where \(p_0\) is the standard atmospheric pressure ( \(101\, 325\, Pa\)) and \(T_\mathrm{f}\) is freezing temperature ( \(273.16\, K\)).
| subroutine photosyncanopyconduct | ( | real, dimension(ilg,icc), intent(in) | AILCG, |
| real, dimension(ilg,icc), intent(in) | FCANC, | ||
| real, dimension(ilg), intent(in) | TCAN, | ||
| real, dimension(ilg), intent(in) | CO2CONC, | ||
| real, dimension(ilg), intent(in) | PRESSG, | ||
| real, dimension(ilg), intent(in) | FC, | ||
| real, dimension(ilg), intent(in) | CFLUX, | ||
| real, dimension(ilg), intent(in) | QA, | ||
| real, dimension(ilg), intent(in) | QSWV, | ||
| integer, intent(in) | IC, | ||
| real, dimension(ilg,ig), intent(in) | THLIQ, | ||
| integer, dimension(ilg,ig), intent(in) | ISAND, | ||
| real, dimension(ilg), intent(in) | TA, | ||
| real, dimension(ilg, icc,ig), intent(in) | RMAT, | ||
| real, dimension(ilg), intent(in) | COSZS, | ||
| real, dimension(ilg), intent(in) | XDIFFUS, | ||
| integer, intent(in) | ILG, | ||
| integer, intent(in) | IL1, | ||
| integer, intent(in) | IL2, | ||
| integer, intent(in) | IG, | ||
| integer, intent(in) | ICC, | ||
| integer, intent(in) | ISNOW, | ||
| real, dimension(ilg,icc), intent(in) | SLAI, | ||
| real, dimension(ilg,ig), intent(in) | THFC, | ||
| real, dimension(ilg,ig), intent(in) | THLW, | ||
| real, dimension(ilg,icc), intent(in) | FCANCMX, | ||
| integer, intent(in) | L2MAX, | ||
| integer, dimension(ic), intent(in) | NOL2PFTS, | ||
| real, dimension(ilg,icc), intent(inout) | CO2I1, | ||
| real, dimension(ilg,icc), intent(inout) | CO2I2, | ||
| real, dimension(ilg), intent(out) | RC, | ||
| real, dimension(ilg,icc), intent(out) | AN_VEG, | ||
| real, dimension(ilg,icc), intent(out) | RML_VEG, | ||
| real, dimension(ilg), intent(in) | DAYL, | ||
| real, dimension(ilg), intent(in) | DAYL_MAX | ||
| ) |
| [in] | ilg | NO. OF GRID CELLS IN LATITUDE CIRCLE |
| [in] | ic | NO. OF CLASS VEGETATION TYPES, 4 |
| [in] | il1 | IL1=1 |
| [in] | il2 | IL2=ILG |
| [in] | ig | NO. OF SOIL LAYERS, 3 |
| [in] | icc | NO. OF CTEM's PFTs, CURRENTLY 9 |
| [in] | isnow | integer, intent(in) (0 or 1) TELLING IF PHTSYN IS TO BE RUN OVER CANOPY OVER SNOW OR CANOPY OVER GROUND SUBAREA |
| [in] | l2max | MAX. NUMBER OF LEVEL 2 PFTs |
| [in] | fcanc | FRACTIONAL COVERAGE OF CTEM's 9 PFTs |
| [in] | ailcg | GREEN LEAF AREA INDEX FOR USE BY PHOTOSYNTHESIS, \(M^2/M^2\) |
| [in] | tcan | CANOPY TEMPERATURE, KELVIN |
| [in] | fc | SUM OF ALL FCANC OVER A GIVEN SUB-AREA |
| [in] | cflux | AERODYNAMIC CONDUCTANCE, M/S |
| [in] | slai | SCREEN LEVEL HUMIDITY IN KG/KG - STORAGE LAI. THIS LAI IS USED FOR PHTSYN EVEN IF ACTUAL LAI IS ZERO. ESTIMATE OF NET PHOTOSYNTHESIS BASED ON SLAI IS USED FOR INITIATING LEAF ONSET. SEE PHENOLGY SUBROUTINE FOR MORE DETAILS. |
| [in] | co2conc | ATMOS. \(CO_2\) IN PPM, AND THEN CONVERT IT TO PARTIAL PRESSURE, PASCALS, CO2A, FOR USE IN THIS SUBROUTINE |
| [in] | pressg | ATMOS. PRESSURE, PASCALS |
| [out] | rml_veg | LEAF RESPIRATION RATE, ( \(\mu mol CO_2 m^{-2} s^{-1}\)) FOR EACH PFT |
| [out] | an_veg | NET PHOTOSYNTHESIS RATE, ( \(\mu mol CO_2 m^{-2} s^{-1}\)) FOR EACH PFT |
| [in] | qswv | ABSORBED VISIBLE PART OF SHORTWAVE RADIATION, \(W/M^2\) |
| [in] | ta | AIR TEMPERATURE IN KELVINS |
| [in] | rmat | FRACTION OF ROOTS IN EACH LAYER (grid cell, vegetation, layer) |
| [in,out] | co2i1 | INTERCELLULAR \(CO_2\) CONCENTRATION FROM THE PREVIOUS TIME STEP WHICH GETS UPDATED FOR THE SINGLE LEAF OR THE SUNLIT PART OF THE TWO LEAF MODEL |
| [in,out] | co2i2 | INTERCELLULAR \(CO_2\) CONCENTRATION FOR THE SHADED PART OF THE TWO LEAF MODEL FROM THE PREVIOUS TIME STEP |
| [in] | thliq | LIQUID MOIS. CONTENT OF 3 SOIL LAYERS |
| [in] | thfc | SOIL FIELD CAPACITY. |
| [in] | thlw | SOIL WILT CAPACITY. |
| [in] | fcancmx | MAX. FRACTIONAL COVERAGES OF CTEM's 8 PFTs. THIS IS DIFFERENT FROM FCANC AND FCANCS (WHICH MAY VARY WITH SNOW DEPTH). FCANCMX DOESN'T CHANGE, UNLESS OF COURSE ITS CHANGED BY LAND USE CHANGE OR DYNAMIC VEGETATION. |
| [out] | rc | GRID-AVERAGED STOMATAL RESISTANCE, S/M |
| [in] | coszs | COS OF ZENITH ANGLE |
| [in] | xdiffus | FRACTION OF DIFFUSED PAR |
| [in] | isand | SAND INDEX. |
| [in] | dayl_max | MAXIMUM DAYLENGTH FOR THAT LOCATION |
| [in] | dayl | DAYLENGTH FOR THAT LOCATION |
IF LAI IS LESS THAN SLAI THAN WE USE STORAGE LAI TO PHOTOSYNTHESIZE. HOWEVER, WE DO NOT USE THE STOMATAL RESISTANCE ESTIMATED IN THIS CASE, BECAUSE STORAGE LAI IS AN IMAGINARY LAI, AND WE SET STOMATAL RESISTANCE TO ITS MAX. NOTE THAT THE CONCEPT OF STORAGE/IMAGINARY LAI IS USED FOR PHENOLOGY PURPOSES AND THIS IMAGINARY LAI ACTS AS MODEL SEEDS.
SET MIN. AND MAX. VALUES FOR STOMATAL CONDUCTANCE. WE MAKE SURE THAT MAX. STOMATAL RESISTANCE IS AROUND 5000 S/M AND MIN. STOMATAL RESISTANCE IS 51 S/M.
IF WE ARE USING LEUNING TYPE PHOTOSYNTHESIS-STOMATAL CONDUCTANCE COUPLING WE NEED VAPOR PRESSURE DEFICIT AS WELL. CALCULATE THIS FROM THE RH AND AIR TEMPERATURE WE HAVE. WE FIND E_SAT, E, AND VPD IN PASCALS.
ESTIMATE PARTIAL PRESSURE OF \(CO_2\) AND IPAR
CONVERT CO2CONC FROM PPM TO PASCALS
CHANGE PAR FROM W/M^2 TO MOL/M^2.S
SUNLIT PART GETS BOTH DIRECT AND DIFFUSED, WHILE THE SHADED PART GETS ONLY DIFFUSED
FOR TWO-LEAF MODEL FIND Kb AS A FUNCTION OF COSZS AND LEAF ANGLE DISTRIBUTION (VEGETATION DEPENDENT)
MAKE SURE -0.4 < CHI < 0.6
MAKE VALUES CLOSE TO ZERO EQUAL TO 0.01
ALSO FIND SUNLIT AND SHADED LAI
FOLLOWING FEW LINES TO MAKE SURE THAT ALL LEAVES ARE SHADED WHEN XDIFFUS EQUALS 1. NOT DOING SO GIVES ERRATIC RESULTS WHEN TWO LEAF OPTION IS USED
FIND FPAR - FACTOR FOR SCALING PHOTOSYNTHESIS TO CANOPY BASED ON ASSUMPTION THAT NITROGEN IS OPTIMALLY DISTRIBUTED. THE TWO-LEAF MODEL IS NOT THAT DIFFERENT FROM THE SINGLE-LEAF MODEL. ALL WE DO IS USE TWO SCALING FACTORS (I.E. SCALING FROM LEAF TO CANOPY) INSTEAD OF ONE, AND THUS PERFORM CALCULATIONS TWICE, AND IN THE END ADD CONDUCTANCE AND NET PHOTOSYNTHESIS FROM THE TWO LEAVES TO GET THE TOTAL.
IF ALL RADIATION IS DIFFUSED, THEN ALL LEAVES ARE SHADED, AND WE ADJUST FPARs ACCORDINGLY. WITHOUT THIS THE TWO LEAF MODELS MAY BEHAVE ERRATICALLY
FIND Vmax, canopy, THAT IS Vmax SCALED BY LAI FOR THE SINGLE LEAF MODEL
-———— Changing Vcmax seasonally –———————
Based on [17] and [3] there is good evidence for the Vcmax varying throughout the season for deciduous tree species. We are adopting a parameterization based upon their paper with some differences. We don't apply it to evergreens like they suggest. Their paper had only one evergreen species and other papers ([70]) don't seem to back that up. Grasses and crops are also not affected by the dayl. [3] seems to indicate that all PFTs except BDL-EVG tropical should vary intra-annually (see their figure 8).
The two leaf is assumed to be affect by the insolation seasonal cycle the same for each sun/shade leaf
-———— Changing Vcmax seasonally –———————///
FIND Vm, unstressed (DUE TO WATER) BUT STRESSED DUE TO TEMPERATURE
ASSUMING THAT SUNLIT AND SHADED TEMPERATURES ARE SAME
CALCULATE SOIL MOIS STRESS TO ACCOUNT FOR REDUCTION IN PHOTOSYN DUE TO LOW SOIL MOISTURE, THREE STEPS HERE
NOTE THAT WHILE SOIL MOISTURE IS UNIFORM OVER AN ENTIRE GCM GRID CELL, THE SOIL MOISTURE STRESS FOR EACH PFT IS NOT BECAUSE OF DIFFERENCES IN ROOT DISTRIBUTION.
WILTING POINT CORRESPONDS TO MATRIC POTENTIAL OF 150 M FIELD CAPACITY CORRESPONDS TO HYDARULIC CONDUCTIVITY OF 0.10 MM/DAY -> 1.157x1E-09 M/S
USE SOIL MOISTURE FUNCTION TO MAKE Vm, unstressed -> Vm STRESSED
FIND TEMPERATURE DEPENDENT PARAMETER VALUES
FIND RUBISCO SPECIFICITY FOR \(CO_2\) RELATIVE TO \(O_2\) - SIGMA
FIND \(CO_2\) COMPENSATION POINT USING RUBISCO SPECIFICITY - TGAMMA. KEEP IN MIND THAT \(CO_2\) COMPENSATION POINT FOR C4 PLANTS IS ZERO, SO THE FOLLOWING VALUE IS RELEVANT FOR C3 PLANTS ONLY
ESTIMATE MICHELIS-MENTON CONSTANTS FOR \(CO_2\) (Kc) and \(O_2\) (Ko) TO BE USED LATER FOR ESTIMATING RUBISCO LIMITED PHOTOSYNTHETIC RATE
CHOOSE A VALUE OF INTERCELLULAR \(CO_2\) CONCENTRATION \((CO_2i)\) IF STARTING FOR THE FIRST TIME, OR USE VALUE FROM THE PREVIOUS TIME STEP
ESTIMATE RUBISCO LIMITED PHOTOSYNTHETIC RATE
ESTIMATE PHOTOSYNTHETIC RATE LIMITED BY AVAILABLE LIGHT
ESTIMATE PHOTOSYNTHETIC RATE LIMITED BY TRANSPORT CAPACITY
INCLUDE NUTRIENT LIMITATION EFFECT BY DOWN-REGULATING PHOTOSYNTHESIS N_EFFECT DECREASES FROM 1.0 AS \(CO_2\) INCREASES ABOVE 288 PPM.
LIMIT N_EFFECT TO MAX OF 1.0 SO THAT NO UP-REGULATION OCCURS
FIND THE SMOOTHED AVERAGE OF THREE PHOTOSYNTHETIC RATES JC, JE, AND JS USING COLLATZ'S TWO QUADRATIC EQUATIONS, OR FIND THE MIN. OF THIS TWO RATES OR FIND MIN. OF JC AND JE.
DOWN-REGULATE PHOTOSYNTHESIS FOR C3 PLANTS
ESTIMATE LEAF MAINTENANCE RESPIRATION RATES AND NET PHOTOSYNTHETIC RATE. THIS NET PHOSYNTHETIC RATE IS /M^2 OF VEGETATED LAND.
RECENT STUDIES SHOW RmL IS LESS TEMPERATURE SENSITIVE THAN PHOTOSYNTHESIS DURING DAY, THAT'S WHY A SMALL Q10 VALUE IS USED DURING DAY.
FIND \(CO_2\) CONCENTRATION AT LEAF SURFACE FOR ALL VEGETATION TYPES. ALTHOUGH WE ARE FINDING \(CO_2\) CONC AT THE LEAF SURFACE SEPARATELY FOR ALL VEGETATION TYPES, THE BIG ASSUMPTION HERE IS THAT THE AERODYNAMIC CONDUCTANCE IS SAME OVER ALL VEGETATION TYPES. CLASS FINDS AERODYNAMIC RESISTANCE OVER ALL THE 4 SUB-AREAS, BUT NOT FOR DIFFERENT VEGETATION TYPES WITHIN A SUB-AREA. ALSO CHANGE AERODYNAMIC CONDUCTANCE, CFLUX, FROM M/S TO \(MOL/M^2/S\)
FIND STOMATAL CONDUCTANCE AS PER BALL-WOODROW-BERRY FORMULATION USED BY COLLATZ ET AL. OR USE THE LEUNING TYPE FORMULATION WHICH USES VPD INSTEAD OF RH
IF LIGHT IS TOO LESS MAKE PARAMETER BB VERY SMALL
FIND THE INTERCELLULAR \(CO_2\) CONCENTRATION BASED ON ESTIMATED VALUE OF GC
SEE IF WE HAVE PERFORMED THE REQUIRED NO. OF ITERATIONS, IF NOT THEN WE GO BACK AND DO ANOTHER ITERATION
WHEN REQUIRED NO. OF ITERATIONS HAVE BEEN PERFORMED THEN FIND STOMATAL CONDUCTANCES FOR ALL VEGETATION TYPES IN M/S AND THEN USE CONDUCTANCES TO FIND RESISTANCES. GCTU IMPLIES GC IN TRADITIONAL UNITS OF M/S
DON'T WANT TO REDUCE RESISTANCE AT NIGHT TO LESS THAN OUR MAX. VALUE OF AROUND 5000 S/M
IF USING STORAGE LAI THEN WE SET STOMATAL RESISTANCE TO ITS MAXIMUM VALUE.
AND FINALLY TAKE WEIGHTED AVERAGE OF RC_VEG BASED ON FRACTIONAL COVERAGE OF OUR 4 VEGETATION TYPES
CONVERT AN_VEG AND RML_VEG TO u-MOL CO2/M2.SEC
1.8.13