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LandscapeDNDC
1.36.0
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LandscapeDNDC
1.36.0
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The electron transport rate depends on radiation intensity [19].
\[ jPot = \frac { (i_{S} + jMax - ((i_{S} + jMax)^ { 2 } - 4.0 \cdot THETA \cdot i_{S} \cdot jMax))^ { 0.5 } }{ 2.0 \cdot THETA } \]
with
The radiation perceived by the photosystem is calculated separately for sunlit and shaded fractions in each canopy layer
\[ i_{S} = par_{S} \cdot (1.0 - 0.15) \cdot 0.5 \]
with
The losses of absorbed radiation are fix ( (1.0 - 0.15) * 0.5 = 0.425), assuming a constant correction for spectral quality of 0.15 [18]. (reduction by a factor of 0.5 is considering an equal distribution between two photosystems).
could be improved by
Carboxylation and oxygenation activities as well as the electron transport rate depend on temperature using an Arrhenius function based on [52] that has been corrected for high temperatures according to [54].
\[ v_{E} = ( v25_{E} \cdot exp( AE_{E} \cdot term_{arrh} ) \cdot add_{peak} ) \]
\[ term_{arrh} = \frac {tempK - TK25} {TK25 \cdot tempK \cdot RGAS} \]
\[ add_{peak} = \frac { 1.0 + exp( \frac {TK25 \cdot SDJ - HDJ} {TK25 \cdot RGAS} ) } { 1.0 + exp( \frac{ tempK \cdot SDJ - HDJ} {tempK \cdot RGAS} ) } \]
with
For these dependencies oxygenation activity vo is assumed to be in a fixed relation (QVOVC) to parameterized carboxylation activity at 25 oC (VCMAX25). Similarly, the electron transport as well as the photorespiration rate at 25 oC is assumed to be in a fixed relation to carboxylation velocity (QJVC, QRD25).
could be improved by
The internal co2 concentration is calculated iteratively considering assimilation and stomatal conductance (which depends on assimilation) until ci = ciPot. With
\[ ciPot = ca - \frac {assi} {gs / FGC} \]
with
Note that there is no iteration if assi < 0 because dark respiration is not influenced by ci and the rest impact is supposed to be negligible. Furthermore, stomatal conductance of water is constraint by minimum and maximum values (GSMIN and GSMAX, respectively).
The co2 compensation point which is also used for defining gs is derived from carboxylation (vc) as well as oxygenation (vo) velocities [70] using an empirical estimate of O2 concentrations in the plant tissue [52], kinetic values that are derived from temperature-corrected species-specific parameteres (KO25, KC25) and enzyme activities (AEKC, AEKO).
\[ c\_star = 0.5 \cdot vo \cdot kc \cdot \frac {oi} {vc \cdot ko} \]
with
This gas exchange module calculates stomatal conductance and photsynthesis based on [20]. The implementation is according to [71].
\[ A = \left( 1.0 - \frac {c^{\ast}} {c_i} \right) \cdot min(w_c, w_j, w_p) - rd \]
with
The calculation of \( w_c, w_j \) and \( w_p \) depend on \( c_i, w_c \) additionally on \( o_i \), \( w_j \) and \( w_p \) additionally on the compensation point:
\[ w_c = vc \cdot \frac {c_i} {c_i + kc \cdot (1.0 + \frac {o_i}{ko}}) \]
\[ w_j = \frac {j} { 4.0 + 8.0 \cdot \frac {c^{\ast}}{c_i} } \]
\[ w_p = \frac { 3.0 \cdot tpu }{ 1.0 - \frac {c^{\ast}}{c_i} } \]
with \( c^{\ast} \) according to [70] :
\[ c^{\ast} = 0.5 \cdot vo \cdot kc \cdot \frac {o_i} {vc \cdot ko} \]
with
All enzyme activities \( (vc, vo, j, tpu, rd) \) rates are calculated using canopy layer-specific temperature and radiation. Regarding temperature dependencies an Arrhenius function is used [52] that has been corrected for high temperatures according to [54]. For these dependencies, process-specific activation energies (AEVC, AEVO, AEJM, AETP, AERD), and activity rates at 25oC are parameterized (VCMAX25, TPU25) or put into a fixed relation to carboxylation activity (QJVC, QVOVC, QRD25). Similarly, also for Michaelis-Menten constants the rates at 25oC have been parameterized (KO25, KC25) and temperature corrected in the same way as carboxylation and oxygenation (using AEKC, AEKO). For C4 plants simplified assumptions are applied for carboxylation dependencies [36] and phosphorylation limits [12].
Radiation intensity is needed to define electron transport rate only [19], using a species-specific parameter to define the slope of the relationship (THETA). Furthermore, it is assumed that the potential (parameterized) carboxylation activity, electron transport rate and photorespiration at 25oC is reduced with increasing canopy depth (linked to specific leaf area) and can be further reduced if nitrogen supply is not sufficient to reach a predefined target value. In addition, the enzymatic activities depend on phenological developments, and are eventually reduced by heat, frost or drought stress (Daily enzyme activity).
Internal carbon dioxide concentration is calculated with the Berry-Ball [5] optimization approach (standard) or the Jarvis [39] multiplicative approach (optional).
The model [5] is the original version to use iteratively with the Farquhar model [20]. The stomatal conductance of every foliage layer is determined by
\[ gs = GSMIN + SLOPE\_{GSA} \cdot assi \cdot \frac {rh}{ca} \]
with
The model [46] has been modified by adding an additional soil water impact [41]. Stomatal conductance of every foliage layer is determined by
\[ gs = GSMIN + SLOPE\_GSA \cdot fwat \cdot assi \cdot \frac{rh}{ca - c\_star} \]
\[ fwat = min \left(1.0, \frac{\frac{wc - wc\_{min}}{wc\_{max} - wc\_{min}}}{H2OREF\_GS} \right) \]
with:
The model [17] considers canopy water potential as influencial for stomatal conductance. Stomatal conductance of every foliage layer is determined by
\[ gs = GSMIN + 0.5 \cdot qac \cdot (sqrt(1.0 + (4.0 \cdot \frac {epsilon}{qac} ) - 1.0) ) \]
\[ qac = \frac {assi\_{ref} - assi}{ca - ci} \]
with
The conductance impact 'epsilon' is a complex interaction of plant conductance modified by canopy water potential and evaporative demand:
\[ epsilon = \frac { 2.0 }{ qkr \cdot rplant \cdot 1.6 \cdot vpd\_{mmol} } \]
\[ qkr = ( \frac {kcr - kcr\_{ref} } { psi\_{mean} - (0.5 \cdot (psi\_{mean}+PSI\_{REF}) ) } ) / kcr \]
\[ kcr = 1.0 - (1.0 - exp(- ( \frac {psi\_{mean} }{ PSI\_{REF} } ) ^ { PSI\_{EXP} } ) ) \]
\[ kcr\_{ref} = 1.0 - (1.0 - exp(- ( \frac { 0.5 \cdot ( psi\_{mean} - PSI\_{EXP}) }{ PSI\_{REF} } ) ^ { PSI\_{EXP} } ) ) \]
with
1.8.13