Modified Energy Cascade (MEC) Models for Plant Growth
Modified Energy Cascade (MEC) models take as inputs photosynthetic photo flux PPF, and the atmospheric carbon dioxide concentration, CO2, and output biomass production, on a dry-mass basis, oxygen O2 production, and water transpiration H2O.
The atmospheric temperatures, one for light periods and a second for dark periods, and the photoperiod are constant. Plant growth is assumed not to be limited by water or nutrients.
These models are crop specific and accommodate daily variations in PPF and CO2, but weighted values of PPF and CO2 should be used to estimate time for canopy closure, tA. The models generally apply over a range of PPF from 200 to 1,000 µmol/m²*s and a range of CO2 from 330 to 1,300 µmol/mol. For rice and wheat, these models apply up to 2,000 µmol/m²*s. The PPF range for lettuce is limited to 200 to 500 µmol/m²*s, because a light integral of only 17 µmol/m²*d is recommended to prevent leaf tip burn.
The model relies on empirical crop data fitting a multivariable polynomial regression (MPR) fit model, which takes the general form:
f(PPFE,CO2)= C1*PPFE-1*CO2-1 +C2*PPFE-1 + C3*PPFE-1*CO2 + C4*PPFE-1*CO22 + C5*PPFE-1*CO23 + C6*CO2-1 + C7 + C8*CO2 + C9*CO22 + C10*CO23 + C11*PPFE*CO2-1 + C12*PPFE + C13*PPFE*CO2 + C14*PPFE*CO22 + C15*PPFE*CO23 + C16*PPFE2*CO2-1 + C17*PPFE2 + C18*PPFE2*CO2 + C19*PPFE2*CO22 + C20*PPFE2*CO23 + C21*PPFE3*CO2-1 + C22*PPFE3 + C23*PPFE3*CO2 + C24*PPFE3*CO22 + C25*PPFE3*CO23
The coefficients C1-C25 vary by crop type and are determined experimentally,
Summary of Modified Energy Cascade Model Variables
(adapted from NASA Advanced Life Support Baseline Values and Assumptions Document)
| Variable | Units | Description | Reference/Value |
|---|---|---|---|
| A | -- | fraction of PPF absorbed by the plant canopy | A =AMAX for t > tA |
| A =AMAX*(t/tA)n for t < tA | |||
| AMAX | -- | maximum value for A | 0.93 |
| BCF | -- | biomass carbon fraction | Table 4.2.29 |
| CGR | g/m²*d | crop growth rate | CGR = MWC*DCG/BCF |
| Ci | varies | coefficients in functions describing tA and CQYMAX | Table 4.2.16 |
| CO2 | µmol(CO2)/mol(Air) | atmospheric concentration of carbon dioxide; model variable | none |
| CQY | µmol(C. Fixed)/µmol(Ab. PPF) | canopy quantum yield | CQY =CQYMAX for t < tQ; |
| CQY =CQYMAX- (CQYMAX- CQYMIN)*(t-tQ)/(tM-tQ) for tQ < t < tM | |||
| CQYMAX | µmol(C. Fixed)/µmol(Ab. PPF) | maximum value for CQY that applies until tQ | MPR |
| CQYMIN | µmol(C. Fixed)/µmol(Ab. PPF) | minimum value for CQY at tM | Table 4.2.15 |
| CUE24 | -- | 24-hour carbon use efficiency; a fraction | CUE24 = CUEMAX for t < tQ; |
| CUE24 =CUEMAX-(CUEMAX-CUEMIN)*(t-tQ)/(tM-tQ) for tQ < t < tM | |||
| CUEMAX | -- | maximum value for CUE24 that applies until tQ | Table 4.2.15 |
| CUEMIN | -- | minimum value for CUE24 at tM | Table 4.2.15 |
| DCG | µmol(Carbon)/m²*d | daily carbon gain | DCG = 0.0036*H*CUE24*A*CQY*PPF |
| DOP | mol(O2)/m²*d | daily oxygen production | DOP = OPF*DCG |
| DPG | h/d | plant growth diurnal cycle (length of sol) | 24 (on Earth) |
| DTR | L(Water)/mA²*d | daily canopy transpiration rate | 3600*H*(MWH2O/H2O)*(VPD/PATM) |
| gA | mol(Water)/mA²*s | atmospheric aerodynamic conductance | gA = 2.5 bean, lettuce, peanut, potato, tomato, etc. |
| gA = 5.5 rice, wheat, etc. | |||
| gC | mol(Water)/m²*s | canopy surface conductance | gC=(gA*gS)/(gA+gS) |
| gS | molWater/m²*s | canopy stomatal conductance | (1.717*TLIGHT-19.96-10.54*VPD)*(PNET/CO2) bean, lettuce, peanut, potato, tomato, etc. |
| gS = 0.1389 + 15.32*RH*(PNET/CO2) rice, wheat, etc. | |||
| H | h/d | Photoperiod (daylight hours) | Table 4.2.27 |
| Ho | h/d | nominal photoperiod | |
| MWC | g/mol | molecular weight of carbon | 12.011 |
| MWH2O | g/mol | molecular weight of water | 18.015 |
| n | -- | canopy closure exponent | Table 4.2.13 |
| OPF | mol(O2)/mol(C) | oxygen production fraction | Table 4.2.29 |
| PATM | kPa | total atmospheric pressure; model variable | Model Input |
| PGROSS | µmol(Carbon)/m²*s | gross canopy photosynthesis | PGROSS= A* CQY*PPF |
| PNET | µmol(Carbon)/m²*s | net canopy photosynthesis | PNET=PGROSS*(DPG-H+H*CUE24)/DPG |
| PPF | µmol(photon)/m²*s | photosynthetic photon flux; model variable | Model Input |
| PPFE | µmol(photon)/m²*s | effective photosynthetic photon flux | PPFE=PPF*(H/Ho) |
| RH | relative humidity | Model Input | |
| TCB | g/m² | total crop biomass, on a dry basis | TCB = 0tMCGR dt |
| TEB | g/m² | total edible biomass, on a dry basis | TEB = XFRT tEtMCGR dt |
| TLIGHT | °C | atmospheric temperature during photoperiod | Model Input |
| t | dAE | time; model variable | none |
| tA | dAE | time until canopy closure | MPR |
| tE | dAE | time at onset of organ formation | Table 4.2.28 |
| tM | dAE | time at harvest or crop maturity | Table 4.2.28 |
| tQ | dAE | time until onset of canopy senescence | Table 4.2.28 |
| VPAIR | kPa | actual moisture vapor pressure | VPAIR=VPSAT*RH |
| VPSAT | kPa | saturated moisture vapor pressure | 0.611*e(17.4*TLIGHT/(TLIGHT+239)) |
| VPD | kPa | vapor pressure deficit | VPD = VPSAT-VPAIR |
| XFRT | fraction of daily carbon gain allocated to edible biomass after tE | Table 4.2.28 | |
| H2O | g/L | density of water | 998.23 |
Values for the Exponent n in MEC Models
| Crop | n |
|---|---|
| Wheat | 1.0 |
| Rice, Soybean, Sweet Potato | 1.5 |
| Dry Bean, Peanut, White Potato | 2.0 |
| Lettuce, Tomato | 2.5 |