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/ρ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
ρ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

Created by admin. Last Modification: Tuesday 12 of April, 2016 18:59:10 CDT by admin.