Garden with Insight v1.0 Help: Plant Growth - Leaf Area Index

In most crops, leaf area index (LAI) is initially zero or small. It increases exponentially during early vegetative growth, when the rates of leaf primordia development, leaf tip appearance, and blade expansion are linear functions of heat unit accumulation (Tollenaar et al., 1979. Watts, 1972). In vegetative crops such as sugarcane and some forages, LAI reaches a plateau, at which time the rates of senescence and growth of leaf are are approximately equal. In many crops, LAI decreases after reaching a maximum and approaches zero at physiological maturity. In addition, leaf expansion, final LAI, and leaf duration are reduced by stresses (Acevedo et al., 1971. Eik and Hanway, 1965).

LAI before leaf decline

LAI is simulated as a function of heat units, crop stress, and crop development stages. From emergence to the start of leaf decline, LAI is estimated with the equations [Equation 259] and [Equation 260] where LAI is th leaf area index, HUF is the heat unit factor, and REG is the value of the minimum (limiting) crop stress factor discussed in more detail below. Subscript mx is the maximum value possible for the crop and delta is the daily change. The exponential function of equation 260 prevents LAI from exceeding LAI(mx) when HUF is adjusted for vernalization of certain crops.

Equation 259, 260

LAI = LAI(i-1) + deltaLAI
deltaLAI = deltaHUF * LAI(mx) * (1.0 - exp(5.0 * (LAI(i-1) - LAI(mx)))) * sqrt(REG)
Code:
if (deltaHUF * LAI(mx)) > 0.0
deltaLAI = deltaHUF * LAI(mx) * dayLengthIsAboveThresholdForGrowth * sqrt(REG)
else
deltaLAI = 0
Variables:
LAI(i-1) = leafAreaIndex
LAI = LeafAreaIndexBeforeLeafDecline
HUF = heatUnitFactorForLAIAndHeight
HUF(i-1) = yesterdaysHeatUnitFactorForLAIAndHeight
LAI(mx) = maxLeafAreaIndex
REG = biomassTempStressFactor_frn

Heat unit factor for LAI and for crop height

The heat unit factor is computed using the equation [Equation 261] where ah(1) and ah(2) are parameters of crop j, and HUI is the heat unit index.

Equation 261

HUF = HUI / (HUI + exp(ah(1) - ah(2) * HUI))
Code:
same
Variables:
HUF = HeatUnitFactorForLAIAndHeight
HUI = heatUnitIndex
ah(1) = heatUnitFactorParamsForLAI[0
ah(2) = heatUnitFactorParamsForLAI[1

LAI during leaf decline

From the start of leaf decline to the end of the growing season, LAI is estimated with the equation [Equation 262] where ad is a parameter that governs LAI decline rate for crop j and subscript o is the day of the year when LAI starts declining.

Equation 262

LAI = LAI(o) * power((1 - HUI) / (1 - HUI(o)), ad)
Code:
LAI = LAI(o) * power(10, log10((1 - HUI) / (1 - HUI(o))) * ad)
there is also a biomass adjustment if LAI is in decline
also if the crop is a tree, LAI does not decline.
Variables:
LAI = LeafAreaIndexDuringLeafDecline
LAI(o) = leafAreaIndexAtStartOfDecline
HUI = heatUnitIndex
HUI(o) = fractionOfGrowingSeasonWhenLeafDeclineStarts_frn
ad = leafAreaIndexDeclineRateFactor