Garden with Insight v1.0 Help: Plant Growth - Winter Dormancy

The day length growth constraint is used to simulate a winter dormant period for fall planted crops. This constraint is only imposed for areas that have a growing season of fewer than 12 months. A 12-month growing season is defined in the model as having no month with mean minimum temperature of lower than 5 degrees C. If there is a dormant winter period, it is defined as the time when day length is within 1 hour of the location's minimum day length.

If a crop becomes dormant in winter, the heat unit summation is set to zero. This provides for rapid new growth when temperatures increase in the spring. During the dormant period, the plants are not allowed to grow. The standing live biomass is actually reduced during this period because of frost and short day length. The day length reduction factor (for biomass) is estimated with the equation [Equation 316] where FHR is the day length reduction factor, HRLT is the day length on day i in hours, and HRLT(mn) is the minimum day length for the location.

Equation 316

FHR = 0.35 * (1.0 - HRLT / (HRLT(mn) + 1))
Code:
FHR = 0.35 * (1.0 - HRLT / (HRLT(mn) + timeOverMinDayLengthForWinterGrowth_hr))
Variables:
FHR = WinterBiomassDayLengthReductionFactor
HRLT = dayLength_hr
HRLT(mn) + timeOverMinDayLengthForWinterGrowth_hr = minDayLengthForWinterGrowth_hr

The frost reduction factor is estimated with the equation [Equation 319] where FRST is the frost damage factor, T(mn) is the minimum temperature on day i in degrees C, and af(1) and af(2) are parameters expressing the crop's frost sensitivity.

Equation 319

FRST = -T(mn) / (-T(mn) - exp(af(1) + af(2) * T(mn)), T(mn) < -1 degrees C
Code:
same except they use abs() instead of -ve for the temperature
(works the same because temp is always -ve when this is called)
Variables:
FRST = WinterBiomassFrostReductionFactor
T(mn, i) = minTempForDay_degC
T(mn, j) = dailyMeanMinTempForMonth_degC
af(1) = frostReductionFactorParams[0
af(2) = frostReductionFactorParams[1

The reduction in standing live biomass is estimated with the equation [Equation 320] where deltaB(AG) is the reduction in above ground biomass in t/ha on day i, HUI is the heat unit index, and B(AG) is the above ground biomass in t/ha on day i. Note that frost damage is greater when plants are small (HUI is close to zero) and approaches zero as the plants near maturity.

Equation 320

deltaB(AG) = 0.5 * B(AG) * (1.0 - HUI) * max(FHR, FRST)
Code:
deltaB = B * (1.0 - min(1.0, HUI)) * max(FHR, FRST)
Variables:
deltaB = WinterReductionInBiomass
deltaB(AG) = WinterReductionInStandingLiveBiomass
B = totalBiomassInclRoot_tPha
B(AG) = standingLiveBiomass_tPha
HUI = heatUnitIndex
FHR = winterBiomassDayLengthReductionFactor
FRST = winterBiomassFrostReductionFactor
max(FHR, FRST) = winterBiomassFrostReductionFactor

There is also a provision for frost kill of annual plants. Kill occurs if [Equation 321] is true, where SNOF is a snow cover factor calculated with the equation [Equation 322] where SNO is the water content of snow cover in mm.

Equation 321

if (FRST * (1.0 - SNOF) >= 0.9) plant dies
SNOF = SNO / (SNO + exp(2.303 - 0.22 * SNO))
Code:
same
Variables:
FRST = AnnualCropIsKilledByFrost
SNOF = snowCoverFactor
SNO = snowWaterContent_mm
FRST = winterBiomassFrostReductionFactor