Garden with Insight v1.0 Help: Weather - Relative humidity

The relative humidity model simulates daily average relative humidity from the monthly average by using a triangular distribution. As with temperature and radiation, the mean daily relative humidity is adjusted to account for wet- and dry-day effects. The assumed relation betweenrelative humidity on wet and dry days is [Equation 112] where RHW is the daily mean relative humidity on wet days for month k, RHD is the daily mean relative humidity on dry days, and omega(H) is a scaling factor ranging from 0.0 to 1.0. An omega(H) value of 0.9 seems appropriate for many locations.

Equation 112

RHW = RHD + omega(H) * (1.0 - RHD)
Code:
omega(H) = 0.9
RHW = RHD + 0.9 * (1.0 - RHD)
RHW = RHD + 0.9 - 0.9 * RHD
RHW = 0.1 * RHD + 0.9
Variables:
RHW = DailyMeanRelHumWetDaysForMonth_frn
RHD = dailyMeanRelHumDryDaysForMonth_frn
omega(H) = relHumResponseToWetDays_frn = 0.9

Using the continuity equation as described in the temperature and radiation sections produces the equation [Equation 113] where RH is the long-term average relative humidity for month k.

Equation 113

RHD = RH - (omega(H) * (NWD/ND)) / (1.0 - omega(H) * (NWD/ND))
Code:
same except for bounds check: if RHD < 0.05 RHD = 0.5 * RH
omega(H) = 0.9
Variables:
RHD = DailyMeanRelHumDryDaysForMonth_frn
RH = dailyMeanRelHumForMonth_frn
omega(H) = relHumResponseToWetDays_frn = 0.9
NWD = numWetDaysForMonth
ND = numDaysInMonth

The appropriate value (RHW or RHD) is used as the peak of a triangular distribution to generate daily relative humidity. The upper limit of the triangular distribution is set with the equation [Equation 114] where RHU is the largest relative humidity value that can be generated on day I and RHP is the peak of the triangular distribution (RHW or RHD).

Equation 114

RHU = RHP + (1.0 - RHP) * exp(RHP - 1.0)
Code:
same (rearranged)
Variables:
RHU = RelHumTriangularDistUpperLimit_frn
RHP = peakOfRelHumTriangularDistr_frn

The lower limit is set with the equation [Equation 115] where RHL is the lowest relative humidity value that can be generated on day i.

Equation 115

RHL = RHP * (1.0 - exp(-RHP))
Code:
same
Variables:
RHL = RelHumTriangularDistLowerLimit_frn
RHP = peakOfRelHumTriangularDist_frn

To assure that the simulated long-term value for mean relative humidity agrees with input RH, the generated value is adjusted by using the equation [Equation 116] where RHG* is the generated relative humidity on day i adjusted to the mean of the triangle, RHG is the relative humidity generated from the triangle, and RH is the mean of the triangle.
(in other code)

If relative humidity data is not available, dew point temperature may be substituted and EPIC estimates the monthly mean relative humidity using equations 52 and 53. If dew point temperature is not available EPIC estimates monthly mean relative humidity using the equation [Equation 117] where delta-t = T(mx) - T(mn) for month k.

Equation 117

RH = 0.9 - (0.8 * delta-t) / (delta-t + exp(5.12 - 0.127 * delta-t))
Code:
same
Variables:
RH = DailyMeanRelHumForMonthFromTempOnly_frn
delta-t = maxMinusMinTemp_degC
T(mx) = dailyMeanMaxTempForMonth_degC
T(mn) = dailyMeanMinTempForMonth_degC