Garden with Insight v1.0 Help: Weather  Air temperature and solar radiation
The model developed by Richardson (1981) was selected for use in EPIC because it simulates temperature
and radiation, which are mutually correlated with rainfall. The residuals of daily maximum and minimum
air temperature and solar radiation are generated from a multivariate normal distribution.
The multivariate generation model used implies that the residuals of maximum temperature, minimum
temperature, and solar radiation are normally distributed and that the serial correlation of each variable
may be described by a firstorder linear autogregressive model. Details of the multivariate generation
model were described by Richardson (1981). The dependence structure of daily maximum temperature,
minimum temperature, and solar radiation were described by Richardson (1982).
The temperature model requires monthly means of maximum and minimum temperatures and their
standard deviations as inputs. If the standard deviations are not available, the longterm observed extreme
monthly minima and maxima may be substituted. The model estimates standard deviation as 0.25 of the
difference between the extreme and the mean for each month. For example: [Equation 100] whre SDTMX
is the standard deviation of the daily maximum temperature, TE is the extreme daily maximum
temperature, and Tbar is the average daily maximum temperature for month k.
Equation 100:
SDTMX = 0.25 * (TE  Tbar)
Code:
equation for max temp is the same. equation for min temp is
SDTMX = 0.25 * (Tbar  TE)
Variables:
SDTMX = StdDevMaxTempFromMeanAndExtremeForMonth_degC or ...Min...
TE = extremeDailyMaxTempForMonth_degC or ...Min...
Tbar = dailyMeanMaxTempForMonth_degC or ...Min...
The solar radiation model uses the extreme approach extensively. Thus, only the monthly means of daily
solar radiation are required as inputs. The equation for estimating standard deviation is [Equation 101]
whre SDRA is the standard deviation of daily solar radiation i MJ/m2, RAMX is the maximum daily solar
radiation at midmonth, and RA is the mean daily solar radiation for month k.
Equation 101:
SDRA = 0.25 * (RAMX  RA)
Code:
same
Variables:
SDRA = StdDevRadiationFromMeanAndExtremeForDay_MJPm2
RAMX = maxPossibleRadiation_MJPm2
RA = meanRadiationForDay_MJPm2
Maximum temperature and solar radiation tend to be lower on rainy days. Thus, it is necessary to adjust
the mean maximum temperature and solar radiation downward for simulating rainy day conditions (note
not min temp). For T(mx) this is accomplished by assuming thta wet day values are less than dry day
values by some fraction of T(mx)  T(mn): [Equation 102] where TW is the daily mean maximum
temperature for wet days in degrees C in month k, TD is the daily mean maximum temperature for dry
days, omega(T) is a scaling factor ranging from 0.0 to 1.0, T(mx) is the daily mean maximum
temperature, and T(mn) is the daily mean minimum temperature. Choosing omega(T) = 1.0 provides
highest deviations on wet days and omega(T) = 0.0 ignores the wet day effect. Observed data indicate that
omega(T) usually lies between 0.5 and 1.0.
Equation 102
TW(mx) = TD(mx)  omega(T) * (T(mx)  T(mn))
Code:
same (omega(T) = 0.5)
Variables:
TW(mx) = DailyMeanMaxTempWetDaysForMonth_degC
TD(mx) = dailyMeanMaxTempDryDaysForMonth_degC
omega(T) = tempResponseToWetDays_frn = 0.5
T(mx) = dailyMeanMaxTempForMonth_degC
T(mx) = dailyMeanMinTempForMonth_degC
Since equation 102 gives lower mean maximum temperature values for wet days, a companion equation is
necessary to slightly increase mean maximum temperature for dry days. The development is taken directly
from the continuity equation
T(mx) * ND = TW(mx) * NWD + TD(mx) * NDD (Equation 103)
where ND is the number of days in a month, NWD is the number of wet days, and NDD is the number of
dry days. The desired equation is obtained by substituing equation 102 into equation 103 and solving for
TD [Equation 104]. Use of the continuity equation guarantees that the longterm simulated value for mean
maximum temperature agrees with the input value of T(mx).
Equation 104
TD(mx) = T(mx) + (NWD / ND) * omega(T) * (T(mx)  T(mn))
Code:
same
probWetDayForMonth_frn = NWD / ND
omega(T) = 0.5
Variables:
TD(mx) = DailyMeanMaxTempDryDaysForMonth_degC
NWD = numWetDaysForMonth
ND = numDaysInMonth
omega(T) = tempResponseToWetDays_frn = 0.5
T(mx) = dailyMeanMaxTempForMonth_degC
T(mx) = dailyMeanMinTempForMonth_degC
The method of adjusting solar radiation for wet and dry days is similar to that of adjusting maximum
temperature. The radiation on wet days is a fraction of the dry day radiation [Equation 105] where RAW
is the daily mean radiation on wet days in MJ/m2, omega(R) is a scaling factor ranging from 0.0 to 1.0,
and RAD is the daily mean solar radiation on dry days. An omega(R) value of 0.5 gives satisfactory
results for many locations.
Equation 105
RAW = omega(R) * RAD
Code:
same (omega(R) = 0.5)
Variables:
RAW = DailyMeanRadiationWetDaysForMonth_MJPm2
omega(R) = radiationResponseToWetDays_frn = 0.5
RAD = dailyMeanRadiationDryDaysForMonth_MJPm2
The dry day equation is developed by replacing temperature with radiation in equation 103 and
substituting equation 105 for RAW. Then, [Equation 106] where RA is the daily mean solar radiation for
month k in MJ/m2.
Equation 106
RAD = (RA * ND) / (omega(R) * NWD + NDD)
Code:
NDD = ND  NWD so
RAD = (RA * ND) / (omega(R) * NWD + (ND  NWD))
divide all terms by ND so
RAD = RA / (omega(R) * (NWD/ND) + ND/ND  NWD/ND)
probWetDayForMonth_frn = NWD / ND so
RAD = RA / (omega(R) * probWetDayForMonth_frn + 1  probWetDayForMonth_frn)
omega(R) = 0.5 so
RAD = RA / (0.5 * probWetDayForMonth_frn + 1  probWetDayForMonth_frn)
RAD = RA / (1.0 + (0.5 * probWetDayForMonth_frn  probWetDayForMonth_frn))
RAD = RA / (1.0  0.5 * probWetDayForMonth_frn)
Variables:
RAD = DailyMeanRadiationDryDaysForMonth_MJPm2
RA = dailyMeanRadiationForMonth_MJPm2
ND = numDaysInMonth
omega(R) = radiationResponseToWetDays_frn = 0.5
NWD = numWetDaysForMonth
NDD = numDryDaysInMonth (= ND  NWD)
