Garden with Insight v1.0 Help: Weather  Wind
The original EPIC wind model (Richardson and Wright, 1984) simulated mean daily wind speed and
daily direction. The new EPIC wind erosion model, WECS (Wind Erosion Continuous Simulation)
requires wind speed distribution within the day and the dominant direction. Daily wind speed distribution
is simulated using the modified exponential equation [Equation 107] where v(j) is the wind speed at f
fraction of the day, V(i) is the mean wind speed for day i, and a(1) and a(2) are parameters. Equation 107
is an expression of wind speed probabilities rather than wind speed as a function of time during the day.
The daily time distribution of wind speed is not required because all other EPIC components operate on a
daily time step. Experimental work with data from Bushland, TX and Temple, TX indicates that 0.1 <
a(2) < 0.6.
Equation 107
v(j) = a(1) * V * power(ln(f(j)), a(2))
Code:
v(j) = power(ln(f(j)), a(2)) / a(1)
Variables:
v(j) = WindSpeedForFractionOfDay_mPsec
a(1) = windSpeedForFractionOfDayParam1
V(i) = meanWindSpeedForDay_mPsec
f(j) = fractionOfDay
a(2) = windSpeedForFractionOfDayParam2
Values of a(2) are generated daily from a triangular distribution with base ranging from 0.1 to 0.6 with a
peak at 0.35. The value of a(1) can be closely appointed with the equation [Equation 108]. Equation 108
assures that
V(i) = integral from 0.0 to 1.0 of v * df (Equation 109)
Equation 108
a(1) = 1.5567 * power(a(2), 0.1508) * exp(0.4336 * a(2))
Code:
a(1) = exp(0.4336 * a(2)) * (1/1.5567) * power(a(2), 0.1508)
a(1) = exp(0.4336 * a(2)) / (1.5567 * power(a(2), 0.1508))
Variables:
a(1) = WindSpeedForFractionOfDayParam1
a(2) = windSpeedForFractionOfDayParam2
Values of v(j) are simulated with f starting with the threshold windspeed for erosion. The threshold f value
(f(o)) is determined using the wind erosion equation 141 and equation 107 in the form [Equation 110]
where v(*tau) is the threshold friction velocity in m/sec. Larger f values produce nonerosive wind speeds.
Windspeeds greater than v(*tau) are produced as f is reduced.
Equation 110
f(o) = exp(power(v*(tau) / (0.0408 * a(1) * V), 1/a(2)))
Code:
f(o) = exp(power(v*(tau) / (0.0408 * V), 1/a(2))
two differences: power, and no a(1)
Variables:
f(o) = FractionOfDayToStartSimulatingWindSpeed_frn
v*(tau) = thresholdFrictionVelocityWE_mPsec
a(1) = windSpeedForFractionOfDayParam1
a(2) = windSpeedForFractionOfDayParam2
V = meanWindSpeedForDay_mPsec
The mean daily wind speed is simulated using the modified exponential equation [Equation 111] where
V(k) is the mean wind speed for month k, RN is a random number b(2) is a parameter for month k, and
b(1) is calculated directly using an approach similar to that described in equation 108. Experimental work
with data from Bushland, TX and Temple, TX indicates that b(2) ~~ 0.3.
Equation 111
V(i) = b(1) * V(k) * power(ln(RN), b(2))
Code:
same (b(1) is assumed to be 1.0)
Variables:
V(i) = MeanWindSpeedForDay_mPsec
b(1) = 1.0
V(k) = dailyMeanWindSpeedForMonth_mPsec
RN = randomNumber
b(2) = paramForModifiedExpWindSpeed
Wind direction
Wind direction expressed as radians from north in a clockwise direction is generated from an empirical
distribution specific for each location. The empirical distribution is simply the cumulative probability
distribution of wind direction. The "Climatic Atlas of the United States" (U.S. Department of
Commerce, 1968) gives monthly percentages of wind from each of 16 directions. Thus, to estimate wind
direction for any day, the model draws a uniformly distributed random number and locates its position on
the appropriate monthly cumulative probability distribution.
