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 non-erosive 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.