EROSION Submodel

Wind Barriers

Up to five wind barriers can be placed arbitrarily on erodible areas or boundaries of the simulation region (Fig. E-1). The submodel inputs required to define each wind barrier include the distances to the barrier ends along the two coordinate directions (Bar. X1, Y1 and Bar. X2, Y2 ). Other inputs needed to define the barrier include the height, optical porosity, and total width of the barrier. (The user interface in WEPS 1.0 currently restricts the maximum number of barriers to four and allows them to be placed only on the simulation region boundaries.)

The barrier effects are simulated by calculating the fraction of open field friction velocity that occurs in the portion of the simulation region that is sheltered by barriers. When two barriers shelter the same area, the lowest fraction of open field friction velocity created by a single barrier is selected for the grid cell for each wind direction.

The rectangular simulation region has a y-axis positioned within ± 45 degrees from north. Wind directions relative the y-axis are calculated for 8 cardinal wind directions as

where

i = index of cardinal wind directions in clockwise direction (1 is north),

awai = wind direction relative to the simulation region y-axis (deg), and

amasim = angle of the simulation region y-axis (deg).

Only 8 cardinal directions were selected, because in WEPS a single wind direction is simulated for each entire day. For each grid cell in the simulation region, calculations are used to determine the influence of each barrier in succession. The accuracy of the calculations could be increased by decreasing the grid cell size relative to the barrier height, but this also increases run time.

A series of calculations were needed to determine the distance along the wind direction from the barrier to a grid cell, and their geometery is illustrated in Fig 1br. First, the distances (xi, yj) to the center of each cell were calculated. Next, distances (a and c) from the grid cell to the barrier ends and the barrier length (b) were determined. If a grid cell was on the barrier, i.e., a plus c equal b, then the fraction reduction is friction velocity was calculated directly.

For cells not on the barrier, angles at the barrier ends (aa and ca) were calculated. For example,

If the angles aa or ca are greater than 90 degrees, then the minimum distance between the cell center and the barrier (dmin) is the minimum of the lengths a or c.. Otherwise dmin was calculated as (Fig. 1br)	.

If dmin is less than 35 times the barrier height, additional calculation were used to determine the range of wind angles for which the barrier is upwind from the cell. To accomplish this task two angles (alpha and ceta) were calculated. Next, for each relative wind direction that is between the angles alpha and ceta, i.e., the barrier is upwind of the grid cell, the distance between the barrier and the grid cell along the wind direction vector (w) is calculated by the sine rule as

The leeward distance w was converted to units of barrier heights, wz, and used in empirical equations to estimate the fraction of open field friction velocity (fu*) in the sheltered area as

(Fig. 2br)

where optical barrier porosity (pbr) is modified to give effective barrier porosity (pb) as

and

xbr = barrier width divided by barrier height.

For all other grid cells which are not in the lee shelter region, but within 5 barrier heights from the barrier, a barrier influence was calculated using the minimum distance, wz, as a negative number in eq. E6.