UPDATE OF SURFACE CONDITIONS DURING WIND EROSION

Changes to the soil surface in response to loss or deposition at various downwind field locations are rarely considered in wind erosion models. However, it appears necessary to update surface conditions during significant erosion events to account for depletion of the reservoir of mobile soil on short fields, and to simulate the increased erodibility typically observed on downwind regions in long fields. In general, few measurements are available to validate the simulated response of field surfaces to erosion. Hence, simple equations based on mass balance in the surface layer were developed to simulate changes in the area represented by each grid cell.

Surface Update Intervals (time steps)

In WEPS 1.0, hourly simulated or measured wind speeds are used as model inputs. When used alone for single days, the EROSION submodel can accommodate input wind speeds with a minimum duration of 15 minutes.

To minimize model run time, a variable update time interval was implemented.

The needed surface update interval depends on the erosion rate, but that is unknown before a simulation is made. Hence, when each new wind speed is input, a relative erosive wind energy (EnGe, m3 s-3) is calculated for the most erosive grid cell during the previous time step as

The number of surface updates (N) for each of the wind speeds input during 24 hours (Ntstep)

is

Surface update intervals as a function of relative erosive wind energy are illustrated in Fig. E-??

Figure E-? . Surface update time interval based on relative erosive wind energy.

Change in Mobile Surface Soil-

The net addition (+) or loss (-) of mobile aggregates during a time interval ( t) over a field length segment ( x) from these reservoirs is estimated as

where

dmt los = net change in mobile soil surface aggregates during time interval t (kg m-2).

The first term represents loss or gain by erosion and the second term represents creation of new mobile aggregates by the abrasion process.

Two reservoirs of mobile soil may be present at the soil surface. These include mobile soil on a consolidated surface, hereafter called crusted, and mobile soil among the rock and immobile aggregates. Because these reservoirs differ in their response to erosion, they are updated separately.

Update of Crusted Surface

Undisturbed, crusted soil surfaces have high threshold wind speeds and are generally stable, unless abraded by mobile soil aggregates. In WEPS, the crust is simulated as a triangular shape (Fig. E-

). Uniform abrasion of this crust shape continually exposes an increasing area of aggregated soil at the surface. The simple triangular shape was selected because there are spatial variations in crust thickness and resistance to abrasion interacting with preferential zones for abrader impact
caused by the surface micro-topography within each grid cell that is, nevertheless, assumed to be homogeneous.

The deflatable mass of mobile soil on the crusted surface is regarded as a constant for all friction velocities above threshold. Hence, it is updated as

where

SM los = mobile soil aggregates per unit area of the crusted surface (kg m-2).

SM los0 = value of SM los at prior time step (kg m-2).

If the crusted or aggregated reservoir cannot supply the simulated soil loss, the additional soil loss I removed from the remaining reservoir.

Updated values of the mobile aggregate mass on the crusted surface are used to update the fraction of mobile crust cover as

The layer thickness of mobile aggregate deposits tends to increase with surface roughness. Hence, the coefficient CR los reduces mobile cover as surface roughness increases, and is estimated as

and

where

SZ rg = ridge height (mm), and

SL rr = random roughness (mm).

Mobile aggregate cover on a crusted surface as a function of mobile mass with various ridge height levels is illustrated in Fig. E-6.

Figure E-8. Loose, mobile cover of aggregates on crust as a function of mobile mass for

a range of ridge heights

If fraction crust cover is > 0.01, crust thickness is reduced by abrasion on the crust and is simulated as

where

SZcr0 = crust thickness at prior time step (mm)

Finally, crust cover is updated in proportion to crust thickness as

where

SFcr0 = is crust cover fraction at prior time step.

Update of Aggregated Surface

On aggregated surfaces some of the mobile material is typically sheltered by micro-roughness of the immobile aggregates. Hence the reservoir of mobile material available for deflation varies with friction velocity. The maximum mass of mobile soil that could be removed under a high friction velocity is SMagmx, while removable soil under a lowered friction velocity is SMaglos as illustrated in Fig. E- . The mobile aggregate cover fraction on the aggregated surface is SF84. The aggregate mixture is assumed to be uniform with depth. Hence, as abrasion lowers the soil surface, the top and bottom boundaries move downward so that SMagmx remains constant.

The net mass of mobile soil removed(-) or added (+) to the reservoir is dmlos.

To simulate the aggregated surface, the cumulative change of mass of mobile material is updated as

where

dmlos = cumulative mobile soil loss or gain on aggregated surface(kg m-2), and

dmlos0 = value of dmlos at prior time step.

When dmlos < 0, mobile soil is removed from the initial reservoir among the immobile aggregates. Based on limited wind tunnel measurements, empirical relationships were developed to estimate the mass of mobile aggregates that could be removed from a flat, bare, aggregated surface for a range of friction velocities as illustrated in Fig. E - 7 .

Figure E-10. Mass of mobile aggregates that can be removed from flat, bare aggregated surface

with various initial mass fractions of mobile aggregates (SF84) for a range of friction velocities without abrasion.

The maximum removable mass in the mobile reservoir was estimated at a friction velocity (WU*) of 0.75 m s-1 for a bare, smooth, aggregated surface as

The total soil mass in the reservoir is then estimated as

The maximum reservoir is reduced by roughness, residue cover, and wetness to estimate the available reservoir at the current friction velocity as

where

WU*to	= threshold friction velocity for bare, aggregated, smooth soil (m s-1),

When the soil removal from the reservoir with the current friction velocity equals SMaglos , erosion is stopped, and the mobile soil fraction (SF84mn) still remaining in the maximum mobile soil reservoir is

When there is net soil mass from the reservoir (dmlos < 0), SF84 is updated as

When there is net deposition (dmlos > 0), the immobile surface aggregates can become slowly buried by the addition of mobile soil to the initial reservoir. In this case, the surface fraction of mobile aggregates is adjusted upward and updated as

Update of Soil Fraction < 2.0 mm Diameter

The soil fraction < 2.0 mm diameter (SF200) is estimated from the values of the soil fraction < 0.84 mm diameter (SF84) as

The estimates of SF200 are illustrated in the following diagram (Fig. E-10).

Figure E-11. Estimate of SF200 as a function of SF84.

Update of Soil Fraction < 0.10 mm Diameter

If dmlos < 0.0, then SF10 is updated in proportion to the changes in SF84

Where

SF10ic = is the SF10 initial condition at the beginning of the erosion event, and

SF84ic = is the SF84 initial condition at the beginning of the erosion event.

When there is mobile soil gain at the soil surface, the suspension-size aggregates less than 0.10 mm diameter (SF10) tend to be sorted out of the depositing soil. Hence, for dmlos > 0.0 the estimate is

Update of Surface Rock Volume

The rocks (< 2.0 mm diameter) are assumed to be mixed with the soil and have a uniform vertical distribution. If an initial desert pavement is present, the surface is generally assumed to be stable. Surface rock volume increases or decreases in proportion to the deflation or deposition from the surface area that is not covered by rock and is estimated to slowly change as

Where

SVroc = soil rock volume (m3 m-3),

SVroc0 = soil rock volume at prior time-step (m3 m-3), and

SVrocic = soil rock volume at initial time-step (m3 m-3).

dmt = net gain(+) or loss(-) of soil from grid interval (kg m-2).

The changes in surface rock volume are illustrated in Fig. E - 9.

Figure E-9. Changes in surface soil volume of rock in response to soil gain or loss.

Update Surface Roughness

Roughness elements consist of random roughness and, if present, oriented roughness such as tillage ridges. The first step in updating roughness is estimating the effects of changes in loose soil depth generated by the various erosion processes.

When the soil surface has roughness elements that actively trap saltation-size aggregates, net deposition (dmtlos > 0) of mobile soil in sheltered areas decreases roughness height, SZv (mm) as

When saltation trapping occurs, but with a net loss (dmtlos < 0) from both sheltered and unsheltered areas roughness height slowly decreases as

When the soil surface is relatively smooth, i.e., random roughness < 10.0 mm and ridge roughness < 50.0 mm, net deposition increase over much of the area decreases roughness height as

While net loss increases roughness as

The change in roughness height caused by abrasion of immobile clods and crust is

Total roughness height change, SZt (mm) is

Ridge height is updated as

Where

SZrg	= ridge height (mm), and

SZrg0	= ridge height at prior time-step (mm).

Random roughness is updated as

Where

SLrr = random roughness (mm), and

SLrr0 = random roughness at prior time-step (mm).