Furrow diking is the practice of building small temporary dikes across furrows to conserve water
for crop production. Since they reduce runoff, they may also aid in erosion control. The EPIC
furrow diking model allows construction of dikes for any ridge spacing and at any interval down
the furrows. Dikes may be constructed or destroyed mechanically on any day of the year. If
estimated runoff for a particular event exceeds the dike storage volume, overtopping occurs and
all of the estimated runoff is lost. If not, all of the rainfall infiltrates and is available for plant
use. When runoff destroys the dikes, the model rebuilds them automatically. Rainstorms that
do not overtop the dikes cause settling and, thus, reduce storage volume. Settling is esimated
with the equation
where Ho is the dike height in m before settling, H is the dike height after settling, and Y is the
USLE estimate of soil loss in tha-1. Ridge height is also reduced with the settling function
contained in equation 341. The dikes are rebuilt automatically when H/Ho<0.7.
The dike storage volume is estimated by assuming that the furrow and the dike are triangular and
that the dike side slopes are 2:1. Given the dike and ridge heights, the dike interval, and the
slope down the furrow, the volume can be calculated directly. There are two possible dike
configurations that require slightly different solutions. Normally, the dike interval is relatively
short (1.0-3.0 m) and the slope along the furrow is relatively flat (<1.0%). When the dike is
full, water extends from the top of the downslope dike up the furrow to a point above the toe of
the upslope dike. The volume is calculated by using cross-sectional areas at the toes of the two
dikes. This approach computes the volume in three parts (between the top and the toe of the
downslope dike; between the toes of the two dikes; and between the toe and the waterline on the
upslope dike). Beginning at the centerline of the downslope dike, the volume equations are
where DV is the dike volume between cross sections in m3, H is the dike height in m, D is the
water depth in m, W is the water surface width in m, DI is the dike interval in m, XD is the
distance from the center of the downslope dike to the waterline on the upslope dike in m, and
subscripts 2 and 3 refer to cross sections 2 and 3. Cross section 2 is a the toe of the downslope
dike and cross section 3 is at the toe of the upslope dike. Water depth is calculated with the
equations
where S is the slope in mm-1 along the furrow. Water surface width is a function of depth and
ridge spacing, RS in m.
The distance XD is computed with the equations
where DZ is the water line elevation on the upslope dike. The constant 2 in equation 348 comes
from the assumed 2:1 dike sideslopes. Simultaneous solution of equations 348 and 349 yields
Substituting D, W, and XD into equations 342, 343, and 344 and summing gives
Equation 351 is divided by the total surface area of a furrow dike to convert volume from m3 to
mm.
In the simpler and more unusual dike configuration, the upslope waterline does not extend to the
toe of the upslope dike. Only one cross section is involved and the volume is computed into two
parts. Equation 342 is used to calculate the most downslope volume, and the upslope volume is
calculated with the equation
Adding equations 342 and 353, substituting D and W, and converting from m3 to mm gives
Thus, the average dike volume of a field is estimated with equation 352 or 354 as dictated by slope and dike height and interval. However, no field is exactly uniform in slope; dike and ridge heights vary, and furrow and dike side slopes may not be triangular. Therefore, the model provides a user-controlled dike efficiency factor to allow for varying conditions across a field. The dike efficiency factor also provides for conservative or optimistic dike system design.
May 20, 1997
Georgie Mitchell, Ray H. Griggs, Verel Benson, and Jimmy Williams, Project Leaders
Steve Dagitz, Webmaster