Furrow Diking

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