Advance and recession

The intake opportunity time is the interval during which water will infiltrate at a specified location. It begins when the water flow first reaches the point (advance) and ends when the water eventually drains from the point (recession). Because infiltration is assumed to be uniform over the field, the variation in intake opportunity time is also an indication of application uniformity.

The time required for the water to advance to the end of the field length or to cover the field completely is an important consideration in managing surface irrigation systems. As will be seen in Section 5, the advance time dictates in large measure when the inflow must be terminated and it provides the time when field tailwater begins flowing from the field or when the field begins to pond. The advance trajectory does not have a concise mathematical description, but can be reasonably well approximated with the simple power function:

(32)

where x is the advance distance in m from the field inlet that is achieved in t_x minutes of inflow, and p and r are fitting parameters. Elliott and Walker (1982) made several

comparisons of Eq. 32 with more elaborate relationships and methods of fitting and concluded that the best results are achieved by a two-point fitting of the equation. The time of advance to a point near one-half the field length, t_.5L, and the advance to the end, t_L, can be

simultaneously solved to define the empirical parameters, p and r: (33)

and

(35)

An example use of these equations is shown in Figure 42 with the axes reversed to be consistent with the normal values of a time space trajectory.

Figure 42. Advance Data (Salazar, 1977)

For borders and basins, the undulations in the ground surface may have a major affect upon both advance and recession. The advancing front may be very uneven so rather than attempt to plot an average length of travel of the advancing front against time, the watered and

dewatered area of the basin are plotted against time. To illustrate this type of analysis of advance-recession data, the basin field study reported by Kundu and Skogerboe (1980) can be examined. A basin 36.6 m wide and 36.6 m long was constructed immediately following land levelling. The soil was a silty clay loam. The basin was staked with a 6 x 6 m grid and irrigated with an inflow of 0.83 m3/min. Advance and recession contours drawn at different times during the tests are shown in Figures 43 and 44.

Figure 43. Advance contours for a basin evaluation (Kundu and Skogerboe, 1980)

Figure 44. Recession contours from basin evaluation (Kundu and Skogerboe (1980)

The data from the advance contours were plotted on a logarithmic scale in Figure 45 and were described by the following function:

(36)

in which A_x is the area wetted (m2) in t_x minutes.

Figure 45. Basin advance data. (Kundu and Skogerboe, 1980)

The recession data could also be plotted as a function of cumulative time but the results would not be usable since the recession occurs over the field in a somewhat varied way. In order to determine the intake opportunity time, it is necessary to record the advance and recession data at each point in the grid. Table 5 summarizes the data in terms of the spatial grid.

Table 5 THE DISTRIBUTION OF INTAKE OPPORTUNITY TIME IN THE KUNDU- SKOGERBOE BASIN TEST, TN MINUTES

Grid Row Grid Column

1 2 3 4 5 6 1 382 408 311 304 328 397 2 386 345 237 277 236 333 3 278 292 221 245 282 302 4 300 320 335 308 335 295 5 375 350 350 360 345 360 6 405 375 405 385 355 355

4.3.3 Flow geometry

It is necessary to segregate the volume of water on the soil surface from the volume which has infiltrated into the soil during the advance phase in order to evaluate the field infiltration

parameters. To do this it is necessary to describe mathematically the shape of the flow cross- section and the flow area. Probably the most useful flow equation is the Manning formula:

(37)

where Q is the discharge in m3/sec, A is the cross-sectional area of the flow in m2, R is the hydraulic radius in m, S_o is the slope of the hydraulic grade lines which is assumed to equal the field slope, if one exists, and n is a resistance coefficient.

The simplest case of Eq. 37 is the sloping border in which a width of one metre is taken as representative of the flow and the relation reduces to:

(38)

in which y is the depth of flow in m, and Q is the flow per unit width.

For basins the problem becomes slightly more complex because the field slope is zero. Under these conditions, it is often assumed that the slope of the hydraulic gradeline can be

approximated by the depth at the field inlet, y_o, divided by the distance over which the water surface has advanced. Equation 37 with this modification becomes:

(39)

where x is the advance distance at time t_x, in m. Thus, the area of flow in a basin is time dependent during the advance phase and is continually changing. In sloping furrows and borders it is assumed constant with time.

The geometry of flow under furrow irrigation is difficult to describe. The furrow shape is

continually changing because of erosion and deposition of soil as the water moves it along, but its typical shape ranges from triangular to nearly trapezoidal. In most cases, simple power functions can be used to relate the cross-sectional area and wetted perimeter with depth. Figure 46 shows a furrow cross-section developed from the profilometer described in Section 3. The simplest way to analyse these data is to first plot the cross-section as shown, then divide the depth into 10-15 equal increments and graphically or numerically integrate area and wetted perimeter. Table 6 summarizes the writer's analysis.

Figure 46. Typical furrow cross-section

Table 6 EXAMPLE FURROW CROSS-SECTION ANALYSIS Furrow Depth, y Area, A Perimeter, WP

cm _cm2 cm 0 0 0 1 2.90 6.137 2 10.65 10.531 3 22.00 14.393 4 36.55 18.086 5 54.10 21.632 6 74.45 25.018 7 97.45 28.319 8 122.95 31.454 9 149.35 34.581 10 179.70 37.798

Assuming a power relation between depth and both area and perimeter, a twopoint fit of the data in Table 6 will determine the parameters:

(40) at y = 5 cm A = 54.1 cm2 = 5.41 x 10-3 m2 at y = 10 cm A = 179.70 cm2 = 1.797 x 10-2 m2 therefore, a₁ = .01797 / 101.732 = 3.331 x 10-4 (41) at y = 5 cm WP = 21.632 cm = .2163 m at y = 10 cm WP = 37.798 cm = .378 m therefore, b₁ = .378 / 10.805 = .05922

Equations 40 and 41 can be combined for the following expression for the hydraulic section in Eq. 37:

where,

p₂ = 1.667 - .667 * b₂ / a₂ = 1.3568 and,

(44)

Then Eq. 37 is written: (45)

The units of depth, area and perimeter can be measured in cm for Eqs. 40 and 41 and converted to metres Eq. 45. Note that in Eq. 44, p₂ reduces to 1.667 and p₁ is equal to 1.0 when applied to border flow conditions