10.5: Management of Sloping Furrow Irrigation Systems

Good management of surface irrigation systems is extremely important. The manager must respond to the effect of infiltration variability on the performance of the system during each irrigation. In addition to satisfying the water needs of the crop, the goals of management might include low runoff, low deep percolation, or that the sum of these two losses be minimized. We’ll discuss management practices to minimize the sum of runoff and deep percolation. In management of surface irrigation, the irrigator has control of three things: set time (i.e. cutoff time), stream size, and the soil water deficit before water is applied. All three can be changed without changing the system characteristics.

Many, if not all, textbooks, management guides, and computer software establish set time and stream size recommendations so that a required or preplanned desirable irrigation depth infiltrates in a large proportion of the field area (such as 90%). Unfortunately, it is only possible to compute the optimum set time-stream size combination if the infiltration vs. time relationship, such as the one illustrated Figure 10.10, is known with reasonable accuracy on the planned day of irrigation. This requirement is seldom, if ever, satisfied. However, even when the infiltration characteristics are known with confidence, simulation results from models can result in set times or stream sizes that are simply too unreasonable to put into practice. Labor constraints are often a problem.

Given these two problems, the infiltration uncertainty and the possible constraints of labor availability, we have chosen to take a reactive or adaptive approach to surface irrigation management. As explained in Chapter 6, we do not have to refill the crop root zone during irrigation to meet the ET requirements. In fact, that is seldom done with pressurized systems. We simply adjust the irrigation schedule according to how much effective water was applied during each irrigation. Here we follow that same philosophy with surface irrigation.

To overcome the labor-set time dilemma we attempt to adjust set times that fall within the constraints of the irrigator’s labor supply. In many areas this may mean that the shortest set time possible is 12 hours or even longer. With methods of semi-automation, such as using surge irrigation valves for example, set times can easily be reduced by 50%. In the Great Plains of the U.S., we commonly refer to set times in intervals of 6 hours, that is, 6, 12, 18, and 24 hours. For example, using a surge irrigation system which irrigates 2 sets simultaneously, 6-hour set times require that the irrigator return to the field only once every 12 hours.

The irrigator can also change stream size. If a water supply rate to a field is constant, then furrow stream size can be changed by changing the number of furrows per set. This is illustrated in the following equation:

\(q_s=\dfrac{Q_t}{N}\) (10.9)

where: q_s = furrow stream size,

Q_t = total inflow rate to the field, and

N = number of furrows irrigated per set.

Maximum furrow stream size must be kept below the flow that will cause erosion and be low enough so that the furrow has adequate capacity to prevent overflowing. The maximum nonerosive stream size is approximated by:

\(q_{max}=\dfrac{10}{S} \) (10.10)

where: q_max = maximum nonerosive stream size (gpm) and

S = field slope (%).

For example, if the field slope is 0.4%, then the maximum nonerosive stream size would be 25 gpm. As stated, Equation 10.10 is an approximation. The NRCS (USDA, 2012) provides more specific guidelines for permissible maximum water velocities to prevent soil erosion in furrows. The important point is that stream size can also be a constraint to the management of furrow irrigation systems.

Another factor that the irrigator can change is the soil water deficit by controlling the frequency of irrigation. The maximum soil water deficit allowable is equal to the management allowed deficit (AD). If an irrigator is having difficulty attaining a high efficiency because of excessive irrigation, the soil water deficit can be increased, up to AD, by irrigating less frequently.

How do stream size, set time, and AD interact? In Section 10.2 we indicated that to obtain a perfectly uniform distribution of water, the advance curve and recession curve have to be parallel. Unfortunately, the tradeoff for uniform distribution is excessive runoff. On the other extreme, if the irrigator’s goal is to reduce runoff, then it might be desirable just to get the water to the end of the field and then shut it off or even shut it off before advance is complete. Obviously, this will result in low runoff, but will also result in poor distribution of infiltration and high deep percolation. So, what is the optimum compromise between runoff and deep percolation that results in the highest system efficiency? A distance-based management parameter that is useful for this determination is called “cutoff ratio.” It is defined as:

\(CR=\dfrac{t_L}{t_{co}} \)

where: CR = cutoff ratio,

t_L = advance time to the end of the field, and

t_co = cutoff time (set time).

A rapid water advance (low t_L) results in a low cutoff ratio. Conversely, a slow water advance (high t_L) will yield a high cutoff ratio. Low cutoff ratios result in large amounts of runoff and good uniformity. High cutoff ratios result in poor distribution of water, high deep percolation, and low runoff. This concept is illustrated in Figure 10.13.

Figure 10.13. Conceptual graph illustrating ELQ vs. cutoff ratio for sloping furrows.

The cutoff ratio that provides maximum efficiency, where the sum of runoff losses and deep percolation are minimized, is dependent upon the soil characteristics and whether or not the system has runoff recovery. In Figures 10.14 to 10.16 you see that efficiency varies with cutoff ratio and by soil texture for sloping furrow irrigation systems. Here the fine textured soils include clays, silty clays, silty clay loams, and clay loams. Silts, silt loams, loams and sandy clays are considered medium textured soils, and sandy clay loams, sandy loams, loamy fine sand and fine sand are course textured soils. The efficiency term in the graph is the application efficiency of the low quarter (E_LQ). Figures 10.14 to 10.16 are based on the assumption that water advance time to the downstream end of the field exceeds water recession time following cutoff. This condition will be met in most cases for long, sloping furrows. This condition might not be met on fields with inadequate slope or small fields with short furrow length (such as smallholder farms). In that case, the principles for border or basin irrigation systems (Section 10.6) may be applicable.

Figure 10.14. ELQ vs. cutoff ratio for sloping furrows with fine textured soils (clays, silty clays, silty clay loams, and clay loams). Assumes advance time exceeds recession time.

Figure 10.15. ELQ vs. cutoff ratio for sloping furrows with medium textured soils (silts, silt loams, loams and sandy clays). Assumes advance time exceeds recession time.

Figure 10.16. ELQ vs. cutoff ratio for sloping furrows with coarse textured soils (sandy clay loams, sandy loams, loamy fine sand and fine sand). Assumes advance time exceeds recession time.

Based on Figure 10.15, if the soil is of medium texture and a closed runoff recovery system is used, the maximum efficiency occurs at a cutoff ratio of about 0.40. Without runoff recovery, the maximum efficiency occurs at about 0.70. How can a manager use these curves? Suppose, because of time constraints, the irrigator can only change sets every 12 hours. If the medium textured soil is considered and the system has runoff recovery, the peak efficiency would occur with a cutoff ratio of 0.40. The desired advance time is then 0.40 × 12 hours or 4.8 hours. Hence, the irrigator would adjust the furrow stream to achieve the 4.8 hours advance time. Of course, the stream size that has been determined may not be feasible if it exceeds the maximum nonerosive stream size for that slope condition.

The expected maximum efficiency for the system described above would be about 85% (Figure 10.15). For these efficiencies to be attainable, the depth infiltrated at the low quarter, d_LQ, must be less than the soil water deficit, SWD. If this is not true, the figures are not applicable and the manager should consider allowing a higher SWD before irrigation without exceeding AD. If SWD already equals AD, then other practices that reduce infiltration depths, such as every other furrow irrigation or shorter set times, must be considered.

As discussed above, usually the irrigator does not know the soil’s infiltration characteristics prior to irrigation. The irrigator learns these characteristics by irrigating a portion of the field. Once the advance time is known for a given furrow flow rate, or stream size, then the irrigator can make the appropriate adjustments to maximize efficiency.

In the example used so far in this chapter, the furrow stream size was 11 gpm (760 ÷ 70) and the advance time was 9 hours. According to Figure 10.15, the cutoff ratio that would result in maximum efficiency is about 0.70 with no runoff recovery. Thus, the desired advance time is 0.70 × 12 hours or 8.4 hours. This is close to the measured 9- hour advance time.

What if in the above example a runoff recovery system is used? Now, the desired cutoff ratio is about 0.40 (Figure 10.15). The desired advance time is 0.40 × 12 hours or 4.8 hours. The ratio of the desired time to the original time is equal to 0.53 (4.8 hours ÷ 9 hours). What would the stream size have to be for this to occur? Or, another way of looking at it, how many furrows would have to operate to achieve this goal? Table 10.2 contains correction factors for the number of furrows to irrigate for a fixed Q_t . The ratio of the new advance time to the old one is 0.53. Interpolating from Table 10.2, the number of furrows that should be watered is 63% of the number of furrows that were originally watered (find this under medium textured soil, N₂/N₁ = 0.63). Thus, the irrigator should irrigate 44 furrows (0.63 x 70) instead of the original 70. The furrow stream size would now be 760 gpm ÷ 44 = 17 gpm per furrow. If the furrow slope in this example is 0.3%, the maximum nonerosive stream size is 33 gpm. Thus, the 17 gpm flow rate is acceptable.

Table 10.2. Correction factor (N2/N1) for predicting how many furrows to irrigate per set with a constant water supply. (Table based on equation in Cahoon et al., 1995.)

TL2/TL1	Fine	Medium	Coarse
0.1	0.1	0.2	0.4
0.2	0.2	0.3	0.5
0.3	0.3	0.4	0.6
0.4	0.4	0.5	0.7
0.5	0.5	0.6	0.7
0.6	0.6	0.7	0.8
0.7	0.7	0.8	0.9
0.8	0.8	0.8	0.9
0.9	0.9	0.9	1.0
1.0	1.0	1.0	1.0
1.1	1.1	1.1	1.0
1.2	1.2	1.1	1.1
1.3	1.3	1.2	1.1
1.4	1.4	1.3	1.2
1.5	1.5	1.4	1.2
1.6	1.6	1.4	1.2
1.7	1.7	1.5	1.3
1.8	1.9	1.6	1.3
1.9	2.0	1.6	1.3
2.0	2.1	1.7	1.4
2.1	2.2	1.7	1.4
2.2	2.3	1.8	1.4
2.3	2.4	1.9	1.5
2.4	2.5	1.9	1.5
2.5	2.6	2.0	1.5
2.6	2.7	2.0	1.5
2.7	2.8	2.1	1.6
2.8	2.9	2.2	1.6
2.9	3.1	2.2	1.6
3.0	3.2	2.3	1.6
4.0	4.3	2.8	1.9
5.0	5.4	3.3	2.1
6.0	6.6	3.8	2.2
7.0	7.7	4.3	2.4
8.0	8.9	4.8	2.5
9.0	10.0	5.2	2.7
10.0	11.2	5.6	2.8
N2 = Correct number of furrows to water per set. TL2 = Desired advance time N1 = Original number of furrows watered per set. TL1 = Original advance time.

What is the depth infiltrated at the low quarter for the new condition? Table 10.3 relates the depth of low quarter to the gross depth applied and the cutoff ratio. The infiltration factor given in Table 10.3 is defined as:

\(\text{Infiltration factor}=\dfrac{d_{LQ}}{d_g}\)

Table 10.3. Infiltration factors (ratio of dLQ to dg) for sloping furrows. (Assumes advance time exceeds recession time.)

Cutoff Ratio	Infiltration Factors Soil Texture Fine	Infiltration Factors Soil Texture Medium	Infiltration Factors Soil Texture Coarse
0.1	0.19	0.32	0.50
0.2	0.32	0.45	0.61
0.9	0.74	0.66	0.61
0.8	0.73	0.69	0.66
0.3	0.42	0.55	0.68
0.4	0.51	0.62	0.68
0.7	0.70	0.70	0.69
0.5	0.59	0.66	0.71
0.6	0.65	0.69	0.72
0.7	0.70	0.70	0.69
0.8	0.73	0.69	0.66
0.9	0.74	0.66	0.61

In Example 10.1, the cutoff ratio was 0.75 and the gross depth applied was 4.2 inches. The depth of low quarter would be equal to 4.2 inches times the factor from Table 10.3 (0.70) or 2.9 inches. This closely agrees with our original graphical analysis (Figure 10.11), 2.8 inches. This number can now be compared with the SWD before irrigation. If it exceeds the SWD, then the irrigator has two choices. The first, and easiest to implement, is to change the irrigation frequency so that SWD is higher during irrigation. Again, the constraint is that AD is the upper limit. The second approach is to change the irrigation cutoff time so that less water infiltrates during the irrigation and thus the depth of low quarter might be maintained less than the soil water deficit.

The irrigation frequency now will be dependent upon the effective water applied. As we discussed in Chapter 5, the effective water applied will be equal to the d_LQ if it is less than or equal to SWD. The effective water applied is equal to SWD if d_LQ is greater than SWD. In our example, where the effective water applied was 2.9 inches, the irrigation interval should be about 10 days if ET is equal to 0.3 inches per day.

The runoff ratio (R_r, Equation 10.8) must be known to calculate E_LQ when a runoff recovery system is used. Table 10.4 gives runoff ratios for various conditions.

Table 10.4. Runoff ratios (Rr) for sloping furrows. (Assumes advance time exceeds recession time.)

Cutoff Ratio	Runoff Ratios Soil Texture Fine	Runoff Ratios Soil Texture Medium	Runoff Ratios Soil Texture Coarse
0.1	0.81	0.68	0.50
0.2	0.68	0.53	0.36
0.3	0.56	0.42	0.26
0.4	0.46	0.32	0.19
0.5	0.37	0.24	0.14
0.6	0.28	0.18	0.09
0.7	0.21	0.12	0.06
0.8	0.14	0.08	0.03
0.9	0.08	0.04	0.02

Notice that the efficiency is lower in Example 10.4 than in Examples 10.2 and 10.3, even though the lower cutoff ratio was supposed to increase efficiency. What went wrong? In Example 10.4, the d_LQ > SWD. To improve efficiency to its potential, the d_LQ must either be reduced or SWD must be increased. Suppose AD = 3.4. The SWD cannot be increased without yield reduction, so a reduction of d_LQ must be attempted. Let us try a 6- hour set time.

An alternative to free flow at the furrow outlet is to block the downstream ends with a dike to prevent runoff. This is usually practical when field slopes are low. While blocking the ends prevents runoff, poor distribution of water can occur because of the ponded water behind the dike (Figure 10.17).

Figure 10.17. Infiltration profile for blocked or diked end sloping furrows.

Cutoff ratio guidelines that result in maximum efficiency have been established for all the cases discussed so far in this chapter. They are presented in Table 10.5. In general, when the ends are blocked, recommended cutoff ratios are higher than for the non-blocked case. This minimizes the size of the pond and the quantity of deep percolation beneath the pond.

Table 10.5. Recommended cutoff ratios to achieve maximum efficiency for sloping furrows.

type of system	Soil Texture Fine	Soil Texture Medium	Soil Texture Coarse
No reuse	0.90	0.70	0.50
Closed reuse system	0.50	0.40	0.20
Open reuse system	0.70	0.50	0.35
Blocked ends (low slope, 0.1%)^[a]	0.95	0.85	0.70
Blocked ends (moderate slope, 0.5%)^[a]	0.90	0.80	0.65
^[a]Based on data from Cahoon et al., 1995.

Example 10.4

If runoff recovery is included in the system described in Examples 10.1 to 10.3 and a cutoff ratio of 0.40 is achieved, determine the system’s E_LQ. Assume that SWD = 3.4 inches and the recovery system returns the water to the same field (closed system).

Given: CR = 0.40 N = 44 furrows

SWD = 3.4 in W = 30 in

Qt = 760 gpm

Find: d_g d_LQ

d_e E_LQ

Solution

\(d_g=1155\left(\dfrac{Q_t\times t_{co}}{N\times W\times L}\right) \) (Eq. 10.4)

\(d_g=1155\left(\dfrac{(760\text{ gpm})(12\text{ hr})}{(44)(30\text{ in})(1200\text{ ft})} \right)=6.65\text{ in} \)

\(d_{LQ}=d_g(\text{Infiltration factor}) \) (Eq. 10.12)

\(d_{LQ}=(6.65)(0.62)=4.1\text{ in} \) (Table 10.3)

\(\text{Since }d_{LQ}>\text{SWD}, d_e=\text{SWD}=3.4\text{ in} \)

\(\text{For a medium textured soil, CR}=0.40 \text{ and }R_r=0.32 \)

\(E_{LQ}=\left(\dfrac{d_e}{d_g-d_gR_rR_t}\right)100\% \) (Eq. 10.6)

\(E_{LQ}=\left(\dfrac{4.3}{6.65-6.65(0.32)(0.85)}\right)100\%=70\% \)

Example 10.5

Determine the number of furrows to irrigate in a set and the E_LQ for the conditions in Example 10.4 if a 6-hour set time is used.

Given: t_co = 6 hr

CR = 0.40

When N =44, t_L = 4.8 hr

Find: t_L d_g

N d_LQ

E_LQ

Solution

\(t_L=(6\text{ hr})(0.4)=2.4\text{ hr}\)

\(\dfrac{t_{L1}}{t_{L2}}=\dfrac{2.4}{4.8}=0.5 \)

\(\dfrac{N_2}{N_1}=0.6 \)

\(N_2=(44)(0.6)=26 \) (Table 10.2)

\(q_s=\dfrac{Q_t}{N}=\dfrac{760\text{ gpm}}{26}=29\text{ gpm} \)

\(\text{Since }q_{ max}\text{ is 33 gpm for the 0.3% slope, 29 gpm is okay.}\)

\(d_g=1155\left(\dfrac{Q_t\times t_{co}}{N\times W\times L}\right) \) (Eq. 10.4)

\(d_g=1155\left(\dfrac{(760\text{ gpm})(6\text{ hr})}{(26)(30\text{ in})(1200\text{ ft})} \right)=5.0\text{ in} \)

\(d_{LQ}= 5.0\text{ (Infiltration factor)} \)

\(d_{LQ}=(5.0)(0.62)=3.1\text{ in} \) (Table 10.3)

\(d_e=3.1\text{ in since }d_{LQ}\text{ is less than SWD} \)

\(E_{LQ}=\left(\dfrac{d_e}{d_g-d_gR_rR_t}\right)100\% \) (Eq. 10.6)

\(E_{LQ}=\left(\dfrac{3.1}{5.0-5.0(0.32)(0.85)}\right)100\%=85\% \)

This is close to the maximum achievable efficiency. By changing the management and adding runoff recovery, the efficiency was improved from 67% (Example 10.1) to 85% (Example 10.5). If ET = 0.3 inches per day, the field should be irrigated every 10 days since d_e = 3.1 inches.

In Examples 10.1 to 10.5, we reacted to what occurred in the field, i.e., we reacted to how fast the water advanced across the field. We refer to this as reactive management of surface irrigation. For someone irrigating a field for the first time, the data shown in Table 10.6 can help keep the flow rates, advance times, and field lengths within reasonable range.

Table 10.6. Furrow irrigation management recommendations for various soil types.

Soil Texture	Basic Infiltration Rate (in/hr)	Basic Infiltration Rate (gpm/100 ft)	Maximum Furrow Length (ft)	Recommended Stream Size[a] (gpm/100 ft)
Loamy sand	2.0–5.0	2.4	600	4.8
Sandy loam	0.5–4.0	1.9	800	3.8
Fine sandy loam	0.2–2.0	1.7	1000	3.4
Silt loam	0.2–1.5	1.1	1100	2.2
Silty clay loam	0.05–0.25	0.1	1300	1.4
^[a]Actual stream size must be less than maximum nonerosive stream size.

Are there alternatives to changing set time, stream size, and soil water deficit? As we have illustrated, one option for improving irrigation efficiency is to recover and reuse runoff water. The facilities necessary for recovering runoff are discussed in Section 10.7. Another option is to consider the furrow spacing. Alternate furrow or irrigating every other furrow should be considered if application depths are too large. In general, this practice will reduce infiltration by about 25 to 30%. For the same stream size, changing to every other furrow will increase advance time by about 30 to 40%, because of the longer time it takes for the wetting fronts between the irrigated furrows to meet. Watering every other furrow is usually a practice that can be used to reduce infiltration because even though the advance time is longer, the set size is twice as large as for every furrow irrigation.

Another field factor that can be changed, although not often desirable, is to reduce the furrow length. If the maximum nonerosive stream size is the limiting factor in achieving high efficiency, then furrow length should be reduced so that optimum advance times can be achieved.

Surface irrigation efficiency can sometimes be improved by land smoothing. Land smoothing and laser grading will remove low and high spots and pot holes and provide uniform surface slopes. This will increase the advance rate of the water and uniformity of application.

Other options that can be used to overcome some of the constraints in surface irrigation are automation and semi-automation. This would eliminate the constraint of set time. Semi-automation of surface irrigation can be easily accomplished using surge flow irrigation valves, which will be discussed later. Another option is to use timers to terminate the inflow at the desired time in the absence of the irrigator. For example, if the irrigator can only return to the field every 12 hours but an 8-hour set time is desired, the timer could be set to shut off the water at 8 hours. The limitation of this procedure is that the system capacity, as discussed in Chapter 5, must be large enough to allow for the off time or down time that occurs between the time the system shuts off and the time that the irrigator returns to restart it.

If infiltration rates are too high to achieve the desired efficiency, then furrow packing and smoothing using special tillage tools might be helpful.