6.4.1: Checkbook Accounting Method

The checkbook accounting or water balance approach can be used to schedule irrigations. This approach accounts for all of the additions and withdrawals to and from the root zone as illustrated in Figure 6.9. The checkbook method keeps track of the soil water deficit (SWD) on a daily basis. SWD on a given day can be calculated as:

SWD_i = SWD_i-1 + ET_i-1 – d_{e i-1} – P_{e i-1} – U_{f i-1}

where: SWD_i = SWD on day i,

SWD_i-1 = SWD on day i-1

ET_i-1 = evapotranspiration on day i-1

d_{e i-1} = effective irrigation on day i-1,

P_{e i-1} = effective precipitation on day i-1, and

U_{f i-1} = upward flow of groundwater from a shallow water table on day i-1.

Figure 6.9. Additions and subtractions from the plant root zone (adapted from Cassel, 1984).

In available water balance form, Equation 6.18 is: AW_i = AW_i-1 – ET_i-1 + d_ei-1 + P_ei-1 + U_fi-1

where: AW_i = water balance on day i and

AW_i-1 = water balance on day i – 1.

Note that runoff and deep percolation are not considered in Equations 6.18 and 6.19. This is because we have used the terms effective precipitation and effective irrigation. Methods were presented in Chapter 5 to determine effective irrigation depths. If the infiltrated depth of water in the low quarter from precipitation and irrigation exceeds SWD, then the effective depth equals the SWD. In mathematical terms:

if d_{LQ i-1} (infiltrated irrigation depth) < SWD_i-1 then d_ei-1 = d_LQi-1

if d_{LQ i-1} > SWD_i-1 then d_ei-1 = SWD_i-1

The same equations can be used for rainfall infiltration to determine effective precipitation. Using Equation 6.19 is analogous to keeping the balance in your checkbook. AW is the balance; irrigation, rainfall, and upward flow are the deposits; and ET is a withdrawal. If the AW becomes lower than the MB, a penalty is paid, such as a reduction in crop yield. To use Equation 6.18 or 6.19, a starting or initial estimation of SWD or AW is needed. This can be done by using one of the soil water measurement techniques discussed in Chapter 2. Another approach is to begin the checkbook accounting procedure following a wet period or following a thorough irrigation when the soils can be assumed to be at or near field capacity. The ET in Equations 6.18 and 6.19 can be calculated from weather data using the approaches given in Chapter 4. A question that often arises is, what should be used as the forecast ET for the LD and ED calculations? Equations 6.18 and 6.19 use ET as determined by the weather that has already occurred. The forecast ET can be based on long-term average weather conditions for a region, such as illustrated in Table 6.4.

Table 6.4. Example of long-term water use data (ET) for crops in Nebraska (adapted from Melvin and Yonts, 2009).

Water Use Rate (in/day)	Corn	Grain Sorghum	Soybeans	Dry Beans	Sugar Beets	Winter Wheat	Alfalfa^[a]
0.18					June 15	spring growth
0.22			full bloom		July 1
0.24	12 leaf			rapid vegetative growth		joint
0.26		flag leaf	begin pod
0.28	early tassel	boot					June 15
0.30	silking	half bloom	full pod	flowering and pod development	July 15	boot	July 1
0.28							August 1
0.26	blister kernel	soft dough			August 1
0.24	milk		seed fill				August 15
0.22
0.20	begin dent
0.18	full dent	hard dough		pod fill and maturation
0.19
[a] Alfalfa water use rates should be multiplied by 0.50 during the first 10 days following cutting and by 0.75 from the 10th to 20th day following cutting.

Another approach is to predict ahead based on what occurred during the past few days. If the weather is forecasted to be similar to what has just occurred, then it can be assumed that the forecasted ET is equal to ET of the prior few days.

When a water table exists close to the root zone, crops may extract water from the capillary fringe, or water may flow upward into the crop root zone. Water tables that are within 3 feet of the bottom of the root zone can provide a substantial fraction of the ET even for saline groundwater if the crop is relatively salt tolerant.

The rate of upward groundwater flow depends on the depth to the water table and the soil type. Shallow water tables supply water more rapidly than deep water tables. The soil type has two influences. First, the capillarity of the soil provides the energy or potential for upward movement. Second, the hydraulic conductivity of the soil determines the rate of upward flow. Sandy soils have a high conductivity when nearly saturated, but the conductivity drops very quickly with distance above the water table as the soil becomes unsaturated. Sandy soils are usually irrigated to prevent large soil water potentials; they provide less energy for upward flow. Therefore, sandy soils usually have small rates of upward flow. Clay soils can produce large potentials for upward flow; however, their low hydraulic conductivity limits the rate of upward flow. Upward flow is generally most significant for medium-textured soils where the soil water potential and conductivity together produce significant flow rates.

A simplified method of estimating upward flow from Doorenbos and Pruitt (1977) is shown in Figure 6.10. More detailed analysis has been presented by Skaggs et al. (1981) for use with combined drainage and subsurface irrigation systems.

Figure 6.10. Upward flow of water from a groundwater table (modified from Dorrenbos and Pruitt, 1977).

For annual crops where the root zone depth is expanding with time, the SWD and AW calculations should consider the soil water conditions that the roots are growing into. For example, if the roots are growing into a soil with soil water levels less than FC, then the ED will decrease because of the extra room for water storage provided by the root zone expansion. The LD might increase or it might decrease depending upon the SWD in the new portion of the root zone and on f_dc. Equations 6.18 and 6.19 each could have a component that accounts for root zone expansion. The root zone expansion can be treated as a continuum or in discrete steps.

If the root zone expansion is treated in discrete steps, Equation 6.18 is modified as follows:

SWD_i = SWD_i-1 + ET_i-1 – d_{e i-1} – P_{e i-1} – U_{f i-1} + ΔSWD_i-1 (6.22)

\(\Delta SWD_{i-1}=(AWC)\left(\dfrac{f_{do}}{100\%}\right)(\Delta R_d)\) (6.23)

where: ∆SWD_i-1 = change in SWD due to the additional root depth (ΔR_d) and f_do = initial fd in the new layer of soil explored by roots.

The modified Equation 6.19 is:

AW_i = AW_i-1 – ET_i-1 + d_ei-1 + P_ei-1 + U_fi-1 + ΔAW_i-1 (6.24)

\(\Delta AW_{i-1}=(AWC)\left(\dfrac{f_{do}}{100\%}\right)(\Delta R_d\) (6.25)

where: ∆AW_i-1 = added available water due to the root zone expansion and

f_ro = initial fr in the new layer of soil explored by roots.

The use of the water balance method is illustrated in Example 6.5. In Example 6.5, Location 1 could be irrigated on June 29. The soil could store the effective depth applied and yet there would be room for storing a 0.5-inch rainfall. At most, irrigation could be delayed until July 6 (8 days after June 28). At Location 2, irrigation is not required until July 7 but it would be allowable to irrigate in 3 days (July 1), based on the ED calculation.

The results of using checkbook accounting are shown graphically in Figures 6.11 and 6.12. Figure 6.11 shows an example where fr is maintained between 0.40 and 0.70 throughout the growing season. In Figure 6.12 you see an example where the soil water is allowed to gradually deplete to below 0.40 fr at plant maturity (PM). Figure 6.12 illustrates an important concept that can be followed in semiarid and subhumid regions. The evolution of the soil water is the result of water applications which, by design, only replace a fraction of ET. This concept, called programmed soil moisture depletion (Fischbach and Somerhalder, 1973), depletes the soil water reservoir to low, yet safe, levels late in the growing season. By depleting soil water, there is room in the soil for storing precipitation during the offseason. Storing offseason precipitation is an effective way of reducing irrigation requirements.

Figure 6.11. Graphical results of soil checkbook accounting method (adapted from Stegman, 1983). Soil water levels are kept between 40 and 70%.

Figure 6.12. Graphical results of checkbook accounting method where soil water was managed to deplete slowly (adapted from Stegman, 1983). Soil water levels were allowed to gradually deplete.

Example 6.5

Corn is grown on a silt loam soil at two different locations . The pertinent site conditions are:

Given: f_dc = 0.45 R_d = 2.5 ft = 30 in

d_e = 1.1 in AWC = 0.2 in/in

r_a = rainfall allowance = 0.5 in

Depth to water table = 10 ft The SWDs at the start of June 25 were 2.2 and 0.80 inches for Locations 1 and 2 in the irrigated area, respectively. The ET and Pe for June 25 to June 28 are given in the table below.

Find: Determine the LD and ED for each location for June 25 to 28

Solution:

Use Equations 6.2, 6.4, 6.10, 6.16, and 6.18:

TAW = (R_d)(AWC) (Eq. 6.2)

TAW = (30 in)(0.2 in/in) = 6 in

AD = f_dc (TAW) (Eq. 6.4)

AD = (0.45)(6 in) = 2.7 in

The results of the calculations using Equations 6.10, 6.16, and 6.18 are shown in the bold italics in the table below.

Corn growth in two locations

Date	Actual ET (in/day)	Forecast ET (in/day)	Pe (in)	Uf (in)	Loc. 1 SWD (in)	Loc. 1 de (in)	Loc. 1 ED (days)	Loc. 1 LD (days)	Loc. 2 SWD (in)	Loc. 2 de (in)	Loc. 2 ED (days)	Loc. 2 LD (days)
June 25	0.20	0.18	0.0	0.0	2.20	0	-	3	0.80	0	4	11
June 26	0.21	0.18	0.0	0.0	2.40	0	-	2	1.00	0	3	9
June 27	0.13	0.18	0.3	0.0	2.61	1.1	-	1	1.21	0	2	8
June 28	0.17	0.18	0.0	0.0	1.34	0	1	8	1.04	0	3	9