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Irrigation Scheduling
Dean E. Eisenhauer, Derrel L. Martin, Derek M. Heeren, Glenn J. Hoffman
Pages 107-130 (doi: 10.13031/ISM.2021.6) in Irrigation Systems Management. ,
Abstract. See https://www.asabe.org/ISM for a PDF file of this entire textbook at no cost.
6.1 Introduction
In Chapter 4 we discussed plant water use (ET). In Chapter 2 we discussed how the soil-plant root zone serves as a reservoir. But how should we manage this reservoir? The ET demand of a crop is supplied from three sources of water: (1) rainfall that occurs during the growing season, (2) precipitation that was stored in the plant root zone during the dormant or off season and (3) irrigation. For example, in central Nebraska, the growing season ET for corn averages about 26 inches per year. Approximately 12 inches of this water would come from growing season rainfall, 4 inches from the stored soil water, and the balance 10 inches from irrigation (net). Good managers of irrigation water strive to maximize the use of precipitation while minimizing deep percolation. Proper irrigation scheduling will help reach these goals.
Irrigation scheduling includes determining how often to apply water and how much water to apply. Irrigation scheduling is imperative for good water management. In this chapter we discuss irrigation scheduling and how system efficiency, available water capacity, plant root zone, and evapotranspiration affect the frequency and amount of water application, i.e., we build on what was covered in Chapters 2, 3, and 4.
In practice irrigation scheduling is often based on the irrigator’s personal experience, plant appearance, watching the neighbor, or just simply irrigating whenever water is available. Sometimes the irrigation controller is set and never adjusted for rainfall or changes in ET. As water resources become limited and as more concern is raised about the effects of irrigation on water quality, the need for improved methods for scheduling will increase. Three general approaches or philosophies for scheduling irrigations are:
- maintain soil water content within desired limits,
- use plant status indicators to signal the need for water, and
- irrigate according to calendar date or other fixed schedule.
The soil water approach uses the plant root zone as a reservoir for storing and releasing water, as we discussed in Chapter 2. This reservoir can be managed using irrigation scheduling. The soil water status can be determined by checkbook accounting or by direct measurement of soil water. Checkbook accounting uses estimates of ET, rainfall, and irrigation to calculate the soil water level. Plant status indicators range from simply observing the stage of plant development to more sophisticated methods, such as measuring plant leaf temperature and plant water potential. Fixed schedules are often associated with irrigation water supply districts that lack the flexibility to deliver water on demand.
No one scheduling philosophy is correct in itself. The emphasis in this chapter is on managing the soil water reservoir, but it also includes a short discussion on plant status indicators. It is likely that in the future a combination of soil water maintenance and plant status will be the most appropriate choice.
6.2 Plant Response to ET and Soil Water
The relationship between crop yield and transpiration and ET is illustrated in Figure 6.1. As illustrated in Figure 6.1b, once soil water evaporation is satisfied, there is a linear increase in yield as evapotranspiration increases until maximum yield is reached. In this book most of the discussion relating to crop or forage production will center on managing water for maximum, or near maximum, yield. More advanced books and papers discuss deficit or limited irrigation, where yield is reduced because less irrigation water is applied than necessary to meet full crop water requirements (English et al., 1990, Trout et al., 2020). With deficit irrigation, ET is less than the crop ET necessary for maximum yield. Figure 6.2 shows the relationship between growth or yield and fr (fraction of available soil water remaining). If soil moisture is maintained above certain limits, maximum, or near maximum, yield is achieved. The minimum fraction of available water remaining that should occur to avoid plant stress and a yield reduction is the critical fraction remaining (frc) a term presented in Chapter 4. When the available soil water is maintained equal to or above frc, maximum yields are attainable because the plants are able to extract adequate water from the soil.
 (a)  (b) |
| Figure 6.1. Relationship between yield, T, and ET. |
 |
| Figure 6.2. Relationship between available water remaining and yield (adopted from Stegman, 1983). |
The frc is related to fdc, the maximum allowable fraction depletion of the available soil moisture, by the following equation:
fdc = 1 – frc (6.1)
fdc is dependent on the plant species and genotype and on weather conditions. Weather influences the maximum ET each day. According to Doorenbos and Kassam (1979), fdc ranges from 0.18 to 0.88, depending upon how plants respond to soil water deficits and on the maximum ET for a given day. Data for various conditions are given in Table 6.1. From the table you can see that for corn with a maximum evapotranspiration of 0.28 inches per day, fdc is 0.5 and frc is 0.50 (from Equation 6.1). A crop, such as onions, grown under the same environment or weather conditions, will have a fdc of about 0.23 (frc = 0.77). Thus, the criteria for management depends on the crop and the environmental conditions. If the weather is relatively cool (low ET), a high percentage of the soil water can be depleted before stress occurs. Conversely, on hot days (high ET), less soil water depletion is allowed before plants undergo stress.
A common level of fdc is 0.50. This is an average value and can be used where more appropriate data, such as that shown in Table 6.1, is not available.
The above discussion has implied that the management goal is to produce maximum (or near maximum) yield or biomass. This may not be the case for landscaping plants and turfgrass. With these plants the goal is satisfactory plant appearance and/or adequate functional quality. To maintain a high-quality golf green will require more water than is required to satisfy the needs of a low-maintenance utility turf.
| Table 6.1. Estimated maximum allowable fraction depletion (fdc) to maintain maximum yields of crops grouped according to sensitivity (modified from Doorenbos and Kassam, 1979). | |||||||||
| Crop Group | |||||||||
| 1 2 3 4 | onion, pepper, potato banana, cabbage, pea, tomato alfalfa, bean, citrus, groundnut, pineapple, sunflower, watermelon, wheat cotton, sorghum, olive, grape, safflower, corn, soybean, sugarbeet, tobacco | ||||||||
| Maximum ET (in/day) | |||||||||
| Crop Group | 0.08 | 0.12 | 0.16 | 0.20 | 0.24 | 0.28 | 0.31 | 0.35 | 0.39 |
| fdc to Maintain Maximum Evapotranspiration Rates | |||||||||
| 1 2 3 4 | 0.50 0.68 0.80 0.88 | 0.43 0.58 0.70 0.80 | 0.35 0.45 0.60 0.70 | 0.30 0.40 0.50 0.60 | 0.25 0.35 0.45 0.55 | 0.23 0.33 0.43 0.50 | 0.20 0.28 0.38 0.45 | 0.20 0.25 0.35 0.43 | 0.18 0.23 0.30 0.40 |
The management objective must be defined for any irrigation scheduling procedure. Possible objectives include:
- maximum yield or biomass production,
- maximum economic return,
- functional value of the plants (e.g., an athletic field),
- aesthetic value (i.e., keeping the plants healthy), and
- maintaining plant life.
6.3 Capacity of the Soil Water Reservoir
As discussed in Chapter 2 and illustrated in Figure 2.8, the plant root zone can be viewed as a reservoir for storing water for use by plants. For non-layered soils, total available water capacity, or TAW, is:
TAW = (Rd)(AWC) (6.2)
where: Rd = root zone depth and
AWC = available water capacity
For layered soils:
TAW = (AWC1)(t1) + (AWC2)(t2) + ... +(AWCn) [Rd–(t1 + t2 + ...+ tn-1)] (6.3)
where: AWC1, AWC2, … = available water capacity in layers 1, 2, etc.,
t1, t2, ... = thickness of soil layer 1, soil layer 2, etc., and
n = number of soil layers.
So, the size of the reservoir is dependent on both the soil and the root zone depth.
Allowable depletion, an important irrigation management term, is the amount of available water that can be removed from a root zone before plants undergo moisture stress. The allowable depletion, AD, is:
AD = fdc(TAW) (6.4)
AD is expressed as a depth of water. Likewise, the minimum allowable available soil moisture, or minimum balance (MB) is:
MB = frc(TAW) (6.5)
Note that MB = TAW – AD or TAW = MB + AD.
In Example 6.1, irrigation should be applied when or before 2.7 inches of soil water have been depleted. If AD is reached, i.e., if SWD = AD at the time of irrigation, the maximum amount of water that the root zone would hold without exceeding field capacity is 2.7 inches. One goal is to keep infiltration less than or equal to the soil water deficit (SWD). As we discussed in Section 2.9, whenever infiltration exceeds SWD, deep percolation will occur.
| Table 6.2. Range of maximum effective rooting depths for fully grown plants (from Martin et al., 1990). | |||||||
| Crop | Maximum Effective Depth (ft) | Crop | Maximum Effective Depth[a](ft) | ||||
| Alfalfa | 3.3–10 | Olives | 2.6–6.6 | ||||
| Banana | 1.3–2.6 | Onions | 2.6–6.6 | ||||
| Barley | 3.3–4.3 | Palm trees | 2.3–3.6 | ||||
| Beans | 1.3–2.6 | Peas | 2.0–3.3 | ||||
| Cabbage | 2.0–3.3 | Peppers | 1.7–3.3 | ||||
| Carrots | 1.6–3.3 | Pineapple | 1.0–2.0 | ||||
| Celery | 1.0–1.7 | Potatoes | 1.3–2.6 | ||||
| Citrus | 3.3–5.9 | Safflower | 3.3–6.6 | ||||
| Clover | 2.0–3.0 | Sorghum | 3.3–6.6 | ||||
| Corn | 3.3–6.6 | Soybeans | 2.6–5.0 | ||||
| Cotton | 3.3–6.6 | Spinach | 1.0–1.7 | ||||
| Cucumber | 2.3–4.0 | Strawberries | 0.7–1.0 | ||||
| Dates | 5.0–8.3 | Sugar beet | 2.6–6.6 | ||||
| Flax | 3.3–5.0 | Sugarcane | 4.0–6.6 | ||||
| Grapes | 3.3–6.6 | Sunflower | 3.3–8.3 | ||||
| Grass | 1.7–5.0 | Sweet potatoes | 3.3–5.0 | ||||
| Groundnuts | 1.7–3.3 | ||||||
| Lettuce | 1.0–1.7 | Tobacco | 1.7–3.3 | ||||
| Maize | 3.3–6.6 | Tomatoes | 2.3–5.0 | ||||
| Melons | 3.3–5.0 | Wheat | 3.3–5.0 | ||||
[a] The maximum values given represent the full expression of the genetic potential for root growth and are only found in uniform, fertile soils of low resistance to root penetration. | |||||||
6.3.1 Plant Root Zone
Established perennial plants such as alfalfa, grasses, trees, and shrubs have relatively constant root zone depths. The maximum effective root depth depends on several environmental, crop, and soil factors. The range of maximum effective root zone depths for various crops is summarized in Table 6.2. The maximum effective depth used for scheduling, which is usually less than the maximum depth where roots are found, represents the depth of the soil profile that has enough rooting density for extraction of available water. Values in Table 6.2 should be used cautiously and adjusted for local soil and climatic conditions.For annual crops the root depth prior to the date of maximum rooting is described by:
Rd = RdMIN + (RdMAX – RdMIN)Rf (6.6)
where: Rd = root depth
RdMIN = minimum root depth for young plants,
RdMAX = maximum effective root depth, and
Rf = root growth factor.
The development of a corn root zone during the season is illustrated in Figure 6.3.
The minimum root depth for seedlings is normally considered to be 4 to 6 inches. The actual initial depth may deviate slightly from this value, but an error on the minimum root depth will have very little effect on the soil water balance or irrigation scheduling.
The root growth factor, which describes the rate of root zone expansion during the season, can be computed as:
(6.7)
where: Dag = days after germination and
Dtm = days from germination to maximum effective depth.
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| Figure 6.3. Development of a corn plant’s root zone. |
The time required for roots to reach the maximum effective depth varies considerably for different environments, crops, and varieties. Local values and individual experience must be used to determine these values. Root zone depths for various stages of crop development are given in Table 6.3.
Plants do not extract water uniformly throughout their rooting depth. Usually there is more water extracted from shallow depths and less from deeper depths. An approximation of the extraction pattern is the 4-3-2-1 rule, i.e., 40% of the water comes from the top 25% of the root zone, 30% from the second 25%, and so forth. This conceptual approximation is illustrated in Figure 6.4. If for example, the root zone depth is 4 feet, and the plants extract 2 inches of water between irrigations, 0.8 inches would be obtained from the first foot, 0.6 inches from the second foot, 0.4 inches from the third foot, and 0.2 inches from the fourth foot. This concept applies only when the root zone is refilled, or nearly refilled, following irrigation. If the root zone is not completely refilled to field capacity during irrigation, then more water will be obtained from the shallower depths. Under these conditions, there is usually a sandwiched layer of dryer soil between the upper part of the root zone and the lower part.
| Table 6.3. Example root zone information for various annual crops grown in Nebraska (adapted from Melvin and Yonts, 2009). | ||||||||
| Assumed Root Depth (ft) | Corn (3)[a] | Grain Sorghum (3)[a] | Soybean (3)[a] | Dry Beans (2.5)[a] | Sugar Beets (3)[a] | Winter Wheat (4)[a] | Alfalfa (4)[a] | |
| 1.0 | vegetative | vegetative | vegetative | vegetative | ||||
| 1.5 | initial flowering pod set | |||||||
| 2.0 | 12 leaf | early bloom | beginning pod fill | June 1 | fall growth | |||
| 2.5 | 16 leaf | flag leaf | full bloom | full seed fill | July 1 | spring growth | ||
| 3.0 | silking | boot | pod elongation | July 15 | joint | |||
| 3.5 | blister | bloom | August 1 | boot | ||||
| 4.0 | beginning dent | dough | full seed fill | Sept. 1 | dough | |||
| 5.0 | ||||||||
| 6.0 | established stand | |||||||
| [a] Maximum crop root depth for irrigation management. | ||||||||
 |
| Figure 6.4. Average water extraction pattern from the plant root zone, the 4-3-2-1 rule. |
Even though root zone depths exceed 3 feet by midseason for many crops, to be on the safe side, many managers use a 3-foot root zone until late in the season. As maturity approaches, the plants are allowed to extract water from the entire root zone.
6.4 Irrigation Scheduling for Soil Water Maintenance
With the soil water maintenance approach, the plant’s needs for water are assumed to be met as long as the soil water is maintained between TAW and MB. As shown earlier, frc and MB are dependent on the plant’s microclimate, specifically the atmospheric demand for water.
An important variable in irrigation is the allowed depletion (AD). The interval between irrigations is controlled by the AD and the evapotranspiration. The maximum time interval between irrigations, TMAX, is as follows:
(6.8)
where: TMAX = maximum time interval between irrigations and
ET = average daily evapotranspiration.
In Example 6.1, AD was 2.7 inches. What is TMAX if ET = 0.3 of an inch a day? The answer is 9 days. This suggests that if water is not applied until AD is reached, then the appropriate maximum time between irrigation is 9 days. And, if irrigation is withheld for 9 days and limited to 2.7 inches, deep percolation is avoided.
Using Equations 6.4 and 6.8 you can determine how the root zone depth, evapotranspiration, and the available water capacity of the soil all influence the frequency and the amount of irrigation. A shallow root zone requires more frequent irrigations but lighter applications. A coarse-textured soil with a lower available water capacity requires lighter and more frequent irrigations. Medium-textured soils combined with deep root zones allow for less frequent irrigations and larger water applications.
The irrigation interval does not have to equal TMAX; it can be less. It is controlled by ET and the effective depth of water application, i.e.:
(6.9)
where: T = the time interval between irrigations and
de = the effective water applied per irrigation.
Many of the modern irrigation systems are managed to apply light, frequent irrigations even when root zones are deep and the AWC is large. For example, a center pivot irrigation system might be managed to apply an effective depth of 0.9 inches even if AD is much larger. Suppose that SWD = AD = 2.7 inches on the day of irrigation. The effective application of 0.9 inches is okay as long as the irrigation frequency is adjusted accordingly. Using our earlier example where ET = 0.3 inches per day, the appropriate interval between irrigations would be:
The basic goals of irrigation management are that the deficit not exceed AD before water is applied and that infiltration not exceed the SWD. To avoid exceeding AD, irrigation should occur on or before the latest date (LD). LD is calculated as:
(6.10)
or using the balance approach: 
(6.11)
where: AW = available water (defined below),
MB = minimum allowable balance, and
 | |
| Figure 6.5. Illustration of latest day (LD) concept. | |
ETf = forecasted daily ET.
The LD concept is illustrated in Figure 6.5.
For non-layered soils,
AW = (?v– ?wp)Rd (6.12)
or AW = fr(AWC)Rd (6.12b)
or AW = fr(TAW) (6.12c)
For layered soils,
AW = (?v1– ?wp1)(t1) + (?v2– ?wp2)t2 + ... + (?vn – ?wpn) [Rd–(t1 + t2 + ...+ tn-1)] (6.13)
where: ?v1, ?v2, ?vn, ?wp1, ?wp2, ?wpn = volumetric water content of soil layer 1, 2, and n, respectively, numbered from the surface layer down;
t1, t2, tn-1= thickness of soil layers 1, 2, and n–1, respectively; and
n = the number of soil layers that contain roots.
It is convenient to combine Equations 2.12 and 2.14 to obtain:
SWD = fd (TAW) (6.14)
Another useful conversion is that
TAW = AW + SWD (6.15)
In Example 6.3, the irrigation system should water this location in the irrigated area within 2 days to prevent plant stress. If it will take 3 days to get there, irrigation will be 1 day late. Usually, a beginning or start position and an ending or stop position is designated within the irrigated area. A record should be kept of each position so that irrigation occurs before AD is exceeded at either position. An example of the starting and ending position for a center pivot system is illustrated in Figure 6.6.
 | |
| Figure 6.7. Illustration of the earliest date (ED) for irrigation concept. |
 |
Figure 6.6. Location of beginning and ending positions for a center pivot irrigation system. |
Another goal is not to irrigate too soon, i.e., not before the earliest date (ED). To avoid deep percolation there must be room in the root zone to store the planned effective depth of water, dep. In addition, in humid and semi-humid regions, it is good management to allow room in the soil profile for storing rainfall that might occur immediately following the irrigation. This is called the rainfall allowance, ra. ED is calculated as:
(6.16)
(6.17)
The ED concept is illustrated in Figure 6.7.
The concepts of TAW, MB, AW, AD, and SWD and how they change with time for an annual crop are shown in Figure 6.8. Note that one goal of irrigation scheduling is to keep the AW between TAW and MB.
 | Figure 6.8. Illustration of key irrigation scheduling terms and their changes with time for annual crops. |
 | Figure 6.9. Additions and subtractions from the plant root zone (adapted from Cassel, 1984). |
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:
SWDi = SWDi-1 + ETi-1 – de i-1 – Pe i-1 – Uf i-1 (6.18)
where: SWDi = SWD on day i,
SWDi-1= SWD on day i-1
ETi-1 = evapotranspiration on day i-1
de i-1= effective irrigation on day i-1,
Pe i-1 = effective precipitation on day i-1, and
Uf i-1 = upward flow of groundwater from a shallow water table on day i-1.
In available water balance form, Equation 6.18 is:
AWi = AWi-1 – ETi-1 + dei-1 + Pei-1 + Ufi-1 (6.19)
where: AWi = water balance on day i and
AWi-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 dLQ i-1(infiltrated irrigation depth) < SWDi-1then dei-1 = dLQi-1(6.20)
if dLQ i-1> SWDi-1then dei-1 = SWDi-1(6.21)
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 | dough | September 1 | |||||
| 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.
 |
| Figure 6.10. Upward flow of water from a groundwater table (modified from Dorrenbos and Pruitt, 1977). |
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.
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 fdc.
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:
SWDi = SWDi-1 + ETi-1 – de i-1 – Pe i-1 – Uf i-1 + ?SWDi-1 (6.22)
(6.23)
where: ?SWDi-1 = change in SWD due to the additional root depth (?Rd) and
fdo= initial fd in the new layer of soil explored by roots.
The modified Equation 6.19 is:
AWi = AWi-1 – ETi-1 + dei-1 + Pei-1 + Ufi-1 + ?AWi-1 (6.24)
(6.25)
where: ?AWi-1 = added available water due to the root zone expansion and
fro = 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 off-season 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. |
6.4.2 Simplified Checkbook Method
A major limitation to the checkbook accounting procedure has been the lack of reliable real time ET data. This has largely been overcome with the advent of automated weather station networks. Weather data from these stations are used to calculate crop ET on a continuous basis. Now with the easier availability of ET data, the biggest problem is estimation of effective irrigation depths. Water measurement is key. Once the water is measured, effective depths can be determined using the techniques described in Chapter 5.
The checkbook accounting procedure requires daily record keeping. This has slowed its acceptance. Computer software eliminates the need to manually perform the daily calculations, but keeping records is still necessary except when all sensors are electronic and data can be transmitted from remote locations directly to computers or hand-held smart devices.
One way that irrigators apply the ET data without daily recording is to simply irrigate when the effective depth has been consumed (Equation 6.9). For example, if ET is 0.25 inches per day and the effective depth is 0.75 inches per application, irrigation must be applied every 3 days. Thus, the water manager is reacting to the amount of water applied and ET. To adjust for rainfall, irrigation can be delayed in accordance with how long it will take to consume the rainfall. If a 0.5-inch rainfall occurs, the irrigation schedule should be delayed 2 days (assuming that you weren’t behind with irrigation before the rainfall occurred and all of the rainfall was effective in satisfying ET).
Another simple checkbook accounting approach is to adjust the effective depth of application according to the amount of ET and rainfall that has occurred over some pre-established time interval. Suppose weekly irrigations are desired. Then the ET and effective precipitation is summed for the time interval. The effective irrigation needed is then equal to the accumulated ET minus the accumulated effective precipitation or
de= ?ET – ?Pe (6.26)
A drawback to the two “simpler” checkbook accounting approaches discussed above is that the water applications lag behind the time of the water use. On soils with low AWC and/or for plants with shallow root zones, the lag may cause some water stress before water is applied.
6.4.3 Soil Water Measurement Method
An alternative, or supplement, to the checkbook accounting method is to measure soil water directly for irrigation scheduling. In concept, it is quite simple. Rather than predicting or calculating SWD, the SWD is inferred from measures of fr, fd, ?m, ?v, or soil water tension. Once SWD or AW is determined, then Equations 6.10 or 6.11 and 6.16 or 6.17 are used to calculate the LD and ED for the location where the measurements were taken. The soil water content must be measured throughout the entire plant root zone. Samples or measurements at 1-foot intervals are usually adequate. If a 3-foot root zone is to be sampled, then sensors could be placed at 6, 18, and 30 inches, respectively, and each sensor would represent a 1-foot interval.
| Table 6.5. Example SWD versus tension for selected soil textures in Nebraska. | ||||
| Tension (cb) | Fine Sand | Loamy Sand | Sandy Loam | Fine Sandy Loam |
| Fraction Depleted (in/in) | ||||
| 0 | 0.000 | 0.000 | 0.000 | 0.000 |
| 10 | 0.008 | 0.000 | 0.000 | 0.000 |
| 20 | 0.025 | 0.025 | 0.025 | 0.017 |
| 30 | 0.042 | 0.033 | 0.042 | 0.042 |
| 40 | 0.050 | 0.042 | 0.050 | 0.058 |
| 50 | 0.054 | 0.050 | 0.058 | 0.067 |
| 60 | 0.058 | 0.058 | 0.067 | 0.083 |
| 70 | 0.067 | 0.067 | 0.071 | 0.092 |
| 80 | - | - | 0.075 | 0.100 |
| AWC (in/in) | 0.083 | 0.092 | 0.117 | 0.150 |
Techniques such as feel and appearance, gravimetric sampling, neutron scattering, and TDR measure water content directly (Chapter 2). Water contents can be used in the LD and ED calculations, just as was done by checkbook accounting in Example 6.5. When soil water potential (soil water tension) is measured, such as with tensiometers, granular matrix sensors, or electrical resistance blocks, a soil water release curve is needed to convert tension to volumetric water content. This is essentially a local calibration. The soil water release curve is not easily determined. Land-grant universities and government agencies, such as the Natural Resources Conservation Service, can provide release curves that represent the soils in question. An example of data used for converting tension to SWD for general soil texture classifications in Nebraska is shown in Table 6.5. More detailed data are provided by Irmak et al. (2016) and Melvin and Martin (2018). The use of soil water sensing to schedule irrigations is illustrated in Example 6.7.
| Table 6.6. Example threshold soil water tensions for irrigation scheduling based on fdc= 0.35. | |
| Texture | Threshold Tension (cb) |
| Fine sand | 20 |
| Loamy sand | 25 |
| Sandy loam | 35 |
| Fine sandy loam | 45 |
| Silt loam | 80 |
| Clay loam | 80 |
An alternative to converting soil water tension to water content is to monitor the soil water sensors frequently and irrigate when the soil water tension has reached a “threshold level” (Irmak et al, 2016) In fact, manufacturers of soil water sensing equipment often provide the users with guidelines for these threshold levels for various crops and soil textures. They are usually based on sensing near the vertical center of the root zone. Example thresholds are given in Table 6.6. One problem with this approach is that it is difficult to predict ahead to determine the LD. This is overcome by more frequent monitoring. Graphical extrapolation, as shown in Figure 6.13, can be used to lessen the frequency of monitoring. The graphical method provides a good visual record of soil water variations during the season. A limitation of the threshold level method is that the irrigator does not know how much water the soil can hold during each irrigation.
A list of questions to consider when selecting a soil water monitoring system, including sensors, communications, and data storage, has been provided by ITRC (2019).
 |
| Figure 6.13. Graphical method of predicted date of irrigation. |
An important, and often frustrating, consideration is the number of locations that must be sampled to reliably estimate the average soil water condition within the area of interest. You must not only consider the spatial variability of the soil itself, but also the spatial variability of water application from the irrigation system. A minimum of four locations should be sampled in a large, irrigated area that has “relatively” uniform soils and slopes. It is often good to sample stress-prone areas (low AWC and/or shallower root zone), areas where infiltration is low (steeper slopes, etc.), areas where water applications are low due to the inherent nature of the system (e.g., the downstream end of furrow irrigated fields), or where ET is the highest (e.g., nonshaded and wind exposed areas within a landscape). Do this only if the stress-prone area represents a “significant” portion of the irrigated area. Using checkbook accounting in conjunction with the soil water sensing method reduces the number of locations that must be sampled. Another method, which can greatly reduce the uncertainty of ?v data from sensors, is to monitor and manage trends in SWD instead of ?v or AW (Singh et al., 2020). In this method, SWD and AD should be calculated using the observational FC (FCobs) for the specific sensor and location, which is determined from the trend in the sensor data when the field is approaching FC conditions (e.g., at the beginning of the season after the profile becomes saturated and ET is low). In this way, much of the uncertainty from the sensor and spatial variability cancels out during the calculation:
SWD = (?FC,obs – ?v)Rd
6.5 Scheduling Using Plant Status Indicators
The emphasis of this chapter has been on management of the soil water reservoir. While soil water management has been successfully employed for irrigation scheduling, it does not directly evaluate all of the factors influencing plant response to water. As pointed out by Jones (2004) plants actually respond directly to change in water status in the plant tissues, whether in the roots or in other tissues, rather than to changes in soil water status. The plant response to a given soil water content varies as evaporative demand varies. Plant status indicators integrate all of the important factors, i.e., soil water conditions, atmospheric demand for water, and plant characteristics. All three factors are taken into account to a degree by selecting the appropriate fdc as suggested by Doorenbos and Kassam (1979) and presented in Table 6.1. Direct measures or indicators of plant water status are often suggested for irrigation scheduling. Jones (2004) presents a good overview of plant-based methods for irrigation scheduling. A few of these are discussed below.
 |
| Figure 6.14. Water potentials expected at different points of the pathway for water transport through a wheat plant growing in soil at a potential of -0.1 bars and in an atmosphere with a potential of -900 bars (adapted from Turner and Burch, 1983). |
6.5.1 Leaf Water Potential
Turner (1990) and Stegman (1983) discussed the use of plant water status indicators for irrigation scheduling. Leaf water potential, a measure of the energy status of the water in a plant leaf, is an indicator of the water status of a plant. Figure 6.14 shows the relationship between the various potentials in the soil plant atmosphere continuum. Instruments used to measure leaf water include pressure chambers and thermocouple psychrometers. Stegman (1983) found that threshold levels of leaf water potential ranged from –12 to –12.5 bars for corn (midafternoon readings). The thresholds were dependent on ambient temperatures much like fdc is dependent on ET.
While leaf water potential is a direct measure of plant water status, using it as a scheduling tool has some limitations. Threshold levels must be developed for the plants in question. Also, like using threshold levels of soil water potential, it lacks in predictability. Third, measuring leaf water potential is time-consuming and must be done during a narrow time window during midday. A large number of samples are necessary for an accurate estimation of the mean.
6.5.2 Plant Canopy Temperature
Since evaporation of water is a cooling process, the foliage of well-watered plants is usually cooler than the surrounding air, especially in arid climates. Plants that are experiencing water stress will have higher leaf temperatures than well-watered plants. With the advent of infrared thermometry, it is relatively easy to measure canopy temperature (Lo et al., 2018; Figure 6.15). In general, two approaches have been developed to use canopy temperature in irrigation scheduling, the crop water stress index method (CWSI) and the time-temperature-threshold (TTT) method.
The temperature difference (DT) between the air and the plant canopy depends on both the plant water status and the vapor pressure deficit (VPD). Jackson (1982) presented an excellent overview of plant water stress response to DT and VPD. Jackson et al. (1981) developed the CWSI method for quantifying plant stress. It relies on baseline values of canopy temperature of non-transpiring reference and a non-stressed canopy. Crop yield can then be related to CWSI as illustrated by Irmak et al. (2000). To apply this technique the base-line or reference lines must be established. Jackson (1982) suggested that the CWSI will be a very useful tool for irrigation scheduling because it is easy to use handheld infrared thermometers for measuring canopy temperature. He points out some of the problems, such as the effects of bare soil in the field of view and the establishment of the threshold stress indicators for various crops or plants. As pointed out by Stegman (1983), the effect of wind and cloud cover on the interpretation of DT data and how it relates to irrigation management must be considered.
 |
| Figure 6.15. Diagram of a hand-held infrared thermometer. |
Another way of using canopy temperature in irrigation scheduling is the time-temperature-threshold method. Wanjura et al. (1995) defined TTT as “the amount of time accumulated above a specific temperature in one day by a crop.” If the time-temperature value exceeds a threshold, a temperature stress exists and irrigation is needed. Peters and Evett (2008) successfully automated the irrigation scheduling of a center pivot irrigation system using the TTT method. They used infrared thermometers mounted on the center-pivot to monitor canopy temperatures as it irrigated the field. The center-pivot was equipped with LEPA drops thus the canopy was not wetted during an irrigation event. The TTT method requires the establishment of both the temperature threshold and the time threshold.
6.5.3 Other Plant Status Indicators
Turner (1990) discussed various other measures of plant water status indicators, including leaf color. With many crops, stressed plants often turn a darker color if soil water stress occurs. This is particularly evident in turfgrass. Bluegrass, for example, will turn to a blue-green color when under stress.
Other plant responses to stress include leaf rolling and wilting. While all of these visual techniques are useful, many often appear too late to be useful for water management. Significant yield and economic losses may have already occurred. Prediction is still a problem for these techniques.
6.5.4 Stage of Plant Development
Often you will hear that irrigating at critical stages of plant growth is a good way of scheduling. In fact, many of the Extension publications have been written on this concept. While the method has merit, local calibration is necessary to account for soil crop climate conditions.
6.6 Variable Rate Irrigation Management
Variable rate irrigation (VRI) or precision irrigation technology allows for spatial management of soil water. The irrigation prescription map determines the application depth throughout the field, which can be varied spatially to account for spatial variability in soils, ET, and topography.
One option for VRI is to utilize the stored soil water in heavier soils by not irrigating them at the beginning of the season (Miller et al., 2018). Soils with lower AWC will need to be irrigated before soils with a larger AWC if all parts of the field begin the season at the same soil water depletion level (e.g., if the field starts at field capacity). An example prescription map based on this approach is shown in Figure 6.16. This particular prescription map would need to be used twice in order to mine the water from the heavier soils. After that, the soil water deficit would equal AD in each irrigation management zone, and uniform irrigation could be used to replace ET. One study estimated that 13% of center pivot irrigated fields in Nebraska could reduce pumping by at least one inch by using VRI to account for spatial variation in AWC (Lo et al., 2016). It is recommended that soil water sensors be placed in each irrigation management zone.
  |
| Figure 6.16. Map of spatial variability in total available water (left) and the corresponding irrigation prescription map (right). |
VRI can also be used to manage problems associated with topography, e.g. applying less water in a low spot that tends to be wet from accumulated runoff. Prescription maps for VRI are often based on soil maps and yield maps (Kranz et al., 2014). Soil properties can be correlated to apparent electrical conductivity (ECa), elevation, or other topographic indices. Prescription maps can include an “avoidance zone” for waterways (Figure 6.16), other non-cropped areas, or low spots where the pivot tends to get stuck. This feature allows producers to utilize chemigation on fields with a waterway, where regulation would prevent application of chemical on a surface water body.
Remote sensing data, whether from satellite or unmanned aircraft, can also be used to inform variable rate irrigation management (Chavez et al., 2020). Data may indicate an area of the field that is under stress and requires special attention. Remote sensing can also be used to quantify the spatial variability of ET in a field. Ongoing development in sensors, big data, communications (e.g., internet of things), decision support systems, and computational intelligence will allow for more advanced management of irrigation systems as a part of precision agriculture (Evett et al., 2020).
6.7 Summary
Irrigation scheduling refers to the timing and amount of irrigation water applications. By accounting for or measuring soil water and by knowing plant water needs, the goals of good irrigation scheduling can be accomplished; production goals can be met with minimum water. By minimizing water applications, deep percolation of water and chemicals is minimized and energy is saved.
Two important concepts in scheduling are: the latest date (LD) and the earliest date (ED). By irrigating on or before the LD, plant water stress is avoided. By waiting, at least until the ED, deep percolation losses are avoided or minimized. Built into the ED is an allowance for storing rainfall in the soil, an important consideration in semiarid and subhumid regions.
Scheduling according to soil water content can be achieved using checkbook accounting, which considers the deposits to the soil water reservoir (rainfall and irrigation) and also considers withdrawals from the soil water reservoir (ET and drainage). An alternative to checkbook accounting is to directly measure soil water content.
Another scheduling option is to irrigate in response to plant water status. Plant water status is an integrator of soil water, plant characteristics, and weather conditions. Several plant water status methods are available including measuring leaf water potential and measuring the canopy temperature. Canopy temperature can be used in the crop water stress index method or the threshold-time-temperature method to schedule irrigations.
Variable rate irrigation (VRI) allows for spatial management of soil water by accounting for variability in soils within a field. Besides being able to irrigate according to the spatial distribution of soils, an additional advantage of VRI is the opportunity to create “avoidance zones” in a field where water or chemigation applications are not desirable.
Questions
1. Explain why irrigation water does not have to be applied on exactly the same day that the AD is reached.
2. How do soil texture and plant rooting depth influence the frequency and amount of irrigation?
3. Explain why fdc is affected by ET.
4. What is the maximum desired depth of infiltration during an irrigation? Why?
5. Explain why infiltration often exceeds the maximum desired amount of infiltration. Does the uniformity of irrigation influence the amount of excessive irrigation?
6. Develop the water balance (AW) equivalent to Example 6.5.
7. Which do you prefer, the SWD approach or AW approach to the checkbook accounting method? Why?
8. Tensiometers where used in a field for estimating soil water depletion. The beginning position and the ending position of the irrigation system were sampled.
a. Determine the latest and the earliest dates for both positions given the following information:
| Layer (in) | Tensiometer Depth (in) | Tension | Root depth = 3 ft Forecast ETc = 0.30 in/d Soil type = fine sandy loam AWC = 0.15 in/in Effective irrigation depth = 1 in Rainfall allowance = 0.5 in fdc = 0.55 | ||
| Beginning Position (cb) | Ending Position (cb) | ||||
| 0–12 | 6 | 40 | 35 | ||
| 12–24 | 18 | 45 | 10 | ||
| 24–36 | 30 | 25 | 35 | ||
b. If the irrigation cycle time is 3 days, when would you recommend that the system be started and why?
9. The layers of a Hastings silt loam (Hc) are described below (taken from Soil Survey of Clay County).
| Depth(in) | Texture | AWC(in/in) | Bulk Density(g/cm3) |
| 0–10 10–38 38–60 | silt loam silty clay loam silt loam | 0.22–0.24 0.11–0.20 0.18–0.22 | 1.20–1.40 1.30–1.40 1.20–1.40 |
If tomato roots are 48 inches deep, determine:
a. Total available water (TAW) in inches
b. AD (in inches) assuming that ETc = 0.24 in/d
c. MB (in inches) assuming that ETc = 0.24 in/d
d. The maximum interval between irrigation (TMAX) in days
10. Tensiometers are used in a loamy sand. Readings are taken as follows:
| Tension (cb) | |
| July 2 July 4 July 6 | 10 12 18 |
a. Using the graphical procedure (Figure 6.13), predict the date when irrigation will be needed.
b. If the root zone is 36 inches deep, at what depth should the tensiometer(s) be placed?
c. Discuss the pros and cons to this approach of scheduling.
11. Rework Example 6.6 given the following data:
| Day | Crop ET (in/d) | Pe(in) |
| Sunday Monday Tuesday Wednesday Thursday Friday Saturday | 0.25 0.35 0.15 0.30 0.15 0.30 0.20 | - 0.70 0.10 - - - - |
12. If crop ET for the previous four days was 0.35, 0.20, 0.30, and 0.15 in/d and the effective depth of water applied per irrigation is 1.25 inches, how often should you irrigate? If a 0.75-inch rainfall occurs during this schedule, how many days can the system be left idle before it is restarted?
13. Site, crop, weather, and irrigation data are for a field area given below. Using the checkbook accounting approach, develop an irrigation schedule for July 1-14 for both the start position and the stop position. Do the ED and LD calculations on July 1 and July 8. For this 2-week period, tell us when the beginning and ending positions would be irrigated (keep in mind how fast the system can get to each point). Assume that on July 1, the system is in the start position.
| Crop: Corn | Irrigated area: 136 ac |
| Emergence date: 4/28 | Gross depth applied: 1.0 in |
| Effective cover date: 7/10 | Cycle time (Tc): 3 d |
| Date of maximum root depth: 8/1 | ELQ: 85% |
| Maximum allowable depletion fdMAX: 0.50 | Allowance for storing rainfall: 0.5 in |
| AWC: 0.18 in/in System capacity: 850 gpm | fr on 7/1 in the root zone: 0.70 (both positions) |
| Forecasted ET: 0.25 in/d | frbelow the root zone: 1.0 |
| Date | Crop ET (in/d) | Rain (in) | Root Depth (in) |
| 7/1 | 0.31 | ||
| 2 | 0.18 | 0.15 | 30 |
| 3 | 0.21 | ||
| 4 | 0.20 | ||
| 5 | 0.25 | ||
| 6 | 0.36 | ||
| 7 | 0.22 | ||
| 8 | 0.25 | 33 | |
| 9 | 0.23 | ||
| 10 | 0.20 | 0.78 | |
| 11 | 0.26 | ||
| 12 | 0.22 | ||
| 13 | 0.35 | ||
| 14 | 0.23 |
References
Cassel, D. K. (1984). Irrigation scheduling I. Crop and soil parameters. Crops Soils (Feb.), 16-20.
Chavez, J. L., Torres-Rua, A. F., Woldt, W. E., Zhang, H., Robertson, C. C., Marek, G. W., Wang, D., Heeren, D. M., Taghvaeian, S., & Neale, C. M. U. (2020). A decade of unmanned aerial systems in irrigated agriculture in the Western U.S. Appl. Eng. Agric., 36(4), 423-436.
Dorrenbos, J., & Kassam, A. H. (1979). Yield response to water. FAO Irrigation and Drainage Paper. 33, 1-193. Rome, Italy: United Nations FAO.
Dorrenbos, J., & Pruitt, W. J. (1977). Guidelines for predicting crop water requirements. FAO Irrigation and Drainage Paper. 24, 1-144. Rome, Italy: United Nations FAO.
English, M. J., Musick, J. T., & Murtz, V. V. (1990). Deficit irrigation (Ch. 17). In G. J. Hoffman, T. A. Howell, & K. H. Solomon (Eds.), Management of farm irrigation systems. St. Joseph, MI: ASAE.
Evett, S. R., O'Shaughnessy, S. A., Andrade, M. A., Kustas, W. P., Anderson, M. C., Schomberg, H. S., & Thompson, A. (2020). Precision agriculture and irrigation: Current U.S. perspectives. Trans. ASABE, 63(1), 57-67.
Fischbach, P., & Somerhalder, B. (1973). Programmed soil moisture depletion. NebGuide G73-58. Nebraska Cooperative Ext. Service, University of Nebraska-Lincoln.
Irmak, S., Haman, D. Z., & Bastug, R. (2000). Determination of crop water stress index for irrigation timing and yield estimation of corn. Agron. J., 92(6), 1221-1227.
Irmak, S., Payero, J., VanDeWalle, B., Rees, J., Zoubek, G., Martin, D., Kranz, W., Eisenhauer, D., & Leininger, D. (2016). Principles and operational characteristics of Watermark granular matrix sensor to measure soil water status and its practical applications for irrigation management in various soil textures. EC 783. University of Nebraska-Lincoln Ext.
ITRC. (2019). Irrigation Consumer Bill of Rights: Soil and plant moisture monitoring systems. ITRC Report No. R 19-004. San Luis Obispo, CA: Irrigation Training and Research Center, California Polytechnic State University.
Jackson, R. D. (1982). Canopy temperature and crop water stress. In D. Hillel (Ed.), Advances in irrigation (Vol. 1, pp. 43-85). New York, NY: Academic Press.
Jackson, R. D., Idso, S. B., Reginato, R. J., & Pinter Jr., P. J. (1981). Canopy temperature as a crop water stress indicator. Water Resour. Res., 17(4), 1133-1138.
Jones, H. G. (2004). Irrigation scheduling: advantages and pitfalls of plant-based methods. J. Exp. Bot., 55(407), 2427-2436.
Kranz, W. L., Irmak, S., Martin, D. L., Shaver, T. M., & van Donk, S. J. (2014). Variable rate application of irrigation water with center pivots. University of Nebraska-Lincoln Ext. Circular EC2000.
Lo, T., Heeren, D. M., Martin, D. L., Mateos, L., Luck, J. D., & Eisenhauer, D. E. (2016). Pumpage reduction by using variable-rate irrigation to mine undepleted soil water. Trans. ASABE, 59(5), 1285-1298.
Lo, T., Rudnick, D. R., Ge, Y., Heeren, D. M., Irmak, S., Barker, J. B., Qiao, X., & Shaver, T. M. (2018). Ground-based thermal sensing of field crops and its relevance to irrigation management. NebGuide G2301, University of Nebraska-Lincoln Ext.
Martin, D. L., Stegman, E. C., & Fererer, E. (1990). Irrigation scheduling principles. In G. J. Hoffman, T. A. Howell, & K. H. Soloman (Eds.), Management of farm irrigation systems. ASAE Monograph. St. Joseph, MI: ASAE.
Melvin, S. R., & Martin, D. L. (2018). Irrigation scheduling strategies when using soil water data. EC 3036. University of Nebraska-Lincoln Ext.
Melvin, S. R., & Yonts, C. D. (2009). Irrigation scheduling: Checkbook method. EC 709. University of Nebraska-Lincoln Ext.
Miller, K. A., Luck, J. D., Heeren, D. M., Lo, T., Martin, D. L., & Barker, J. B. (2018). A geospatial variable rate irrigation control scenario evaluation methodology based on mining root zone available water capacity. Precis. Agric., 19(4), 666-683.
Peters, R. T., & Evett, S. R. (2008). Automation of a center pivot using the temperature-time-threshold method of irrigation scheduling. J. Irrig. Drain. Eng., 134(3), 286-291.
Singh, J., Heeren, D. M., Rudnick, D. R., Woldt, W. E., Bai, G., Ge, Y., & Luck, J. D. (2020). Soil structure and texture effects on the precision of soil water content measurements with a capacitance- based electromagnetic sensor. Trans. ASABE, 63(1), 141-152.
Skaggs, R. W., Fausey, N. R., & Nolte, B. H. (1981). Water management model evaluation for North Central Ohio. Trans. ASAE, 24(4), 922-928.
Stegman, E. C. (1983). Irrigation scheduling: Applied timing criteria. In D. Hillel (Ed.), Advances in irrigation (Vol. 2, pp. 1-30). New York, NY: Academic Press.
Trout, T. J., Howell, T. A., English, M. J., & Martin, D. L. (2020). Deficit irrigation strategies for the Western U.S. Trans. ASABE, 63(6), 1813-1825.
Turner, N. C. (1990). Plant water relations and irrigation management. Agric. Water Manag., 17(1), 59-73.
Turner, N. C., & Burch., G. J. (1983). The role of water in plants. In I. D. Teare, & M. M. Peet (Eds.), Crop water relations (pp. 73-125). New York, NY: John Wiley & Sons.
Wanjura, D. F., Upchurch, D. R., & Mahan, J. R. (1995). Control of irrigation scheduling using temperature-time thresholds. Trans. ASAE, 38(2), 403-409.