Crop Water Use and Crop Coefficients of Maize in the Great Plains

Increased water requirements for growing populations and environmental restoration, along with declining groundwater supplies, will result in reduced water supply for irrigated agriculture in the western United States and many semiarid areas of the world. However, the productivity of irrigated agriculture must be sustained and increased to meet increasing global food needs. Thus, irrigated agriculture must become more productive with reduced water supplies.

Efficient irrigation water use depends on correct irrigation scheduling to meet, but not exceed, crop water requirements. A common way to predict crop water requirements for irrigation scheduling is the two-step method described in Food and Agriculture Organization of the United Nations Irrigation and Drainage Paper #56 (FAO-56) (Allen et al. 1998). This method relates the crop evapotranspiration, ${ET}_c$, to that of a reference crop, ${\mathit{ET}}_{\mathrm{ref}}$, with a crop coefficient, ${\mathit{K}}_{\mathit{c}}$. Accuracy of this methodology is improved by use of a dual crop coefficient (Allen et al. 1998), in which the crop coefficient ${\mathit{K}}_{\mathit{c}}$ is partitioned into a basal crop coefficient, ${\mathit{K}}_{\mathit{cb}}$, and a wet soil evaporation coefficient, ${\mathit{K}}_{\mathit{e}}$. The basal crop coefficient includes plant transpiration from a nonstressed crop and slow diffusive evaporation through a dry soil surface. When soil water availability or plant hydraulics is inadequate to meet the atmospheric evaporative demand, actual transpiration is decreased and ${\mathit{K}}_{\mathit{cb}}$ is multiplied by a stress coefficient to predict the resulting reduced transpiration.

Reference ET is calculated from weather parameters that are used to predict energy transfers at the crop surface. Two reference crops are commonly used: a short 0.12-m grass surface and a tall 0.5-m alfalfa surface. Although use of the grass reference, ${\mathit{ET}}_{\mathit{o}}$, is more common worldwide for a wide variety of crops, the taller alfalfa reference better describes the midseason ${\mathit{ET}}_{\mathit{c}}$ of many annual field crops (Wright and Jensen 1972; Jensen and Allen 2016) and is commonly used in the Great Plains of the United States.

Crop coefficients are derived by careful measurement of the ${\mathit{ET}}_{\mathit{c}}$ of a nonstressed crop and comparing the crop ${\mathit{ET}}_{\mathit{c}}$ with the ${\mathit{ET}}_{\mathrm{ref}}$ over the same time period

${\mathit{ET}}_{\mathit{c}}$ is commonly measured by water balance (WB) techniques either in lysimeters or open fields through careful measurement of water inputs (precipitation and irrigation) and of soil water content changes. Weighing lysimeters are precise tools to measure ${\mathit{ET}}_{\mathit{c}}$ over short time intervals. Allen et al. (2011a, b) described factors important in measuring and reporting ${\mathit{ET}}_{\mathit{c}}$ data. The authors follow those guidelines in this paper.

Doorenbos and Pruitt (1977) in FAO Irrigation and Drainage Paper #24 published the first comprehensive set of ${\mathit{ET}}_{\mathit{o}}$-based crop coefficients based partially on weighing lysimeter measurements made in Davis, California. These ${\mathit{K}}_{\mathit{c}}$ values were updated in FAO-56 based on the Penman-Monteith combination equation for a grass reference. The dual crop coefficient method was also presented in FAO-56, which presented ${\mathit{K}}_{\mathit{cb}}$ values for many crops. Wright (1982) presented new crop coefficients measured in weighing lysimeters in Idaho based on an alfalfa-reference crop. Allen et al. (2007) and Jensen and Allen (2016) in ASCE Manual of Practice #70 (MOP #70) presented lists of ${\mathit{K}}_{\mathit{c}}$ and ${\mathit{K}}_{\mathit{cb}}$ values based mainly on the Wright data but adapted to the ASCE Standardized Penman-Monteith equation for an alfalfa reference (ASCE 2005). The maize crop coefficients measured in this study will be compared with values presented in these publications.

Many maize water use studies have been carried out in the western United States (Wright 1982; Stegman 1988; Steele et al. 1996; Nielsen and Hinkle 1996; Howell et al. 1997, 1998, 2006; Suyker and Verma 2009; Piccinni et al. 2009; Payero and Irmak 2011; Djaman and Irmak 2013), China (Li et al. 2003; Kang et al. 2003; Parkes et al. 2005; Zhao et al. 2013; Zhang et al. 2013), India (Tyagi et al. 2003), Portugal (Rosa et al. 2012), and Brazil (Martins et al. 2013). Most of these studies report single crop coefficient values based on a grass reference. Howell et al. (2006) and Djaman and Irmak (2013) measured maize alfalfa-reference ${\mathit{K}}_{\mathit{c}}$ values in Bushland, Texas, and south-central Nebraska, respectively. Recent studies in Portugal, China, and Brazil estimated ${\mathit{K}}_{\mathit{cb}}$ values for maize based on grass reference using the SIMDualKc model (Rosa 2011; Rosa et al. 2012; Zhao et al. 2013; Zhang et al. 2013; Martins et al. 2013).

There remains a need for additional data on standardized alfalfa-reference basal crop coefficients, including methods to adjust crop coefficients for temporal variation, for current high-yield maize varieties and for varying cultural practices. In 2008, the USDA-ARS Water Management Research Unit in Fort Collins began a field study of the water use of maize under a range of irrigation levels. The objective of this paper is to present ${\mathit{ET}}_{\mathit{c}}$ and alfalfa- and grass-based ${\mathit{K}}_{\mathit{cb}}$ values from 6 years (2008–2013) of fully irrigated maize from the study.

Table 1 shows maize growth stages (Abendroth et al. 2011) for each year of the study. The crop was planted in early May each year, reached the R1 growth stage (tassel and silk formation) between 83 and 90 days after planting (DAP), reached the R6 growth stage (physiological maturity) 140–156 DAP, and reached full senescence (usually by killing frost) 145–160 DAP. Table 1 also shows these stages in terms of maize growing degree days (GDD) since planting [10°C min, 30°C max; MOP #70, Eq. (F1)]. Grain yields (15.5% grain moisture content) were 13.2, 12.1, 11.2, 13.6, 15.5, and $15.0\mathrm{Mg}{\mathrm{ha}}^{-1}$ for 2008–2013, respectively, and averaged about 20% higher than the county average yield for irrigated maize (USDA-NASS 2015). In 2009, a hail event just before the R1 stage [day of year (DOY) 210] damaged leaves and reduced the horizontal canopy structure, and may have reduced ET slightly.

Fig. 2 shows the measured SWD and the estimated readily available water (RAW) in the developing root zone in 2011. The RAW was estimated to be 55% of TAW (27.5% of field capacity) and increased as the root zone depth increased from 5 to 105 cm. The figure also shows the predicted SWD from the modeled water balance. The SWD fluctuated between 0 and 50 mm and did not exceed the RAW limit (dashed line) at any time during the season, or at any time during the 6-year study except in 2010 at the end of the season (after DOY 246) when irrigation was terminated too early. Soil water measurements indicated very little water uptake below a 45-cm depth, as would be expected with well-scheduled, frequent drip irrigation.

Table 2 shows the seasonal water balance components for each year. Precipitation during the growing season was near the long-term average for the location (215 mm) each year except 2012. For this location, seasonal ${\mathit{ET}}_{\mathit{r}}$ exceeded ${\mathit{ET}}_{\mathit{o}}$ by 20–25%, which is similar to ${\mathit{ET}}_{\mathit{r}}/{\mathit{ET}}_{\mathit{o}}$ ratios measured in the central Great Plains by Djaman and Irmak (2013) and Payero and Irmak (2011). Seasonal irrigation applications varied from 366–664 mm to meet crop water requirements and prevent the soil water deficit from exceeding the readily available water. Seasonal change in soil water storage in the root zone varied depending on the amount of early- and late-season precipitation. Deep percolation was predicted to have occurred only in 2008 when a large multiday precipitation event followed an irrigation. Seasonal ${\mathit{ET}}_{\mathit{c}}$ averaged 666 mm or 68% of seasonal ${\mathit{ET}}_{\mathit{r}}$ and 82% of seasonal ${\mathit{ET}}_{\mathit{o}}$. The portion of ${\mathit{ET}}_{\mathit{c}}$ lost to surface evaporation was estimated to be about 10%. More than 75% of the estimated surface evaporation was from early- and late-season precipitation events and less than 20% derived from drip irrigation.

Fig. 3 shows the daily ASCE Standardized alfalfa-reference ${ET}_r$ for the 2011 crop and the daily crop ${ET}_c$ calculated from the two-step dual crop coefficient approach, in which the $K_{cb}$ value was calibrated to fit the water balance measurements. The graph shows typical daily fluctuations in midseason daily ${ET}_r$ that typically range from 6 to $10\mathrm{mm}{\mathrm{d}}^{-1}$ for the region, and ${ET}_c$ values that closely match ${ET}_r$ midseason but are less than ${ET}_r$ at the beginning and end of the season, except following precipitation events that wet the soil surface and result in high soil evaporation.

In 2008, 2010, and 2012, the ${ET}_c$ from an adjoining drip-irrigated maize field was measured with a BREB system. Fig. 4 shows the comparison of the cumulative ${ET}_c$ measured by the BREB system and the water balance–measured ${ET}_c$ from the plots. In 2008 and 2012, water balance ${ET}_c$ exceeded BREB ${ET}_c$ in the adjoining field, with a seasonal difference of 7%. This difference likely resulted from minor stress in the BREB field due to less frequent and less total irrigation applications than the plots. In 2010, water balance ${ET}_c$ was slightly less than BREB ${ET}_c$ in the first half of the season, but slightly greater in the second half of the season with nearly the same seasonal ${ET}_c$ values.

The maize basal crop coefficient curves derived in this 6-year field study are similar to the standard curves for alfalfa reference from MOP #70 (Jensen and Allen 2016) and for grass reference from FAO-56 (Allen et al. 1998) but exceed the standard midseason value for alfalfa-reference $K_{cb}$ by about 10%. These data indicate an alfalfa-reference midseason $K_{cb}$ value of about 1.05 and a grass-reference value of about 1.22 that continue for about 40 days from about the V14 growth stage (10–15 days before tassel) to a few days before the R4 growth stage. This coincides with the period in which $f_c$ exceeds 0.8. It is not unexpected that maize could have midseason ${ET}_c$ similar to or slightly exceeding that of the alfalfa reference, since it is a taller and aerodynamically rougher crop. It is also likely that current maize cultivars with upright leaf architecture planted at high populations and producing high yields could have slightly higher ${ET}_c$ than those used in the 1976–1977 lysimeter measurements (Wright 1982) on which the MOP #70 crop coefficients are based.

MOP #70 (Table E–1) lists a peak $K_c$ value for maize (field corn) of 1.0, but midseason values decline to 0.98 after 20 days, implying that surface evaporation contributes 2–4% of ETc in the midseason. Howell et al. (2006) estimated midseason $K_c$ values near 1.0 based on 3 years of lysimeter data (1989, 1990, and 1994) from Bushland, Texas. Djaman and Irmak (2013) estimated midseason maize alfalfa-reference $K_c$ values of 1.05 in a 2-year field water balance study in south-central Nebraska. Both of those studies used sprinkler irrigation and did not estimate the wet soil evaporation component, implying that the midseason $K_{cb}$ would be slightly lower than these values. In this study with drip irrigation, estimated midseason soil evaporation was less than 1% of ${ET}_c$, implying that the midseason $K_c$ and $K_{cb}$ values are essentially equal.

The standard alfalfa $K_{cb}$ curve (MOP #70, Table E–2) indicates that the midseason $K_{cb}$ values decline by about 0.7% per day beginning about 25 days after full cover. The AquaCrop model (Raes et al. 2017, Section 3.10.3) assumes that the midseason $K_{cb}$ value for maize declines by 0.3% per day beginning 5 days after full cover because of canopy aging. In these data, a decline in midseason $K_{cb}$ values is not evident until $f_c$ begins to decline about 40 days after full cover.

The midseason grass-reference $K_{cb}$ value in this study is very close to the FAO-56 midseason value (1.15) when adjusted for nonstandard climatic conditions. Several recent studies have measured grass-reference $K_c$ values for maize in the Great Plains of the United States. Reported midseason $K_c$ values were 1.03 (Suyker and Verma 2009), 1.17 (Howell et al. 2006), 1.2 (Piccinni et al. 2009; Payero and Irmak 2011), and 1.26 (Djaman and Irmak 2013). Reported midseason grass-reference $K_c$ values reported in Asia were 1.23 (Tyagi et al. 2003), 1.25 (Parkes et al. 2005), 1.26 (Li et al. 2003), and 1.4 (Kang et al. 2003). Rosa et al. (2012), Zhao et al. (2013), Martins et al. (2013), and Zhang et al. (2013) estimated grass-based midseason basal crop coefficients for maize of 1.05, 1.10, 1.12, and 1.15, respectively, using the SIMDualKc model. The results of many of these studies are difficult to interpret because of the lack of adequate description of the field, climate, and crop conditions and measurement processes. The AquaCrop model uses a crop transpiration coefficient at full cover of 1.05 (Raes et al. 2017).

Because of the field layout and experimental conditions, it is possible that ${ET}_c$ of the maize in this study exceeded the equivalent ${ET}_c$ of uniform, adequately irrigated maize grown in a large uniform field environment. Although the experimental field was located within a predominantly irrigated area with several kilometers of irrigated crops in the predominant fetch direction, the 1-ha maize section was usually adjacent to crops with a shorter height and shorter season. Also, the individual treatment plots used were small ($9\times 44\mathrm{m}$) and randomly located among maize plots that were deficit irrigated to varying degrees. Thus, the fully irrigated maize tended to be somewhat taller than the surrounding crop, possibly resulting in increased effective roughness, and likely experienced slightly higher air temperature and lower relative humidity than would have occurred in a large well-irrigated field. Crop height among the maize irrigation treatments varied from 240 cm for the well-watered maize to 150 cm for the most stressed plots, with an average for the deficit treatments and border plots of 200 cm which is 40 cm shorter than the well-watered plots. The seasonal ${ET}_c$ values of the adjacent and nearby deficit-irrigated and border plots averaged 21% less than that measured in the well-watered plots. Although the soil water measurement location within each plot was surrounded by at least 4 m of similarly irrigated plants, this fetch would not be adequate to completely eliminate border effects due to increased advection (Allen et al. 2011a).

Wet soil evaporation in this study was estimated to be about 10% of seasonal ${ET}_c$, which is low compared to estimates of surface evaporation in several other studies (Zhao et al. 2013; Zhang et al. 2013; Martins et al. 2013; Kang et al. 2003). Although the field study was designed to minimize evaporation with surface residue and in-row drip irrigation, an underestimate of evaporation would result in an overestimate of basal ${ET}_{cb}$ and $K_{cb}$. Because the evaporation component was low when the crop canopy ground cover was high, potential error in midseason $K_{cb}$ due to evaporation would be small.

Some researchers and practitioners feel that crop coefficients must be regionally derived for local climate and management conditions. Although the literature indicates a range of $K_c$ values, the authors are not convinced that variations in midseason alfalfa-reference $K_{cb}$ values are location dependent and must be locally calibrated. As long as local conditions meet the FAO-56 and MOP #70 criteria (vigorous full-cover crop with adequate fetch condition and recommended climatic adjustment), midseason $K_{cb}$ values for most field crops should be transferable among locations.

However, adjustments are often needed for the timescale of the $K_{cb}$ relationship based on local climate and cropping practices (Nielsen and Hinckle 1996). These adjustments are not only regional but also seasonal and may be grower and variety specific. They can be best made through measurements or estimates of crop development. Maize growth and senescence rates vary with variety, climate, season, and management practice. The most difficult aspect of developing appropriate crop coefficient relationships is the timescale. Fig. 6 demonstrates the variability due only to interseasonal differences. Normalizing the time axis based on days from planting to effective full cover (Fig. 7) reduces the interseasonal variability. Use of normalized thermal time (Fig. 8) further reduces interseasonal effects. While normalization can improve the accuracy of crop coefficients when seasonal information is known, this approach cannot be applied to real-time irrigation scheduling during crop development because full cover dates are not known. The largest seasonal weather effect on plant growth in temperate climates is during the early season when low air and soil temperatures may delay germination and emergence by several days. Initiating $K_{cb}$ relationships based on emergence date rather than planting date would further improve $K_{cb}$ estimates.

A better method to estimate $K_c$ relationships is to relate the crop coefficient directly to plant canopy development and senescence. Fractional ground cover correlates well with $K_{cb}$ and these data indicate that this relationship is linear up to an $f_c$ saturation value of about 0.8. Allen and Pereira (2009) and Raes et al. (2017) have proposed that this relationship should be slightly curvilinear (concave downward), although adequate data to support that hypothesis are lacking. Some crop models such as AquaCrop (Raes et al. 2017) and CropSyst (Stöckle et al. 2003) use $f_c$ to estimate $K_{cb}$, whereas many other crop models use leaf area index to estimate solar radiation interception.

The authors believe that $f_c$ is a better parameter to estimate $K_{cb}$ than leaf area index because it is can be estimated visually and measured at multiple scales (e.g., with nadir imaging or remotely sensed vegetation indices) and is linearly related to both $K_{cb}$ and the normalized difference vegetation index (NDVI) for many crops. Increasing availability of satellite and unmanned autonomous vehicle (UAV) imagery makes the use of $f_c$ and vegetation indices a practical operational option to estimate the evolution of $K_{cb}$ relationships (Johnson and Trout 2012).

Adjustments in the soil evaporation component are also necessary to adapt to irrigation method and frequency, precipitation amount and frequency, soil and residue conditions, and plant population and configuration. These adjustments are made through the use of dual crop coefficients. Thus, studies of crop coefficients should derive basal crop coefficients by estimating wet soil evaporation by the same methods that would be used by practitioners to estimate the soil evaporation coefficient.

Six years of field water balance measurements of maize ${ET}_c$ in the Great Plains of the United States indicate that midseason $K_{cb}$ values are 1.05 and 1.22 for alfalfa and grass references, respectively. The standard alfalfa-reference $K_{cb}$ value of 0.96 is likely too low for current varieties and practices. The measured grass-reference value closely matches the standard value after adjustment for aridity. The timescales of the standard $K_{cb}$ curves fit the measured data fairly well but are improved by normalization relative to full cover and use of thermal time. The basal crop coefficient is linearly related to fractional canopy ground cover up to an effective full ground cover of 0.8. This relationship should be used to adapt $K_{cb}$ values for specific conditions and is a better option than regionally specific $K_{cb}$ relationships.

The following symbols are used in this paper:

$DP$

deep percolation loss of soil water below the root zone (mm);

$ET$

evapotranspiration (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

${ET}_c$

crop evapotranspiration (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

${ET}_{cb}$

basal crop evapotranspiration, excluding evaporation from wet soil surface (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

${ET}_o$

short (grass) reference evapotranspiration (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

${ET}_r$

tall (alfalfa) reference evapotranspiration (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

${ET}_{\mathrm{ref}}$

reference evapotranspiration (mm, $\mathrm{mm}{\mathrm{d}}^{-1}$);

$f_c$

crop canopy ground cover;

I

irrigation application (mm);

$K_c$

crop coefficient;

$K_{cb}$

basal crop coefficient;

$K_e$

soil evaporation coefficient;

$P$

precipitation (mm);

$RO$

surface runoff (mm);

$UF$

upflux of water from below the root zone (mm); and

$\mathrm{\Delta }S$

change in soil water storage (mm).

A field study of this scope involves extensive planning and data collection. The authors acknowledge the diligent contributions of Walter Bausch, Dale Shaner, Garrett Banks, Liam Cummins, Doug Barlin, Ted Bernard, Gerald Buchleiter, and dozens of Colorado State University students who managed the crops and collected data. USDA is an equal opportunity provider and employer.