University of Missouri Extension

Equations Used

Reference ET equation

The Blaney-Criddle evapotranspiration equation is used. Daily values of evapotranspiration (ETBC) are calculated using a splining function upon published monthly mean values of daily maximum and minimum temperatures. Latitudinal values are used to calculate daylight hours, part of the Blaney-Criddle equation. A database was established that contains, for each Missouri county, daily maximum temperature, daily minimum temperature, and daily ETBC. These data were based on 30-year weather records.

The result gives a smooth curve of daily reference evapotranspiration values for the entire year (Fig. 1).

Figure 1
Figure 1. Historic daily reference evapotranspiration for
Mexico, MO using the Blaney-Criddle method.

The software has an adjusting factor that can lower or raise ET values. This adjustment tool is located on the same screen that displays the crop's seasonal water use value (inches) and peak water use (inches per day [ipd]); this screen appears right before the final Woodruff graph is generated. If either water unit value seems too high or too low, the adjustment factor can be used, which then adjusts all daily values accordingly. As an example, the screen might show that a corn hybrid that emerged April 25 in Mexico, MO is projected to have a seasonal water use of 21.1 inches with a peak water use of 0.28 ipd. If the grower has reason to believe that the peak water use of corn for his area is 0.30 ipd he can toggle up the peak water use to 0.30 and this will raise all daily ETBC values by 1.07 (0.30/0.28). The new seasonal water use then becomes 22.6 inches.

Kc values used

Crop coefficients for corn, soybeans, and cotton are Heat Unit-based and are calculated on a procedure that involves percentage of seasonal Heat Units. The fourth order polynomial that describes daily crop coefficient values is:

Kcj equals A times %SHUj + B times (%SHUj) to the 0.5 + C times (%SHUj) squared + D times (%SHUj) cubed + E

where,

%HUj = % of accumulated Seasonal Heat Units as of day, j

Kcj = crop coefficient on any day, j

and A,B,C,D and E are coefficients.

Calculations for Heat Unit-driven Kc values for corn and soybean are the similar to ones used in the University of Missouri's weather station network as seen on AgEBB, (University of Missouri Outreach and Extension's electronic bulletin board) except that they have been adjusted to reflect the fact that AgEBB uses potential evapotranspiration as their reference ET value. The adjustment values were very close to the value (0.80) used by Gregory and Schottman when they had investigated the problem in the 1980's. The cotton Kc values were derived by extracting values of daily water use of soybean and cotton under conditions of same emergence and termination rate and same weather conditions in 10-day increments from the Arkansas Scheduler computer program. The ratios of water use between the two crops were used to adjust the soybean Kc so that it reflected the Kc value of what cotton would be. The parameters used on the Kc equations for the various crops is shown in Table 1.

Table 1. Parameters used in Kc euqations

crop intercept % HU % HU^0.5 %HU^2 %HU^3
Corn 0.1134 -0.0985 0.7476 2.6551 -2.8851
Soybean 0.1347 0.6402 0.4641 1.0837 -1.8921
Cotton 0.1502 0.4561 -0.2223 4.5172 -4.6066

The farmer provides emergence date in the program, but since crop coefficients are reported as a function of % of seasonal Heat Units, it is important to know when the crop terminates so that total Heat Units can be calculated. The last date of water use in the season is based on these estimates are:

The figures below show Kc values used in the program.

Kc Value for Corn

Kc Value for Soybeans

Kc Value for Cotton

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