THE TRANSITION OF THE BLANEY-CRIDDLE FORMULA TO THE PENMAN-MONTEITH EQUATION IN THE WESTERN UNITED STATES Theodore W. Sammis Department of Plant and Environmental Sciences New Mexico State University Junming Wang Department of Agricultural Sciences Tennessee State University David R. Miller Department of Natural Resources and Environment University of Connecticut 2011 Journal of Service Climatology Volume 5, Number 1, Pages 1-11 A Refereed Journal of the American Association of State Climatologists The Transition of the Blaney-Criddle Formula to the Penman-Monteith Equation in the Western United States Theodore W. Sammis Department of Plant and Environmental Sciences New Mexico State University Junming Wang Department of Agricultural Sciences Tennessee State University David R. Miller Department of Natural Resources and Environment University of Connecticut Corresponding Author: Theodore W. Sammis, MSC 3Q, Department of Plant and Environmental Sciences, New Mexico State University, Las Cruces, NM 88003, USA. Tel. 575-646-2104, [email protected]. Abstract This paper reviews the history of calculating “consumptive water use,” later termed evapotranspiration (Et), for plants in the western U.S. The Blaney-Criddle formula for monthly and seasonal consumptive water use was first developed for New Mexico in 1942 for limited crops. The formula was based on the input of monthly mean air temperature and an empirical monthly/seasonal coefficient. Subsequent changes improved the Blaney-Criddle formula by adding more weather and crop variables. The availability of data from automated weather stations, after about 1980, that measure more weather input variables has allowed the empirical Blaney-Criddle formula to be replaced by the mechanistic standardized Penman-Monteith equation with an appropriate crop coefficient to calculate Et. The Penman-Monteith equation calculates Et under non-stressed conditions and represents the maximum Et and associated yield of the crop. Water rights in the western U. S. have historically, and continue to be, adjudicated using variations of the Blaney-Criddle formula. The Blaney-Criddle formula, derived in farmers’ fields under water stress conditions, calculates an Et that is most closely related to average county yields during the years the measurements were taken. But the empirical relationship and the originally derived coefficients are outdated and invalid for today’s agriculture production systems and should be replaced with the Penman-Monteith equation when adjudicating water rights. Sammis, T. W. et al. 2011. Journal of Service Climatology. www.journalofserviceclimatology.org 1 1. Literature Review Table 1. Time table for the development of evapotranspiration equations used in the a. Formula development of western US. Evapotranspiration equations Dates Event The consumptive water use divided by the Blaney-Criddle (BC) formula was water application efficiency is the general first published from measurements of approach used to calculate the water Consumptive Water Use (CWU) in requirements of a crop. The term “consumptive 1942 alfalfa, cotton, deciduous trees in the water use” was replaced in the literature by NM Pecos River Valley (Blaney et “evapotranspiration (Et),” a term more descrip- al. 1942a) tive of the water sources involved, which are the Measurements of CWU on other amount of water evaporated from the soil and 1942- crops in other western states (Blaney transpired by the plant per unit area (Jensen, M. 1962 and Criddle 1962) E. 1990). Irrigation requirements are deter- mined by subtracting the rainfall that contributes Hargreaves formula was developed. water to the evapotranspiration process, termed 1947 It used crop coefficient. “effective rainfall” from the estimated Et. A large number of evapotranspiration Penman equation was published that formulas were developed from 1942 to 2005 1948 is based on Energy and Aerodynamic (table 1) to calculate water uses of crops starting balance. with the development of the Blaney-Criddle BC Formula was simplified leaving formula (BC) and ending with the Penman- out humidity parameter due to lack Monteith equation that became the American 1950 of measurements at most weather Society of Civil Engineers (ASCE) Standardized stations. Reference Et equation. This equation is the BC Formula(s) was first used in current recommended equation that should be 1958 water rights adjudication (USDI- used to calculate the evapotranspiration rate BIA,1958) from a non-water stressed crop. The history of the development of these formulas is discussed Jensen-Hays formula was developed in the following sections of the paper. 1963 and used solar radiation and The Blaney-Criddle formula was first calculated “reference Et”. developed from soil moisture depletion and air USDA SCS modified to reflect crop growth stage and included an temperature and humidity measurements in 1970 empirical “climatic” parameter as the alfalfa, cotton, and deciduous trees in farmers’ temperature parameter. (USDA SCS fields by Blaney and Criddle in the Pecos River, 1970) Roswell-Artesia area of New Mexico (Blaney et Modified Penman equation was al. 1942b, Blaney et al. 1950). Measurements in published for use by Food and other western states and crops, including 1975 Agriculture Organization of the potatoes, corn, and small grains in Colorado United Nations (FAO) (Doorenbos and Pruitt 1975) were later made to extend the formula’s usefulness (Blaney and Criddle 1962). During FAO Blaney-Criddle formula was made compatible with crop these periods, water limitations resulted in crops 1975 coefficients developed with the that were regularly stressed for water. Therefore modified Penman equation. the consumption use values did not represent a non-water stressed condition. The originally Penman equation was modified to published Blaney-Criddle formula included a 1998 Penman-Montieth (P-M) formula . relative humidity parameter (Blaney et al. 1942). But due to the lack of relative humidity P-M equation becomes ASCE 2005 Standardized Reference Et equation Sammis, T. W. et al. 2011. Journal of Service Climatology. www.journalofserviceclimatology.org 2 data throughout the western United States, a progression, measured by growing degree day simplified formula excluding the humidity that have occurred since planting (Sammis et al. parameter was published in 1950 where the 1985). monthly or seasonal consumptive water use (Et) During this same time period, the Hargreaves of a crop, in inches was: equation was developed from research on consumptive water use conducted in California (Hargreaves 1947). This equation also uses air Et = kc × ∑ F (1) temperature and a crop coefficient to calculate consumptive water use and was modified by F= (T × p) / 100 (2) Hargreaves and Samani (1982). Hargreaves adapted his equation to calculate consumptive The monthly consumptive water use factor (F) water use requirements for any location around is the mean monthly temperature (T) in the world where air temperature data was Fahrenheit times the monthly percent of daytime available (Hargreaves and Allen 2003). hours (p) divided by 100. The crop coefficient k c In the 1960s, the energy available to evaporate is an empirical seasonal factor relating the water was included as an important factor. seasonal plant water usage for a specific crop to Jensen and Haise (1963) used the additional the total seasonal consumptive water use factor climate measurement of solar radiation as the generated under experimental conditions where measurement of the energy available for k can be calculated from measured F and Et. c evapotranspiration: The formula can be applied on a monthly basis by calculating F for each month and scaling it by Et = C × (T - T ) × R (5) a monthly k , which is dependent on the growth r T x S c development rate of the crop. Consequently, the where: Et = reference Et is in energy units of Blaney-Criddle formula applies to both seasonal r langleys per day (41.84 kJ/m2). and monthly consumptive water use calcu- To convert to inches per day lations. multiply by 0.000673, In 1970, the USDA Soil Conservation Service R = solar radiation in langleys per day, (USDA SCS 1970) expanded the air temperature S T = mean air temperature in degrees F, term to account for the different development T = a temperature axis intercept with a rates in different climates so the monthly crop x value of 26.4, and growth stage coefficient could be used C = an empirical coefficient with a throughout the western United States. They used T value of 0.014 referenced to a linear fit for the air temperature data and alfalfa. modified the original Blaney-Criddle formula to: The terminology of reference evapotrans- Et (monthly) = k × k (T × p / 100) (3) t c piration was used at that time, with the two major reference crops being fescue grass where: (maintained at a height of 0.15 m and under non- k is a monthly crop growth stage coefficient c stressed conditions) and alfalfa. Equation 5 is and k is a climatic coefficient related to the t reference Et for alfalfa. The actual Et for mean monthly air temperature (t): different crops is calculated by multiplying equation 4 by the daily, monthly or seasonal where: k = 0.0173t - 0.314, with a minimum t crop coefficient after calculating the reference value of 0.300. (4) evapotranspiration for that time period or by accumulating the daily values of Et for the Temperature is again in degrees Fahrenheit desired time period. and Et in inches. Crop development and the In 1948 the Penman equation was published monthly