Paul W. Brown
Extension Specialist, Biometeorology
University of Arizona


    The Arizona Meteorological Network (AZMET) calculates reference crop evapotranspiration (ETo) using a modification of the Penman Equation developed for the California Irrigation Management Information System (CIMIS) by Snyder and Pruitt (1985). Reference crop evapotranspiration computed using this procedure provides an estimate of ET by a cool season grass, 8-15 cm in height, that completely covers the soil surface and is well watered. A detailed discussion of computational procedures employed by AZMET are provided in the paragraphs below.


    The CIMIS Penman Equation was developed for use with hourly weather data. Required input data for the ETo computation include hourly means of air temperature (Ta; units of degrees C), vapor pressure deficit (VPD; units of kilopascals: kPa), wind speed (U2; units of m/s), and net radiation (Rn: units of mm/hr of equivalent evaporation). Hourly values of ETo (EToh) in mm/hr are computed using the following:

    EToh = W*Rn + (1-W)*VPD*FU2              (1)

    where W is a dimensionless partitioning factor, and FU2 is an empirical wind function (units: mm/hr/kPa). Daily values of ETo are computed by simply summing the twenty-four hourly EToh values computed from Eq. 1 for the period ending at midnight (end of AZMET day). Specific computational procedures used to obtain the required parameters for Eq. 1 are provided below.

    Net Radiation (Rn)

    CIMIS originally measured Rn using instruments known as net radiometers. CIMIS abandoned the use of net radiometers in the early 1990s for a variety of reasons. AZMET chose not use net radiometers and has computed hourly net radiation since network inception (1986) using a simple, clear sky estimation procedure that uses solar radiation (SR) expressed in units of MJ/m*m/hr and mean hourly vapor pressure (ea; units: kPa). The procedure is provided below:

    For Daytime Conditions (SR>=0.21 MJ/m*m/hr):

    Rno = 277.8*(-0.3 + 0.767*SR)              (2)

    For Nighttime Conditions (SR<0.21 MJ/m*m/hr):

    Rno = 277.8*(-0.17 + 0.767*SR + 0.056*ea)              (3)

    where the constant 277.8 converts the units of Rno from MJ/m*m/hr to W/m*m.

    Vapor pressure (ea) is computed by subtracting VPD from the saturation vapor pressure (es):

    ea = es - VPD              (4)

    where es is computed using the following:

    es = 0.6108*exp((17.27*Ta)/(Ta+237.2))              (5)

    It is important to note that this simple computational procedure for Rn works well in Arizona because: 1) the vast majority of the days are clear and 2) vapor pressure is reasonably constant throughout much of the year. Use of this Rn estimation procedure in regions with abundant cloudiness and high humidity is not recommended.

    The Rno computed from Equations 2 and 3 is in units of W/m*m. Equation 1 requires net radiation in units of mm of equivalent water evaporation (Rn). This conversion of units is accomplished by dividing Rno in W/m*m by the latent heat of vaporization as follows:

    Rn = Rno/(694.5*(1-0.000946*Ta))              (6)

    where Ta is the mean hourly air temperature.

    Partitioning Factor (W)

    The partitioning factor, W, is computed using Equation 7:

    W = S/(S+G)              (7)

    where S is the slope of the saturation vapor pressure curve at Ta and G is the psychrometer constant.

    The value of S in units of kPa/C is computed using the following:

    S = es*(597.4-0.571*Ta)/(0.1103*(Ta+273.16)^2)          (8)

    where es is the saturation vapor pressure at Ta.

    The psychometer constant, G, is computed using the following:

    G = 0.000646*P*(1+0.000949*Ta)              (9)

    where P is atmospheric station pressure in units of kPa.

    For computation of ETo, P is considered a constant and computed from elevation above sea level.

    Vapor Pressure Deficit (VPD)

    Vapor pressure deficit is computed by AZMET dataloggers and therefore no computation is required to obtain VPD. The AZMET datalogger computes VPD by 1) computing the saturation vapor pressure (es) from air temperature, 2) multiplying es by the relative humidity fraction to obtain actual vapor pressure (ea), and 3) subtracting ea from es to obtain VPD. The hourly VPD value used in the ETo computation is the mean of 360 individual VPD computations (dataloggers scan sensors and make computations every 10 seconds).

    Wind Function (FU2)

    Two wind functions (FU2; units mm/hr/kPa) are used to compute ETo -- one for daytime conditions (Rn>0) and one for nighttime conditions (Rn<=0). These wind functions are as follows:

            Daytime: Rn>0

    FU2 = 0.03 + 0.0576*U2              (10)

            Nighttime: Rn<=0

    FU2 = 0.125 + 0.0439*U2              (11)

    where U2 is the mean hourly wind speed obtained at a height of 2 m in units of m/s. AZMET measures wind speed at a height of 3m (U3); thus AZMET wind speeds are adjusted using:

    U2 = 0.93*U3              (12)

    where the constant 0.93 is derived from the standard power law equations that predict the variation of wind speed with height.


    Both AZMET and CIMIS provide ETo data for locations along the Colorado River for use in on-farm water management and to aid in overall management of the Colorado River. It is therefore important that AZMET and CIMIS compute ETo in a similar manner. Both CIMIS and AZMET use the same basic procedure for estimating ETo from hourly weather data. The only significant difference between AZMET and CIMIS ETo procedures rests with the computation of Rn -- an important parameter in the ETo computation. AZMET uses a relatively simple clear sky procedure for estimating Rn. This procedure compares well with Rn measured with net radiometers. CIMIS originally used net radiometers to measure Rn; however, CIMIS abandoned measurement of Rn in the early 1990s and now uses an hourly Rn estimation procedure based on the work of Dong et al. (1992). A direct comparison of AZMET and the current CIMIS Rn procedures is nearing completion and should be available in written form by June 1998. Completion of this work will determine how much difference (if any) we can expect between AZMET ETo and CIMIS ETo.


      A. Dong, S.R. Grattan, J.J. Carroll and C.R.K. Prashar. 1992. Estimation of daytime net radiation over well-watered grass. J. Irr. & Drain. Eng. 118(3): 466-479. ASCE.

      Snyder, R. and W. Pruitt. 1985. Estimating reference evapotranspiration with hourly data. In R. Snyder et al. (ed.) California Irrigation Management Information System Final Report. June 1985, Vol. 1. Land, Air and Water Resources Paper #10013-A. Univ. of California-Davis. Chpt. VII.