CONVERTING KC VALUES BETWEEN ETo AND ETr Atef Ghandour1, Richard L. Snyder2, Kent Frame3, Simon Eching4, Bekele Temesgen5, and Baryohay Davidoff6
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1
Agricultural Engineering Research Institute, Giza, Egypt, PH 20 2-3375853; FAX 20 2 3356867; email:
[email protected], 2University of California, Department of Land, Air and Water Resources, Davis, California, PH (530) 752-4628; FAX (530) 752-1793; email:
[email protected], 3California Department of Water Resources, Office of Water Use Efficiency, Sacramento, California; PH (916) 651-7030; FAX (916) 651-9849; email:
[email protected], 4California Department of Water Resources, Office of Water Use Efficiency, Sacramento, California; PH (916) 651-9667; FAX (916) 651-9849; email:
[email protected], 5California Department of Water Resources, Office of Water Use Efficiency, Sacramento, California; PH (916) 651-9679; FAX (916) 651-9849; email:
[email protected], and 6California Department of Water Resources, Office of Water Use Efficiency, Sacramento, California; PH (916) 651-9666; FAX (916) 651-9849; email:
[email protected] Abstract The ASCE-EWRI recently published a report on the estimation of reference evapotranspiration for short canopies (ETo) and tall canopies (ETr) using a modified Penman-Monteith equation. Currently, another EWRI committee is developing crop coefficient (Kc) values to estimate crop evapotranspiration by multiplying by either ETo or ETr. Most crop coefficients were developed using either ETo or ETr, and, because the relationship between ETo and ETr varies with microclimate, it is difficult to convert crop coefficients from one reference surface to the other. In this paper, a simple method to convert between ETo and ETr and between the corresponding Kco and Kcr factors is discussed. Introduction The ASCE-EWRI (2005) development of standardized equations for estimating reference evapotranspiration for short (ETo) and tall (ETr) canopies was a big advance for agronomists and engineers to better share information for estimating crop evapotranspiration (ETc). The difficulty, however, is that crop coefficients developed using either ETo or ETr are not easily converted to the other reference surface. ETo and ETr are estimated using a modified Penman-Monteith equation (ASCE-EWRI, 2005) with fixed values for canopy resistance and aerodynamic resistance computed as a function of wind speed that is specific to the height of the reference surface. The difficulty is that aerodynamic terms in the ETo and ETr equations do not respond in the same manner to climate. Therefore, Kc factors, developed using one reference equation, have no direct conversion to the other reference equation. In this paper, we studied the ETo and ETr from 49 weather stations in a wide range of climates to determine if a method to estimate ETr from ETo and visa versa can be estimated without having access to the climate data that were originally used to compute reference evapotranspiration. This will allow for the conversion of
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ETr crop coefficients (Kcr) to ETo crop coefficients (Kco) and visa versa. The methodology will be presented in this paper.
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Methods Using daily and monthly climate data for 2003 from 49 California Irrigation Management Information System (CIMIS) weather stations (Table 1), ETo and ETr (mm d-1) were computed using both the daily and monthly data (Eq. 1) from ASCE-EWRI (2005). In equation 1, Rn (MJ m-2d-1) is the net radiation, G (MJ m-2s-1), u2 (m s-1) is the wind speed at 2 m height, es is the mean saturation vapor pressure, ea (kPa) is the actual vapor pressure, (kPa oC-1)is the slope of the saturation vapor pressure curve at mean air temperature, and is the psychrometric constant (kPa oC-1). The coefficients Cn and Cd are given in the boxes below Eq. 1 for both the ETo and ETr equations. For the daily (24-hour) equation, the soil heat flux is assumed to be G = 0 MJ m2 -1 d . For the monthly equation, G is estimated from the change in the monthly mean air temperature. Computation of the other variables in Eq. 1 is presented in ASCE-EWRI (2005).
ETsz =
0.408 (R n
G) +
Cn u 2 (e s T + 273 + (1 + C d u 2 )
ea )
(1)
Short Canopy ETo Tall Canopy ETr Cn Cd Cn Cd 900 0.34 1600 0.38 For the 49 stations, plots of ETr versus ETo were generated and slopes of linear regressions through the origin were determined for both monthly and daily reference evapotranspiration equations. See the example for Twitchell Island in Figures 1 and 2. Most of the R2 values were close to unity and the slopes varied considerably by location. There was almost no difference in the slope of the regression lines for daily or monthly calculations. The results were similar associations for the other 48 locations. The relationship between the regression slopes and several climate variables were investigated and ultimately, an excellent relationship was found between the regression slopes of ETr versus ETo and the mean ETo rate during the month of July. The linear regression equation and R2 value for estimating the slope of ETr versus ETo versus the July ETo rate is: S rvo = 0.043 ETo + 1.023
R 2 = 0.88
(2)
Similarly, the linear regression equation and R2 value for estimating the slopes of ETo versus ETr versus the July ETr rate is: S ovr = 0.016 ETr + 0.904
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R 2 = 0.91
(3)
The views expressed are those of the author, not the State of California World Environmental and Water Resources Congress 2006 World Environmental and Water Resource Congress 2006
If one is attempting to convert Kc factors from an ETo to an ETr base, the July ETo rate is determined for the location where the Kco values were developed. Then the Srvo is calculated using Eq. 1, and ETr is determined as the product of ETo and Srvo. Finally, the Kcr value is calculated as:
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K cr = K co
ETo ETr
(4)
To find a Kco factor from a Kcr value, the Soyr is calculated from the July ETr rate and Eq. 2. Then ETo corresponding to ETr is calculated as the product of ETr and Soyr. The Kco value is computed as: ETr (5) K co = K cr ETo To use this method, one should have the published Kco or Kcr data and the ETo or ETr rates to make the conversions discussed above. If the Kco or Kcr and ETc are available, then the ETo or ETr can be calculated as: ET (6) ETo = c K co or ET ETr = c (7) K ro before using the conversion method. Conclusions Using weather data from 49 CIMIS stations in California in a wide range of climates, a good relationship was found between the slope of monthly mean ETr versus ETo rates and the mean daily ETo rate for July. Similarly, a good relationship was found between the slope of monthly mean ETo versus ETr rates and the mean daily ETr rate for July. The slopes of regressions of daily ETr versus ETo rates and daily ETo versus ETr rates through the origin were nearly identical to slopes based on monthly calculations. The relationships can be used to estimate ETr from ETo and visa versa and to make crop coefficient conversions between the two reference evapotranspiration surfaces. References ASCE-EWRI. (2005). The ASCE Standardized Reference Evapotranspiration Equation. Technical Committee report to the Environmental and Water Resources Institute of the American Society of Civil Engineers from the Task Committee on Standardization of Reference Evapotranspiration. 173 p.
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Table 1. CIMIS station locations and mean ETr and ETo rates for June through August 2003.
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Station Number 125 134 146 35 47 84 57 41 152 19 170 88 6 182 168 153 131 80 133 94 122 162 75 86 166 145 43 87 132 77 136 61 147 156 39 161 157 160 99 68 165 15 123 137 173
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Station Name Arvin Edison Barstow NE Belridge Bishop Brentwood Browns Valley Buntingville Calipatria Camarillo Castroville Concord Cuyama Davis Deleno Denair Escondido2 Fair Oaks Fresno St Glendale Goleta Foothills Hastings Tract Indio Irvine Lindcove Lodi West Madera McArthur Meloland Morgan Hill Oakville Oasis Orland Otay Lake Oxnard Parlier Patterson Point San Pedro San Luis Obisdpo West Santa Monica Seeley Sisguoc Stratford Suisun Valley Temecula East II Torrey Pines
latitude deg 35.2 34.9 35.5 37.4 37.9 39.3 40.3 33.0 34.2 36.8 38.0 34.9 38.5 35.8 37.6 33.1 38.7 36.8 34.2 34.5 38.3 33.8 33.7 36.4 38.1 37.0 41.1 32.8 37.2 38.4 33.5 39.7 32.6 34.2 36.6 37.4 38.0 35.3 34.0 32.8 34.8 36.2 38.2 33.6 32.9
longitude deg 118.8 116.9 119.7 118.4 121.7 121.3 120.4 115.4 119.0 121.8 122.0 119.6 121.5 119.3 120.8 117.0 121.2 119.7 118.2 119.9 121.8 116.3 117.7 119.1 121.4 120.2 121.5 115.5 121.6 122.4 116.2 122.2 116.9 119.2 119.5 121.1 122.5 120.7 118.5 115.7 120.2 119.9 122.1 117.0 117.3
elevation m 152.4 621.8 125.0 1271.0 13.7 286.5 1220.7 -34.0 39.6 3.0 10.7 698.0 18.3 91.4 42.7 118.9 81.0 103.3 338.6 195.1 3.0 12.2 125.0 146.3 7.6 70.1 1008.9 -15.2 117.3 57.9 3.7 60.4 176.8 14.6 103.0 55.8 1.5 86.9 103.6 12.2 163.4 58.8 10.7 468.2 102.1
ETr mm 7.6 12.7 8.7 7.5 7.9 7.9 8.4 10.1 4.8 3.4 7.7 9.3 8.9 8.2 8.3 6.2 7.9 9.4 5.1 5.0 9.9 13.9 5.0 7.6 6.2 9.1 7.3 10.4 7.7 6.5 10.6 8.3 4.8 3.8 8.0 4.7 5.4 4.7 4.3 9.7 5.0 10.4 7.8 6.9 3.4
ETo Mm 6.1 8.9 6.7 5.9 6.2 6.2 6.3 7.7 4.2 3.0 5.9 6.8 6.7 6.4 6.3 5.0 6.2 7.1 4.3 4.2 7.1 9.5 4.4 6.2 5.2 6.8 5.7 7.8 5.9 5.3 7.7 7.0 4.2 3.5 6.3 4.0 4.6 4.0 3.8 7.4 4.2 7.6 6.1 5.5 3.1
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Station Name Tracy Tulelake Fs Twitchell Is. Union City
latitude deg 37.7 42.0 38.1 37.6
longitude deg 121.5 121.5 121.7 122.1
elevation m 25.0 1229.9 -0.3 4.9
ETr mm 9.8 6.7 10.4 5.3
ETo Mm 7.2 5.4 7.4 4.5
18.0
y = 1.42x 2 R = 0.99
12.0
-1
ETrs (mm d )
15.0
9.0 6.0 3.0 0.0 0.0
3.0
6.0
9.0
12.0
ET os (mm d-1)
Figure 1. Plot of ETr versus ETo using daily climate data from the Twitchell Island CIMIS station. 15.0
12.0
-1
ETrs (mm d )
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Station Number 167 91 140 171
y = 1.42x 2 R = 1.00
9.0
6.0
3.0
0.0 0.0
3.0
6.0
9.0
-1
ET os (mm d )
Figure 2. Plot of ETr versus ETo using monthly climate data from the Twitchell Island CIMIS station.
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