Estimation of Evapotranspiration using the FAO Penman-Monteith Equation


To complement the pan evaporation observations, the FAO-56 approach is also applied to the study basin, using available meteorological data.

Penman-Monteith Equation

The FAO-56 standard approach is based on the Penman-Monteith Equation, which is a combination method to calculate evapotranspiration, taking the effects of radiation, aerodynamic and surface (stomatal, cuticular and soil) resistances into account:

(1)

where: is the latent heat flux; , slope of saturated vapour pressure curve; Rn, the net radiation; G, the soil heat flux; , mean air density; cp, the specific heat of the air; (es - ea) the vapour pressure deficit of the air; ra, aerodynamic resistance; , the psychrometric constant; and rs, the bulk surface resistance.

The Reference Crop and Reference Evapotranspiration

The original Penman-Monteith equation (1) could be used for any surface as the surface and aerodynamic resistances are surface specific. The FAO apply the equation onto a hypothetical reference crop (or surface) with height of 0.12 m, surface resistance of 70 s m-1 and albedo of 0.23 to get a reference evapotranspiration (ETo). This reference surface resembles an extensive surface of green grass of uniform height, actively growing, completely shading the ground with adequate water. With this control over the variation on surfaces, an explicable and constant ETo could be determined for all regions of different climates. Consequently, ETo is only affected by climatic parameters and the FAO Penman-Monteith equation can be utilize basing on weather data alone:

(2)

where: ETo is the reference evapotranspiration; T, the mean air temperature; and u2, the wind speed.

Various data for the computation of equation (2) is required and their sources are listed in Table 1 below:

Variable Unit Source
Temperature °C 3-times monthly measurement from Xinfengjiang Dam station
Absolute Humidity mb
Wind speed m/s
Extraterrestrial Radiation MJ/m2/day Allen et al. (1998), Annex 2 meteorological tables.
Daylight hours hour
Actual sunshine duration hour 廣東省地方史志編纂委員會 (1999)

Table 1: Input data for reference evapotranspiration calculation and their respective sources.

East River Model Input: Potential Evapotranspiration

The resultant dataset is a time series comprises of 3-times monthly values of potential evapotranspiration [mm/day]. The potential evapotranspiration for the first 10 days of a month is assumed to be equal to the first monthly value, while the second monthly value is used for the 11th to 20th day and the third value is applied on the rest of the days in that particular month. A diurnal cycle is subsequently applied on the daily values to obtain the hourly time series. The resultant time series (ET0) together with the pan evaporation (PanE) measurements are plotted in Figure 1. It is observed that PEt is generally lower than pan evaporation, however their general tendency is quite similar. The statistics of ET0 is presented in Table 2 and the mean seasonal cycle is plotted on Figure 2.

Figure 1: Monthly reference evapotranspiration (ET0) and pan evaporation measurement (PanE), 1969 - 1978.

 

  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual
Unit

[mm/month]

[mm/year]
1969 80.5 55.9 95.8 144.2 121.1 128.6 161.9 150.9 130.1 124.9 92.0 69.6 1325.5
1970 66.9 70.7 62.9 97.7 118.5 130.8 159.4 146.3 125.0 119.2 86.7 69.2 1253.2
1971 76.3 64.1 82.5 100.6 118.7 124.8 158.9 143.4 125.3 129.6 109.5 84.9 1318.6
1972 84.2 67.0 102.2 93.8 118.5 135.2 164.4 147.1 126.8 115.7 95.0 77.0 1327.1
1973 68.3 67.1 87.7 95.6 115.7 123.0 147.6 145.5 125.6 128.1 103.3 101.0 1308.6
1974 66.1 55.0 70.4 91.2 116.8 115.2 147.6 147.9 121.6 124.7 79.2 63.5 1199.1
1975 64.0 67.4 74.5 100.8 108.4 123.1 151.8 146.8 126.3 116.3 91.5 90.0 1260.7
1976 85.4 70.9 74.2 89.0 117.2 117.7 149.8 149.3 128.0 105.7 92.2 83.6 1262.8
1977 68.1 76.2 100.4 133.5 130.3 126.4 151.6 153.5 142.4 115.1 103.0 81.0 1361.6
1978 75.4 66.3 69.7 92.4 113.7 128.4 160.4 145.8 136.1 124.4 80.7 69.6 1262.9
Avg. 73.5 66.1 82.0 98.9 117.9 125.3 155.4 147.7 128.7 120.4 93.3 78.9 1288.0

Table 2: Statistics of adopted reference evapotranspiration, 1969 - 1978.

 

Figure 2: Average seasonal cycle of reference evapotranspiration, 1969 - 1978

References:

Allen, R.G., Pereira, L.S., Raes, D. and Smith, M., 1998. Crop evapotranspiration - Guidelines for computing crop water requirements. FAO Irrigation and drainage paper, 56. FAO, Rome.

廣東省地方史志編纂委員會(1999) 廣東省志 地理志. 廣東人民出版社.


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2003 Pat Yeh and Lincoln Fok