07 Evaporation

Evapotranspiration

General

Evaporation can be estimated directly from pan evaporation measurements. Due to exposure conditions an evaporation pan generally overestimates potential evaporation. Evaporation rates can be calculated from water balances, energy balances and by heat and mass transfer methods. By combining the energy balance and the mass transfer method, Penman developed a procedure to estimate open water evaporation from measurement of simple climatic variables at 2 meter above the evaporating surface.

HYMOS offers the following computational methods for potential evapotranspiration:

1. Penman Method:
   • Standard,
   • Standard with FAO Correction,
   • Modified
2. FAO Pan-evaporation Method,
3. Christiansen Method,
4. FAO Radiation Method,
5. Makkink Radiation Method,
6. Jensen-Haise Method,
7. Blaney-Criddle Method,
8. Mass Transfer Method.

The methods are presented in following sections.

Penman Method

Standard

Following formula is used:

(1)

with:

Vapour pressure-temperature gradient

The quantity Δ is computed from:

(2)

with:

Psychrometric constant

The psychrometric constant follows from:

γ = 0.00066 p (1 + 0.00115 t) (3)

with:

Air pressure

If the air pressure is not available, it is computed from the altitude of the station:

p = 1013 - 0.1152 z + 5.44*10^-6^ z² (mb) (4)

with:

Radiation

Where net radiation R_n is not available, it can be substituted in turn by net shortwave and net longwave radiation, and then by bright sunshine totals which are more commonly measured at standard climatological stations. Thus net radiation can be computed from:

R_n = R_ns - R_nl (5)

where:

The net shortwave radiation reads:

R_ns = (1-α) R_s (6)

with:

Reflection coefficients or albedo

The shortwave radiation, if not available, is computed from:

R_s = R_a (a₁ + b₁ n/N) (7)

with:

Mean monthly Extra Terrestrial Radiation (Ra) in mm of Evaporation Water/Day, Northern Latitude

Mean monthly Extra Terrestrial Radiation (Ra) in mm of Evaporation Water/Day, Southern Latitude

Mean Daily values of Possible Sunshine Duration Hours N, Northern Latitudes

Mean Daily values of Possible Sunshine Duration Hours N, Southern Latitudes

The net longwave radiation, if not available, is estimated by:

R_nl = σT⁴ (a₂ - b₂ √e_a )(a₃ + b3~ n/N) (8)

with:

Wind function

The wind function, as proposed by FAO, is given by:

f(u) = 0.26 (1 + U₂₄ / 100) (9)

where:

Vapour pressure

The saturation vapour pressure e~s~ is the vapour pressure at which the water vapour is in equilibrium with a plane water surface of the same temperature and pressure. The saturated vapour pressure is computed by the Goff-Gratch formula:

(10)

A correction can be made for salinity:

e_s = e_gg (1 - 0.000537 S) (11)

where:

The actual vapour pressure e_a is computed by one of the following 3 formulas:

e_a = e_s . rh/100 (12)
e_a = e_s (t_wb ) - γ(t_db - t_wb ) (13)
e_a = e_s (t_dew ) (14)
with:

Penman method with FAO-correction

A correction has been proposed to the standard Penman method by FAO to compensate for the effect of day and night weather conditions:

E_corr = E*c (15)

with:

This correction is particularly of importance for locations with strong dry winds and large cloud cover (see FAO pub. no. 24, 1977).

Modified Penman method

Recently some modifications were proposed in calculating some of the components in the Penman equation. In the modified Penman method calculation of the following components are changed:

• Saturated Vapour pressure
• Vapour pressure-temperature gradient
• Psychrometric constant
• Air pressure

Vapour pressure-temperature gradient and saturated vapour pressure

The vapour pressure-temperature gradient is computed from:

(16)

where:

and the saturated vapour pressure is calculated from:

(17)

Compared with the Goff-Gratch equation for saturated vapour pressure the error in e_s for 0 < t < 50 ⁰C is smaller than 0.06 %. The saturated vapour pressure and the vapour pressure-temperature gradient are presented graphically

psychrometric constant

The psychometric constant is the difference between the saturation vapour pressure at the wet bulb temperature and the actual vapour pressure divided by the difference of the dry bulb (ambient air temperature) and wet bulb temperatures:

(18)

where:

Where the air pressure is not measured, it is estimated as:

(19)

where:

The latent heat of vaporisation lis the energy which is required to vaporise one unit of mass of liquid water without change in temperature (t in ⁰C):

λ= 2501 - 2.361*t (20)

With these new equations the same procedure is used with the Standard Penman method to calculate the evapotranspiration.

Pan evaporation method

Reference crop evapotranspiration is obtained from:

E = K_p . E_pan (21)

where:

The K_p values refer to the Class A pan (metal pan 122 cm in diameter, 25 cm high and mounted with its bottom 10 cm above the surrounding soil).
Two cases are distinguished:

• case 1: pan is located within cropped plots surrounded by or downwind from dry surface area.
• case 2: pan is located within a dry or fallow field but surrounded at some distance by irrigated or rainfed upwind cropped areas.

The pan coefficient is a function of relative humidity, daily windrun and the fetch.

The fetch is:

• for case 1: length of upwind green crop from pan
• for case 2: length of upwind dry surface between the crop and the pan

Christiansen Method

Reference crop evapotranspiration is computed from equation (21), however with E_pan estimated by one of the following two formulas:

1. if incoming solar radiation data are available:
E_pan = 0.482 . R_s . C_tc . C_u . C_rh (22)

2. or from extra terrestrial solar radiation:
E_pan = 0.324 - R_a . C_tc . C_u . C_rh . C_n . C_z (23)

with:

where:

Radiation Method

The Radiation Method is an adaptation of the Makkink formula. The method has been proposed by fao. It reads:

(29)

where:

Makkink Method

Use is made of the radiation method equation with c = 0.65.

Jensen-Haise method

The method is classified as a radiation method. It is a modified form of the original Jensen-Haise equation as the constants in the original formula are replaced by quantities dependent on long term climatic data and altitude. The modified Jensen-Haise equation reads:

E = C_tj (t - t_x ) R_s (30)

where:

The coefficients C_t,j and t_x are computed from:
C_tj = 1/(C₁ + 7.3 C_vp ) (31)

with:
C₁ = 38 - 2.z/305 (32)
C_vp = 50/(e₂ - e₁ ) (33)
t_x = - 2.5 - 0.14 (e₂ - e₁ ) - z/550 (34)

where:

Blaney-Criddle method

The original temperature based Blaney-Criddle method has been modified by FAO. The modified formula has the following form:

E = c P_d (0.46 t + 8)q (35)

where:

Mass Transfer method

The general mass transfer has the following form:

E = (a + b.u) (e_o - e_a ) (36)

where:

This type of equation is often used for computation of lake evaporation. For Lake Hefner e.g. with E in mm/day and e_a taken at 2 m above the water surface:

a = 0 and b = 0.291/A^0.05 ,

where A = surface area of the water surface in m² (to be used only for A > 4 * 10⁶ m² as variations in wind exposure may become important for smaller water surfaces).

Data requirements

The evaporation rate is influenced by atmospheric and water quality factors. Each method for used for evaporation computation requires one ore more of these factors The underneath table gives some of the factors affecting the evaporation rate.

(from: G. Das, Hydrology and soil conservation energy, 2000, Prentice-Hall)

Following information for the methods are required or optional:

Information Method

1. Code of evaporation series all
2. Start and end date of computational period all
3. Air pressure series code 1,4,5,8
4. Air temperature series code 1,3,4,5,6,7
5. Relative humidity series code 1,2,3,4,8
6. Maximum relative humidity series code 1
7. Minimum relative humidity series code 7
8. Dry and wet bulb temperatures series codes 1,8
9. Dew point temperature series codes 1,8
10. Wind run series code 1,2,3,4,7,8
11. Height of the wind velocity measurements 1,2,3,4,7,8
12. Day to night wind velocity series code 1
13. Day to night wind velocity value 4,7
14. Coefficients in wind function 8
15. Net radiation series code 1
16. Short wave radiation series code 1,3,4,5,6
17. Long wave radiation series code 1
18. Number of sunshine hours series code (Cloudiness) 1,3,4,5,6,7
19. Albedo 1
20. Parameters for computation of short wave radiation 1,4,5,6
21. Parameters for computation of long wave radiation 1
22. Series code of pan evaporation 2
23. Fetch length series code 2,3
24. Long term minimum and maximum temperature in warmest month 6
25. Salinity 1,4,5,6,8

Note that not all data indicated for a particular method must be available to run the option.

Application

The 'Evaporation' function can be started by selecting the function from the 'Compilation' function group.

Series Codes

First select the series code of the evaporation series which will be calculated. This can be done by selecting a series code from the series codes listbox and pressing the <Series> button under this series listbox. The latitude and altitude of the station will be presented in the textboxes, these data are read from the 'station Characteristics' table of the HYMOS database.

Evapotranspiration method

The evapotranspiration method used can be selected by selecting the method from the listbox. When a method is selected HYMOS will change the series and parameter selection and input boxes to the ones necessary for the selected method
Selection the necessary series, for 'air pressure', 'humidity', 'wind speed', etc. on the same way as for the evaporation series. The appropriate values for 'albedo', 'salinity', etc. must be entered in the textboxes.

When all series are selected and the values given, press <Execute> to calculate the evaporation values. The result can be viewed in a Graph or in a spreadsheet form by pressing <Graph> and <View> respectively. It is also possible to Save the series to the database by pressing <Save> or exporting the series by pressing the <Export> button from the function tab of the HYMOS main window.