Lecture (12)

The Combination Methods

Initially developed by Penman (1948)who combined the creodynamic and energy budget methods to compute ETo. The method has been modified by many researchers.

Doorenbos and Pruitt Equation

ETo= WQn + (1-W) (es – ea) f (u)W = a temperature and elevation related weighting factor (table 4-1)

es and ea = saturated and air vapor pressures at mean air temperature (mb)

f (u) = a wind related fn = 0.27 (1+u/100) ; where u is the average wind speed (km/day)

ea = es × RH

RH = relative humidity

T = mean air temperature, ºC

FAO Penman – Monteith Equation

G = Soil heat flux; Gi = 0.057 (MTi – MTi-1)

Where Gi is soil heat flux during month i , MTi is the mean air temperature of month I and MTi-1 is the mean air temperature of the previous month

mb 237.3 T

T 17.27 exp 6.108 es

)U 0.34(1 γ Δ

)e- (e U )g(T γ G) - (Q Δ 0.408 ET

2

as22no

(m) level sea above elevation Z

2930.0065z) - (293

101.3

Pa) (k pressureatm Pa

Pa 10 0.665 γ

Ce,temperatur air mean T 237.3) (T

es 4098

etemperatur air mean versus esof slope Δ

(m/s) height2m at speed wind U

273) (T900

)g(T

height2m at etemperatur daily mean T

5.26

-3

ο

2

2

22

2

Computation of the Net Solar Radiation: (Qn)

7)Table(4

Nn

f

N0.9n) (0.1

6)Table(4

)f(ee 0.044 - 0.34

5)-(4 Table

)(Tf 273) (T 102

R

3)-4 (table latitude and month

of function a is which radiation lterrestria Extra R

2)-4 (table latitude and monthof fn a is

which hours sunshire possiblemaximum N

measured) be (to hours sunshire actual n

R )Nn

0.5 (0.25 Rs

radiation wave short incomming R where,

R - R 0.75 Q then

0.25) - (0.23 albedo α

/daycal/cm )RL - (RL - R α) - (1 Q

a

a

a

4a

9-

ln

a

a

s

Lnsn

2iosn

R L

SR

LR

S u n

R a

i o

aRaR

R S

The Empirical Methods

• Much simpler but less accurate than the above 3 methods

• They are based on one or more of the following parameters:

(Ta , RH, U, Qn , ea, .. etc)

• They are usually used when data need for modified Penman equation is not available

• Two empirical methods are addressed here:

a. Blany – Griddle (Temperature) method

b. Pan Evaporation method

a. Bland – Griddle method

ETO = C [P (0.46 Tm + 8.13)] mm/dayC = adjustment factor ; figure (4-2)P = mean daily hours as a percentage of the total /annual day time

hours; table (4-8)Approximate values for RH min, n/N and U may be used id fingure (4-2)

b. Pan Evaporation Method

Class A : - 121cm in diameter - 255 cm deep- Galvanized iron- Mounted on wooden frame- Bottom is 15 cm above ground

ETo = Kp Ep

Ep = measured on daily basis

Kp= from table (4-9)

D r ysu r f a c e

5 0 m o r m o r e

c r o pG r e e n P a n

W i n d

C a se A

F e t c h

F e t c h

C a se B

W i n d

P a nG r e e nc r o p

5 0 m o r m o r e

su r f a c e D r y