Ce-418-lecture 5-et- 2018

Different methods to measure ET ◦Laboratory or Field – Lysimeters ◦Field observation ◦Various Mathematical Equations Penman; Modified Penman; BlaneyCriddle (SCS and FAO); FAO Crop Coefficient , Wright Crop Coefficient; Hammon, Thornthwaite

Penman Equation For Potential Evaporation

Location of the field (latitude in degrees) Elevation of the field (mean sea level) Day-of-the-year for the prediction Mean air temperature for this day

• A measure of the average humidity for this day (Relative humidity or Dew Point Temperature or Vapor Pressure) • Daily Solar Radiation • Average wind speed for this day

 ET0  D 

PENMAN EQUATION D Rn  G    D 

6.43(1.0  0.53V2 es  ed 

D  0.20 ( 0.0073 8T  0.8072 )  0.000116 7

D is the slope of the vapor pressuretemperature curve at the mean air temperature. T is the mean air temperature in oC

 = the latent heat of vaporization of water at the mean air temperature in MJ / kg

  2.501  0.002361T P  101.3  0.01055EL EL is the field elevation in meters above mean sea level. P = the atmospheric pressure in kPa at this field elevation.

  0.00163

P



 is the psychrometric constant for this temperature and pressure in kPa / oC.

es  3.38639 [ (0.00738 T  0.8072 )  0.00019 | 1.8T  48.0 |  0.001316 ] es is the saturation vapor pressure in kPa at the mean air temperature

8

ed  (RH )(es ) / 100 • RH is the mean relative humidity for this site and this day • ed is the actual vapor pressure for this temperature and relative humdity in kPa. OR • Can be determined by using es equation and substituting the mean dew-point temperature for T.

Rn  1    R s  T

4

0.34  0.139 e

0 .5 d



n    0 .1  0 .9  N 

Rn is the estimated net radiation energy supply to this field on this day in MJ / m2 / day  is the Stefan-Boltzmann constant for radiant energy emission = 4.903 x 10-9 MJ / m2 / day / 0k4 n / N is the ratio of actual to possible sunshine for this day

Rs / Rso

n  0.35  0.61 N

Now the maximum clear-day solar radiation at a location for any day can be estimated from the following equation. Rso = A + B cos ( 2p / 365 ( J-172 )) langleys / day

PENMAN EQUATION MJ ET0  2 m day MJ  kg  MJ  kg  1m3  1000mm    ET0   2   m   m day  MJ  1000kg   mm / day

Crop Coefficient for a Grass reference crop, ETo

Blaney – Criddle Method  Developed for ET from Climatic and irrigation data in 1950 U = KP(0.46T +8.13)  U = Monthly ET, mm  K = Monthly ET coefficient (from local data)  T = Mean monthly Temperature, 0C  P = Monthly % of total day time hours of the year (Monthly day time hours x 100/total annual day time hours)

PENMAN EQUATION MJ ET0  2 m day MJ  kg  MJ  kg  1m  1000mm    ET0   2   m   m day  MJ  1000kg   mm / day 3

Rough estimates of ET (mm/day) Mean daily temperature Climatic zone

high (more than 25°C)

Desert/arid

low (less medium than (15-25°C) 15°C) 4-6 7-8

Semi arid

4-5

6-7

8-9

(Moist) Sub- 3-4 humid Humid 1-2

5-6

7-8

3-4

5-6

9-10

Infiltration

 Infiltration is the actual rate at which water is entering the soil at any given time(SCSA, 1976).  Infiltration capacity: Maximum rate (LT-1).

Factors affecting infiltration  Precipitation: Intensity and duration  The infiltrated water often seeps into streambeds with extended period of time, and stream often continues to flow which is called ‘baseflow’ when there is no direct runoff from recent precipitation.  Soil characteristics: clay vs. sand  Soil saturation: Soils already saturated from previous rainfall or irrigation will produce more surface runoff than infiltration.

Factors affecting infiltration  Land cover: Significant impact on infiltration. Vegetation can slow the movement of runoff. Impervious surfaces act as a "fast lane" for rainfall to streams.  Agriculture and tillage changes the infiltration patterns.  Slope: Water falling on steeper slopes runs off more quickly and infiltrates less than water falling on flat land.  ET: Some infiltrated water stays in the root zone where plants use by the process of ET, and water moves back into the atmosphere.

q

Q A

K

 The flux density, q, is the rate of water movement through a medium.  q is a function of ΔH and the hydraulic conductivity of the medium.  ΔH = H1 – H2 is the difference between total water potential inlet and outlet.  H = Pressure head + Gravitational head

DH L H1

A

Ksat L

H2

Horton‘s Equation • Horton's theory is based on the fact that infiltration is faster in dry ground, so as rain continues and the ground becomes wetter, the infiltration rate decreases. • The reason that infiltration is faster when the ground is dry is that there are more spaces for the water to fit so capillary forces that pull the water down into the ground are stronger.

Horton’s Equation – Solve the equation for the rate of moisture diffusion at soil surface f(t) = fc + (f0 – fc) e–kt – k = positive constant ~ T-1 – f0 and fc are initial and final infiltration capacity (in/hr) of the soil

Limits to Horton's Theory

F=



( f0- fc) - kt fdt  f c t + [1 - e ] k

• Horton's equation and integral assume that the rainfall rate, R is greater than the infiltration rate throughout the rain. • If at any time the rainfall rate is slower than the infiltration rate, the ground will lose some water to lower levels, and Horton's theory must be modified.

Infiltration Equations • Green-Ampt (1911):

i = ic + b/I Where I is cumulative infiltration, ic and b are constants.

• There are several other equations: • Horton (1940) • Philip (1957)

• Philip Equation: I = Sp (t)0.5 + Ap (t) I = Infiltration depth, cm t = time of infiltration, min Sp = Sorptivity constant, cm/(min) 0.5 Ap = Conductivity constant, cm/min

• Kastiakov Equation: I = C(t)α I = Infiltration depth, cm t = time of infiltration, min C and α are empirical constants • SCS Equation: (Intake family concept) I = a(t)b + C I = Infiltration depth, cm t = time of infiltration, min a and b are function of intake family