HYD 301.3
Dr. Hari Krishna Shrestha
Associate Professor, Dept. of Civil Engineering, Nepal Engineering College
Director, Center for Disaster Risk Studies
Contact: shrestha_h@hotmail.com
June 2007

(4 hours)

The meteorological factors determining evapotranspiration are weather parameters which provide energy for vaporization and remove water vapor from the evaporating surface. The principal weather parameters to consider are:

2.1 Solar Radiation

2.2 Air Temperature

2.3 Air Humidity

2.4 Wind Speed
Solar Radiation
Air Temperature
Wind Speed
ET

2.5 Evaporation

2.6 Transpiration
 2.7 Penman’s Equation
Humidity ET
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Radiation: a mode of heat transfer by electromagnetic waves

Solar Radiation can be termed as the fuel essential for operation of the engine that drives the hydrologic cycle. Solar radiation determine weather and climate of earth.

Radiation is emission of heat energy. When the earth is at mean distance from the sun, the rate (intensity) at which solar radiation reaches the upper limits of earth’s atmosphere on a surface normal to the incident radiation is called solar constant (1374 W/m 2 ).
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

Terminology :

Insolation: incident solar radiation

Albedo: ratio of the amount of solar radiation reflected by a surface to the amount incident up on it (%)

Reflectivity: ratio of the amount of electromagnetic radiation reflected by a body to the amount incident up on it (%)
Very little of earth’s surface is normal to incident solar radiation. This irregularity of earth surface causes variation in heat absorption by the earth surface at different location. This difference in insolation is one of the primary factors in determining global circulation of the earth’s atmosphere.
Actinometers and radiometers are used to measure intensity of radiant energy. The data is used in studies of evaporation and snowmelt.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College
Source: USGS

Heat Balance of Earth’s Surface and Atmosphere
Solar Radiation Earth’s Radiation
100 (340 W/m 2 )
6 + 64 = 70 LW
19 absorbed
30 reflected
Emission by clouds
15 absorbed by atmosphere
30 heat flux
51 absorbed by surface of earth
June 2007
21 (LW)
Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Average (or Mean) Temperature: Arithmetic mean temperature for a given period

Mean Daily Temperature: Average of hourly temperature, if hourly data are available
Average of temperature data at pre-specified times, if data of only certain times are available
Average of the daily max and min temperature, if only maximum and minimum data are available
 Normal Temperature: Arithmetic mean temperature based on previous 30 years’ data

Normal Daily Temperature: The average mean daily temperature of a given date computed for a specific 30-year period.

Lapse Rate: The rate at which temperature decreases with increase in altitude through free and undisturbed air

Inversion (or temperature inversion): It is a negative lapse rate, i.e., temperature increases with altitude. This condition usually occurs on still, clear nights because there is little turbulent mixing of air and because outgoing radiation is unhampered by clouds.

Mean monthly Temperature: It is the average of the mean monthly maximum and minimum temperature.

Mean Annual Temperature: It is the average of the monthly means for the year.

Degree Day: It is a departure of one degree for one day in the mean daily temperature from a specified base temperature.

Dew Point: The dew point is the temperature at which the air mass just becomes saturated if cooled at constant pressure with moisture neither added nor removed.

Dry Adiabatic Lapse Rate: Rate of decrease in temperature of a air parcel due to increase in volume when it rises in altitude. The value of dry adiabatic lapse rate is 1 ˚C per 100 m.

Adiabatic Saturation Lapse Rate: When air parcel rises beyond the condensation level the lapse rate is lower (0.3 to 1 degree Celsius per 100 m) due to the addition of latent heat of condensation on the rising air parcel. This lower lapse rate is Adiabatic Saturation Lapse Rate (also known as moist (or wet) adiabatic lapse rate).
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


The thermometers used to measure temperature must be placed where air circulation is relatively unobstructed, and yet they must be protected from the direct rays of the sun and from precipitation. Also, all thermometers should be placed at the same height above the ground for the recorded temperatures to be comparable.
The maximum-minimum thermometers are used to record daily maximum and minimum temperature.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Humidity is the state of atmosphere in relation to amount of water vapor it contains. Humidity is closely related to its temperature – higher the air temperature, more vapor the air can hold. For this reason, saturation vapor pressure (e w
) goes up with air temperature; i.e., as temperature goes up e w also goes up.

Significance of Humidity : The amount of water vapor in air effectively controls the weather condition by controlling evapotranspiration from land and water surfaces. Evaporation rate is proportional to difference between saturated vapor pressure at water temperature
(e w
) and actual vapor pressure in air (e a
).
E
L
= C (e w
– e a
), where, E
L is lake evaporation rate, C is a constant of proportionality.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

:

Molecules of water having sufficient kinetic energy to overcome attractive forces tending to hold them within the body of liquid water are projected through the water surface into the air. The process by which liquid water is converted into vapor is called vaporization or evaporation . Since the kinetic energy increases and surface tension decrease as temperature rises, evaporation rate increases with temperature.
Solar radiation
Rise in kinetic energy of air
Water vapor molecules within water body
Rise in air temperature
Evaporation
Decrease in surface tension
 forces
Most of the atmospheric vapor is the product of evaporation from water surfaces. The direct transformation from ice to vapor, and vice versa, is called sublimation . The process by which vapor changes to the liquid or solid state is called condensation .
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

Properties of Water Vapor

The partial pressure exerted by water vapor is called vapor pressure (e). If all the water vapor in a closed container of moist air with an initial total pressure p were removed, then the final pressure p’ of dry air alone would be less than p. Then, e = p – p’

When the maximum amount of water vapor for a given temperature is contained in a given space, the space is saturated with water vapor. The pressure exerted in a saturated space is called saturation vapor pressure (e w pressure possible at a given temperature. e w
) , which is the maximum vapor
= f (air temperature)

Vaporization removes heat from liquid being vaporized, while condensation adds heat.
Vaporization is the reason for feeling colder on a hot day when we stand in front of a fan.
Vaporization of sweat molecules removes heat from sweat on our skin. The latent heat of vaporization is the amount of heat absorbed by a unit mass of a substance, without change in temperature, which passing from liquid to vapor state. A change from vapor state to liquid state releases equal amount of heat. Latent heat of vaporization (

)
June 2007
The latent heat of vaporization,

, expresses the energy required to change a unit mass of water from liquid to water vapor in a constant pressure and constant temperature process. The value of the latent heat varies as a function of temperature. At a high temperature, less energy will be required than at lower temperatures. As
 varies only slightly over normal temperature ranges a single value of 2.45 MJ kg -1 is taken in the simplification of the FAO Penman-Monteith equation. This is the latent heat for an air temperature of about 20 ° C.
Source: FAO
Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

(continued)

The heat of vaporization of water (Hv) varies with temperature, but can be determined accurately up to 40 ° C by

Hv = 2.50 – 0.00236 T (Hv is in kilojoules per gram, and T is in degree
Celsius) or by

Hv = 597.3 – 0.564 T (Hv is in calories per gram, and T is in degree Celsius).

The latent heat of fusion for water is the amount of heat required to convert one gram of ice to liquid water at same temperature. When one gram of liquid water at 0 ° C freezes into ice at same temperature, the latent heat of fusion (0.337 kJ/g or ≈ 80 cal/g) is liberated.

The latent heat of sublimation for water is the amount of heat required to convert one gram of ice into vapor at same temperature without passing through intermediate liquid state. It is equal to the sum of the latent heat of vaporization and latent heat of fusion. At 0 ° C the latent heat of sublimation for water is about 2.837 kJ/g (2.5 + 0.337). Direct condensation of vapor into ice at same temperature liberated an equivalent amount of heat ( ≈ 677 cal/g). The value of 677 comes from the addition of 597.3 and 80.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College







June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


One of the empirical equations used to calculate vapor pressure (e) is:
 e = e w
– (0.000367) (5 p /9) (T – T w
) [1 + (5 T w
– 448)/14139] where,
T and T w are dry- and wet-bulb temperature ( of a psychrometer consisting of two
°C) thermometers, e w is the saturation vapor pressure (mb) corresponding to T w
, and p is the atmospheric pressure (mb).
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

The atmospheric pressure, P, is the pressure exerted by the weight of the earth's atmosphere. Evaporation at high altitudes is promoted due to low atmospheric pressure as expressed in the psychrometric constant. The effect is, however, small and in the calculation procedures, the average value for a location is sufficient. A simplification of the ideal gas law, assuming 20 °C for a standard atmosphere, can be employed to calculate P: where,

P atmospheric pressure [kPa], z elevation above sea level [m],
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Absolute Humidity : It is the mass of water vapor contained in a unit volume of air at any instant.
ρw = 217 (e/T) where e is in mb and T is in °C.

Specific Humidity (q): It is the mass of water vapor per unit mass of moist air.
q = (0.622 e) / (p – 0.378 e) ≈ 0.622 e /p, where e = vapor pressure (mb) and p = total pressure of the moist air (mb).
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

It is the percentage ratio between the actual vapor pressure (e) and the saturation vapor pressure (e w
) at the same temperature. The relative humidity is not a direct measure of moisture in air.
H = 100 (e/e w
)
H = [(112 – 0.1 T + T d
)/(112 + 0.9 T)] 8

The relative humidity may also be defined as the percentage ratio between the amount of water vapor actually contained per unit volume and the amount of water vapor that it can hold at the same temperature when saturated.

Relation between relative humidity, air temperature and dew point temperature:
T –Td ≈ (14.55+0.1147 T) (1 – H) + [(2.5+0.007 T) (1–
H)] 3 + [(15.9 + 0.117 T) (1 –H)] 14 where, T is in °C and H is in decimal fraction. This relation is correct within 0.3
°C.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Dew point : It is the temperature at which the space becomes saturated when air is cooled under constant pressure and with constant water vapor content. It is the temperature having saturation vapor pressure e w pressure e.
= existing vapor

Mixing Ratio (w r
): The mixing ratio is the mass of water vapor per unit mass of perfectly dry air in a humid mixture. w r
= 0.622 e/p (?)

Depth of precipitable water : It is the amount of water vapor in a layer of air.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

Wind is a moving air. Wind is one of the major factors that affect the climate and evapotranspiration rate from water surface. Higher wind speed results in higher ET rate from a water surface as the wind replaces saturated air just above the water surface by unsaturated air.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College
Source: FAO Corporate Document Repository

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

Basically there are six types of wind .
 a) Sea and land breezes : See breeze is the blowing of wind from sea to land due to higher temperature (lower atmospheric pressure) at land during day time. Sea breeze is the reason we feel cooler near large water body at day time in a hot day. Land breeze is the blowing of wind from land to sea due to quicker cooling of land, and hence denser air above land surface.
 b) Monsoon (seasonal) Winds : Winds whose direction depends on season.
 c) Cyclone : Cyclones are caused when a low pressure area is surrounded by high pressure areas. A cyclone is generally followed by heavy rain.
 d) Anticyclone : Anticyclones result when low areas surround a high pressure area.
 e) Tornadoes : Tornadoes are similar to cyclone, but they generally form over ocean. Tornadoes are generally destructive to land and property.
 f) Local winds : They affect only limited areas and blow for short durations.
The cause of local winds is mostly local temperature depressions,
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


The wind direction is the direction from which it is blowing. Wind direction is usually expressed in terms of 16 compass points (N,
NNE, NE, NEE, E, SEE, SE, SSE, S, SSW, SW, SWW, W, NWW,
NW, NNW) for surface winds and for winds aloft in degrees from
North, measured clockwise. Wind speed is given in KPH or knots (1 knot = 1.143 miles per hours). Wind speed is measured by anemometers. For comparable data, all anemometers are installed at same elevation above ground. Wind speed varies greatly with height above the ground due to ground friction, trees, buildings and other obstacles. Approximate adjustment for anemometers set at different height above ground is
(V/V
0
) = (Z/Z ground, V
0
0
)k where V is the wind speed at height Z above the
= Wind speed at anemometer level Z
0
, k = 1/7.
Wind Rose :

The wind rose is a diagrammatic representation of the wind data
(direction and speed). There are many types of wind roses.
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

A) Measurement of Evaporation

Class A Pan

ISI Standard Pan

Colorado Sunken Pan

USGS Floating Pan
Pan Coefficient (C p
)
Lake Evaporation = C p
× Pan evaporation
B) Empirical Evaporation Equations a) Meyer’s Formula: E b) p a
)(0.44+0.0733 u
0
L
Rohwer’s Formula: E
= K
M
(e w
-e a
)(1+u
9
/16)
= 0.771 (1.465 – 0.000732
L
) (e w
-e a
)
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College

C) Analytical Methods of Evaporation

Water Budget Method
E
L
= P + (V is
- V os
) + (V ig
- V og
) – T

Energy-balance Method
L
-
D
S
H n
= H a
+ H e
+ H g
+ H s
+ H i
H n
H e
= H c
(1-r) – H b
= r
L E
L
E
L
= (H n
– H g
– H s b
= Ha / r
L E
L
- H i
)/[ r
L (1 + b
)]
= 6.1
×10 -4 p a
(T w
-T a
)/(e w
-e a
)

Mass-transfer Method
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


Potential Evapotranspiration (PET)

Actual Evapotranspiration (AET)
 AET≤ PET

AET = PET when plenty of water is available

Consumptive use

Field capacity

Permanent wilting point

Available water

Measurement of Evapotranspiration:

A) Lysimeter

B) Field Plots
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College


PET = [A H n
+ E a g
] / [A + g
]

PET = Daily Potential Evapotranspiration rate (mm/day)

A = slope of the saturation vapor pressure vs. temperature curve at the mean air temperature, mmHg/ °C

H n
= net radiation of mm evaporable water per day

E a
= parameter including wind velocity and saturation deficit = 0.35(1+u
2
/160)(e w
-e a
)
 g
= psychrometric constant = 0.49 mm Hg/
°C

H n
= A + B + C

A = H a

B = s
T
(1-r) (a + b c) a
4 (0.56 – 0.092 √e

C = (0.10 + 0.90 c) a
)
 a = constant depending on latitude f
, a = 0.29 cos f; b = 0.52
 c = n/N, n = actual duration of bright sunshine, N = maximum potential duration of sunshine
 r = albedo = reflection coefficient
 e w
= saturation vapor pressure, u
2

The values of A, H a
, N, and e w
= wind speed at 2 meters above ground are normally can be found in standard textbooks
June 2007 Dr. Hari K. Shrestha
Nepal Engineering College