Download Engineering Hydrology HYD 301.3

Engineering Hydrology
HYD 301.3
Dr. Hari Krishna Shrestha
Associate Professor, Dept. of Civil Engineering, Nepal Engineering College
Director, Center for Disaster Risk Studies
Contact: [email protected]
June 2007
Chapter 2
Evapotranspiration (ET) Factors (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:
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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
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Humidity
ET
2.1 Radiation
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June 2007
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/m2).
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
Radiation Balance
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/m2)
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
2.2 Temperature
Temperature is a measure of hotness
of an object. Air temperature directly
affects the evapotranspiration from a
basin and hence affects the water
balance. Temperature of atmospheric
air decreases at an average rate of
about 6˚C per 1000 m increase in
altitude within the troposphere, but is
relatively constant in the lower part of
the stratosphere.
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
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Terminologies
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
Temperature measurement
 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
Factors Affecting Temperature
 The temperature of a locality is a complex
function of several variables such as
latitude, altitude, ocean currents, distance
from sea, winds, cloud cover, and aspect
(land slope and its orientation).
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
2.3 Humidity
 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 (ew) goes up with air temperature; i.e., as
temperature goes up ew 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
(ew) and actual vapor pressure in air (ea).
EL = C (ew – ea),
where, EL is lake evaporation rate, C is a constant of
proportionality.
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Causes of Humidity:
 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
molecules within water body
Rise in air
temperature
Water vapor
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
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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’
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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 (ew), which is the maximum vapor
pressure possible at a given temperature. ew = f (air temperature)
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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 ()
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
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Properties of Water Vapor (continued)
 The heat of vaporization of water (Hv) varies with temperature, but can be
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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
Measures of Atmospheric Moisture
Commonly used measures of humidity:
 Vapor pressure
 Absolute humidity
 Specific humidity
 Mixing ratio
 Relative humidity
 Dew point
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Vapor Pressure
 One of the empirical equations used to calculate
vapor pressure (e) is:
 e = ew – (0.000367) (5 p /9) (T – Tw) [1 + (5 Tw – 448)/14139]
where,
T and Tw are dry- and wet-bulb temperature (°C)
of a psychrometer consisting of two
thermometers,
ew is the saturation vapor pressure (mb)
corresponding to Tw, and
p is the atmospheric pressure (mb).
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Atmospheric pressure (P)
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 and Specific Humidity
 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
Relative Humidity
It is the percentage ratio between the actual vapor pressure (e) and
the saturation vapor pressure (ew) at the same temperature. The
relative humidity is not a direct measure of moisture in air.
H = 100 (e/ew)
H = [(112 – 0.1 T + Td)/(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
 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 ew = existing vapor
pressure e.
 Mixing Ratio (wr): The mixing ratio is the mass of
water vapor per unit mass of perfectly dry air in
a humid mixture. wr = 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
2.4 Wind Speed
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
Types of Wind
Basically there are six types of wind.
 a) Sea and land breezes: See breeze is the blowing of wind from sea to
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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
Wind Measurements
 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/V0) = (Z/Z0)k where V is the wind speed at height Z above the
ground, V0 = Wind speed at anemometer level Z0, 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
Types of
Wind
roses
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Evaporation
A) Measurement of Evaporation
 Class A Pan
 ISI Standard Pan
 Colorado Sunken Pan
 USGS Floating Pan
Pan Coefficient (Cp)
Lake Evaporation = Cp × Pan evaporation
B) Empirical Evaporation Equations
a) Meyer’s Formula: EL = KM (ew-ea)(1+u9/16)
b) Rohwer’s Formula: EL = 0.771 (1.465 – 0.000732
pa)(0.44+0.0733 u0) (ew-ea)
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Evaporation
C) Analytical Methods of Evaporation
 Water Budget Method
EL = P + (Vis - Vos) + (Vig - Vog) – TL - DS
 Energy-balance Method
Hn = Ha + He + Hg + Hs + Hi
Hn = Hc (1-r) – Hb
He = r L EL
EL = (Hn – Hg – Hs - Hi)/[r L (1 + b)]
b = Ha / r L EL = 6.1×10-4 pa (Tw-Ta)/(ew-ea)
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Mass-transfer Method
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College
Evapotranspiration
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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
Penman Equation to Estimate
Potential Evapotranspiration (PET)
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PET = [A Hn + Ea 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
Hn = net radiation of mm evaporable water per day
Ea = parameter including wind velocity and saturation deficit = 0.35(1+u2/160)(ew-ea)
g = psychrometric constant = 0.49 mm Hg/°C
Hn = A + B + C
A = Ha (1-r) (a + b c)
B = s Ta4 (0.56 – 0.092 √ea)
C = (0.10 + 0.90 c)
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
ew = saturation vapor pressure, u2 = wind speed at 2 meters above ground
The values of A, Ha, N, and ew are normally can be found in standard textbooks
June 2007
Dr. Hari K. Shrestha
Nepal Engineering College