Engineering%20Hydrology%20HYD%20301.3

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Engineering HydrologyHYD 301.3

• Dr. Hari Krishna Shrestha
• Associate Professor, Dept. of Civil Engineering,
  Nepal Engineering College
• Director, Center for Disaster Risk Studies
• Contact shrestha_h_at_hotmail.com
• June 2007

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Chapter 2Evapotranspiration (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
• 2.1 Solar Radiation
• 2.2 Air Temperature
• 2.3 Air Humidity
• 2.4 Wind Speed
• 2.5 Evaporation
• 2.6 Transpiration
• 2.7 Penmans Equation

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2.1 Radiation

• 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 earths atmosphere on a surface
  normal to the incident radiation is called solar
  constant (1374 W/m2).

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• 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 earths 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
  earths atmosphere.
• Actinometers and radiometers are used to measure
  intensity of radiant energy. The data is used in
  studies of evaporation and snowmelt.

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Radiation Balance
Source USGS
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Heat Balance of Earths Surface and Atmosphere
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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 6C per
  1000 m increase in altitude within the
  troposphere, but is relatively constant in the
  lower part of the stratosphere.

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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).

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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.

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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).

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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.

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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.
• 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.

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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 (ew), which is the
  maximum vapor pressure possible at a given
  temperature. ew 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 (?)

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 20C. Source FAO
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Properties of Water Vapor (continued)

• The heat of vaporization of water (Hv) varies
  with temperature, but can be determined
  accurately up to 40C 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 0C 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 0C
  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.

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Measures of Atmospheric Moisture

• Commonly used measures of humidity
• Vapor pressure
• Absolute humidity
• Specific humidity
• Mixing ratio
• Relative humidity
• Dew point

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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).

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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
  20C for a standard atmosphere, can be employed
  to calculate P
• where,
• P atmospheric pressure kPa,z elevation above
  sea level m,

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Absolute and Specific Humidity

• Absolute Humidity It is the mass of water vapor
  contained in a unit volume of air at any instant.
  
• ?w 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).

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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
• TTd (14.550.1147 T) (1 H) (2.50.007 T)
  (1 H)3 (15.9 0.117 T) (1H)14
• where, T is in C and H is in decimal fraction.
  This relation is correct within 0.3C.

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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.

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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.

Source FAO Corporate Document Repository
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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 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,

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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.

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Types of Wind roses
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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
• Meyers Formula EL KM (ew-ea)(1u9/16)
• Rohwers Formula EL 0.771 (1.465 0.000732
  pa)(0.440.0733 u0) (ew-ea)

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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)
• Ha / r L EL 6.110-4 pa (Tw-Ta)/(ew-ea)
• Mass-transfer Method

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Evapotranspiration

• 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

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Penman Equation to Estimate Potential
Evapotranspiration (PET)

• 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(1u2/160)(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 vea)
• 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