Evaporation

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Evaporation

• Principles
• Estimation and analytic techniques

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Units and Quantities

• Millibars pressure N/m2
• Pascals pressure 100 mb
• cp - specific heat of the atmosphere at constant
  pressure 1004 J/(Kkg)

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Water Vapor

• Vapor is a gas
• Water vapor comprises 4 of well-mixed lower
  portion of atmosphere
• Saturation vapor pressure (es) - max water vapor
  holding capacity
• es varies with temperature, pressure and moisture
  content of the air

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Evaporation

• Globally 62 of water received at land surface
  is returned by evapotranspiration processes
• 97 is returned from land surfaces by plant
  processes and evaporation from soil and plant
  surfaces
• 3 is returned from open water
• ET amounts usually gtgt runoff

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Evaporation Process

• Constant exchange of water molecules between
  liquid and gas phases
• Some molecules that hit the water surface
  rebound, but capture rate is proportional to rate
  of collision
• Loss rate is proportional to number of molecules
  that have sufficient energy to escape

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Factors affecting loss rate

• Temperature
• Relative humidity
• Presence of solutes in water
• Rate of air exchange over a water surface
• Amount of solar energy received

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Potential evaporation

• Potential quantity of water evaporated per unit
  area per unit time from an idealized, extensive
  free water surface
• Differs from actual evaporation because
  conditions may be different than those used to
  develop estimates of potential

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Evapotranspiration (ET)

• Evaporation and plant transpiration vapor
  transfer are often combined
• Evaporation estimates are most appropriate for
  open water surfaces
• In others water vapor transfers by both
  mechanisms are combined

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Annual potential evapotranspiration v. rainfall
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Importance of accurate estimation

• ET equates to water demand for agriculture and
  horticulture
• ET very significant with respect to quantity and
  quality of reservoirs
• Evaporated water vapor leaves dissolved solids
  behind, which creates salinity problems in soils
  and surface water bodies

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Salty water
Concentration (ppm)
Brackish water
Water surface elevation (ft)
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Evaporation Estimation

• Based on analog measurements and mass and energy
  transfer concepts
• Practically applied using weather data (like UNR
  station on Valley Road)
• Represents application of the Penman equation
  (widely used method for estimating ET combined
  evaporation and transpiration)

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Approaches

• ET measurement is difficult, usually must be
  derived from a variety of other measurements
• Theoretically, by Law of Diffusion
  EKeva(es-ea)E Evaporation rate (L/T)Ke
  coefficient related to vertical transfer of vapor
  by wind va speed of air movement (L/T)(es-ea)
  vapor pressure differences, surface and air
  (M/LT2)

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Complicating factors

• Equation is a simple representation of complex
  system of processes
• Ke cannot be measured directly
• Air movement can be horizontal and vertical
• Vapor pressures of both media change with
  temperature and relative humidity
• Inputs and outputs (rain, solar energy) must be
  accounted for

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Approaches

• Analog measurements
• Water balance and error term estimation
• Energy balances
• Combinations
• Important aspects what is considered,
  technique, required data, expected level of
  accuracy

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Analog Measurements

• Class A Evaporation Pans
• Standardized by U.S. Weather Bureau
• Most widely applied method for estimating
  potential evapotranspiration
• One of many designs
• Very simple to install, operate and maintain

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Installation requirements

• Mounted on open wooden frame
• Bottom .15 m above ground level
• Water level is within .05 m of the top of the pan
• Water level fluctuates less than .075 m
• Protective coverings such as mesh should be
  avoided

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Strengths and Weaknesses of Pan Approach

• Pan reading is sensitive to surroundings
• Evaporation amount is difficult to relate to crop
  needs
• Published correction factors (pan coefficients)
  account for a limited range of conditions,
  including relative humidity and wind speeds

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Pan Coefficients

• ErcKpanA EpanA
• rc reference crop (e.g. grass)
• panA a class A evaporation pan
• K a coefficient

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Calibration KpanA factor
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Relationship between reference crop estimates and
observed pan evaporation amounts

• ErcKpanAEpanA
• As KpanA decreases(increases), the estimated
  amount of actual ET decreases(increases)
• KpanA 1/f(Wind Speed)
• KpanA f(Relative Humidity)
• KpanA f(fetch)
• Does this make sense?

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Seasonal variation of KpanA for corn over the
growing season. In early June, KpanA .4. In
early August .8.
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Water Balance Approach

• DS I - O
• DS Net change in volume of water during time
  interval of interest(Dt)
• I Influent water (i?Dt)(L3)
• O Outflowing water (o?Dt)(L3)

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Aspects of water balance approach

• What is considered the difference between all
  measurable inflows and outflows
• EWSWinGWin-SWout-GWout-DV
• W precipitation
• GW groundwater flow
• SW surface water flow
• DV change in volume

IN
OUT
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Technique, Required Data

• Account for all measurable inflows and outflows
• Account for changes in volume
• Requires highly accurate estimates of inflow and
  outflow and volume of surface water body
• Volume estimates come from bathymetric surveys,
  stream gaging stations in inlets and outlets
• Groundwater flow cannot be measured

EWSWinGWin-SWout-GWout-DV
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Expected Level of Accuracy

• Result incorporates all measurement error
• Accuracy increases as the accuracy of
  measurements of individual quantities increases
  (importance of error decreases)
• Under best case result may be ?20
• Under most cases result may be ?100

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Example Importance of Measurement Precision

• Lake Tahoe average surface area 191 mi2
• .25 drop in water level 2550 aft
• average daily runoff at Farad, Ca. gaging
  station from 1909-1999

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Energy balance

• DS I - O
• DS ? Net change in stored energy during time
  interval of interest (Dt)
• I ? Influent energy (i?Dt)(W/m2)
• O ? Outflowing energy (o?Dt)(W/m2)

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Elements of Energy Balance Considered

• DQ QNRQv-(QeQhQw)
• NR - net solar radiation
• v - net energy advected
• e - evaporative energy
• H - sensible heat

e,H
ea low
Ta low
v
NR
ea high
Ts high
v
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Developing the Energy Balance with Measurable
Quantities

• K recd short wave radiation
• L recd long wave radiation
• Aw energy recd in water (precip)
• H sensible heat exchange with atmosphere
• G heat transfer to soils
• DQ/Dt change in energy stored in the control
  volume

Qin
Qout
DQ
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Application

• ?Q Qin-Qout
• If ?Q lt0, assume loss of energy from the system
  due to evaporation
• Use relationships between energy and changes in
  state to estimate mass of water loss
• Mass is converted to volume (1 gm/cm3)
• Volume surface area inches evaporated

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Refinement Combined approach

• Incorporates mass and energy balance approaches
• ca - specific heat of the atmosphere at constant
  pressure 1004 J/(Kkg)

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(T)v

• E Amount of evaporated water
• K recd short wave radiation
• L recd long wave radiation
• Aw energy recd in water (precipitation,
  inflowing groundwater, surface water)
• H sensible heat exchange with atmosphere
• G heat transfer to soils
• DQ/Dt change in energy stored in the control
  volume

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?(T)v Latent heat of evaporation as a function
of temperature

• Latent heat of evaporation ?2.5 kJ needed to
  evaporate 1 gm water
• ?(T)v 2500.3 - 2.361 T (ºC) (J/g)

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(T)v

• What must be measured and how?
• System is complex, driven by energy gradients
• Energy gradients include both temperature and
  vapor pressure differences between the free water
  surface and air
• This implies both sensible and latent heat
  tranfers
• Involves energy transferred by diffusion and
  turbulent transport (wind)

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Assumptions

• On an appropriate time step some elements can be
  considered insignificant
• Energy gradients (represented by temperature and
  vapor pressure differences between the free water
  surface and air) likely represent the most
  significant routes of energy transfer
• Energy transfer occurs as sensible and latent
  heat and diffusion and turbulent transport (wind)

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Penman Assumptions

• Free water surface (unlimited water supply)
• No transfer of heat energy between water body and
  surrounding soils
• No water advected energy enters the system
• No net change in energy stored within the system

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K Shortwave solar radiation

• Relative to surface of reservoir
• K can be measured, but more likely must be
  estimated
• Estimation can be done with tables and programs
• Accurate estimation accounts for changes in
  received solar radiation (date) and cloud cover

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Estimation of L

• L sT4(0.5 - .08?e)(0.20.8 (n/N))
• s Stefan-Boltzmann constant
• T Average air temperature (ºK)
• e average vapor pressure (mb)
• n/N actual v. potential number of hours of
  sunshine received (cloudiness factor)

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HKhva(Ts-Ta)
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Remember Evaporation due to vapor pressure
gradients alone is expressed as E
KEva(es-ea) This assumes that vapor pressure at
a free water surface is the equivalent of
saturated vapor pressure
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eventually, using the relationship between
relative humidity and saturated vapor pressure,
substitution (using the above) and a relationship
to estimate KH, we end up with the Penman
equation.
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Penman Equation for Evaporation from a Free Water
Surface
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Psychrometric constant (mb/C)
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Measurement Implications

• Need
• relative humidity
• temperature at two elevations
• estimates of net radiation
• wind velocity

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Adaptation for evapotranspiration Estimation
Monteith Modifications

• Increased wind turbulence effects and
  transpiration quantities due to presence of
  vegetation are addressed partly through
  modifications of KH term
• For Penman approach
• caheat capacity of air
• Z roughness height of surface (0),
  measurementheight (m) and height of reference
  plane (d)

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Penman Monteith ET Equation
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ca, Cat, Ccan, ?

• ca heat capacity of air (.001 MJ/(kgK))
• Ccan canopy conductance fsLAICleaf
• fs shelter factor, that accounts for leaf cover
  that leads to lower transpiration rates (.5-1)
• Cat atmospheric conductance

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• zm top of vegetation 2m
• z0 0.1 zveg (tabled or measured values)
• zd 0.7 zveg
• LAI leaf area index (total leaf area with
  respect to equivalent ground area)
• Cleaf maximum leaf conductance (tabled value)

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Priestly-Taylor
Assumes that heat flux into the ground (G) is
significant, but treats it as a function of LK
(0.1(LK))
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Assumes

• Net energy expended on evaporation lt ((LK)-G)
  (based on assumption that the sensible heat
  gradient is relatively constant)
• Net energy expended on evaporation gt
  ?/(??)((LK)-G)
• Can be accounted for with a coefficient (?) such
  that
• ? lt (? ?) /(?) and ? gt 1

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Priestly-Taylor

• Substitutes a proportionality factor for mass
  transfer component of the Penman Monteith model.
• Estimated average value of 1.26 for short grasses
  and humid conditions.
• Increased for arid and semi-arid climates.

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Spreadsheet model of Penman Monteith

• Penman Monteith Spreadsheet Model
• Ornamental grass irrigation management
  application http//www.washoeet.dri.edu/washoeEt
  .html

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• www.washoeet.dri.edu/washoeEt.html

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Expected level of accuracy

• Instrumentation must be available
• Ignores turbulent, advective transport due to
  wind
• Relies on few point estimates, which implies
  homogeneity of system within control volume
• Difficult to apply to mixed or internally
  variable surfaces

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Summary

• Discussed different approaches for evaporation
  estimation and combination
• Mass balance approach requires careful
  measurement of inflows and outflows and reservoir
  of interest
• Both require careful measurement or accuracy
  suffers
• Important to understand assumptions

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Next Time

• Condensation, precipitation and precipitation
  estimation