Evaporation

1
Evaporation

• Slides prepared by Daene C. McKinney and
  Venkatesh Merwade
• Reading Applied Hydrology Sections 4.1 and 4.2

2
Evaporation

• Terminology
• Evaporation process by which liquid water
  passes directly to the vapor phase
• Transpiration - process by which liquid water
  passes from liquid to vapor through plant
  metabolism
• Sublimation - process by which water passes
  directly from the solid phase to the vapor phase

3
Factors Influencing Evaporation

• Energy supply for vaporization (latent heat)
• Solar radiation
• Transport of vapor away from evaporative surface
• Wind velocity over surface
• Specific humidity gradient above surface
• Vegetated surfaces
• Supply of moisture to the surface
• Evapotranspiration (ET)
• Potential Evapotranspiration (PET) moisture
  supply is not limited

4
Evaporation from a Water Surface

• Simplest form of evaporation
• From free liquid of permanently saturated surface

5
Evaporation from a Pan

• National Weather Service Class A type
• Installed on a wooden platform in a grassy
  location
• Filled with water to within 2.5 inches of the top
• Evaporation rate is measured by manual readings
  or with an analog output evaporation gauge

6
Methods of Estimating Evaporation

• Energy Balance Method
• Aerodynamic method
• Combined method

7
Energy Method

• CV contains liquid and vapor phase water
• Continuity - Liquid phase

No flow of liquid water through CS
8
Energy Method

• Continuity - Vapor phase

Steady flow of air over water
9
Energy Method

• Energy Eq.

10
Energy Method

• Energy Eq. for Water in CV

Assume 1. Constant temp of water in CV 2. Change
of heat is change in internal energy of water
evaporated
Recall
Neglecting sensible and ground heat fluxes
11
Transport Processes

• Sun is the major source of energy in hydrologic
  cycle
• Energy transport takes place through
• Conduction
• Convection
• Radiation

12
Flux

• The rate of flow of extensive property per unit
  area of surface through which it passes is called
  the flux.

Volumetric flux
Mass flux
Mass flux density x volumetric flux
Momentum flux
Momentum flux mass flux x velocity
Energy flux
13
Conduction

• Heat is transferred as molecules with higher
  temperature collide with lower temperature
  molecules
• Results from random molecular motion in
  substances
• Eg. Heating of earths land surface

14
Conduction of mass, momentum and energy

• Flux is proportional to the gradient of a
  potential

Momentum flux (laminar flow)
Newtons law of viscosity
Mass flux
Ficks law of diffusion
Energy flux
Fouriers law of heat conduction
m is dynamic viscosity, D is diffusion
coefficient, and k is heat conductivity. Dynamic
viscosity (m) is related to kinematic viscosity
(n) as m r n
The direction of transport of extensive
properties is transverse to the direction of
flow.
15
Convection

• Energy transfer through the action of turbulent
  eddies or mass movement of fluids with different
  velocities.
• Turbulence mechanism causing greater rate of
  exchange of mass, energy, and momentum than
  molecular exchanges
• Unlike conduction, convection requires flowing
  fluid
• Eg. Convection causes vertical air circulation in
  which warm air rises and cool air sinks,
  resulting in vertical transport and mixing of
  atmospheric properties

16
Convection of mass, momentum and energy
Momentum flux (turbulent flow)
Km is momentum diffusivity or eddy viscosity
Mass flux
Kw is mass diffusivity
Energy flux
Kh is heat diffusivity

• Km is 4-6 orders of magnitude greater than n.
• tturb is the dominant momentum transfer in
  surface water flow and air flow.

The direction of transport of extensive
properties is transverse to the direction of
flow.
17
Velocity Profile

• Determining momentum transfer requires knowing
  velocity profile
• Flow of air over land or water log velocity
  profile

Von Karman constant Roughness height
Shear velocity
Wall shear stress
Velocity gradient
18
Wind as a Factor in Evaporation

• Wind has a major effect on evaporation, E
• Wind removes vapor-laden air by convection
• This Keeps boundary layer thin
• Maintains a high rate of water transfer from
  liquid to vapor phase
• Wind is also turbulent
• Convective diffusion is several orders of
  magnitude larger than molecular diffusion

19
Aerodynamic Method

• Include transport of vapor away from water
  surface as function of
• Humidity gradient above surface
• Wind speed across surface
• Upward vapor flux
• Upward momentum flux

20
Aerodynamic Method

• Log-velocity profile
• Momentum flux

Thornthwaite-Holzman Equation
21
Aerodynamic Method

• Often only available at 1 elevation
• Simplifying

22
Combined Method

• Evaporation is calculated by
• Aerodynamic method
• Energy supply is not limiting
• Energy method
• Vapor transport is not limiting
• Normally, both are limiting, so use a combination
  method

Priestly Taylor
23
Example

• Use Combo Method to find Evaporation

• Elev 2 m,
• Press 101.3 kPa,
• Wind speed 3 m/s,
• Net Radiation 200 W/m2,
• Air Temp 25 degC,
• Rel. Humidity 40,

24
Example (Cont.)

• Use Combo Method to find Evaporation

• Elev 2 m,
• Press 101.3 kPa,
• Wind speed 3 m/s,
• Net Radiation 200 W/m2,
• Air Temp 25 degC,
• Rel. Humidity 40,

25
Example (Cont.)

• Use Combo Method to find Evaporation

• Elev 2 m,
• Press 101.3 kPa,
• Wind speed 3 m/s,
• Net Radiation 200 W/m2,
• Air Temp 25 degC,
• Rel. Humidity 40,

26
Example

• Use Priestly-Taylor Method to find Evaporation
  rate for a water body

• Net Radiation 200 W/m2,
• Air Temp 25 degC,

Priestly Taylor
27
Evapotranspiration

• Evapotranspiration
• Combination of evaporation from soil surface and
  transpiration from vegetation
• Governing factors
• Energy supply and vapor transport
• Supply of moisture at evaporative surfaces
• Reference crop
• 8-15 cm of healthy growing green grass with
  abundant water
• Combo Method works well if B is calibrated to
  local conditions

28
Potential Evapotranspiration

• Multiply reference crop ET by a Crop Coefficient
  and a Soil Coefficient

http//www.ext.colostate.edu/pubs/crops/04707.html
29
Resources on the web

• Evaporation maps from NWS climate prediction
  center
• http//www.cpc.ncep.noaa.gov/soilmst/e.shtml
• Climate maps from NCDC
• http//www.nndc.noaa.gov/cgi-bin/climaps/climaps.p
  l
• Evapotranspiration variability in the US
• http//geochange.er.usgs.gov/sw/changes/natural/et
  /