Evaporation and Transpiration (ET)• Evaporation – process by which water is

transferred from the land and water masses of the earth to the atmosphere

• Transpiration – is the evaporation counterpart from plants which is the process by which soil moisture is taken up by vegetation and eventually evaporated as it exits the plant pores.

• Combined term describing total losses that occur by these mechanisms is Evapotranspiration

Significance of ET• Importance of this system abstraction depends on the

scale and purpose of study• Evaporation and transpiration can account for the majority

of losses from a system over the long term– In temperate areas, 66% of all annual precipitation may be lost to

ET, 500 to 750 mm (20-30 inches)– In arid regions can be up to 90% lost to ET, up to 2000 mm (80

inches)• However, most ET occurs between rainfall and runoff

events• Over the scale of a single rainfall or runoff event, ET is

usually small and usually neglected• However it is a critical parameter for design and operation

of reservoirs for water supply.• Transpiration becomes more important in heavily

vegetated areas and producers of agricultural products

Significance of Evaporation and Transpiration

• In reservoirs especially for water supply purposes the effects of evaporation must be accounted for.

• As an example Kansas experiences 55 inches of evaporation annually, which equates to 1 inch per week.

• Also evaporation of moisture from soils causes the reduction of the moisture content of the soil, affects the AMC of the soil between storm events

Evaporation• There is a continuous exchange of water

molecules between an evaporating surface and the atmosphere

• Common to label this as the net rate of vapour transfer.

• Conversion of snow directly to vapour is called sublimation, overall effect is the same

• Water surfaces are 100% available to evaporation at all times (not that it is always occurring). Soil surfaces may be 100% available if saturated, but can be 0% if soil moisture is low.

• Direct measurement of evaporation is difficult.

Factors influencing Evaporation• Process is dependent on

– Temperature/Energy Input to system– Vapour pressure– Wind Velocity– Barometric/Atmospheric pressure– Water Quality– Nature of the evaporating surface (water depth,

soil type,etc.)

Temperature• The movement/kinetic energy of water molecules

increases with temperature.• Increased energy permits water molecules to

escape more rapidly.• The amount of heat/energy to evaporate one gram

of water called the latent heat of evaporation (Le)• Le = 597.3 – 0.57T, [cal/g], where T is oC

• Therefore energy required for evaporation decreases as temperature of the evaporating water surface increases

• Water also evaporates from snow and ice in a process called sublimation. This quantity can still be significant, but not as significant as from water surfaces

Vapour Pressure• As indicated during the discussion of precipitation, the

concentration of water vapour in the air is expressed in terms of the pressure the water molecules exert on the air. This term is called vapour pressure.

• Water vapour will move into the atmosphere if there is a vapour pressure deficit and saturation of the air has not been achieved. The bigger the deficit the greater the evaporation.

• The evaporation of water from a surface is often described as a thin layer of continuous mixing at the air/water interface due to vapour pressure gradient between air and water.

• A thin layer of water saturated air develops near the water surface. Due to a pressure gradient between the saturated air at the water surface water moves from saturated area to air further above water which is less saturated

Vapour Pressure

• Thin layer concept is Dalton’s Law• E = κ (es-ea)

• E = Evaporation rate (cm/day)• es = saturated vapour pressure at water surface temperature• ea = saturated vapour pressure of air at air temperature• κ = coefficient depending on barometric pressure, wind and other

factors

• When pressure gradient (es-ea) is large then evaporation is increased.

• As air becomes saturated (approaches dewpoint vapour pressure) the rate slows and stops at dew point pressure.

Water Surface

Wind• If the air is very still, the vapour pressure gradient may not

be as pronounced due to the air becoming more saturated with time.

• Wind can disturb the thin film of saturated water vapour over the water surface and the air above the surface thus exposing the water surface to unsaturated air increasing the vapour pressure gradient.

• Also wind can move dryer air into an area over water, maintaining a higher pressure gradient.

• Wind can also cause increased water turbulence due to wave action causing water to spray into air, and accumulate on shorelines (depressions or rocks surfaces) promoting increased evaporation

• Wind velocity effect is related to the size of the water body where water vapour can be more quickly removed from small bodies versus large bodies of water

Atmospheric Pressure• Fewer air molecules are present in less dense air

(lower atmospheric pressure) and less likelihood of water molecules colliding with air molecules

• As such evaporation rate is higher in lower atmospheric pressure

• Thus, evaporation rate can be higher at higher altitudes. However, lower temperatures at higher altitudes can offset the effect.

• Under changing atmospheric conditions (low/high pressure systems) evaporation rate conditions will also change

Water Quality• Overall the water quality impact is small• The vapour pressure of water with

increased total dissolved solids (TDS) is reduced

• Thus, evaporation is lower in salt water than in freshwater.

• A salt content of 1%, slows the evaporation by about 1%

• Oceans have a salt content of about 3%, and therefore their evaporation rate is about 3% less than freshwater

Water Depth and Soil Type• Smaller shallow lakes are more rapidly heated

than large bodies and therefore are evaporated more rapidly

• Precipitation intercepted in shallow pools or forest canopy warms quickly and evaporates

• Dark soils, rocks or dark pond bottoms absorb heat and warm the water bodies more rapidly, promoting increased evaporation

• Heat can penetrate into soil and evaporate moisture contained within the soil pores. Ground surfaces with mulch or debris covering (such as forests) reduce evaporation from soil.

Estimation of Evaporation• Evaporation cannot be measured directly, most

methods make use of the budget equation and balance the inflow outflow and change in storage

• Methods used often depend on required accuracy and type of instrumentation available

• Methods of calculating include:– Water Budget Calculation– Pan Evaporation Method– Energy Budget Method– Mass Transfer Method

• Usually the instrumentation required for energy budget and mass transfer methods is expensive to purchase and maintain

• Most common methods are the water budget and evaporation pan methods

Water Budget Method• The water budget equation can be rearranged as follows:

• Es = P – R – I – ∆S

• All terms are in volume units for a time period of interest, and ∆t should be at least a week

• Accuracy depends on the type and quantity of instrumentation available.

• P and R can be measured most easily and some information is available from various sources

• For reservoir systems often ∆S information readily and continuously available

• For natural systems ∆S information often not recorded, therefore difficult to apply method

• Infiltration not easily measurable so often this is not separated and would be included in the evaporation term.

• All errors in measuring inflow, outflow, precipitation, seepage and ∆S are within evaporation estimate

Evaporation Pan Method• Evaporation Pan is simplest field method which

directly measured evaporation. • Class A pan constructed of galvanized steel of 1.2

m (4 ft) diameter, 25 cm (10 in) deep installed 30 cm (1 ft) off the ground with water filled to 5 to 7.5 cm from to top edge of the pan.

• Eactual = Epan*PC– Eactual = actual evaporation from lake– Epan = evaporation observed from pan– PC = pan coefficient

• Through observations the pan coefficient is typically 0.7-0.75 but can range between 0.67 to 0.81

Evaporation Pan Method

Evaporation Pan Method• Ratios of pan evaporation are often consistent

from year to year, but can be quite variable from month to month.

• This is due to increased warming of the water within the pan compared to the water body being measured (advected energy and heat transfer through the pan)

• These variations from within the pan compared to within the lake are significant

• Installations should be located in an area that is representative of the body of water being considered so the pan is under similar conditions

• Pans can also be installed underground or floating to have more representative conditions.

Evaporation Pan Method• Advantages:

– Reasonable cost– Reasonable estimate of evaporation rates– Coefficient is relatively stable– Easily accessible and understood

• Disadvantages:– The coefficient is not fixed in time and space

and will vary

Evaporation Pan Method• To account for advected energy and heat

transfer through the pan, the following expression is presented in your text:

• EL = 0.7[Ep+0.00051Pαp(0.37+0.0041up)(T0-Ta)0.88], and• αp = 0.13+0.0065T0-(6.0x10-8T0

3)+0.016up0.36

• EL = Lake evaporation (in/day)• Ep = evaporation (in/day)• P = atmospheric pressure (inches of Hg)• αp = proportion of advected energy (Class A Pan)• up = wind velocity (mi/day)• Ta = Air temperature (oF) • To = Outerface temperature of pan (oF)

• A graphical solution of this equation is provided in your text

Energy Budget MethodEnergy

advected by evaporated water, Qw

Energy Conducted Out

as Sensible Heat, Qh

Solar Radiation In, Qs

AdvectedEnergy In, Qvin

Energy used in Evaporation,

Qe

Long Wave Radiation Emitted by Water, Qbs

Reflected Long Wave

Radiation, Qar

AdvectedEnergy Out,

Qvout

Incoming Long Wave

Radiation, Qa

Reflected Solar Radiation out,

Qr

Increase in Stored Energy in Water, Q0

Qo = Qs-Qr+Qa-Qar+Qvin-Qvout-Qbs-Qe-Qh-Qw

Energy Budget Method• All terms in calories per square centimetre per day

(cal/cm2-day)• Similar to mass balancing (conservation of mass) but

rather balancing of energy (conservation of energy)• Still require estimate of inflow and outflow to determine net

advected energy due to inflow and outflow.• Accuracy of estimates highly dependant on reliability of

measured data.• Equation 6.8 and 6.9 in text provides further breakdown of

equations to allow solving for evaporation. Many other forms of these equations have also been developed

• This method aids in understanding the evaporation process, but in terms of practical application in hydrology it is use is limited

• However with improvements and reduction of costs of instrumentation, method could be used more extensively in future.

Mass Transfer Method• Many forms of the mass transfer method

have been developed. All are based on Dalton’s Law:

• E = κ(es-ea)» E = Evaporation» κ = a coefficient dependant on the wind velocity,

atmospheric pressure and other factors» es, ea = the saturation vapour pressure at the water

surface temperature and the vapour pressure of air, respectively

• This is the same vapour pressure gradient described previously

Mass Transfer Method• One popular method is the Meyer formula:

• E = C(es-ea)(1+W/16)» E = daily evaporation in cm/day» C = empirical coefficient, for a daily evaporation rate

varies between 0.36 for an ordinary lake and 0.5 for small puddles, shallow pans, wet soils

» es, ea = same as previous slide (mb)» W = wind velocity in km/h measure 8 m above water

surface

• Mass transfer methods rely identification of the vapour pressure deficit and various methods to identify the constant

Mass Transfer Method• Another method is based on Lake Hefner studies

use the following:– E = Nu (eo-ea)

• E = daily evaporation in cm/day• N = a coefficient• eo, ea = same as previous slide (mb)• u = wind velocity in m/s measure 2 m above water surface

• N value can be determined through studies of mass transfer and energy budget approaches. Also can be approximated (with caution) by:

– N = 0.0291/A0.05

• A = surface area of water body in m2, where area must be > 4x106 square metres

Transpiration• Most of the water lost by transpiration is through stomatal

openings within leaves• Basically it is the process by which water is evaporated

from the plant pores and is affected by the same factors as evaporation

• A vapour pressure gradient develops at the leaf/air interface as leaves can heat above air temperature as much as 5-10oF

• Plants transpire little if any during rainfall event when vapour pressure gradient, transpire rapidly when sunshine, warmth and adequate soil moisture is present

• Different species of plants can display large differences on soil moisture demands

– Oak tree – 170 quarts of water/day– Corn – 2 quarts of water/day

• Stomata actively transpire water during daylight hours but close after darkness

Transpiration/Evapotranspiration• Determining water abstractions due to only

transpiration difficult to achieve, and usually not of much value for hydrologic analyses

• Instead transpiration typically combined with evaporation to form a combined term of evapotranspiration (ET)

• The method most commonly used to calculate ET is the Penman Method

Evapotranspiration• An estimation of transpiration from crops is by Consumptive Use which

actually combines both transpiration and evaporation• Consumptive Use differs from Transpiration only in that it includes water

that is used to make plant tissue, which for all practical purposes is negligible

• Blaney Criddle Method– U = ksB

• U = the consumptive use of water during the growing season (in.)• ks = a seasonal consumptive use coefficient applicable to a particular crop• B = the summation of the monthly consumptive use factors for a given season • B = Σ(tp/100)

– t = the mean monthly temperature (oF)– p = the monthly daytime hours given as percentage of the year

– If monthly k values are available the monthly consumptive use (u) can be found using:

• u = ktp/100 • By this method one can determine the amount of water that must be

applied to a crop. Quantity should also include water lost to runoff and other losses

Evapotranspiration• Method most often used is a combination of the energy

budget and mass transfer called the Penman Equation:– ET = [∆H + 0.27E]/[∆ + 0.27]

• ET = evapotranspiration (mm/day)• ∆ = the slope of the saturated vapour pressure curve of air at absolute

temperature (mm Hg/oF)• H = the daily heat budget at the surface (estimate of net radiation)

(mm/day)• E = daily evaporation (mm)

• ∆ is the slope of the which is equal to (es-ed)/(Ts-Td) which is the difference of saturated and dew point vapour pressure divided by the difference in temperature of the water surface and dew point temperature

• E is considered the “drying capacity” of the air, based on mass transfer parameters

• H is considered the net radiation made up of the incoming short wave radiation and the outgoing thermal radiation, energy budget portion of the equation

• Where E and H are calculated as follows

Evapotranspiration

Evapotranspiration• E = 0.35 (ea-ed)(1+0.0098u2)

– ea = the saturated vapour pressure at mean air temperature (mm Hg)

– ed = the saturated vapour pressure at mean dew point (actual vapour pressure of the air) (mm Hg)

– u2 = the mean wind speed at 2 m above the ground (mi/hr)

• H = R(1-r)(0.18 + 0.55S) – B(0.56-0.092ed0.5)(0.1+0.9S)

– R = the mean monthly extraterrestrial radiation (mm H2O evaporated per day)

– r = the estimated percentage of reflecting surface– B = a temperature dependent coefficient– S = the estimated ratio of actual duration of bright

sunshine to maximum possible duration of bright sunshine.

• Other methods of calculating H are also used

Evapotranspiration• The coefficient r is also termed “albedo” which is

the reflectivity of the surface to short wave radiation

• For water the albedo is a function of the time of year, calmness of the water surface, wind velocity and water quality typically between 0.05 to 0.12

• Albedo of other surfaces• Vegetated area: 0.1 to 0.3• Bare soils: 0.15 to 0.4• Snow covered area: 0.9

• The values of ea and ∆ can be obtained from graphs and R and B from tables

• Use of equation requires knowledge of vapour pressures, sunshine duration, net radiation, wind speed, and mean temperature.