EVAPORATION AND TRANSPIRATION
(70% of annual budget)
Evaporation:
- change of liquid to vapor from a free water surface (net)
Transpiration:
- change of liquid to vapor through a plant
- main loss for storms
- major loss for annual budgets
- incorporation of water into plant tissue - consumptive use
(note: not the consumptive use defined by the SWFWMD)
Sublimation - the change in phase from solid to vapor change
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TRANSPIRATION - function of vegetation type, degree of
cover, soil & moisture conditions
e/ z
very large gradient; basic driving process for pumping
water through the plant
Order of Importance, for planning (Ref. Plant Physiology,
Salisbury & Ross, Chapter 3):
1.
Vapor pressure gradient at leaves (20 - 30 atms)
2.
Osmosis at roots (<= 8 atms)
3.
Capillarity (<= 1 atm) 1 atm
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33 ft
Transpiration Modeling
Assume:
-
upper limit to rate at which moisture can be moved to
leaves = Qi f(plant) (pumping)
-
upper limit at which atm can "absorb" water; upper limit to
evap. into atm = potential evapotranspiration = PET
If PET > Qi
- remove water until wilting occurs, soil
moisture wilting point
If Qi > PET
- remove at rate = PET
Sometimes transpiration is evident in well records:
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EVAPORATION
Ways to handle evaporation:
Diffusion (mass transfer)
Water budget (mass balance)
Energy budget
Measure in field (pan evap.)
Combination of methods
1) Diffusive Process
Diffusion - transport from high concentration to low
concentration
Ts - water temperature (assume vapor is at Ts)
ea - atmospheric concentration of vapor (vapor pressure)
- real profile is very sharp
- build up vapor layer at the surface
- increase time until increase flux of vapor (by diffusion)
= evaporation rate
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Evaporation as a Diffusion Process (cont.)
Flux = - K (dc/dz)
K increases as wind increases
Diffusive Process
but don't measure v
Em - mass flux of vapor [mass/area-time]
v - absolute humidity (vapor density)
K
- eddy diffusivity [length2/time]
-vapor pressure
- e is measurable
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Problems:
- where is dz measured?
- what is K?
hard to measure (function of wind speed)
- leads to equations of the following form (empirical):
- Dalton's Law; Stelling, 1882; Diffusion method
es = saturation vapor pressure at the water surface temp, Ts
ea = vapor in atm
E = evaporation rate
R.H. x es (es is f(Tatm))
"velocity" [length/time] (in/hr)
w = wind speed @ specific height
a, b = empirical coefficients
(see Table 2-2)
Ex. TVA region - Rohwer worked well
a = 0.308 (in./day)/(in. Hg)
b = 0.0827 (in./day)/(mph-in. Hg)
e - in. Hg
E - in./day - agrees with handout for atm
Patm = 29.92 in. Hg
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Name
Formula
Units
Time
Remarks
Lake
Hefner
E=6.25x10-4W(es - ea)
cm/3 hr,
knots, mb
3 hrs
Day
Lake Hefner, Ok. 2587 acres, Good agreement
with Lake Mead (138), Lake Eumbene, Russian
Lakes (Dalton)
Kohler
E=.00304W(es - ea)
in/day,
mi/day, in
Hg
Day
Lake Hefner, Ok. 2587 acres, Essentially the same
as the Lake Hefner
Zaykov
E=(.15+.1W)(es-ea)
mm/day,
m/s, mb
Meyer
E=C(es-ea)(1+.1W)
in/month,
mph, in Hg
Monthly
Small Lakes and Reservoirs, ea is obtained daily
from mean morning and evening measurements of
Ta, RH. Increase constants by 10% If ave. of max
and min are used.
Morton
E=(300+50W)(es-ea)/p
in/month,
mph
Monthly
Class A pan, Data from meteorological stations.
Measurement Heights assumed.
Rohner
E=.771
(1.465-.0186B)
(.44+.118W)(es-ea)
in/day,
mph, in Hg
Daily
Pans 85ft diam. tank 1300 acre reservoir,
Extensive pan measurements using several types
of pans. Correlated with tank and reservoir data.
Ponds & Small Reservoirs, Based on Russian
experience. Recommended by Shulyakovskiy
W - a function of the horizontal wind speed
es - the saturation vapor pressure at the water surface temperature
ea - the vapor pressure of the overlaying air
B - atmospheric pressure
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2)
Water Budget Method - conservation of mass; basis for
all simple hydrology
3)
-
measures inflows, determines all outflows and changes in
storage can determine E
-
careful about units (volume
ac of area)
-
change in storage ( S/ t) may be
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[ac-ft] - 1 ft of water over 1
zero for annual budget
3)
Energy Budget Method - more rigorous, most popular for
long-term modeling
-
try to find all energy sources: sun, atmosphere, inflows,
discharges
Ein -
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Eout = S/ T (per unit area)
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Energy In:
Long waves - heat; convert sun's short wave radiation to long
wave in the atmosphere; some of this long wave
radiation is incoming to the lake
Short waves - majority of energy we feel from the sun; visible
light, infrared, heat waves from sun; incoming
and reflected
Qs - Qr
= Incoming - reflected short wave radiation
= Qs (1 - A) where A = Albedo
Qa - Qar =Incident - reflected long wave radiation
(primarily from atm)
Qv
= net advection by inflows - outflows
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Energy Out:
Qvs
Qh
=
=
=
Long wave back radiation
Combined convection and conduction (mostly
heat loss) of sensible heat from surface
- airCsp.heat airK(dTa/dz) where K is turbulent
diffusivity
Heat from a stove - long wave radiation
Energy in Lake:
dSE/dt = dQo/dt = (1/Asurface)
V - volume of water in lake
Tw - temperature of water
Cpw - specific heat of water
Cpw(dV/dt)Tw
w
1 cal/goC
Max flux <<< 1.94 cal/cm2sec
(1.94 is if you could capture all energy incoming)
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Energy Loss from Evaporation:
Le = Latent Heat of Vaporization - add to ENERGY OUT
Qe + Qw = QE
= wCpwTwE + LeE
= Advective Evap. Loss + Latent Heat Loss
Waterways cooler than ambient air temp. because losing
heat in evaporation.
E = Evap. Loss = volume flux [in/hr]
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4) Field Measurement - Open Pan Evaporation
-
Measured daily
-
Annual pan total in Florida
-
Annual actual total in Florida
-
Different because:
60 - 70 in/yr
50 in/yr
pan water temp. > lake water temp.
pan vapor pressure diff. > lake v.p.d.
-
Actual evap. = pan coefficient x pan evap.
-
What is the pan coefficient?
lakes
Most common is 0.7 for
- Other examples:
Reference
Weaver & Stevens
(ref 45)
Brutsaert (ref 43)
Texas (ref 44)
S. F. Shih et. al.
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Pan coeff.
0.77 (St. Augustine grass)
0.85 - 1.04 (Bell peppers)
0.8 (grass, cloves)
1.2 (oak "woods")
0.7 (with Penman eq)
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Recommendation: Penman eq. worked best for Florida; Actual
ET = pan coeff. x Penman value
See handout for Florida stations
See Brutsaert, p. 253-4, for ways to improve pan estimates for
lakes if measure pan temp., lake temp., and air temp.
5) Combining Methods - can simplify
Diffusion Method + Energy Budget Method
= Penman Equation (Review in text)
Concentrate on evap. from open waterways THEN correlate
between evaporation from open waterways and
evapotranspiration
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EVAPOTRANSPIRATION - combined land surface E loss
- function of Potential Evaporation or PET
- similar to lake E formula
- some argument whether Elake = PETland
- function of plant community type
- more succulent plants have higher ET
- f (atmospheric conditions, insolation, temp, wind, humidity)
- f (available soil moisture) - especially in root zone
Potential Evapotranspiration (PET)
For given atmospheric conditions (i.e., temperature, mixing,
wind speed, humidity), it is the maximum ET rate possible. It is
a function of atmospheric conditions, not so much land use or
vegetation.
Evaplake
PET for a given region
In central Florida: Evaplake
50"/yr
PET
See Appendix - TABLE I, Florida stations (mean monthly,
seasonal, ...); Table 5-2, Summary of pan coefficients,
Hydrology for Engineers, Linsley 1982 p.151
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Actual ET (AET)
AET < PET
For Florida AET
35"/yr (about 70% PET)
First, determine PET (atmospheric conditions). Then, consider
all other factors that may effect it (vegetation, land use, etc.):
1)
2)
3)
4)
-
atmosphere - f(humidity, temperature, insolation, wind)
plant community - higher for lush vegetation, depth of
roots
available moisture supply - rainfall, surface water, and soil
water in root zone
PET
ET rates capped by high humidity even though temps. are
higher and more water available.
Decrease humidity, increase ET rate
Insolation - incoming solar radiation, f (cloudiness, latitude)
Plants (sparse vs. lush vegetation, more or less leafy)
Available moisture supply,
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wp
<
fc
-
moisture content, associated with the wilting point of
plants, may be around 0.005, decrease , increase
neg. pressures - osmotic conditions in soil, can't get
water up from roots
-
field capacity, total amount it can hold under the
action of gravity; maximum soil moisture that can
occur under action of gravity under wetting; if allow
soil column to drip dry, fc is the moisture content
remaining; f(soil composition, grains, % org., etc.)
wp
fc
<
Irrigation - only want to irrigate
fc
wp
,
fc
-
<<
fc
- may be approx. 15%
sat
influence losses at root zone
Evaporation - influences losses at surface
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Consumptive Use
Hamon, Blaney-Criddle (see Viessman & paper by Shih et. al.)
See Appendix - Agricultural Consumptive Use Explained,
SWFWMD Hydroscope Oct. 1975
-
ALL water that leaves property by ET or runoff
Does not include water which infiltrates and recharges
groundwater
ET rate, 40 - 50 in/yr
Total Consumptive Use, CU
CU = water lost by irrigation + water lost by ET
Total C.U. = Qp * Ka + CUc * A
(irrigation) + (ET loss)
Ka = f (irrigation method)
For a crop in central FL:
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Total ET = "natural ET" + amount
above natural
natural ET = 39 in/yr
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Table II gives ET above natural
e.g., CUc = 10.6 in/yr = 790 gpd/ac
Allowed pumping rate = annual precip. - annual natural ET
= 52.5 in/yr - 39 in/yr
= 13.5 in/yr = 1000 gpd/ac
- can pump the annual recharge
e.g., -
Own 240 acres, put citrus on 200 ac, irrigate by daytime
sprinkling
-
Allowed to pump 240 x 1000 = 240,000 gpd
(allowed to "use" this amount)
Actually pump 300,000 gpd
How much is consumed?
Actual CU = 300,000 * 0.25 + 790 gpd/ac * 200 ac
(= Qp * Ka + CUc * Acrop)
= 233,000 gpd < 240,000 gpd (allowed)
OK
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