estimating evaporation from water surfaces• the obvious solution –move the pan site, and...

ESTIMATING EVAPORATION FROM WATER SURFACES

(With emphasis on shallow water bodies)

1ET Workshop12‐Mar‐2010

INTRODUCTIONINTRODUCTION

• Evaporation is rarely measured directlyEvaporation is rarely measured directly

• Estimating methods include:ffi i t d ti– pan coefficient xmeasured pan evaporation

– water balance

– energy balance

– mass transfer

– combination techniques

• Emphasis will be practical methods


BACKGROUNDBACKGROUND

• Evaporation theories – to the 8th centuryEvaporation theories to the 8 century

• Dalton (1802), E = f(ū) (eo – ea)

( 926) h i h i f• Bowen (1926), the Bowen ratio, the ratio of sensible heat to latent heat gradients (Δt/Δe)

• Applications were made to lake evaporation by Cummings and Richardson 1927; McEwen 1930


ENERGY CONSIDERATIONSENERGY CONSIDERATIONS

• Evaporation requires a lot of energyEvaporation requires a lot of energy

• Incoming solar radiation is the main source

l d ll l di i• In contrast to land, not all net solar radiation is absorbed on the surface

• In pure water, about 70% is adsorbed in the top 5 m (16 ft)

• Solar radiation adsorbed below the surface is “stored energy”gy


ENERGY (continued)ENERGY (continued)

• Estimating energy storage in water (Qt) canEstimating energy storage in water (Qt) can be more difficult than estimating soil heat flux (G)

• Part of solar radiation may penetrate to great depths depending on the clarity of the water

• Stored energy affects the evaporation rate• Example temperature profiles in deep water:Example temperature profiles in deep water:

– profiles during increasing solar cycle– profiles during decreasing solar cyclep g g y


Solar Radiation Penetrates Deep in Water

Evaporation pans are two Evaporation pans are two shallow and hold too shallow and hold too much “warmth” at themuch “warmth” at themuch warmth at the much warmth at the surface. surface. Therefore, they can Therefore, they can overestimate the overestimate the evaporation from large evaporation from large reservoirs and lakes.reservoirs and lakes.

ENERGY STORAGE & RELEASEENERGY STORAGE & RELEASE

• Lake Berryessa 8 100 ha (20 000 ac ) and 58Lake Berryessa, 8,100 ha (20,000 ac.) and 58 m (190 ft) deep, average 40 m

• Little or no inflow during the summer• Little or no inflow during the summer

• Thermal profiles during increasing Rs

• Thermal profiles during decreasing Rs

• Example temperatures by depth and timep p y p

• Reason for studying evaporation—improve estimates of evaporation to calculate inflowestimates of evaporation to calculate inflow


Lake Berryessa

Lake Berryessa

California, USACalifornia, USA

LB 05

LB 10

LB 04

LB 12

LB 03

LB 06(New-USBR

WS)

LB 07A-E

LB 01

Old-USBR

LB 02

Portable WSLB 08

(Dam)LB 09

(USBR)

LB 11Old-USBR WS


Temperature Profile Data - 7/10/03

010 12 14 16 18 20 22 24 26 28

-10

-5

m

-20

-15

Dept

h, m

-30

-25

30

Temperature, C

LB 01 LB 02 LB 03 LB 04 LB 05 Avg


Temperature Profile Data - 10/30/03Temperature Profile Data - 10/30/03

010 12 14 16 18 20 22 24 26 28

-10

-5

20

-15

-10

Dept

h, m

-25

-20

-30

Temperature, C

LB 01 LB 02 LB 03 LB 04 LB 05 AvgLB 01 LB 02 LB 03 LB 04 LB 05 Avg


30.0

2005

20.0

25.0

C

15.0

Wat

er te

mp,

C

10.0

5.0

1/1

2/1

3/1

4/1

5/1

6/1

7/1

8/1

9/1

10/1

11/1

12/1

0.15 m 5.2 m 7.6 m 12.8 22.6 m


WHY STUDY EVAPORATION ON LB?WHY STUDY EVAPORATION ON LB?

• The pan site was moved from the original site• Measured pan evaporation x original coefficients underestimated reservoir evaporation and inflow

• Negative inflows were calculated during low and zero• Negative inflows were calculated during low and zero inflows late in the summer

• The obvious solution – move the pan site, and h k th ffi i trecheck the pan coefficients

• Data were needed to justify to the USBR the need to change the pan siteg p

• View of the evaporation pan site• Estimated rate of energy storage


Original USBR Pan SiteOriginal USBR Pan Site


Rate of Energy StorageRate of Energy Storage15.0

5.0

10.0

y-1

-5.0

0.0

Qt,

MJ

m-2

day

15 0

-10.0

-15.0

M-0

3

J-03

S-0

3

N-0

3

J-04

M-0

4

M-0

4

J-04

S-0

4

N-0

4

J-05

M-0

5

M-0

5

J-05

S-0

5

N-0

5

J-06

Est 2 Qt(rate) Meas Qt(rate) 03 Meas Qt(rate) 04 Meas Qt(rate) 05Est-2 Qt(rate) Meas-Qt(rate)-03 Meas-Qt(rate)-04 Meas-Qt(rate)-05


ENERGY STORAGE EXAMPLESENERGY STORAGE EXAMPLES

• Maximum energy storage rates of 5 to 10 MJ m‐2 a u e e gy sto age ates o 5 to 0 Jd‐1 to a depth of 25 m measured in Lake Berryessa and about 10 MJ m‐2 d‐1 to a depth of

d k d45 m measured in Lake Mead• Water surface temperatures reached a

i i J l i LB d i A t i L kmaximum in July in LB and in August in Lake Mead (lag is related to depth of water)

• Evaporation rate also lagged solar radiation• Evaporation rate also lagged solar radiation• Advected energy can be large in reservoirs on rivers (example along Colorado River)rivers (example along Colorado River)


8.0

9.0d

-1

5.0

6.0

7.0

ratio

n, m

m

2 0

3.0

4.0

ated

eva

por

0.0

1.0

2.0

Est

ima

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Davis-Parker Parker-Imperial Imperial-Morelos


Surface Temp ‐ Lake Berryessa

30.0

35.0

Surface Temp Lake Berryessa

25.0

15.0

20.0

°C

5.0

10.0

0.0

J‐05 F‐05 M‐05 A‐05 M‐05 J‐05 J‐05 A‐05 S‐05 O‐05 N‐05 D‐05

12‐Mar‐2010 ET Workshop 17

Surface Temp

Other MethodsOther Methods

• Water budget procedureWater budget procedure

• Aerodynamic methodsd i l l l k d i– used mainly on large lakes and reservoirs

• Example – American Falls reservoir in Idaho by Allen et al.– estimates using water and air temperature

– estimated evaporation relative to ETr• Why the low summer rate? Cold inflow water?y


Temperature of water from American Falls outfall follows Temperature of Air

(b)(b)

Year 2000

American Falls Temperatures

15202530

ture

, C

p2004

10-505

10

Tem

pera

t

Year 2004-10

24-Feb09-Mar

23-Mar

06-Apr26-Apr

11-May

25-May09-Jun

22-Jun

07-Jul20-Jul

03-Aug

17-Aug01-Sep

14-Sep

28-Sep12-Oct

26-Oct

09-Nov22-Nov

07-Dec

20-Dec

DateWater Temp 10 day mean Air Temp

Evaporation ratio for Alfalfa Reference ETReference ET

1

American Falls, Evaporation/ETr ratios2004

0.70.80.9

1

/ ETr

0 30.40.50.6

pora

tion

00.10.20.3

Eva

0 1 2 3 4 5 6 7 8 9 10 11 12Month

ETrF from Am.Falls study 2004 Aerodynamic ETrF from Tmean

SHALLOWWATER BODIESSHALLOW WATER BODIES

• Early estimating methodsEarly estimating methods– Equilibrium temperature (Edlinger et al. 1968)

– Further developed and tested by KeijmanFurther developed and tested by Keijman(1974), Fraederich et al. (1977), de Bruin (1982), and Finch (2001)

• Finite difference model (Finch and Gash, 2002)

• Pan evaporation x pan coefficientp p

• Energy balance and combination methods

• Reference ET x coefficient (E = ET x K )Reference ET x coefficient (E = ETo x Kw)


EVAPORATION PAN COEFFICIENTSEVAPORATION PAN COEFFICIENTS

• Pan coefficient studiesa coe c e t stud es• Rohwer (1931) – a classic detailed study conducted on the CSU campusp

• Rohwer compared evaporation from a Class A pan and an 85‐diameter (26 m) reservoir

• Young (1947) also did a classic study in CA• Others: Kohler (1954); Kohler et al. (1959); Farnsworth et al. (1982)

• Fetch effects and obstructions (fixed & variable)


Ratio of Lake Evaporation to Class Pan Evaporation

1.20

0.80

1.00

pan

-1

0.40

0.60

ake

evap

E

0.00

0.20

La


Lake Elsinore Lake Okeechobee


1

0.8

0.9

0.6

0.7

y = ‐0.000x3 + 0.016x2 ‐ 0.056x + 0.6230.4

0.5

0.2

0.3Ratio ‐ Reservoir to Class A pan, Apr‐Nov ‐ Rohwer 1931

0

0.1

3 4 5 6 7 8 9 10 11 121926 1927 1928 Avg 0 7 Poly (Avg)


1926 1927 1928 Avg 0.7 Poly. (Avg)

30.0

Rohwer ‐ 1931

25.0

Rohwer ‐ 1931

20.0

C

10 0

15.0

Temp, C

5.0

10.0

0.0

Sep Oct Nov Apr May Jun Jul Aug Sep Oct Nov Apr May Jun Jul Aug Sep Oct Nov


Air temp‐1‐inch Water temp

12.0

14.0

8.0

10.0

, mm

d1

Jun-Jul

Aug

4 0

6.0

Eva

pora

tion Aug

Sep

Oct

2.0

4.0NovDec

0.0

0 1 10 100 1000Upwind fetch of irrigated grass, m


ObstructionsObstructions

• FixedFixed– buildings

shelter belts– shelter belts

– other (shown in previous example)

V i bl• Variable– adjacent corn field (most common), can have a

j ff tmajor effect

– weeds and other adjacent crops


OTHER ESTIMATING METHODSOTHER ESTIMATING METHODS

• Aerodynamic (used mainly on large water bodies)y ( y g )• Energy balance (requires detailed measurements)• Combination methods: Penman (1948, 1956, 1963); Penman‐Monteith (1965); Priestley‐Taylor (1972)

• All require estimating net radiation using standard equations and estimating energy storage (moreequations and estimating energy storage (more difficult for deep water bodies)

• Reference ET x coefficient (E = ETo x Kw)( o w)– for shallow water bodies– for ice‐free water bodies


ENERGY STORAGE RATESENERGY STORAGE RATES

• Difficult to quantify without measurementsDifficult to quantify without measurements

• Example rates of storagek t f 5 t 10 MJ 2 d 1– peak rates can range from 5 to 10 MJ m‐2 d‐1

– equivalent to 2 to 4 mm d‐1 evaporation

• Example rates calculated from lake studies– Pretty Lake in Indiana

– Williams Lake in Minnesota


Reported Energy Storage Rates - Pretty Lake (63-65) & Williams Lake (82-86)

10.0

15.0

d-1

0.0

5.0

t, M

J m

-2 d

-10.0

-5.0

0 30 60 90 120 150 180 210 240 270 300 330 360

Q

0 30 60 90 120 150 180 210 240 270 300 330 360

Day of Year

Pretty Lake Williams Lake Poly. (Pretty Lake) Poly. (Williams Lake)y y ( y ) y ( )


ASCE‐EWRI REFERENCE ETASCE EWRI REFERENCE ET

• ASCE‐EWRI (2005) and Allen et al (1998)ASCE EWRI (2005) and Allen et al. (1998)

• ETref x coefficient for open ice‐free water (Kw)

h i f h ( ) d 1• where ETref is for short grass (ETos), mm d‐1

• First check input weather data for quality

0.408 Δ(Rn ‐ G) + γ [900/(T + 273)] u2 (es ‐ ea)ET f = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ETref = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Δ + γ (1 + 0.34 u2)


EXAMPLE – HOME LAKE, COEXAMPLE HOME LAKE, CO

• Location San Luis ValleyLocation San Luis Valley– Elevation 2297 m (7536 ft) above sea level

Average depth about 1 5 m (5 ft)– Average depth, about 1.5 m (5 ft)

• Estimated energy storage

• Estimated evaporation– May‐October

– ETref x Kw also agrees with PM in November

• Results (May‐October)( y )


0.5

1.0

0.0

m2 d

-1

-0.5

Qt,

MJ

-1.5

-1.0


Est-Qt


8.0Home Lake, Alamosa, CO

6 0

7.0

8.0

5.0

6.0

p, m

m d

-1

3.0

4.0

imat

ed e

vap

1.0

2.0Est

0.0

Apr May Jun Jul Aug Sep Oct

E - PM E = ETo x 1.10


ROHWER’S CLASS A PAN COEFFICIENTS

• K by months for Colorado:Kp by months for Colorado:

• Based on mean ratios (polynomial)A 0 60 A t 0 75– Apr 0.60 August 0.75

– May 0.63 September 0.78

– June 0.67 October 0.77

– July 0.71

– Average, April‐October 0.70


ESTIMATED EVAPORATION HOME LAKE – MAY‐OCT.

• PM Penman NWS‐33 ET f x 1.10PM Penman NWS 33 ETref x 1.10

• mm

• (inches)• (inches)

• 894 906 890 892

• (35.2) (35.7) (35.0) (35.1)

• Percent of PM

• 100 101 100 99.8

• All give similar values for May through Octoberg y g


ESTIMATED EVAPORATION ( )LAKE BERRYESSA (3 YR AVG)

• PM Penman P‐T USBR originalg• mm• (inches)• 1,325 1,425 1,277 955• (52.2) (56.1) (50.3) (37.7)• 100 108 96 72• The same Rn and Qt used for first three methodsV l fi ff f “ i ”• Values confirm effects of “poor pan site”

• P‐T equation does not have wind speed


estimating evaporation from water surfaces• the obvious solution –move the pan site, and...

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