A Model for Estimating Hourly Lake

Evaporation Rates

NWRI

Raoul Granger

Newell Hedstrom

www.ec.gc.ca

IP3 Study of Lake Evaporation :

Evaporation is the link between the energy and water budgets;

Meteorology, climate and hydrology models operate with short

time steps; ~ 1 hr;

Open water evaporation responds differently than landsurface

evapotranspiration;

Need Open water evaporation model for hourly time steps.

Evaporation Models are

parameterizations of one or more of

the conditions required for

evaporation to occur:

For evaporation to occur there must be:

- a supply of water at the surface,

- a supply of energy to satisfy the requirement for the phase

change, and

- a transport mechanism to carry the vapour away from the

surface (wind, vapour gradient).

For Open Water:

- The supply of water at the surface is not an issue.

The surface is saturated; this non-varying state does not

provide useful information for the parameterization of the

evaporation rate.

4/1/2009

For Open Water:

- The radiant energy penetrates deeply and so is not

immediately partitioned at the surface.

One should not expect a direct correspondence between

net radiant and evaporation for short time periods.

Quill Lake, 1993

-1 0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

A u g 2 3 A u g 2 4 A u g 2 5

Ev

ap

ora

tio

n,

W/m

² L a n d L a k e

For Open Water:

- The transport mechanism remains as the

single, most important condition which can be used

to describe evaporation at sub-daily rates.

The governing parameters are:

- vapour gradient

- wind speed

- stability

The available observations are:

- water surface temp.(?), wind speed(?)

Evaporation from open water (lakes and ponds)

involves advection:

- Conditions over the water are affected by

conditions over the adjacent land surface;

- Gradients of Water Vapour and Temperature over

the water are affected by the land-water contrast.

Weisman and Brutsaert (1973), using

dimensional analysis, developed the following:

Where the coefficients a and b are related to dimensionless advection

parameters.

b

ofassalZXqquaEE )()(

*

-1 0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

A u g 2 3 A u g 2 4 A u g 2 5

Ev

ap

ora

tio

n,

W/m

²

L a n d

L a k e

L a k e (W -B )

4/1/2009 Page 9

Diurnal Cycle of Stability: Land and Water

-2

-1

0

1

2

1 7 5 .0 1 7 5 .5 1 7 6 .0 1 7 6 .5 1 7 7 .0

J u lia n D a te

Sta

bili

ty In

dic

ato

r

w a te r

la n d

4/1/2009 Page 10

Seasonal Cycle of Stability

Crean Lake

-100

0

100

200

300

400

500

600

700

800

140 190 240 290 340Julian Date 2007

Cu

mu

lati

ve

Flu

x, m

m e

q.

-5

0

5

10

15

20

25

Evap H Rn Tsf (lake) Ta (land)

1.75 mm/d

0.01 mm/d

2.99 mm/d

1.32 mm/d

3.93 mm/d

2.54 mm/d

2.87 mm/d

Effect of Fetch on Evaporation

LE = a*U*(es-ea) + b

y = 3.27Ln(x) + 0.67

15

17

19

21

23

25

27

29

31

33

100 1000 10000 100000Fetch, m

Co

eff

icie

nt,

a

4/1/2009 Page 12

Crean Lake, PANP, 2006

4/1/2009 Page 13

Crean Lake, 2006

4/1/2009 Page 14

Landing Lake, NWT, 2007

4/1/2009 Page 15

Landing Lake, NWT, 2007

4/1/2009 Page 16

Effect of Wind, T, VP and Rn on Lake Evaporation

y = 1.61x2 + 7.89x + 26.53

R2 = 0.67

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10 12

Wind Speed, m/s

LE

, W

/m²

y = 0.62x2 - 4.18x + 81.82

R2 = 0.20

0

50

100

150

200

250

300

350

400

-15 -10 -5 0 5 10

Land-Water Temperature Contrast, °C

LE

, W

/m²

y = 56.33x + 50.50

R2 = 0.07

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2

Water-Land VP Contrast, kPA

LE

, W

/m²

y = 0.02x + 90.68

R2 = 0.01

0

50

100

150

200

250

300

350

400

-200 0 200 400 600 800 1000

Net Radiation, W/m²

LE

, W/m

²

Modeling Hourly Lake Evaporation

Approach using the development of relationships

based on:

- Vapour gradient

(land-water VP contrast)

- wind speed,

- stability

(land-water temperature contrast)

- distance from shore

Modeling Hourly Lake Evaporation

Data from Crean Lake (2006-2008) and Landing

Lake (2007-2008) were sorted into:

- stable and unstable categories

- distance from shore (fetch)

- land-water temperature contrast

- LE related to wind speed

Modeling Hourly

Lake Evaporation

- LE = a*U

- a = f(dT, X)

Fetch: 5300m; deltaT = -1.25°C

y = 19.047x

0

50

100

150

200

250

300

350

0 2 4 6 8 10

Wind Speed, m/s

LE

, W

/m2

Fetch: 5300m; deltaT = -9.7°C

y = 29.201x

0

50

100

150

200

250

300

350

0 2 4 6 8 10

Wind Speed, m/s

LE

, W

/m2

Modeling Hourly

Lake Evaporation

- LE = a*U

a = f(dT, X)

Refine the slope (a) relationship

a = f(dT, dVP, X)

Fetch: 5300m; Unstable

y = 22.72x - 15.98

-30

-20

-10

0

10

20

30

40

0 0.5 1 1.5 2

delta VP

Slo

pe

Co

rre

cti

on

Hourly Lake Evaporation ModelLE = a*U ; a = f(dT, dVP, X)

a = b + m*dT + n*dVP

b, m, n = f(X)

b, m, n values for stable, unstable

Hourly Lake Evaporation Model

Verification data sets :

Crean 2005 (land data from mixedwood site)

Quill 1993 (Heatmex data)

Hourly Lake Evaporation ModelVerification results Crean 2005

y = 0.99x

R2 = 0.86

0

50

100

150

200

250

300

0 50 100 150 200 250 300

LE (Obs), W/m²

LE

(M

od

), W

/m²

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 223

0

50

100

150

200

250

300

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 224

0

50

100

150

200

250

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 225

0

50

100

150

200

250

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 226

0

50

100

150

200

250

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 227

0

50

100

150

200

250

300

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean'05

D# 228

0

50

100

150

200

250

0 600 1200 1800 2400

Time, CST

Evap

, W

/m²

LE,obs

LE, mod

Hourly Lake Evaporation ModelVerification results Crean 2005

Crean Evaporation, 2005

0

50

100

150

200

250

210 230 250 270 290 310

Day#

Ev

ap

, m

m

Observed

Modeled

Hourly Lake Evaporation Model

Verification results Quill 1993

Quill Lake, D#242

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Time, CST

Lake E

vap

, W

/m²

Lake Evap

Evap calc

Hourly Lake Evaporation Model

Verification results Quill 1993

Quill Lake, D#243

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Time, CST

Lake E

vap

, W

/m²

Lake Evap

Evap calc

Hourly Lake Evaporation Model

Verification results Quill 1993

Quill Lake, D#244

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Time, CST

Lake E

vap

, W

/m²

Lake Evap

Evap calc

Hourly Lake Evaporation Model

Verification results Quill 1993

Quill Lake, D#245

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Time, CST

Lake E

vap

, W

/m²

Lake Evap

Evap calc

Hourly Lake Evaporation Model

Verification results Quill 1993

Quill Lake, 1993

0

50

100

150

200

250

300

210 230 250 270 290

Day #

Ev

ap

., m

m

Tower Calc

Modeled

4/1/2009 Page 36

Conclusions

• First-generation model for Hourly Lake

Evaporation.

• Relatively simple, reliable

• Requires land data: Ta, VP, Udir

• Requires lake data: Tsf, U, Fetch

4/1/2009 Page 37

Things to do

• Relationship between Lake and Land windspeeds

• Verification with Whiteswan Lake

– Fill fetch gap

• Apply to total lake area.

– (Effective fetch vs Wind Direction)

• Test in model framework (RCM?, MESH?)

• Redo and simplify Weisman-Brutsaert advection analysis with better parameterizations for stable conditions.

4/1/2009 Page 38

www.ec.gc.ca

• IP3, IPY ($$)

• Chris Spence (Baker Creek Land data)

• PANP (logistics support)

4/1/2009 Page 39

Effect of Stability on Lake Wind Speed

Crean Lake 2007 (5-day)

y = -0.274x + 1.866

R2 = 0.591

0

1

2

3

4

5

-6 -4 -2 0 2 4

Ta(land)-Ts(lake), °C

U(l

ake)-

U(l

an

d),

m/s

4/1/2009 Page 40

Crean Lake Energy Balance, 2008

Crean Lake, 2008

0

100

200

300

400

500

600

700

800

130 180 230 280 330

Julian Day

Flu

x, m

me

q.

Evap

H

Rn

Res

4/1/2009 Page 41

Landing Lake Energy Balance, 2008

Landing, 2008

-100

0

100

200

300

400

500

600

100 150 200 250 300

Julian Day

Flu

x, m

m e

q.

Evap

H

Rn

Res.

4/1/2009 Page 42

Ratio of transfer coefficients : stable conditions

Ke/Km = exp(-8.0Z/L)

0

0.2

0.4

0.6

0.8

1

1.2

0.0001 0.001 0.01 0.1 1 10

z/L

Ke

/Km