Parameterizing Open Water
Evaporation Rates
Raoul Granger
Newell Hedstrom
National Water Research Institute
Environment Canada
IP3 Study of Lake Evaporation :
Evaporation is the process that links the energy and water
balances at the earth’s surface;
Meteorology, Climate and Hydrology Models operate with
short time steps; ~ 1 hr;
Modifying, Adjusting or Transporting Land-based models for
Open water evaporation does not work;
OBJECTIVE: An Open Water Evaporation Model for
Hourly time steps.
Crean Lake, PANP, 2006-2010
9/10/2011
Page 3
Landing Lake, NWT, 2007-2009
9/10/2011
Page 4
Whiteswan Lake (#4), SK, 2009-2010
9/10/2011
Page 5
Landing Lake, NWT, 2007-2009
9/10/2011
Page 6
Controls on Evaporation
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 non-varying.
The surface is continuously saturated;
Unlike for land surfaces, parameterizing the water supply does
not help.
For Open Water:
- The radiant energy penetrates deeply and so is not
immediately partitioned at the surface.
One should not expect a relationship between net radiant
and evaporation for short time periods.
Quill Lake
1993
9/10/2011
Evaporation, W/m²
500
Land
400
Lake
300
200
100
0
-100
Aug 23
Aug 24
Aug 25
For Open Water:
- The transport mechanism : the single, most
important approach 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 over water(?)
Evaporation from open water (lakes and ponds)
involves advection:
Conditions over the water are affected by:
- Conditions over the adjacent land surface
(Vapour and Temperature Gradients are
affected by the land-water contrast);
- Distance from the upwind shore.
Seasonal Cycle of Stability
800
25
Crean Lake
700
20
500
2.87 mm/d
400
2.54 mm/d
10
300
3.93 mm/d
2.99 mm/d
200
100
5
1.75 mm/d
Evap
-100
140
H
190
0
1.32 mm/d
0.01 mm/d
0
9/10/2011
15
Rn
Tsf (lake)
240
JulianPage
Date
12 2007
Ta (land)
290
-5
340
Temperature, °C
Cumulative Flux, mm eq.
600
Modeling Hourly Lake Evaporation
Approach using the development of relationships
based on:
- Wind speed,
- Stability
(land-water temperature contrast)
- Distance from shore
- Vapour gradient
(water-land VP contrast)
Effect of Wind, T, VP and Rn on Lake Evaporation
400
400
y = 1.61x2 + 7.89x + 26.53
350
300
250
LE, W/m²
LE, W/m²
R2 = 0.20
R2 = 0.67
300
y = 0.62x2 - 4.18x + 81.82
350
200
150
250
200
150
100
100
50
50
0
0
0
2
4
6
8
10
12
-15
-10
Wind Speed, m/s
-5
0
5
Land-Water Temperature Contrast, °C
400
400
350
350
y = 0.02x + 90.68
R2 = 0.01
y = 56.33x + 50.50
300
300
2
R = 0.07
250
LE, W/m²
LE, W/m²
10
200
150
250
200
150
100
100
50
50
0
0
9/10/2011
0.5
1
Water-Land VP Contrast, kPA
1.5
2
Page 14
0
-200
0
200
400
600
Net Radiation, W/m²
800
1000
Modeling Hourly Lake Evaporation
Half-hourly data from
Crean Lake (2006-2010)
Landing Lake (2007-2009)
Whiteswan Lake (2009-2010)
Oscar Lake (2010)
Sorted into:
- stable and unstable categories
- distance from shore (fetch: 90m – 10,000m)
- land-water temperature contrast
Succssive regression
- LE related to wind speed, dT, dVP, Fetch
Fetch: 5300m; deltaT = -1.25°C
300
250
LE, W/m2
Modeling Hourly
Lake Evaporation
350
y = 19.047x
200
150
100
50
LE = a*U
0
0
2
4
6
8
10
8
10
Wind Speed, m/s
Fetch: 5300m; deltaT = -9.7°C
300
250
LE, W/m2
Using coefficients
from all categories
a = f(X, ΔT, ΔVP)
350
200
y = 29.201x
150
100
50
0
0
2
4
6
Wind Speed, m/s
Hourly Lake Evaporation Model
LE = a*U ; a = f(ΔT, ΔVP, X)
For Unstable cases:
a = b + m* ΔT + n* ΔVP
For Stable cases:
a = b + c*exp(m* ΔT) + n* ΔVP
b, c, m, n = f(X)
Modeling Hourly Lake Evaporation
35
0
30
Unstable
y = 0.0904Ln(x) - 1.758
coefficient "n"
coefficient "m"
-0.5
-1
-1.5
Stable
y = 0.420Ln(x) - 4.584
-2
25
20
15
5
-3
0
1000
Fetch, m
10000
Stable
y = -0.0011x + 20.256
10
-2.5
100
Unstable
y = -0.0008x + 26.525
100
1000
Fetch, m
10000
Hourly Lake Evaporation Model
LE = a*U ; a = f(ΔT, ΔVP, X)
a = b + m* ΔT + n* ΔVP
Stable cases: a = b + c*exp(m* ΔT) + n* ΔVP
b = -23.78 + 2.1212•ln(X)
c = 22.387 – 0.0007*X
m = -0.442 + 0.035•ln(X)
n = 15.607 – 0.0007•X
Unstable cases: a = b + m* ΔT + n* ΔVP
b = 2.489 + 0.0002•X
m = -1.805 + 0.095•ln(X)
n = 27.053 – 0.0008•X
Hourly Lake Evaporation Model
Verification data sets :
Crean 2005 (land data from mixedwood site)
Quill 1993 (Heatmex data)
Hourly Lake Evaporation Model
Verification results Crean 2005
300
Crean'05
D# 223
LE,obs
250
LE, mod
Evap, W/m²
200
150
100
50
0
0
600
1200
Time, CST
1800
2400
Hourly Lake Evaporation Model
Verification results Crean 2005
250
Crean'05
D# 224
LE,obs
LE, mod
Evap, W/m²
200
150
100
50
0
0
600
1200
Time, CST
1800
2400
Hourly Lake Evaporation Model
Verification results Crean 2005
250
Crean'05
D# 225
LE,obs
LE, mod
Evap, W/m²
200
150
100
50
0
0
600
1200
Time, CST
1800
2400
Hourly Lake Evaporation Model
Verification results Crean 2005
250
Crean'05
D# 226
LE,obs
LE, mod
Evap, W/m²
200
150
100
50
0
0
600
1200
Time, CST
1800
2400
Hourly Lake Evaporation Model
Verification results Crean 2005
300
250
LE (Mod), W/m²
y = 0.99x
R2 = 0.86
200
150
100
50
0
0
50
100
150
LE (Obs), W/m²
200
250
300
Hourly Lake Evaporation Model
Verification results Crean 2005
250
Crean Evaporation, 2005
200
Observed
Evap, mm
Modeled
150
100
50
0
210
230
250
270
Day#
290
310
Hourly Lake Evaporation Model
Verification results Quill 1993
250
Quill Lake, D#242
Lake Evap
Evap calc
Lake Evap, W/m²
200
150
100
50
0
0
400
800
1200
Time, CST
1600
2000
2400
Hourly Lake Evaporation Model
Verification results Quill 1993
250
Quill Lake, D#243
Lake Evap
Evap calc
Lake Evap, W/m²
200
150
100
50
0
0
400
800
1200
Time, CST
1600
2000
2400
Hourly Lake Evaporation Model
Verification results Quill 1993
250
Quill Lake, D#244
Lake Evap
Evap calc
Lake Evap, W/m²
200
150
100
50
0
0
400
800
1200
Time, CST
1600
2000
2400
Hourly Lake Evaporation Model
Verification results Quill 1993
250
Cumulative Evaporation, mm
Observed
Modeled
200
150
100
50
0
210
230
250
Julian Day 1993
270
290
Daily Lake Evaporation Model
LE = a*U ;
a = f(ΔT, ΔVP, X)
For Unstable cases:
a = b + m* ΔT + n* ΔVP
For Stable cases:
a = b + c*exp(m* ΔT) + n* ΔVP
b, c, m, n = f(X)
Daily Lake Evaporation Model
LE = a*U ; a = f(ΔT, ΔVP, X)
a = b + m* ΔT + n* ΔVP
Stable cases: a = b + c*exp(m* ΔT) + n* ΔVP
b = -22.905 + 2.098•ln(X)
c = 22.336 – 0.0007*X
m = -0.572 + 0.049•ln(X)
n = 15.668 – 0.0008•X
Unstable cases: a = b + m* ΔT + n* ΔVP
b = 3.701 + 0.0007•X
m = -1.878 + 0.106•ln(X)
n = 28.723 – 0.0008•X
Comparing Hourly and Daily
Lake Evaporation Estimates
450
Oscar Lake
Cumulative Evap., mm
400
EC
350
Model Hourly
300
Model Daily
250
200
150
100
50
0
120
170
220
Day#, 2010
270
320
Testing Lake Evaporation Model
Water Balance Application
Sandy Lake, PANP
300
Evaporation or Precipitation, mm
Sandy Lake
250
Precip
200
Lake Evap
E (waterbalance)
150
100
50
0
-50
190
220
250
Julian Day, 2007
280
310
Summary
• A model for Hourly Lake Evaporation has been
developed.
• Relatively simple, reliable
• Requires land data: Ta, VP, U, Udir
NB: In forested areas, these data must be obtained above
the forest canopy!
• Requires lake data: Tsf, U, Fetch
• Model coefficients were generated for Daily values.
9/10/2011
Page 35
Possible Next Steps
• Testing and Application
– Waskesiu
– Diefenbaker ?
• Expand range of Fetch sizes
– Larger lakes: Lake Okanagan;
• Apply to total lake area.
– (“Effective fetch” vs Wind Direction)
• Test in model framework (RCM?, MESH?)
9/10/2011
Page 36
www.ec.gc.ca
• IP3, IPY ($$)
• Chris Spence (Baker Creek Land data)
• PANP (logistics support)
9/10/2011
Page 37
Publication
• Granger, R. J. and Hedstrom, N.: Controls on open
water evaporation, Hydrol. Earth Syst. Sci.
Discuss., 7, 2709-2726, doi:10.5194/hessd-72709-2010, 2010.
• Granger, R. J. and Hedstrom, N.: Modelling hourly
rates of lake evaporation, Hydrol. Earth Syst. Sci.
Discuss., 7, 2727-2746, doi:10.5194/hessd-72727-2010, 2010.
9/10/2011
Page 38
Mean Evaporation, Unstable Case
16
Latent Heat Flux, W/m²
LE
Unstable
350
Avg
14
300
U
12
250
10
200
8
150
6
100
4
50
2
0
0
8000
0
1000
2000
3000
4000
Fetch, m
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Page 39
5000
6000
7000
Wind Speed, m/s
400
Mean Evaporation, Stable Case
140
7
Avg
120
Stable
6
U
100
5
80
4
60
3
40
2
20
1
0
0
8000
0
1000
2000
3000
4000
Fetch, m
9/10/2011
Page 40
5000
6000
7000
Wind Speed, m/s
Latent Heat Flux, W/m²
LE
Crean Lake, 2006
9/10/2011
Page 41
Effect of Stability on Lake Wind Speed
5
Crean Lake 2007 (5-day)
y = -0.274x + 1.866
R2 = 0.591
U(lake)-U(land), m/s
4
3
2
1
0
-6
-4
-2
0
Ta(land)-Ts(lake), °C
9/10/2011
Page 42
2
4
Hourly Lake Evaporation Model
Verification results Crean 2005
300
Crean'05
D# 227
LE,obs
250
LE, mod
Evap, W/m²
200
150
100
50
0
0
600
1200
Time, CST
1800
2400