www.ec.gc.ca
A Model for Estimating Hourly Lake
Evaporation Rates
NWRI
Raoul Granger
Newell Hedstrom
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.
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
E v a p o ra tio n , W /m ²
500
Land
400
Lake
300
200
100
0
-1 0 0
4/1/2009
Aug 23
Aug 24
Aug 25
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:
b
El
Ea
a u* (q s
q as ) ( X f Z o )
Where the coefficients a and b are related to dimensionless advection
parameters.
500
Land
E v a p o ra tio n , W /m ²
400
Lake
L a k e (W -B )
300
200
100
0
-1 0 0
Aug 23
Aug 24
Aug 25
Diurnal Cycle of Stability: Land and Water
2
w ater
la n d
S ta b ility In d ic a to r
1
0
-1
-2
175.0
4/1/2009
175.5
176.0
9 D a te
J u Page
lia n
176.5
177.0
Seasonal Cycle of Stability
800
25
Crean Lake
700
20
Cumulative Flux, mm eq.
600
500
2.87 mm/d
400
15
2.54 mm/d
10
300
3.93 mm/d
2.99 mm/d
200
100
5
1.75 mm/d
0
1.32 mm/d
0.01 mm/d
0
Evap
-100
4/1/2009
140
H
190
Rn
Tsf (lake)
240
Page 10
Julian Date 2007
Ta (land)
290
-5
340
Coefficient, a
Effect of Fetch on Evaporation
33
31
29
27
25
23
21
19
17
15
LE = a*U*(es-ea) + b
y = 3.27Ln(x) + 0.67
100
1000
10000
Fetch, m
100000
Crean Lake, PANP, 2006
4/1/2009
Page 12
Crean Lake, 2006
4/1/2009
Page 13
Landing Lake, NWT, 2007
4/1/2009
Page 14
Landing Lake, NWT, 2007
4/1/2009
Page 15
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
4/1/2009
0.5
1
Water-Land VP Contrast, kPA
1.5
2
Page 16
0
-200
0
200
400
600
Net Radiation, W/m²
800
1000
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
350
Fetch: 5300m; deltaT = -1.25°C
300
LE, W/m2
Modeling Hourly
Lake Evaporation
250
y = 19.047x
200
150
100
50
0
0
2
4
6
8
10
8
10
Wind Speed, m/s
- LE = a*U
350
Fetch: 5300m; deltaT = -9.7°C
300
LE, W/m2
- a = f(dT, X)
250
200
y = 29.201x
150
100
50
0
0
2
4
6
Wind Speed, m/s
- LE = a*U
a = f(dT, X)
40
Fetch: 5300m; Unstable
30
Slope Correction
Modeling Hourly
Lake Evaporation
20
10
0
-10
y = 22.72x - 15.98
-20
-30
0
0.5
1
delta VP
Refine the slope (a) relationship
a = f(dT, dVP, X)
1.5
2
Hourly Lake Evaporation Model
LE = 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 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
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
Crean'05
D# 227
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# 228
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 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
Quill Lake, D#245
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
300
Quill Lake, 1993
250
Tower Calc
Evap., mm
200
Modeled
150
100
50
0
210
230
250
Day #
270
290
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 36
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 37
www.ec.gc.ca
• IP3, IPY ($$)
• Chris Spence (Baker Creek Land data)
• PANP (logistics support)
4/1/2009
Page 38
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
4/1/2009
Page 39
2
4
Crean Lake Energy Balance, 2008
800
Crean Lake, 2008
700
Evap
600
H
Flux, mmeq.
Rn
500
Res
400
300
200
100
0
130
4/1/2009
180
230
Julian Day
Page 40
280
330
Landing Lake Energy Balance, 2008
600
Landing, 2008
500
Evap
H
Flux, mm eq.
400
Rn
Res.
300
200
100
0
-100
100
4/1/2009
150
200
Julian Day
Page 41
250
300
Ratio of transfer coefficients : stable conditions
1.2
1
Ke/Km = exp(-8.0Z/L)
Ke/Km
0.8
0.6
0.4
0.2
0
0.0001
0.001
0.01
0.1
z/L
4/1/2009
Page 42
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