Off-line lake water and ice
simulations: a step towards
the interactive lake coupling
with the Canadian Regional
Climate Model
Andrey Martynov, Rene Laprise, Laxmi Sushama
Canadian regional climate modelling and diagnostics (CRCMD) Network
University of Quebec in Montreal @ Ouranos
Outline1. Lakes in Canada: motivation and objectives
2. Lakes: complex physical systems
3. Lakes: thermal structure
4. Lake models: candidates for coupling
• Description of lake models
6. Off-line tests:
- Small lakes: the LTER NTL project
- Great Lakes
- Lake of Geneva
7. Conclusions and plans
9% of Canada’s surface is covered by lakes.
• Total: 2 millions lakes of all kinds and sizes.
Lakes influence the regional climate in many ways:
thermal moderation, enhanced evaporation, etc.
• Large lakes: strong influence on the regional
climate (lake-effect snow, the Great Lakes)
• Even small lakes are important for regions,
where they are abundant: “cumulative effect”
(most part of Canada, especially the Canadian shield)
In Canada, lakes form an important element
of the climate system and must be taken into account
in local climate simulations.
Objectives of this work: to test different lake models and to
find candidates for interactive coupling
with the Canadian Regional Climate Model (CRCM)
Lakes in Canada
Source: The Atlas of Canada
Source: The Atlas of Canada
Lakes are complex inhomogenious 3D systems. Radiative processes, horizontal and vertical
mixing, density stratification, water evaporation/condensation, ice/snow formation and thawing…
For RCM coupling, no detailed reproduction of lake state is required (or even possible):
• Input fields from RCM are homogenous on RCM grid tiles (10-50 km)
• No detailed description of most lakes is available
• Coupled lake models will act as parts of surface schemas:
Only surface conditions will be used by RCM, no need to reproduce in details the interior,
if surface Is OK.
But lake models for RCM should be able to reproduce correctly most important lake patterns,
including mixing regime, surface temperature behavior, ice onset and duration…
Lakes: complex physical systems
Mixing processes in a lake
(Imboden and Wuest, 1995)
0 2 4 6 8 10999.6
999.7
999.8
999.9
1000.0
T!
max
=3.98oC
!,
kg
/m3
T, oC
Lakes: thermal structure
Fresh liquid water
equation of state
Source: Minnesota See Grant,
University of Minnesota
The lake thermal regime depends on
• Density stratification
• Annual cycle of insolation (latitude)
• Mixing (wind-driven, etc.)
• Salinity (relatively rare in Canada)
Typical mixing regimes
for temperate-latitude lakes:
• Freezing dimictic lakes
• Non-freezing warm monomictic lakes
Source:
U.S. EPA Great Lakes
National Program Office.
Tsurface
Thermocline
Mixing
layer
HypolimnionTbottom
Summer and winter
stratifications
Lake models: candidates for couplingWhich interactive lake models could be used with CRCM?
In this work, only 1D lake models are considered. In such models:
• Horizontal fluxes in lakes are ignored, horizontal homogeneity assumed.
• Only vertical processes are simulated.
• Few input data are required.
• Most kinds of lakes can be simulated.
• Relatively simple and computationally cheap.
Two 1D lake models, having water and ice/snow modules, are presently available:
• The model of S.W. Hostetler: Hostetler S.W., Bates G.T., Georgi F.,1993: J Geoph.
Res., 98(D3), pp 5045-57
Coupling with RCM : RegCM3, MM4
• FLake (Freshwater Lake model): D. Mironov et al., http://lakemodel.net
Coupling with RCM : RCA3
Off-line tests of models: estimation and validation
• Small lakes: single column mode, where the whole lake is modeled as a water column of
the constant depths.
• Large lakes: multiple points simulation, imitating the current 45-km CRCM grid.
Input data in off-line tests: observations or re-analysis.
• Eddy diffusion model:
with the parameterized eddy diffusion constant K(z,t).
• No explicit assumptions about the temperature profile.
It depends on the K(z,t) vertical profile.
• Bottom: zero heat flux. Tbottom is usually at the maximum
density temperature (4 °C) in deep lakes.
The model of S.W. Hostetler
( )zcdz
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!
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Tbottom Tsurface
0
h
D
z
Thermocline
Bottom (zero heat flux)
T(z)
Mixing layer
Hypolimnion
The water temperature profile
structure in summer
(Hostetler’s model)
The FLake model• The shape of the water temperature profile is prescribed
(empirically-based):
- The water temperature is constant in the mixing layer
- Between the mixing layer and bottom,
the temperature profile is given by a polynomial function,
depending on the parameter CT .
The mixing layer depth h and CT
define the profile shape.
.
• By construction, the thermocline extends
from the mixing layer depth h
to the lake bottom (no hypolimnion).
- This gives unrealistic temperature profiles in deep lakes.
A “virtual bottom” at 60 meters is used, if the depth exceeds 60 m.
• Bottom: either zero heat flux or sediment layer
• Ice/snow model: the same approach as in other layers, but the proflie is linear. No minimal ice
thickness is prescribed. To account for the presence of snow, the ice albedo is modified.
Tbottom Tsurface
0
h
D
z
Thermocline
Bottom or sediments
T(z)
Mixing layer
The water temperature profile
structure (FLake)
Source of data: the LTER NTL project (Wisconsin, USA). 11 lakes are observed since 1980th
• Sparkling Lake: dimictic freezing lake
Lat. 46.003, lon. -89.612, area: 0.64 km2.
Mean depth: 10.9 m, max. depth: 20 m.
Secchi depth: 7.5 m.
• Simulations:
perpetual year 2005, timestep: 1 hour,
no sediments (FLake), vertical resolution: 1 m (Hostetler),
maximum lake depth.
• Observed parameters, used as lake model input:
Air temperature, wind force, relative humidity (raft data)
Longwave and shortwave radiation downward
(measured at the nearby airport)
• Observed data, used for comparison with model output:
water temperature profiles, ice thickness,
latent and sensible heat fluxes (Sparkling Lake only).
Lake simulations: small lakes
Observation raft on the Sparkling Lake
Source:
North Temperate Lakes
Long Term Ecological Research
NSF/ Univ. of Wisconsin-Madison
Lake simulations: small lakesSparkling lake, 2005: annual evolution
• Surface temperature: good
for both models
- Hostetler’s model:
rapid shifts of temperature
in autumn and spring
• Mixing layer depth: higher in
FLake in spring (full overturning)
• Ice thickness and duration: good
for both models
0
10
20
30
Wate
r surf
ace
tem
pera
ture
, o
C
Observation Hostetler FLake
-200-1000100200300
Sensib
le h
eat
flux, W
/m2
0
5
10
15
20
Mix
ing
depth
, m
0.00.20.40.60.81.0
Ice
thic
kness, m
0 50 100 150 200 250 300 350
-400-300-200-100
0100
Late
nt heat
flux, W
/m2
Julian day (2005)
Ice-free period
(observation)
Sparkling lake, 2005: water temperature profiles
• Summer: good results for both models.
• Under the ice cover:
Hostetler’s model profile is different
from observed and FLake’s. Why?
- Hostetler’s model: no effective
eddy mixing in winter stratification.
- The winter profile is “frozen” at 4ºC.
- Only a thin surface layer has to be
heated up in spring or cooled down
in autumn.
- Surface temperature changes
in overturning periods are rapid
FLake has to cool down or to heat up
the whole water column, from the bottom
to the surface (thermocline)
Surface temperature changes are slow.
Observed profiles suggest that there is some mixing (current-driven?) even under the ice.
FLake implicitly presumes it.
0 5 10 15
De
pth
, m
0 10 20
0 10 20 30
NovemberSeptemberJulyMayMarchJanuary
0 5 10 15
Twater
,oC
-2.5 0.0 2.5 5.0
20
15
10
5
0
-2.5 0.0 2.5 5.0
Lake simulations: small lakes
0
10
20
30
Wa
ter
su
rfa
ce
tem
pe
ratu
re,
o
C
Observation Hostetler FLake
-200-1000100200300
Se
nsib
le h
ea
t
flu
x,
W/m2
0
5
10
15
20
Mix
ing
de
pth
, m
0.00.20.40.60.81.0
Ice
thic
kn
ess,
m
0 50 100 150 200 250 300 350
-400-300-200-100
0100
La
ten
t h
ea
t
flu
x,
W/m2
Julian day (2005)
NDBC Buoys Simulation grid
Lake simulations: Great Lakes• Simulation period: 1971-2000, 10 years spin-up.
• Simulations timestep: 1hour.
• FLake: « virtual bottom » at 60 m, if the depth
exceeds 60 m.
• 144 points over the Great Lakes
(horizontal resolution 45 km, corresponding
to the current CRCM resolution)
• Input data:
- ERA40 reanalysis (2.5º, interpolated)
• Validation data:
- Buoy observation data
(NOAA’s National Data Buoy Center)
- NOAA Great Lakes Ice Atlas
- G.J. Irbe 1992 Great Lakes surface water climatology, Environment Canada,
- S. Goyette et al, 2000 (water surface climatology data)
Simulation points and NDBC buoys
Lake Superior, Buoy 45001, depth: 261.6 m and the nearest simulation point
• ERA40 interpolated air temperatures are different from locally observed: ERA40 mostly reflects
the land observations, lake effects are hardly present.
• Surface temperature patterns, ice duration and thickness are not correctly reproduced by both
lake models.
• Hostetler’s model predicts earlier and longer ice-cover period, lower mixing depth that FLake.
Lake simulations: Great Lakes
-20
0
20
Wa
ter
su
rfa
ce
tem
pe
ratu
re,
o
C
19931992
Air
tem
pe
ratu
re,
o
C
ERA40 interpolation Buoy observations
0.0
0.5
1.0
Mix
ing
de
pth
, m
Ice
thic
kn
ess,
m
05101520
Hostetler FLake
0204060
Years
NDBC Buoys Simulation grid
Simulation points and NDBC buoys
Lake Michigan, Buoy 45002, depth: 175.3 m and the nearest simulation point
• The Hostetler’s model produces much ice, even when there was no ice observed in this year.
• FLake predicts better the ice thickness, duration and presence/absence in different years, but
it can hardly be considered a satisfactorily result.
• The Hostetler's mixing layer depth is consistently lower than simulated by FLake.
Lake simulations: Great Lakes
-20
0
20
Wa
ter
su
rfa
ce
tem
pe
ratu
re,
o
C
19931992
Air
tem
pe
ratu
re,
o
C
ERA40 interpolation Buoy observations
0.0
0.5
1.0
Mix
ing
de
pth
, m
Ice
thic
kn
ess,
m
05101520
Hostetler FLake
0204060
Years
NDBC Buoys Simulation grid
Simulation points and NDBC buoys
0102030
Wate
r surf
ace
tem
pera
ture
, o
C
0.0
0.5
1.0
19931992 YearsM
ixin
gdepth
, m
Ice
thic
kness, m
0204060
-20
0
20
Air
tem
pera
ture
, o
C
Lake Erie, 45005, depth: 12.6 m and the nearest simulation point
• The surface temperature in the shallow lake Erie is reproduced much better, than in deeper
lakes.
• Simulated ice is much closer to observations, though again Hostetler gives more ice than FLake.
• Mixing layer depths, simulated by two models, are closer one to another.
Lake simulations: Great Lakes
-20
0
20
Wa
ter
su
rfa
ce
tem
pe
ratu
re,
o
C
19931992
Air
tem
pe
ratu
re,
o
C
ERA40 interpolation Buoy observations
0.0
0.5
1.0
Mix
ing
de
pth
, m
Ice
thic
kn
ess,
m
05101520
Hostetler FLake
0204060
Years
NDBC Buoys Simulation grid
Simulation points and NDBC buoys
0102030
Wa
ter
su
rfa
ce
tem
pera
ture
, o
C
0.0
0.5
1.0
19931992Years
Mix
ing
de
pth
, m
Ice
thic
kn
ess,
m
0
5
10
-200
20
Air
tem
pe
ratu
re,
o
C
Averaged annual water surface temperatures:
comparison of simulations with observed climatology
• Shallow lakes are better reproduced that deep lakes.
• But even shallow lakes are not very good.
Possible reasons?
• Great Lakes are large and horizontally
inhomogeneous lakes with strong currents,
many other horizontal effects. 1D lake models
are not able to take into account 3D patterns.
• ERA40 data, used in simulations, are rather land
data for this region and do not reflect lake effects.
• Both tested 1D lake models are better fit for shallow lakes.
Hostetler’s model:
- No mixing in winter inversion and under the ice:
can be valid only for very shallow, small and quiet lakes.
Even in the Sparkling lake, 0.5x1.5 km, some mixing is present under the ice.
FLake:
- The assumption of the thermocline, going up to the bottom, is not physically correct in deep
lakes. A virtual bottom at 60 m is an arbitrary choice and does not solve the problem.
Lake simulations: Great Lakes
1 2 3 4 5 6 7 8 9 1011120
102030
Erie
Months
Observed Hostetler FLake
0
10
20Ontario
0
10
20 Huron
Avera
ge w
ate
r surf
ace
tem
pera
ture
, o
C
0
10
20Michigan
0
10
20Superior
150
100
50
0
5 10 15 20
Observations Hostetler 309 m FLake 60 m
Twater
, oC
Depth
, m
150
100
50
0
5 10 15 20
Observations Hostetler 309 m FLake 60 m SIMSTRAT 309 m
Twater
, oC
Depth
, m
(In collaboration with the C3i team, University of Geneva)
• Depth: 309 m (maximal), size: 70x15 km
• Meromictic or monomictic mixing regime
• Non-freezing lake
• Simulated year 2004, starting in mid-December 2003
Both “our” lake models show their characteristic
patterns:
• Hostelters’s model:
- Shallow mixing layer
- Thin thermocline
• FLake:
- Better mixing layer depth and thermocline thickness
- The virtual bottom at 60 meters
constraints the profile evolution.
Lake simulations: Lake of Geneva
At UNIGE, another 1D lake model is used: SIMSTRAT, using the k-! closure, developed in the
Swiss Federal Institute for Environmental Science and Technology in Duebendorf, Switzerland
(Goudsmit et al, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C12, 3230)
This model takes into account some 3D effects, like seiching (internal gravity waves
in the thermocline). No ice model at the moment, but it is being developed.
Some simulations of Great Lakes and the Sparkling Lake with this model are planned.
Conclusions• Two 1D lake water/ice models were tested in different conditions: shallow subgrid lakes and
the Great Lakes. Water and ice behavior was simulated and compared with observations.
• In the case of small shallow lakes, both models have successfully reproduced the annual
water temperature evolution, latent and sensible heat fluxes, ice formation and break-up
timing, and the ice thickness.
• In the case of Great Lakes, observed water temperature/ice cover is simulated reasonably well
for lake Erie, unlike in the case of Superior/Michigan. In general, better results were obtained
for Lake Erie, which is the shallowest of the five. This could be partially explained by the
biases in the ERA40 reanalysis data (lakes treated as land points), and the lack of inclusion of
complicated processes in the models, such as horizontal transfer of water and heat, water and
wind ice drift, etc. The main reason, however, is that these models are by construction
better fit to shallow lakes than to deep ones.
• Both lake models produce similar results for small shallow lakes. For Great Lakes the FLake
model produces results that are closer to observations. Results suggest that both models can
be used for simulating small shallow lakes and the FLake model appears to be a more
reasonable choice in the case of deeper lakes.
• Other interesting 1D lake models exist and will be tested in similar conditions.
Current activity: Coupling the lake models with CRCM/CLASS
• Works have begun recently in collaboration with Michel Giguère and Richard Harvey
(Ouranos). At first, resolved lakes will be coupled with CRCM4 / CLASS, then subgrid lakes
are expected in CRCM5 / CLASS
• The possibility to use different lake models is assumed. A kind of common interface?
CRCM and lakes:
interactive interaction
The role of lake model in the regional climate
modeling is analogous to the role of surface
schemes:
• The atmospheric module provides the surface
conditions to the lake model: radiation fluxes, air
temperature, wind force, humidity, precipitations.
• The lake model has to return the surface boundary
conditions to the atmospheric module: lake surface
temperature, latent and sensible heat fluxes, etc.
The lake model can be incorporated to the surface
schema:
• For resolved lakes, providing the surface conditions
on grid cells, covered by these lakes;
• For subgrid lakes: on corresponding mosaic
elements.
Place and role of lake models in RCM
Land Lake
Soil
Atmosphere
L,Q,!*,…
Vegetation
", q, Vh,…
Atmospheric module
Surface
schema
Lake
model
