An inventory and description of
ice forecasting models at ice centers
Prepared
by
Frode Dinessen
The Norwegian Meteorological Institute
Introduction
At the 1st meeting of the International Ice Charting Work Group (IICWG) the standing
committee on Data, Information and Customer Support identified twelve projects as important
and ten of them were designed for action.
This paper address the action on “Provide an inventory and description of each center’s ice
forecasting models”
Ice forecasting models from the National Ice Center, the Canadian Ice Center, the Finish Ice
Center, the Danish Meteorological Institute and the Norwegian Meteorological Institute are
described here.
National Ice Center
The operational sea ice forecasting model used by the U.S. Fleet Numerical and
Oceanography Center is the Polar Ice Prediction System PIPS 2.0. The model achieves its
final form by coupling the Hibler sea-ice model with the Bryan/Cox ocean model. This
coupled model is atmospherically forced by using the Navy Operational Global Atmospheric
Prediction System.
PIPS standard operational products are 0-24-48-72-120 hour forecasts of ice concentration,
ice thickness, and ice drift for the northern hemisphere from the north pole and southward to
approximately 30N.
A PIPS 3.0 model is under development. The new model involves improvements in sea ice
dynamics and thermodynamics, and a reduction in the grid resolution from 18 km to 9 km.
Canadian Ice Center
The Canadian Ice Service has several ice models currently in operational use at their center.
There are also several new ice models under development. The models described here are the
CIOM – Community Ice-Ocean Model – east coast, CIOM – Gulf of St Lawrence, CIOM ice
module. In addition an Iceberg model, Ice Thickness Model and Ice Freeze-up model is
described.
Finish Ice Center
The Finnish Ice Service operates a dynamic sea ice forecast model for the Baltic Sea. The
model has been developed in several stages since 1973. To day the model produces ice
forecasts of thickness, concentration and drift, on a 114-hour time scale and with a resolution
of 18.5 km. The model is wind forced by using data from the High Resolution Limited Area
Model (HIRLAM), operationally running at the Finnish Meteorological Institute.
A thermodynamic model is under development and will be coupled to the dynamic model.
Danish Meteorological Institute
The Danish Meteorological Institute (DMI) has a sea ice forecast model under development.
The model is a dynamic ice drift model and is forced by using wind field from the HIRLAM
model, operationally running at the DMI, and a climatological ocean state.
The model covers the area around Cape Farewell and about 300 km up the east and west
coast. The system is almost finished, but it still needs a proper validation before put into
operation.
Norwegian Meteorological Institute
The Norwegian Meteorological Institute has a dynamic-thermodynamic sea ice forecast
model under development as part of the Regional Climate Change under Global Warming
(REGCLIM) project at DNMI. The model is based on the elastic-viscous-plastic dynamic of
Hunke and Dukowicz and the thermodynamics of Mellor and Kantha. The ice model is
coupled to the DNMI ocean model and it covers the Nordic seas. The model is still under
development and needs a proper validation before is can be put into operation.
National Ice Center Polar Ice Prediction System (PIPS) 2.0
Model Description
Designated as PIPS in 1987, the Polar Ice Prediction System is the operational sea ice
forecasting model used by the U.S. Fleet Numerical and Oceanography Center (FNMOC). It
is the latest of several U.S. Navy Computer based sea-ice models, the first of which had its
inception in 1968. The configuration was developed at NRL Stennis Space Center .
The current PIPS ocean model has 15 vertical levels, with each level of thickness increasing
with depth while the ice thickness model is a two-level model defining both thick and thin ice
categories. The PIPS grid resolution is 0.28, which varies from 17 to 33 km depending upon
the location of the grid square within the spherical coordinate system. The final output is
converted to a fixed 18 km x 18 km grid. This system places a new equator coincident with
the 10E-170W great circle and a new north pole at the intersection of the 100E meridian
and the true equator. This coordinate system provides numerical stability at high latitudes and
eliminates numerical singularity as well.
The model achieves its final form by coupling the Hibler sea-ice model (which calculates ice
drift, thickness, and concentration) with the Bryan/Cox ocean model (which calculates ocean
temperature, salinity, and currents). Both the sea-ice and ocean models are run separately
prior to the exchange of data, thereby maintaining their integrity. The sea-ice model utilizes a
time step of two hours. The ocean model however, utilizes a dual time step. Ocean
temperatures and salinity equation step sequences are set to .5 hours whereas velocity
equations are stepped at .05 hours. Heat and salinity fluxes are exchanged in the coupling
process and interfacial stresses of wind, ice motion, and ocean currents are also entrained.
The boundaries for these processes are defined as solid walls and are placed away from the
sea-ice regions.
PIPS is initialized by its previous 24-hour forecast. In addition, the modeled ice concentration
field is initialized by current ice conditions obtained by using ice data from the Special Sensor
Microwave/Imager (SSM/I). SSM/I brightness temperatures are converted into fractional ice
coverage. Then, the Optimal Interpolation method is employed to map the SSM/I data to the
PIPS grid. The ice thickness and ocean mixed-layer temperatures are adjusted to be
consistent with the SSM/I ice coverage.
The coupled model is atmospherically forced using the Navy Operational Global Atmospheric
Prediction System (NOGAPS). Surface air temperature, surface pressure, surface vapor
pressure, shortwave radiation, sensible plus latent heat flux, and total heat flux are the
contributed fields from NOGAPS.
PIPS standard operational products are 0-24-48-72-120 hour forecasts of ice concentration,
ice thickness, and ice drift for the northern hemisphere. Areal coverage extends from the
north pole southward to approximately 30N. There is no southern hemisphere coverage.
Canadian Ice Service Operational Ice Models
At the Canadian Ice Service (CIS) there are a number of ice models currently in operational
use at the center. Below is a list of the models with a brief description. More documentation
can be found at the public web site http://www.cis.ec.gc.ca/model/
In addition to those models mentioned here the Canadian Ice Service have also several new
ice models under development.
Sea Ice Models
CIOM - Community Ice-Ocean Model - east coast
Area of coverage: 40 to 66N and 40 to 66W
Resolution: 1/5 lat by 1/6 lon
Description:
A coupled ice ocean model with Hibler type ice dynamics and thermodynamics.
The ocean module is the Princeton Ocean Model. The model was developed at
the Bedford Institute of Oceanography where it is also used for climate and
process studies. At CIS it is used from November to July for sea ice
nowcasts and 24 and 48 hour forecasts. The ocean is initialized from
climatology in November and has surface and lateral boundary forcing
afterwards. Ice is initialized daily from CIS ice charts through a nudging
technique. Atmospheric forcing comes from the Canadian Meteorological
Centre's (CMC) Regional GEM NWP model.
CIOM - Gulf of St Lawrence
Area of coverage: Gulf of St Lawrence
Resolution: 5 km
Description:
A coupled ice ocean model with Flato's McPIC (multi-category
particle-in-cell model) ice module. The ocean module is called GF8 and is a
derivative of the Bachaus model. The model was developed at the Institut
Maurice Lamontagne where it is also used for climate and process studies. At
CIS it is used from January to May for 24 and 48 hour sea ice forecasts. The
current operational version does not include ice thermodynamics. Each day
the ocean module has a pre-forecast three day spin-up and also has lateral
boundary forcing. Ice is initialized daily from CIS ice charts by data
insertion. Atmospheric forcing comes from the CMC's Regional GEM NWP model.
CIOM ice module
Area of coverage: all other areas of Canada and their approaches where sea
ice affects navigation
Resolution: variable
Description:
This is simply the CIOM east coast without POM and without thermodynamics.
This version of the module is used for 24 and 48 hour sea ice forecasts in
all other operational areas during shipping seasons: winter-spring in the
south and summer-fall in the north. The ocean module is replaced by
climatological annual mean currents. Ice is initialized daily from CIS ice
charts by data insertion. Atmospheric forcing comes from the CMC's Regional
and Global GEM NWP models.
Iceberg Model
International Ice Patrol iceberg model
Area of coverage: northwest Atlantic
Resolution: various environmental grid forcing
Description:
This model is used to provide iceberg nowcasts and short range forecasts. It
was developed by the IIP and is implemented almost identically at IIP. Ocean
forcing comes from climatological annual mean currents with a wind driven
Ekman layer and updates from drogued drifter buoys. Atmospheric forcing is
provided by CMC's Global GEM NWP model. SST and wave heights are provided by
the US FNMOC.
Ice Thickness Model
Landfast Sea Ice Thickness Model
Area of coverage: Canadian sea ice waters
Resolution: 1 degree lat by 1 degree lon as currently implemented
Description:
This is a 1-D ice thickness model developed by Flato and Brown. It is used
to estimate landfast ice thickness. Atmospheric forcing is provided by CMC's
Global GEM NWP model.
Ice Freeze-up Models
Billelo Freeze-up Model
Area of coverage: Canadian sea ice waters
Resolution: selected locations in the St lawrence Seaway and eastern Canada
Description:
This is a 1-D statistical model which is used to estimate the time of ice
formation. Forcing is provided by nearby meteorological station synoptic
weather reports.
NUMERICAL SEA ICE FORECAST IN THE FINNISH
ICE SERVICE1
B. Cheng, A. Seinä, J. Vainio, S. Kalliosaari, H. Grönvall, J. Launiainen
Finnish Institute of Marine Research, Helsinki, Finland
ABSTRACT
In this report, the development of the numerical sea ice model for the Baltic Sea in the Finnish
Ice Service is reviewed and the operational routine forecasting of sea ice is introduced. Using
the HIRLAM (HIgh Resolution Limited Area Model, the Finnish Meteorological Institute)
atmospheric forcing data, the ice drift forecasts by the dynamic model can cover up to 5 days.
A one-dimensional thermodynamic sea ice model is used to calculate the ice thickness
variation. The thermodynamic model will be coupled with the dynamic model and the whole
ice model will be coupled with the HIRLAM. A few test examples of the ice models are
given.
1. INTRODUCTION
All the Finnish ports are surrounded by ice during a normal mid-winter. The ice season lasts
from a few weeks in the southern Baltic Sea up to more than half a year in the far north. The
maximum extent of sea ice cover varies between 12 and 100% (50000 to 420000 km 2) of the
Baltic Sea area. Marine transportation is very important in the area. About 0.5 billion tons are
annually transported in the Baltic Sea. More than 80% of the foreign trade of Finland are
carried out as the marine transport. In 1997, for example, 75 million tons were transported by
ship and about 30 million tons from this were transported during the winter months (Sandven,
et al., 1998). Normally, the vessels have to navigate at least 40 nautical miles through sea ice
during an average mid-winter season in order to enter the ports in south-east Finland, and
about 160 nautical miles to enter the northern ports of the Bothnian Bay. During severe
winters, vessels may even have to navigate through 650 nautical miles in the sea ice area
(Seinä, 1994).
Information service for the Baltic Sea ice have been run for more than 80 years in
Finland. The Finnish Ice Service was set up in 1918 on behalf of the Finnish Institute of
Marine Research (FIMR) to provide information on sea ice conditions in order to coordinate
winter navigation. The ice information service consists of three operative systems, i.e. ice
observation network, ice analysis and forecasts, and ice information communication system
(Seinä, et al., 1997). Experience and field data show that the Baltic Sea ice cover and the ice
fields have a dynamic nature. The ice can drift up to 30 km per day during the frequent storms
leading to converging (closing) or diverging (opening). Accordingly, ice drift forecasts play
an important role in the Baltic Sea ice navigation.
1
Published earlier in Tuhkuri, J and K. Riska (eds.) Proceedings of the 15 th International Conference on Port and
Ocean Engeneering under Arctic Conditions, POAC’99, Espoo, Finland, August 23-27, 1999, pp. 131-140.
2. SEA ICE MODEL
Research work on modeling of the sea ice in the Baltic Sea has been intensively carried out
for several decades in the FIMR. The primarily aim has been to develop methods for sea ice
forecasting for winter navigation. Field experiments have been accomplished to obtain
experimental data for the physical processes and parameterization of the sea ice problems.
The ice model was developed in several stages. The modeling work on the Baltic Sea
ice drift began already in 1973. In the beginning, the model covered the Gulf of Bothnia. A
model for short-term forecast of ice drift velocity and mass distribution was established and
tested for daily calculation in the ice season 1976/77. The results were transmitted in a chart
format with facsimile to the icebreakers (Leppäranta, 1977). The weather forcing data, i.e.
30h statistical prediction for the regional surface wind (Lange, 1973) were obtained from the
Finnish Meteorological Institute (FMI). The model was in routine use since 1978. However,
the model output was some coarse and only 30h forecasts could be made. On the other hand,
the sea ice model proved to be useful, and it was extended to the whole Baltic Sea.
The next generation of ice model in the FIMR was established in 1988 as a joint SinoFinnish cooperation (Wu and Leppäranta, 1988). The new model was first linked with the
weather forecasting system in China, and since then it has been used successfully in
operational routine sea ice drift forecasting in the Bohai Sea (Wu and Leppäranta, 1990). The
model was taken as a basis for the Baltic Sea ice model in the Finnish Ice Service, and it was
tested in operative use in the winter of 1991/92 (Leppäranta and Zhang, 1992).
In 1993, in addition to some modification of the model based on the Chinese sea ice
forecast system, significant improvements in the forecast system (initialization, ice drift and
figure plot program) and the format of the model products have been performed. The system
was in test use in the winter of 1993/94. Analytical surface wind field with respect to 11 subregions over the Baltic Sea was obtained from the FMI allowing later an extension of the ice
forecast time period (42h). The model resolution was 18.5 km. In 1994 the model was running
continuously for 85 days and yielded rather satisfactory results in comparison and verification
(Bai et al., 1995).
In the winter of 1996/97, data for the initial ice fields (ice thickness and concentration)
could be gathered automatically in a digital format from the routine ice charts, based on the
IceMap system. This shortened the daily forecast running time from 1-2 hours to a few
minutes. The initial ice field was earlier obtained manually from an ice chart to each grid of
the model with a maximum of 638 points, for both the ice thickness and concentration. Using
the wind forcing data from the HIRLAM model the ice forecast could be extended up to 114 h
time scale in 1997.
2.1 Dynamic sea ice model
The basic equations of the Baltic Sea ice dynamic model are the momentum and mass balance
(Hibler, 1979, Leppäranta, 1981).
h  du dt  fk  u   a   w    F
m t    ( mu)  
m  hA  (hl  hr ) A
(1)
(2)
(3)
where  is the ice density, h is the mean ice thickness, u is the ice velocity, f is the Coriolis
parameter, k is the unit vector vertically upward,  a and  w are the air and water stress acting
on sea ice, respectively.  is the internal ice stress tensor and F is the gravitational force due
to sea surface tilt. m is the ice mass,  is the thermodynamic ice growth rate, A is the ice
concentration, hl and hr represent the thickness of level and ridged ice, respectively.
A High correlation between the velocities of ice and wind in the Baltic Sea can be
found especially during divergent ice motion. Internal ice stress  , however, tends to be very
important factor in ice dynamics. Consequently, the constitutive law of the ice dynamic model
(ice rheology) is often used to evaluate the model. Another important issue is to better
describe the mass conservation Eq. (2) in terms of A, hl and hr .
2.2 Thermodynamic sea ice model
The thermodynamic ice model was developed in the FIMR in the recent years. A onedimensional thermodynamic sea ice model was constructed with the emphasis on the vertical
multi-layer mass and energy balance. Various processes of the surface heat balance are taken
into account. The model (Launiainen and Cheng, 1998, Cheng and Launiainen, 1998)
includes a full coupling with the lower atmosphere and calculation of the air-ice interface
temperature and surface fluxes, as well as the heat conduction in the snow and ice and the
heat flux and ice thickness variations at the ice-ocean boundary . The main equations of the
model are the mass and energy balance of the ice surface and an ice sheet.
(1   )(1  e
 i ,s hi ,s
)Qs  Qd  Qb (Tsfc )  Qh (Tsfc )  Qle (Tsfc )  Fc (Tsfc )  Fm (Tf )  0 (4)
Ts,i ( z, t )
T ( z, t )
 

    ks ,i s , i
 q( z, t )

t
z 
z
 i  Lif  dhi dt  (ki Ti z)bot  Fw 
( c) s,i
(5)
(6)
where Qs is the short-wave radiation, Qd is the incoming atmospheric long-wave radiation
and Qb is the outgoing long-wave radiation from the surface. Qh and Qle are the turbulent
sensible and latent heat fluxes, respectively. Fc is the surface heat conductive flux and Fm is
the heat flux due to surface melting. Tsfc is the surface temperature and T f is the freezing
point. The further most meaningful parameters are surface albedo  , extinction coefficient
 , and thickness of the interfacial ice surface layer h . ( c)s,i is the volumetric heat
capacity, Ts,i is the temperature and t is time. ks,i is the thermal conductivity and q( z, t ) is an
internal heat source term. Lif is the latent heat of freezing. hi is the ice thickness variation at
the ice bottom. Fw is the oceanic heat flux. Subscript s and i denote the snow and ice,
respectively.
Table 1 gives the main characteristics of the ice model used in the Finnish Ice Service.
In the near-future the thermodynamic model will be coupled with the dynamic model.
Table 1. Main characteristic of the sea ice model in the Finnish Ice Service
Time
Main characteristic of the model
Reference
ice rheoloy
mass
thermal effect
conservation
1970's
linear viscous A
No
Leppäranta (1977, 1981)
1980/1990's viscousNo
Wu and Leppäranta
A, hl , hr
plastic
(1988)
Leppäranta and Zhang
(1992)
1990's ---- viscous1-D model
Launiainen and Cheng
A, hl , hr
plastic
(1998)
3. NUMERICAL SEA ICE FORECAST
In order to produce a sea ice forecast, the weather forcing and initial ice conditions need to be
specified. Information from various sources are used in the Ice Service. The ice model's
operational routine scheme is shown in Fig. 1 with respect to the three development stages, as
1970-80's, early 1990's and late 1990's. For the present, the data sources have been extended
especially by taking of space borne data with better resolution and weather independent SAR
data into the operational use. Significant improvement for the ice model was a better accuracy
of the ice field for initialization. A longer period weather prediction also made some extension
of the ice forecasts.
ICE CHARTS
SPACEBORNE DATA
1970's ---1980's
early 1990's ---
( ESSA, NOAA VHRR, NOAA AVHRR )
( NOAA AVHRR, ERS SAR )
( NOAA AVHRR, RADARSAT SAR )
1997/1998 --AUTOMATIC SAR DATA ICE TYPE CLASSIFICATIONS
AIRBORNE DATA
1970's---
(aircrafts and helicopters)
GROUND TRUTH
1970's---
( ships, icebreakers, coastal stations )
DIGITIZED ICE CHARTS FOR DYNAMIC MODEL INITIAL FIELD DATA
1970's --- early 1990's
1997/1998
(manual input)
(auto-correction program)
WEATHER FORECASTS
1970's ---1980's ( statistical wind prediction 36 h)
early 1990's ---
( numerical and analytical wind prediction 48 h)
1997/1998 ---
( HIRLAM model based wind prediction 120 h)
1970's ---1980's (30 h)
NUMERICAL SEA ICE FORECAST
early 1990's (42 h)
ice concentration, ice drift speed ice concentration and thickness
and direction, ice pressure
ice drift speed (maximum and field)
and direction, ice pressure
(convergence or divergence)
(convergence or divergence)
1997/1998 (114 h)
ice concentration and thickness
ice drift speed (maximum and field)
and direction, ice pressure
(convergence or divergence)
Figure 1. Numerical sea ice forecast scheme
For the short-term forecast (1-2 days), the ice drift is the dominate factor and the
thermal effects must be taken into account for longer forecast periods. However, the input
forcing data (air temperature, wind speed, relative humidity and cloudiness) for the ice
thermodynamic model are not yet available on a routine basis for the FIMR. Additionally, due
to the divergence of the wind stress on stratification, the thermodynamic air-ice model should
finally give a more realistic wind forcing to the dynamical model.
The direct output of the ice model contains the digitized ice information. Ice thickness,
concentration and drift field can be plotted in each time step of the model calculation. Figure
2 shows a numerical ice forecast charts published in Finland in 1970's and one recent
example.
Figure 2a. Ice forecast (30 h) in winter 1976/77 (From Leppäranta, 1981).
This was the first operational numerical sea ice forecast chart in the world.
Figure 2b. A sea ice forecast (48 h) in winter 1996/97.
In order to verify our thermodynamic ice model, historical data from IDA data bank (Haapala
et al.,1996) were used to calculate the thermal ice growth for three winters at Kemi in the
northern part of the Baltic Sea. In the study, daily means of forcing data were used, but the air
temperature was interpolated linearly to hourly values corresponding to the time step of the
model. The time histories of the atmospheric forcing data are given in Figures 3, 4 and 5.
Table 2 gives the model parameters and information for the three studied ice seasons.
Simulation started from the day of first freezing. When existing, the snow thickness was also
used as an input data, linearly interpolated from observations made once a week. Calculations
without snow taking into account were also carried out for comparison.
Figure 3. Time series of the atmospheric forcing in winter 1983/84.
Figure 4. Time series of the atmospheric forcing in winter 1986/87.
Figure 5. Time series of the atmospheric forcing in winter 91/92.
Table 2. Model parameters, average atmospheric forcing data, and other characteristics
for the ice seasons 1983/84,1986/87 and 1991/92.
model parameters
value Other
Winter Winter Winter
information
83/84
86/87 91/92
density of ice (kg/m3)
916
time step (s)
3600
3600
3600
3
density of snow (kg/m )
300
Air temperature -7.4 C
-8.2 C -3.8 C
(A)
extinction coefficient of ice (m- 1.5-17 Relative
82 
78 
85 
1)
humidity (A)
extinction coefficient of snow 15-25 Wind speed (A) 3.6 m/s
3.4 m/s 4.2 m/s
-1
(m )
ice salinity (ppm)
2.0
Cloudiness (A) 0.67
0.61
0.67
2
oceanic heat flux (W/m )
2.0-5.0 Initial date
15, Nov. 2, Dec. 10,
Dec.
surface albedo of ice
0.75- Initial Hi
0.04m
0.02m 0.05m
0.5
surface albedo of snow
0.85- Initial Ti
-1.8C
-1.8C -1.8C
0.8
thermal conductivity of ice 1.99
Layers in ice
10
10
10
(W/mK)
thermal conductivity of snow 0.19
Layers in snow 5
5
5
(W/mK)
(A): average value during that winter.
winter83/84
winter 91/92
winter 86/87
Figure 6. Ice thickness simulation for the
ice seasons of 1983/84, 86/87 and 91/92.
"x" gives the observed ice thickness once a
week, "o" gives the snow observations with
linear interpolation. Solid line is the ice
thickness simulation with snow layer to be
taken into account. Dotted line gives the
pure ice thickness simulation without snow
layer effect.
Table 3. Verification of ice thickness simulation.
ice winter
AV (m)
ME (m)
RMSE (m)
observed
calculated
N
Y
N
Y
N
Y
winter
0.52
0.69
0.56
0.18
0.05
0.20
0.10
83/84
winter
0.68
0.80
0.72
0.15
0.07
0.18
0.09
86/87
winter
0.34
0.33
0.36
0.01
0.02
0.07
0.05
91/92
AV: average value; ME: mean error; RMSE: root mean square error.
N: calculation without snow taking into account; Y: calculation with snow taking into
account.
The calculated time series of the ice thickness are given in Figure 6. The verification
of ice thickness simulation in Table 3 indicate that in general the ice model system is doing
better by taking snow into account. However, the variability of ice in this study is not covered
very well, especially during the ice equilibrium stage. In another words, ice variation have
been damped a lot if the snow effect is taken into account. On the other hand, we may notice
that the forcing data are mostly daily mean value, and for the snow data interpolated from 7
days interval observations, and this may have filtered out partial variation of the results. The
snow-ice formation was not taken into account in the calculations. It is also difficult to
account the equivalent water of internal melting (Launiainen and Cheng, 1998) quantitatively.
Those may lead to error in the ice thickness simulation. Further high quality data and analysis
are needed. Numerical simulation of ice thickness for those three winters have been done also
by Haapala and Leppäranta (1996), by a coupled ice-ocean model, and by Saloranta (1998),
by a thermodynamic ice model with consideration of snow ice formation. By comparing with
those studies, our results are of improvement as to the consistency of the spring melting
against the observations. This may because of the proper consideration of the penetrating
solar radiation. On the other hand, Saloranta (1998) gave better accuracy of the ice thickness
simulation because of the snow ice formation was taken into account.
Figure 7. Average ice growth rate for
winters of 1983/84, 86/87 and 91/92.
"o" gives the observed mean ice growth
calculated from observations made once a
week. Solid line gives the calculated ice
growth with snow taking into account and
dotted line gives the calculated ice growth
rate without snow taking not into account.
The mean ice growth rate i.e. the time derivative of ice changes for certain time period
is given in Figure 7. The modeled and observed ice growth rate show encouraging general
agreement but indicate distinct discrepancies for the very early stages of ice growth. At the
moment we do not know whether those are inaccuracies of modeling or of observational
origin. Table 4 lists the monthly mean ice growth for each season. It shows that the ice in a
normal winter tends to grow most intensively until the end of January, to reach an equilibrium
level, and to melt in April. In the severe winter of 86/87 the ice growth was intense still in
February. During the mild winter of 91/92, ice formation began late and the ice started to melt
already in March.
Table 4. Monthly mean value of ice growth rate (mm/hour).
Month
11
12
1
2
3
4
5
Winter 83/84
0.941
0.237
0.151
0.385e-2
0.251e-1
-0.235
-1.2
Winter 86/87
0.711
0.358
0.125
0.155e-1
-0.186
-1.5
Winter 91/92
0.318
0.222
0.452E-1
-0.161e-1
-0.155
-1.6
We may see that the present thermodynamic model yields encouraging simulations for
the ice thickness (also see, e.g. Launiainen and Cheng, 1998). The results indicate that the
atmospheric boundary layer (ABL) dynamically coupled with ice, and heat conduction in the
ice control the ice growth. In addition to the ice thickness variations, the model yields e.g. the
time development of the ice surface temperature and the air-ice fluxes, as well as the in-ice
temperatures. The model will further be used for process studies and coupled as a module
with high resolution limited area atmospheric model (HIRLAM); for getting a better
description of the atmospheric surface boundary layer and with models of sea ice dynamics.
4. CONCLUSIONS
In the recent years, the dynamic ice model has been successfully used in the operational
Finnish Ice Service. The thermodynamic model is constructed and evaluated by comparison
of simulation and field data. The thermodynamic ice model will be coupled with the dynamic
model. However, the models still need further development in many aspects. For instance, the
initial ice drift needs to be specified, instead of the motionless initialization as now is in use.
This can be done e.g. with the aid of remote sensing data such as SAR (Leppäranta, et al.,
1998). With the development and coupling of weather forecast systems such as HIRLAM, a
better accuracy may be expected in ice forecasts, since the dynamic and thermodynamic
behavior of ice are strongly influenced by the atmospheric forcing. The air-ice-sea is a fully
coupled system with mutual interaction, and the ice-ocean coupling is finally also important
to the ice forecasts. In the Finnish Ice Service, the kind of work is being done to create a next
generation of the ice forecast system. The forecasting time period of the ice models is still to
be extended, in the frame as favoured by the available meteorological predictions, in order to
better cover the customers needs.
5 REFERENCES
Bai, S. Grönval, H. and Seinä, A. 1995. The numerical sea ice forecast in Finland in the
winter 1993-1994. Rep. Series of Finnish Inst. of Marine Res., MERI (1995) 21: 4-11.
Cheng, B. and Launiainen, J. 1998. A one dimensional thermodynamic air-ice-sea model:
technical and algorithm description report. Rep. Series of Finnish Inst. of Marine Res.,
MERI (1998) 37: 15-36.
Haapala, J. et al. 1996. Ice data bank for Baltic Sea climate studies. Report Series in
Geophysics, 35. Dept. of Geophysics, University of Helsinki.
Haapala, J. and Lepparantä, M. 1996. Simulating the Baltic Sea ice season with a coupled iceocean model. Tellus 48 A: 622-643.
Hibler, W.D. III 1979. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., 9: 815846.
Lange, A. 1973. Statistical surface wind prediction in Finland. Finnish Meteorol. Inst. Techn.
Rep., No. 6.
Launiainen, J. and Cheng, B. 1998. Modelling of ice thermodynamics in natural water bodies.
Cold Reg. Sci. Technol., 27: 153-178.
Leppäranta. M. 1977. Model for ice forecast in the Gulf of Bothnia. In Geofysiikan päivät
Helsingissä 10,-11,3,1977, 291-300 (ed. J. Helminen). Geophysical Society of Finland.
Leppäranta, M. 1981. An ice drift model for the Baltic Sea. Tellus 33 (6): 583-596.
Leppäranta, M. and Zhang, Z. 1992. A viscous-plastic ice dynamic test model for the Baltic
Sea. Finnish Inst. of Marine Res., Internal Report (1992) 3.
Leppäranta, M. Sun, Y. and Haapala. J. 1998. Comparison of sea-ice velocity fields from
ERS-1 SAR and a dynamic model. J. Glaciol., 44(147): 248-262.
Saloranta, T.M. 1998. Snow and snow ice in sea ice thermodynamic modeling. Report Series
in Geopgysics, 39. Dept. of Geophysics, University of Helsinki.
Sandven, S. Grönvall, H. Seinä, A. Valeur, H.H. Nizovsky, M. Andersen, H.S. and Haugen,
V.E.J. 1998. Operational sea ice monitoring by satellites in Europe. Final Report. OSIMS
Rep. No 4. European Commission Environmental and Climate Programme 1994-1998,
Theme 3 Area 3.2. NERSC Technical Report No. 148.
Seinä, A. Palosuo, E. and Grönvall, H. 1997. Merentutkimuslaitoksen Jääpalvelu 1919-1994.
Rep. Series of Finnish Inst. of Marine Res., MERI (1997) 32.
Seinä, A. 1994. Extent of ice-cover 1961-1990 and restriction to navigation 1981-1990 along
the Finnish coast. Finnish Mar. Res. No 262.
Wu, H. and Leppäranta, M. 1988. On the modeling of ice drift in the Bohai Sea. Finnish Inst.
of Marine Res., Internal Report (1988) 1.
Wu, H. and Leppäranta. M. 1990 Experiments on numerical sea ice forecasting in the Bohai
Sea. IAHR Ice Symposium Proceeding: 178-186.
A sea ice forecasting system for the Cape Farewell area
Nicolai Kliem
Danish Meteorological Institute
May 24, 2000
1 Introduction
A sea ice forecasting system is under development at the Danish Meteorological Institute (DMI).
The objective is to be able to predict sea ice drift in the waters around Cape Farewell.
The Danish Meteorological Institute produces maps of sea ice concentration in the Cape
Farewell area. The maps are mainly used for safe navigation and are produced every 2-3 days.
They are based on remote sensing, that is, satellite-borne measurements primarily from Radarsat,
and by airborne measurements with a specially-equipped aircraft and helicopter. Development of
the ice service goes in two directions. One is to exploit the number of different kinds of satellite
observations [Gill, 1998; Gill and Valeur, 1999]. The other is to use numerical models to predict
sea ice drift [Kliem, 1999], in order to produce forecasts of the ice extent a few days ahead and to
fill the gab between two successive ice maps. This paper describes the forecasting system. The
system is almost ready, but it still needs a proper validation before being put into operation.
2 Forecasting system
2.1 System description
The forecasting system is based on a numerical sea ice model and is intended to be an extension to
the present ice service. The flowchart of sea ice prediction is shown in Fig. 1. When new observations
are available, they are analyzed manually to produce a map of the sea ice concentration. This
is the present ice service used for nowcasting, with the ice concentration map showing the current
ice state. It is not considered as a part of the forecasting procedure, but as an independent system
providing the necessary data for the initialization and validation of the forecasting system. The
forecast procedure proceeds as follows. The ice map is transformed to gridded data to be used as
initial condition for the model. The ice maps do not in general cover the entire model domain, and
the missing initial values are extracted from the preceding forecast. The sea ice model then uses
the actual wind forecast and a climatological ocean state to force the ice drift producing a forecast
for the ice cover.
The philosophy behind the forcing is that the ocean (the East Greenland Current) gives a mean
drag on the ice transporting it along the coast of Greenland while the daily variations are mainly
due to the wind. Thus, the actual wind forecast is essential for the ice drift forecasts on the short
time scales, while it is sufficient with a realistic steady-state sea surface current field. In the
simulations the wind thus tend to accelerate the ice, while the ocean drag tend to decelerate the ice
or, in other words, to keep a steady motion.
Figure 2 illustrates the schedule of the forecasting system. Each time a new ice map has been
produced, this is used as initial condition for a new forecast. The observations do not necessary
come in fixed interval, but the forecast period is long enough to cover the time span until the next
available observations.
2.2 Numerical sea ice model
The simulations of the ice drift is performed with a dynamic finite element sea ice model (described
more detailed in Chapter 3). The model is based on a continuum formulation with a
velocity, a thickness and a concentration field and the usual momentum and continuity equations.
Currently the ice is considered as consisting of just one type, but the model is easily extended to
include several types, for example first year and multi year ice, having different properties.
The momentum equation includes the Coriolis force, a gravity force due to the tilt of the sea
surface, the wind drag and sea surface current drag, and a force due to the divergence of the internal
ice stress. The thickness and concentration fields evolve in time according to advection-diffusion
equations.
The sea ice model includes the following features:
 Feasibility to choose between Cartesian and spherical coordinates.
 Discritisation by the finite element method.
 The cavitating fluid ice rheology [Flato and Hibler, 1992].
 Quadratic drag formulation of the air and water stresses.
The model is set up for a domain covering the area around Cape Farewell with open
boundaries normal to the isobaths about 300 km up the east and west coasts, respectively, and an open
boundary on deep water almost parallel to the coast and isobaths about 250 km offshore. The
inflow of water and sea ice takes place at the boundary normal to the east coast, and outflow will
primarily be at the boundary normal to the west coast, while the currents at the boundary on the
deep water will be very small.
The computational mesh is shown in Fig. 3. It consists of 3420 nodes connected by 6611
elements. The generation of the mesh exploits the possibility with the finite element method to
have a varying resolution, thus having high resolution on the shelf and continental slope, where
most of the ocean dynamics take place and where the ice is usually found.
2.3 Sea ice observations
The ice observations are primarily made by the satellite Radarsat. These observations are made
approximately once a day, with varying degree of coverage of about 50% to almost 100% of the
model domain. The observations are received in real time at DMI. The analysis transforming a
satellite image to a useful map of the sea ice cover are performed manually by special trained staff.
2.4 Wind forcing
The model is forced by 10 m wind fields from the High Resolution Limited Area Model (HIRLAM)
run operationally at the Danish Meteorological Institute [Sass et al., 1999]. The HIRLAM system
consist of several nested models. The wind fields are extracted from the two models named “DMIHIRLAM-G” and “DMI-HIRLAM-N”covering Greenland. DMI-HIRLAM-G is the coarser model
with a resolution of 0.45 and a forecast length of 60 hours, while the inner model DMI-HIRLAM-N
has a resolution of 0.15 and a forecast length of 36 hours.
_
_
2.5 Ocean forcing
The sea surface current and elevation used for the ocean forcing are calculated by the linear harmonic
model, Fundy [Lynch and Werner, 1987; Greenberg et al., 1998]. It is a diagnostic model
where the time dependence is based on the assumption that the dependent variables are harmonic
oscillating. The model is set up on the same computational mesh as the sea ice model (see Fig. 3).
The calculation is performed for homogeneous water with rather arbitrary boundary condition.
The reason for this is mainly the lack of useful data and is a topic for further development.
3 Model description
The numerical sea ice model is based on the assumption that the sea ice is a continuum with a

velocity field  , a thickness field h, and a concentration field A. The thickness is the area mean
thickness, and the actual ice thickness is equal to h / A for A  0. Currently the ice is considered as
consisting of just one type, but the model is easily extended to include several types, for example
first year and multi year ice, each having a thickness and concentration.
The thickness and concentration fields evolve in time according to the advection-diffusion
equations
where D is a diffusion-coefficient. The diffusion is necessary to keep the solution smooth and
stable.
The momentum equation includes the Coriolis force, a gravity force due to the tilt of the sea


Surface  , the wind drag  a on the ice, the surface current drag 
due to the divergence of the internal ice stress


on the ice, and a force F
(

where f is the Coriolis parameter written as a vector pointing upward and  is the density of sea
ice.
The wind and ocean current stresses are calculated using the quadratic formulations
Where Cai and Cωi are dimensionless air-ice and water-ice drag coefficients,  a and   are the air


and water densities, and  a and   are the wind and surface current velocities.
The internal ice stress is based on the cavitating fluid rheology [Flato and Hibler, 1992]. The
internal ice stress is then calculated as a pressure P, usually called the ice strength. The ice
strength depends on the thickness and concentration as
where P* and C are empirical constants.
To make the model suitable for large domains, it includes the ability of using
latitude/longitude coordinates. This is done similar to Greenberg et al. [1998] by the transformation to
curvilinear coordinates
where  and  denote the longitude and latitude, respectively, and R is the radius of the earth.
References
Flato, G. M., and W. D. Hibler, III, Modeling pack ice as a cavitating fluid, J. Phys. Oceanogr.,
22, 626–651, 1992.
Gill, R. S., Evaluation of the RADARSAT imagery for the operational mapping of sea ice around
Greenland in 1997, Scientific Report 98-5, DMI, Copenhagen, Denmark, 1998.
Gill, R. S., and H. H. Valeur, Ice cover discrimination in the Greenland waters using first-order
texture parameters of ERS SAR images, Int. J. Remote Sensing, 20, 373–385, 1999.
Greenberg, D. A., F. E. Werner, and D. R. Lynch, A diagnostic finite-element ocean circulation
model in sperical-polar coordinates, J. Atmos. Ocean. Technol., 15, 942–958, 1998.
Kliem, N., Numerical ocean and sea ice modelling: the area around Cape Farewell, Ph.D. thesis,
Departement of Geophysics, NBIfAFG, University of Copenhagen, Copenhagen, Denmark,
1999.
Lynch, D. R., and F. E. Werner, Three-dimensional hydrodynamics on finite elements. part I:
Linearized harmonic model, Int. J. Numer. Methods Fluids, 7, 871–909, 1987.
Sass, B. H., N. W. Nielsen, J. U. Jørgensen, and B. Amstrup, The operational DMI-HIRLAM
system, 2nd rev. ed., Technical Report 99-21, DMI, Copenhagen, Denmark, 1999.
___________________________
Nicolai Kliem, Danish Meteorological Institute, Lyngbyvej 100, DK-2100 Copenhagen, Denmark.
(e-mail: nk@dmi.dk)
The DNMI REG CLIM ice model
ØIVIND SÆTRA, LARS PETTER RØED
AND JON ALBRETSEN
Norwegian Meteorological Institute,
P.O. Box 43 Blindern
0313 Oslo, Norway
Abstract
A new dynamic-thermodynamic sea ice model has recently been developed based on the elasticviscous-plastic dynamics of Hunke and Dukowicz and the thermodynamics of Mellor and Kantha.
This model replaces the earlier Häkkinen-Mellor model earlier coupled to the DNMI ocean model ( a
version of the Princeton Ocean Model). The formulation of the new ice model, its dynamics and
thermodynamics, is briefly presented. Also some idelaized experiments comparing the response of
the new ice model to that of the earlier Häkkinen-Mellor model is presented. Based on these results
and some results from an early stage of a six year long simulation starting January 1990, it is
concluded that the behavior of the new ice model is satisfactory.
1.
Introduction
Considered is the new dynamic-thermodynamic sea ice model developed as part of the
REG CLIM project at DNMI. Earlier reports (Sætra et al. 1998, Røed et al. 1999) has shown
that the Häkkinen and Mellor (1992) model, implemented early on in the project, tends to give
too much ice and excessive ice thicknesses in areas featuring obstructions like islands and
promontories. One possible explanation for this behavior is that the ice model is too stiff, and
hence arrests the ice in areas where there are obstructions. This led naturally to consider other
ice models that hopefully was more pliant. Reported here is the new ice model, in which the
dynamics are based on the elastic-viscous-plastic rheology suggested by Hunke and
Dukowicz (1997), while the thermodynamics are based on that suggested by Mellor and
Kantha (1989) as formulated in Häkkinen and Mellor (1992). In the latter the incoming solar
radiation is replaced by that suggested by Drange and Simonsen (1996).
In contrast to many ice models in use for climate studies, Hunke and Dukowicz (1997)
suggested the use of an elastic-viscous-plastic (EVP) rheology, rather than the common
viscous-plastic rheology when computing the ice stresses. It should be noted that the
introduction of elasticity is a pure numerical artifact and does not necessarily reflect any
physical characteristics of the ice as a medium. The advantage of the EVP rheology is that it
allows the time step required by the numerical stability criterion for an explicit computation
of the internal ice stresses to be dramatically increased, and thereby allows for the use of an
excplicit solution scheme rather than the slower and more cumbersome implicit elliptic solver
commonly applied in pure viscous-plastic rheology models (Hibler 1979). Thus the
integration of the model equations becomes much more efficient on the computer, and hence
more practical for use in long term climate simulations. Moreover, a positive definite
advection scheme known as MPDATA (Smolarkiewicz and Margolin 1997) for the advection
of ice thickness and concentration is implemented. This minimizes the diffusion of the steep
gradients in ice thickness and concentration, and hence retains a sharper ice edge in the
marginal ice zone (MIZ).
The model equations are first briefly presented (Chapter 2). It should be noted that the
model is coupled to the ocean model routinely used at DNMI to produce their daily forecasts
of ocean variables (Engedahl 1995). Thus also the boundary conditions at the ocean-ice
interface is described in some detail. In Chapter 3 is presented some results from idealized
experiments that is performed to verify the implementation of the new ice model. In this the
model results are compared with those obtained by performing the same idealized
experiments using the Häkkinen-Mellor model. Also included (Chapter 4) are some
prelimiary results from a realistic test case covering the Nordic seas and the Arcticv Ocean.
Finally Chapter 5 gives some conclusions.
2.
Mathematical formulation
2.1. Dynamics
The equations of motion for the sea ice is given in a two-dimensional Cartesian coordinate
system with the x- and y-axis in the horizontal plane. For the thermodynamic fluxes, a z-axis
which is positive upward will be applied. The sea ice drift is described by the twodimensional vector
u = (u,) , assuming that the ice cover can be modelled as a continium. If the nonlinear terms
for Eulerian advection of momentum is neglected and the mass per unit area is denoted with
m , the equations for conservation of momentum of the sea ice are given by
H o
u σ11 σ 21
,


 mfv  Aτ oi( x )  Aτ (aix )  mg
t
x
y
x
H o
v σ 22 σ 21
,
m


 mfu  Aτ oi( y )  Aτ (aiy )  mg
t
y
x
y
m
(1)
(2)
Here, σ ij is the two dimensional stress tensor describing the internal stresses in the ice. The
Coriolis parameter is given by f  2 sin  , where  is the angular frequency of the earth
and  is the latitude. A is the fractional ice cover, g is the acceleration of gravity and H o is
the sea surface elevation. The stresses from the ocean and the atmosphere are given by
(τ oi( x ) , τ oi( y ) ) and ( τ (aix ) , τ (aiy ) ) respectively. The wind stresses are related to the 10 meter wind
speed, U a  (U a ,Va ) , through the relation
τ (aix )  ρa Cai Ua - u (U a  u) ,
(3)
τ (aiy )  ρa Cai Ua  u (Va  v) ,
(4)
where  a is the air density and C ai is a nondimensional drag coefficient for the momentum
transfer between the atmosphere and the ice. As can be seen, the wind stress is taken to be in
the same direction as the 10 meter wind speed. By some authors, the wind stresses are turned
an angle to the 10 meter wind speed based on the assumption that the wind vector turns left
towards the ground on the northern hemisphere. This will of course give an additional term in
the expressions for the stresses. In a similar way, the stresses from the ocean current are
related to the current speed from the upper layer of the ocean model, U o  (U o ,Vo ) , as
τ (oix)  ρ o Coi U o  u (U o  u) ,
(5)
τ (oiy )  ρ oCoi U o  u (Vo  v) ,
(6)
For the calculation of the stress tensor, it is most common to use the viscous-plastic rheology
originally introduced by Hibler (1979). Here, the tensor for the internal stresses in the ice is
calculated from the relationship:
σ ij  2ηε ij  (ζ  η)(ε 11  ε 22 )δ ij 
P
δ ij ,
2
(7)
where P is the ice pressure,  is the shear viscosity and  is the bulk viscosity.  ij is the
Kronecker delta. The strain rate tensor, ε ij ,is given by
ε ij 
1  ui u j

2  x j xi

,


(8)
The ice rheology used in this model is based on the ideas of Hunke & Dukowicz (1997),
where an additional elastic term is incorporated into the equation for the stress tensor. For
later use it is therefore convenient to rewrite this equation as
1
(ζ  η)
P
σ ij 
(σ11  σ 22 )δij  δij  ε ij ,
2η
4
4ζ
(9)
The pressure term in the rheology is taken to be a function of the ice thickness and
concentration
P  P  Ahe  c (1 A) ,
(10)
where c and P * are constants given in Table 1 and h is the average or mean ice thickness over
that fraction of an area actually covered by ice. The shear and bulk viscosity are calculated
from the ice pressure as
ζ 



P
2
(11)

e2

(12)

2
2
  11
  222 1  e 2  4e 212
 211 22 1  e 2

12
(13)
where e is the eccentricity of the yield curve (Hibler 1979). ζ is bounded by the maximum
value 2.5  108 P , which also implies a an upper bound on η . Assuming that the parameters in
the ice rheology are constant, the stability criterion for an explicit solution to these equations
imposes a time step according to
t 
m 2
x ,
2
(14)
which for realistic values of the stress parameters and resolution gives a time step less than
one second. The application of such a small time step is problematic in the sense that it
severely slows down the speed by which the calculations for a given simulation period can be
performed, in particular if the model is going to be used for long term climate simulations. To
resolve this problem, implicit solvers have traditionally been applied. Another approach is
used by Hunke & Dukowicz (1997) who instead introduce an additional time dependent
elastic term in the equation for the stress tensor. By introducing a time dependent term in the
rheology equation, the time step criterion for a numerical solution is affected in such a way
that an explicit solution may be possible. It is important to note that this elastic term is not
meant to represent any real physics in the ice, but is simply a convenient way to get around
the problem imposed by the short time step limitation for the explicit numerical solution. It
will therefore be important later to try to minimize the effect of this term on the ice physics.
When using this formulation the stress tensor equation becomes
        P    ,
1 ij 1
 ij 
11
22
ij
ij
ij
E t 2
4
4
(15)
where E is an elasticity modulus. Instead of the criterion given by (14), an explicit numerical
solution of the momentum equation now imposes the time step criterion
t 
m
x ,
E
(16)
Now it will be possible to choose the elasticity modulus in such a way that an explicit solution
is possible from a practical point of view.
To establish a mathematical formulation for the mass conservation, it would be straight
forward to outline an equation only for the mass m, which gives the change of mass within a
unit area as a function of ice advection and freezing/melting. However, also the ice
concentration or compactness is of great interest. For this reason it is common to divide the
ice mass into two components: the ice concentration A, and the mean ice thickness h. As
alluded to the mean ice thickness is defined as the average taken only over the area actually
covered with ice. From these definitions the mass of ice per unit area will be , where ρ i is the
mean density of the sea ice. If the ice density is assumed to be constant, this will give two
prognostic variables for calculating the ice mass. From the principal of mass conservation, the
equation for the ice mass gives
ρ



( Ah)  (uAh)  ( vAh)  o A(Wio  Wai )  (1  A)Wao  ,
t
x
y
ρi
(17)
where ρ o is the water density. The production rate at the ice-ocean interface is Wio , which is
positive for freezing. At the air-ice interface, the production rate is Wai . This term is defined
as positive for melting. Wao is the production rate at the boundary between the ocean and the
atmosphere, and is defined as positive for freezing. A detailed description of these production
rates will be given in the thermodynamic section, where the freezing and melting of ice will
be calculated from the radiation balance.
Since only one equation can be derived from the principal of mass conservation, an additional
empirical equation must be outlined for the ice concentration A . Following the model by
Mellor and Kantha (1989) such an equation is
 A 
 ρ

h   (uA)  (vA)  o Φ(1  A)Wao  ,
y
 t x
 ρi
(18)
where  is an empirical constant (Mellor and Kantha 1989).
2.2. Thermodynamics
Most of the thermodynamics implemented in the DNMI ice model are based on the coupled
ice-ocean model of Mellor and Kantha (1989) as formulated by Häkkinen and Mellor (1992).
The equations expressing the forcing from solar radiation are replaced with those of Drange
and Simonsen (1996).
The ice thermodynamics are represented by temperatures at the snow surface, ice surface, the
interior of the ice and the bottom surface of the ice. Melting and freezing rates are calculated
at the interfaces between ice and atmosphere, ice and ocean and atmosphere and ocean. A
certain amount of summer meltwater is stored on the ice/snow surface and refrozen in the fall.
The model has three layers in the vertical. The top layer is a snow layer which is working as
an insulator and as an absorber of incoming radiation in the melting period, i.e., spring. The
two remaining layers are pure ice layers. The snow is assumed to have no heat capacity while
the ice conductivity is influenced by small pockets of brine trapped in the ice during bottom
accretion.
The net heat flux between atmosphere and the topmost layer (wether snow or ice), Qai , is
given by
Qai  (1  α is ) SW  ε is LW  Qsi  Qli  ε isσTai4 ,
(19)
where α is is the ice (or snow) albedo, ε is is the emissivity of an ice (or snow) surface, SW is
the incoming shortwave radiation, LW is the longwave radiation, Q si is the sensible heat
transfer and Q si is the latent heat transfer. The outgoing longwave radiation from the ice (or
snow) surface is where is the Stefan-Boltzman constant and Tai is the temperature at the
interface between the ice (or snow) and the atmosphere.
The net heat flux between the atmosphere and the ocean, Q ao , through open ocean or leads is
given by
Qao  (1  α o ) SW  ε o LW  Qso  Qlo  εσTo4 ,
(20)
where α o is the albedo of open water, ε o is the emissivity of open water, Qso is the sensible
heat transfer, Qlo is the latent heat transfer and To is the sea surface temperature (SST).
The heat conduction in the middle layer (or top ice layer) is equal to the heat conduction
through the snow, an equality used to obtain the temperature at the various interfaces. When
Tai is below the freezing point, Qai and the heat conduction at the top of the ice layer are
equated to obtain a new Tai . Otherwise this temperature equals the freezing temperature
( 0C ) and ice (or snow) will melt.
The heat conduction at the bottom of the lowermost ice layer is
Qio  2
ki
(T0  T1 )
h
(21)
where k i is the termal ice conductivity, h is the thickness of the ice, T0 is the temperature at
the ice-ocean interface and T1 is the temperature at the interface between the two ice layers.
Melted ice (or snow) and precipitation (rain) is stored at the surface as melt water. If the
stored water reaches a specified maximum thickness, the excess melt water runoff, Wro , is
combined with the bottom freeze or melt rate and enters the ocean surface layer as a
freshwater source.
2.2.1 Surface boundary conditions for the ocean
The heat balance in this model combines the energy across the ice-ocean interface and the
atmosphere-ocean interface (leads): Thus the heat flux balance at the ice ocean interface is
FT  (1  A)Qao  AQio  L0 AWio  (1  A)Wao  ,
(22)
where L0 is an extended variant of latent heat of fusion including brine fraction.
The salt balance across the ocean interface is similarly calculated as
FS  AWio  (1  A)Wao  AWai ( Si  S0 )  AWro S0  (1  A) Pr S0 ,
(23)
where Si is the sea ice salinity, S 0 is the sea surface salinity and Pr is the amount of
precipitation
3.
Idealized experiments
The new ice model is first tested and compared with the Häkkinen and Mellor (1992) model.
For this purpose both the Häkkinen-Mellor model and the new ice model was configured for
an idealized experiment. To this end the response to wind forcing of the two ice models in a
zonal channel 1000 km long and 120 km wide featuring closed boundaries (walls) to the north
and south (Figure 1) was studied. The ocean underneath was specified to be stagnant. The grid
spacing applied is 20 km. The eastern and western boundary were open and the flow
relaxation scheme (FRS, Martinsen and Engedahl 1987) was used for transporting ice in and
out at these boundaries. At the western boundary ice of 2 m height and a concentration of
75% is specified to flow into the channel. At the eastern boundary there is specifeid to be no
ice, which means that this boundary act as a sponge. In the middle of the channel an
obstruction in the form of a promontory (Figure 1) is introduced to see how the ice model
handles the transport of ice around such an obstruction. This was done since earlier realistic
runs (Sætra et al., 1998, Røed et al. 1999) utilizing the Häkkinen-Mellor model showed that
this particular model tended to slow down the ice motion in the vicinity of such obstructions,
thereby producing unrealistically high values of ice thickness and concentration in such areas.
The ice model is forced with a constant wind speed of 7 m/s from the west. The atmospheric
temperature is set to -10 degree Celsius over the whole domain and the ocean temperature is
set to be at the freezing point.
Figure 1 shows the initial situation with 2 m thick ice cover which ends 60 km ahead of the
impeding promentory. The initial ice concentration is 75% and the initial ice drift is 0.25 m/s.
In Figure 2, the result from the Häkkinen-Mellor ice model is shown after 180 hours of
simulation time. A thin ice sheet has frozen over the whole model domain. The initial ice edge
has advected, and has just passed the obstruction. Note that already at this stage, the ice drift
decreases in the areas with 2 m thick ice west of the promontory, and that there is no sign of a
southward drift which should be expected due to the effect of the Coriolis force. Figure 3
shows the result of the simulation for the same time from the new ice model. Also here, a thin
ice sheet has frozen all over the model domain. The original ice edge seems to have been
advected slightly longer than is the case for the Häkkinen-Mellor model. There is also a build
up of ice along the southern boundary, especially at the up stream side of the promontory due
to the effect of the Earths rotation. Similarly the response is shown after 720 hours (~ one
months) simulation for the Häkkinen-Mellor model (Figure 4) and the new ice model (Figure
5). As can be seen from figure 4, the ice drift in the Häkkinen-Mellor model has been almost
completely suppressed upstream of the obstruction, and very little ice has actually been
transported through the sound between the promontory and the northern boundary. This is in
contrast to the new ice model which drifts smoothly around the promontory (Figure 5).
Also other experiments are done with closed as well as open boundaries (not shown). They all
show responses that appears dynamically consistent with what is expected both with respect
to drift and build up of ice thickness.
4.
Preliminary results from a Nordic Seas and Arctic Ocean coupled iceocean simulation
As alluded to the new ice model is, as the former Häkkinen-Mellor ice model, coupled to
DNMIs operational ocean model (Engedahl 1995). The aim is to use the coupled system to
perform a long term (decadal) simulation of the circulation and hydrography of the Nordic
Seas and Arctic Ocean. At present only some preliminary results are produced as shown in
Figure 6 and 7, which shows the ice average (mean) ice thickness and concentration for
January 1982. These may be compared with those produced earlier (Sætra et al. 1998).
Although the one month simulation is too short to make any concrete conclusion it appears
that the ice motion is much smoother than for the previous similar run utilizing the HäkkinenMellor ice model. Finally Figures 8 and 9 show the similar picture for the fully coupled iceocean model for January 1990. This month is very atypical in tha sense that the wind forcing
is dramatically different from the climatology fior this month, featuring a low pressure in the
Beaufort Sea. Also the icelandic low is absent and hence the ice motion tends to be northward
in the Fram strait and the commonly drift across the North Pole, known as the Transpolar
Drift does not build up.
5.
Conclusion
A new dynamic-thermodynamic sea-ice model based on the ideas of Hunke and Dukowicz
(1997) is developed. The new model is tested and compared with the Häkkinen-Mellor ice
model (Häkkinen and Mellor 1992) in an idealized basin. In particular is tested the models
ability transport ice around an obstruction in the form of an obtrusive promontory. The reason
for this test was that the Häkkinen-Mellor model, as also is demonstrated here, seemed to
have a too stiff ice rheology which resulted in a too low ice transport between islands etc. The
result of this is that the influence of the obstruction extends far beyond the areas where one
would expect it to be. In addition, the Häkkinen-Mellor ice model seemed to give too low
drift velocities. The reason for this is also found to be associated with the too stiff ice
rheology.
It is demonstrated that the new ice model handles obstructions in a much more realistic way.
The influence of the obstruction is limited to a much smaller area, and also, the ice drift
velocities are larger and more consistent with empirical rules for ice drift. The new ice model
is coupled to the DNMI ocean model and simulations utilizing the new coupled system s in
progress.
Acknowledgment: Many thanks goes to Morten Ødegaard for many stimulating
discussions on the new ice model and its coupling to the DNMI ocean model. The work
reported here is funded by the Research Council of Norway, through grant no. 120656/720
to the Norwegian Meteorological Institute.
REFERENCES
Drange, H., and K. Simonsen, 1996: Formulation of air-sea fluxes in the ESOP2 version of
MICOM, NERSC Tech. Rep., 125, 23 p. (Available from Nansen Environmental and
Remote Sensing Center, Edv. Griegsv. 3A, 5037 Bergen, Norway.)
Engedahl, H., 1995: Implementation of the Princeton Ocean Model (POM/ECOM3D) at the
Norwegian meteorological Institute. DNMI Res. Rep. No. 5, 38 p. ISSN 0332-9879.
Häkkinen, S., and G. L. Mellor, 1992: Modeling the seasonal variability of a coupled Arctic
ice-ocean system. J. Geophys. Res., 97(C12), 20,285-20304.
Hibler, W. D. III, 1979: A dynamic thermodynamic sea ice model, J. Phys. Oceanogr., 9, pp.
815-846
Hunke, E. C. and J. K. Dukowicz, 1997: An elastic-viscous-plastic model for sea ice
dynamics, J. Phys. Oceanogr., 27, pp. 1849-1867.
Martinsen, E. A., and H. Engedahl, 1987: Implementation and testing of a lateral boundary
scheme as an open boundary condition in a barotropic ocean model. Coastal Eng., 11,
603-627.
Mellor, G. L. and L. Kantha (1989): An Ice-Ocean coupled model, J. Geoph. Res., 94, pp.
10.937-10.954
Røed, L. P., H. Engedahl, B. Hackett, A. Melsom, X. B. Shi, and Ø. Sætra, 1999: Circulation
and hydrography in the Nordic Seas inferred from ocean model experiments at DNMI.
In: RegClim Techn. Rep. No. 2, eds. T. Iversen and T. Berg, 109-124. (Available from
Norwegian Institute for Air Research, P.O. Box 100, 2007 Kjeller, Norway.)
Smolarkiewicz, P. K., and L. G. Margolin, 1997: MPDATA: a finite difference solver for
geophysical flows. J. Comp. Phys., 140, 459-480.
Sætra, Ø, C. Wettre, and L. P. Røed, 1998: Coupled ice-ocean modelling. In: RegClim Techn.
Rep. No. 1, 107-118. (Available from Norwegian Institute for Air Research, P.O. Box
100, 2007 Kjeller, Norway.)