Polar Science Center, APL/UW, Seattle, WA, 98105 USA
July, 1998
The dynamics and thermodynamics of sea ice models were largely developed during the AIDJEX project of the 1970's. A major result of that effort was the landmark paper by Hibler (1979) in which a practical sea ice model was described that could be used for both operational and research (climate) purposes. The model was coupled to an ocean model in 1987 (Hibler and Bryan, 1987). Through much of the 1980's and until quite recently the physics of sea ice models (including PIPS 2.0) evolved relatively slowly. Some of the parameterizations used in these models are:
Ice models
In the last few years a renewed interest in the Arctic has led to a rapid acceleration in sea ice model development. In particular, more researchers have begun to use a mass balance model that explicitly resolves the thickness distribution g(h) at each grid cell (e.g., Flato and Hibler, 1995). The advantages of this model are: (i) a true representation of ridging, and (ii) a better description of ice melt and growth (i.e., the surface energy balance) as it varies over different ice thicknesses. Validation of these models is also easier, using data from moored and/or submarine sonars as well as satellites that detect thin ice (e.g., Yu and Rothrock, 1996). The inclusion of ridging tends to increase the mean thickness of sea ice in the Arctic Ocean by as much as 50%. Growth and melt cycles are also affected. Some sensitivity experiments have been performed on the number of thickness levels that are minimally necessary to "do the job", but more work is needed. In our experience, a model that resolves 12 levels of undeformed (smooth) ice and 12 levels of deformed (ridged) ice takes about 5 times longer to run than a 2-level model. These numbers are of course highly dependent on model resolution, time step, number of processors and their speed, etc.
Another trend is the inclusion of thermal inertia in the ice/snow system, i.e. allowing a non-linear temperature gradient. Neglecting this effect leads to substantial errors in the timing of melt and growth seasons, as has long been recognized (Semtner, 1976). Most models that include the effect have not bothered to advect thermal enthalpy from grid cell to grid cell, although a global sea ice model has recently been developed that does (Fichefet and Maqueda, 1997). These authors found significant model sensitivity when thermal inertia was neglected.
Ocean models
Climate restoring is a "fix" for unknown model errors. It is falling out of favor among researchers, for example by the group at NCAR developing a coupled air-ice-ocean-land model, the Climate System Model. The problem is that real anomalies are difficult to produce in a model that is constrained back to a fixed climatology. Further, different restoring schemes give substantially different results (Zhang et al., 1998), in terms of both dynamics (ice drift) and thermodynamics (mass balance).
However, for forecasting purposes this practice might be tolerable. The results will of course be highly dependent on the quality of the climatology towards which the simulation is restored. PIPS 2.0 (and most other models) currently use the Levitus (1982) climatology. Both this and the newer 1994 version have well known large errors: they are heavily biased towards summer and contain very little data in the Arctic Ocean proper. This can lead to large errors in the simulation (e.g., Smith et al., 1997). A new data set is now available that contains a synthesis of previously classified Russian and Western winter and spring data in the Arctic regions (EWG, 1997). Its data coverage in the Arctic Ocean is much higher, and with the impending release of the summer atlas will provide a true seasonal description for the four decades 1950-1989. The use of this data set for model initialization, restoring, and validation will most likely proceed quickly within the modeling community.
Environmental Working Group (EWG), NSIDC, Boulder, CO, Web Site: http://ns.noaa.gov/atlas., 1997.
Fichefet, T. and M. Maqueda, J. Geophys. Res., 102 , 12,609-12,646, 1997.
Flato, G. M. and W. D. Hibler III, J. Geophys. Res., 100 , 18,611-18,626, 1995.
Hibler, W. D. III, J. Phys. Oceanogr., 9 , 815-846, 1979.
Hibler, W. D. III and K. Bryan, J. Phys. Oceanogr., 17 , 987-1015, 1987.
Levitus, S., NOAA Prof. Pap. 13 , 173 pp., 1982; Levitus, S. and T. Boyer, NOAA/NESDIS CDROM, 1994.
Semtner, A. J. Jr., J. Phys. Oceanogr., 6 , 379-389, 1976.
Smith, D. M., et al., Ann. Glaciol, 25, 423-428, 1997.
Yu, Y., and D. Rothrock, J. Geophys. Res., 101, 25,753-25,766, 1996.
Zhang, J., W. Hibler, M. Steele, and D. Rothrock, J. Phys. Oceanogr., 28, 191-217, 1998.