Sea ice and iceocean models

The first robust thermodynamic sea ice model was developed by Maykut and Untersteiner (1971). This one-dimensional model passes heat fluxes from the atmosphere and ocean into the ice and snow by conduction. The temperature of the snow (or air-ice) interface is determined by the surface energy balance. The balance at the ice-ocean interface determines the melt/freeze state at the sea ice bottom. The first successful three-dimensional dynamic/thermodynamic model is that of Parkinson and Washington (1979). Four vertical layers are represented within each grid cell: a mixed layer ocean, an ice layer, a snow layer and an atmospheric boundary layer. At the ice-ocean interface, ocean currents provide water stress and a constant dynamic topography

Figure 9.5 Basin averaged snow water equivalent (SWE) for March (approximately the month of the annual maximum) from the 21 PILPS 2e land surface models (listed as A-U) over the period 1989-98 (from Bowling et al., 2003, by permission of Elsevier).

Figure 9.6 Total basin mean annual surface and subsurface runoff from the 21 PILPS 2e land surface models (listed as A-U) over the period 1989-98. The dashed horizontal line is the observed mean annual runoff at the mouths of the Torne and Kalix rivers combined (from Bowling et al., 2003, by permission of Elsevier).

Figure 9.6 Total basin mean annual surface and subsurface runoff from the 21 PILPS 2e land surface models (listed as A-U) over the period 1989-98. The dashed horizontal line is the observed mean annual runoff at the mouths of the Torne and Kalix rivers combined (from Bowling et al., 2003, by permission of Elsevier).

(recall that because of density variations, the ocean surface is not entirely flat). A constant ocean heat flux is also used. Atmospheric heat fluxes and surface stresses are applied at the air-ice interface. Ice dynamics is treated as free drift (again see Chapter 7). The Parkinson and Washington (1979) thermodynamics approach is still widely used.

Hibler (1979) developed the first widely used dynamic/thermodynamic model, which included the effects of internal ice stress. The model, driven by observed winds and SAT, was able to reproduce observed patterns of ice drift and ice thickness. The model incorporates the equations of continuity for ice thickness and concentration. In early versions of the model, ice growth rates were prescribed. Hibler (1980) subsequently developed formulations whereby the growth rates are calculated from a heat budget. Hibler (1980) also included a variable ice thickness distribution model.

All dynamic/thermodynamic models of the Hibler variety contain a constitutive law, which relates the ice deformation to the forces applied. A variety of formulations have been examined. Arbetter et al. (1999) provide a useful review. For example, the "cavitating fluid" approximation differs from free drift by allowing non-zero ice pressure under converging conditions but, like free drift, offers no resistance to divergence or shear (Flato and Hibler, 1992). The Hibler (1979) model uses a viscous-plastic constitutive law, which relates the strength of the ice interaction to a thickness distribution. This basic formulation, which still finds wide use, allows the ice strength to be greater in regions of ice convergence and weaker in regions of divergence. More recent formulations include the modified Coulombic law described by Hibler et al. (1998) and Hibler and Schulson (2000).

Snow cover was not included explicitly in the Hibler (1979) model. The effects of snow cover were approximated by setting the ice surface albedo to that of snow when the surface temperature is below freezing and to that of snow-free ice when the surface is at the melting point. Walsh et al. (1985) include treatments of "thick" ice and snow using seven thickness levels. In most sea ice models, heat calculated via the energy balance is used to melt all of the snow before it is used to melt ice at the upper surface.

The field of ice-ocean modeling has quickly grown. Such models couple a dynamic/thermodynamic ice model of the Hibler variety with ocean models of varying complexity. The first ice-ocean model was that of Hibler and Bryan (1987), which coupled the Hibler ice model to the Bryan-Cox multilevel ocean model (Bryan, 1969). Other early efforts include Semtner (1987), Fleming and Semtner (1991) and Riedlinger and Preller (1991).

The study of Zhang et al. (2000) is a good example of the application of an ice-ocean model. They examined the response of Arctic sea ice to forcing by the North Atlantic Oscillation (NAO) (see Chapter 11). The model had a horizontal resolution of 40 km, with 21 ocean levels and 12 ice thickness categories. The model was forced by winds, SAT, specific humidity and longwave and shortwave radiation fluxes.

Figure 9.7 shows simulated annual mean ice velocity and mean sea level pressure fields for the two periods, 1979-88 and 1989-96, along with corresponding ice velocity anomaly fields. These two decades characterize the generally low and high index phases of the NAO, respectively. Readily seen are large differences in the shape and intensity of the Beaufort Gyre and Transpolar Drift Stream. Note the strongly cyclonic anomaly during the high NAO phase (1989-96) and the implied increase in the Fram Strait outflow. Figure 9.8 gives simulated fields of mean annual ice thickness for the two periods and the difference field. Observations show a pattern of thicker ice off the Canadian Archipelago and north Greenland coast and thinner ice on the Siberian side of the Arctic (Figure 7.5). The model captures this basic pattern, but over both decades gives unrealistically large thicknesses along the Alaskan

Figure 9.7 Simulated mean ice velocity and mean annual sea level pressure for (a) 197988; (b) 1989-96; anomaly fields of ice velocity based on the difference (c) between the 1979-88 mean and the 1979-96 mean and (d) between the 1989-96 mean and the 1979-96 mean. Vectors are given at every sixteenth grid point with contours of sea level pressure given at every 1 hPa (from Zhang et al., 2000, by permission of AMS).

Figure 9.7 Simulated mean ice velocity and mean annual sea level pressure for (a) 197988; (b) 1989-96; anomaly fields of ice velocity based on the difference (c) between the 1979-88 mean and the 1979-96 mean and (d) between the 1989-96 mean and the 1979-96 mean. Vectors are given at every sixteenth grid point with contours of sea level pressure given at every 1 hPa (from Zhang et al., 2000, by permission of AMS).

coast. However, useful information is provided by the difference fields - the model results suggest a general tendency for the ice under the persistently positive NAO phase of 1989-96 to have been thinner in the eastern Arctic and thicker in the western Arctic. These findings support arguments by Holloway and Sou (2002) that at least part of the observed thinning of the perennial ice over the central Arctic Ocean in the 1990s, as assessed from submarine sonar records (Rothrock et al., 1999), represents a redistribution of thick ice to along the North American coast (Chapter 11).

A major project is underway known as the Arctic Ocean Model Intercomparison Project (AOMIP). This is an international effort to identify and diagnose systematic errors in a variety of different Arctic Ocean models under realistic forcing. The primary aims of the project are to simulate Arctic Ocean variability on seasonal to interannual scales, and to understand the behavior of the different models. Model forcings for the AOMIP effort include observed climatology and daily atmospheric pressure and SAT fields. Examples of recent ice-ocean models participating in AOMIP include those of

Figure 9.8 Simulated mean ice thickness fields for (a) 1979-88 and (b) 1989-96 and (c) their difference field (b-a). The contour interval is 0.5 m (from Zhang et al., 2000, by permission of AMS).

Häkkinen (1999), Maslowski etal. (2000) and Zhang etal. (2000). The AOMIP models variously incorporate no river discharge to a full accounting. Most of the models include restoring salinity or temperature (or both) toward climatology to reduce drift (the tendency of model fields to drift away from physical reality). The time scale of restoring has a major effect on the model results for the upper layers of the Arctic Ocean.

Further details of the AOMIP models are provided by Steele et al. (2001), who compared model simulations of winter mean surface salinity in the Arctic Ocean. Models are in general agreement in the Nordic seas, but large differences are found on the Arctic continental shelves. Also noted is a climate drift that leads to a high salinity bias in most models within the Beaufort Gyre. This bias seems to be sensitive to the wind forcing and the simulation of freshwater sources from the shelves and elsewhere. Steiner et al. (2004) compare vertically integrated properties of the Arctic Ocean, including heat and freshwater content. Again, large differences are found between various AOMIP models.

An emerging direction in sea ice modeling is data assimilation. Data assimilation is a technique that constrains a model to physical reality by incorporating observed data. Data assimilation can also fill in gaps in observations and provide better estimates of parameters that cannot be directly observed (e.g., basin-wide ice thickness). There are several assimilation methods, ranging from the trivial such as "direct replacement" of modeled with observed data (either of ice velocity or concentration) to sophisticated approaches such as "optimal interpolation" or "Kalman filtering". These account for the error characteristics of both the model and data, as well as the spatial distribution of the data, to minimize error in a statistical sense. Another approach is a variational scheme, where a "cost function" that measures the mismatch between model and data is minimized under the constraint that appropriate model quantities (e.g., mass, momentum, energy) are conserved (see Ghil and Malanotte-Rizzoli, 1991). Data assimilation methods were first developed for atmospheric models to improve weather forecasts (Charney et al., 1969). A good example of the direct replacement method applied to sea ice velocities is the study of Maslanik and Maybee (1994). Examples of more sophisticated schemes to assimilate ice velocity include Meier et al. (2000), Meier and Maslanik (2003) and Zhang et al. (2003). Assimilation of observed ice concentrations has been addressed by Thomas and Rothrock (1989,1993) and Thomas et al. (1996).

100 Bowling Tips

100 Bowling Tips

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