Department of Atmospheric Sciences
University of Washington
Seattle, WA 98195-1630
Discussions during the PIPS 3.0 Workshop indicated a general agreement that the revised model should include: (1) greater resolution of the ice thickness distribution, (2) non-linear thermodynamics to describe the storage and vertical transport of heat in the ice, (3) more detailed treatment of interactions between shortwave radiation, the ice and upper ocean, and (4) better characterization of the snow cover. Most of the recommended improvements are fairly straightforward and many, in fact, are being tested or implemented in other models. It should be stressed, however, that results from ongoing projects such as SHEBA and SCICEX are likely to produce substantial improvements in our ability to treat ice thermodynamics, so it is imperative that the PIPS 3.0 computer code be designed to accommodate these improvements as they become available. Specific recommendations are as follows:
1. PIPS 3.0 should include a formal treatment of the ice thickness distribution in
each grid cell, with sufficient resolution to give reliable estimates of regional heat
and mass fluxes.
Total ice production, buoyancy fluxes to the mixed layer, and turbulent heat exchange with
the atmosphere in each grid cell are extremely sensitive to the distribution of ice thickness, g(h).
Of particular importance is thin (h < 1m) ice where these quantities exhibit a strongly non-linear
dependence on ice thickness and typically vary by more than an order of magnitude. To estimate
regional totals it is first necessary to partition g(h) into a number of thickness categories, then to
sum up the individual contributions made by each category. Because of the non-linear dependence
of heat and mass fluxes on h, the most efficient way to partition g(h) is to have high resolution at
the thin end, and progressively lower resolution as h increases. Sensitivity studies with the
complete PIPS 3.0 model should be used to examine how the number and partitioning of the
thickness categories affect predicted heat and mass fluxes. These results should indicate the level
of detail needed to characterize g(h) in this model. If user needs warrant, it would be possible to
keep track of the distribution of ridged ice separately, although the accuracy of such predictions are
questionable due to large uncertainties in both the mechanical redistribution of thin ice and the rate
of mass loss from ridge keels. It should be possible to verify g(h) predictions in some regions
using upward-looking sonar data taken by submarines and bottom-moored buoys. Complicating
the treatment of g(h) in PIPS 3.0 is the desire to predict lead orientation which will require
directional information on ice thickness variations. While theoretical work is underway to address
this problem, it may prove difficult to accommodate directionality within the original thickness
distribution theory. Also of concern is whether the statistical representation of processes
associated with g(h) will remain valid as grid sizes approach 10 km or less.
2. Problems produced by the assumption of linear temperature gradients in the ice
should be addressed by incorporating the heat conduction equation and vertical
salinity profile estimates into PIPS 3.0 calculations.
The assumption of a linear temperature gradient in the ice does a poor job of simulating the
growth of thicker ice when there is rapid warming or cooling as, for example, during the spring
and fall. Such treatments are unable to properly account for the storage and release of heat
accumulated during the summer, adversely affecting subsequent predictions of growth rates and
thicknesses. Likewise, they do not properly resolve the effects of changes related to diurnal
variations or to the passage of weather systems. The heat conduction equation is now routinely
included in many thermodynamic ice models and its solution presents few challenges. The best
approach is to select a fixed number of layers (5-10) and allow the thickness of each layer to vary
as the ice grows or ablates. For purposes of treating noise from thermally-induced fracturing or
effects of rapid changes in atmospheric forcing, it may be desirable to have increased vertical
resolution near the surface and consideration should be given to the possibility of using layers of
unequal thickness. Because of its relatively low thermal mass, it may still be possible to assume a
linear temperature gradient in the snow without introducing large errors. However, questions
remain as to a suitable value for thermal conductivity, given the normal presence of a low density
depth hoar layer near the ice-snow interface.
In addition to solving the heat conduction equation, it will be necessary to take into account vertical variations in the conductivity and specific heat of each ice layer. Since both of these quantities are well-know functions of temperature and salinity, the problem essentially boils down to specifying salinity profiles in each ice thickness category. Modeling work by Cox and Weeks (1988) suggest that salinity variations in first-year ice may be largely independent of growth history, making it fairly easy to estimate salinity profiles for such ice. Likewise, we know the general shape of salinity profiles in multiyear ice and simple parameterizations have been developed (e.g. Maykut and Untersteiner, 1971) that give salinity profiles in any thickness of undeformed, multiyear ice. Finally, it will be necessary to take into account internal heating within each layer due to the absorption of shortwave radiation during the summer. This also should be straightforward as this problem has received considerable attention and internal heating rates beneath bare ice can now be estimated fairly accurately.
3. PIPS 3.0 should contain an explicit treatment of how shortwave radiation affects the oceanic heat flux at the bottom of the ice, lateral melting on floe edges, and energy absorption in areas of ponded ice.
Substantial amounts of shortwave energy enter the mixed layer through leads, thin ice and melt ponds. In the Central Arctic this is the primary source of energy for the oceanic heat flux at the bottom of the ice (Fw), a major factor in determining the overall thickness of the ice pack. This means that, instead of being constant throughout the year, Fw is strongly time-dependent. Data from the Beaufort Sea indicate that Fw is extremely small during the winter while reaching values in excess of 40-60 W/m2 during the summer. It is important that PIPS 3.0 keep track of the magnitude of solar input, along with how this energy is stored and released by the mixed layer. About half of the solar energy entering leads is absorbed in the upper 2-3 m of the water column. Much of this energy subsequently goes to lateral melting on floe edges, a positive feedback process that may cause a substantial reduction in summer ice concentration. Again, this is a process that should be included in PIPS 3.0.
Summer melt ponds have albedos as low as 0.2-0.3, resulting in greatly accelerated melting and surface storage of absorbed shortwave energy as latent heat. Ponds are also responsible for areally-averaged albedos which are much lower than those of bare ice alone. On multiyear ice, heat contained in the ponds is stored only temporarily, being released back to the atmosphere during the fall freezeup without a major impact on ice thickness. On the thinner and more level first-year ice, however, pond coverage is typically 50-90% which can result in the complete melting of such floes. Inadequate consideration of melt ponds and lateral melting in PIPS 2.0 is probably responsible for its problems in predicting summer retreat of the ice pack. If PIPS 3.0 is to produce realistic albedos for comparison with those measured by satellites or aircraft, it must take into account how ponds absorb and redistribute solar energy.
4. Treatment of the snow cover should be improved to include spatial variations in snowfall rates and albedos that more accurately reflect environmental conditions near the surface.
The depth and properties of the snow cover have a large effect on rates of ice growth and surface heat exchange. PIPS 3.0 should take into account spatial variations in the amount of snow on the ice. Initially this can be done using the new snow depth climatology of Warren et al. (in press), but investigations should be carried out to examine whether NOGAPS or net precipitation derived from the TOVS satellite can provide acceptable real-time estimates. If PIPS 3.0 includes an ice thickness distribution, each thickness category will have to have somewhat different snow depths determined from estimated snowfall rates. Snow albedos in PIPS 2.0 have only 2 possible values, a weakness that needs to be addressed in PIPS 3.0. While snow albedos could be specified from climatological information, a much better approach would be to try and relate them to structural changes taking place in the snow cover as it warms, making the transition to the summer melt season dependent on current conditions rather than long-term averages.
References
Cox, G.F.N. and W.F. Weeks, Numerical simulations of the profile properties of undeformed first-year sea ice during the growth season, J. Geophys. Res., 93, 12,449-12,460, 1988.
Maykut, G.A. and N. Untersteiner, Some results from a time-dependent, thermodynamic model of sea ice, J. Geophys. Res., 76, 1550-1575, 1971.
Warren, S.G., I.G. Rigor, N. Untersteiner, V.F. Radionov, N.N. Bryazgin, Y.I. Aleksandrove and R. Colony, Snow depth on arctic sea ice, J. Climate, in press.