1. Non-numerical forecasting of sea ice concentration induced by lateral melting
Jinping Zhao, Hongli Fu, Shugang Zhang (Ocean University of China)
Abstract
It is difficult to project the sea ice concentration variation caused by lateral melting, because the shapes of sea ice are various. We wished to find a simple method to estimate the variation. In this study, an algorithm is developed to calculate the lateral melting related variation of ice concentration.
With this algorithm, as long as we get an image of ice covered region, and the lateral melting speed is known, the variation of ice concentration aftertime could be projected accurately. Different from the numerical modeling of ice concentration, this algorithm is a non-numerical method.
5. Erosion operators and residual perimeters
The Erosion operators are used to calculate the area contraction of ice floe. In each step, putting the central square at every grids of open water and marks all the other eight squares to be open water.
As sometimes, the sea ice area decreases to zero, whereas the perimeters of the ice floe is not equal to zero, the perimeter left is called residual perimeter, with which, the 8CR could be satisfied by any case.
1. Basic formula for lateral melting
Based on Steele (1990), the ice melting could be expressed by
(1)
(2)
(3)
Area variation by lateral melting
Thickness variation by top and bottom melting
2. A eightfold constriction rate is identified
As we know, the lateral melting is related to the shape of the ice floe. People must face to infinite shapes of ice floes. Here, we studied the relation between ice perimeter and the ice melting speed. If the ice is simulated by squares with margin width of Δl, we found that if the ice contracts 1 unit, the perimeter will decrease 8 units, i.e.
We call this as eight contraction rate.
6. An example:
Ice concentration deceases 50% within 50 days by a lateral melting rate of 0.2 m/day.
3. Calculate area variation of ice floe
The 8CR could be expressed by
(4)
Substitute into Eq. (2), and integrate, the area variation of a sea ice floe could be estimated by
(5)
If the ice floe totally melts, the area An is equal to zero, and the time used for ice floe melt is solved from Eq. (5).
(6)
7. Summary
1. The eightfold contraction rate (8CR) widely exists for various shapes of sea ice.
2. Based on the 8CR, The relation between sea ice perimeter and lateral melting is built, which can be used to calculate the lateral melting of ice floe.
3. The non-numerical method takes the ice as solid, more close to the reality.
4. The algorithm of lateral melting is simple and accurate, limited by image resolution.
5. The non-numerical simulation solves mostly the lateral melting issue. More effort in the future will focus on the study and observation for the lateral melting rate.
4. Calculate ice concentration variation
Considering all ice floes, the variation of ice concentration can be obtained by
（t<Tn） (7)
Using Eq. (7), four parameters must be known:
C0, initial ice concentration
Pn0, initial ice perimeter
S, area of observed region
wlat, lateral melting speed
These parameters could be obtained through a photo of sea ice from a helicopter or an airplane. It can also obtained by high resolution satellite remote sensing image.