As sea ice is advected on the surface of the ocean, the ice concentrat
ion (0 less than or equal to A less than or equal to 1) and the mean i
ce thickness change in response to thermodynamic and mechanical forcin
g. In this paper the authors review the existing advection schemes and
compare their properties in the absence of thermodynamic effects. In
Hibler's classical scheme, the ice area fraction at a material particl
e changes due to the divergence of the large-scale horizontal velocity
held, and a further constraint is applied in order to keep A less tha
n or equal to 1. This scheme is used in almost all sea ice models, alt
hough Hibler and Shinohara have both since included a ridging sink ter
m. In this paper the authors show that the Hibler advection scheme is
a special case of Gray and Morland's ridging model and compare the rid
ging schemes of Hibler and Shinohara with the simple scheme of Gray an
d Morland. It is demonstrated that the Hibler scheme still allows ice
concentrations to exceed unity in maintained convergence and that both
Hibler and Shinohara schemes admit the possibility of negative ice co
ncentrations during maintained shearing. A general framework is formul
ated for the functional form of the ridging sink term that guarantees
0 less than or equal to A less than or equal to 1. Finally, some eleme
ntary analytic solutions are derived, which imply that, if ridging is
independent of shear effects, quantities are conserved along particle
paths.