| Summary: | Ridges are elongated ice cover features created by local deformation. In the Baltic the visible part of the ridge, the sail, is typically 1-3 m high while the bulk of the ridge volume is contained to the 5-15 m deep subsurface keel. In larger scales ridging creates ridged ice fields. The modeling of ridges and ridged ice fields is important for dynamic ice drift models, for ice navigating ships, and for the estimation of ice loads exerted against offshore structures. Ridge fields are quantified in terms of ridge heights and ridge spacings which are distances between ridge sails. The present work formulates an equation governing the evolution of ridge spacing distribution. The usual lognormal and exponential distribution models for spacing distributions are obtained as solutions. The equation also explains several statistical features found in the analysis of ice surface profile data from the Baltic and from the Kara Sea. Conservation equations for continuum fields of spacing distributions are formulated. These can be included in dynamic ice forecast models. The parameterisation links the evolution to the decrease of ice area and to the fields of concentration and strain rate. An estimate for the equivalent thickness of ridge rubble is thereby obtained and is much larger than the values estimated previously. The parameterisation requires cross-sectional modelling of the ridges. A new type of feature, a ridge cluster, is introduced to describe ridges in keel contact. Concepts to describe cluster structure and cluster occurrence are developed. The spacing equation is a specific formulation of the Kolmogorov-Feller equation which is the basic equation governing discontinuous Markov processes. Another specific formulation is the equation governing the evolution of ice thickness distribution. A general presentation of discontinuous Markov processes is given. It can be used to construct evolution equations for ice morphological quantities. In the present context it is used to formulate alternatives to the spacing ...
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