Distributions of the main morphometric characteristics of ridged features

From the 1970s to the present time, a great deal of field work and analysis has been done on the physical and mechanical properties of sea ice ridges. Sail and keel thicknesses have almost always been measured in the field expeditions. Emphasis is placed on the thickness of the consolidated layer (CL) within the ridge. This paper was motivated by a number of new findings on the distributions of the main morphometric characteristics of ice ridges. The wide range of opinions about the distributions is, apparently, primarily due to the number of ice ridges and stamukhas studied in the different expeditions, i.e., the sample size. This article attempts to systematize the various opinions and add some clarity to the matter. It focuses on the development of approaches to determining the statistical distributions of the main morphometric parameters of first-year ice ridges: sail height, keel depth and consolidated layer thickness. Measurements of ice cover thickness were carried out in 2006–2009 from Russian vessels and icebreakers using a digital television complex. The distribution of first-year ice thickness along the navigation route of vessels shows that Arctic ice is normally distributed with a mathematical expectation of 1.24 m and a standard deviation (RMS) of 0.34 m. The histogram of ridging ice thickness in the Arctic region presented in L. Strub-Klein and D. Sudom’ review and based on a large data set is satisfactorily approximated by the exponential distribution law. It is known from literature sources that sail heights scale with the square root of ice thickness. One of the properties of the exponential distribution is as follows: if a random variable (the thickness of ridging ice) adheres to the exponential distribution, then the random variable “sail height” connected with the thickness of ridging ice has the Weibull–Gnedenko distribution. The ice ridge keel draft can be also shown as adhering to the Weibull–Gnedenko distribution. If we compare the formation process of the sail of ice ridges and stamukhas, it can be concluded that the energy of these processes is similar. Therefore, it can be presumed that the distribution of stamukha sails is also the Weibull–Gnedenko distribution. As for the distribution of the stamukha keel, it also adheres to the Weibull–Gnedenko distribution, since the stamukha draft is determined by the keel draft of an ice ridge which ran aground in shallow water and became its embryo. When considering the distribution of the CL thickness, let us use Høyland's formula, which gives a direct correspondence between the rubble porosity and the CL and level ice thickness. We shall generate an array of pairs of random level ice thickness values normally distributed with a mathematical expectation of 1.24 m and RMS of 0.34 m. We shall assume that the porosity is constant and equal to η = 0.23. For each pair values, we will calculate the CL thickness corresponding to them from Høyland's formula and plot a histogram of the resulting array of values. The best approximation of the histogram is the normal distribution with a mathematical expectation of 1.82 and RMS of 0.88. However, given the gradual reduction of the keel porosity the normal distribution transforms into the Weibull–Gnedenko distribution. Thus, as a result of the simulations performed, a certain pattern of distribution of the sail height, keel draft and the CL thickness of ice ridges has been revealed. The thickness of the ridging ice obeys the exponential distribution law. The height of the sail, the draft of the keel and the thickness of the consolidated layer of ice ridges obey the Weibull–Gnedenko distribution.