A Novel Method For Estimating Equivalent-Volume Ice Thickness Without Ridging Parameters

For the past decades, the trend of reduction of extent and thickness of ice cover in the Arctic has been noticed. While there are numerous opposing opinions about the nature and underlying reasons behind the mechanics of this process, one thing is certain – it is happening.

One of the industries that will most clearly benefit from this phenomenon is the shipping industry since lighter ice conditions in the Arctic will allow for the opening of shipping routes between the continents that were previously inaccessible. This mainly pertains to the so-called Northern Sea Route (NSR), which has the potential to shorten the trip between Northern Europe and Northeastern Asia by 40-70% compared to the conventional routes through Suez Canal or around the Cape of Good Hope.

However, even if the ice conditions in the Arctic are not as severe as some decades ago, it is still not possible to traverse the Arctic Ocean without encountering sea ice (especially in the winter), and, according to most of the future climate models, this will remain to be the case for the foreseeable future. In shipping terms, this means that ice-capable ships — either independent icebreaking ships and icebreakers or ice-strengthened ships escorted by an icebreaker — will continue to be needed if the Arctic shortcuts are to be utilized for commercial shipping.


A ship’s resistance in ice is one of the key inputs required for accurate estimation of the ship’s transit time and fuel consumption. Considering that the economic justification for use of the Arctic shortcuts is primarily based on fuel and/or time savings, the importance of accurate estimation of a ship’s ice resistance becomes obvious in this context.

A key parameter for the calculation of ships’ resistance in ice is the ice conditions, which are defined by several parameters describing the ice cover. Ice cover consists of ice floes, which are continuous pieces of ice surrounded by open water, ranging in size from meters to several kilometers across. These ice floes consist of so-called undeformed or level ice parts, which are areas of thermally-grown ice of fairly uniform thickness and which has not been deformed due to the mechanical forcing of winds and waves.

In addition to level ice, floes often contain areas of deformed ice where the original ice sheet has broken due to mechanical forcing and different deformed ice features have been formed. Most notable of these are so-called ice ridges, which present a significant obstacle for ships passing through ice-covered waters. Therefore, since the nature of sea ice cover is highly complex and dynamic, simplifications of it are often used in engineering studies.

One of these simplification models is the so-called equivalent ice thickness, which is a concept used to average all ice features in an area into a single value, which can then be used for ships’ resistance estimations. To calculate the equivalent ice thickness, several ice parameters are needed. First, ice concentration, in terms of a percentage of ice-covered water in the area; then, the thickness of ambient-level ice; and finally, information about the deformed ice features, mainly ridges, in form of ridges size and spacing. Ice concentration and level ice thickness are readily available from the ice charts in form of so-called egg code, which is a World Meteorological Organization (WMO) standard for classification of ice conditions.

Egg code consists of information about ice concentration, level ice thickness, and floe size for three predominant ice types in the area, which are classified by ice age or stage of development of ice (SOD). Each SOD is associated with a level ice thickness range, e.g. SOD Medium first-year ice has level ice thickness range between 70 and 120 cm. Here, it becomes clear that for calculation of equivalent ice thickness, data available from the egg code is insufficient, since it lacks information about deformed ice features, i.e. ice ridges.

Granted, ridging parameters are sometimes available as a supplement to the egg code in ice charts, but this is usually not the case for areas in the Arctic, since deformed ice features are not easily detectable using the remote sensing techniques (mainly satellite images), based on which the ice charts for these areas are created. In this case, ridging parameters can be obtained from one of the historical databases for the certain area and season, which are developed based on long-term observations.

In our paper published in Cold Regions Science and Technology, we address the issue of unavailability of ridging parameters, test the applicability of parameters obtained from historical databases, and develop a novel method for estimation of equivalent ice thickness when the ridging parameters are either unavailable or unreliable. We use submarine-mounted sonar measurements of the ice draft to estimate the actual amount of ice encountered along multiple routes across the Arctic Ocean. Comparing the actual amount of ice along the route to the predicted one based on data from ice charts supplemented with ridging parameters from historical databases, we conclude that this method underestimates the actual amount of ice on average by approximately 29%.

Therefore, to address this issue, we develop a novel method which proposes to substitute level ice thickness ranges from WMO egg code classification with so-called equivalent-volume ice thickness ranges (EVITRs), which account for both undeformed ice (level ice) and deformed ice (ridges). The EVITRs are established for each SOD from WMO classification based on analysis of submarine-measured ice draft profiles and by correlating the total amount of ice in an area to the thickness of ambient level ice. This, in turn, allows for a more accurate estimation of the total amount of ice and its components, without requiring ridging parameters as an input, and based only on the information available from the egg code.

The proposed EVITR-based method shows an improvement compared to the method where ridging parameters are obtained from historical databases by reducing the average error in the total amount of ice predicted from 29% to 2%. However, the obtained results need to be used with caution, since ridging is a highly stochastic process dependent on numerous dynamic parameters.

Therefore, the established EVITRs can only be used for areas and seasons where the data they were built on was gathered, but the developed methodology can be applied to any set of ice draft measurements, and applicable EVITRs can be established for any ice-covered sea in the world.

These findings are described in the article entitled A method for estimation of equivalent-volume ice thickness based on WMO egg code in absence of ridging parameters, recently published in the journal Cold Regions Science and Technology. This work was conducted by Aleksandar-Saša Milaković, Peter Schütz, and Henry Piehl from the Norwegian University of Science and Technology, and Sören Ehlers from the Hamburg University of Technology.