## 1 Introduction  
The recent decades have seen an increasing interest and resulting demand for development of Arctic ships and offshore structures. These are used for exploration and extraction of natural resources, and for navigation throughout the Arctic and Antarctic corridors [1, 2]. A number of different ice features will generally be of concern in these areas, such as ice ridges and icebergs. These features are assumed to represent a major hazard to the integrity of ship hulls and may accordingly govern the design loads [3]. Design of ships for Polar regions is mainly based on rules and regulations, such as the International Maritime Organization (IMO) Polar code, the Finnish-Swedish Ice Class Rules (FSICR), the International Association of Classification Societies (IACS) Polar Class rules, etc. These codes and rules are primarily based on experience and deterministic solutions, and they are attractive in connection with practical design due to their simplicity [4]. However, ship-ice loads are random by nature [5, 6]. This randomness is due to the inherent variability of ice conditions (such as the physical ice characteristics including the mechanical properties) and also by the great span of ship-ice interaction processes [7]. Accordingly, probabilistic methods are required in order to account for the inherent randomness of the ship-ice loads. Hence, reliability-based design methods based on proper representation of the statistical variation of ice loads could serve to supplement current rule-based design methods. Regarding structural design principles, criteria corresponding to the Ultimate Limit State (ULS) are intended to ensure that no extensive structural damage is likely to take place during the intended lifetime of the structure. For Polar ships, criteria associated with the ULS condition imply that the ship should have the capacity to resist the ice load actions corresponding to a specific return period (or a specific exceedance probability) without critical damage taking place. This applies both to the local and the global load effects within the vessels [8]. In general, it is assumed that the most accurate approach for estimation of the extreme ice loads is to perform a full long-term response analysis. As part of this analysis, each individual ice condition is weighted by the associated probability of occurrence. However, this type of analysis is usually time-consuming since high-fidelity numerical response analyses are usually involved [9]. Regarding the Accidental Limit State, a range of different design scenarios also need to be analyzed. Since highly nonlinear structural response behavior is generally involved, the associated computational efforts easily become tremendous. Particularly for the case of so-called shared energy design, complex dynamic interaction processes involving both the ice mass and the floating structure must be modeled in a proper way. This requires careful building of computational models and numerical algorithms [10]. In order to make ULS and ALS design procedures more efficient, the environmental contour method offers an effective alternative to the full long-term analysis. The contour will then represent a set of environmental conditions (presently corresponding to ice ridge and iceberg characteristics) for a given vessel lifetime [11]. The extreme response which corresponds to the ice loads for this specified \"return period\" can subsequently be calculated by identifying the critical ice conditions along the generated environmental contour. The advantage of this approach lies in the fact that the environmental characteristics are uncoupled from the structural response during the first step of the analysis [12]. Numerical simulations (in some cases supplemented by experiments) are then only required for a very limited number of conditions that are located on the contour in order to identify the most critical structural response level. The environmental contour is generally identified by application of the IFORM (inverse first order reliability method).