The desire to conduct research in the Arctic on an ever-larger spatio-temporal scales has led to the development of long-range autonomous underwater vehicles (AUVs), such as the Autosub Long-Range 1500 (ALR1500). Whilst these platforms open up a world of new applications, their actual use is limited in GPS-denied environments since self-contained navigation remains yet unavailable. In response, this study evaluates whether terrain-aided navigation (TAN) can enable multi-month deployments using basic navigation sensors and sparse bathymetric maps. To evaluate the potential, ALR1500 undertakes a hypothetical science-driven mission from Svalbard (Norway) to Point Barrow (Alaska, USA) under the sea ice (a mission over 3200 km). Therefore, a simulated environment is developed which integrates a state-of-the-art model of water circulation, error models for heading estimation at high latitudes and an Arctic bathymetric map. Recognising that this map is constructed based on sparse depth measurements and interpolation techniques, a bathymetric uncertainty model is developed. The performance of the TAN algorithm is examined with respect to the type of the heading sensor utilised and a range of vertical map distortions, calculated using the developed bathymetric uncertainty model. Simulations show that unaided navigation experiences an error of hundreds of kilometres, whereas TAN provides acceptable accuracy given a moderate map distortion. By degrading the quality of the map further, it appears that the navigation filter may diverge when traversing large regions subject to interpolation. Therefore, a Rapidly-exploring Random Tree Star (RRT * ) algorithm is used to design a new path such that the AUV traverses reliable and rich in topographic information areas.