Abstract. Evacuation of the population from a tsunami hazard zone is vital to reduce life-loss due to inundation. Geospatial least-cost distance modelling provides one approach to assessing tsunami evacuation potential. Previous models have generally used two static exposure scenarios and fixed travel speeds to represent population movement. Some analyses have assumed immediate departure or a common evacuation departure time for all exposed population. Here, a method is proposed to incorporate time-variable exposure, distributed travel speeds, and uncertain evacuation departure time into an existing anisotropic least-cost path distance framework. The method is demonstrated for hypothetical local-source tsunami evacuation in Napier City, Hawke's Bay, New Zealand. There is significant diurnal variation in pedestrian evacuation potential at the suburb level, although the total number of people unable to evacuate is stable across all scenarios. Whilst some fixed travel speeds approximate a distributed speed approach, others may overestimate evacuation potential. The impact of evacuation departure time is a significant contributor to total evacuation time. This method improves least-cost modelling of evacuation dynamics for evacuation planning, casualty modelling, and development of emergency response training scenarios. However, it requires detailed exposure data, which may preclude its use in many situations.