The facility location problem (FLP) has broad applications in transportation, ranging from siting electric vehicle charging stations to positioning emergency vehicles. The spatial facility location problem (SFLP) considers continuous demand of a region where facilities can be placed anywhere. One of the approaches to solving the SFLP is to aggregate the demand into discrete points first and then solve the corresponding point-based FLP as a surrogate model. The model performance, however, is measured by the percentage of the continuous space actually covered. The solution to the classic FLP is often not unique. In this paper, we explore how the behavior of the solution to the FLP would affect the quality of the coverage to the spatial demand. We examine in detail the property of the surrogate model and identify the key contributing factor that would affect the quality of the solution to the original coverage problem for covering continuous spatial demand. Our goal is to find a surrogate model that is detailed enough to capture all the key elements of the problem and achieve the desired accuracy level, yet has the size that is sufficiently small to ensure that it is computationally feasible.