Digital Elevation Model (DEM) differencing involving more than two DEMs is used to estimate glacier elevation change. A good regression model fit to the time series of glacier elevations is crucial for both prediction and error assessment. Weighted or unweighted linear models are traditionally used for this purpose and typically have a good fit over area of a glacier where surface mass balance is the major factor affecting glacier elevation. These models are less credibile in regions experiencing dynamic changes in ice flow. A non-linear model may be a good alternative, and recent advances have shown how powerful models, such as the Gaussian progress regression, can be. However, a non-linear model suffers from over-fitting and poor extrapolation, and the model itself does not consider the underlying physical mechanism. Motivated by this background, we focus on the ArctiDEM strip data set over glacier areas with dynamic signals of elevation change, including calving, surging, subglacial draining, and ice collapse. We qualitatively classify them into several patterns. Each pattern can be modeled by a distinct linear or non-linear model for better performance. For example, an elevation time series classified as calving can be modeled with a step function for a more accurate future extrapolation. We envision these classifications as a good foundation for creating a training data set for an automatic elevation change analysis using AI.