We develop and study two approaches for the prediction of optical refraction effects in the lower atmosphere. Refraction can cause apparent displacement or distortion of targets when viewed by imaging systems or produce steering when propagating laser beams. Low-cost, time-lapse camera systems were deployed at two locations in New Mexico to measure image displacements of mountain ridge targets due to atmospheric refraction as a function of time. Measurements for selected days were compared with image displacement predictions provided by (1) a ray-tracing evaluation of numerical weather prediction data and (2) a machine learning algorithm with measured meteorological values as inputs. The model approaches are described and the target displacement prediction results for both were found to be consistent with the field imagery in overall amplitude and phase. However, short time variations in the experimental results were not captured by the predictions where sampling limitations and uncaptured localized events were factors.