A Displacement and Amplitude Score Employing an Optical Flow Technique

Abstract

A field verification measure for precipitation forecasts is presented that combines distance and amplitude errors. It is based on an optical flow algorithm that defines a vector field that deforms, or morphs, one image to match another. When the forecast field is morphed to match the observation field, then for any point in the observation field, the magnitude of the displacement vector gives the distance to the corresponding forecast object (if any), while the difference between the observation and the morphed forecast is the amplitude error. Similarly, morphing the observation field onto the forecast field gives displacement and amplitude errors for forecast features. If observed and forecast features are separated by more than a prescribed maximum search distance, they are not matched to each other, but they are considered to be two separate amplitude errors: a missed event and a false alarm. The displacement and amplitude error components are combined to produce a displacement and amplitude score (DAS). The two components are weighted according to the principle that a displacement error equal to the maximum search distance is equivalent to the amplitude error that would be obtained by a forecast and an observed feature that are too far apart to be matched. The new score, DAS, is applied to the idealized and observed test cases of the Spatial Verification Methods Intercomparison Project (ICP) and is found to accurately measure displacement errors and quantify combined displacement and amplitude errors reasonably well, although with some limitations due to the inability of the image matcher to perfectly match complex fields.