Root mean square error (rms, or its square, the variance distance) is often used to measure differences between simulated and observed fields. In this case, scientists measured the distance between a model forecast field within its grid and the verifying analysis field that represents all real-world observations. However, one must consider that atmospheric features, like fronts and pressure systems are three dimensional weather features in space that computer models displace and also structurally distort as the numerical forecast moves away from initiation. Variance or rms error metrics do not quantify the displacement and distortion of weather systems.

In a recently published paper in Advances in Atmospheric Sciences, a team of scientists with the National Oceanic and Atmospheric Administration (NOAA), the Massachusetts Institute of Technology (MIT), and the University of Connecticut set out to find a general approach to assess the positional and structural components of the total difference between two fields. Essentially, meteorologists want to assess the accuracy of many different weather features within a model forecast compared to a verifying analysis based on real-world observations.

Sai Ravela from MIT, a co-author of this study, previously developed a Field Alignment method. In this case, his approach aligns the model forecast field with the observationally based analysis in a smooth fashion so their difference is minimized. Next, small scale errors from uncertain origins are removed from all three fields (the original and aligned forecast as well as the verifying analysis, or proxy for observations) through a process called spatial filtering or smoothing. The total variance distance, or difference, is then partitioned into three unique components. Positional error, which is the variance distance between the smoothed original model forecast and smoothed aligned forecast fields, and structural error that is the variance distance between the smoothed aligned forecast and the smoothed verifying analysis fields, are two sides of a right angle triangle, and fine scale noise, which are the uncertain small-scale errors removed from the original model forecast and verifying analysis, or observation fields.