  Recently, data-driven weather forecasting methods have received significant
attention for surpassing the RMSE performance of traditional NWP (Numerical
Weather Prediction)-based methods. However, data-driven models are tuned to
minimize the loss between forecasted data and ground truths, often using
pixel-wise loss. This can lead to models that produce blurred outputs, which,
despite being significantly different in detail from the actual weather
conditions, still demonstrate low RMSE values. Although evaluation metrics from
the computer vision field, such as PSNR, SSIM, and FVD, can be used, they are
not entirely suitable for weather variables. This is because weather variables
exhibit continuous physical changes over time and lack the distinct boundaries
of objects typically seen in computer vision images. To resolve these issues,
we propose the advection and convection Error (ACE) metric, specifically
designed to assess how well models predict advection and convection, which are
significant atmospheric transfer methods. We have validated the ACE evaluation
metric on the WeatherBench2 and MovingMNIST datasets.
