Modulated Adaptive Fourier Neural Operators for Temporal Interpolation of Weather Forecasts

TL;DR

An interpolation model that reconstructs the atmospheric state between two points in time between two points in time for which the state is known and is trained to interpolate between two time steps 6 h apart is introduced.

Abstract

Weather and climate data are often available at limited temporal resolution, either due to storage limitations, or in the case of weather forecast models based on deep learning, their inherently long time steps. The coarse temporal resolution makes it difficult to capture rapidly evolving weather events. To address this limitation, we introduce an interpolation model that reconstructs the atmospheric state between two points in time for which the state is known. The model makes use of a novel network layer that modifies the adaptive Fourier neural operator (AFNO), which has been previously used in weather prediction and other applications of machine learning to physics problems. The modulated AFNO (ModAFNO) layer takes an embedding, here computed from the interpolation target time, as an additional input and applies a learned shift-scale operation inside the AFNO layers to adapt them to the target time. Thus, one model can be used to produce all intermediate time steps. Trained to interpolate between two time steps 6 h apart, the ModAFNO-based interpolation model produces 1 h resolution intermediate time steps that are visually nearly indistinguishable from the actual corresponding 1 h resolution data. The model reduces the RMSE loss of reconstructing the intermediate steps by approximately 50% compared to linear interpolation. We also demonstrate its ability to reproduce the statistics of extreme weather events such as hurricanes and heat waves better than 6 h resolution data. The ModAFNO layer is generic and is expected to be applicable to other problems, including weather forecasting with tunable lead time.

Figures (5)

• Figure 1: a) Overview of the ModAFNO interpolation network. b) The modulated AFNO layer. A time-dependent embedding is added to the MLPs in the spectral and spatial domains to enable temporal interpolation. c) Detailed view of the modulated MLP. A separate MLP produces the scale and shift activations from the time embedding.
• Figure 2: Example of ModAFNO interpolation of wind speeds from Storm Ophelia approaching Ireland on October 16, 2017. Top row: the actual ERA5 wind speed; middle row: the ModAFNO interpolated wind speed; bottom row: wind speed obtained with linear interpolation.
• Figure 3: Normalized RMSE error of the interpolation for the ModAFNO model (blue) and linear interpolation (orange) as a function of the interpolation time. The line with triangles indicates the mean of the pointwise RMSE while the box plots indicate the median (midline of the box), the 25th and 75th percentiles (ends of the box) and the 9th and 91st percentiles (whiskers).
• Figure 4: Maximum $10$ m wind speed during Hurricane Irma in the Caribbean and Florida on September 2--8, 2017. Left: obtained with $6$ h temporal resolution. Middle: with ModAFNO interpolation to $1$ h resolution. Right: the true maximum at $1$ h resolution.
• Figure 5: $2$ m temperature at the grid square containing the city of Milan, Italy, during a heat wave on August 3--4, 2017, as indicated by linear interpolation between $6$ h resolution time steps (orange dotted line), interpolation to $1$ h resolution (blue solid line) and the true $1$ h resolution data (green dashed line).