The ensemble weather forecasting by using the error of floating-point numbers

Abstract:

The computational cost of meteorological model calculations is increasing with higher resolution, more precise physics schemes, ensemble prediction experiments, etc., and the computational performance is still inadequate. Since computation cost and computation accuracy are a trade-off, it is necessary to sacrifice some of the accuracy of the computation results in order to reduce the computation cost (e.g., Palem 2003). Although there is no randomness in floating-point arithmetic itself, the effect of arithmetic error can be evaluated by treating floating-point number (FPN) error as a stochastic variable (Yamaura et al. 2019). The FPN error is an unavoidable problem in running numerical calculations on a computer, and although the magnitude of the error may vary depending on the implementation and optimization of the meteorological model, it is a factor that can be adjusted to some extent by using variable-precision FPNs. Utilizing the property that FPN error can be treated like a stochastic variable in ensemble prediction experiments, this study identifies the advantages and disadvantages compared to existing ensemble predictions.

There are two main methods for creating ensemble members using FPN errors: 1) Insertion of FPN error when creating the initial value, 2) Insertion of FPN error during calculation. Method 1 allows us to create members of about 40x2 (rounding up and down) if we take the double-precision FPN as the highest precision and reduce the precision to less than the half-precision FPN. This method is comparable to the traditional method for creating ensemble members and may be useful in discussing the nature of ensemble members due to FPN errors. The advantage of method 1 is that the ensemble members can be allocated instantly without the need to perform operations. The method 2 is completely different from the conventional method for creating ensemble members, in that it performs ensemble prediction experiments from the same initial values; since FPN errors occur even during computation, it is possible to run multiple experiments adjusting for the magnitude of the errors to automatically perform ensemble predictions. This method cannot be performed by conventional methods.