Generation of Ensemble Perturbations Using Low-Precision Floating-Point Numbers

Abstract

The objective of this study is to improve forecast accuracy by using low-precision floating-point arithmetic when performing ensemble weather forecasting. Low-precision floating-point arithmetic is reproduced using a software emulator developed to allow the mantissa bit length of floating-point numbers to be adjusted in one-bit increments. First, two different methods of generating an ensemble forecast using low-precision techniques were compared with a conventional ensemble-generation approach. For one, the precision of the initial conditions is reduced (called initial value ensemble), and for the other, the precision of the model calculations is reduced (called model ensemble). Then, it is found that the former technique is inadequate for generating sufficient ensemble spread, but the latter gives an ensemble spread comparable to the reference. In order to further evaluate the ensemble method using low-precision floating-point arithmetic in accordance with the model ensemble method, ensemble forecasting experiments were conducted in combination with the conventional ensemble method. As a result, the combined ensemble forecast had a higher spread evaluation index than the ensemble forecast using only the low-precision floating-point arithmetic and the conventional ensemble method. The reasons why the ensemble forecasts have higher index when incorporating low-precision floating-point ensemble methods are considered as follows: weather forecast models do not reproduce weather phenomena below the grid scale due to their low spatio-temporal resolution, and some models incorporate statistical assumptions to reduce computational load, which suppress the random nature of weather phenomena rather than actual weather events. On the other hand, ensemble methods using low-precision floating-point arithmetic can compensate for this randomness, and thus are expected to have higher evaluation index. This suggests that low-precision floating-point arithmetic, implemented in hardware by using Field Programmable Gate-Arrays (FPGAs) for example, may allow for faster operations without compromising forecast accuracy in ensemble forecasting.