Tim Palmer

Abstract:

Representing all variables in double‐precision in weather and climate models may be a waste of computer resources, especially when simulating the smallest spatial scales, which are more difficult to accurately observe and model than are larger scales. Recent experiments have shown that reducing to single‐precision would allow real‐world models to run considerably faster without incurring significant errors. Here, the effects of reducing precision to even lower levels are investigated in the Surface Quasi‐Geostrophic system, an idealised system that exhibits a similar power‐law spectrum to that of energy in the real atmosphere, by emulating reduced precision on conventional hardware. It is found that precision can be reduced much further for the smallest scales than the largest scales without inducing significant macroscopic error, according to a ‐4/3 power law, motivating the construction of a ‘scale‐selective’ reduced‐precision model that performs as well as a double‐precision control in short‐ and long‐range forecasts but for a much lower estimated computational cost. A similar scale‐selective approach in real‐world models could save resources that could be re‐invested to allow these models to be run at greater resolution, complexity or ensemble size, potentially leading to more efficient, more accurate forecasts.

Abstract:

Flow-dependent spread (FDS) is a desirable characteristic of probabilistic forecasts; ensemble spread should represent the expected forecast error. However this is difficult to estimate for seasonal hindcasts as they tend to have a relatively small sample size. Here we use a long (110 year) seasonal hindcast dataset to evaluate FDS in forecasts of boreal winter North Atlantic Oscillation (NAO) and Pacific North American pattern (PNA). A good FDS relationship is found for interannual variations in both the NAO and PNA , with mild underdispersion for negative NAO and PNA events and slight overdispersion for positive NAO. Decadal-scale variability is seen in forecast errors but not in ensemble spread, which shows little variation on this timescale. Links between forecast errors and tropical heating anomalies are also investigated, though no strong links are found. However a weak link between strong El Niño warming in the East Pacific and reduced PNA error is suggested.

Abstract:

A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain due to the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed towards, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double, single and half precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double precision assimilation.