Tim Palmer

Abstract:

Motivated by the increasing energy consumption of supercomputing for weather and climate simulations, we introduce a framework for investigating the bit-level information efficiency of chaotic models. In comparison with previous explorations of inexactness in climate modelling, the proposed and tested information metric has three specific advantages: (i) it requires only a single high-precision time series; (ii) information does not grow indefinitely for decreasing time step; and (iii) information is more sensitive to the dynamics and uncertainties of the model rather than to the implementation details. We demonstrate the notion of bit-level information efficiency in two of Edward Lorenz’s prototypical chaotic models: Lorenz 1963 (L63) and Lorenz 1996 (L96). Although L63 is typically integrated in 64-bit ‘double’ floating point precision, we show that only 16 bits have significant information content, given an initial condition uncertainty of approximately 1% of the size of the attractor. This result is sensitive to the size of the uncertainty but not to the time step of the model. We then apply the metric to the L96 model and find that a 16-bit scaled integer model would suffice given the uncertainty of the unresolved sub-grid-scale dynamics. We then show that, by dedicating computational resources to spatial resolution rather than numeric precision in a field programmable gate array (FPGA), we see up to 28.6% improvement in forecast accuracy, an approximately fivefold reduction in the number of logical computing elements required and an approximately 10-fold reduction in energy consumed by the FPGA, for the L96 model.

Abstract:

©2017. American Geophysical Union. All Rights Reserved. Seasonal hindcast experiments, using prescribed sea surface temperatures (SSTs), are analyzed for Northern Hemisphere winters from 1900 to 2010. Ensemble mean Pacific/North American index (PNA) skill varies dramatically, dropping toward zero during the mid-twentieth century, with similar variability in North Atlantic Oscillation (NAO) hindcast skill. The PNA skill closely follows the correlation between the observed PNA index and tropical Pacific SST anomalies. During the mid-century period the PNA and NAO hindcast errors are closely related. The drop in PNA predictability is due to mid-century negative PNA events, which were not forced in a predictable manner by tropical Pacific SST anomalies. Overall, negative PNA events are less predictable and seem likely to arise more from internal atmospheric variability than positive PNA events. Our results suggest that seasonal forecasting systems assessed over the recent 30 year period may be less skillful in periods, such as the mid-twentieth century, with relatively weak forcing from tropical Pacific SST anomalies.