Accurate forecasts of weather and climate will become increasingly important as the world adapts to anthropogenic climatic change. Forecasts' accuracy is limited by the computer power available to forecast centres, which determines the maximum resolution, ensemble size and complexity of atmospheric models. Furthermore, faster supercomputers are increasingly energy-hungry and unaffordable to run. In this thesis, a new means of making computer simulations more efficient is presented that could lead to more accurate forecasts without increasing computational costs. This 'scale-selective reduced precision' technique builds on previous work that shows that weather models can be run with almost all real numbers represented in 32 bit precision or lower without any impact on forecast accuracy, challenging the paradigm that 64 bits of numerical precision are necessary for sufficiently accurate computations. The observational and model errors inherent in weather and climate simulations, combined with the sensitive dependence on initial conditions of the atmosphere and atmospheric models, renders such high precision unnecessary, especially at small scales. The 'scale-selective' technique introduced here therefore represents smaller, less influential scales of motion with less precision. Experiments are described in which reduced precision is emulated on conventional hardware and applied to three models of increasing complexity. In a three-scale extension of the Lorenz '96 toy model, it is demonstrated that high resolution scale-dependent precision forecasts are more accurate than low resolution high-precision forecasts of a similar computational cost. A spectral model based on the Surface Quasi-Geostrophic Equations is used to determine a power law describing how low precision can be safely reduced as a function of spatial scale; and experiments using four historical test-cases in an open-source version of the real-world Integrated Forecasting System demonstrate that a similar power law holds for the spectral part of this model. It is concluded that the scale-selective approach could be beneficially employed to optimally balance forecast cost and accuracy if utilised on real reduced precision hardware.

This dissertation studies the effects of radiation-induced single-event upsets (SEUs) on digital signal processing (DSP) systems designed for field-programmable gate arrays (FPGAs). It presents a novel method for evaluating the effects of radiation on DSP and digital communication systems. By using an application-specific measurement of performance in the presence of SEUs, this dissertation demonstrates that only 5-15% of SEUs affecting a communications receiver (i.e. 5-15% of sensitive SEUs) cause critical performance loss. It also reports that the most critical SEUs are those that affect the clock, global reset, and most significant bits (MSBs) of computation. This dissertation also demonstrates reduced-precision redundancy (RPR) as an effective and efficient alternative to the popular triple modular redundancy (TMR) for FPGA-based communications systems. Fault injection experiments show that RPR can improve the failure rate of a communications system by over 20 times over the unmitigated system at a cost less than half that of TMR by focusing on the critical SEUs. This dissertation contrasts the cost and performance of three different variations of RPR, one of which is a novel variation developed here, and concludes that the variation referred to as "Threshold RPR" is superior to the others for FPGA systems. Finally, this dissertation presents several methods for applying Threshold RPR to a system with the goal of reducing mitigation cost and increasing the system performance in the presence of SEUs. Additional fault injection experiments show that optimizing the application of RPR can result in a decrease in critical SEUs by as much 65% at no additional hardware cost.

A central component of modern computing is the idea that computation requires determinism. Contrary to this belief, the primary contribution of this work shows that useful computation can be accomplished in an error-prone fashion. Focusing on low-power computing and the increasing push toward energy conservation, the work seeks to sacrifice accuracy in exchange for energy savings. Probabilistic computing forms the basis for this error-prone computation by diverging from the requirement of determinism and allowing for randomness within computing. Implemented as probabilistic CMOS (PCMOS), the approach realizes enormous energy sav- ings in applications that require probability at an algorithmic level. Extending probabilistic computing to applications that are inherently deterministic, the biased voltage overscaling (BIVOS) technique presented here constrains the randomness introduced through PCMOS. Doing so, BIVOS is able to limit the magnitude of any resulting deviations and realizes energy savings with minimal impact to application quality. Implemented for a ripple-carry adder, array multiplier, and finite-impulse-response (FIR) filter; a BIVOS solution substantially reduces energy consumption and does so with im- proved error rates compared to an energy equivalent reduced-precision solution. When applied to H.264 video decoding, a BIVOS solution is able to achieve a 33.9% reduction in energy consumption while maintaining a peak-signal-to-noise ratio of 35.0dB (compared to 14.3dB for a comparable reduced-precision solution). While the work presented here focuses on a specific technology, the technique realized through BIVOS has far broader implications. It is the departure from the conventional mindset that useful computation requires determinism that represents the primary innovation of this work. With applicability to emerging and yet to be discovered technologies, BIVOS has the potential to contribute to computing in a variety of fashions.