Bitwise efficiency in chaotic models.

Area of Science:

• Computational science
• Climate modeling
• Information theory

Background:

• Supercomputing for weather and climate simulations faces high energy demands.
• Previous methods for analyzing inexactness in climate models have limitations.

Purpose of the Study:

• Introduce a framework for investigating bit-level information efficiency in chaotic models.
• Develop an information metric with advantages over previous approaches.
• Demonstrate the metric's application and implications for computational resource allocation.

Main Methods:

• Developed and tested a novel information metric for chaotic models.
• Applied the metric to Lorenz 1963 (L63) and Lorenz 1996 (L96) models.
• Evaluated computational resource allocation trade-offs (spatial resolution vs. numeric precision) on a Field Programmable Gate Array (FPGA).

Main Results:

• Identified that only 16 bits hold significant information content for L63 with 1% initial uncertainty.
• Determined that a 16-bit scaled integer model is sufficient for L96, considering sub-grid-scale dynamics uncertainty.
• Achieved up to 28.6% improvement in forecast accuracy on an FPGA by prioritizing spatial resolution over numeric precision.

Conclusions:

• The proposed information metric is sensitive to model dynamics and uncertainties, not implementation details.
• Optimizing computational resources towards spatial resolution can significantly enhance forecast accuracy and reduce energy consumption.
• Findings suggest potential for more energy-efficient and accurate climate simulations.