[Paper Review] Climate Modelling in Low-Precision: Effects of both Deterministic & Stochastic Rounding

E. Adam Paxton, Matthew Chantry+3 more|arXiv (Cornell University)|Apr 30, 2021

Meteorological Phenomena and Simulations21 references4 citations

TL;DR

This paper evaluates the use of low-precision arithmetic—down to 10-bit half-precision—in climate models using a Wasserstein distance-based metric to rigorously quantify rounding error. It demonstrates that single precision (23 bits) is sufficient for climate simulations, and even 12-bit precision can maintain negligible error; stochastic rounding further mitigates stagnation issues in slow processes, enabling robust long-term climate statistics with minimal deviation from high-precision results.

ABSTRACT

Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system; a shallow water approximation for flow over a ridge; and a coarse resolution global atmospheric model with simplified parameterisations (SPEEDY). Although double precision (52 significant bits) is standard across operational climate models, in our experiments we find that single precision (23 sbits) is more than enough and that as low as half precision (10 sbits) is often sufficient. For example, SPEEDY can be run with 12 sbits across the entire code with negligible rounding error and this can be lowered to 10 sbits if very minor errors are accepted, amounting to less than 0.1 mm/6hr for the average grid-point precipitation, for example. Our test is based on the Wasserstein metric and this provides stringent non-parametric bounds on rounding error accounting for annual means as well as extreme weather events. In addition, by testing models using both round-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigate rounding error across a range of applications. Thus our results also provide evidence that SR could be relevant to next-generation climate models. While many studies have shown that low-precision arithmetic can be suitable on short-term weather forecasting timescales, our results give the first evidence that a similar low precision level can be suitable for climate.

Motivation & Objective

• To assess whether low-precision arithmetic (down to 10 bits) can maintain accurate long-term climate statistics in numerical models.
• To develop a robust, non-parametric metric for quantifying rounding error across both mean states and extreme events.
• To compare deterministic (round-to-nearest) and stochastic rounding in mitigating error accumulation over long integration timescales.
• To evaluate the viability of low-precision computing for next-generation climate models, extending prior work focused on short-term weather forecasting.

Proposed method

• Uses the Wasserstein distance (WD) with L1 cost (|x−y|) as a non-parametric, interpretable metric to compare probability distributions of model outputs between high- and low-precision runs.
• Applies the WD to annual means and extreme events, enabling bounds on expected values including mean and extreme precipitation.
• Employs a stress-test framework that runs multiple long integrations to minimize initial-condition variability and isolate rounding error effects.
• Tests both round-to-nearest (RN) and stochastic rounding (SR) in models ranging from the Lorenz system to a global atmospheric model (SPEEDY).
• Uses the Kantorovich-Rubinstein duality to interpret WD bounds in physical units, such as mm/6hr for precipitation.
• Implements stochastic rounding with high-precision intermediate computation to generate probabilistic rounding decisions, while storing and communicating results at low precision.

Experimental results

Research questions

• RQ1 Can climate models maintain accurate long-term statistical behavior when computed in low-precision arithmetic, such as 10–12 bits?
• RQ2 Does stochastic rounding reduce rounding error accumulation in turbulent and slow processes compared to round-to-nearest?
• RQ3 To what extent do rounding errors in short-term forecasts affect long-term climate statistics in chaotic systems?
• RQ4 Can the Wasserstein distance serve as a reliable, interpretable metric for quantifying rounding error in climate model comparisons?
• RQ5 Is the error introduced by low-precision arithmetic bounded in physical units (e.g., mm/6hr) and does it remain below acceptable thresholds for climate applications?

Key findings

• Single-precision arithmetic (23 bits) is sufficient for climate simulations, with negligible impact on long-term statistics across tested models.
• Half-precision arithmetic (10 bits) can be used with only minor errors, amounting to less than 0.1 mm/6hr in average grid-point precipitation in the SPEEDY model.
• A 12-bit precision version of SPEEDY maintains negligible rounding error, with Wasserstein distance bounds indicating minimal deviation from high-precision results.
• Stochastic rounding mitigates systematic errors in slow processes such as land-surface heat diffusion, where round-to-nearest causes stagnation due to repeated rounding down.
• The Wasserstein metric provides interpretable, physically meaningful bounds on error, with a 1 mm/6hr WD implying a maximum difference of 1 mm/6hr in expected precipitation or extreme rainfall.
• Rounding errors from short-term forecasts do not accumulate in time to disrupt the long-term invariant distribution of climate systems, supporting the viability of low-precision climate modeling.