[Paper Review] Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1), part II: a semi-discrete error analysis framework for assessing coupling schemes

Christopher J. Vogl, Hui Wan+2 more|arXiv (Cornell University)|Jun 8, 2023

Atmospheric chemistry and aerosolsEarth and Planetary Sciences17 references3 citations

TL;DR

This paper introduces a semi-discrete error analysis framework to mathematically evaluate numerical coupling schemes in Earth system models, specifically applied to aerosol processes in EAMv1. It isolates splitting errors from time integration errors, demonstrating that the original EAMv1 coupling artificially amplifies dry removal effects, while the revised scheme reduces this artifact, improving physical fidelity without altering time integration methods.

ABSTRACT

This paper complements the empirical justification of the revised scheme in Part I of this work with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The novelty of the framework is that splitting error is distinguished from the process time integration errors, i.e., the errors caused by discrete time integration of individual processes, leading to expressions that are more easily interpreted utilizing existing physical understanding of the processes that the terms represent. This application of this framework to dust life cycle in EAMv1 showcases such an interpretation, using the leading-order splitting error that results from the framework to confirm (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes, and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes, and (ii) the choices of input state and timestep size for the isolated integration of processes.

Motivation & Objective

• To provide a mathematical justification for a revised coupling scheme in EAMv1 that reduces artificial sensitivity of dust lifetime to vertical resolution.
• To isolate splitting error from time integration error in multi-process numerical models, enabling clearer interpretation of coupling-induced inaccuracies.
• To develop a generalizable framework applicable to any number of physical processes with varying time integration methods.
• To validate that the revised coupling in EAMv1 reduces artificial strengthening of dry removal processes, as identified empirically in Part I.
• To enable rapid development of improved coupling schemes by linking physical process behavior to splitting error components.

Proposed method

• The framework employs a semi-discrete analysis to decompose the leading-order splitting error in multi-process time integration schemes.
• It separates splitting error from time integration error by analyzing the order of magnitude of terms arising from sequential integration of processes.
• The method uses Taylor expansions of process operators to derive expressions for the leading-order splitting error in a three-process system (emission, dry removal, turbulent mixing).
• It identifies that splitting error arises from integrating processes in isolation and from choices of input state and timestep size during isolated integration.
• The framework allows evaluation of coupling schemes independently of specific time integration methods, while still permitting inclusion of those errors if needed.
• The approach is applied to the dust life cycle in EAMv1 to interpret and quantify the impact of different coupling strategies on dry removal strength.

Experimental results

Research questions

• RQ1 How can splitting errors in multi-process numerical models be isolated from time integration errors to enable clearer diagnosis of coupling-induced inaccuracies?
• RQ2 Why does the original EAMv1 coupling scheme artificially strengthen the effect of dry removal on dust aerosols, and how can this be mathematically explained?
• RQ3 To what extent does the revised coupling scheme in EAMv1 reduce the artificial enhancement of dry removal due to numerical splitting?
• RQ4 Can a general-purpose framework be developed to evaluate and improve process coupling schemes across different physical systems and time integration methods?
• RQ5 How do choices of input state and timestep size during isolated process integration contribute to overall splitting error in sequential splitting schemes?

Key findings

• The original EAMv1 coupling scheme introduces a leading-order splitting error that artificially strengthens the impact of dry removal on dust aerosols, particularly at high vertical resolution.
• The revised coupling scheme reduces this artificial strengthening by modifying the sequence and treatment of process integration, leading to more physically consistent dust lifetime simulations.
• The semi-discrete error analysis framework successfully isolates splitting error from time integration error, enabling direct interpretation of coupling artifacts in terms of physical processes.
• The framework explains that splitting error arises from both the sequential integration of processes and the choice of input state and timestep size for each isolated process.
• The framework is general and can be applied to any number of processes with arbitrary time integration schemes, enabling systematic evaluation of coupling strategies.
• The analysis confirms that the revised coupling in EAMv1 produces a numerically more accurate solution by reducing spurious numerical artifacts in the dust life cycle.