Further evaluating the generalized Itô correction for accelerating convergence of  stochastic parameterizations with colored noise

Johns, William; Fang, Lidong; Lei, Huan; Stinis, Panos

doi:10.5194/gmd-19-2373-2026

Articles | Volume 19, issue 6

https://doi.org/10.5194/gmd-19-2373-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-19-2373-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 19, issue 6

Development and technical paper

|

24 Mar 2026

Development and technical paper |

| 24 Mar 2026

Further evaluating the generalized Itô correction for accelerating convergence of stochastic parameterizations with colored noise

William Johns, Lidong Fang, Huan Lei, and Panos Stinis

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Final revised paper (published on 24 Mar 2026)
Preprint (discussion started on 07 Apr 2025)

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-765', Anonymous Referee #1, 07 Nov 2025
The study addresses an important problem in stochastic parameterizations and shows that the generalized Itô correction improves convergence toward the Stratonovich solution under colored noise.

The manuscript should more clearly position GIC relative to commonly used operational stochastic schemes (e.g., SPPT, SKEB), explaining conceptual differences and complementary roles.

Provide clearer implementation guidance for computing ∂g/∂ug in complex models, including when symbolic differentiation, automatic differentiation, or numerical approximations are suitable.

Strengthen the explanation of the observed critical timestep behavior and convergence order transitions, ideally through a simplified stability or scaling argument.

Add a complete parameter and configuration table for the 2D experiments, and ensure reproducibility instructions meet GMD standards.

Include a summary comparison table listing all numerical schemes (Euler, Milstein, KP, KP2, RK2), their convergence orders with and without GIC, and the interpretation (Itô or Stratonovich) they approach.

Clarify in figure captions the error norm, number of realizations, and the definition of error bars.

If possible, provide a short workflow or example demonstrating how GIC can be embedded into a simplified atmospheric or ocean model component to enhance practical applicability.

Recommendation: Major Revision
Citation: https://doi.org/10.5194/egusphere-2025-765-RC1
- AC1: 'Reply on RC1', William Johns, 04 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-765/egusphere-2025-765-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-765-AC1
RC2:
'Comment on egusphere-2025-765', Anonymous Referee #2, 08 Jan 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-765/egusphere-2025-765-RC2-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-765-RC2
- AC2: 'Reply on RC2', William Johns, 04 Feb 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-765/egusphere-2025-765-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-765-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

AR by William Johns on behalf of the Authors (04 Feb 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (22 Feb 2026) by Rohitash Chandra

RR by Anonymous Referee #2 (22 Feb 2026)

RR by Anonymous Referee #1 (22 Feb 2026)

ED: Publish subject to technical corrections (09 Mar 2026) by Rohitash Chandra

AR by William Johns on behalf of the Authors (16 Mar 2026) Manuscript

Short summary

Colored noise processes can be used to imitate processes that are two small to include fully in a model. The naïve introduction of a colored noise process to a numerical algorithm can lead to unrealistic outputs. This is remedied by the introduction of the recently introduced the Generalized Ito Correction (GIC). We demonstrate the effectiveness of GIC to improve results at a low cost on two models from the atmosphere modeling literature for a range of colored noise processes.