the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Jul 2024
Implementation of implicit filter for spatial spectra extraction
Abstract. Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It is now broadly used to analyze energy spectra and energy transfers in eddy-resolving ocean simulations. However, for data from unstructured-mesh models it requires interpolation to a regular grid. We present a high-performance Python implementation of an alternative coarse-graining method which relies on implicit filters using discrete Laplacians. This method can work on arbitrary (structured or unstructured) meshes and is applicable to the direct output of unstructured-mesh ocean circulation atmosphere models. The computation is split into two phases: preparation and solving. The first one is specific only to the mesh. This allows for auxiliary arrays that are then computed to be reused, significantly reducing the computation time. The second part consists of sparse matrix algebra and solving linear system. Our implementation is accelerated by GPUs to achieve unmatched performance and scalability. This results in processing data based on meshes with more than 10M surface vertices in a matter of seconds. As an illustration, the method is applied to compute spatial spectra of ocean currents from high-resolution FESOM2 simulations.
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RC1: 'Comment on egusphere-2024-1119', Anonymous Referee #1, 10 Oct 2024
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This article describes an efficient Python implementation of a smoothing filter that can be applied on unstructured meshes. The mathematical method and sample results were described in a previous paper. This paper describes the new implementation and addresses some additional questions about higher-order filtering. A few parts are unclear and some of the language is overblown, but mostly it is a great article.
1. Some of the language is overblown and sounds more like a sales pitch than a scientific paper. Some examples:
"unmatched performance and scalability". This would require a huge comparison study to demonstrate unequivocally. Perhaps say "excellent" instead of "unmatched" unless you have good evidence for "unmatched"
The second sentence of the introduction is too long and convoluted. Removing the clauses leaves:
"Which scales contribute most to the kinetic and available potential energy, ... are among questions frequently asked". Consider rephrasing to something like this, using a bulleted list?
"Decomposing the motions into a spectrum of scales is useful for calculating:
* which scales contribute most to kinetic and available potential energy
* which scales contribute most to energy generation and dissipation
* how energy is transferred between scales.
"Line 285:
"The second phase leverages cutting-edge sparse matrix algebra and GPU acceleration, harnessing the power of modern graphics processing units to achieve unparalleled performance and scalability. This computational prowess enables the processing of high-resolution data from meshes with millions of surface vertices within seconds."On line 217, rather than saying "exclusively utilised", could you simplify your language and just say "used".
Could you make the description of the computer less of a sales pitch. Rather than:
"This high-performance node boasts an impressive configuration, featuring ..."
just say:
"The JUWELS Booster Module has ..."
Rather than:
"To optimise computational efficiency and resource utilisation, only a single GPU was employed for the duration of this study."
say:
"A single GPU was used for this study."Simplify the language:
"The second phase leverages cutting-edge sparse matrix algebra and GPU acceleration, harnessing the power of modern graphics processing units to achieve unparalleled performance and scalability. This computational prowess enables the processing of high-resolution data from meshes with millions of surface vertices within seconds."Please simplify the rest of the language in a similar way.
2. There is a lot of content describing how to solve a Poisson equation on an unstructured mesh. These are established techniques and so perhaps should be moved to an appendix?
3. Please describe more clearly how you calculate the wavenumber spectra for the original data, for the box filter and for the interpolated data.
4. Please define what you mean by "convergence of biharmonic filters". In what way are these iterative and what are you trying to converge towards?
5. Line 277 says:
"Unlike its predecessors, the implicit filter method directly operates on unstructured meshes, such as triangular and quasi-hexagonal meshes, eliminating the need for computationally expensive interpolation to regular grids."
My understanding is that you have smoothed the data on the native grid by solving a Poisson equation. The solution of a Poisson equation on an unstructured grid is established. I thought that you still have to interpolate onto a lat-lon grid to calculate power spectra. You are just interpolating coarser data. Please explain.Citation: https://doi.org/10.5194/egusphere-2024-1119-RC1
Model code and software
Implicit_filter: v1.0.0 Kacper Nowak and Sergey Danilov https://zenodo.org/records/10907365
Interactive computing environment
Implementation of implicit filter for spatial spectra extraction Kacper Nowak, Sergey Danilov, Vasco Müller, and Caili Liu https://zenodo.org/records/10957614
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