Algorithmic Improvements to Finding Approximately Neutral Surfaces

Abstract Interior oceanic motions occur predominantly along, rather than across, the neutral tangent plane. These planes do not link together to form well‐defined surfaces, so oceanographers use approximately neutral surfaces. To date, the most accurate such surface is the ω‐surface, but its practic...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Geoffrey J. Stanley, Trevor J. McDougall, Paul M. Barker
Formato:	article
Lenguaje:	EN
Publicado:	American Geophysical Union (AGU) 2021
Materias:	density neutral surfaces optimization Poisson's equation Physical geography GB3-5030 Oceanography GC1-1581
Acceso en línea:	https://doaj.org/article/328f5ab31f824c94b8cd3256b0899469
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:328f5ab31f824c94b8cd3256b0899469
record_format	dspace
spelling	oai:doaj.org-article:328f5ab31f824c94b8cd3256b08994692021-11-24T08:11:41ZAlgorithmic Improvements to Finding Approximately Neutral Surfaces1942-246610.1029/2020MS002436https://doaj.org/article/328f5ab31f824c94b8cd3256b08994692021-05-01T00:00:00Zhttps://doi.org/10.1029/2020MS002436https://doaj.org/toc/1942-2466Abstract Interior oceanic motions occur predominantly along, rather than across, the neutral tangent plane. These planes do not link together to form well‐defined surfaces, so oceanographers use approximately neutral surfaces. To date, the most accurate such surface is the ω‐surface, but its practical utility was limited because its numerical implementation was slow and sometimes unstable. This work upgrades the speed, robustness, and utility of ω‐surfaces. First, we switch from solving an overdetermined matrix problem by minimal least squares, to solving an exactly determined matrix problem, obtained either by the normal equations (multiplication by the matrix's transpose) or by discretizing Poisson's equation derived from the original optimization problem by the calculus of variations. This reduces the computational complexity, roughly from O(N1.6) to O(N1.2), where N is the number of grid points in the surface. Second, we update the surface's vertical position by solving a nonlinear equation in each water column, rather than assuming the stratification is vertically uniform. This reduces the number of iterations required for convergence by an order of magnitude and eliminates the need for a damping factor that stabilized the original software. Additionally, we add “wetting” capacity, whereby incrops and outcrops are reincorporated into the surface should they become neutrally linked as iterations proceed. The new algorithm computes an ω‐surface in a 1,440 by 720 gridded ocean in roughly 15 s, down from roughly 11 h for the original software. We also provide two simple methods to label an ω‐surface with a (neutral) density value.Geoffrey J. StanleyTrevor J. McDougallPaul M. BarkerAmerican Geophysical Union (AGU)articledensityneutral surfacesoptimizationPoisson's equationPhysical geographyGB3-5030OceanographyGC1-1581ENJournal of Advances in Modeling Earth Systems, Vol 13, Iss 5, Pp n/a-n/a (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	density neutral surfaces optimization Poisson's equation Physical geography GB3-5030 Oceanography GC1-1581
spellingShingle	density neutral surfaces optimization Poisson's equation Physical geography GB3-5030 Oceanography GC1-1581 Geoffrey J. Stanley Trevor J. McDougall Paul M. Barker Algorithmic Improvements to Finding Approximately Neutral Surfaces
description	Abstract Interior oceanic motions occur predominantly along, rather than across, the neutral tangent plane. These planes do not link together to form well‐defined surfaces, so oceanographers use approximately neutral surfaces. To date, the most accurate such surface is the ω‐surface, but its practical utility was limited because its numerical implementation was slow and sometimes unstable. This work upgrades the speed, robustness, and utility of ω‐surfaces. First, we switch from solving an overdetermined matrix problem by minimal least squares, to solving an exactly determined matrix problem, obtained either by the normal equations (multiplication by the matrix's transpose) or by discretizing Poisson's equation derived from the original optimization problem by the calculus of variations. This reduces the computational complexity, roughly from O(N1.6) to O(N1.2), where N is the number of grid points in the surface. Second, we update the surface's vertical position by solving a nonlinear equation in each water column, rather than assuming the stratification is vertically uniform. This reduces the number of iterations required for convergence by an order of magnitude and eliminates the need for a damping factor that stabilized the original software. Additionally, we add “wetting” capacity, whereby incrops and outcrops are reincorporated into the surface should they become neutrally linked as iterations proceed. The new algorithm computes an ω‐surface in a 1,440 by 720 gridded ocean in roughly 15 s, down from roughly 11 h for the original software. We also provide two simple methods to label an ω‐surface with a (neutral) density value.
format	article
author	Geoffrey J. Stanley Trevor J. McDougall Paul M. Barker
author_facet	Geoffrey J. Stanley Trevor J. McDougall Paul M. Barker
author_sort	Geoffrey J. Stanley
title	Algorithmic Improvements to Finding Approximately Neutral Surfaces
title_short	Algorithmic Improvements to Finding Approximately Neutral Surfaces
title_full	Algorithmic Improvements to Finding Approximately Neutral Surfaces
title_fullStr	Algorithmic Improvements to Finding Approximately Neutral Surfaces
title_full_unstemmed	Algorithmic Improvements to Finding Approximately Neutral Surfaces
title_sort	algorithmic improvements to finding approximately neutral surfaces
publisher	American Geophysical Union (AGU)
publishDate	2021
url	https://doaj.org/article/328f5ab31f824c94b8cd3256b0899469
work_keys_str_mv	AT geoffreyjstanley algorithmicimprovementstofindingapproximatelyneutralsurfaces AT trevorjmcdougall algorithmicimprovementstofindingapproximatelyneutralsurfaces AT paulmbarker algorithmicimprovementstofindingapproximatelyneutralsurfaces
_version_	1718415787038867456

Algorithmic Improvements to Finding Approximately Neutral Surfaces

Ejemplares similares