On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform

Jean Schmith; Vitor Nardelli; Paul Harris; Bardo Bodmann

doi:10.1007/978-3-032-04458-7_25

On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform

Jean Schmith
, Vitor Nardelli
, Paul Harris
, Bardo Bodmann

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

Abstract

This proposal is focused on using a repository of historical climate and meteorology data to develop a method for SACZ identification. To this end we propose a Discrete Valued Bi-dimensional Singular Transform in the spirit of the Hilbert transform, which among others provides besides a local amplitude also a local phase. Here the term “local” stands for the analogue of the conception of “instantaneous” in the original Hilbert transform for time evolution analysis of non-linear systems. This transform opens a pathway to define a similarity measure, which is used to analyze phase asymmetries in the spatial distributions and is used to setup an indication index for identifying the occurrence of the SACZ formation. The elaborated conception is applied to the meteorological data of the year 2011 available from the NOAA-CIRES Twentieth Century Reanalysis (V2c) database.

Original language	English
Title of host publication	Integral Methods In Science and Engineering
Subtitle of host publication	Study and Solutions of Mathematical Models
Editors	Christian Constanda, Bardo E.J. Bodmann, Paul J. Harris
Place of Publication	Cham
Publisher	Birkhäuser
Chapter	25
Pages	387-398
Number of pages	12
Edition	1
ISBN (Electronic)	9783032044587
ISBN (Print)	9783032044570
DOIs	https://doi.org/10.1007/978-3-032-04458-7_25
Publication status	Published - 1 May 2026

Bibliographical note

Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

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10.1007/978-3-032-04458-7_25

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Schmith, J., Nardelli, V., Harris, P., & Bodmann, B. (2026). On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform. In C. Constanda, B. E. J. Bodmann, & P. J. Harris (Eds.), Integral Methods In Science and Engineering: Study and Solutions of Mathematical Models (1 ed., pp. 387-398). Birkhäuser. https://doi.org/10.1007/978-3-032-04458-7_25

Schmith, Jean ; Nardelli, Vitor ; Harris, Paul et al. / On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform. Integral Methods In Science and Engineering: Study and Solutions of Mathematical Models. editor / Christian Constanda ; Bardo E.J. Bodmann ; Paul J. Harris. 1. ed. Cham : Birkhäuser, 2026. pp. 387-398

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abstract = "This proposal is focused on using a repository of historical climate and meteorology data to develop a method for SACZ identification. To this end we propose a Discrete Valued Bi-dimensional Singular Transform in the spirit of the Hilbert transform, which among others provides besides a local amplitude also a local phase. Here the term “local” stands for the analogue of the conception of “instantaneous” in the original Hilbert transform for time evolution analysis of non-linear systems. This transform opens a pathway to define a similarity measure, which is used to analyze phase asymmetries in the spatial distributions and is used to setup an indication index for identifying the occurrence of the SACZ formation. The elaborated conception is applied to the meteorological data of the year 2011 available from the NOAA-CIRES Twentieth Century Reanalysis (V2c) database.",

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Schmith, J, Nardelli, V, Harris, P & Bodmann, B 2026, On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform. in C Constanda, BEJ Bodmann & PJ Harris (eds), Integral Methods In Science and Engineering: Study and Solutions of Mathematical Models. 1 edn, Birkhäuser, Cham, pp. 387-398. https://doi.org/10.1007/978-3-032-04458-7_25

On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform. / Schmith, Jean; Nardelli, Vitor; Harris, Paul et al.
Integral Methods In Science and Engineering: Study and Solutions of Mathematical Models. ed. / Christian Constanda; Bardo E.J. Bodmann; Paul J. Harris. 1. ed. Cham: Birkhäuser, 2026. p. 387-398.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

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AU - Schmith, Jean

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AU - Harris, Paul

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N1 - Publisher Copyright: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

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N2 - This proposal is focused on using a repository of historical climate and meteorology data to develop a method for SACZ identification. To this end we propose a Discrete Valued Bi-dimensional Singular Transform in the spirit of the Hilbert transform, which among others provides besides a local amplitude also a local phase. Here the term “local” stands for the analogue of the conception of “instantaneous” in the original Hilbert transform for time evolution analysis of non-linear systems. This transform opens a pathway to define a similarity measure, which is used to analyze phase asymmetries in the spatial distributions and is used to setup an indication index for identifying the occurrence of the SACZ formation. The elaborated conception is applied to the meteorological data of the year 2011 available from the NOAA-CIRES Twentieth Century Reanalysis (V2c) database.

AB - This proposal is focused on using a repository of historical climate and meteorology data to develop a method for SACZ identification. To this end we propose a Discrete Valued Bi-dimensional Singular Transform in the spirit of the Hilbert transform, which among others provides besides a local amplitude also a local phase. Here the term “local” stands for the analogue of the conception of “instantaneous” in the original Hilbert transform for time evolution analysis of non-linear systems. This transform opens a pathway to define a similarity measure, which is used to analyze phase asymmetries in the spatial distributions and is used to setup an indication index for identifying the occurrence of the SACZ formation. The elaborated conception is applied to the meteorological data of the year 2011 available from the NOAA-CIRES Twentieth Century Reanalysis (V2c) database.

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Schmith J, Nardelli V, Harris P, Bodmann B. On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform. In Constanda C, Bodmann BEJ, Harris PJ, editors, Integral Methods In Science and Engineering: Study and Solutions of Mathematical Models. 1 ed. Cham: Birkhäuser. 2026. p. 387-398 doi: 10.1007/978-3-032-04458-7_25

On the Elaboration of an Index for Identifying SACZ Occurrences Using a Discrete Valued Bi-dimensional Singular Transform

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