The Efficient Identification of Meandering and other Low-Frequency Phenomena in Raw Ultrasonic Anemometer Data

The Efficient Identification of Meandering and other Low-Frequency Phenomena in Raw Ultrasonic Anemometer Data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Efficient Identification of Meandering and other Low-Frequency Phenomena in Raw Ultrasonic Anemometer Data Patrizia Favaron, Simone Zintu, Cristiana Morosini This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4482735/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Feb, 2025 Read the published version in Bulletin of Atmospheric Science and Technology → Version 1 posted 9 You are reading this latest preprint version Abstract This short conference paper shows a new experimental method for the detection and identification of meandering and other low-frequency components in raw data from three-axial ultrasonic anemometers and other high resolution, high sampling-rate three-dimensional wind sensors. The proposed method is a combination of autocorrelation-based detection and delay-free recursive filtering, both described in recent published works. The results of the application of the described method to a sample of hourly raw data files are also shown. The method can be used as a building block for eddy covariance and other data processing procedures as well as in all the situations where very short time scales (about 10s) are relevant, such as in odour or toxic chemical dispersion field. Figures Figure 1 Introduction Meandering and other low-frequency phenomena not directly attributable to turbulence are known to play an important role in the dispersion of tracers (for example odours) emitted by a point source, thus detecting their presence in ultrasonic anemometer elementary data sets and identifying their time evolution have a great application value. Low-frequency phenomena may occur at a time scale between 1s and 60s, much smaller than the time step used in air quality and odour modelling (600s to 3600s), and are conglobated in turbulence, possibly overestimating its magnitude and, consequently, underestimating the modelled ground concentrations. Detection and identification of low-frequency phenomena are two distinct aspects, their focus being, respectively, determining whether a low-frequency component may be found in a data set and estimating its time evolution. Detection has been extensively investigated (Cava et al., 2017 ; Mortarini et al., 2016 ) and various methods have been proposed: among all, the wavelet analysis and the study of oscillations in autocorrelation functions are worthy to be cited. In this paper, a combined detection-and-identification method is proposed based on the iterative application of the recursive filter presented in Falocchi et al. ( 2018 ), followed by autocorrelation analysis, and results of the method applied to a sample of data collected by the micro-meteorological surface station located at Parco Nord, Cinisello Balsamo (part of the SHAKEUP network by Lombardy Environmental Protection Agency) are shown. The associated algorithms have been distributed as open-source code (Favaron, 2024 ). Methods and results Raw data, consisting of quadruples \(\left(u,v,w,t\right)\) collected continuously by the station sonic anemometer at a nominal rate of 20Hz and 2 out of 1 averaging, are automatically organized and archived in hourly files, four of which have been selected for 2016-03-08 12:00–13:00 and 18:00–19:00 and for 2016-08-01 10:00–11:00 and 23:00–24:00. All the four selected hours, expressed in Central Europe Time zone, contain the 100% of sonic quadruples labelled as plausible by the anemometer. Processing was executed using the procedures in a dedicated accessible open-source repository (Favaron, 2024 ); focus was placed on meandering and then the two horizontal wind components \(u,v\) : the vertical wind component and sonic temperature have been neglected. Hourly data have been processed using a two-phase iterative process. In the first phase, the hourly signals have been replaced by the residual after applying the filter described in Falocchi et al. ( 2018 ), that is \({u}_{r}=u-{f}_{\tau =900\text{s}}\left(u\right)\) and \({v}_{r}=v-{f}_{\tau =900\text{s}}\left(v\right)\) , where \({f}_{\tau }\left(s\right)\) is the filter applied to the generic signal \(s\) ; this high-pass filtering operation is done to remove changes occurring at time scales longer than or equal to 900s (15 minutes), plausibly much longer than meandering and other interesting low-frequency phenomena. The so obtained residuals are then filtered iteratively, with \(\tau =1,\dots ,60\) , obtaining the smoothed signals \({u}_{\tau }={f}_{\tau }\left({u}_{r}\right)\) , \({v}_{\tau }={f}_{\tau }\left({v}_{r}\right)\) . Autocorrelations, \({\alpha }_{\tau }\) and \({\beta }_{\tau },\) have been computed on the smoothed signals \({u}_{\tau }\) and \({v}_{\tau },\) respectively, and the lags at which passages through zero occur, if any, located and stored in the sequences \({S}_{u}\) and \({S}_{v},\) respectively. It is worth to remind that the presence of passages through zero, in the autocorrelation function of a signal \(s,\) denotes oscillation; if \(s\left(t\right)=a\text{sin}\left(2\pi \omega t\right)\) , the autocorrelation is \(\rho \left(\tau \right)=\underset{s\to \infty }{\text{lim}}\frac{1}{s}{\int }_{-s/2}^{s/2}a\text{sin}\left(2\pi \omega t-\tau \right)\cdot a\text{sin}\left(2\pi \omega t\right) dt=\frac{{a}^{2}}{2}\text{cos}\left(2\pi \omega \tau \right)\) , that is a sinusoidal oscillation having the same frequency and with a predictable amplitude. This suggests to use twice the median time distance between consecutive passages through zero as an estimate of the meandering period. Given the sequences \({S}_{u}\) and \({S}_{v}\) , it is then possible to identify their respective medians \({t}_{u}\) and \({t}_{v}\) . In general, it may be \({t}_{u}\ne {t}_{v}\) , and, in this case, the lower is considered, assuming that the low-frequency oscillations occur in direction mostly occurring around the slower-varying direction. In Fig. 1 , the relationship between the filtering time \(\tau\) and the median \(\text{m}\text{i}\text{n}\left({t}_{u},{t}_{v}\right)\) is shown. Discussion According to the definition of “period” of a sinusoidal oscillation, its value is twice the time difference between two subsequent passages through zero; in this paper, a half-period is used instead, in sake of simplicity. The graphs in Fig. 1 show that when \(\tau\) increases, \(\delta t=\text{m}\text{i}\text{n}\left({t}_{u},{t}_{v}\right) increases as well\) . This increase however is not continuous, but occurs step-wise: this suggests that more aggressive smoothing is used, more different oscillation periods emerge, revealing the superposition of low-frequency phenomena characterized by well-defined and separated periods. In Fig. 1 , the plot line for 2016-03-08 12:00–13:00 interrupts at \(\tau =8\text{s}\) . This reflects the fact that the number of passages through zero of the autocorrelation function is zero or one for higher speeds and so the difference between successive passages from 0 is not defined. The reason could be that the filtered signal does not contain oscillating components beyond 1/16s or that no meandering nor other low-frequency phenomena have been detected. The above described method has been coded as an R script (R Core Team, 2023 ), named detect_identify.R , and available in the src directory of a dedicated repository (Favaron, 2024 ). The algorithm devised, an iterated calculation of autocorrelation nested within another external iteration with respect to \(\tau\) , has a complexity \(O\left(mn\text{log}n\right)\) , where \(n\) is the number of data points (about 36000 sonic quadruples in each hourly file) and \(m\) the number of iterations with respect to \(\tau\) . The execution time was reasonable for the paper evaluations (about 2 minutes for each of the four files on the Apple MacBook Pro M1 of one of the authors), but further gains can be achieved by implementing it in modern Fortran using parallel extensions. In case, exploration of multi-years raw data collections from all the SHAKEUP stations may become realistically possible and may constitute the subject of a future work. Declarations Competing Interests Author P.F. is on the board of directors of Servizi Territorio srl and receives no compensation as member of the board of directors. Funding The authors received no financial support for the research, authorship and/or publication of this article. Author Contribution P.F. wrote the main manuscript text; all authors took part in the definition of work and the data processing. All authors reviewed the manuscript. Acknowledgement The authors kindly thank the meteorological office of ARPA Lombardia for providing the data used in this work. Data Availability All data used have been uploaded along with the main manuscript, and are available for inspection along with R code allowing to decode them. References Cava D, Mortarini L, Giostra U, Richiardone R, Anfossi D (2017) A wavelet analysis of low-wind-speed of submeso motions in a nocturnal boundary layer, Q. J. R. Meteorol. Soc. 143, 661-669 Falocchi M, Giovannini M, de Franceschi M, Zardi D (2018) A Refinement of McMillen (1988) Recursive Filter for the Analysis of Atmospheric Turbulence, Boundary Layer Meteorology, 168, 517-523 Favaron P (2024), https://github.com/micrometeo/meander/tree/main McMillen T R (1988) An eddy correlation technique with extended applicability to non-simple terrain, Boundary Layer Meteorology, 43(3), 231-245 Mortarini L, Stefanello M, Degrazia G, Roberti D, Trini-Castelli S, Anfossi D (2016) Characterization of Wind Meandering in Low-Wind-Speed Conditions, Boundary Layer Meteorology, 161, 165-182 R Core Team (2023) R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, https://www.R-project.org/ Additional Declarations Competing interest reported. Author P.F. is on the board of directors of Servizi Territorio srl and receives no compensation as member of the board of directors. Cite Share Download PDF Status: Published Journal Publication published 01 Feb, 2025 Read the published version in Bulletin of Atmospheric Science and Technology → Version 1 posted Editorial decision: Revision requested 17 Jul, 2024 Reviews received at journal 16 Jul, 2024 Reviews received at journal 12 Jun, 2024 Reviewers agreed at journal 04 Jun, 2024 Reviewers agreed at journal 03 Jun, 2024 Reviewers invited by journal 02 Jun, 2024 Editor assigned by journal 28 May, 2024 Submission checks completed at journal 27 May, 2024 First submitted to journal 27 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4482735","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":310345714,"identity":"b847ad87-99d8-4b57-8b5a-dadc18e5603c","order_by":0,"name":"Patrizia Favaron","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYLCCBAY5KKsCiJmZGwioZ2ZsSGAwhnLOQAQIa2GAaWFsA5P4tZiznz/+4AGDgbzB8bMPHxfOq43mbwdq+VGxDacWy55kkMMMDDecSTc2nrnteO6Mw4wNjD1nbuPUYnAArOUP48yGNDZp3m3HchuAWpgZ2/BoOf8YbIv9zP5nQC1zjuXOJ6jlBsRhif0SIFsaanI3ENJiOeOx4YwEA4PkfolnzMY8xw7kbgRqOYjPL+b8iQ8+/qgwsG3jT2N8zFNTlzvv/OGDD35U4HEYEgkCh8HkAZzqURRDQB0+xaNgFIyCUTBCAQAgEVdmqgOpVgAAAABJRU5ErkJggg==","orcid":"","institution":"Servizi Territorio srl","correspondingAuthor":true,"prefix":"","firstName":"Patrizia","middleName":"","lastName":"Favaron","suffix":""},{"id":310345716,"identity":"b666aa8c-2a8f-4fb6-8b40-0c5d8a71a169","order_by":1,"name":"Simone Zintu","email":"","orcid":"","institution":"Università dell’Insubria","correspondingAuthor":false,"prefix":"","firstName":"Simone","middleName":"","lastName":"Zintu","suffix":""},{"id":310345718,"identity":"5d364b73-ec77-44a3-a9b8-849b1f944ec5","order_by":2,"name":"Cristiana Morosini","email":"","orcid":"","institution":"Università dell’Insubria","correspondingAuthor":false,"prefix":"","firstName":"Cristiana","middleName":"","lastName":"Morosini","suffix":""}],"badges":[],"createdAt":"2024-05-27 06:32:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4482735/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4482735/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s42865-025-00089-y","type":"published","date":"2025-02-01T15:57:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58058396,"identity":"89dedb57-d10f-4d3b-b872-8a8a83a4634a","added_by":"auto","created_at":"2024-06-10 14:52:02","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":32881,"visible":true,"origin":"","legend":"\u003cp\u003eMedian time difference vs filter time width; black line: 2016-03-08, 12 to 13; red line: 2024-03-16, 18 to 19; blue line: 2016-03-08-01 10 to 11; green line: 2016-08.01 12 to 13\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4482735/v1/a6a3228b97d9bcddbb3412a6.jpg"},{"id":75351262,"identity":"5a510304-31ba-41a9-8e0d-129aaf35f4da","added_by":"auto","created_at":"2025-02-03 16:08:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":337553,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4482735/v1/8823e1e9-4e9c-44e7-aa2d-d6482e81c761.pdf"}],"financialInterests":"Competing interest reported. Author P.F. is on the board of directors of Servizi Territorio srl and receives no compensation as member of the board of directors.","formattedTitle":"The Efficient Identification of Meandering and other Low-Frequency Phenomena in Raw Ultrasonic Anemometer Data","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMeandering and other low-frequency phenomena not directly attributable to turbulence are known to play an important role in the dispersion of tracers (for example odours) emitted by a point source, thus detecting their presence in ultrasonic anemometer elementary data sets and identifying their time evolution have a great application value.\u003c/p\u003e \u003cp\u003eLow-frequency phenomena may occur at a time scale between 1s and 60s, much smaller than the time step used in air quality and odour modelling (600s to 3600s), and are conglobated in turbulence, possibly overestimating its magnitude and, consequently, underestimating the modelled ground concentrations.\u003c/p\u003e \u003cp\u003eDetection and identification of low-frequency phenomena are two distinct aspects, their focus being, respectively, determining whether a low-frequency component may be found in a data set and estimating its time evolution.\u003c/p\u003e \u003cp\u003eDetection has been extensively investigated (Cava et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Mortarini et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) and various methods have been proposed: among all, the wavelet analysis and the study of oscillations in autocorrelation functions are worthy to be cited.\u003c/p\u003e \u003cp\u003eIn this paper, a combined detection-and-identification method is proposed based on the iterative application of the recursive filter presented in Falocchi et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), followed by autocorrelation analysis, and results of the method applied to a sample of data collected by the micro-meteorological surface station located at Parco Nord, Cinisello Balsamo (part of the SHAKEUP network by Lombardy Environmental Protection Agency) are shown. The associated algorithms have been distributed as open-source code (Favaron, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e"},{"header":"Methods and results","content":"\u003cp\u003eRaw data, consisting of quadruples \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(u,v,w,t\\right)\\)\u003c/span\u003e\u003c/span\u003e collected continuously by the station sonic anemometer at a nominal rate of 20Hz and 2 out of 1 averaging, are automatically organized and archived in hourly files, four of which have been selected for 2016-03-08 12:00\u0026ndash;13:00 and 18:00\u0026ndash;19:00 and for 2016-08-01 10:00\u0026ndash;11:00 and 23:00\u0026ndash;24:00. All the four selected hours, expressed in Central Europe Time zone, contain the 100% of sonic quadruples labelled as plausible by the anemometer.\u003c/p\u003e \u003cp\u003eProcessing was executed using the procedures in a dedicated accessible open-source repository (Favaron, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); focus was placed on meandering and then the two horizontal wind components \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(u,v\\)\u003c/span\u003e\u003c/span\u003e: the vertical wind component and sonic temperature have been neglected.\u003c/p\u003e \u003cp\u003eHourly data have been processed using a two-phase iterative process. In the first phase, the hourly signals have been replaced by the residual after applying the filter described in Falocchi et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), that is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({u}_{r}=u-{f}_{\\tau =900\\text{s}}\\left(u\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}_{r}=v-{f}_{\\tau =900\\text{s}}\\left(v\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{\\tau }\\left(s\\right)\\)\u003c/span\u003e\u003c/span\u003e is the filter applied to the generic signal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s\\)\u003c/span\u003e\u003c/span\u003e; this high-pass filtering operation is done to remove changes occurring at time scales longer than or equal to 900s (15 minutes), plausibly much longer than meandering and other interesting low-frequency phenomena.\u003c/p\u003e \u003cp\u003eThe so obtained residuals are then filtered iteratively, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau =1,\\dots ,60\\)\u003c/span\u003e\u003c/span\u003e, obtaining the smoothed signals \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({u}_{\\tau }={f}_{\\tau }\\left({u}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}_{\\tau }={f}_{\\tau }\\left({v}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAutocorrelations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }_{\\tau }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{\\tau },\\)\u003c/span\u003e\u003c/span\u003e have been computed on the smoothed signals \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({u}_{\\tau }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({v}_{\\tau },\\)\u003c/span\u003e\u003c/span\u003e respectively, and the lags at which passages through zero occur, if any, located and stored in the sequences \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}_{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}_{v},\\)\u003c/span\u003e\u003c/span\u003e respectively.\u003c/p\u003e \u003cp\u003eIt is worth to remind that the presence of passages through zero, in the autocorrelation function of a signal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s,\\)\u003c/span\u003e\u003c/span\u003e denotes oscillation; if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s\\left(t\\right)=a\\text{sin}\\left(2\\pi \\omega t\\right)\\)\u003c/span\u003e\u003c/span\u003e, the autocorrelation is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho \\left(\\tau \\right)=\\underset{s\\to \\infty }{\\text{lim}}\\frac{1}{s}{\\int }_{-s/2}^{s/2}a\\text{sin}\\left(2\\pi \\omega t-\\tau \\right)\\cdot a\\text{sin}\\left(2\\pi \\omega t\\right) dt=\\frac{{a}^{2}}{2}\\text{cos}\\left(2\\pi \\omega \\tau \\right)\\)\u003c/span\u003e\u003c/span\u003e, that is a sinusoidal oscillation having the same frequency and with a predictable amplitude. This suggests to use twice the median time distance between consecutive passages through zero as an estimate of the meandering period.\u003c/p\u003e \u003cp\u003eGiven the sequences \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}_{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({S}_{v}\\)\u003c/span\u003e\u003c/span\u003e, it is then possible to identify their respective medians \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{u}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{v}\\)\u003c/span\u003e\u003c/span\u003e. In general, it may be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{u}\\ne {t}_{v}\\)\u003c/span\u003e\u003c/span\u003e, and, in this case, the lower is considered, assuming that the low-frequency oscillations occur in direction mostly occurring around the slower-varying direction.\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the relationship between the filtering time \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e and the median \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{m}\\text{i}\\text{n}\\left({t}_{u},{t}_{v}\\right)\\)\u003c/span\u003e\u003c/span\u003e is shown.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAccording to the definition of \u0026ldquo;period\u0026rdquo; of a sinusoidal oscillation, its value is twice the time difference between two subsequent passages through zero; in this paper, a half-period is used instead, in sake of simplicity.\u003c/p\u003e \u003cp\u003eThe graphs in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e show that when \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e increases, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta t=\\text{m}\\text{i}\\text{n}\\left({t}_{u},{t}_{v}\\right) increases as well\\)\u003c/span\u003e\u003c/span\u003e. This increase however is not continuous, but occurs step-wise: this suggests that more aggressive smoothing is used, more different oscillation periods emerge, revealing the superposition of low-frequency phenomena characterized by well-defined and separated periods.\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the plot line for 2016-03-08 12:00\u0026ndash;13:00 interrupts at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau =8\\text{s}\\)\u003c/span\u003e\u003c/span\u003e. This reflects the fact that the number of passages through zero of the autocorrelation function is zero or one for higher speeds and so the difference between successive passages from 0 is not defined. The reason could be that the filtered signal does not contain oscillating components beyond 1/16s or that no meandering nor other low-frequency phenomena have been detected.\u003c/p\u003e \u003cp\u003eThe above described method has been coded as an R script (R Core Team, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), named \u003cem\u003edetect_identify.R\u003c/em\u003e, and available in the \u003cem\u003esrc\u003c/em\u003e directory of a dedicated repository (Favaron, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The algorithm devised, an iterated calculation of autocorrelation nested within another external iteration with respect to\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e, has a complexity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(O\\left(mn\\text{log}n\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e is the number of data points (about 36000 sonic quadruples in each hourly file) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(m\\)\u003c/span\u003e\u003c/span\u003e the number of iterations with respect to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e. The execution time was reasonable for the paper evaluations (about 2 minutes for each of the four files on the Apple MacBook Pro M1 of one of the authors), but further gains can be achieved by implementing it in modern Fortran using parallel extensions. In case, exploration of multi-years raw data collections from all the SHAKEUP stations may become realistically possible and may constitute the subject of a future work.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthor P.F. is on the board of directors of Servizi Territorio srl and receives no compensation as member of the board of directors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors received no financial support for the research, authorship and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eP.F. wrote the main manuscript text; all authors took part in the definition of work and the data processing. All authors reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors kindly thank the meteorological office of ARPA Lombardia for providing the data used in this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data used have been uploaded along with the main manuscript, and are available for inspection along with R code allowing to decode them.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCava D, Mortarini L, Giostra U, Richiardone R, Anfossi D (2017) A wavelet analysis of low-wind-speed of submeso motions in a nocturnal boundary layer, Q. J. R. Meteorol. Soc. 143, 661-669\u003c/li\u003e\n\u003cli\u003eFalocchi M, Giovannini M, de Franceschi M, Zardi D (2018) A Refinement of McMillen (1988) Recursive Filter for the Analysis of Atmospheric Turbulence, Boundary Layer Meteorology, 168, 517-523\u003c/li\u003e\n\u003cli\u003eFavaron P (2024), https://github.com/micrometeo/meander/tree/main \u003c/li\u003e\n\u003cli\u003eMcMillen T R (1988) An eddy correlation technique with extended applicability to non-simple terrain, Boundary Layer Meteorology, 43(3), 231-245\u003c/li\u003e\n\u003cli\u003eMortarini L, Stefanello M, Degrazia G, Roberti D, Trini-Castelli S, Anfossi D (2016) Characterization of Wind Meandering in Low-Wind-Speed Conditions, Boundary Layer Meteorology, 161, 165-182\u003c/li\u003e\n\u003cli\u003eR Core Team (2023) R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, https://www.R-project.org/ \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-atmospheric-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bast","sideBox":"Learn more about [Bulletin of Atmospheric Science and Technology](http://www.springer.com/journal/42865)","snPcode":"42865","submissionUrl":"https://submission.nature.com/new-submission/42865/3","title":"Bulletin of Atmospheric Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4482735/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4482735/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis short conference paper shows a new experimental method for the detection and identification of meandering and other low-frequency components in raw data from three-axial ultrasonic anemometers and other high resolution, high sampling-rate three-dimensional wind sensors.\u003c/p\u003e\n\u003cp\u003eThe proposed method is a combination of autocorrelation-based detection and delay-free recursive filtering, both described in recent published works.\u003c/p\u003e\n\u003cp\u003eThe results of the application of the described method to a sample of hourly raw data files are also shown.\u003c/p\u003e\n\u003cp\u003eThe method can be used as a building block for eddy covariance and other data processing procedures as well as in all the situations where very short time scales (about 10s) are relevant, such as in odour or toxic chemical dispersion field.\u003c/p\u003e","manuscriptTitle":"The Efficient Identification of Meandering and other Low-Frequency Phenomena in Raw Ultrasonic Anemometer Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-10 14:51:58","doi":"10.21203/rs.3.rs-4482735/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision 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