{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T11:19:24Z","timestamp":1774351164195,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T00:00:00Z","timestamp":1671667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Most time series from real-world processes are stained with noise. Therefore, much attention should be paid to data noise removal techniques. In this study, we use the family of biorthogonal wavelet, high-pass, and low-pass filters, to investigate the power of the wavelet method in removing noise from time series data. Using the wavelet discrete transformation, the variability of precipitation and sea surface temperature is analyzed for a southern region of the Caspian Sea. At each stage of decomposition, the previous wave is decomposed into two waves. In this research, the SST and precipitation data are decomposed into several levels based on discrete wavelet transformation. In each level of decomposition, the previous wave is decomposed into two waves. This can be done many times and at each stage, reducing the amount of data. This method is reversible, and the original wave can be reconstructed using the decomposed values. In the study of discrete wavelet transforms, it was observed that the analysis based on wavelets leads to more accurate results. The reconstruction error in the proposed method is shown to be very small.<\/jats:p>","DOI":"10.3390\/axioms12010010","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T01:42:13Z","timestamp":1671759733000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Investigation and Analysis of Sea Surface Temperature and Precipitation of the Southern Caspian Sea Using Wavelet Analysis"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1242-4989","authenticated-orcid":false,"given":"Mahboubeh","family":"Molavi-Arabshahi","sequence":"first","affiliation":[{"name":"School of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2121-1520","authenticated-orcid":false,"given":"Jafar","family":"Azizpour","sequence":"additional","affiliation":[{"name":"Iranian National Institute for Oceanography and Atmospheric Science, No. 3, West Fatemi Avenue, Etemadzadeh, Tehran 14118-13389, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"Omid","family":"Nikan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, Iran"}]},{"given":"Abdolmajid","family":"Naderi Beni","sequence":"additional","affiliation":[{"name":"Iranian National Institute for Oceanography and Atmospheric Science, No. 3, West Fatemi Avenue, Etemadzadeh, Tehran 14118-13389, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6039","DOI":"10.1002\/joc.6564","article-title":"Wind variability over the Caspian Sea, its impact on Caspian seawater level and link with ENSO","volume":"40","author":"Arpe","year":"2020","journal-title":"Int. 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