{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:46:13Z","timestamp":1760121973906,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,5]],"date-time":"2023-02-05T00:00:00Z","timestamp":1675555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research Program of China","award":["2017YFA0604100","B220201024","41606021","QNHX2120"],"award-info":[{"award-number":["2017YFA0604100","B220201024","41606021","QNHX2120"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2017YFA0604100","B220201024","41606021","QNHX2120"],"award-info":[{"award-number":["2017YFA0604100","B220201024","41606021","QNHX2120"]}]},{"name":"National Science Foundation of China","award":["2017YFA0604100","B220201024","41606021","QNHX2120"],"award-info":[{"award-number":["2017YFA0604100","B220201024","41606021","QNHX2120"]}]},{"name":"Open Fund of State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography","award":["2017YFA0604100","B220201024","41606021","QNHX2120"],"award-info":[{"award-number":["2017YFA0604100","B220201024","41606021","QNHX2120"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The ocean behaves as a typical multiscale fractal structure, whose dynamic and thermal variabilities extend over a wide range of spatial scales, r, spanning from 10\u22123 to 107 m. Studying the statistical characteristics of multiscale fractal structures is crucial to understanding the interactions and energy cascade processes between different spatial scales. Remote sensing data are one of the best choices for revealing these statistical characteristics. This work analyzes the multiscale (1\u20131000 km) fractal structures of sea surface temperature (SST) from the Level-2+ (L2P) satellite orbit Visible Infrared Imaging Radiometer Suite (VIIRS) products over the Kuroshio Extension (KE) region (145\u00b0E\u2013160\u00b0W, 20\u00b0N\u201350\u00b0N), using a conventional method (second-order structure function, D(r)) and a newly developed statistical method (spatial variance, V(r)). The results show that both the power-law distribution slopes of D(r) and V(r) are close to 2\/3, which is equivalent to the \u22125\/3 wavenumber spectrum. V(r) is found to be more robust when depicting the fractal structure and variance density, V\u2019(r), compared with D(r). V\u2019(r) is slightly larger at the mesoscale (50\u2013150 km) than at the large scale (higher than 150 km) and is much smaller than that at the submesoscale (smaller than 50 km). Additionally, V\u2019(r) has an indiscernible diurnal variation but remarkable seasonal and latitudinal variations. For the seasonal variability, the maximum V\u2019(r) appears in winter at the large scale and mesoscale, and gradually shifts towards spring at the submesoscale, which implies that a forward energy cascade process may occur during this period. The maximum of the latitude-dependent V\u2019(r) appears around 40\u00b0N for all the scales. It is consistent with the latitude of the strongest background SST gradient, indicating that the background SST front is the main source of the strong SST multiscale spatial variabilities over the KE region. This work benefits the application of other high-resolution remote sensing data in this research field, including the forthcoming Surface Water Ocean Topography (SWOT) satellite product.<\/jats:p>","DOI":"10.3390\/rs15040881","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T05:29:05Z","timestamp":1675661345000},"page":"881","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Statistical Characteristics of the Multiscale SST Fractal Structure over the Kuroshio Extension Region Using VIIRS Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6048-0059","authenticated-orcid":false,"given":"Kai","family":"Yu","sequence":"first","affiliation":[{"name":"Key Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing 210024, China"},{"name":"State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310005, China"},{"name":"College of Oceanography, Hohai University, Nanjing 210024, China"}]},{"given":"Changming","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0365-1496","authenticated-orcid":false,"given":"Jin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Xuhua","family":"Cheng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing 210024, China"},{"name":"College of Oceanography, Hohai University, Nanjing 210024, China"}]},{"given":"Yi","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310005, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,5]]},"reference":[{"key":"ref_1","first-page":"299","article-title":"The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers","volume":"30","author":"Kolmogrov","year":"1941","journal-title":"Dokl. Akad. Nauk SSSR."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1063\/1.1762301","article-title":"Inertial ranges in two-dimensional turbulence","volume":"10","author":"Kraichnan","year":"1967","journal-title":"Phys. Fluids."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1175\/1520-0469(1971)028<1087:GT>2.0.CO;2","article-title":"Geostrophic turbulence","volume":"28","author":"Charney","year":"1971","journal-title":"J. Atmos. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1175\/1520-0469(1978)035<0774:UPVFPI>2.0.CO;2","article-title":"Uniform potential vorticity flow. Part I: Theory of wave interactions and two-dimensional turbulence","volume":"35","author":"Blumen","year":"1978","journal-title":"J. Atmos. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1357\/002224098765213595","article-title":"Three-dimensional stirring of thermohaline fronts","volume":"56","author":"Klein","year":"1998","journal-title":"J. Mar. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1175\/1520-0469(1979)036<1950:EFALIR>2.0.CO;2","article-title":"Evidence for a k-5\/3 law inertial range in mesoscale two-dimensional turbulence","volume":"36","author":"Gage","year":"1979","journal-title":"J. Atmos. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"950","DOI":"10.1175\/1520-0469(1985)042<0950:ACOAWS>2.0.CO;2","article-title":"A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft","volume":"42","author":"Nastrom","year":"1985","journal-title":"J. Atmos. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1017\/S0022112099004851","article-title":"Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence?","volume":"388","author":"Lindborg","year":"1999","journal-title":"J. Fluid Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1175\/JPO2771.1","article-title":"Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry","volume":"35","author":"Scott","year":"2005","journal-title":"J. Phys. Oceanogr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2456","DOI":"10.1175\/JPO-D-13-063.1","article-title":"Interpreting energy and tracer spectra of upper-ocean turbulence in the submesoscale range (1\u2013200 km)","volume":"43","author":"Callies","year":"2013","journal-title":"J. Phys. Oceanogr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1175\/JPO-D-14-0023.1","article-title":"Estimates of ocean macroturbulence: Structure function and spectral slope from Argo profiling floats","volume":"45","author":"McCaffrey","year":"2015","journal-title":"J. Phys. Oceanogr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1109\/TGRS.2013.2247768","article-title":"Early on- orbit performance of the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (S-NPP) satellite","volume":"52","author":"Cao","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1175\/BAMS-87-2-191","article-title":"The NPOESS VIIRS day\/night visible sensor","volume":"87","author":"Lee","year":"2010","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2256","DOI":"10.1175\/2008JPO3810.1","article-title":"Mesoscale to submesoscale transition in the California Current System. Part III: Energy balance and flux","volume":"38","author":"Capet","year":"2008","journal-title":"J. Phys. Oceanogr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1175\/JPO-D-14-0071.1","article-title":"Seasonal mesoscale and submesoscale eddy variability along the North Pacific Subtropical Countercurrent","volume":"44","author":"Qiu","year":"2014","journal-title":"J. Phys. Oceanogr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6862","DOI":"10.1038\/ncomms7862","article-title":"Seasonality in submesoscale turbulence","volume":"6","author":"Callies","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"11304","DOI":"10.1002\/2016GL071349","article-title":"Seasonality of submesoscale dynamics in the Kuroshio Extension","volume":"43","author":"Rocha","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1007\/s10236-017-1083-y","article-title":"Regionality and seasonality of submesoscale and mesoscale turbulence in the North Pacific Ocean","volume":"67","author":"Sasaki","year":"2017","journal-title":"Ocean Dynam."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"44011","DOI":"10.1038\/srep44011","article-title":"Observed and simulated submesoscale vertical pump of an anticyclonic eddy in the South China Sea","volume":"7","author":"Zhong","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1002\/2014JC010239","article-title":"Spatial variances of wind fields and their relation to second-order structure functions and spectra","volume":"120","author":"Vogelzang","year":"2015","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4482","DOI":"10.1002\/2016JC012404","article-title":"Turbulent kinetic energy of the ocean winds over the Kuroshio Extension from QuikSCAT winds (1999\u20132009)","volume":"122","author":"Yu","year":"2017","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5644","DOI":"10.1175\/2010JCLI3346.1","article-title":"Western boundary currents and frontal air-sea interaction: Gulf stream and Kuroshio extension","volume":"23","author":"Kelly","year":"2010","journal-title":"J. Clim."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1175\/2009JCLI3064.1","article-title":"The signature of the midlatitude tropospheric storm tracks in the surface winds","volume":"23","author":"Booth","year":"2010","journal-title":"J. Clim."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2641","DOI":"10.1029\/JC081i015p02641","article-title":"Eddy energy in the oceans","volume":"81","author":"Wyrtki","year":"1976","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1827","DOI":"10.1175\/1520-0485(1995)025<1827:VAEOTK>2.0.CO;2","article-title":"Variability and energetics of the Kuroshio Extension and its recirculation gyre from the first two-year TOPEX data","volume":"25","author":"Qiu","year":"1995","journal-title":"J. Phys. Oceanogr."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e2020GL087388","DOI":"10.1029\/2020GL087388","article-title":"The seasonality of submesoscale energy production, content, and cascade","volume":"47","author":"Dong","year":"2020","journal-title":"Geophys. Res. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1002\/qj.49709038520","article-title":"Ratio of spectrum and structure-function constants in the inertial subrange","volume":"90","author":"Webb","year":"1964","journal-title":"Quart. J. Roy. Meteor. Soc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1175\/1520-0469(1992)049<0128:TESOFT>2.0.CO;2","article-title":"The energy spectrum of fronts: Time evolution of shocks in Burgers\u2019 equation","volume":"49","author":"Boyd","year":"1992","journal-title":"J. Atmos. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1175\/JPO-D-19-0030.1","article-title":"The vertical structure of open-ocean submesoscale variability during a full seasonal cycle","volume":"50","author":"Erickson","year":"2020","journal-title":"J. Phys. Oceanogr."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1970","DOI":"10.1175\/JCLI3793.1","article-title":"Decadal variability in the Kuroshio\u2013Oyashio extension simulated in an eddy-resolving OGCM","volume":"19","author":"Nonaka","year":"2006","journal-title":"J. Clim."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1175\/JPO-D-18-0159.1","article-title":"Mesoscale SST dynamics in the Kuroshio\u2013Oyashio extension region","volume":"49","author":"Jing","year":"2019","journal-title":"J. Phys. Oceanogr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1029\/GL009i005p00575","article-title":"A universal spectrum of buoyancy waves in the atmosphere","volume":"9","author":"VanZandt","year":"1982","journal-title":"Geophys. Res. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1175\/1520-0469(1983)040<0749:STATMV>2.0.CO;2","article-title":"Stratified turbulence and the mesoscale variability of the atmosphere","volume":"40","author":"Lilly","year":"1983","journal-title":"J. Atmos. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1002\/qj.49712354209","article-title":"Balanced mesoscale motion and stratified turbulence forced by convection","volume":"123","author":"Vallis","year":"1997","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"10223","DOI":"10.1029\/2000JD900814","article-title":"Horizontal velocity structure functions in the upper troposphere and lower stratosphere: 1. Observations","volume":"106","author":"Cho","year":"2001","journal-title":"J. Geophys. Res."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"D18110","DOI":"10.1029\/2008JD009785","article-title":"Mesoscale spectrum of atmospheric motions investigated in a very fine resolution global general circulation model","volume":"113","author":"Hamilton","year":"2008","journal-title":"J. Geophys. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1175\/JAS-D-11-0347.1","article-title":"Mesoscale energy spectra of moist baroclinic waves","volume":"70","author":"Waite","year":"2013","journal-title":"J. Atmos. Sci."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1126\/science.1201515","article-title":"Enhanced turbulence and energy dissipation at ocean fronts","volume":"332","author":"Lee","year":"2011","journal-title":"Science"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"24349","DOI":"10.1038\/srep24349","article-title":"Observed 3D structure, generation, and dissipation of oceanic mesoscale eddies in the South China Sea","volume":"6","author":"Zhang","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_40","first-page":"13","article-title":"ECCO2: High resolution global ocean and sea ice data synthesis","volume":"31","author":"Menemenlis","year":"2008","journal-title":"Mercator Ocean Quart. Newsl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3653","DOI":"10.5194\/gmd-8-3071-2015","article-title":"ECCO version 4: An integrated framework for non-linear inverse modeling and global ocean state estimation","volume":"8","author":"Forget","year":"2015","journal-title":"Geosci. Model Dev."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/881\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:24:52Z","timestamp":1760120692000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/881"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,5]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["rs15040881"],"URL":"https:\/\/doi.org\/10.3390\/rs15040881","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,2,5]]}}}