{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T23:26:42Z","timestamp":1767914802569,"version":"3.49.0"},"reference-count":55,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T00:00:00Z","timestamp":1661990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT) I.P.\/MCTES","doi-asserted-by":"publisher","award":["UIDB\/50019\/2020"],"award-info":[{"award-number":["UIDB\/50019\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The calculation of the tropopause height is crucial to the investigation of fundamental interactions between the troposphere and stratosphere, playing an essential role in areas such as climatology, geodesy, geophysics, ecology, and aeronautics. Since the troposphere and stratosphere have many distinct features, it is possible to define the boundary between them using different variables, such as temperature lapse rate, potential vorticity and chemical concentrations. However, according to the chosen variable, different tropopause definitions are created, each one with some limitations. Using 41 years of European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) data, we examined the variability of the tropopause for the north and south hemispheres and developed two models, both based on blending the potential vorticity and thermal tropopauses. One model (based on a sigmoid function, named STH) depends only on latitude and day of the year, while the other model (based on bilinear interpolation, named BTH) requires an additional look-up table. In order to account for the different behaviors of the tropopauses in the north and south hemispheres, we estimated two sets of model coefficients (one for each hemisphere). When compared against a benchmark of estimated tropopause heights during three years of radiosonde data, we obtained an average RMSE for the differences of 0.88 km for the STH model and 0.67 km for the BTH model. A similar comparison for alternative models available in the literature shows that the new models have superior performance and represent a significant improvement in tropopause height determination.<\/jats:p>","DOI":"10.3390\/rs14174303","type":"journal-article","created":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T03:55:38Z","timestamp":1662004538000},"page":"4303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Global Empirical Models for Tropopause Height Determination"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8027-2142","authenticated-orcid":false,"given":"Pedro","family":"Mateus","sequence":"first","affiliation":[{"name":"Instituto Dom Luiz, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7362-8996","authenticated-orcid":false,"given":"Virg\u00edlio B.","family":"Mendes","sequence":"additional","affiliation":[{"name":"Instituto Dom Luiz, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1700-6607","authenticated-orcid":false,"given":"Carlos A.L.","family":"Pires","sequence":"additional","affiliation":[{"name":"Instituto Dom Luiz, Faculdade de Ci\u00eancias, Universidade de Lisboa, 1749-016 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,1]]},"reference":[{"key":"ref_1","unstructured":"Wallace, J., and Hobbs, P. (2006). Atmospheric Science: An Introductory Survey, Academic Press. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1029\/96GL01722","article-title":"On the Correlation between Tropopause Pressure and Ozone above Central Europe","volume":"23","author":"Hoinka","year":"1996","journal-title":"Geophys. Res. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"19183","DOI":"10.1029\/98JD01929","article-title":"Correlations between Tropopause Height and Total Ozone: Implications for Long-Term Changes","volume":"103","author":"Steinbrecht","year":"1998","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21104","DOI":"10.1029\/2004JD005075","article-title":"Identification of Anthropogenic Climate Change Using a Second-Generation Reanalysis","volume":"109","author":"Santer","year":"2004","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4745","DOI":"10.5194\/amt-12-4745-2019","article-title":"Ozone Profile Climatology for Remote Sensing Retrieval Algorithms","volume":"12","author":"Yang","year":"2019","journal-title":"Atmos. Meas. Tech."},{"key":"ref_6","first-page":"1091","article-title":"Passenger Aircraft Project CARIBIC 1997\u20132002, Part I: The Extratropical Chemical Tropopause","volume":"4","author":"Zahn","year":"2004","journal-title":"Atmos. Chem. Phys. Discuss."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1002\/qj.49712253207","article-title":"A Comparison of Ozone and Thermal Tropopause Heights and the Impact of Tropopause Definition on Quantifying the Ozone Content of the Troposphere","volume":"122","author":"Bethan","year":"1996","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"25695","DOI":"10.1029\/98JD02243","article-title":"Comparisons of Ozone Measurements from the MOZAIC Airborne Program and the Ozone Sounding Network at Eight Locations","volume":"103","author":"Thouret","year":"1998","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1109\/TGRS.2013.2259632","article-title":"Variations of the Tropopause over Different Latitude Bands Observed Using COSMIC Radio Occultation Bending Angles","volume":"52","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3947","DOI":"10.5194\/amt-7-3947-2014","article-title":"Characteristics of Tropopause Parameters as Observed with GPS Radio Occultation","volume":"7","author":"Rieckh","year":"2014","journal-title":"Atmos. Meas. Tech."},{"key":"ref_11","first-page":"301","article-title":"A Novel Tool for the Determination of Tropopause Heights by Using GNSS Radio Occultation Data","volume":"7","author":"Vespe","year":"2017","journal-title":"Atmos. Clim. Sci."},{"key":"ref_12","unstructured":"WMO World Meteorological Organization (WMO): Geneva, Switzerland, 1957."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.1029\/2003GL018240","article-title":"Determining the Tropopause Height from Gridded Data","volume":"30","author":"Reichler","year":"2003","journal-title":"Geophys. Res. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1002\/qj.951","article-title":"A Global Blended Tropopause Based on ERA Data. Part I: Climatology","volume":"138","author":"Wilcox","year":"2012","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1579","DOI":"10.1002\/qj.49712454911","article-title":"The Tropical Tropopause","volume":"124","author":"Highwood","year":"1998","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_16","first-page":"299","article-title":"Thermal versus Dynamical Tropopause in Upper-Tropospheric Balanced Flow Anomalies","volume":"126","author":"Wirth","year":"2000","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3117","DOI":"10.1175\/1520-0442(2001)014<3117:TTITPR>2.0.CO;2","article-title":"The Tropopause in the Polar Regions","volume":"14","author":"Hoinka","year":"2001","journal-title":"J. Clim."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7857","DOI":"10.1029\/2000JD900837","article-title":"Climatological Characteristics of the Tropical Tropopause as Revealed by Radiosondes","volume":"106","author":"Seidel","year":"2001","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"D21101","DOI":"10.1029\/2006JD007363","article-title":"Variability and Trends in the Global Tropopause Estimated from Radiosonde Data","volume":"111","author":"Seidel","year":"2006","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1175\/1520-0469(1997)054<0869:GTOTFT>2.0.CO;2","article-title":"GCM Tests of Theories for the Height of the Tropopause","volume":"54","author":"Thuburn","year":"1997","journal-title":"J. Atmos. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1175\/1520-0469(1955)012<0226:ASOACT>2.0.CO;2","article-title":"A Study of a Characteristic Tpye of Upper-Level Frontogenesis","volume":"12","author":"Reed","year":"1955","journal-title":"J. Meteorol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1175\/1520-0469(1968)025<0502:STEBOR>2.0.CO;2","article-title":"Stratospheric-Tropospheric Exchange Based on Radioactivity, Ozone and Potential Vorticity","volume":"25","author":"Danielsen","year":"1968","journal-title":"J. Atmos. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1175\/1520-0493(1978)106<1100:FEOTMA>2.0.CO;2","article-title":"Further Evidence of the Mesoscale and Turbulent Structure of Upper Level Jet Stream\u2013Frontal Zone Systems","volume":"106","author":"Shapiro","year":"1978","journal-title":"Mon. Weather Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1175\/1520-0469(1980)037<0994:TMWTFA>2.0.CO;2","article-title":"Turbulent Mixing within Tropopause Folds as a Mechanism for the Exchange of Chemical Constituents between the Stratosphere and Troposphere","volume":"37","author":"Shapiro","year":"1980","journal-title":"J. Atmos. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"D18102","DOI":"10.1029\/2006JD008295","article-title":"A Lagrangian Perspective of the Tropopause and the Ventilation of the Lowermost Stratosphere","volume":"112","author":"Berthet","year":"2007","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1029\/2010JD014343","article-title":"Dynamical Tropopause Based on Isentropic Potential Vorticity Gradients","volume":"116","author":"Kunz","year":"2011","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_27","unstructured":"WMO (1986). Atmospheric Ozone 1985: Global Ozone Research and Monitoring Report, World Meteorological Organization (WMO)."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1816","DOI":"10.1175\/1520-0493(1991)119<1816:GOTA>2.0.CO;2","article-title":"Global Objective Tropopause Analysis","volume":"119","author":"Hoerling","year":"1991","journal-title":"Mon. Weather Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"808","DOI":"10.3103\/S1068373913120029","article-title":"The Tropopause: Variety of Definitions and Modern Approaches to Identification","volume":"38","author":"Ivanova","year":"2013","journal-title":"Russ. Meteorol. Hydrol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","article-title":"The ERA5 Global Reanalysis","volume":"146","author":"Hersbach","year":"2020","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_31","unstructured":"Lanyi, G. (1984). Tropospheric delay effects in radio interferometry. TDA Prog. Rep., 42\u201378."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1029\/RS020i006p01593","article-title":"Geodesy by Radio Interferometry: Effects of Atmospheric Modeling Errors on Estimates of Baseline Length","volume":"20","author":"Davis","year":"1985","journal-title":"Radio Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1038\/ngeo1733","article-title":"Physical Processes in the Tropical Tropopause Layer and Their Roles in a Changing Climate","volume":"6","author":"Randel","year":"2013","journal-title":"Nat. Geosci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1175\/JAS-D-14-0216.1","article-title":"Variability of Zonal Mean Tropical Temperatures Derived from a Decade of GPS Radio Occultation Data","volume":"72","author":"Randel","year":"2015","journal-title":"J. Atmos. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"29537","DOI":"10.1038\/srep29537","article-title":"Decadal Variability of Tropical Tropopause Temperature and Its Relationship to the Pacific Decadal Oscillation","volume":"6","author":"Wang","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1002\/2017JD027120","article-title":"The Effects of Deep Convection on Regional Temperature Structure in the Tropical Upper Troposphere and Lower Stratosphere","volume":"123","author":"Johnston","year":"2018","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3433","DOI":"10.1175\/JAS-D-18-0032.1","article-title":"Determination of Best Tropopause Definition for Convective Transport Studies","volume":"75","author":"Maddox","year":"2018","journal-title":"J. Atmos. Sci."},{"key":"ref_38","unstructured":"Hersbach, H., Bell, B., Berrisford, P., Hor\u00e1nyi, A., Sabater, J.M., Nicolas, J., Radu, R., Schepers, D., Simmons, A., and Soci, C. (2019). Global Reanalysis: Goodbye ERA-Interim, Hello ERA5. ECMWF Newsl., 17\u201324."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"ACL 1-1","DOI":"10.1029\/2002JD002258","article-title":"Behavior of Tropopause Height and Atmospheric Temperature in Models, Reanalyses, and Observations: Decadal Changes","volume":"108","author":"Santer","year":"2003","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_40","unstructured":"Martin, J. (2006). Mid-Latitude Atmospheric Dynamics: A First Course, Wiley."},{"key":"ref_41","unstructured":"Buja, L.E. (1993). CCM Processor Users\u2019 Guide (UNICOS Version), University Corporation for Atmospheric Research. No. NCAR\/TN-384+IA."},{"key":"ref_42","unstructured":"Hinze, W.J., Von Frese, R.R.B., and Saad, A.H. (2010). Gravity and Magnetic Exploration: Principles, Practices, and Applications, Cambridge University Press."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3303","DOI":"10.1175\/1520-0493(1998)126<3303:SOTGTP>2.0.CO;2","article-title":"Statistics of the Global Tropopause Pressure","volume":"126","author":"Hoinka","year":"1998","journal-title":"Mon. Weather Rev."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2248","DOI":"10.1175\/1520-0493(1999)127<2248:THAWAT>2.0.CO;2","article-title":"Temperature, Humidity, and Wind at the Global Tropopause","volume":"127","author":"Hoinka","year":"1999","journal-title":"Mon. Weather Rev."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1126\/science.1084123","article-title":"Contributions of Anthropogenic and Natural Forcing to Recent Tropopause Height Changes","volume":"301","author":"Santer","year":"2003","journal-title":"Science"},{"key":"ref_46","unstructured":"Ackerman, S.A., and Knox, J.A. (2013). Meteorology: Understanding the Atmosphere, Jones & Bartlett Learning. [4th ed.]."},{"key":"ref_47","unstructured":"Mendes, V.B. (1999). Modeling the Neutral-Atmospheric Propagation Delay in Radiometric Space Techniques, UNB Geodesy and Geomatics Engineering. Technical Report."},{"key":"ref_48","unstructured":"Snedecor, G.W., and William, G. (1989). Cochran Statistical Methods, Iowa State University Press. [8th ed.]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1002\/qj.49712656515","article-title":"Properties of the Arctic Tropopause","volume":"126","author":"Highwood","year":"2000","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"10119","DOI":"10.1029\/2006JD008087","article-title":"Tropopause Height and Zonal Wind Response to Global Warming in the IPCC Scenario Integrations","volume":"112","author":"Lorenz","year":"2007","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3227","DOI":"10.1029\/95JB03048","article-title":"Global Mapping Functions for the Atmosphere Delay at Radio Wavelengths","volume":"101","author":"Niell","year":"1996","journal-title":"J. Geophys. Res. B Solid Earth"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"53-1","DOI":"10.1029\/2001GL014394","article-title":"Improved Mapping Functions for Atmospheric Refraction Correction in SLR","volume":"29","author":"Mendes","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Seber, G.A.F., and Wild, C.J. (2003). Nonlinear Regression, Wiley.","DOI":"10.1002\/9780471722199"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1175\/JCLI3594.1","article-title":"Overview of the Integrated Global Radiosonde Archive","volume":"19","author":"Durre","year":"2006","journal-title":"J. Clim."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1724","DOI":"10.1175\/JAS-D-13-0137.1","article-title":"On the Role of Planetary-Scale Waves in the Abrupt Seasonal Transition of the Northern Hemisphere General Circulation","volume":"71","author":"Shaw","year":"2014","journal-title":"J. Atmos. Sci."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/17\/4303\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:21:29Z","timestamp":1760142089000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/17\/4303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,1]]},"references-count":55,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["rs14174303"],"URL":"https:\/\/doi.org\/10.3390\/rs14174303","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,1]]}}}