{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T00:13:20Z","timestamp":1784160800231,"version":"3.55.0"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T00:00:00Z","timestamp":1608595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013076","name":"National Major Science and Technology Projects of China","doi-asserted-by":"publisher","award":["2018YFC1507004"],"award-info":[{"award-number":["2018YFC1507004"]}],"id":[{"id":"10.13039\/501100013076","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global Positioning System (GPS) radio occultation (RO) and radiosonde (RS) observations are two major types of observations assimilated in numerical weather prediction (NWP) systems. Observation error variances are required input that determines the weightings given to observations in data assimilation. This study estimates the error variances of global GPS RO refractivity and bending angle and RS temperature and humidity observations at 521 selected RS stations using the three-cornered hat method with additional ERA-Interim reanalysis and Global Forecast System forecast data available from 1 January 2016 to 31 August 2019. The global distributions, of both RO and RS observation error variances, are analyzed in terms of vertical and latitudinal variations. Error variances of RO refractivity and bending angle and RS specific humidity in the lower troposphere, such as at 850 hPa (3.5 km impact height for the bending angle), all increase with decreasing latitude. The error variances of RO refractivity and bending angle and RS specific humidity can reach about 30 N-unit2, 3 \u00d7 10\u22126 rad2, and 2 (g kg\u22121)2, respectively. There is also a good symmetry of the error variances of both RO refractivity and bending angle with respect to the equator between the Northern and Southern Hemispheres at all vertical levels. In this study, we provide the mean error variances of refractivity and bending angle in every 5\u00b0-latitude band between the equator and 60\u00b0N, as well as every interval of 10 hPa pressure or 0.2 km impact height. The RS temperature error variance distribution differs from those of refractivity, bending angle, and humidity, which, at low latitudes, are smaller (less than 1 K2) than those in the midlatitudes (more than 3 K2). In the midlatitudes, the RS temperature error variances in North America are larger than those in East Asia and Europe, which may arise from different radiosonde types among the above three regions.<\/jats:p>","DOI":"10.3390\/rs13010001","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T20:39:29Z","timestamp":1608669569000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Global 3D Features of Error Variances of GPS Radio Occultation and Radiosonde Observations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0907-3885","authenticated-orcid":false,"given":"Xu","family":"Xu","sequence":"first","affiliation":[{"name":"Joint Center of Data Assimilation for Research and Application, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolei","family":"Zou","sequence":"additional","affiliation":[{"name":"Joint Center of Data Assimilation for Research and Application, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kuo, Y.-H., Schreiner, W.S., Rossiter, D.L., Wang, J., and Zhang, Y. (2005). Comparison of GPS radio occultation soundings with radiosondes. Geophys. Res. Lett., 32.","DOI":"10.1029\/2004GL021443"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.3390\/rs2051320","article-title":"Global Evaluation of Radiosonde Water Vapor Systematic Biases using GPS Radio Occultation from COSMIC and ECMWF Analysis","volume":"2","author":"Ho","year":"2010","journal-title":"Remote. Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7718","DOI":"10.1002\/2013JD021398","article-title":"Assessing the performance of GPS radio occultation measurements in retrieving tropospheric humidity in cloudiness: A comparison study with radiosondes, ERA-Interim, and AIRS data sets","volume":"119","author":"Vergados","year":"2014","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"23429","DOI":"10.1029\/97JD01569","article-title":"Observing Earth\u2019s atmosphere with radio occultation measurements using the Global Positioning System","volume":"102","author":"Kursinski","year":"1997","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1175\/BAMS-89-3-313","article-title":"The COSMIC\/FORMOSAT-3 Mission: Early Results","volume":"89","author":"Anthes","year":"2008","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"E1107","DOI":"10.1175\/BAMS-D-18-0290.1","article-title":"The COSMIC\/FORMOSAT-3 Radio Occultation Mission after 12 Years: Accomplishments, Remaining Challenges, and Potential Impacts of COSMIC-2","volume":"101","author":"Ho","year":"2020","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"086841","DOI":"10.1029\/2019GL086841","article-title":"COSMIC-2 Radio Occultation Constellation: First Results","volume":"47","author":"Schreiner","year":"2020","journal-title":"Geophys. Res. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1175\/2009MWR3097.1","article-title":"Relative Short-Range Forecast Impact from Aircraft, Profiler, Radiosonde, VAD, GPS-PW, METAR, and Mesonet Observations via the RUC Hourly Assimilation Cycle","volume":"138","author":"Benjamin","year":"2010","journal-title":"Mon. Weather. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/asl.169","article-title":"Forecast impact experiment with a constellation of GPS radio occultation receivers","volume":"9","author":"Healy","year":"2008","journal-title":"Atmos. Sci. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1002\/qj.521","article-title":"The impact of GPS radio occultation assimilation at the Met Office","volume":"136","author":"Rennie","year":"2010","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2117","DOI":"10.1175\/JTECH-D-17-0224.1","article-title":"A Quality Control Procedure Based on Bending Angle Measurement Uncertainty for Radio Occultation Data Assimilation in the Tropical Lower Troposphere","volume":"35","author":"Liu","year":"2018","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s00376-019-8231-x","article-title":"Antarctic Radiosonde Observations Reduce Uncertainties and Errors in Reanalyses and Forecasts over the Southern Ocean: An Extreme Cyclone Case","volume":"37","author":"Sato","year":"2020","journal-title":"Adv. Atmos. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zou, X. (2020). Three-Dimensional Variational Data Assimilation, Elsevier BV.","DOI":"10.1016\/B978-0-12-820950-9.00008-8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"033508","DOI":"10.1117\/1.3094060","article-title":"Test of a non-local excess phase delay operator for GPS radio occultation data assimilation","volume":"3","author":"Shao","year":"2009","journal-title":"J. Appl. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1002\/qj.830","article-title":"Observation errors in all-sky data assimilation","volume":"137","author":"Geer","year":"2011","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"ACL 19-1","DOI":"10.1029\/2001JD001552","article-title":"The impact of observational weighting on the assimilation of GPS\/MET bending angle","volume":"107","author":"Shao","year":"2002","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"507","DOI":"10.2151\/jmsj.2004.507","article-title":"Inversion and Error Estimation of GPS Radio Occultation Data","volume":"82","author":"Kuo","year":"2004","journal-title":"J. Meteorol. Soc. Jpn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1175\/2010MWR3260.1","article-title":"Observational Error Estimation of FORMOSAT-3\/COSMIC GPS Radio Occultation Data","volume":"139","author":"Chen","year":"2011","journal-title":"Mon. Weather Rev."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Steiner, A.K. (2005). Error analysis for GNSS radio occultation data based on ensembles of profiles from end-to-end simulations. J. Geophys. Res. Space Phys., 110.","DOI":"10.1029\/2004JD005251"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.3319\/TAO.2008.01.21.02(F3C)","article-title":"Quality Control, Error Analysis, and Impact Assessment of FORMOSAT-3\/COSMIC in Numerical Weather Prediction","volume":"20","author":"Poli","year":"2009","journal-title":"Terr. Atmos. Ocean. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4239","DOI":"10.5194\/amt-11-4239-2018","article-title":"Estimating observation and model error variances using multiple data sets","volume":"11","author":"Anthes","year":"2018","journal-title":"Atmos. Meas. Tech."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gray, J.E., and Allan, D.W. (1974, January 29\u201331). A Method for Estimating the Frequency Stability of an Individual Oscillator. Proceedings of the 28th Annual Symposium on Frequency Control, Institute of Electrical and Electronics Engineers (IEEE), Atlantic City, NJ, USA.","DOI":"10.1109\/FREQ.1974.200027"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xu, X., and Zou, X. (2020). Estimating GPS radio occultation observation error standard deviations over China using the three-cornered hat method. Q. J. R. Meteorol. Soc.","DOI":"10.1002\/qj.3938"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1016\/j.jastp.2011.04.017","article-title":"Global (50\u00b0S\u201350\u00b0N) distribution of water vapor observed by COSMIC GPS RO: Comparison with GPS radiosonde, NCEP, ERA-Interim, and JRA-25 reanalysis data sets","volume":"73","author":"Kishore","year":"2011","journal-title":"J. Atmos. Sol.-Terrestrial Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.5194\/amt-8-1819-2015","article-title":"Climate intercomparison of GPS radio occultation, RS90\/92 radiosondes and GRUAN from 2002 to 2013","volume":"8","author":"Steiner","year":"2015","journal-title":"Atmos. Meas. Tech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4493","DOI":"10.5194\/acp-17-4493-2017","article-title":"Characterization of the long-term radiosonde temperature biases in the upper troposphere and lower stratosphere using COSMIC and Metop-A\/GRAS data from 2006 to 2014","volume":"17","author":"Ho","year":"2017","journal-title":"Atmos. Chem. Phys. Discuss."},{"key":"ref_27","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_28","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1175\/2008JAMC1809.1","article-title":"Robust Automated Quality Assurance of Radiosonde Temperatures","volume":"47","author":"Durre","year":"2008","journal-title":"J. Appl. Meteorol. Clim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/qj.828","article-title":"The ERA-Interim reanalysis: Configuration and performance of the data assimilation system","volume":"137","author":"Dee","year":"2011","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.5194\/amt-11-2567-2018","article-title":"Reducing representativeness and sampling errors in radio occultation\u2013radiosonde comparisons","volume":"11","author":"Gilpin","year":"2018","journal-title":"Atmos. Meas. Tech."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lohmann, M.S. (2007). Analysis of Global Positioning System (GPS) radio occultation measurement errors based on Satellite de Aplicaciones Cientificas-C (SAC-C) GPS radio occultation data recorded in open-loop and phase-locked-loop mode. J. Geophys. Res. Space Phys., 112.","DOI":"10.1029\/2006JD007764"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zou, X., and Zeng, Z. (2006). A quality control procedure for GPS radio occultation data. J. Geophys. Res. Space Phys., 111.","DOI":"10.1029\/2005JD005846"},{"key":"ref_33","unstructured":"(2019, June 30). ROM SAF, 2019: The Radio Occultation Processing Package (ROPP) Forward Model Module User Guide, SAF\/ROM\/METO\/UG\/ROPP\/006. Available online: https:\/\/www.romsaf.org\/romsaf_ropp_ug_fm.pdf."},{"key":"ref_34","unstructured":"Ingleby, B. (2017). An Assessment of Different Radiosonde Types 2015\/2016, ECMWF. ECMWF Technical Memoranda 807."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2791","DOI":"10.1175\/1520-0493(2002)130<2791:ESBAME>2.0.CO;2","article-title":"Ensemble Size, Balance, and Model-Error Representation in an Ensemble Kalman Filter","volume":"130","author":"Mitchell","year":"2002","journal-title":"Mon. Weather. Rev."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/1\/1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:48:23Z","timestamp":1760179703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/1\/1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,22]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["rs13010001"],"URL":"https:\/\/doi.org\/10.3390\/rs13010001","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,22]]}}}