{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T03:44:38Z","timestamp":1772250278857,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,31]],"date-time":"2018-05-31T00:00:00Z","timestamp":1527724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The mass change information from the Gravity Recovery And Climate Experiment (grace) satellite mission is available in terms of noisy spherical harmonic coefficients truncated at a maximum degree (band-limited). Therefore, filtering is an inevitable step in post-processing of grace fields to extract meaningful information about mass redistribution in the Earth-system. It is well known from previous studies that a number can be allotted to the spatial resolution of a band-limited spherical harmonic spectrum and also to a filtered field. Furthermore, it is now a common practice to correct the filtered grace data for signal damage due to filtering (or convolution in the spatial domain). These correction methods resemble deconvolution, and, therefore, the spatial resolution of the corrected grace data have to be reconsidered. Therefore, the effective spatial resolution at which we can obtain mass changes from grace products is an area of debate. In this contribution, we assess the spatial resolution both theoretically and practically. We confirm that, theoretically, the smallest resolvable catchment is directly related to the band-limit of the spherical harmonic spectrum of the grace data. However, due to the approximate nature of the correction schemes and the noise present in grace data, practically, the complete band-limited signal cannot be retrieved. In this context, we perform a closed-loop simulation comparing four popular correction schemes over 255 catchments to demarcate the minimum size of the catchment whose signal can be efficiently recovered by the correction schemes. We show that the amount of closure error is inversely related to the size of the catchment area. We use this trade-off between the error and the catchment size for defining the potential spatial resolution of the grace product obtained from a correction method. The magnitude of the error and hence the spatial resolution are both dependent on the correction scheme. Currently, a catchment of the size \u224863,000 km     2    can be resolved at an error level of    2  cm    in terms of equivalent water height.<\/jats:p>","DOI":"10.3390\/rs10060852","type":"journal-article","created":{"date-parts":[[2018,6,1]],"date-time":"2018-06-01T03:02:50Z","timestamp":1527822170000},"page":"852","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":107,"title":["What Is the Spatial Resolution of grace Satellite Products for Hydrology?"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4787-8470","authenticated-orcid":false,"given":"Bramha Dutt","family":"Vishwakarma","sequence":"first","affiliation":[{"name":"Institute of Geodesy, University of Stuttgart, 70174 Stuttgart, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8098-9813","authenticated-orcid":false,"given":"Balaji","family":"Devaraju","sequence":"additional","affiliation":[{"name":"Institute of Geodesy, Leibniz University of Hannover, 30167 Hannover, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1796-0131","authenticated-orcid":false,"given":"Nico","family":"Sneeuw","sequence":"additional","affiliation":[{"name":"Institute of Geodesy, University of Stuttgart, 70174 Stuttgart, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1038\/nclimate2425","article-title":"The global groundwater crisis","volume":"4","author":"Famiglietti","year":"2014","journal-title":"Nat. Clim. Chang."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1007\/s10712-014-9300-4","article-title":"Estimating Runoff Using Hydro-Geodetic Approaches","volume":"35","author":"Sneeuw","year":"2014","journal-title":"Surv. Geophys."},{"key":"ref_3","unstructured":"Dahle, C., Flechtner, F., Gruber, C., K\u00f6nig, D., K\u00f6nig, R., Michalak, G., and Neumayer, K.H. (2012). GFZ GRACE Level-2 Processing Standards Document for Level-2 Product Release 05, GFZ. Scientific Technical Report-Data 12\/02."},{"key":"ref_4","unstructured":"Mayer-G\u00fcrr, T., Behzadpour, S., Ellmer, M., Kvas, A., Klinger, B., and Zehentner, N. (2017, April 30). ITSG-Grace2016\u2014Monthly and Daily Gravity Field Solutions from GRACE. Available online: https:\/\/www.tugraz.at\/institute\/ifg\/downloads\/gravity-field-models\/itsg-grace2016\/."},{"key":"ref_5","first-page":"2193","article-title":"Methods for inferring regional surface-mass anomalies from Gravity Recovery and Climate Experiment (GRACE) measurements of time-variable gravity","volume":"107","author":"Swenson","year":"2002","journal-title":"J. Geophys. Res."},{"key":"ref_6","unstructured":"Wahr, J., Swenson, S., and Velicogna, I. (2007, January 15\u201317). Some Hydrological and Cryospheric Applications of GRACE. Proceedings of the GRACE Science Team Meeting and DFG SPP1257 Symposium, Potsdam, Germany."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2111","DOI":"10.1175\/JHM-D-13-0157.1","article-title":"Large-scale runoff from landmasses: A global assessment of the closure of the hydrological and atmospheric water balances","volume":"15","author":"Lorenz","year":"2014","journal-title":"J. Hydrometeorol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"30205","DOI":"10.1029\/98JB02844","article-title":"Time variability of the Earth\u2019s gravity field: Hydrological and oceanic effects and their possible detection using GRACE","volume":"103","author":"Wahr","year":"1998","journal-title":"J. Geophys. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1111\/j.1365-246X.2005.02756.x","article-title":"Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement","volume":"163","author":"Han","year":"2005","journal-title":"Geophys. J. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"L08402","DOI":"10.1029\/2005GL025285","article-title":"Post-processing removal of correlated errors in GRACE data","volume":"33","author":"Swenson","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s00190-007-0143-3","article-title":"Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models","volume":"81","author":"Kusche","year":"2007","journal-title":"J. Geod."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1111\/j.1365-246X.2008.03922.x","article-title":"The design of an optimal filter for monthly GRACE gravity models","volume":"175","author":"Klees","year":"2008","journal-title":"Geophys. J. Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"L17311","DOI":"10.1029\/2009GL039459","article-title":"An effective filtering for GRACE time-variable gravity: Fan filter","volume":"36","author":"Zhang","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_14","unstructured":"Devaraju, B. (2015). Understanding Filtering on the Sphere\u2014Experiences from Filtering GRACE Data. [Ph.D. Thesis, Universit\u00e4t Stuttgart]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1111\/j.1365-246X.2009.04355.x","article-title":"Evaluation of GRACE filter tools from a hydrological perspective","volume":"179","author":"Werth","year":"2009","journal-title":"Geophys. J. Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10712-008-9049-8","article-title":"A Comparison of Global and Regional GRACE Models for Land Hydrology","volume":"29","author":"Klees","year":"2008","journal-title":"Surv. Geophys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sneeuw, N., Nov\u00e1k, P., Crespi, M., and Sans\u00f2, F. (2013, January 17\u201321). On the Spatial Resolution of Homogeneous Isotropic Filters on the Sphere. Proceedings of the VIII Hotine-Marussi Symposium on Mathematical Geodesy, Rome, Italy.","DOI":"10.1007\/978-3-642-22078-4"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1365-246X.2006.03017.x","article-title":"Choice of optimal averaging radii for temporal GRACE gravity solutions, a comparison with GPS and satellite altimetry","volume":"166","author":"King","year":"2006","journal-title":"Geophys. J. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"W11517","DOI":"10.1029\/2009WR008564","article-title":"GRACE Hydrological estimates for small basins: Evaluating processing approaches on the High Plains Aquifer, USA","volume":"46","author":"Longuevergne","year":"2010","journal-title":"Water Resour. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.5194\/hess-11-1227-2007","article-title":"The bias in GRACE estimates of continental water storage variations","volume":"11","author":"Klees","year":"2007","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5868","DOI":"10.1002\/2016WR018960","article-title":"Minimizing the effects of filtering on catchment scale GRACE solutions","volume":"52","author":"Vishwakarma","year":"2016","journal-title":"Water Resour. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1002\/2014WR016853","article-title":"Global analysis of approaches for deriving total water storage changes from GRACE satellites","volume":"51","author":"Long","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_23","unstructured":"Vishwakarma, B.D. (2017). Understanding and Repairing the Signal Damage Due to Filtering of Mass Change Estimates from the GRACE Satellite Mission. [Ph.D. Thesis, University of Stuttgart]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"W04531","DOI":"10.1029\/2011WR011453","article-title":"Accuracy of scaled GRACE terrestrial water storage estimates","volume":"48","author":"Landerer","year":"2012","journal-title":"Water Resour. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9824","DOI":"10.1002\/2017WR021150","article-title":"A Data-Driven Approach for Repairing the Hydrological Catchment Signal Damage Due to Filtering of GRACE Products","volume":"53","author":"Vishwakarma","year":"2017","journal-title":"Water Resour. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1111\/j.1365-246X.2009.04139.x","article-title":"Signal and error in mass change inferences from GRACE: The case of Antarctica","volume":"177","author":"Horwath","year":"2009","journal-title":"Geophys. J. Int."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"B06407","DOI":"10.1029\/2008JB006239","article-title":"GRACE-derived ice-mass variations over Greenland by accounting for leakage effects","volume":"114","author":"Baur","year":"2009","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1038\/nature11621","article-title":"Lower satellite-gravimetry estimates of Antarctic sea-level contribution","volume":"491","author":"King","year":"2012","journal-title":"Nature"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1007\/s00190-015-0824-2","article-title":"Reducing leakage error in GRACE-observed long-term ice mass change: A case study in West Antarctica","volume":"89","author":"Chen","year":"2015","journal-title":"J. Geod."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10712-008-9033-3","article-title":"Hydrological Signals Observed by the GRACE Satellites","volume":"29","author":"Schmidt","year":"2008","journal-title":"Surv. Geophys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"L04310","DOI":"10.1029\/2004GL021908","article-title":"Resolving mass flux at high spatial and temporal resolution using GRACE intersatellite measurements","volume":"32","author":"Rowlands","year":"2005","journal-title":"Geophys. Res. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.rse.2014.10.006","article-title":"A spaceborne multisensor approach to monitor the desiccation of Lake Urmia in Iran","volume":"156","author":"Tourian","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.rse.2017.10.040","article-title":"Efficient basin scale filtering of GRACE satellite products","volume":"204","author":"Khaki","year":"2018","journal-title":"Remote Sens. Environ."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Heiskanen, W.A., and Moritz, H. (1967). Physical Geodesy, W. H. Freeman and Company.","DOI":"10.1007\/BF02525647"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s00190-012-0585-0","article-title":"An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit","volume":"87","author":"Weigelt","year":"2013","journal-title":"J. Geod."},{"key":"ref_36","unstructured":"Colombo, O.L. (1981). Numerical Methods for Harmonic Analysis on the Sphere, Department of Geodetic Science, The Ohio State University. Technical Report 310."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1111\/j.1365-246X.1994.tb03995.x","article-title":"Global spherical harmonic analysis by least squares and numerical quadrature methods in historical perspective","volume":"118","author":"Sneeuw","year":"1994","journal-title":"Geophys. J. Int."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5876","DOI":"10.1109\/TSP.2011.2166394","article-title":"A Novel Sampling Theorem on the Sphere","volume":"59","author":"McEwen","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Freeden, W., and Schreiner, M. (2009). Spherical functions of mathematical geosciences. Advances in Geophysical and Environmental Mechanics and Mathematics, Springer.","DOI":"10.1007\/978-3-540-85112-7"},{"key":"ref_40","unstructured":"Jekeli, C. (1981). Alternative Methods to Smooth the Earth\u2019s Gravity Field, Department of Geodetic Science and Surveying, The Ohio State University. Technical Report 327."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"6562","DOI":"10.1002\/2017WR020793","article-title":"The potential of GRACE gravimetry to detect the heavy rainfall-induced impoundment of a small reservoir in the upper Yellow River","volume":"53","author":"Yi","year":"2017","journal-title":"Water Resour. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1175\/BAMS-85-3-381","article-title":"The Global Land Data Assimilation System","volume":"85","author":"Rodell","year":"2004","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_43","unstructured":"Werth, S. (2010). Calibration of the Global Hydrological Model WGHM with Water Mass Variations from GRACE Gravity Data. [Ph.D. Thesis, Universit\u00e4t Potsdam]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5698","DOI":"10.1002\/2014WR015595","article-title":"Global-scale assessment of groundwater depletion and related groundwater abstractions: Combining hydrological modeling with information from well observations and GRACE satellites","volume":"50","author":"Schuh","year":"2014","journal-title":"Water Resour. Res."},{"key":"ref_45","unstructured":"Thor, R. (2013). Least-Squares Prediction of Runoff. [Bachelor\u2019s Thesis, University of Stuttgart]."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"8450","DOI":"10.1002\/2014WR016794","article-title":"Basin-scale runoff prediction: An Ensemble Kalman Filter framework based on global hydrometeorological data sets","volume":"51","author":"Lorenz","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/0022-1694(70)90255-6","article-title":"River flow forecasting through conceptual models part I\u2014A discussion of principles","volume":"10","author":"Nash","year":"1970","journal-title":"J. Hydrol."},{"key":"ref_48","first-page":"3","article-title":"STL: A Seasonal-Trend Decomposition Procedure Based on Loess (with Discussion)","volume":"6","author":"Cleveland","year":"1990","journal-title":"J. Off. Stat."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10712-015-9338-y","article-title":"What Can be Expected from the GRACE-FO Laser Ranging Interferometer for Earth Science Applications?","volume":"37","author":"Flechtner","year":"2016","journal-title":"Surv. Geophys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF02522279","article-title":"On the nonhomogeneity of the global covariance function","volume":"51","author":"Rummel","year":"1977","journal-title":"Bull. Geod."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/852\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:06:41Z","timestamp":1760195201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/852"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,31]]},"references-count":50,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["rs10060852"],"URL":"https:\/\/doi.org\/10.3390\/rs10060852","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,31]]}}}