GRACE çözümlerinde korelasyon etkilerinin yüksek dereceden polinomlarla giderilmesi

Yeryuvarının gravite alanındaki zamansal değişimleri belirlemek amacıyla tasarlanan GRACE Gravity Recovery and Climate Experiment uydu sisteminin sonuç ürünleri son on yıldır çeşitli veri merkezleri tarafından kullanıcılara sunulmaktadır. L2 Seviye - 2 verisi olarak adlandırılan bu veri türü, tam normalleştirilmiş küresel harmonik katsayılarından ve standart sapmalarından oluşmaktadır. Aylık GRACE harmonik katsayıları yardımıyla yer sistemi içerisindeki kütle değişimlerinin izlenebilmesi için, çözümler içinde var olan bazı sistematik hataların giderilmesi gerekmektedir. GRACE gravite alanı çözümlerinde yer alan bu hataların giderilmesi ya da etkilerinin azaltılması için çeşitli filtre yöntemleri tasarlanmıştır. Bunlardan en bilineni Gauss filtresidir. Ancak, söz konusu filtre çözümlerdeki sistematik hataların tamamen giderilmesinde yeterli olmayıp, bu filtre sonunda yüzey kütle yoğunluğu veya eşdeğer su kalınlığı haritalarında halen bazı sistematik hataların varlığı görülmektedir. Katsayılar arasındaki korelasyonların neden olduğu bu hataları gidermek için Gauss filtresinin yanında korelasyon etkilerini de giderecek ek bir filtreye ihtiyaç vardır. Bu çalışmada, Chambers 2006 tarafından uygulanan bir yöntem ele alınmaktadır. Uygulamalar için UTCSR University of Texas at Austin Center for Space Research veri merkezinden alınan 2003‒2010 yıl aralığına ait aylık L2 verisi kullanılmaktadır. Söz konusu katsayılara 7. dereceden polinom ve farklı yumuşatma yarıçapına sahip Gauss filtreleri uygulanarak elde edilen değişimler incelenmektedir.

Destriping of GRACE solutions by fitting high‒degree polynomials

The gravity field solutions from GRACE Gravity Recovery and Climate Experiment system, designed for the determination of the temporal variations in the Earth’s gravity field, has been provided by some data centers during the last decade. These solutions, the so‒called Level 2 L2 Data, consist of fully normalized spherical harmonic coefficients and their standard deviations. In order to monitor the mass variations in the Earth system based on GRACE monthly harmonic coefficients, some systematical errors existing in the solutions should be removed. Several filtering methods have been developed to eliminate or reduce the effects of these errors in the GRACE gravity field solutions. Among them, Gaussian filter is one of the most well known filtering methods. However, this filter is not enough to remove all the systematic errors in the solutions, thus there still remains some errors in the surface mass density or equivalent water thickness maps. To reduce these remaining errors caused by the correlations between the coefficients, an extra de‒correlating filter is necessary in addition to the Gaussian filter. In this study, we focus on the de‒correlation method proposed by Chambers 2006 . The monthly L2 data provided by UTCSR for the time period 2003‒2010 are used. The temporal variations are discussed by applying a seventh degree polynomial and Gaussian filters with different smoothing radii.

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  • Bettadpur S., (2007), GRACE Level-2 Gravity Field Product User Handbook, Center for Space Research, the University of Texas at Austin.
  • Case K., Kruizinga G.L.H., Wu S.C., (2004), GRACE Level 1B Data Product User Handbook, JPL.
  • Cazenave A., Chen J., (2010), Time-variable gravity from space and present-day mass redistribution in the earth system, Earth and Planetary Science Letters, 298, 263-274.
  • Chambers D.P., (2006), Evaluation of new GRACE time-variable gravity data over the ocean, Geophysical Research Letters, 33 (L17603).
  • Chambers D.P., (2009), Calculating trends from GRACE in the presence of large changes in continental ice storage and ocean mass, Geophysical Journal International, 176, 415-419.
  • Chen J.L., Wilson C.R., Tapley B.D., Grand S., (2007), GRACE Detects coseismic and postseismic deformation from the Sumatra - Andaman earthquake, Geophysical Research Letters, 34(L13302).
  • Chen Y., Schaffrin B., Shum C.K., (2008), Continental water storage changes from GRACE line-of-sight range acceleration measurements, VI Houtine-Marussi Symposium on Theoretical and Computational Geodesy'nin içinde, Cilt 132,Bölüm I, 62- 66.
  • Choi S., Oh C.W., Luehr H., (2006), Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data, Gondwana Research, 9, 62-67.
  • Davis J. L, Tamisiea M. E., Elósegui P., Mitrovica J. X., Hill E. M., (2008), A statistical filtering approach for gravity recovery and climate experiment (GRACE) gravity data, Journal of Geophysical Research, 113(B04410).
  • Elsaka B., (2010), Simulated Satellite Formation Flights for Detecting the Temporal Variations of the Earth’s Gravity Field, Doktora tezi, Institut für Geodaesie und Geoinformation, Universitaet Bonn, Bonn.
  • Han S. C., Shum C.K., Jekeli C., Kuo C.Y., Wilson C., Seo K.W., (2005), Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement, Geophysical Journal International, 163, 18-25.
  • Han S.C., Simons F.J., (2008), Spatiospectral localization of global geopotential fields from the Gravity Recovery and Climate Experiment (GRACE) reveals the coseismic gravity change owing to the 2004 Sumatra-Andaman Earthquake, Journal of Geophysical Research, 113( B01405).
  • Jekeli C., (1981), Alternative methods to smooth the Earth’s gravity field, Bildiri no. 327, The Ohio State University, Columbus, Ohio.
  • Kless R., Revtova A., Gunter B.C., Ditmar P., Oudman E., Winsemius H. C., Savenije H. H. G., (2008), The design of an optimal filter for monthly GRACE gravity models, Geophysical Journal International, 175, 417-432.
  • Kusche J., (2007), Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-Type gravity field models, Journal of Geodesy, 81, 733-749.
  • Kusche J., Schmidt R., Petrovic S., Rietbroek R., (2009), Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model, Journal of Geodesy, 83, 903-913.
  • Liu X., (2008), Global Gravity Field Recovery from Satellite- To-Satellite Tracking Data with the Acceleration Approach, Doktora Tezi, Delft University of Technology, Delft.
  • Mikhailov V., Tikhotsky S., Diament M., Panet I., Ballu V., (2004), Can tectonic processes be recovered from new gravity satellite data?, Earth and Planetary Science Letters, 228, 281-297.
  • Rangelova E., Sideris M.G., (2008), Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America, Journal of Geodynamics, 46, 131-143.
  • Schmidt R., Schwintzer P., Flechtner F., Reigber C.H., Güntner A., Döll P., Ramillien G., Cazenave A., Petrovic S., Jochmann H., Wünsch J., (2006), GRACE observations of changes in continental water storage, Global and Planetary Change, 50, 112-126.
  • Schrama E.J.O., Wouters B., Lavallée D.A., (2007), Signal and noise in gravity recovery and climate experiment (GRACE) observed surface mass variations, Journal of Geophysical Research, 112( B08407).
  • Seo K.W., Wilson C.R., (2005), Simulated estimation of hydrological loads from GRACE, Journal of Geodesy, 78, 442-456.
  • Slobbe D.C., Ditmar P., Lindenbergh R.C., (2009), Estimating the rates of mass change, ice volume change and snow volume change in greenland from ICESat and GRACE data, Geophysical Journal International, 176, 95-106.
  • Steffen H., Petrovic S., Müller J., Schmidt R., Wünsch J., Barthelmes F., Kusche J., (2009), Significance of secular trends of mass variations determined from GRACE solutions, Journal of Geodynamics, 48, 157-165.
  • Swenson S., Wahr J., (2003), Monitoring changes in continental water storage with GRACE, Space Science Reviews, 108, 345- 354.
  • Swenson S., Wahr J., (2006), Post-processing removal of correlated errors in GRACE data, Geophysical Research Letters, 33( L08402).
  • Wahr J., Molenaar M., (1998), Time-variability of the earth’s gravity field: hydrological and oceanic effects and their possible detection using GRACE, Journal of Geophysical Research, 103, 30205-30229.
  • Wahr J., Swenson S., Velicogna I., (2006), Accuracy of grace mass estimates, Geophysical Research Letters, 33 (L06401).
  • Wahr J., (2007), Time-Variable Gravity from Satellites, Treatise on Geophysics, 3, 231-237.
  • Wouters B., Schrama E.J.O., (2007), Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics, Geophysical Research Letters, 34( L23711).
  • Van Der Wal W., (2009), Contributions of Space Gravimetry to Postglacial Rebound Modeling with Different Rheologies, Doktora Tezi, University of Calgary, Department of Geomatics Engineering, Calgary, Alberta.
  • Url 1, Earth observatory, Gravity Recovery and Climate Experiment (GRACE), http:// earthobservatory.nasa.gov/ Features/ GRACE/, [Erişim 13 Ekim 2011].
  • Url 2, Jet Propulsion Laboratory, NASA and DLR Sign Agreement to Continue Grace Mission Through 2015, http://www.jpl. nasa.gov/news/news.cfm?release=2010-195, [Erişim 14 Ekim 2011].
  • Url 3, GFZ, International Centre for Global Earth Models (ICGEM), http://icgem.gfz-postdam.de/ICGEM/, [Erişim 13 Ekim 2011].