The GFZ-GRGS satellite-only gravity field model EIGEN-6S2 ========================================================= Contact: Christoph Foerste e-mail: foer@gfz-potsdam.de EIGEN-6S2 (Rudenko et al. 2014) is a global satellite-only gravity field model up to degree and order 260. This model is technically a time variable version of the 4th release of ESA's GOCE gravity field model via the direct approach (Bruinsma et al. 2013) and contains the following satellite data: - LAGEOS (deg. 2 - 30): 1985 - 2010 - GRACE RL02 GRGS (deg. 2 - 100): 200302 - 201101 Bruinsma et al. 2009) - GRACE RL05 GFZ (deg. 55 - 180): 200310 - 201209 (Dahle et al. 2012) - GOCE-SGG data, processed by the direct approach (Pail et al. 2011, Bruinsma et al. 2013): 837 days Txx, Tyy, Tzz and Txz out of the time span 20091101 - 20120801 225 days Txx, Tyy and Tzz out of the time span 20120901 - 20130524 The GOCE polar gaps were stabilized by the Spherical Cap Regularization (Metzler and Pail 2005) using the combined gravity field model EIGEN-6C2 EIGEN-6S2 contains time variable parameters (gfct, trnd, acos, asin, t0, t1 and period) up to d/o 50. The computation of the values of the time variable spherical coefficients G at a certain epoch t within the respective time span between t0 and t1 must be done by applying the drift parameters trnd as well as the periodic terms acos and asin in the following way. In the given rule the two periodic terms are denoted by asin1/acos1 and asin2/acos2 in accordance with the two periods p1 = 1.0 year and p2 = 0.5 year. G(t)=gfct(t0)+trnd*(t-t0)+asin1*sin(2pi/p1*(t-t0))+acos1*cos(2pi/p1*(t-t0)) +asin2*sin(2pi/p2*(t-t0))+acos2*cos(2pi/p2*(t-t0)) where t0 <= t <= t1 for the respective gfct, trnd and periodic terms. The details of the format description are available at http://icgem.gfz-potsdam.de/ICGEM/documents/ICGEM-Format-GOCE.pdf References: ------------ Bruinsma, S.L., J.M. Lemoine, R. Biancale, N. Vales (2009) CNES/GRGS 10-day gravity field models (release 2) and their evaluation, Adv. Space Res., doi:10.1016/j.asr.2009.10.012. Bruinsma, S.L., Foerste, C. Abrikosov, O., Marty, J.-C., Rio, M.-H. Mulet, S and Bonvalot, S. (2013), The new ESA satellite-only gravity field model via the direct approach, Geophys. Research Letters, Vol. 40, 3607\u20133612, doi:10.1002/grl.50716, 2013 Dahle C., Flechtner F., Gruber C., Koenig D., Koenig R., Michalak G. and Neumayer K.-H. (2012): GFZ GRACE Level-2 Processing Standards Document for Level-2 Product Release 0005, (Scientific Technical Report - Data , 12/02), Potsdam, 20 p. DOI: 10.2312/GFZ.b103-1202-25 Metzler B. and Pail R., 2005, GOCE Data Processing: The Sperical Cap Regularization Approach, Stud. Geophys. Geod. 49 (2005), 441-462 Pail R., Bruinsma S., Migliaccio F., Foerste C., Goiginger H., Schuh W.-D, Hoeck E, Reguzzoni M., Brockmann J.M, Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sanso F. & Tscherning C.C., 2011, First GOCE gravity field models derived by three different approaches. Journal of Geodesy, 85, 11, 819-843 Rudenko S., Dettmering D., Esselborn S., Schoene T., Foerste C., Lemoine J-M., Ablain M., Alexandre D., Neumayer K.-H. (2014) Influence of time variable geopotential models on precise orbits of altimetry satellites, global and regional mean sea level trends. Advances in Space Research, doi: 10.1016/j.asr.2014.03.010 begin_of_head ===================================== format icgem2.0 product_type gravity_field modelname EIGEN-6S2 earth_gravity_constant 0.3986004415E+15 radius 0.6378136460E+07 max_degree 260 errors formal norm fully_normalized tide_system tide_free key L M C S sigma C sigma S t0[yyyymmdd.xxxx] t1[yyyymmdd.xxxx] period[y] end_of_head ============================================================================================================= gfc 0 0 1.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 gfc 1 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 gfct 2 0 -4.84165442874E-04 0.00000000000E+00 1.3920E-11 0.0000E+00 19500101.0000 19850109.1751 trnd 2 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 19500101.0000 19850109.1751 gfct 2 0 -4.84165442874E-04 0.00000000000E+00 1.3920E-11 0.0000E+00 19850109.1751 19860101.0000 trnd 2 0 1.24657017393E-11 0.00000000000E+00 2.2600E-11 0.0000E+00 19850109.1751 19860101.0000 gfct 2 0 -4.84165430707E-04 0.00000000000E+00 8.6720E-12 0.0000E+00 19860101.0000 19870101.0000 trnd 2 0 2.24347107494E-11 0.00000000000E+00 1.8180E-11 0.0000E+00 19860101.0000 19870101.0000 gfct 2 0 -4.84165408273E-04 0.00000000000E+00 9.5070E-12 0.0000E+00 19870101.0000 19880101.0000 trnd 2 0 1.28987611358E-10 0.00000000000E+00 1.7360E-11 0.0000E+00 19870101.0000 19880101.0000 gfct 2 0 -4.84165279285E-04 0.00000000000E+00 7.8510E-12 0.0000E+00 19880101.0000 19890101.0000 trnd 2 0 -8.33020306695E-11 0.00000000000E+00 1.4760E-11 0.0000E+00 19880101.0000 19890101.0000 gfct 2 0 -4.84165362587E-04 0.00000000000E+00 6.9040E-12 0.0000E+00 19890101.0000 19900101.0000 trnd 2 0 6.49257734499E-12 0.00000000000E+00 1.4200E-11 0.0000E+00 19890101.0000 19900101.0000 gfct 2 0 -4.84165356094E-04 0.00000000000E+00 7.2950E-12 0.0000E+00 19900101.0000 19910101.0000 trnd 2 0 1.62048658823E-11 0.00000000000E+00 1.4490E-11 0.0000E+00 19900101.0000 19910101.0000 gfct 2 0 -4.84165339889E-04 0.00000000000E+00 7.1940E-12 0.0000E+00 19910101.0000 19920101.0000 trnd 2 0 -5.25073564333E-12 0.00000000000E+00 1.4450E-11 0.0000E+00 19910101.0000 19920101.0000 gfct 2 0 -4.84165345140E-04 0.00000000000E+00 7.2570E-12 0.0000E+00 19920101.0000 19930101.0000 trnd 2 0 7.26731498694E-11 0.00000000000E+00 1.3110E-11 0.0000E+00 19920101.0000 19930101.0000 gfct 2 0 -4.84165272467E-04 0.00000000000E+00 5.8500E-12 0.0000E+00 19930101.0000 19940101.0000 trnd 2 0 3.32661884379E-11 0.00000000000E+00 1.1210E-11 0.0000E+00 19930101.0000 19940101.0000 gfct 2 0 -4.84165239201E-04 0.00000000000E+00 5.3610E-12 0.0000E+00 19940101.0000 19950101.0000 trnd 2 0 -2.16185714552E-11 0.00000000000E+00 1.0920E-11 0.0000E+00 19940101.0000 19950101.0000 gfct 2 0 -4.84165260819E-04 0.00000000000E+00 5.5590E-12 0.0000E+00 19950101.0000 19960101.0000 trnd 2 0 9.12798998887E-11 0.00000000000E+00 1.1050E-11 0.0000E+00 19950101.0000 19960101.0000 gfct 2 0 -4.84165169540E-04 0.00000000000E+00 5.4920E-12 0.0000E+00 19960101.0000 19970101.0000 trnd 2 0 -3.53116283650E-11 0.00000000000E+00 1.1000E-11 0.0000E+00 19960101.0000 19970101.0000 gfct 2 0 -4.84165204851E-04 0.00000000000E+00 5.5050E-12 0.0000E+00 19970101.0000 19980101.0000 trnd 2 0 2.60132731715E-12 0.00000000000E+00 1.0500E-11 0.0000E+00 19970101.0000 19980101.0000 gfct 2 0 -4.84165202250E-04 0.00000000000E+00 4.9960E-12 0.0000E+00 19980101.0000 19990101.0000 trnd 2 0 -8.22364105345E-11 0.00000000000E+00 1.0010E-11 0.0000E+00 19980101.0000 19990101.0000 gfct 2 0 -4.84165284486E-04 0.00000000000E+00 5.0150E-12 0.0000E+00 19990101.0000 20000101.0000 trnd 2 0 -4.04274387662E-11 0.00000000000E+00 9.9220E-12 0.0000E+00 19990101.0000 20000101.0000 gfct 2 0 -4.84165324914E-04 0.00000000000E+00 4.9070E-12 0.0000E+00 20000101.0000 20010101.0000 trnd 2 0 -2.33799739142E-11 0.00000000000E+00 9.8020E-12 0.0000E+00 20000101.0000 20010101.0000 gfct 2 0 -4.84165348294E-04 0.00000000000E+00 4.8950E-12 0.0000E+00 20010101.0000 20020101.0000 trnd 2 0 7.29395316452E-11 0.00000000000E+00 9.5530E-12 0.0000E+00 20010101.0000 20020101.0000 gfct 2 0 -4.84165275354E-04 0.00000000000E+00 4.6580E-12 0.0000E+00 20020101.0000 20030101.0000 trnd 2 0 2.61477983048E-11 0.00000000000E+00 9.4530E-12 0.0000E+00 20020101.0000 20030101.0000 gfct 2 0 -4.84165238139E-04 0.00000000000E+00 1.9820E-11 0.0000E+00 20030101.0000 20040101.0000 trnd 2 0 -1.07051002478E-10 0.00000000000E+00 3.0540E-11 0.0000E+00 20030101.0000 20040101.0000 gfct 2 0 -4.84165345190E-04 0.00000000000E+00 1.0720E-11 0.0000E+00 20040101.0000 20050101.0000 trnd 2 0 1.18149675994E-10 0.00000000000E+00 2.0040E-11 0.0000E+00 20040101.0000 20050101.0000 gfct 2 0 -4.84165227049E-04 0.00000000000E+00 9.3160E-12 0.0000E+00 20050101.0000 20060101.0000 trnd 2 0 -7.87378877917E-11 0.00000000000E+00 1.7970E-11 0.0000E+00 20050101.0000 20060101.0000 gfct 2 0 -4.84165305787E-04 0.00000000000E+00 8.6500E-12 0.0000E+00 20060101.0000 20070101.0000 trnd 2 0 3.92408997920E-11 0.00000000000E+00 1.7630E-11 0.0000E+00 20060101.0000 20070101.0000 gfct 2 0 -4.84165266546E-04 0.00000000000E+00 8.9790E-12 0.0000E+00 20070101.0000 20080101.0000 trnd 2 0 -2.83150243227E-11 0.00000000000E+00 2.0590E-11 0.0000E+00 20070101.0000 20080101.0000 gfct 2 0 -4.84165294861E-04 0.00000000000E+00 1.1610E-11 0.0000E+00 20080101.0000 20090101.0000 trnd 2 0 -9.43320784610E-11 0.00000000000E+00 2.5920E-11 0.0000E+00 20080101.0000 20090101.0000 gfct 2 0 -4.84165389193E-04 0.00000000000E+00 1.4310E-11 0.0000E+00 20090101.0000 20100101.0000 trnd 2 0 8.70342406588E-11 0.00000000000E+00 2.5510E-11 0.0000E+00 20090101.0000 20100101.0000 gfct 2 0 -4.84165302159E-04 0.00000000000E+00 1.1190E-11 0.0000E+00 20100101.0000 20110101.0000 trnd 2 0 -7.35363996161E-11 0.00000000000E+00 2.0690E-11 0.0000E+00 20100101.0000 20110101.0000 gfct 2 0 -4.84165375695E-04 0.00000000000E+00 9.4960E-12 0.0000E+00 20110101.0000 20120101.0000 trnd 2 0 -3.37998268890E-12 0.00000000000E+00 2.2270E-11 0.0000E+00 20110101.0000 20120101.0000 gfct 2 0 -4.84165379075E-04 0.00000000000E+00 1.2770E-11 0.0000E+00 20120101.0000 20500101.0000 trnd 2 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 20120101.0000 20500101.0000 acos 2 0 3.86222759789E-11 0.00000000000E+00 3.7480E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 asin 2 0 5.42428904167E-11 0.00000000000E+00 3.4040E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 acos 2 0 3.79017840266E-11 0.00000000000E+00 3.6170E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 asin 2 0 -1.63073508081E-11 0.00000000000E+00 3.4940E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 gfct 3 0 9.57230649180E-07 0.00000000000E+00 2.0640E-11 0.0000E+00 19500101.0000 20030101.0000 trnd 3 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 19500101.0000 20030101.0000 gfct 3 0 9.57230649180E-07 0.00000000000E+00 2.0640E-11 0.0000E+00 20030101.0000 20040101.0000 trnd 3 0 -3.56703733670E-11 0.00000000000E+00 2.9970E-11 0.0000E+00 20030101.0000 20040101.0000 gfct 3 0 9.57194978807E-07 0.00000000000E+00 9.3380E-12 0.0000E+00 20040101.0000 20050101.0000 trnd 3 0 3.08093802616E-11 0.00000000000E+00 1.7280E-11 0.0000E+00 20040101.0000 20050101.0000 gfct 3 0 9.57226944519E-07 0.00000000000E+00 7.9380E-12 0.0000E+00 20050101.0000 20060101.0000 trnd 3 0 -2.78269686170E-11 0.00000000000E+00 1.6280E-11 0.0000E+00 20050101.0000 20060101.0000 gfct 3 0 9.57199117551E-07 0.00000000000E+00 8.3430E-12 0.0000E+00 20060101.0000 20070101.0000 trnd 3 0 -1.30773225160E-11 0.00000000000E+00 1.7890E-11 0.0000E+00 20060101.0000 20070101.0000 gfct 3 0 9.57186040228E-07 0.00000000000E+00 9.5480E-12 0.0000E+00 20070101.0000 20080101.0000 trnd 3 0 2.05157925353E-11 0.00000000000E+00 1.8710E-11 0.0000E+00 20070101.0000 20080101.0000 gfct 3 0 9.57206556021E-07 0.00000000000E+00 9.1630E-12 0.0000E+00 20080101.0000 20090101.0000 trnd 3 0 -1.82456060326E-11 0.00000000000E+00 1.8600E-11 0.0000E+00 20080101.0000 20090101.0000 gfct 3 0 9.57188310415E-07 0.00000000000E+00 9.4370E-12 0.0000E+00 20090101.0000 20100101.0000 trnd 3 0 5.50107990134E-12 0.00000000000E+00 1.7480E-11 0.0000E+00 20090101.0000 20100101.0000 gfct 3 0 9.57193811495E-07 0.00000000000E+00 8.0420E-12 0.0000E+00 20100101.0000 20110101.0000 trnd 3 0 3.46875561982E-12 0.00000000000E+00 1.7210E-11 0.0000E+00 20100101.0000 20110101.0000 gfct 3 0 9.57197280250E-07 0.00000000000E+00 9.1660E-12 0.0000E+00 20110101.0000 20120101.0000 trnd 3 0 -2.39216234841E-11 0.00000000000E+00 2.3140E-11 0.0000E+00 20110101.0000 20120101.0000 gfct 3 0 9.57173358627E-07 0.00000000000E+00 1.3970E-11 0.0000E+00 20120101.0000 20500101.0000 trnd 3 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 20120101.0000 20500101.0000 acos 3 0 -1.98043168686E-11 0.00000000000E+00 3.1810E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 asin 3 0 8.46099539065E-11 0.00000000000E+00 3.0640E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 acos 3 0 1.03484588578E-11 0.00000000000E+00 3.2840E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 asin 3 0 -9.57608731050E-12 0.00000000000E+00 3.1510E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 gfct 4 0 5.40014095747E-07 0.00000000000E+00 8.1020E-12 0.0000E+00 19500101.0000 20030101.0000 trnd 4 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 19500101.0000 20030101.0000 gfct 4 0 5.40014095747E-07 0.00000000000E+00 8.1020E-12 0.0000E+00 20030101.0000 20040101.0000 trnd 4 0 -7.71550486919E-12 0.00000000000E+00 1.1370E-11 0.0000E+00 20030101.0000 20040101.0000 gfct 4 0 5.40006380242E-07 0.00000000000E+00 3.2670E-12 0.0000E+00 20040101.0000 20050101.0000 trnd 4 0 -2.57613639068E-11 0.00000000000E+00 6.1040E-12 0.0000E+00 20040101.0000 20050101.0000 gfct 4 0 5.39980658801E-07 0.00000000000E+00 2.8370E-12 0.0000E+00 20050101.0000 20060101.0000 trnd 4 0 -3.39011179460E-12 0.00000000000E+00 5.9500E-12 0.0000E+00 20050101.0000 20060101.0000 gfct 4 0 5.39977268689E-07 0.00000000000E+00 3.1130E-12 0.0000E+00 20060101.0000 20070101.0000 trnd 4 0 8.93546315817E-13 0.00000000000E+00 6.2200E-12 0.0000E+00 20060101.0000 20070101.0000 gfct 4 0 5.39978162236E-07 0.00000000000E+00 3.1080E-12 0.0000E+00 20070101.0000 20080101.0000 trnd 4 0 3.02642992745E-11 0.00000000000E+00 6.3590E-12 0.0000E+00 20070101.0000 20080101.0000 gfct 4 0 5.40008426535E-07 0.00000000000E+00 3.2510E-12 0.0000E+00 20080101.0000 20090101.0000 trnd 4 0 6.50363033165E-12 0.00000000000E+00 6.8900E-12 0.0000E+00 20080101.0000 20090101.0000 gfct 4 0 5.40014930165E-07 0.00000000000E+00 3.6390E-12 0.0000E+00 20090101.0000 20100101.0000 trnd 4 0 -5.34743057105E-11 0.00000000000E+00 7.0800E-12 0.0000E+00 20090101.0000 20100101.0000 gfct 4 0 5.39961455860E-07 0.00000000000E+00 3.4400E-12 0.0000E+00 20100101.0000 20110101.0000 trnd 4 0 4.16424917919E-12 0.00000000000E+00 6.9250E-12 0.0000E+00 20100101.0000 20110101.0000 gfct 4 0 5.39965620109E-07 0.00000000000E+00 3.4850E-12 0.0000E+00 20110101.0000 20120101.0000 trnd 4 0 8.86388087748E-12 0.00000000000E+00 7.9420E-12 0.0000E+00 20110101.0000 20120101.0000 gfct 4 0 5.39974483990E-07 0.00000000000E+00 4.4580E-12 0.0000E+00 20120101.0000 20500101.0000 trnd 4 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 20120101.0000 20500101.0000 acos 4 0 -6.10800875827E-12 0.00000000000E+00 1.2090E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 asin 4 0 -1.26312751925E-12 0.00000000000E+00 1.1260E-12 0.0000E+00 19500101.0000 20500101.0000 1.0 acos 4 0 5.57873529327E-12 0.00000000000E+00 1.1660E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 asin 4 0 -1.48660001597E-11 0.00000000000E+00 1.1520E-12 0.0000E+00 19500101.0000 20500101.0000 0.5 gfct 5 0 6.87122664048E-08 0.00000000000E+00 6.1050E-12 0.0000E+00 19500101.0000 20030101.0000 trnd 5 0 0.00000000000E+00 0.00000000000E+00 0.0000E+00 0.0000E+00 19500101.0000 20030101.0000 gfct 5 0 6.87122664048E-08 0.00000000000E+00 6.1050E-12 0.0000E+00 20030101.0000 20040101.0000 trnd 5 0 -2.24859957377E-11 0.00000000000E+00 8.5610E-12 0.0000E+00 20030101.0000 20040101.0000 gfct 5 0 6.86897804090E-08 0.00000000000E+00 2.4560E-12 0.0000E+00 20040101.0000 20050101.0000 trnd 5 0 -1.20206617157E-11 0.00000000000E+00 4.6140E-12 0.0000E+00 20040101.0000 20050101.0000 gfct 5 0 6.86768179622E-08 0.00000000000E+00 2.1580E-12 0.0000E+00 20050101.0000 20060101.0000 trnd 5 0 4.81638210830E-12 0.00000000000E+00 4.5470E-12 0.0000E+00 20050101.0000 20060101.0000 gfct 5 0 6.86816343443E-08 0.00000000000E+00 2.3880E-12 0.0000E+00 20060101.0000 20070101.0000 trnd 5 0 -6.90560943155E-12 0.00000000000E+00 4.7510E-12 0.0000E+00 20060101.0000 20070101.0000 gfct 5 0 6.86747287349E-08 0.00000000000E+00 2.3630E-12 0.0000E+00 20070101.0000 20080101.0000 trnd 5 0 9.42534485154E-12 0.00000000000E+00 4.8590E-12 0.0000E+00 20070101.0000 20080101.0000 gfct 5 0 6.86841540798E-08 0.00000000000E+00 2.4960E-12 0.0000E+00 20080101.0000 20090101.0000 trnd 5 0 -2.36712221149E-11 0.00000000000E+00 5.2520E-12 0.0000E+00 20080101.0000 20090101.0000 gfct 5 0 6.86604828577E-08 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