Gravity model development for precise orbit computations for satellite altimetry

Gravity model development for precise orbit computations for satellite altimetry
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  Adv.  Space Res.  Vol.  6.  No. 9,  pp.  89—98.  1986  0273—1177/86  S0.OO  +  .50 Printed  in  Great  Britain. Al!  rights  reserved.  Copynght ©  COSPAR GRAVITY MODEL  DEVELOPMENT  FOR PRECISE ORBIT COMPUTATIONS FOR  SATELLITE  ALTIMETRY James  G. Marsh,* Francis J.  Lerch,*  David  E. Smith,*Steven  M.  Klosko,**  Erricos  Pav1is~~* and  Ronald  G.  Williamson** *NASA  Goddard   Space   Flight Center,  Geodynamics  Branch! Code  621,  Greenbelt,  MD  20771,  U.S.A. **EG&G   Washington  Analytical  Services  Center,  Incorporated,  Lanham,  MD  20706,  U.S.A. ABSTRACT Satellite  altimeters  have been  developed which  have  the  capability  of’  measuring  the  surface topography  of  the  ocean  over  entire  basins  for time  periods  of  several  years  with  a precision  of  a  few  cm.  The  combination  of  these  data with  accurate satellite positionInformation, subsurface  measurements and models  of  the  density  field  can  be used to determine  the  general  circulation  of  the  ocean  and its  variability.  The  Topex altimeter oceanographic  experiment proposed  for the  early  1990’s  requires  a  radial  orbit accuracy approaching  10  cm.  Considerable  progress  has been  made  at  the  Goddard  Space  Flight  Center in  developing  precision  orbit  determination  to  support satellite altimetry  analysis.  This progress  is  attributed  to  the  development  of  more  accurate  models  of  the  earth  gravity field,  earth  and  ocean  tidal  effects,  a  reference  coordinate  system  as  well  as Improveddrag  and  solar  radiation  pressure computations.  This  computational  system  has been usedfor  the Seasat  data  acquired  during  the  1978 time period  and has  produced  an  rms  radial accuracy  of  about  50  cm.  A  first  step  towards  the  development  of  a  new  Interim gravity model  is  presented.  Global  orbit  determination  accuracies  have been  improved  using these new  PGS-T1  and  T2  fields. INTRODUCTION  - Gravity  field  development  has been  art  on—going  activity  at  Goddard  Space  Flight  Center (GSFC) for  at  least fifteen  years.  The models  which  have been  produced,  have  been designated  with  the  acronyms  “GEM”  standing  for  Goddard  Earth  Models and  “PGS”  for Preliminary Gravity  Solutions.  When  published,  global  models  are  given  the GEM  designation,whereas  models  of  interest  (e.g.  tailored  fields,  preliminary  solutions)  are  named  PGS. Over  the last  decade  these  models  have  generally  kept pace  with  the  rapid  improvementswhich  have  occurred  in  the  precision  by  which near—earth satellites  are  tracked  and  the orbital  accuracy requirements  of  the  missions themselves.  In  order  to do so when  global models  were  inadequate,  some  models  of  a  satellite—specific, tailored character  were developed. However,  new  NASA  missions foreseen  for the  1990’s  require  further  global gravity  model improvement  to  achieve  their  mission  objectives.  In  particular,  the Topex/Poseidon oceanographic  satellite  (planned  for the  early  1990’s)  which  will  carry  a radar  altimeter,  as  its  primary instrument, requires  a  radial  orbit accuracy  of  ±13 cm.The  achievement  of  ±13cm radial  accuracy  for the  1300km  altitude  TOPEX/Poseidon  satellite is  quite  difficult.  Many  force  and  measurement models must  be  evaluated and  undoubtedlyimproved  to  achieve  this  stringent requirement. Table  1  lists  some  of  the  requirements which  need to  be  addressed. Although  the  adequacy  of each of  these  models  needs reassessment,  the  principal limitation  in  reaching  the  TOPEX!  Poseidon  objective  is  the adequacy  of  the  gravity field modeling available  today.  Current  orbit  determination  capa - bilities using  any contemporary  gravity  model  would produce  a  ±50 cm or so  radial  uncer - tainty  on  TOPEX/Poseidon.  Even  after  an  extensive development  effort  for the  improvement of  the  geopotential  model,  gravity  error  is  expected  to  remain  as  the  largest contributing error  source  for  altimetry  utilization. Table  2  /1/  presents  the  error  budget  projected for  TOPEX altimeter experiments. The  recovery  of  a  new  Interim  Gravity  Model  is  both  costly and  time  consuming.  It requires  the  arduous  analysis  of  large  amounts  of  data  spanning  diverse observational systems  and the  building  of  large  numerical  systems  of  equations permitting  a  simultaneous solution  of  several thousand  unknowns.  Consequently,  the  preparation of   an improved  model for  missions  which  are  still  in  the  planning  stages  requires extensive pre—launchresearch.  Also,  the  errors  in  the the  field  must be  thoroughly understood  to  obtain reasonable estimates  of  future  trajectory  determination  accuracy  on TOPEX. Approximately  two  years  ago,  a  major  gravity field improvement  effort  was  undertaken  by GSFC  and the  Center  for  Space Research  at  the  University  of Texas.  This  report discusses  two preliminary gravity models  which  have been  recently  developed  as  a  first  stepin  reaching  the  TOPEX/Poseidon  modeling  goals. They have been  obtained  by GSFC from  an 89 JASR  6~9—G  90  J. G. Marsh  et   al. analysis  of   exclusively  satellite  tracking observations.  These  spherical  harmonic  models are  complete  to  degree  and  order  36  and  are  called  Preliminary Gravity Solutions  -  Ti  and T2.  Other  models  which  will  include  satellite—to—satellite  tracking, spaceborne radar altimeter observations  and  surface gravity  measurements  are  in the  planning  stages.  These later  fields will  all  be  based  upon  the  long  wavelength  information  contained within  the  Ti and  12  fields. Although  the  demands  of  future  orbital missions  made  the  re—recovery  of’  a  gravity modeldesirable,  the  availability  of  the  CYBER  205  “super—computer”  at  GSFC  played  a  large  role in  making  this  task both  feasible  within  the  time  constraints  imposed  upon us  and  practical from  a  resource assessment.  The vectorization  of  our  orbit  determination GEODYN system and the  SOLVE  least  squares solution  system  was  a  major  step in  laying  the  foundation  for  a complete  and  total  re—iteration  of   our  previous  gravity modeling  activities.  The  last such re—iteration  of  all  least—squares  normal  matrices  occured  more than  ten  years  ago  in preparation  for  the  GEM—7  gravity  model  /3/. THE  DEVELOPMENT  OF PGS-Ti  and  12 The  total reiteration  of the data  analysis  and  matrix generation  activities  for  PGS—T1  and T2  permitted  a  consistency  heretofore  unobtainable  in  earlier  GEM  models  in  terms  of  adopted  constants,  data  treatment,  non-conservative  force  modeling and  in the  definition  of a  reference  frame.  In the  past,  as the  state  of   the  science  evolved, only  the  most  recent data  sets benefitted  from  improved  modeling.  The  inconsistencies associated  with  an evolving  science  and  the  lag  time  required  for  their  implementation  in our data  analysis have  been  avoided  by  design in the  creation  of   PGS-T1  and  —T2.  Models  with  “clear parentage”  have  now  been  produced which  are  based  largely  on  the  constants  defined  by  the MERIT  Standards  /14/   with  some  significant  improvements.  Additionally, other  NASA  activ - ities  like  the  Crustal  Dynamics  Program  have  provided  a  priori station  coordinates  and earth  rotation  series  going  into  the  development  of  our  new  fields.  These models,  values and  treatments are described  within  this  report.  The  speed  of the  Cyber  205  system  allowed the  new  computation  of   500  normal  matrices in  less  than  three  months  time. A  brief   overview  of the  activities  which  have been  completed  at  Goddard  to  develop  PGS—T1 and  T2  is  shown  in  Table  3.  The  woCk   which  is  described  therein  was  quite  extensive,  but was  found  to  be  necessary.  The  unique  internal  consistency of the  fields  could only  be obtained  through  this  elaborate preparation  of  reference  parameters,  station  coordinates, and  constants  and  the  implementation  of’  significant  advancements  in  our  software  systems. A  general  description  of’  the  constants  and  force  models  employed  in  solution is  found  in Table  l4~  The  details  of the  computation  of a  new  set  of   apriori  tracking  station coordinates  Is  found  in  Table  5.  Never  before  have  we  spent  so  much  effort  in  the preparation of the  apriori  reference  coordinate  system  and  corresponding  station  geodetics for a  new  gravity  field. An  overview  of the  P05—Ti  and  72  solutions  is  presented in Figure  1.  The  fields areidentical  in  size  and  data  content.  However  in  PGS—T2,  66  ocean  tidal  parameters  were adjusted  simultaneously  with  the  gravity  field.  The  PGS—T1  and  T2  are  very  close  since both  fields  were  calculated  using  large  models  for  earth  and  ocean  tides.  The  earth tidal model  was  that  developed  by Wahr  /5/.  The  ocean  tidal  models  were  developed  as part of   our solution  preparation  and  were  predicted  from  point admittances  wi~hin  the  long  period, semi—  diurnal  and  diurnal  bands. As  a  result,  over  600  ocean  tidal  coefficients  were utilized  to give long  wavelength  modeling  for  thirty—two  major  and  minor  tidal  constituents  /6/. TRACKING  DATA There  are  perhaps Sixty satellites  which  received Sufficient tracking  to  warrant their consideration for  inclusion  in  our  gravity  modeling  activities.  The  TOPEX  orbit determination requirements  are  such  that  at least  a  four—fold  Improvement over  existing field accuracies  is  necessary.  Such  an  improvement  can  only  be  accomplished with  improved data  handling  and  validation directed  at  existing historical  data  sets.  Some  manageable framework   for  selecting,  qualifying  and  processing  those  data  which  were  deemed  most important  was  developed  as  a  preliminary  step  in the  creation  of   PGS—Ti  and  T2. One  of the  first  tasks  was  the  selection  of the  most  important  data  sets  upon  which  a“satellite—only”  field  could  be  computed.  The  sixty objects  which had  geodetic  quality data  sets  and  orbits  which  were  reasonably  free  of  large perturbations  due  to  air  drag  were evaluated according  to  certain  criteria:  (a)  the  quality,  quantity and  global  distribution of’  their  tracking  data  sets,  (b)  the  uniqueness  of  orbital  characteristics,  Cc)  an  estimate of  the  size of  the  non-conservative  perturbations  on  the  satellite,  Cd)  the  similarity  of the  orbit  to that  anticipated  for  TOPEX,  Ce)  the  distribution  of  the  data  set  over  the satelite’s apsidal  period and  (f)  the  sensitivity  of  the  satellite’s  orbit  to  presentweaknesses  in  existing gravity  models.  Gravity  Model  Development  91 Laser  systems  are  currently  the  most  accurate  and  advanced means  of  precision satellite tracking.  These  ranging systems  have also  substantially evolved  and  have  undergone  nearly a  ten—fold improvement  in  system precision  every  five  years  of  the  last  decade.  The  evolu - tion  of  laser systems  typify  the  progress  which  has  been  made  in  monitoring the motion  of near-earth satellites  and has  resulted  in much more  stringent demands  for  geopotential models  capable  of  utilizing  data  which  now  are accurate  to  a  few  centimeters. Obviously, our  data  selection  criteria found  that the  laser  data  was very  important  and  it  was  heavily used in  the  development  of PGS—T1  and  T2.  There  are ten  satellites which  were  tracked  by NASA’s  laser  systems.  The  seven satellites which  had  third  generation  laser  tracking  were used  In  our  new  models. Eleven  satellites which  were ranked  in  the top  fifteen  overall,  were  selected.  A  summary of’  the data  which  were  used  to  form  the  new  models  is  presented  in  Table  6.  The  number  of  observations,  the  number  of   individual  normal  matrices  and  the data types are  described. While  approximately 80%  of  the  data  found  in PGS—Ti  and  72  have  not  been  used  previously  in GEM  solutions,  the  overall amount  of data  which  is  now  utilized  is  comparable  to  that  which was  analyzed  to  produce “satellite—only” fields such  as  GEM—9  /7/.  Preparation  of  seven additional  low inclination satellite  data  sets for  inclusion  in  the  TI  and  T2  models  is already  underway.  A  field  containing these  additional  data sets  (a  19  satellite  solution) will  be  published  as  GEM—Ti. Preliminary  tests  with  a  subset  of  these  new  low  inclination data  incorporated within  the  solution indicate  that the  zonal  harmonics  are  better resolved,  but  little  else  changes  in  the  performance  of  the  field  on  our  test data  sets. EVALUATION  OF  THE  PGS—T1  AND  T2  GRAVITY MODELSOne  of  the  best  ways,  and  in  our  case,  most  relevant means  for  assessing  the  accuracy  of  a gravity model comes  through  tests using orbital tracking  data.  A  stzeable  number  of such tests  have been  performed  on  our  new  fields.  Table  7  compares  the RMS  of  fit  to  satellitetracking  data sets  obtained  from  several  contemporary  geopotential  models  (both  ours  and those  from  Europe) with  what  is  now  obtained  in  PGS—T2.  The  results  indicate  a  very significant  amount  of  improvement  in  orbital  modeling  with  the use  of  PGS-T2.  This improvement  is  noteworthy because  PGS—T2  now  out—performs  even  “tailored”  models  in  orbitcomputational accuracy. Starlette  is an  excellent  vehicle  for  field  assessment.  It is  orbiting  at  a  much  lower altitude  than  Lageos  (950Km  vs  5900km)  yet has  small  non—conservative  perturbations  (like Lageos) given  its  great  density and  small  surface  area.  Starlette  has  been  tracked  by  a global  network  of’  lasers  and has  a  geographically well—distributed  data  complement.  By orbiting  at 950km,  Starlette  sees  a  richer  and  more complicated gravity  field  than  TOPEX and  therefore  is  important  for  assessing  TOPEX  modeling  capabilities.  In  the past  a tailored  gravity  model  /2/  called  PGS-1331  was  developed  for  Starlette  and  adopted  for use on  this  orbit  for  the  MERIT Campaign. Remarkably,  as  shown  in  Figure  2,  the  new PGS—T2  nowfits the  Starlette  data  at  the  20cm  RMS  level  compared  to 75cm  found  with  PGS—i331.  This is  a  very  dramatic  reduction  in  rms fit and  indicates  to us  that all  of  our  work  towards the  recovery  of’  an  improved  gravity  model  has  been  successful.  We  believe  that 10cm  radial accuracies  are  now  being  achieved  for  Starlette  based  upon  these  results. Test  againstindependent  Lageos observations comparing GEM—L2 and PGS—T2  also  indicate field  improve - ment.  These  results are  shown  in  Table  8.  GEM-L2  was  adopted  for  MERIT  Lageos  analyses. Seasat  altimetry  has  also  been  used  to  test  the  radial  performance  of the  new  fields.  By using  an  altimeter  crossing  arc  technique,  the  non—geographically  correlated  radial  errors in  the  orbit  can  be  directly  measured.  In the  past,  as  indicated  in Figure  3,  altimetry data  was  needed  in  the  gravity  solution  to  achieve  sub—meter  radial  modeling  on  this orbit. To  achieve  the  best results, Seasat  altimetry was  used.  Our  PGS-T2  model  is independent  of  all  altimetry  yet  still  performs  at  a  considerably  improved  level  from that obtainable  in  PGS—S14  /8/  which  was  a  Seasat  tailored  field.  The  improvement presented  in Figure  3  Is  global  in  nature,  as  shown  in Figure  14  where  PGS—T2  outperforms  PGS-S14  in  all geographic  locations. The  results which  have been  shown indicate  that  a  single  new  model  out—performs  even tailored  models  on  all  satellite orbits  tested. Clearly,  at  least  to  us,  an  improved global  estimate  of  the  field  has  been  achieved  with  an  improved  description  of  the  geoid.This  later  conclusion  Is  confirmed  with  tests  against  Seasat derived oceanic  mean  gravityanomalies.  A  base  model  has  been  developed  which, when  augmented  with  additional satellitetracking,  satellite  tracking satellite, altimetry,  and  surface  gravity  data  sets,  will yield  a  highly accurate  new  interim gravity  model  for  TOPEX operations. SUMMARY The  salient  points  describing  GSFC’s latest gravity  field development activities  are  shown in  Table  9.  While preliminary,  we feel  that the  accomplishments  to date  are  of  great  92  J.  G.  Marsh  et   al. significance  and  Indicate major  modeling  advancements.  Much  remains  to  be  accomplished  as our  TOPEX  objective  Is  approached.  The  plans  for our  future are  shown  in  Table  10. Nevertheless,  results  to date  Indicate  that  substantial progress  has  been made in  our contemporary  models  of  the  earth’s geopotential.REFERENCES 1.  R.  Stewart,  L.L.  Fu,  and  M.  Lefebvre, “Science  opportunities  from  the  Topex/Poseidon mission,”  Jet  Propulsion  Laboratory  Publication  86—18,  (1986) 2.  J.G.  Marsh,  F.J.  Lerch,  and  R.G.  Williamson, “Precision  geodesy and  geodynamics  using Starlette  laser  ranging,”  J.  Geophys.  Res.,  90, 811,  93335-93145,  (1985) 3.  C.A.  Wagner,  F.J.  Lerch,  3.  Brownd,  and  J.  Richardson,  “Improvement  In the geopotentialderived  from  satellite  and  surface  data  (GEM  7  and  8),”  J.  Geophys.  Res., 82,  5,  (1977) LI.  N.  Melbourne,  et  al.,  “Project Merit Standards,”  U.S.N.0.  Circular  No.  167,  December (1983) 5.  J.  Wahr,  “The  tidal  motions  of a  rotating, elliptical, elastic,  and  oceanless  earth,” Ph.D.  Dissertation,  Univ.  of   Colorado,  (1980) 6.  D.C.  Christodoulidis,  R.G.  Williamson,  0. Chinn  and  R.  Estes,  “On  the  prediction  of  ocean  tides  for  minor  constituents,”  10th  InternatIonal  Symposium  on  Earth Tides, Madrid,  Spain,  1986. 7.  F.J.  Lerch,  S.M.  Klosko,  R.E.  Laubscher,  and  C.A.  Wagner,  “Gravity  model Improvement using  GEOS—3 (GEM  9  and  10),”  J.  Geophys.  Rem.,  84, 138,  3897-3915  (1979)8.  F.J.  Lerch,  J.G.  Marsh,  S.M.  Klosko, and  R.G.  Williamson,  “Gravity  model  improvement for  Seasat,”  J.  Geophys.  Rem.,  87,  C5,  3281—3296  (1982.1)  Gravity Model  Development  93 TAStE  1  Precision  Orbit  Computations  in  Support of  Satellite  Altimetry:  Requirements •  SOFTWARE  DEVELOPMENT  FOR  PRECISION ORBIT  DETERMINATION  AND  GEODETIC PARAMETER  ESTIMATION •  IMPROVED EARTH  GRAVITY  AND  TIDAL  MODELS •  IMPROVED  NON-CONSERVATIVE  FORCE MODELS S ACCURATE EARTH ORIENTATION  AND TRACKING  STATION  COORDINATES S  CONSISTENT CONSTANTS S  GOOD  UNDERSTANDING  OF  HISTORICAL  DATAS ACCURATE  TRACKING SYSTEMS TABLE 2  Topex/Poseidon  Measurement  Uncertainty  (1  Sigma) [ERROR SOURCE  [UNCERTAINTY[ ALTIMETER •  instrument  noise  2.0  cm •  bias/drIft  2.0 MEDIA •  EM  bias  2.0 •  skewness  1.0 •  tropospheric refraction-dry  term  0.7 •  tropospheric  refraction-wet  term  1.2 •  ionospheric refraction  1.3 0R~IT •  gravity  10.0 •  station  geodetics  5.0 •  higher  order  ionosphere (doppler) 5.0 •GM  2.0 •  atmospheric  drag  1.0 •  solar radiation pressure  1.0 •  earth  albedo radiation  1.0 •  earth and ocean  tides  1.0 •  station  and  spacecraft clock  1.0 •  tropospheric  effects  1.0RSS  Absolute  Error  [~i3.3 cmi MAJOR  ASSUMPTIONS I. duel  frequencq  altimeter  ‘1. -‘1300  km  altitude 2. duel  frequencij  radiometer  8.  no  anomalous dots 3.  upgraded   TRAN(T  tracking  sqstem   (eq   no  rain) (40  ,tstion,)  9.  improved  qr.vit~j model 4.  altimeter  data  averaged  over 3s tO. ~3  mbar  surface pressure 5.  H  1/3  =2m,  wave  skewness  0.1  from weather  charts 6.  tabular  corrections  b.~ed on  limited  Il.  100 ~.ts  spececraft clock waveform  tracker  comparisons
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