============================================================================= | NOAA/NGS ANALYSIS STRATEGY SUMMARY | | (template version 2.0, 07 Aug. 2006) | ============================================================================= | Analysis Center | National Oceanic & Atmospheric Administration (NOAA) | | | National Geodetic Survey (NGS) | | | SSMC3; N/NGS2 | | | 1315 East-West Highway | | | Silver Spring, MD 20910 | | | USA | | | | | | Analysis Center code: NGS | | | website: http://www.ngs.noaa.gov/ | | | phone: 301-713-3209, fax: 301-713-4322 | |---------------------------------------------------------------------------| | Contact people | William Kass | | | e-mail: Bill.Kass@noaa.gov | | | phone : 301-713-3209 ext.164 | | | Robert Dulaney | | | e-mail: bobd@ngs.noaa.gov | | | phone : 301-713-3209 ext.168 | | | Jake Griffiths | | | e-mail: Jake.Griffiths@noaa.gov | | | phone : 301-713-3205 ext.153 | | | Stephen Hilla | | | e-mail: Steve.Hilla@noaa.gov | | | phone : 301-713-2851 ext.208 | | | Jim Ray | | | e-mail: jimr@ngs.noaa.gov | | | phone : 301-713-2850 ext.112 | | | Jim Rohde | | | e-mail: Jim.Rohde@noaa.gov | | | phone : 301-713-2851 ext.209 | | | Gerald Mader | | | e-mail: Gerald.L.Mader@noaa.gov | | | phone : 301-713-2854 ext.201 | | | William Dillinger | | | e-mail: William.H.Dillinger@noaa.gov | | | phone : 301-713-2850 ext.210 | | | | |---------------------------------------------------------------------------| | Software used | "pages" developed at NOAA/NGS for the primary | | | observations & parameter set-up; | | | "gpscom" for the combination of reduced normal | | | equation systems for subnetworks of observations | |---------------------------------------------------------------------------| | GNSS system(s) | GPS | |---------------------------------------------------------------------------| | Final products | ngsWWWWn.sp3 daily orbit & satellite clock files | | generated for | ngsWWWW7.erp weekly ERP file of daily values | | GPS Week 'WWWW' | ngsWWWW7.sum weekly analysis summary file | | day of Week 'n' | ngsWWWW7.snx weekly SINEX file | | (n=0,1,...,6) | ngsWWWWn.tro daily tropo estimates at 1-hr intervals | | | | | Rapid products | ngrWWWWn.sp3 daily orbit & satellite clock files | | generated daily | ngrWWWWn.erp daily ERP file | | | | | | NOTES: | | | * Ephemeris files use SP3c format | | | * SP3c accuracy codes based on formal errors of orbit | | | parameters | | | * Clock values are extracted from Broadcast message | | | * ERP files contain estimates for pole, pole-rate, & | | | LOD; the initial UT1-UTC is a constrained a-priori | | | value; subsequent UT1-UTC values are estimates | | | consistent with the reported LOD values | | | * Tropo files began starting week 1404 | | | | |---------------------------------------------------------------------------| | Preparation date | 2006-12-05 (original updated version) | |---------------------------------------------------------------------------| | Modification dates| 2007-01-10: add tropo product files (from week 1404) | | | 2007-01-14: begin using Delaunay triangulation to | | | create double-differenced baseline networks | | | (from Rapid week 1409-6, Final week 1410) | | | 2007-01-28: begin using elevation-dependent obs | | | weights (from Rapid week 1413-2, Final week 1412) | | | 2007-03-11: begin using IGS polar motions as a-priori | | | values (from Rapid and Final week 1418) | | | 2007-04-22: begin modeling lunar eclipses (from Rapid | | | and Final weeks 1424) | | | 2007-06-29: change orbit model parameterization to | | | CODE-like (Rapid week 1433-4, Final week 1433) | | | 2007-08-12: begin deleting eclipse data for pre-IIR | | | satellites in Final (week 1440); same change in | | | Rapids from week 1453-4; previous text here on yaw | | | attitude modeling was incorrect & was corrected | | | 2007-12-03: begin using IAU 2000 nutation model to | | | replace IAU 1980 model (Rapid 1456-0, Final 1455) | | | 2008-05-30: gravity model changed from GEM-T3 to | | | EGM96 starting Rapid 1481-5, Final 1479 | | | 200?-??-??: ... | | | | |---------------------------------------------------------------------------| | Effective date | 2006-11-05 (GPS week 1400) and later, including IGS | | for data analysis | reanalysis campaign (for data before week 1460) | |---------------------------------------------------------------------------| | Instructions: Please provide as complete information as possible. The | | template below is illustrative only; replies should reflect | | actual analysis implementation. Please accumulate changes | | with effective dates of usage, rather than remove earlier | | information. | ============================================================================= ============================================================================= | MEASUREMENT MODELS | |---------------------------------------------------------------------------| | Preprocessing | RINEX files pre-screened using TEQC metrics to reject | | | small/incomplete files (<85%), excessive phase slips | | | (>500), or high multipath (>1.2 m). | | | | | | Phase preprocessing in a baseline by baseline mode | | | using double-differences. In most cases cycle slips | | | are fixed automatically looking simultaneously at | | | different linear combinations of L1 and L2. Rarely, | | | manual editing is done on baselines showing larger | | | than normal post-fit RMS statistics in the all- | | | baseline combined solution. In that case, bad data | | | points are removed or new phase bias ambiguities are | | | estimated. | | | | | | 1 ms RINEX clock jumps fixed using clockprep. | |---------------------------------------------------------------------------| | Basic observables| Double-differenced carrier phase; code only used for | | | receiver clock synchronization and to aid in fixing | | | phase ambiguities using the Melbourne-Wuebbena widelane| | | method. Double-differenced baseline network defined | | | using optimal Delaunay triangulation algorithm (from | | | 2007-01-14); see Renka (1997). | | |--------------------------------------------------------| | | elevation angle cutoff: 10 degrees | | | sampling rate: 30 seconds | | | weighting: (for raw obs *before* iono correction) | | | * carrier phase = 5 cm sigma (nominally) at zenith | | | * uniform weighting applied (no elevation-dependent | | | scaling) before week 1412 | | | * weighting model changed starting week 1412 to: | | | sigma = (5 + 2/sin(elevation)) cm | | | * parameter sigmas rescaled to give reduced chi^2 | | | of 1 for the postfit phase residuals | | | deweighting: a few consistently ill-behaved satellites | | | are deweighted by a factor of 2 a-priori | | | smoothing: no smoothing is applied | | | code biases: C1 & P2' corrected to P1 & P2 using | | | cc2noncc tool depending on receiver type | |---------------------------------------------------------------------------| | Modeled | Double-differenced carrier phase with ionosphere-free | | observables | linear combination applied | |---------------------------------------------------------------------------| |*Satellite antenna| SV-specific z-offsets & block-specific x- & y-offsets | | -center of mass | (from manufacturers) from file igs05_wwww.atx based on | | offsets | GFZ/TUM analyses using fixed ITRF2000 coordinates | | | [refer to IGS Mail #5189, 17 Aug 2005] | |---------------------------------------------------------------------------| |*Satellite antenna| block-specific nadir angle-dependent "absolute" PCVs | | phase center | applied from file igs05_wwww.atx; no azimuth-dependent | | corrections | corrections applied | | | [refer to IGS Mail #5189, 17 Aug 2005] | |---------------------------------------------------------------------------| |*Satellite clock | 2nd order relativistic correction for non-zero | | corrections | orbit ellipticity (-2*R*V/c) applied | | | [NOTE: other dynamical relativistic effects under | | | Orbit Models] | |---------------------------------------------------------------------------| | GPS attitude | GPS satellite yaw attitude model: none applied; | | model | data during eclipse deleted for pre-IIR satellites | |---------------------------------------------------------------------------| |*RHC phase | phase wind-up applied according to Wu et al. (1993) | | rotation corr. | | |---------------------------------------------------------------------------| |*Ground antenna | "absolute" elevation- & azimuth-dependent (when | | phase center | available) PCVs & L1/L2 offsets from ARP applied from | | offsets & | file igs05_wwww.atx | | corrections | [refer to IGS Mail #5189, 17 Aug 2005] | |---------------------------------------------------------------------------| |*Antenna radome | calibration applied if given in file igs05_wwww.atx; | | calibrations | otherwise radome effect neglected (radome => NONE) | |---------------------------------------------------------------------------| |*Marker -> antenna| dN,dE,dU eccentricities from site logs applied to | | ARP eccentricity | compute station marker coordinates | |---------------------------------------------------------------------------| | Troposphere | met data input: latitude, longitude, height, & DOY | | a priori model | climate model from Boehm et al. (2007) | | | (GPT version 2006June16); | | | rel. humidity set to 50% for all sites | | (parameter |--------------------------------------------------------| | estimation is | zenith delay: Saastamoinen (1972) "dry" + "wet" using | | below) | synthesized input met data | | |--------------------------------------------------------| | | mapping function: GMF (Boehm et al., 2006) for dry & | | | wet zenith delays individually | | |--------------------------------------------------------| | | horiz. grad. model: no a priori gradient model is used | |---------------------------------------------------------------------------| |*Ionosphere | 1st order effect: accounted for by dual-frequency | | | observations in linear combination | | |--------------------------------------------------------| | | 2nd order effect: no corrections applied | | |--------------------------------------------------------| | | other effects: no other corrections applied | |---------------------------------------------------------------------------| |*Tidal |*solid Earth tide: IERS 2003 (dehanttideinel.f routine, | | displacements | based on Ch. 7.1.2) | | |--------------------------------------------------------| | |*permanent tide: zero-frequency contribution left in | | (IERS Conventions| tide model, NOT in site coordinates | | 2003, Ch. 4, eqn |--------------------------------------------------------| | 11 contributions)|*solid Earth pole tide: IERS 2003; mean pole removed | | | by linear trend (Ch. 7, eqn 23a & 23b) | | |--------------------------------------------------------| | |*oceanic pole tide: no model is applied | | | [IERS Conventions updated, Ch. 7, | | | eqn 27] | | |--------------------------------------------------------| | |*ocean tide loading: IERS Conventions 2003 (updated | | | Ch. 7, 2006) using site-dependent | | | amps & phase for 11 main tides from | | | Bos & Scherneck website for FES2004 | | | model; NEU site displacements computed | | | using hardisp.f from D. Agnew; CMC | | | corrections applied to station tidal | | | coefficients and to SP3 orbits. | | | (See also NOTES below.) | | |--------------------------------------------------------| | |*ocean tide geocenter: site-dependent coeffs corrected | | | for center of mass motion of whole | | | Earth; CMC corrections also applied | | | to SP3 orbits. (See also NOTES below.) | | |--------------------------------------------------------| | | atmosphere tides: corrections for S1 & S2 tidal | | | pressure loading not applied (no model | | | available yet) | | | [IERS model under development] | |---------------------------------------------------------------------------| |*Non-tidal | atmospheric pressure: not applied | | loadings |--------------------------------------------------------| | | ocean bottom pressure: not applied | | |--------------------------------------------------------| | | surface hydrology: not applied | | |--------------------------------------------------------| | | other effects: none applied | |---------------------------------------------------------------------------| |*Earth orientation| ocean tidal: diurnal/semidiurnal variations in x,y, & | | variations | UT1 applied according to IERS 2003 (ortho_eop.f)| | |--------------------------------------------------------| | (near 12 & 24 hr | atmosphere tidal: S1, S2, S3 tides not applied | | only; longer | [no IERS model specified yet] | | period tidal |--------------------------------------------------------| | corrections | high-frequency nutation: prograde diurnal polar motion | | should not be | corrections (IERS 2003, Table 5.1) applied | | applied) | using IERS routine PMsdnut.for | | |--------------------------------------------------------| | | | [NOTE: effects are included in observation model as well as in the | | transformation of orbits from inertial to terrestrial frame] | ============================================================================= ============================================================================= | REFERENCE FRAMES | |---------------------------------------------------------------------------| | Time argument | GPS time as given by observation epochs, which is | | | offset by only a fixed constant (approx.) from TT/TDT | | | | | | [NOTE: Please specify which general relativistic | | | timescale is the underlying basis for the time | | | argument used in the analysis. For instance, | | | geocentric time, TCG, is recommended by the IAU but | | | is not generally used in practice; see NOTES below.] | |---------------------------------------------------------------------------| | Inertial | geocentric; mean equator and equinox of 2000 Jan 1.5 | | frame | (J2000.0) | |---------------------------------------------------------------------------| | Terrestrial | ITRF2005 reference frame realized through the set of up| | frame | to 130 station coordinates and velocities given in the | | | IGS internal realization IGS05.snx (aligned to | | | ITRF2005). Some reference stations may be excluded | | | based on significant non-linear motions or | | | discontinuities. | | | The datum is specified tightly for Rapid solutions by | | | fixing the orientation and origin to IGS05 using | | | NNR+NNT constraints wrt IGS05 coordinates. | | | The datum for Finals is specified only for orientation | | | using NNR constraints wrt IGS05 coordinates. | |---------------------------------------------------------------------------| | Tracking | use all available stations of the 132 IGS05 set, plus | | network | add others based mostly on geometry up to a total of | | | ~ 315 stations; data are processed in double-difference| | | subnets and combined at the normal equation level; | | | a core net ensures interconnection of the subnets. | | | Double-differenced baseline network defined using | | | optimal Delaunay triangulation algorithm (from | | | 2007-01-14); see Renka (1997). | |---------------------------------------------------------------------------| | Interconnection | precession: IAU 1976 Precession Theory | | |--------------------------------------------------------| | (EOP parameter | nutation: IAU 1980 Nutation Theory until 2007-12-02; | | estimation is | updated to IAU 2000 Nutation model beginning | | below) | 2007-12-03 (Rapid week 1456-0, Final week | | | 1455) | | |--------------------------------------------------------| | | a priori EOPs: UT1 interpolated from IERS Bulletin A, | | | updated weekly. Polar motion interpolated | | | from IGS Rapid and Ultra-rapid realizations, | | | updated every six hours. | ============================================================================= ============================================================================= | ORBIT MODELS | |---------------------------------------------------------------------------| | Geopotential | GEM-T3 model up to degree and order 8 till wk 1479; | | (static) | changed to EGM96 for Finals wk 1479, Rapids 1481-5; | | | C21 & S21 modeled according to polar motion variations | | | (IERS 2003, Ch. 6) | | |--------------------------------------------------------| | | GM=398600.4415 km**3/sec**2 (for TT/TDT time argument) | | | [NOTE: see Relativity Notes below.] | | |--------------------------------------------------------| | | AE = 6378136.3 m | |---------------------------------------------------------------------------| | Tidal variations |*solid Earth tides: C20,C21,S21,C22, and S22 as in IERS | | in geopotential | (1992); n=2 order-dependent Love numbers & frequency | | | dependent corrections for 6 (2,1) tides from Richard | | | Eanes (private comm., 1995) | | |--------------------------------------------------------| | | ocean tides: no model applied | | |--------------------------------------------------------| | |*solid Earth pole tide: no model applied | | |--------------------------------------------------------| | | oceanic pole tide: no model applied | |---------------------------------------------------------------------------| | Third-body | Sun & Moon as point masses | | forces | | | |--------------------------------------------------------| | | ephemeris: Generated from the MIT PEP program | | |--------------------------------------------------------| | | GM_Sun 132712440000.0000 km**3/sec**2 | | | GM_Moon 4902.7989 km**3/sec**2 | |---------------------------------------------------------------------------| | Solar radiation | a priori: Berne 9-parameter SRP model with D,Y,B | | pressure model | scales plus once-per-rev sines & cosines; | | | a priori values from fit to prior day's | | | orbit & weak constraints applied to the | | | 6 periodic terms. (thru wk 1432) | | | | | | From wk 1433 the CODE operational version of | | | their SRP model is applied, which adjusts | | | the D,Y,B offsets plus once-per-rev sine & | | | cosine only for the B direction (orthogonal | | | to the Direct and Y-axis directions). In | | | addition, the velocities of all SVs are | | | allowed to change at noon each day subject | | | to a constraint of 10^-6 to 10^-5 m/s. No | | | other constraints are applied. A priori | | | values continue to come from fit to prior | | | day's orbit. | | | | | | Shielding from solar radiation by the earth | | | and moon is handled by scaling the SRP | | | acceleration according to the fraction of | | | the shielding (e.g., 0 <= lambda <= 1). | | (parameter |--------------------------------------------------------| | estimation is | Earth shadow model: umbra & penumbra included | | below) |--------------------------------------------------------| | | Earth albedo: not applied | | |--------------------------------------------------------| | | Moon shadow model: umbra & penumbra included (from | | | wk 1424) | | |--------------------------------------------------------| | | satellite attitude: no model applied; eclipse data | | | deleted for pre-IIR satelllites | | |--------------------------------------------------------| | | other forces: none applied | |---------------------------------------------------------------------------| |*Relativitic | dynamical correction: not applied | | effects | (see IERS 2003, Ch. 10, eqn 1) | | |--------------------------------------------------------| | | gravitational time delay: IERS 2003, Ch. 11, eqn 17 | | | applied | | |--------------------------------------------------------| | | | [NOTE: see NOTES ON RELATIVISTIC EFFECTS below.] | |---------------------------------------------------------------------------| | Numerical | variable (high) order Adams-Moulton predictor-corrector| | integration | with direct integration of second-order equations | | |--------------------------------------------------------| | | integration step-size: variable | | |--------------------------------------------------------| | | starter procedure: Runge-Kutta Formulation; initial | | | conditions taken from prior orbit solution at 12:00 | | |--------------------------------------------------------| | | arc length: 24 hours (00:00:00 - 23:59:30 GPS time) | ============================================================================= ============================================================================= | ESTIMATED PARAMETERS (& APRIORI VALUES & CONSTRAINTS) | | | | Note on NGS parameter estimation: PAGES uses batch weighted least-squares | | estimation. Time-varying quantities can be modeled using offset | | parameters for specified intervals. Offset parameters at boundaries | | between fitting intervals can be constrained to be equal, which gives | | a piecewise linear, continuous model. Otherwise, piecewise linear step | | offsets are estimated. In general, a priori constraints can be applied | | for any parameter. | | | | For efficiency, the processing of large networks is usually done by first | | processing suitable subnetworks down to reduced normal equations, which | | are then combined to determine global parameters. | | | |---------------------------------------------------------------------------| | Adjustment | weighted least squares and Helmert blocking to | | method | process subnetworks separately (pages) and then | | | combined (gpscom). | |---------------------------------------------------------------------------| | Data span | 24 hours used for each daily analysis | | | (00:00:00 - 23:59:30 GPS time) | |---------------------------------------------------------------------------| |*Station | all station coordinates are adjusted, relative to the | | coordinates | a priori values from IGS05.snx; a no-net-rotation | | | condition is applied wrt the IGS05 frame using up to | | | 132 reference frame stations; apriori sigmas for non- | | | reference frame stations are 1 m for each component. | |---------------------------------------------------------------------------| | Satellite clocks | not estimated but eliminated by double-differencing; | | | Broadcast values reported in SP3 files. | | |--------------------------------------------------------| | | sp3,clk files: Broadcast values inserted | |---------------------------------------------------------------------------| | Receiver clocks | not estimated but eliminated by double-differencing; | | | observations are adjusted in the preprocessing using | | | receiver clock offsets derived from the pseudoranges | | | (to ensure that all obs are aligned to the same time | | | scale) but no receiver clocks are truly estimated. | |---------------------------------------------------------------------------| | Orbits | thru wk 1432: | | | Geocentric position and velocity, solar radiation | | | pressure scales and once-per-revolution perturbation | | | terms. Radiation pressure scaling factors and | | | perturbation terms are estimated for each of the | | | orthogonal directions: satellites - sun, body centered | | | Y, and orthogonal third directions estimated as | | | constant offsets for each one-day arc; plus once-per- | | | rev sine/cosine terms are estimated with apriori values| | | from the prior day, and weak apriori constraints | | | | | | from wk 1433: | | | Geocentric positions and velocities, solar radiation | | | pressure scales in 3 directions and once-per-rev terms | | | in 1 direction, & noon velocity breaks in 3 directions.| | | Radiation pressure scale factors estimated for each | | | orthogonal direction: satellite-sun, body-centered Y, | | | & orthogonal 3rd component, estimated as constant | | | offsets for each one-day arc; plus once-per-rev sine & | | | cosine terms estimated only for 3rd component. | | | Geocentric velocity breaks adjusted in all 3 | | | components with change constraints of 10^-6 to | | | 10^-5 m/s. No apriori applied on estimates. | | |--------------------------------------------------------| | | sp3 files: orbits transformed to crust-fixed (rotating)| | | frame accounting for geocenter motions due | | | to ocean tides and for subdaily tidal EOP | | | variations | | | [NOTE: see NOTES below for details] | |---------------------------------------------------------------------------| | Satellite | no attitude parameters are adjusted | | attitude | | |---------------------------------------------------------------------------| | Troposphere | zenith delay: residual delays are adjusted for each | | | station assuming mostly dominated by | | | "wet" component; before Rapid week 1420-1| | | and Final week 1416, the zenith delay was| | | parameterized by a piecewise linear, | | | continuous model with 1-hr intervals. | | | Now, the delay is parameterized by a | | | piecewise-constant, discontinuous model. | | |--------------------------------------------------------| | | mapping function: GMF (Boehm et al., 2006) wet function| | | used to estimate zenith delay residuals | | |--------------------------------------------------------| | | zenith delay epochs: each integer hour | | |--------------------------------------------------------| | | gradients: one N-S & one E-W gradient parameter at the | | | beginning and end of each day for each | | | station, with continuous linear variation| | | during the day; no a priori constraints | | | are applied (see Bar-Sever et al, 1998) | |---------------------------------------------------------------------------| | Ionospheric | not estimated | | correction | | |---------------------------------------------------------------------------| | Ambiguity | real-valued double-differenced phase cycle ambiguities | | | adjusted except when they can be resolved confidently | | | (<4.5 cm uncertainty), in which case they are fixed; | | | roughly 95% of all ambiguities are fixed using modern | | | network data | |---------------------------------------------------------------------------| |*Earth orientation| daily x & y pole offsets, pole-rates, and LOD at noon | | parameters (EOP) | epochs; x and y pole estimated as piece-wise, linear | | | offsets from IERS Bulletin A a prioris and IGS ERP | | | a prioris over each 1-day segment; estimates then | | | transformed to equivalent offsets and rates at noon | | | epochs to be consistent with IGS conventions; UT1 not | | | adjusted | |---------------------------------------------------------------------------| | Other | none | | parameters | | ============================================================================= ============================================================================= | NOTES ON RELATIVISTIC EFFECTS | |---------------------------------------------------------------------------| | Here is a brief summary of the relativistic effects involved in modeling | | satellite orbits to determine a terrestrial reference frame (TRF), etc: | | * The dynamical formulation should be in an geocentric frame, applying | | the relativitistic corrections listed below for the effects on signal | | propagation and satellite dynamics. | | * If the TDT time scale (i.e., no secular rate term included between TT = | | TAI+32.184s and the time coordinate used for the dynamics) is used, as | | is still common despite IAU/IUGG recommendations to use TCG, then the | | appropriate value for GM = 398600.4415 km**3/sec**2. However, this | | choice of modeling will result in a TRF which differs from TCG units; | | the TRF will need to be scaled upward by (1 + L_G) = (1 + 0.69... ppb) | | to be consistent with a TCG timescale. | | * If the IAU-recommended TCG timescale is used (the secular rate term | | included between TT and the TCG time coordinate used for the dynamics), | | then the appropriate value for GM = 398600.4418 km**3/sec**2. For this | | choice of modeling, the TRF scale will be consistent with IAU/IUGG | | recommendations. | | * The observation modeling should include the following relativistic | | effects: | | [1] The 1st-order effects on GPS satellite clocks due to time dilation | | and gravitational potential shifts have been accounted for by offsets | | applied in the oscillator settings aboard the spacecraft, assuming | | nominal orbital elements. The 2nd-order effects due to non-circular | | orbits must be handled by applying a periodic time correction: | | -2(R V)/c^2 | | where R is the satellite position, V its velocity, and c the speed of | | light; see IS-GPS-200 (formerly ICD-GPS-200). | | [2] The coordinate time of propagation, including the gravitational delay | | ("gravitational bending"), as given in IERS Conventions 2003, Ch. 11, | | eqn 17, for the effect of the Earth's mass. | | [3] The "dynamical correction" to the acceleration of near-Earth | | satellites, as given in IERS Conventions 2003, Ch. 10, eqn 1. The | | 2004 version differs from earlier editions by the addition of terms | | for the Lense-Thirring precession (frame dragging) and geodesic (de | | sitter) precession, which are probably negligible for the short arcs | | used in most GPS analyses. | | Note that the IERS/IGS formulation for clock modeling neglects the Earth's| | oblateness, an effect estimated by Kouba (2004) to be ~0.2 ns/day (same | | level as IGS clock accuracy) with periodic variations at 6 hrs and near | | 14 days. | ============================================================================= ============================================================================= | NOTES ON HANDLING OCEAN TIDAL LOADING DISPLACEMENT EFFECTS | |---------------------------------------------------------------------------| | There are three main parts involved in implementing model corrections for | | ocean tidal loading (OTL) effects in GPS analyses to be fully self- | | consistent: | | [1] Site-dependent tidal coefficients | | Site-dependent amplitude & phase values for the 11 main tides (in BLQ | | format) are generated upon request by the Bos-Scherneck OTL service at | | http://www.oso.chalmers.se/~loading/ | | Users are advised to select one of the more modern ocean models from the | | list available, such as FES2004 models. | | For the option "Do you want to correct your loading values for the [center| | of mass] motion?" the answer should be "YES" (but the default is "NO"). | | [Note that for users of IGS orbits (in sp3 format) it is generally *not* | | necessary to consider the center of mass effect because this has already | | been taken into account by the IGS (see below). That is, the IGS orbits | | are expressed with respect to the Earth's crust as a fixed frame. So, for| | such applications, site-dependent coefficients should be with the option | | "Do you want to correct your loading values for the motion?" set to the | | default "NO".] | | [2] Site-dependent tidal displacements | | Given previously computed site-dependent amp & phase values for the 11 | | main tides (in BLQ format), the hardisp.f routine, written by Duncan Agnew| | (UCSD), determines local dU, dS, dW displacements. The code can be found | | at the IERS Conventions Update site at | | ftp://tai.bipm.org/iers/convupdt/chapter7/hardisp.f | | This routine considers a total of 141 constituent tides using a spline | | interpolation of the tidal admittances, achieving a precision is about 1%.| | [3] Center-of-mass orbit correction | | After the Analysis Centers determine the GPS orbits in an inertial frame, | | taking account of the OTL effects as described above, it is necessary as | | a final step in generating sp3 format orbit results to account for the | | crust-frame motions due to the ocean tidal mass. This can be done by | | computing the net crustal frame translations dX(t), dY(t), and dZ(t) | | according to the method given by Scherneck at | | http://www.oso.chalmers.se/~loading/cmc.html : | | | | dX(t) = SUM_i=1,11 { Xin(i) * cos(ANGLE(t,i)) + Xcr(i) * sin(ANGLE(t,i)) }| | dY(t) = SUM_i=1,11 { Yin(i) * cos(ANGLE(t,i)) + Ycr(i) * sin(ANGLE(t,i)) }| | dZ(t) = SUM_i=1,11 { Zin(i) * cos(ANGLE(t,i)) + Zcr(i) * sin(ANGLE(t,i)) }| | | | where ?in(i) are the in-phase and ?cr(i) are the cross-phase amplitudes | | for the 11 main ocean tides. ANGLE(t,i) is the angular argument returned | | by the IERS subroutine ARG(YEAR,DOY,ANGLE) for YEAR being the (current | | year - 1900) and DOY being the day of year and fraction thereof. The ARG | | routine is available at the IERS Conventions Update website: | | ftp://tai.bipm.org/iers/convupdt/chapter7/ARG.f | | Scherneck has tabulated the center of mass motion in-phase and cross-phase| | coefficients for the various ocean models at: | | http://www.oso.chalmers.se/~loading/CMC/ | | Note that on each tidal constituent record, the entries are ordered as: | | tide, model name, Zin, Zcr, Xin, Xcr, Yin, Ycr | | using the format (a,1p,t42,3(2x,2e12.4)). | | In order to correct the GPS inertial orbits (ORB_cm) to the moving | | crust-fixed frame (ORB_sp3), in addition to whatever other transformations| | are applied, the following translations should also be made: | | ORB_cm(t) - dXYZ(t) --> ORB_sp3(t) | | where dXYZ(t) is the dX(t), dY(t), dZ(t) vector computed above. Note that| | this correction is exactly analogous to the rotational corrections that | | must be applied to create sp3 orbits whenever a sub-daily EOP tidal model | | is used in the GPS data analysis. | ============================================================================= ============================================================================= | REFERENCES | |---------------------------------------------------------------------------| | Bar-Sever, Y.E., New GPS attitude model, IGS Mail #591, 1995, | | http://igscb.jpl.nasa.gov/mail/igsmail/1994/msg00166.html | | | | Bar-Sever, Y., P.M. Kroger, & J.A. Borjesson, Estimating horizontal | | gradients of tropospheric delay with a single GPS receiver, J. Geoph. | | Res., 103(B3), 5019-5035, 1998. | | | | Boehm, J., A.E. Niell, P. Tregoning, & H. Schuh, Global Mapping Function | | (GMF): A new empirical mapping function based on numerical weather | | model data, Geophys. Res. Lett., 33, L07304, doi: 10.1029/2005GL025545, | | 2006. | | | | Boehm, J., R. Heinkelmann, & H. Schuh, Short Note: A global model of | | pressure and temperature for geodetic applications, J. Geod., | | doi:10.1007/s00190-007-0135-3, 2007. | | | | Bos, M.S., & H.-G. Scherneck, website at www.oso.chalmers.se/~loading/ | | | | IERS Conventions 2003, D.D. McCarthy & G. Petit (editors), IERS Technical | | Note 32, Frankfurt am Main: Verlag des Bundesamts fuer Kartographie und | | Geodaesie, 2004. (see also updates at website) | | | | Kouba, J., Improved relativistic transformations in GPS, GPS Solutions, | | 8(3), 170-180, 2004. | | | | Renka, R., Algorithm 772: STRIPACK, Delaunay triangulation and Voronoi | | diagram on the surface of a sphere, ACM Transactions on Mathematical | | Software, 23(3), 1997. available at: | | http://orion.math.iastate.edu/burkardt/f_src/stripack/stripack.html | | | | Saastamoinen, J., Atmospheric correction for the troposphere and | | stratosphere in radio ranging of satellites, in The Use of Artificial | | Satellites for Geodesy, Geophys. Monogr. Ser. 15 (S.W. Henriksen et al.,| | eds.), AGU, Washington, D.C., pp.247-251, 1972. | | | | Wu, J.T., S.C. Wu, G.A. Hajj, W.I. Bertiger, & S.M. Lichten, Effects of | | antenna orientation on GPS carrier phase, Manuscripta Geodaetica,18, | | 91-98, 1993. | ============================================================================= |* = strong consistency with IERS/IGS conventions is especially important | | for these items | =============================================================================