Flechtner F.M., Gruber Th., G?ntner A., Mandea M., Rothacher M., Sch?ne T., Wickert J. (Eds.) System Earth via Geodetic-Geophysical Space Techniques

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GGOS-D Integration with Low Earth Orbiters

Daniel König and Rolf König

1 Introduction

The general goal is to determine consistently the dynamic and the geometric part

of a terrestrial reference system. The dynamic part is deﬁned by the Earth’s grav-

ity ﬁeld, the geometric part is given by the Earth’s shape and orientation in space.

Determining both the dynamic and geometric part is done very efﬁciently by making

use of a global navigation satellite system (GNSS) as well as of some Low alti-

tude Earth Orbiters (LEOs). The dynamic part is mainly determined by the LEOs

whose orbits are highly sensitive to its variations. Using the GNSS signals collected

onboard the LEOs their orbits can be determined very accurately and thus the vari-

ations in the dynamic part. Processing the GNSS signals collected at the ground

stations allows for deriving their positions that represent the geometric part.

Conventionally, the dynamic and geometric parts are determined separately and

they are combined later on the normal equation level. These separate process-

ings are commonly carried out following the two-step approach where ﬁrstly the

orbits and clock offsets of the GPS satellites are determined and then introduced as

ﬁxed for processing the LEOs in a second step. Thus the two-step approach suffers

from a loss of consistency by neglecting the correlations inherent to the parameter

estimation problem.

Opposed to this processing scheme the method applied here is the integrated

approach (IA) of satellite orbit determination and parameter estimation (Zhu et al.,

2004) where all measurements collected by the LEOs and the ground stations are

already combined on the observation level. Thus a consistent solution considering

all correlations is achieved. Within this method the high-orbiting GNSS satellites

provide stability to the whole conﬁguration whereas the LEOs scan the Earth’s grav-

ity ﬁeld very densely with a high temporal resolution. The GNSS used in this context

is the Global Positioning System (GPS).

D. König (B)

Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences,

Department 1: Geodesy and Remote Sensing, Telegrafenberg, 14473 Potsdam, Germany

e-mail: dkoenig@gfz-potsdam.de

577

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_48,



Springer-Verlag Berlin Heidelberg 2010

578 D. König and R. König

2 Characterization of the Integrated Processings

The processings following the IA are carried out by differential orbit improvement

(Kaula, 1966). They are characterized by the satellites involved, the observational

data used, and the parameters estimated.

The satellites involved comprise the full GPS constellation with semi-major axes

of the orbits of about 26,600 km as well as the LEOs CHAMP, GRACE-A, and

GRACE-B having semi-major axes of about 6,800 km.

The link between the Earth and the several types of satellites is established

through the observations used. They comprise GPS phase and code measure-

ments collected on the one hand at the ground stations of the International GNSS

Service’s (IGS; Dow et al., 2005) network (GPS/ground) and on the other hand

collected onboard the LEOs by satellite-to-satellite tracking (GPS/SST), K-band

range-rate measurements from the GRACE intersatellite link, down-weighted satel-

lite laser ranging normal points (SLR NPs), as well as accelerations and attitude

measured onboard the LEOs, see Table 1. The GPS observations are processed as

L3 ionosphere-free linear combinations. About 50 globally distributed GPS ground

stations are selected per day out of the IGS network. The SLR NPs are measured

by the station network of the International Laser Ranging Service (ILRS; Pearlman

et al., 2002) and exhibit a non-uniform and sparse distribution in space and time.

Table 1 Characterisation of the observations used

Observation type Source Time spacing

GPS/ground IGS station network 30 s

GPS/SST CHAMP, GRACE 30 s

K-band range-rate GRACE 5 s

Accelerations CHAMP, GRACE 5 s

Attitude CHAMP, GRACE 5 s

SLR normal points ILRS station network Sporadic

The whole processing consists of orbit determination and parameter estimation

“runs” each covering a single day. In case of K-band data gaps the length of a

run might be reduced. The processings have been carried out using GFZ’s EPOS

software (Earth Parameter and Orbit System) and cover the period 2004-02-04 to

2004-12-31.

Besides a multitude of parameters set up in order to model the various non-

conservative forces acting on each satellite or to precisely model observation errors

only a rather small set of Earth system parameters is of interest. As listed in Table 2,

this set comprises the positions of the GPS ground stations, the spherical harmonic

coefﬁcients C

of the Earth’s gravity ﬁeld up to degree and order 2, and Earth

rotation parameters (ERPs). They are all constrained to their a priori values with a

sigma corresponding to 10 cm on the Earth’s surface. The parameter estimation is

done by least squares adjustment and is based on the GPS and K-band observations.

GGOS-D Integration with Low Earth Orbiters 579

Table 2 Solved-for Earth system parameters

Characteristics

Estimated parameters

Up to degree and order 2

Station positions GPS stations

ERPs Polar motion, UT1-UTC

Ofﬂine parameters

Parameters of Helmert

transformations between

estimated and a priori station

positions

3 translations, global scale, 3

rotations

Entering the parameter estimation as well, the SLR NPs do not inﬂuence the solution

due to their low weight.

The dynamic part of the terrestrial reference system is made up by the estimated

spherical harmonic coefﬁcients C

of the Earth’s gravity ﬁeld. Thereby the

coefﬁcients of degree one – C

– represent the position of the Earth’s

centre of mass, i.e. the origin of the dynamic part (dynamic origin), in x-, y-, and

z-direction, respectively. The ERPs describe part of the Earth’s orientation in space.

In order to concisely describe the geometric part of the terrestrial reference sys-

tem additionally its origin, its scale as well as its orientation with respect to the

a priori station coordinates are determined ofﬂine, i.e. subsequently to each orbit

adjustment run, by carrying out seven-parameter Helmert transformations between

the estimated and the a priori station positions. The resulting parameters are indi-

cated in Table 2. Notably, all Earth system parameters are determined with daily

resolution.

3 Comparison with a Two-Step Processing

In order to assess the beneﬁt of simultaneously estimating all Earth system parame-

ters in a single step, a two-step processing has been carried out that is comparable to

the processing following the IA. I.e., in a ﬁrst step the GPS orbits, all GPS-related

parameters like clock offsets and carrier phase ambiguities, as well as the ground

station positions and the ERPs were estimated. Then, the GPS orbits and clock off-

sets as well as the estimated ground station positions and ERPs were introduced as

ﬁxed into the second step the orbits of the LEOs and the gravity harmonic coefﬁ-

cients were estimated in. The performance of both parameter estimation processes

is revealed by the resulting residuals and the deviations of the estimated parameters

from their expectations.

The residuals considered here are those of the GPS/SST phase measurements

as well as those of the SLR NPs of the LEOs. As the SLR NPs do not inﬂuence

the solutions of either processing scheme their residuals act as an absolute quality

indicator. The GPS/SST phase residuals, on the other hand, are of relative nature

revealing the inner quality of the adjustments.

580 D. König and R. König

RMS per orbit [cm]

2004 2004.5 2005

0.5

1.5

2.5

Integrated (0.4 cm global RMS)

Two-step (1.3 cm global RMS)

GPS/SST phase

Year

RMS per orbit [cm]

2004 2004.5 2005

Integrated (3.6 cm global RMS)

Two-step (7.4 cm global RMS)

SLR NPs (LEOs)

Fig. 1 Time series of orbit-wise RMS values of GPS/SST phase and LEO SLR residuals for the

IA (“Integrated”) and a corresponding two-step processing (“Two-step”)

For both types of residuals the RMS values per run are shown in Fig. 1. As is

clearly visible from the plots and indicated by the global RMS values the IA leads

to much reduced residuals as well for GPS/SST phase as for SLR observations.

Concerning the estimated parameters the IA delivers more reasonable and accu-

rate results, too. For example, this is revealed by the time series of the gravity

harmonic coefﬁcients of degree one determined by both methods as shown in Fig. 2.

Especially in C

, the z-component, which in general is the problematic direction in

GNSS, the scatter of the time series around its expectation of zero is much smaller

for the IA than for the two-step processing.

Thus it can be concluded that the IA stabilizes the GNSS geocenter considerably

compared to standard solutions.

4 Time Series of the Dynamic Origin

Out of the various Earth system parameter solutions the components of the dynamic

origin are presented here (Fig. 2). The unweighted standard deviations are in

the range of about a centimeter revealing a stable solution despite the ambitious

GGOS-D Integration with Low Earth Orbiters 581

[m]

2004 2004.5 2005

–0.2

–0.1

0.1

0.2

[m]

2004 2004.5 2005

–0.2

–0.1

0.1

0.2

Integrated

Two-step

Year

[m]

2004 2004.5 2005

–0.2

–0.1

0.1

0.2

Fig. 2 Time series of the components of the dynamic origin from the IA and a corresponding two-

step processing. Mean values with standard deviations of time series referring to the integrated

approach: –0.8 ± 9.8 mm (C

), +0.2 ± 10.8 mm (S

), and –6.3 ± 13.5 mm (C

)

resolution of one day. A higher scatter is visible in C

and S

around August 2004

due to reduced lengths of the corresponding orbit runs because of K-band data gaps.

and S

exhibit no signiﬁcant offsets from their expectations of zero. The

comparatively high mean in C

is obviously due to its strong signal with a period

of approximately 1 year. Due to the restricted length of the series of less than 1 year

a conﬁrmation of the long-term presence of an annual signal is not possible. The

reason for the occurrence of the signal is not yet understood.

5 Conclusions and Outlook

In the framework of determining a geodetic Earth reference frame the IA has been

applied to process GPS ground, CHAMP, and GRACE data simultaneously for esti-

mating various parameters constituting both the dynamic and the geometric part.

582 D. König and R. König

Corresponding time series have been determined for GPS ground station positions,

gravity harmonic coefﬁcients up to degree and order two, and ERPs covering almost

the year 2004.

Evidence was given that the IA performs much better than a comparable two-step

method as revealed by the SST phase and SLR residuals of the LEOs and the scatter

in the components of the dynamic origin. The time series of the dynamic origin

currently exhibit a precision in the range of a centimetre showing no signiﬁcant

offsets from their expectations.

The time series of the gravity harmonic coefﬁcients still needs to be validated,

however external solutions with daily resolution are not available on the market. For

geophysical interpretation t he processing period needs to be extended which is not

easily achievable due to heavy computational requirements.

Acknowledgments This study was funded within the Geotechnologien program under the grant

1286 of the German Federal Ministry of Education and Research (BMBF). Data was provided by

the IAG services IERS, IGS, and ILRS.

References

Dow JM, Neilan RE, Gendt G (2005) The International GPS Service (IGS): Celebrating the

10th anniversary and looking to the next decade. Adv. Space Res. 36(3), 320–326, doi:

10.1016/j.asr.2005.05.125.

Kaula WM (1966) Theory of Satellite Geodesy. Blaisdell Publication Cie., Waltham.

König D, König R, Panaﬁdina N (2007) Combination of ground observations and LEO data.

Geotechnologien Science Report No. 11, ISSN 1619–7399.

Pearlman MR, Degnan JJ, Bosworth JM (2002) The international laser ranging service. Adv. Space

Res. 30(2), 135–143, doi: 10.1016/S0273–1177(02)00277–6.

Zhu S, Reigber C, König R (2004) Integrated adjustment of CHAMP, GRACE and GPS data. J.

Geod., 78(1–2), 103–108.

Index

A-10 absolute gravity values, 281

Absolute gravity meters A-10, 278–280, 294

Accelerometer, 4, 7, 41–43, 52–53, 56, 95–96,

101–102, 105–109, 113, 115–118,

131, 135–136, 143, 147–149,

151–154, 156, 159, 162, 164,

205–207, 217–218, 255, 265,

482, 534

Accelerometer biases, 147

Accumulated error, 46, 234

Accuracy assessment of spectral

parameters, 379

ACC variability, 187, 198

Advanced Stellar Compass, 5, 108, 482,

490–493

Agreement between in-situ and GRACE

measurements, 175

AJISAI, 140

Algonquin Park, 568

Aliasing, 119, 163, 174, 188, 192, 196, 198,

239, 290, 300, 379, 413

effect, 413

All different GRACE products, 181–182

Altimeter Database and Processing System

(ADS), 317–318, 359

Altimetry, 4, 49, 132, 134, 150, 155, 169,

203–204, 211, 235, 272, 313–322,

326, 332, 351–357, 359–364, 371,

530–531, 533–534, 536

Amazon river basin, 420

Amplitudes of variability, 176

Analysis centre, 37, 335–336, 339, 555

Analysis tool, 532, 542–543

Angular acceleration, 113, 207–208

Annual cycle, 179–180, 183, 192, 327,

330–331, 344

Annual model solutions, 352

Antarctic Circumpolar Current (ACC), 103,

136, 146, 148, 152, 154, 169,

172–173, 176–178, 182–183,

187–189, 191–195, 197–198, 307,

327, 482

dynamics, 187

Antarctic geoid project, 245

Antarctic Oscillation (AAO), 187

AOD1B product, 100, 103, 131–133, 135–138,

140, 143, 151, 156

Apache Webserver, 23

Application framework, 23

Arc length, 7, 32, 43, 81, 102, 153–155, 164,

446, 547

Arc speciﬁc parameters, 145–147

Arctic, 44, 50, 102, 124, 132, 170, 178–179,

182, 245, 300

Arctic gravity project, 50, 245

Arctic ocean, 44, 102, 124, 132, 179,

182, 300

ARGO, 298, 315, 351–357

Assimilation, 123, 138, 211, 298, 300, 302,

305–308, 314–315, 322, 325–332,

355–356, 373, 378, 385, 430–431,

433–434, 436–439, 443, 461–470

Astrogeodetic deﬂection data, 287

Astrogeodetic proﬁles, 279, 286

Astrogeodetic vertical deﬂections, 278,

285–289, 294

Astronomic levelling, 286

Atlantic meridional overturning

circulation, 179

Atmospheric drag, 61–63, 144, 147,

207, 216

Atmospheric parameters, 67, 430, 433, 455,

536, 548, 565

Atmospheric pressure gradient, 187

Atmospheric sounding, 437–438

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8,



Springer-Verlag Berlin Heidelberg 2010

583

584 Index

Atmospheric tides, 80, 135, 137, 140, 144,

151, 156, 320

Attitude, 5, 10, 20, 29–31, 33–39, 69, 72,

108, 113, 144, 147, 207, 484, 488,

491–493, 578

Autocorrelation, 220–221

Averaged bottom pressure, 188

Background models (GRACE background

models), 12, 42–43, 46–48, 50,

55–56, 63, 99, 101, 103, 143–144,

149–151, 153, 156, 192, 257, 373,

400, 402

Backup, 27

Band-limited base functions, 244, 246–247,

249, 251–252

Barotropic, 12, 44, 47, 55, 101–102, 132, 140,

176, 183, 187–188, 190, 297–298,

302, 307–308, 353–355

Barotropic component, 176

Barotropic ocean circulation, 297, 302

Barotropic stream function, 353–355

Barotropic variations in the ACC, 188

Baseline, 10, 12, 38, 42, 46, 55, 69, 100, 103,

136–138, 143, 145–147, 149–150,

152–154, 156, 205, 270, 478,

548–550, 569

Basin-average, 370, 373

Bending angle, 430, 434, 436–437, 443,

455–456, 459, 461–470

Bernese GPS Software, 338, 548, 557

Block-diagonal normal equations, 236–238

Block-diagonal-techniques, 241

Bonn, 98, 164, 167, 213, 549, 556–557

Bottom pressure, 8, 12, 42, 44, 47, 95–103,

120, 123, 125–126, 132, 137–138,

151, 169–184, 188–197, 204, 211,

277, 297–308, 348, 355, 369

BRIDGE, 96

Calc/Solve software, 549

Calibration, 4–5, 7, 41, 56, 96–97, 162, 173,

205–206, 208–209, 211–212, 270,

275, 277, 279, 286, 319, 346–347,

373–374, 377, 384–385, 413–414,

417–425, 429, 433, 461, 485,

487–490, 534, 559

parameters, 7, 41, 162, 206, 275, 418–419,

485, 487

Cal/val, 277

Camera noise, 151–153

C20-coefﬁcient, 156, 239

Challenging Mini-Satellite Payload (CHAMP),

3–12, 15–28, 29–39, 41–56, 59–65,

67–75, 79–92, 95–96, 99–100, 102,

108, 131, 137–138, 174, 176, 209,

211, 215, 218, 231, 239, 255, 284,

313, 429–431, 433–439, 443–453,

455–459, 461–470, 475–524, 534,

578, 581

decay scenario, 6

Characteristic periods, 373, 377–385

Cholesky decomposition, 238, 240

Closed-loop, 143, 228, 270, 272–273

simulation, 143, 228

Coastal north east Paciﬁc, 180

Coherent OBP variability, 172, 176–179

Combination

methodology, 556–558

models, 41, 210, 231–241, 272

scheme, 161, 239

solutions, 210, 231–232, 240, 278

Common-mode, 207–209, 215

Commuting matrices, 250, 252

Comparison, 31–32, 34, 50–55, 61–62, 69,

101, 114–115, 117, 124, 137,

171–172, 174–176, 182, 190, 211,

258, 261, 265, 269–270, 277, 278,

282, 284, 287–288, 292, 297–308,

327–328, 330–331, 337, 344, 348,

354, 360, 362–364, 373, 382, 388,

392–393, 399–406, 417, 420, 439,

462, 485, 488, 519, 530–531, 534,

552, 556, 559, 561–562, 569, 574,

579–580

with GRACE, 171–172, 174, 299, 302, 399

Complete normal equations, 237, 239, 241

Complex XML Type, 21

Component deployment, 26–27

Computer cluster, 87, 213–214, 223

Concentration problem, 249

Constrained and unconstrained solutions, 175

Continental water storage, 12, 47, 55, 131,

369–374, 407–414, 417

Core ﬁeld, 475–477, 480, 498, 505–506, 509,

513, 515–516

Correction terms, 126–127, 235, 485

Correlations, 8, 12, 48–49, 55, 63, 100,

102–103, 137, 139–140, 143,

146–148, 160–162, 165, 172, 174,

176–183, 187, 190–198, 213–214,

220–221, 223, 225–227, 236,

292, 300, 302–304, 306, 329–330,

344–347, 351, 378, 380–382,

Index 585

392–396, 401–403, 405, 410,

420–421, 469, 510, 513, 530, 549,

569, 577

analysis, 102, 172, 176

COSMIC, 10, 67, 71, 75, 429–431, 433, 437,

455, 467, 469–470

Cross-over, 211, 265–270, 274–275, 277

DART, 171–172, 180, 182–183

tsunami early warning system, 172, 180

Data assimilation, 307–308, 315, 325–332,

373, 378, 443, 461–463, 470

Data ﬂow, 3, 22–23, 98, 456–457

Data gaps, 45, 146, 149, 164, 216, 249, 325,

344

Data lifecycle management, 17–19

Data management, 17–18, 27, 530–532, 536,

539–544

IERS, 540

Data mining, 18, 26

Data product, 9, 16–21, 23–26, 68, 97, 410,

434–436, 455–457, 459, 479, 532

retrieval, 23

Data reduction, 209, 480

Data retrieval, 16–17

Data sampling, 100, 149

Data transactions, 24, 26

De-aliasing

models, 174–175, 179, 181–183

tidal and non-tidal short-term

variability, 171

Decorrelation, 161–162, 221, 223, 226–227,

378, 381–382

ﬁlter, 223, 226–227, 378, 381–382

Deﬂections of the vertical, 210

Deformation (load deformation), 400–401

Degree-weighted pseudo-observations, 240

Deployment diagram, 26

De-striped data, 189

De-striped solutions, 189, 196–197

Determination of arbitrary periods, 385

De-tided/tiding, 173–174, 176

in GRACE, 174

DHSN96, 279–281

DIF elements, 21

Differential accelerometry, 205–206

Digital Ion Drift Meter (DIDM), 5, 482

Digital Topography Model (DTM), 271

2-Dimensional layout of the mooring sites,

171–172

Direct approach, 233, 493

Directory Interchange Format (DIF), 19–21

Distributed memory architecture, 81

Disturbing potential, 217–218, 271, 278

DOGS, 533, 550, 552, 556–557

Dominant periodic features, 381–382

Dominant periodic variations, 381, 384

Doris, 80, 95, 319, 320

Downward continuation, 222, 256, 258,

263, 513

Dragfree, 207

Drake Passage, 103, 171–172, 176, 180,

182–183, 187–189, 192–195,

198, 306

Drift correction, 173

Droughts, 372

DSGN94, 279

Dynamic ﬂow velocity, 410–411, 414

Dynamic ocean topography, 101, 204, 211

Dynamic orbit modelling, 72

Dynamic topography, 209, 314, 346–347,

352, 354

Earth

albedo, 4, 106, 115, 144, 404

deformations, 370, 399

gravity ﬁeld, 3, 6, 15, 63, 95, 119, 144, 188,

203–205, 209, 210, 213–228, 231,

233, 246, 252, 278, 369–370, 387,

417, 530, 533, 546–547, 550–551,

577–579

interior, 42, 204

orientation parameters, 61, 530, 535–536,

547–548, 555, 569–572, 574

rotation parameters, 17, 144, 320, 336, 530,

546, 549, 570, 578

system parameter estimation, 578–580

Earth Parameter and Orbit System (EPOS), 8,

29, 43, 60, 143, 550, 556, 578

EPOS-OC, 60, 80–82, 86–88, 91, 143–145,

147, 151, 156, 319

Earth System Science Pathﬁnder (ESSP), 96

ECCO modeling and assimilation framework,

300

EGG2008, 283–284, 286–287

EGM08, 245, 248, 252

EGM2008, 53, 159, 165, 240, 282–284,

287–288

EGM96S, 7–8

Eigenvalues, 250–251, 343

problem, 249–252

Ekman transport, 187, 190

El-Niño-Southern Oscillation (ENSO), 372

Empirical accelerations, 147

586 Index

Empirical Orthogonal Functions (EOF), 314,

360, 379, 402

Empirical tidal ﬁt, 174

Energy balance approach, 214, 216

Energy conservation, 209, 215–216

method, 209

EOF, 197, 306–307, 314, 327, 332, 379

EPOS-PV2 software, 335, 548

ERA-40, 120, 122–123, 125–126, 133,

137–138

re-analysis, 140

Error

model, 111–112, 228, 274, 287, 467

sources, 111, 143, 147, 149–150, 153, 277

Estimation of arbitrary periods, 379

ETOPO5 topography, 133

Eurasian (ERS), 315, 317–320, 516–517,

522, 534

European Center For Medium-Rangeweather

Forecast (ECMWF)

analyses, 121–122, 124, 438

reanalysis, 120

European Gravity and Geoid Project, 283

European Improved Gravity Field Of The

Earth By New Techniques (EIGEN)

EIGEN-2, 7

EIGEN-5C, 12, 42, 49–51, 53, 55, 159,

231–232, 237, 239, 282–284

EIGEN-5S, 12, 42, 49–51, 55, 159,

232, 284

EIGEN-CG01C, 43, 50, 63, 71, 282

EIGEN-CG03C, 41, 43, 50–51, 144–145,

149, 282

EIGEN-CHAMP03S, 41, 51–55, 100, 284

EIGEN-CHAMP05S, 8, 12, 42, 48–49,

51–55

EIGEN-GL04C, 43, 45, 49–51, 265, 272,

282, 287–288

EIGEN-GL04S1, 231–232, 284, 336, 547,

552

EIGEN-GRACE01S, 46, 284, 326

geoid, 326

EIGEN-GRACE02S, 100, 231–232,

271, 284

EIGEN-GRACE03S, 41, 43

EIGEN-GRACE04S, 43, 317, 320

EIGEN-GRACE05S, 12, 42–50, 55, 99

European Space Agency (ESA), 12, 55, 203,

213, 220, 233, 243, 246, 255, 265,

269–270, 272, 274, 277, 482, 523

Eustatic, 99, 328, 330–331

sea level change, 328

Evapotranspiration, 371–372, 417, 419

Exponential-linear ﬁt function, 173

External calibration, 209, 211, 277, 319

Extremes, 99, 150, 194, 372, 417

FES2000, 44

FES2004, 44, 102, 120, 144, 146, 150, 164,

173–174, 320, 547

model, 44, 150, 164, 174

tide model, 120, 173–174

FG-5 absolute gravity meters, 279

Fibre Channel RAID System, 26

Filter

ARMA, 221, 227

butterworth, 227, 269

functions, 370

high-pass, 227, 301

notch, 221, 227

Finite Element Sea Ice-Ocean (FESOM), 103,

177, 189–190, 192–198

Floods, 372

Fluxgate Magnetometer, 5, 477–478, 482,

485–489

Forecasts, 67, 102, 119, 121–123, 127,

132–133, 135, 137, 140, 410,

418, 429–431, 433–434, 437, 439,

461–463, 465, 467, 469–470

Formal errors, 45, 54, 162, 234, 238,

248–249, 261

Fortran95, 80, 86–87

Fourier coefﬁcients, 150, 269–270,

274, 395

Fram Strait, 171–172, 178–179, 182–183

Free Core Nutation (FCN), 536, 571–572

Free kite numbering scheme, 225

Freshwater ﬂuxes, 102, 119–120, 122–127,

132–133, 140, 327

FTP directories, 23–24, 26

Full normal equations, 236, 238–240

GAC

GAC/D, 174–175, 178–179, 182

GAC/D de-aliasing models, 179, 182

GAD, 47–49, 170, 174–182, 300

product, 170, 174, 182, 300

Ganges river basin, 382–383

Gap ﬁlling, 342–344, 346, 349

Gaps in the time series, 173

Gaussian ﬁlter, 165, 175, 178, 181, 188–189,

287–288, 300, 419

Gaussian grid, 262