Satellite Navigation Systems for Earth and Space Sciences Editorial

Home , Satellite geodesy, Satellite navigation

INTERNATIONAL SPACE SCIENCE INSTITUTE No 10, June 2003

Published by the Association Pro ISSI

It was in 1915 when the German Global satellite navigation systems Impressum scientist Alfred Wegener pub- are based on a constellation of lished the “The Origin of Con- Earth orbiting spacecraft emitting tinents and Oceans” outlining the signals with precise orbital and concept of continental drift for time data. Suitable receiver equip- SPATIUM the first time. According to this ment combines the signals from at Published bythe theory, all the continents on Earth least four spacecraft yielding the Association Pro ISSI had formed from one single mass time and the three space coordi- twice a year about 300 million years ago,called nates. The US Global Positioning Pangaea. Later on, Pangaea had System (GPS) for instance consists split, and its pieces had been mov- of 24 spacecraft orbiting the Earth INTERNATIONAL SPACE ing away from each other ever in six different planes. The Russ- SCIENCE since. Where such continental ian Glonass system as well as the INSTITUTE plates collide, mountain ranges planned European Galileo system Association Pro ISSI may be pushed up, like for exam- are based on the same concepts. Hallerstrasse 6,CH-3012 Bern ple the Alps that are the collision Phone +41 (0)31 631 48 96 product of the African and the Of course, the GPS originally was Fax +41 (0)31 631 48 97 Eurasian plate. not conceived as a scientific tool but much more as a sophisticated President Initially, Wegener’s theory was military infrastructure for the ful- Prof.Heinrich Leutwyler, strongly contested not least be- filment of navigational tasks. It University of Bern cause he did not provide convinc- was only after its commissioning Publisher ing explanations for the mechan- that its scientific value became ap- Dr.Hansjörg Schlaepfer, ics allowing for the movement of parent. The continental drift ve- legenda schläpfer wort & bild, the continents through the oceans locities measurement is just one of Winkel (as it was seen at that time). Today a number of fascinating scientific Layout we know that below the continen- applications of global navigation Marcel Künzi,marketing · kom- tal plates there is a hot liquid zone, systems to which the present issue munikation, CH-8483 Kollbrunn the asthenosphere, on which the of Spatium is devoted. We are Printing continents f loat. The plates are greatly indebted to Prof. Gerhard Druckerei Peter + Co dpc separated by ridges, where fresh Beutler, Astronomical Institute, CH-8037 Zurich magma spills out from the as- University of Berne for his kind thenosphere providing the thrust permission to publish herewith a to the continental plates moving revised version of his exciting them apart thereby. lecture of November 12, 2002 for the members of our association. In the meantime such different scientific branches as geology, palae- ontology, botany and zoology have provided ample proof in support Hansjörg Schlaepfer of Wegener’s theory. Even space Zürich, June 2003 technology has contributed by the direct measurement of the continental drift.As an example,the drift Front Cover: The Galileo naviga- velocity between America and Eu- tion satellite in an artist’s view rope has been determined to be in (credit: European Space Agency the order of 2.5 centimetres/year. ESA)

SPATIUM 10 2 Satellite Navigation Systems for Earth and Space Sciences *)

Gerhard Beutler, Astronomical Institute, University of Bern

Navigation and Figure 1 also shows that relative rived either from the Sun [local local and absolute positioning was solar time] or from the stars [side- Science in the performed with the same instru- rial time]) between the unknown ments, the so-called cross-staffs, in site and Greenwich. The problem Past and Today Apian’s days. Global positioning resided in the realisation of Green- meant the determination of the wich time at the observing site in observer’s geographical latitude and the pre-telecommunication era. The introduction to Peter Apian’s longitude (relative to an arbitrarily One astronomical solution to this Geographia from 1533 in Figure 1 selected site – first Paris, then problem, illustrated in Figure 1, nicely illustrates that positioning in Greenwich was used for this pur- consisted of measuring the so- the “good old times” in essence pose). The latitude of an observ- called lunar distances (angles be- meant measuring angles –the scale ing site was easily established by tween bright stars and the Moon). was eventually introduced by one determining the elevation (at the With increasing accuracy of the known distance between two sites observer’s location) of the Earth’s (prediction of the) lunar orbit the (as indicated by the symbolic rotation axis, approximately repre- angular distances between the measurement rod in the centre of sented by the polar star. In princi- Moon and the stars could be accu- the wood-cut). ple, longitude determination was rately predicted and tabulated in Figure 1 simple, as well: One merely had to astronomical and nautical al- Geographia by Peter Apian,dated 1533. determine the time difference (de- manacs with Greenwich local

th *) Pro ISSI lecture, Bern,12 November 2002 SPATIUM 10 3 time as argument. Lunar distances were used for centuries for precise positioning. For navigation on sea the method became eventually ob- solete with the development of marine chronometers, which were capable of transporting accurately Greenwich time in vessels over time spans of weeks. Figure 2 shows the first chronometer developed by the ingenious British watch- maker J.Harrison (1693–1776).

The principles of precise global positioning and precise navigation remained in essence the same from Apian’s times till well into the second half of the 20th century. The development of the accuracy was dramatic: The cross-staff was replaced by increasingly more sophisticated optical telescopes. More precise star catalogues (fundamental catalogues) were pro- duced and the art of predicting the motion of planets was developed in analytical celestial mechanics.A long list of eminent astronomers, mathematicians, and physicists, from L.Euler (1707–1783), P.S. de Laplace (1749–1827), to S. New- comb (1835–1909) were steadily improving the ephemerides.High- ly precise pendulum clocks and marine chronometers allowed it eventually to time-tag the observations in the millisecond accura- cyrange. The relationship between science on one hand and precise positioning and navigation on the other hand were truly remarkable: The discipline of fundamental astronomy emerged from this interaction between theory and application. In Figure 2 Harrison I, first marine Chronometer (credit: D. Sobel und W.J.H. Andrewes: fundamental astronomy one de- Längengrad, Berlin Velag 1999). fines and realises the global terres-

SPATIUM 10 4 trial and the celestial reference systems including the transformation The Earth’s rotation axis in inertial space between the systems. The terres- pole of ecliptic instantaneous trial system was realised by the pole of rotation geographical coordinates of a network of astronomical observatories. Until quite recently the celestial reference system was realised through fundamental catalogues of stars. Celestial mechanics, so to speak the fine art of accurately de- scribing the motion of celestial 23.5º bodies in the celestial reference systems, is also part of fundamental astronomy. Earth’s axis The establishment of the transformation between the two systems implies the monitoring of Earth rotation in inertial space. Figure 3 illustrates that the rotation axis of the Earth moves in inertial Sun space. Earth’s orbit

It is well known that the rotation Earth’s orbital plane axis approximatelymoves on a ° straight cone inclined by 23.5 Figure 3 w. r.t. the pole of the ecliptic, an ef- Precession and Nutation. fect known as precession, which was already discovered in the Greek era (and usually attributed to the great Greek astronomer Year Discoverer Effect Hipparchos). This motion is not fully regular but shows short-peri- 300 B.C Hipparchos Precession in longitude (50.4”/y) od variations, which is why the astronomers make the distinction 1728 A.D. J. Bradley Nutation (18.6 years period, amplitudes between precession and nutation. of 17.2” and 9.2” in ecliptical longitude A study of ancient solar eclipses and obliquity, respectively) revealed eventually that the length 1765 A.D. L. Euler Prediction of polar motion of day was slowly (by about 2 msec (with a period 300 days) per century) growing. The Earth 1798 A.D. P.S. Laplace Deceleration of Earth rotation axis also moves on the Earth’s sur- (length of day) face, an effect known as polar mo- 1891 A.D. S.C. Chandler Polar motion, Chandler period of 430 days tion.This and other discoveries re- and Annual Period lated to Earth rotation made in the era of optical astronomy are sum- Table 1 marised in Table 1. Discoveries related to Earth rotation in the optical era of fundamental astronomy

SPATIUM 10 5 The Global Posi- vantages over optical navigation intersecting three spheres with were considerable: the observa- known centres and radii. (One tioning System tions were weather-independent may remember from school that in and available in digital form from general two solutions emerge (GPS) the outset. The system worked re- from the intersection process, but markably well. Using the observa- one easily recognises that one solutions of one pass of one satellite tion – lying far above the Earth’s over a receiver (duration about surface –may be ruled out).As one Sputnik-I, launched on October 4 5–10 minutes), the (two-dimen- wishes to use rather cheap oscilla- of the International Geophysical sional) position of the observer tors in the receivers,one cannot as- Year 1957, did broadcast a (rela- could be established with an accu- sume that the receiver clock error tively) stable radio-frequency f. racy of a few ten meters. Apart is zero (or known a priori),but that The relative Doppler shift ∆f /f of from the limited precision the it has to be estimated together such signals is proportional to the most serious disadvantage of the with the three coordinates of the radial component v of the relative system had to be seen in the limi- receiver.The unknown position of velocity between satellite and re- tations of the system for high- R may thus be found by intersect- ceiver, i.e., ∆f /f = v/c,where c is speed navigation (the necessity to ing three hyperboloids with foci the speed of light.Actually,this re- collect observations over several (S1,S2), (S1,S3), (S1,S4), and the cor- lationship is only the non-relativis- minutes ruled out the use of the responding differences of the tic approximation of the more NNSS for air- or space borne ap- semi-major axes ( 1– 2), ( 1,– 3), elaborate relativistic expression. plications). ( 1 – 4). If a satellite system shall be used for positioning and navi- The Doppler shift of radio signals The second-generation satellite gation in this sense, one therefore emitted by satellites may be easily navigation systems cured this has to make sure that at any time measured by standard radio equip- problem.They are based on and for any location of the receiver ment. As the orbital velocity of a the measurement of the propa- R on the Earth’s surface at least low Earth orbiter (LEO) is rather gation times of radio signals be- four navigation satellites are above big (about 7 km /sec), the radial tween the satellites and the ob- the observer’s horizon. This im- velocity is expected to vary rough- server and on plies that the navigation satellites ly between the limits ±5 km /s. the simultaneous observation of are rather high above the Earth’s One may therefore expect to re- several satellites. surface, that the inclinations of construct rather accurately the orbit of the satellite using the Neglecting propagation delays Doppler shift of the signal, as caused by the atmosphere and as- measured by a few receivers locat- suming that all clocks (those of ed at known positions on the sur- satellites and receivers) are syn- face of the Earth. If, on the other chronised, the known numerical hand, the orbit is assumed known, value of the speed of light c allows the measurement of the Doppler it to calculate (from the signal shifted signal recorded at an un- travelling time) the distance be- known location may be used to tween the satellite S at signal emis- determine its position on the sion time and the receiver R at sig- Earth. The first generation of nav- nal reception time. The receiver R igation satellite systems, e. g., the thus must lie on a sphere with cen- NNSS (U.S. Navy Navigation tre S and radius . If three satellites Satellite System) was based on are observed simultaneously, the Figure 4 these simple principles. The ad- receiver’s position is obtained by GPS constellation

SPATIUM 10 6 tion Satellite System) or the Euro- pean GALILEO system, to be deployed by the European Space Agency (ESA) in the first decade of the third millennium. All systems are based on the same principles.

In order to fully appreciate the results presented subsequently we have to inspect the actual observables of second-generation navigation satellite systems in more de- tail. The signal transmitted by satellite S at time t S (satellite clock reading) contains this transmis- sion epoch. This information may be used by the receiver R to com- pute the so-called pseudorange p using the reading of the receiver

clock at signal reception time t R:

S p = c(tR – t ) 1 In the “best possible of fundamen- Figure 5 tal-astronomical worlds” p would GPS IIR spacecraft (credit USAF). just be equal to the geometric distance . Because neither the satel- their orbital planes w.r.t. to the sidereal day. There are (at least) lite nor the receiver clocks are ex- equatorial plane are rather big, and four satellites, well separated from actly synchronised with atomic that the satellites are well separat- each other,in each orbital plane. time, because the signal has to ed (equally spaced) in the orbital The satellites transmit informa- travel through the Earth’s atmos- planes. tion on two L-band wavelengths, phere,and because of the measure- L1 and L2, with wavelengths of ment error the actual relationship The best known of these second 1 =19 cm, 2 =24 cm. Figure 5 between the pseudorange and the generation satellite systems is the shows a GPS satellite. Obviously, distance reads as fully deployed U.S. Global Posi- the antenna array always has to S tioning System (GPS). Figure 4 il- point towards the centre of the p = +c tR – c t + T + I ( )+ 2 lustrates the GPS configuration as Earth. The solar panels axes have seen from a latitude of 35° from to be perpendicular to the line where is the distance between outside the actual configuration. Sun–satellite at any time.The atti- satellite S and receiver R, tR the The constellation consists of six tude emerging from these require- receiver clock error, t S the satel- ° orbital planes, each inclined by 55 ments is actively maintained using lite clock error, T the propaga- w.r.t. the equator and separated by momentum wheels within the tion delay due to the electrically 60o in it.The satellite orbits them- satellite’s body. neutral atmosphere, I the delay selves are almost circular with due to the ionosphere (caused by radii of about 26.500 km – giving Alternative systems are the Russ- the free electrons in layers be- rise to revolution periods of half a ian GLONASS (Global Naviga- tween 200 km and 1200 km

SPATIUM 10 7 height), and the measurement measurement error ’ is very small, which clock corrections and at- error. For the code measurements of the order of few millimetres, mosphere delays do not exist. The the error is of the order of a few whereas the code-derived meas- following results will show that decimetres allowing for real time urement error is about a factor of this label is not really justified positioning with about one meter 100 larger. This positive aspect is when interested in other than geo- accuracy. For scientific purposes somewhat counterbalanced by the metrical aspects. The clock- and the phase-derived pseudorange p’ term N ,the initial phase ambigu- atmosphere-related “nuisance” is extensively used. The receiver R ity term, which is unfortunately terms are, as a matter of fact, ex- generates this observation by unknown. The parameter N, ploited to synchronise clocks counting the incoming carrier known to be integer,has to be esti- worldwide and to describe the waves (integers plus fraction part) mated as a real-valued parameter. Earth’s atmosphere. The limited and by multiplying the result by Under special conditions it is pos- space allows us only to present one the speed of light c.This observ- sible a posteriori to assign the cor- of these aspects (the derivation of able is related to the geometrical rect integer number to the esti- ionosphere models from a world- and atmospheric quantities by mated real-valued unknown. Note wide net of GPS receivers). All the that the ionospheric signal delay in other results are related to the S p’= +c tR–c t + T – I( )+N + ’ 3 equation 2 is replaced by a phase ad- term , the distance between satel- vance in equation 3. lite and receiver. The satellite or- Obviously, the code- and phase- bits, the positions (and tectonic derived pseudoranges are inti- The term “best possible of funda- motions) of the observing sites, mately related. The key difference mental-astronomical worlds” was and the Earth rotation parameters resides in the fact that the phase coined to characterise a world, in are derived from .

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Figure 6 The IGS network in March 2003 (credit: IGS Central Bureau; JPL; Pasadena,California.

SPATIUM 10 8 The International global data centres, from where to reconstruct the satellites’ posi- they can be retrieved by the wider tions and velocities with cm-pre- GPS Service (IGS) scientific community, but also cision for anytime argument (perhaps more importantly) bythe within the day. These satellite or- and the IGS Analysis Centres to generate bits originally were the primary Code Analysis the IGS products. There are cur- IGS product. They are a big relief rently seven IGS Analysis Centres for research and production organ- Centre (three in the USA,one in Canada, isations using the GPS for high-ac- two in Germany (where the one at curacy surveys. It is, e.g., worth ESA should be considered as mentioning that since 1991 the multi-national) and one, called Swiss first order geodetic survey is The International GPS Service CODE, situated at the University uniquely based on GPS and on the (IGS) was created in 1991. It be- of Bern. CODE is a joint venture IGS products. A similar develop- came fully operational,after a pilot of the University of Bern’s Astro- ment was observed in most other phase of about two years, on Janu- nomical Institute (AIUB) with countries worldwide. ary 1, 1994. The IGS is based on a the Swiss Bundesamt für Landes- voluntary collaboration of scien- topographie (Swisstopo), the Ger- The IGS Analysis Coordinator is tific and academic organisations in man Bundesamt für Kartographie und first comparing, then combining the fields of geodesy,space science, Geodäsie (BKG) and the French In- the orbits of all IGS Analysis Cen- and fundamental astronomy. Big stitut Géographique National (IGN). tres into one official IGS orbit. The research organisations like NASA, The work of the IGS Analysis work of the individual centres is JPL, ESA, etc. contribute as well as Centres (AC) is truly remarkable. rated by the root mean square National Geodetic Survey institu- Every day, a table of geocentric or- error per satellite position (actual- tions, and universities. The IGS bital positions is generated by each ly per geocentric coordinate) w.r.t. deployed and maintains a net work of the AC's for each active GPS this official, so called final orbit, of more than 200 globally distrib- satellite with a spacing allowing it available about one week after real uted permanent GPS sites. Figure 6, taken from the IGS homepage, 300 gives an impression of the net- COD EMR work. ESA GFZ The IGS network ref lects to some JPL NGS ex tent the fac t that the IGS is a vol- 200 SIO untary collaboration: The station

[mm] IGR distribution is far from homoge- neous, but one can also see that RMS there are only few “empty” areas left today. Each IGS station tracks each GPS satellite in view. At least 100 once per 30 seconds all available Weighted code and phase measurements on the two frequencies are stored – giving rise to 2 x 8640 measure- 0 ment epochs per day. At least on a 700 800 900 1000 1100 1200 daily turnaround cycle the raw Time [GPS weeks] data are sent (via internet or tele- Figure 7 phone modems) to regional and RMS-error per satellite coordinate for IGS-AC-orbits.

SPATIUM 10 9 time.Figure7 shows these root mean Scientific mates of polar motion by the square errors for each centre since CODE Analysis Centre since 1994 to March 2003. The consis- Applications 1993. Note that the units are arc tency of the best contributions is seconds,implying that the daily es- today of the order 2–3 cm. Not timates of the Earth’s rotation axis without pride we note that the are accurate to about 2–3 mm. CODE-contribution (red curve) always was among the best since In 1991 it was the intention to base the advent of the IGS.(Note that the IGS orbit determination on Polar Motion the green curve labelled “IGR” the Earth rotation parameters cal- characterises the combined IGS culated by the (at that point in One arc second corresponds to rapid solution, which is already time) well established space tech- about 30 m on the Earth’s surface. available within one day after “real niques VLBI (Very Long Baseline The motion of the pole between time”.) Elementary geometric con- Interferometry) and Satellite 1993 and 2003 thus roughly takes siderations show that this orbit ac- Laser Ranging (SLR).It turned place within a circle of about 7 m curacy of few cm is sufficient for out that the required information centred roughly at the endpoint of millimetre precision positioning on was not available in due time for the Earth’s axis of the maximum the Earth or in Earth-near space IGS orbit production. This is why moment of inertia. Bigger excur- (e.g., for LEO's). It is a remarkable each IGS Analysis Centre has to sions may occur occasionally. A IGS achievement that the GPS or- solve for the daily position (and spectral analysis of polar motion bits may be considered virtually velocity) of the Earth rotation reveals two dominating periods, “error-free” for most applications. pole. Figure 8 shows the daily esti- one of 430 days (amplitude of about 0.17”), the so-called Chan- dler period, and one of one year CODE Polar Motion: 19-June-1993 to 27-Mar-2003 (amplitude of about 0.08”). The POLXTR_IERS Chandler period is related to the motion of a solid (not completely –0.2 2002 1996 rigid) body.The period maybe derived from the numerical values of 1995 the Earth’s principal moments of –0.1 inertia and from the elastic prop- 123/2003 2003 2001 200/1993 erties of the Earth. The annual period originates from the interac- 1997 0 1994 tion between the solid Earth and 2000 the atmosphere (and oceans).

0.1 1998 The superposition of the Chan- dler and annual periods results in a 1999 beat period of about six years let- X-Coordinate [arc-seconds] 0.2 ting the pole move on a (“bad”) circle with a radius varying between 2 m and 8 m. Many short- 0.3 period variations show up in Figure 0.6 0.5 0.4 0.3 0.2 0.1 0 8. Most of them are related to the exchange of angular momentum Y-Coordinate [arc-seconds] Figure 8 between atmosphere and solid Daily estimates of polar motion by CODE since 1993. Earth.

SPATIUM 10 10 CODE Excess Length of Day: 19-June-1993 to 27-Mar-2003 global analysis. The annual varia- POLXTR_IERS tions with amplitudes of about one millisecond are more interest- ing. 3 The phenomenon is explained by comparing the polar component of the solid Earth’s angular mo- 2 mentum (which may be derived from the length of day variations) with the so-called atmospheric 1 angular momentum (which is derived from the global meteorological networks, registering pressure,

Excess Length of Day [ms] temperature,and wind profiles). 0 Figures 10a and 10b compare the relative polar (axial) angular mo- –1 menta of the solid Earth (red line) 700 800 900 1000 1100 1200 and of the Earth’s atmosphere. Time [GPS-weeks] The “true” angular momentum of

Figure 9 the solid Earth was used in the case Length of day variations 1993–2003. of Figure 10a, whereas a low-order polynomial was removed from this time series in Figure 10b. The Length of Day

0.2 In inertial space (i.e., w.r.t. the cod stars) the Earth rotates once about ncep its axis in a sideral day, corresponding to about 23 h 56 m of atomic 0.1 time. Figure 9, emerging from the daily estimates of the CODE AC, shows that the actual length of day 0 is “far” from constant. Short period variations (e.g., of two weeks) are easily explained by the tidal de- chi_3 formation of the Earth due to the –0.1 Moon (the tidal displacement causes a varying polar moment of inertia, which in turn leads to a varying angular velocity of Earth –0.2 rotation). Observe that the bi- monthly changes in the length of 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 day (lod) are small (amplitude Year well below the millisecond), but Figure 10a that they are easily detected in this Polar angular momenta solid Earth and athmosphere.

SPATIUM 10 11

0.15 components (the equatorial com- cod ncep ponents) of the solid Earth’s angular momentum and to compare 0.1 them with the corresponding atmospheric quantities, as well. The 0.05 correlation between the two series is rather pronounced,but with correlation coefficients around r = 0.7 0 not nearly as high as in the case of

chi_3 the polar component.

–0.05 Plate Motion Velocities

–0.1 The Chandler period of 430 days (instead of 300 days) clearly indi- –0.15 cates that the Earth is not rigid. 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 This fact is also supported by Fig- Year ure 11 showing that the observing Figure 10b sites are not fixed. The figure is Polar angular momenta solid Earth (trend removed) and athmosphere. derived from weekly estimates of the coordinates of the tracking sta- correlation of the two curves – inner shells (in particular to the tions of the IGS network. It turns which are completely independent f luid outer and the rigid inner core out that in the accuracy range – is striking in both cases. In Figure of the Earth). It would be very nice achieved by the IGS analyses 10b the correlation coefficient is to present pictures corresponding ([sub]cm accuracy for the daily es- r = 0.98, implying that the polar to Figures 10a,b proving the ex- timates of the coordinates of the component of the system (solid change of angular momentum tracking sites) it is not possible to Earth plus atmosphere) is almost with the inner layers, namely man- assume that the polyhedron of ob- perfectly conserved –at least when tle, inner and outer core. Unfortu- serving sites is rigid. One has to considering variations with peri- nately there are no direct measure- take the relative motion of the sta- ods of one year or smaller. ments of the angular momenta of tions into account. Figure 11 shows these layers. This may be consid- the “velocity” estimates for the Obviously there are variations of ered as a disadvantage. On the stations processed daily by the longer period (“decadal” varia- other hand, one has to acknowl- CODE analysis centre (from a tions) in the polar angular mo- edge that the study of the decadal long series solutions). Other space- mentum (Figures 10a, 9a), which do lod-variations (Figure 9) or of the geodetic techniques are of course not occur in the polar component corresponding angular momen- also capable of determining sta- of the atmospheric angular mo- tum (red curve in Figure 10a) con- tion velocities. The unique aspect mentum. They are undoubtedly tains very valuable information of GPS analyses is the compara- real. These variations are most in- concerning the rotational behav- tively high density of observing teresting from the global geody- iour of the Earth’s interior. Geody- sites. The velocities seem small at namics point of view.They may be namical Earth models must ex- first sight. One is inclined to con- explained by the fact that the IGS plain the long-term development sider velocit ies of the order of 1–10 observing sites are attached to the in Figure 10a. With the polar mo- cm / year as irrelevant. Nothing Earth’s crust, which is, however, tion time series of Figure 8 it is pos- could be more wrong: A velocity not rigidly attached to the Earth’s sible to calculate the other two of 1 cm /year gives rise to a posi-

SPATIUM 10 12 nya1 thu1 nyal tro1 trom tixi bili fair kely kiru yell yakz whit hofn mets mago chur reyk onsa artu flin lama mdvo kstu will sch2 wsrt bor1 irkt dubo kosgpots bogo zwen petr drao hers wtzr jozeglsv albh algo bruswett gopepenc nrc1 stjo sjdvzimm graz zeck urum yssk quin nlib toul upadmedi ankr pol2 amc2 code wes2 casc gras sell daes gol2 madr mate nssp taes juwn piet1 usno vill cagl nico kit3 xian tskb noto lhas shao usud monp brmu mdo1 aoml ramo bahr wuhn kokb rom6 mas1 taiw jama mkea cro1 pimo guam moin barb iisc kwj1 bogt kour gala ykro ntus fort mali bako sey1 asc1 dgar darw tahi areq coco pama braz karr alic tow2 eisl hark noum cord hrao yar1 sant pert suth cedu tid2 lpgs auck goug chat hob2 kerg riog mac1 cas1 ohig maw1 dav1 vesl mcmu 1 cm/year velocity

Figure 11 Station velocities estimated by CODE Analysis Center. tion change of 1000 km in 100 the total number of electrons in lengths. As all the other terms are million years! As a matter of fact, the atmosphere. The information wavelength independent, we ob- these velocities explain the “conti- is extracted from the ionospheric tain a direct observation of ionos- nental drift” postulated by Alfred refraction term I ( )in equations pheric refraction along the line of Lothar Wegener (1880–1930) in 2, 3. Whereas the results presented sight between observer and satel- 1915.At Wegener’s epoch the con- so far were obtained by analysing lite by using this difference of ob- tinental drift, referred to more ap- the so-called ionosphere-free lin- servations. The result is propor- propriately as plate motion, was ear combination of the L1- and tional to the number of electrons pure speculation – today we are L2-observables (which eliminate contained in a straight cylinder be- monitoring it in real time. the wavelength-dependent ionos- tween observer and satellite. pheric refraction term), the Using the phase and code observa- so-called geometry-free linear tions from the entire IGS network Electron Density in the combination of the L1- and L2- one may derive maps of the elec- Atmosphere observations is used for the pur- tron density (the simplest model pose we have in mind now. This assumes that all free electrons are Let us continue our review of the particular linear combination of contained in a layer in a given scientific exploitation of the GPS observations is the plain differ- height H – usually set to H = 400 by an example related to the at- ence of the equations of type 2 or 3 km).At CODE,such maps are pro- mosphere, the determination of for the L1- and the L2-wave- duced with a time resolution of

SPATIUM 10 13 CODE’s rapid ionosphere maps for day 17, 2003 – 10:00 UT

–30 Geographical latitude [degrees]

–60

–180 –13 5 –90 –45 0 45 90 135 180 Geographic longitude [degrees]

0 1020304050607080 TEC [TECU]

Figure 12 Map of total ionospheric content of electrons (1 TECU =1016 electrons per m3). two hours. Figure 12 shows one of This is why the “spot” of maxi- ical harmonics series with about these snapshots. The electron den- mum electron density closely fol- 250 terms. The zero-order term sity is given in TECU's (Total lows the projection of the Sun represents the mean electron den- Electron Content Units), 1 TECU onto the Earth’s surface (subsolar sity. Figure 13 shows the develop- corresponding to 1016 electrons point). The maximum is actually ment of this mean electron densi- per m2. lagging behind the subsolar point ty, which may be inspected as a by about two hours. In Figure 12 we function of time. Several mechanisms are responsi- see a bifurcation of the ionosphere ble for producing free electrons in density along the geomagnetic This is a good example for solar- the Earth’s atmosphere. The most equator (dotted line), an interest- terrestrial relationships. A spec- important is related to the Sun’s ing aspect due to the Earth’s mag- trum of the time series underlying UV radiation ionising the mole- netic field. Internally, the electron Figure 13 shows that the shortest cules in the upper atmosphere. density is represented by a spher- period corresponds to the rotation

SPATIUM 10 14 CODE GIM time series from 01-Jan-1995 to 31-Mar-2003 vealed that the next better approximation for the shape of the Earth 60 was that of a spheroid with a f lat- 1 tening of about f= /300 (giving rise to one second-order term of the 50 gravity field, the so-called “dy- namical f lattening”). (Gravimeter measurements on the Earth’s sur- 40 face indicated that there were sig- nificant local and regional variations of the Earth’s gravity field,

TEC [TECU] 30 but it was not possible to use these measurements to derive a consis-

Mean tent global gravity field of the 20 Earth).

The analysis of the orbits of artificial Earth satellites, starting in the 10 1960s, greatly improved our knowledge of the Earth’s gravity field. Instead of only two terms 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 (the mass of the Earth and the dy- Time [years] namical f lattening) a few thou- Figure 13 sand terms could be determined Mean TEC values 1995 –2003. with reasonable accuracy in the first era of satellite geodesy. The two Lageos satellites (the acronym period of the Sun (about 27 days), Determination of the Earth’s standing for Laser GEOdetic indicating that the UV radiation Gravity Field: Review and Satellite) were paramount for this is related to the sunspots. Another Outlook task. The satellites were designed prominent period is the annual to minimise the impact of non- period,which is due to the varying It would have been fair and appro- gravitational forces (the sphere of distance between Sun and Earth priate to discuss our knowledge of 70 cm diameter consists of Urani- (because of the Earth’s orbital the Earth’s gravity field in the in- um) on the orbital motion and to eccentricity of e = 0.016). The troductory section together with optimise their observation by the longest period corresponds to the the geometrical properties of the Laser technique (Lageos II is 11-year sunspot cycle. It should Earth. This was not done because shown in Figure 14). be pointed out that Figure 13 prob- our knowledge of the global as- ably represents the best history pects of the Earth’s gravity field Figure 15 shows University of of the density of free electrons. was very poor in the pre-space age: Bern’s 1 m telescope at Zimmer- Many more figures of this type It was of course known that the wald,which may be used as an op- might be generated by replacing Earth is, in good approximation, a tical telescope, but also as trans- the zero order term of the devel- sphere (meaning that the gravity mission and receiving device for opment of electron densities by field is that of a point mass). Satellite Laser Ranging (SLR). the higher-order coefficients of Thought experiments due to I. The Laser technique is used to the harmonic series underlying Newton and expeditions per- generate very short light pulses Figure 12. formed in the 18th century then re- (few ten picoseconds). The meas-

SPATIUM 10 15 urement simply is the light travel- has, however, also severe disadvan- This circumstance was one of the ling time of the Laser pulse from tages: good weather is a precondi- key motivations to look for alter- the observatory to the satellite and tion (the clouds in Figure 15 would native space borne methods to de- back. Due to the divergence of the not allow it to track satellites). termine the Earth’s gravity field. Laser beam and due to the limited Moreover, a Laser observatory is All new methods rely on GPS to number of ref lectors onboard the rather bulky and expensive, which determine the orbit of the space satellite (Figure 14) only few re- is why there exist only about thirty vehicle(s) used to determine the f lected photons may be detected observatories today,which are glob- Earth’s gravity field and on the in the observatory. The technique ally coordinated by the Internation- IGS products to model the GPS has outstanding properties: The al Laser Ranging Service (ILRS). orbits and clocks. Figure 16 shows accuracy is high (few picoseconds an artist’s view of the German re- corresponding to about 1 cm in The sparseness of the Laser sites search satellite CHAMP (ChAl- range) and the atmospheric effects makes it therefore impossible to lenging Minisatellite Payload). may be modelled with highest ac- continuously track the orbit of a Champ was launched in July curacy (sub-cm) using only stan- particular satellite. This situation 2000.It is,as the name implies,a dard meteorological measure- is not at all ideal for the analysis of multipurpose satellite, allowing ments at the sites. The technique satellite orbits. atmospheric sounding, and the determination of the magnetic and the gravity fields.The gravity field is recovered from analysing the satellite’s orbits using the GPS. This is possible because the satellite carries a space borne GPS receiver (JPL ’s blackjack receiver). CHAMP f lies at rather low alti- tudes (from initially 450 km to 300 km at end of the mission in 2005). In view of the bulkiness of the satellite non-gravitational forces, residual air drag in particular, do seriously affect the orbit of the satellite – and therefore also the determination of the Earth’s gravity field. CHAMP copes with this problem by so-called ac- celerometers, in essence a probe mass in the satellite’s interior (shielded against non-gravitational forces).The displacement of this probe mass in the satellite-fixed reference frame may be used to “determine” the non-gravitational forces. This is, of course, only possible within certain limits given by the error spectrum of the ac- Figure 14 celerometers. It turns out that the The Lageos satellite. separation of gravitational and

SPATIUM 10 16 Figure 15 The Zimmerwald 1-m telescope. non-gravitational forces is rather ously the two satellites are similar A relative to GRACE B is, howev- good for short periods and rather in shape to CHAMP. GRACE fo- er, reconstructed with a so-called poor for the longer periods. It is in cuses on the time variability of the K-band link (distance measure- any case most encouraging to see Earth’s gravity field. For that pur- ments in the microwave range) be- that one month of CHAMP data pose it determines the Earth’s grav- tween the two spacecraft.This K- gives better results for the short ity field with a high time resolu- band link establishes the distance periodic part of the gravity field tion allowing it, e.g., to study the between the two satellites with spectrum than about 40 years of seasonal water cycle (evaporation extreme precision. The measure- Laser tracking! CHAMP marks over oceans, precipitation over con- ments may be used to determine the beginning of the new era of tinents, ground water variability, directly the second derivatives of gravityfield determination. f lowing off into the oceans). It is the Earth’s gravity potential. Both, amazing that such experiments can the satellite orbit established by The two satellites GRACE A and be performed by studying the GPS and the K-band measure- GRACE B (see Figure 17) flyin the Earth’s gravity field! The orbits of ments, are used to reconstruct the same orbit, separated by about 20 GRACE A and B are reconstructed Earth’s gravity field. It is expected km. GRACE,launched in March exactly like in the case of CHAMP that the results will significantly 2002, stands for Gravity Recover by using the data of space borne improve our knowledge in a wide And Climate Experiment. Obvi- GPS receivers.The orbit of GRACE spectrum of Earth sciences.

SPATIUM 10 17 The third of the new generation importance for the determination Unfortunately we could only satellites to determine the Earth’s and monitoring of ocean circula- touch a few aspects related to this gravity field is ESA’s GOCE satel- tion. For this purpose it is,in addi- new era of gravity field determi- lite, shown in Figure 18 (GOCE tion,necessaryto determine the so- nation. For more information we standing for Gravity field and called sea surface topography using refer to the proceedings of the steady-state Ocean Circulation Ex- the measurements of altimeter workshop Earth Gravity Field from periment). As the name implies, satellites,reconstructing the sea sur- Space – From Sensors to Earth Sciences, GOCE is a combined mission to face using the radar echo tech- which was hosted by the ISSI in measure gravity and Ocean circu- nique. The difference between the March 2002. The workshop lation. GOCE wants to establish geometrically established sea sur- brought together the leading ex- the mean gravity field of the Earth face and the GOCE geoid gives the perts in celestial mechanics, geo- with the highest possible accuracy elevation of the sea surface over the desy, Earth sciences, and in instru- and spatial resolution. When de- geoid. Exactly as in the continents, ment manufacturing. The termining the gravity field associ- the water in the oceans has to f low proceedings of the workshop un- ated with a mass distribution, one “mountains” to “valleys”. It is in- derline the tremendous impact of obtains, as a by-product, equipo- deed fascinating to see that sci- this new sequence of space mis- tential surfaces. The equipotential ences which were considered spe- sions on a very broad field of sci- surface at sea level is called the cial disciplines for few experts are ence. geoide. The geoid to be determin- now developing into one multidis- ed by GOCE will be of greatest ciplinary topic in Earth sciences.

Figure 16 The CHAMP spacecraft launched in July 2000 (credit Astrium).

SPATIUM 10 18 The scientific aspects emerging from the new navigation systems are co-ordinated by the Interna- tional GPS Service (IGS).Polar motion,length of day,plate tecton- ics, and the Earth’s ionosphere are monitored with unprecedented accuracy. The IGS products are also paramount for the success of gravity field determination with the new generation of gravity mis- sions. The new era of gravity field determination will lead to a unifi- cation of geometric and gravitational aspects, truly bringing together the three pillars of modern geodesy and fundamental astronomy, namely (1) positioning and Figure 17 navigation, (2) Earth rotation, (3) The pair of GRACE spacecraft launched in March 2002 (credit NASA). gravityfield determination.

Summary trum. In view of the fact that the “old” methods were used for centuries,one can trulyspeak of a revolution in navigation, geodesy, and Navigation and fundamental as- fundamental astronomy. tronomy are intimately related since hundreds of years. Until about thirty years ago global navigation relied on measuring angles. Scientific discoveries include the phenomena of precession, nutation, secular deceleration of Earth rotation,and polar motion.

With the advent of the space age the astrometric observation of stars and planets was replaced by the measurement of distances (or distance differences) between ob- servers and artificial satellites. As weather-and daytime-independ- ence is an impor tant aspect of navigation, the observation techniques were moreover moved from the optical to the microwave Figure 18 band of the electromagnetic spec- The GOCE spacecraft to be launched in 2006 (credit: ESA).

SPATIUM 8 19 The author

Later on, he held positions as re- Based on his initiative the CODE search associate from 1983 until Processing Centre of the Interna- 1984 at the University of New tional Geodetic Society was creat- Brunswick, Fredericton, Canada ed. CODE today is a joint venture and from 1984 until 1991 at the of the Astronomical Institute of University of Berne. During the the University of Berne, the Swiss latter period he was engaged in Federal Office of Topography, the the development of the Bernese Institute for Applied Geodesy in Global Positioning System Soft- Germany, and the Institut Géo- ware, which is used today at about graphique National in France. 150 research institutions worldwide. In 1991 he was elected Pro- Gerhard Beutler is a fervent sup- fessor of Astronomy and Director porter of the planned European of the Astronomical Institute of navigation and positioning system the University of Berne. His lec- Galileo, not only because this sys- tures cover such fields as celestial tem would make more satellites mechanics, Earth rotation, stellar available but also because its dif- Gerhard Beutler was borne in dynamics and statistics, parameter ferent orbit characteristics as com- Kirchberg in the Canton Berne in estimation theory and digital fil- pared to the US GPS system would 1946,where he visited the elemen- tering theory. provide the scientific user with an tary school. After receipt of the increased potential of positioning type C maturity in 1964 he en- The main research interests of accuracy. rolled at the University of Berne Gerhard Beutler are devoted to in astronomy,physics and mathe- fundamental astronomy, celestial Gerhard Beutler lives with his matics. These subjects turned out mechanics, global geodynamics family in Schüpfen in the Canton to be the ideal theoretical founda- and satellite-based positioning Berne.In his free time he likes tion when it came to exploring the und navigation. He is a member biking through the wonderful scientific potential of navigation of numerous national and inter- landscapes of the Canton Berne,as satellites when the U. S. Global national committees and working well as playing tennis. Not with- Positioning System became opera- groups,as for example the Schwei- out pride he counts himself to the tional. zerische Geodätische Kommis- world top league of the celestial sion, the American Geophysical mechanics tennis players. In 1976 G. Beutler received the Union and the European Space Ph.D. degree with a thesis on Inte- Agency’s Scientific Advisory gral Evaluation of Satellite Obser- Board on the European Naviga- vations. The second thesis was de- tion Satellite System Galileo.As voted to the Solution of Parameter of July 2003 he will serve as Pre- Estimation Problems in Celestial sident of the International Asso- Mechanics and Satellite Geodesy. ciation of Geodesy (IGS).