Radio occultation data analysis by the radioholographic method

Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 Radio occultation data analysis by the radioholographic method K. Hocke a, *, A.G. Pavelyev b, O.I. Yakovlev b, L. Barthes c, N. Jakowski a a German Aerospace Center/German Remote Sensing Data Center (DLR/DFD), Kalkhorstweg 53, 17235, Neustrelitz, Germany b Institute of Radio Engineering and Electronics of Russian Academy of Sciences (IRE RAS), 1 Vvedenskogo Sq., Fryazino, 141120, Russia c Centre d'etude des Environnements Terrestre et PlaneÂtaires (CETP), 10±12 Avenue de l'europe, bat. Mermoz, 78140, Velizy, France Received 29 April 1999; received in revised form 23 September 1999; accepted 23 September 1999 Abstract The radioholographic method is brie y described and tested by using data of 4 radio occultation events observed by the GPS/MET experiment on 9 February 1997. The central point of the radioholographic method (Pavelyev, 1998) is the generation of a radiohologram along the LEO satellite trajectory which allows the calculation of angular spectra of the received GPS radio wave eld at the LEO satellite. These spectra are promising in view of detection, analysis and reduction of multipath/di raction e ects, study of atmospheric irregularities and estimation of bending angle error. Initial analysis of angular spectra calculated by the multiple signal classi cation (MUSIC) method gives evidence that considerable multibeam propagation occurs at ray perigee heights below 20 km and at heights around 80±120 km for the 4 GPS/MET occultation events. Temperature pro les obtained by our analysis (radioholographic method, Abel inversion) are compared with those of the traditional retrieval by the UCAR GPS/ MET team (bending angle from slope of phase front, Abel inversion). In 3 of 4 cases we found good agreement (standard deviation s T 01.58K between both retrievals at heights 0±30 km). # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction For atmospheric research, Global Navigation Satellite Systems (GNSS) such as GPS or GLONASS can be regarded as transmitter systems sounding structures of the Earth's atmosphere with high precision. The radio occultation technique only requires a small GPS receiver aboard a low Earth orbit (LEO) satellite measuring the atmospheric refracted GPS radio wave * Corresponding author. Tel.: +49-331-288-1757; fax: +49-331-288-1759. E-mail address: hocke@gfz-potsdam.de (K. Hocke). eld in limb sounding geometry (Melbourne et al., 1994). The radioholographic method is one possibility for retrieval of atmospheric refractivity pro les from phase and amplitude observations of the radio wave eld along the LEO trajectory during a radio occultation. In the data analysis, radioholograms are generated along the LEO trajectory by interference of the observed signal wave eld with a reference wave eld which is analytically calculated by the radio physical model of the IRE Institute using a simple model atmosphere and the orbit information of both satellites (Pavelyev et al., 1996). The radiohologram can be now investigated by high resolution spectral methods in order to estimate the directions of arrival of the 1364-6826/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S1364-6826(99)00080-2

1170 K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 received GPS signals at the LEO satellite. These directions of arrival (or angular spectra) are closely related to the atmospheric bending angle and refractivity pro- le. To some extent the radioholographic data analysis is related to the phase lock technique which is ``a technique for making the phase of an oscillator signal follow exactly the phase of a reference signal. Accomplished by comparing the phases between the two signals and using the resultant di erence signal to adjust the frequency of the reference oscillator'' (TECNET Info). Moreover the method is related to the occultation data processing of wideband recordings by Lindal et al. (1987), who ``mixed the bandwidth reduced data with the signal from a local oscillator that was programmed to compensate for the changing Doppler shifts'' due to the movement of Voyager 2. The authors derived power spectra as a function of time showing multibeam propagation caused by a turbulent methane cloud layer in the troposphere of Uranus. In this paper, we select the multiple signal classi cation (MUSIC) method (Schmidt, 1986) for determination of the angular spectra from the radiohologram. Atmospheric bending angle pro les are derived from the position of the main spectral peak in subsequent spectra. This means that the radioholographic method may reduce or avoid retrieval errors due to multipath/ di raction e ects since disturbing e ects by minor beams or spectral broadening of the main beam should be removed by concentration on the central position of the main beam. The angular spectra are interesting for study of atmospheric multipath/di raction e ects of radio wave propagation, study of atmospheric irregularities and error estimation of the bending angle pro le. The data analysis of the traditional retrieval method is quite di erent from the radioholographic method. In short, the bending angle and impact parameter are calculated from the Doppler-shifted frequencies (time derivation of phase path) and the observation geometry using Snell's law. Since this derivation is only valid for single ray propagation, possible multipath/di raction e ects contained in the observed phase path have to be taken into account. According to Gorbunov and Gurvich (1998), uncorrected multipath/di raction e ects may introduce a temperature retrieval error of about 5±108K. Various correction methods have been developed (Gorbunov and Gurvich, 1998; Karayel and Hinson, 1997; Melbourne et al., 1994; Mortensen and Hoeg, 1998). In general, the observed radio wave eld is recalculated in an auxiliary plane which is nearer to the ray perigee than the LEO satellite. This `wave back propagation' disentangles possibly observed multibeam structures, and the bending angle pro le can be derived from the corresponding phase path series of the auxiliary plane without errors due to multipath/di raction e ects. The retrieval of temperature pro les from bending angle pro les is carried out in the present study by Abel inversion and is described in Hocke (1997) and Steiner et al. (1999). For a detailed description of the GPS/MET experiment and the UCAR data analysis the reader is referred to Rocken et al. (1997). Recently, O. Yakovlev described the radio occultation technique and related themes in a textbook with special note on research work at the IRE Institute since 1964 (Yakovlev, 1998).l 2. Data analysis and results The mathematical treatment of the radioholographic method was already delineated by Pavelyev et al. (1996, 1999) and Pavelyev (1998). In the following, the application of this method to GPS/MET radio occultation data is emphasized. These data consist of orbit information of both GPS/LEO radio link satellites, phase path excesses and signal/noise ratios of the GPS dual carrier frequencies ( f 1 =1575.42 MHz, l 1 =19.03 cm, f 2 =1227.6 MHz, l 2 =24.42 cm) observed at the LEO satellite with a sampling time of 0.02 s. Since the retrieval of the bending angle is analogous for both GPS carrier waves, the GPS frequency indices are not used in the formulae below. 2.1. Radiohologram The signal to noise ratio (0E - (t ), electric eld magnitude) and the phase path excess (l j(t )/2p, j: radio wave phase) are combined in order to achieve the complex electric eld E(t ) of the GPS radio wave eld along the LEO orbit during the occultation event: E t ˆ E t exp ij t : Beside the observed signal wave eld E(t ), the radioholographic method requires a reference wave eld E m t ˆ exp ij m t for generation of the radiohologram. Knowing the positions and velocities of the radio link satellites and having a simple model atmosphere (e.g., described by an exponential refractivity pro le) the radio wave phase at the LEO satellite can be calculated by using Abel transformation and Snell's law. This is one application for the radiophysical model of IRE which can derive the radio wave phases at the LEO positions during the occultation event in a fast, analytical manner (Pavelyev et al., 1996). The radiohologram DE(t ) is then given by DE t ˆ E t exp i j t j m t Š: 1 2

K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 1171 Table 1 Selected GPS/MET occultations on 9 February 1997 (UCAR GPS/MET data base) Event UT [h, min, s] latitude longitude 0200-04.15-97.040 7:11:58 27.88N 104.38E 0205-04-25-97.040 7:15:32 36.18N 127.68E 0206-04.25-97.040 7:19:53 48.48N 133.68E 0218-07.23-97.040 7:54:02 16.08S 112.88W analysis of the observed GPS radio wave eld with respect to the reference wave eld. In this paper we calculate spectra of segments of the radiohologram by using a sliding window with a window length of 0.64 s and a step width of 1/3 of the window length. In order to achieve a high spectral resolution in spite of the small window length, the multiple signal classi cation (MUSIC) method was applied. The many applications of this method and its mathematical derivation are described by Schmidt (1986). Barthes et al. (1998) tested and validated this method for separation of multiple radar echoes from ground and ionosphere in data of the SuperDARN HF radars. The only shortcoming may be the MUSIC spectral estimation of broad spectral line pro les (Barthes et al., 1998). In short, the MUSIC method assumes a signal composed of a sum of damped complex sine waves with additional noise. The number of sine waves is calculated by the MUSIC method itself. (We selected an upper limit of n R 5 complex sine waves. The power of the noise was found to be around 1/100 of the total power of the radiohologram spectra.) Thus the radiohologram is approximated by DE t 0 Xn kˆ1 E k exp b k t exp ido k t noise 3 Fig. 1. (a) Power ratio P 1 =P total derived as a function of perigee height from GPS/MET limb sounding measurements of the L1 and L2 carrier waves (occultation event 0200, Table 1). P 1 is power maximum of the main beam and P total is sum of power maxima of all spectral lines P n kˆ1 P k). In the case of monobeam propagation the total power is contained in one beam and the ratio is equal to 1, while the ratio diminishes in the case of multibeam propagation. (b) Same as (a), but for occultation event 0205 (Table 1). (c) Same as (a), but for occultation event 0206 (Table 1). (d) Same as (a), but for occultation event 0218 (Table 1). 2.2. Spectral analysis The radiohologram is the starting point for spectral Here, Do k is the di erence of the observational Doppler-frequency shift of spectral component k with respect to the Doppler-frequency shift of the reference wave. E k is magnitude and b k the damping factor of spectral component k. The MUSIC method yields power and spectral position of each wave component and power of noise. Moreover the damping factor is determined which gives information about the spectral line width. In Fig. 1(a±d) the ratio between power maximum of main component (P 1 ) and total power of all components P total ˆ Pn kˆ1 P k is shown as a function of ray perigee height (point of closest approach) for the selected occultation events. If the radio occultation data are without multibeam/di raction e ects, the ratio is equal to 1 since all power is contained in a single ray P total ˆ P 1. The depicted height pro les indicate that atmospheric multibeam propagation reduces the power of the main beam and redistributes

1172 K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 corresponding deviations of the impact parameters from the model impact parameter are given by (assuming spherical symmetry of the atmosphere) Dp k ˆ Da k r L cos f L : 5 Finally the bending angles a k p k of the observed k- beams are a k ˆ a m Da k, p k ˆ p m Dp k, k ˆ 1, 2, 3,..., n: 6 Fig. 2. Bending angle pro le of L2 carrier wave derived by the radioholographic method for occultation event 0206 (Table 1). The bending angle pro le of the main beam is depicted by open circles, while minor beams are shown by dots. The circle/dot diameter is proportional to the ray amplitude. it to multiple beams. The major spectral component can diminish to half of the total spectrum power at tropospheric heights below 20 km. In Fig. 1(c) enhanced multibeam propagation occurs below 10 km corresponding to the lower tropopause height at higher geographic latitudes. The occultation places are listed in Table 1. The possible e ect of ionospheric layers or disturbances around h = 100±110 km and around h = 80 km on radio wave propagation is also obvious in Fig. 1(c). The enhanced multibeam propagation at ionospheric and tropospheric heights is probably due to strong gradients in the atmospheric refractivity pro- le (e.g. caused by irregularities or strong vertical and/ or horizontal gradients in electron density, temperature or water vapour). 2.3. Angular spectra and bending angle pro le The di erence angular spectrum Da k, E k, k ˆ 1,..., n is derived from the spectrum of di erence Dopplerfrequency shift Do k, E k, k ˆ 1,..., n by using the relation explained by Pavelyev (1998) Da k ˆ ldo k 2pr L df L dt, 4 where Da k is the di erence between the refraction angle predicted by the theoretical model and the bending angle corresponding to kth ray trajectory. f L is the angle between the direction of the model ray (determined by model bending angle a m, impact parameter p m ) at the LEO and the LEO position vector ~r L. The In Fig. 2 a bending angle pro le is depicted as an example showing enhanced multibeam propagation in the lower troposphere. The pro le was derived from L2 carrier wave data of occultation event 0206-04.25-97.00. The circle diameters are proportional to the ray amplitudes. While the minor beams are denoted by dots, the main beam is given by open circles. In the present data analysis we only use the bending angle pro le of the main beam for Abel inversion into the refractivity pro le. As mentioned before the whole angular spectrum of the radioholographic method may in future be evaluated for a study of atmospheric irregularities (e.g., inversion layers, turbulence). It has already been shown that the radio occultation technique can provide information on turbulence (Armand et al., 1987; Yakovlev et al., 1995). 2.4. Spectral line width The error of bending angle and impact parameter is related to the spectral line width which can be derived from the damping factor b k in Eq. 3. The error of the bending angle pro le is especially required for data assimilation of radio occultation data into climate or numerical weather prediction models (e.g., Eyre, 1994; Zou et al., 1999). The full width at half maximum (FWHM a ) of the major line of the angular spectrum is FWHM a ˆ l2b 1 2pr L df L dt : 7 Here 2b 1 is the line width of the major spectral line of the di erence Doppler-frequency shift spectrum. In Fig. 3(a) FWHM a of the major component of the angular spectra is depicted as function of height for occultation event 0206. For this event strong ionospheric in uence occurs beyond 70 km height where spectral line broadening is obvious. Below the tropopause (h < 10 km) FWHM a increases too. If FWHM a is interpreted as a measure of uncertainty of the spectral line position, the minimal error pro le of the bending angle is given by the FWHM a pro le. It is clear that the FWHM a pro le will have di erent characteristics for each occultation event. Considering Eq. (5), the error of the impact parameter is closely re-

K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 1173 Fig. 3. (a) Spectral line width FWHM a of the main beam as a function of height for occultation event 0206 showing spectral broadening at ionospheric and tropospheric heights. (b) TEC variation (total electron content along GPS-LEO ray path) as a function of height of closest approach for event 0206. TEC enhancements are obviously correlated to the spectral broadening in (a). (c) Estimate of impact parameter error FWHM p of the main beam as a function of height for event 0206. (d) Estimate of relative bending angle error FWHM a (0da/a ) for event 0206. Below 40 km height the relative error is less than 1%. lated to the spectral line width FWHM a : FWHM p ˆ FWHM a r L cos f L : Fig. 3(c) depicts the estimated impact parameter error as a function of height. So, the radioholographic method allows an estimation of the height-dependent error of the bending angle pro le determined from the angular spectra. Till now the bending angle error was estimated by determination of the phase rms error at heights around 60±80 km. It was not possible to derive an individual height pro le of the bending angle error by the traditional retrieval method. Fig. 3(d) shows the relative error of the bending angle (da/a0fwhm a /a ). The relative error is below 1% at heights below 40 km in the example. Beyond 50±60 km the relative error 8 becomes too large, so that usage of the observational data is questionable at these heights. Gaps in the height pro le are caused by negative a values and the logarithmic scale of the x-axis. The occultation event 0206 took place during daytime at middle latitudes. Thus the spectral broadening of GPS rays with closest approach at around h = 110 km is likely due to the E-layer, while the spectral broadening around 70±90 km can be due to mesospheric layers. From earlier scienti c work it is known that there is a close relationship between radio wave scintillations, spectral broadening and spatial and/or temporal variation of the electron content (TEC) integrated along the ray path (e.g., Aarons, 1997; Woo, 1997). TEC can be simply calculated by a linear combination of the observed L1 and L2 phase path excess

1174 K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 Fig. 4. (a) GPS/MET occultation event 0200. Middle graph: Temperature pro les obtained by the radioholographic method (solid line) and by the well-veri ed UCAR retrieval (dash-dotted line). Left hand graph: Temperature di erence between both retrievals. Right hand graph: Signal to noise ratio (CASNR: SNR of coarse-acquisition ranging code) of L1 carrier wave showing the sensitivity of the signal magnitude to vertical temperature gradients (e.g., at the tropopause). (b) Same as (a), but for occultation event 0205. (c) Same as (a), but for occultation event 0206. (d) Same as (a), but for occultation event 0218.

K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 1175 (e.g., Melbourne et al., 1994): TEC ˆ 1 40:3! f 2 1 f 2 2 f 2 1 f 2 F 1 F 2 2 cycle ambiguity term bias term : 9 The units are [electrons/m 2 ] for TEC, [Hz] for GPS dual carrier frequencies f 1 and f 2, and [m] for phase path excess F 1 and F 2. The cycle ambiguity term and the bias term disappear if the TEC variations during the occultation event are calculated. TEC hteci h is depicted in Fig. 3(b). hteci h is the `background TEC pro le' which was calculated by smoothing the TEC series with a sliding window of about 3 s (corresponding to height intervals between 5±10 km). It is obvious that the spectral broadening (Fig. 3(a)) correlates with the TEC variation (Fig. 3(b)). Even for rays of closest approach at around h = 30 km a sharp TEC enhancement (somewhere on the path between GPS and LEO satellite) seems to induce a signi cant spectral broadening in this example. 2.5. Comparison of temperature pro les For removal of the ionospheric part on signal bending, the linear correction of bending angle has been applied (Vorob'ev and Krasil'nikova, 1994). Dp L1 and Dp L2 are determined from the position of the major peak in the spectrum of L 1 and L 2 signal of the same time interval. Then the ionospheric corrected impact parameter p and bending angle a are given by Dp ˆ f 2 1 Dp L 1 f 2 2 Dp L 2 f 2 1 f 2 2 p ˆ p m Dp Da ˆ r L a ˆ a m Da: Dp cos f L 10 The correction for the Earth's oblateness (Syndergaard, 1998) has not yet been included in our retrieval. Temperature pro les are now retrieved from the ionospheric corrected bending angle pro le of the main beam by using Abel inversion, dry air assumption, hydrostatic equilibrium and equation of state. More details are described by Hocke (1997) and Steiner et al. (1999). The pro les can be compared to pro les retrieved by the UCAR GPS/MET team (Rocken et al., 1997). In contrast to the radioholographic method, the UCAR data retrieval derives no angular spectra, but it can remove di raction/multipath e ects by using the wave back propagation method described in the introduction. In the case of the selected occultation events di raction correction was not used by UCAR. Therefore, the comparison only gives an impression of accuracy and resolution of the radioholographic method. In Fig. 4(a±d) the temperature di erence of both retrievals is shown on the left hand side. In the middle, the absolute temperature pro les are shown (sold line: radioholographic retrieval, dash-dotted line: UCAR retrieval). Vertical gradients of temperature (e.g., at the tropopause) are mostly accompanied by signi cant structures of the signal to noise ratio CASNR (SNR of coarse-acquisition ranging code, L1 wave) which is depicted on the right hand side. The average values of the standard deviation between both retrievals have been calculated for the selected occultations for heights below 30 km. The mean di erence is 1.78K for event 0200 in (a), 1.68K for 0205 in (b), 1.28K for 0206 in (c), and 3.38K for 0218 in (d). The large di erence in (d) is most likely due to a lack of the radioholographic method. So, in 3 of the 4 cases we nd our preliminary retrieval to be in good agreement with the well-veri ed UCAR retrieval. The relatively large di erences between the temperature pro les of our retrieval and the UCAR retrieval in the middle and upper stratosphere (above 35 km) are caused by the radioholographic method and di erent data ltering as well as by small di erences in the upper boundary condition and the statistical optimization procedure which are required for the Abel inversion (Hocke, 1997). Similar di erences occur if we retrieve the bending angle and temperature pro le by our traditional retrieval program and compare them with the UCAR retrieval result. Thus the reason for these di erences is mainly a di erent treatment of the noisy phase data by the program of UCAR and by our program (high relative error of phase path above 35 km). 3. Discussion The radioholographic method requires more elaboration and validation before it is as reliable as the wellveri ed traditional retrieval. The next task is the further development of the radioholographic method by using simulation data of radio occultation events. The high resolution spectral analysis and the evaluation of the angular spectrum have to be studied in detail. An important question is the choice of the data window length. In the present paper the data window length was chosen to be as small as possible. We applied the high-resolution spectral analysis MUSIC since the spectral resolution of FFT was not su cient.

1176 K. Hocke et al. / Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 1169±1177 From experimental data it follows that the spatial (angular) resolution of the radioholographic method may achieve 3±5 microradians. The angular distance between the spectral peaks may achieve 50±100 microradians. If the data window length is increased, the resolution of the spectrum increases too. The disadvantage is that the evaluation of the spectrum will be more di cult since the connection between the spectral component and the place of reception is more uncertain. An advantage of the radioholographic method (compared to the traditional retrieval) is the enhanced consideration of the signal amplitude in the data analysis. Furthermore the calculation of the time derivative of the phase path is not required. The retrieval is a small perturbation method evaluating the small di erence between observed and modelled ratio occultation data. Especially for GPS sounding of the Earth's atmosphere, detailed a priori knowledge of the mean atmospheric state can support the retrieval. Holographic methods are widely used for measurement of small deviations between similar objects, in our case the objects are the 1-D model pro le and the Earth's atmosphere pro le. Beside this work, an extension of the traditional retrieval of GPS radio occultation data by spectral methods may be considered. The spectrum gives information on error and quality of the received GPS radio wave eld, while the Doppler frequency shift can be further derived from the time derivative of the phase path excess. 4. Conclusion The retrieval of GPS/MET data using the radioholographic method has been described in an illustrative manner using 4 GPS/MET radio occultation events. The comparison between the ``dry'' temperature retrievals obtained by the radioholographic method and the well-veri ed traditional retrieval method provides insight into the accuracy and resolution of the radioholographic method. The radioholographic method is quite promising because of the high analytical value of the angular spectrum, which is a key element of the retrieval method. The relation between the power of the main beam and the total power of the spectrum for a given occultation indicates the altitudes at which multibeam propagation probably occur. This detection and analysis of multibeam propagation in radio occultation data may provide valuable, global information on radio communication links between satellites. Other applications of the angular spectrum are study of atmospheric irregularities and layers by using occurrence/peak position/magnitude/line width or various spectral components. For a day-time radio occultation event (0206) at mid-latitudes a correlation is found between angular broadening of the major spectral component and the TEC variation along the GPS- LEO radio link when the radio beam passes electron density layers at the Earth's limb or traverses ionospheric irregularities. The present study shows that the multiple signal classi cation (MUSIC) method is a good choice for derivation of high resolution angular spectra from the radiohologram. A simple evaluation of the spectra (considering only the spectral position of the main peak) may reduce di raction/multipath e ects, and allows a temperature retrieval with a standard deviation of around 1.58K compared to the traditional retrieval in 3 of 4 cases. For estimation of the bending angle error the MUSIC estimation of the damping factor (related to spectral line width) is used. 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