GPSRO Capabilities

The SAC-C, CHAMP (since 2001), GRACE, and COSMIC satellites (since 2002 and 2006, respectively) provide atmospheric parameters retrieved during RO events such as temperature, pressure, water vapor, and geopotential height. The obtained profiles have vertical resolutions ranging from 0.5 km in the troposphere up to 1.4 km in the stratosphere (Kursinski et al. 1997) (nevertheless, the data are usually interpolated every 200 m) and horizontal resolution of 150 km along each LOS.

The perigee of the LOS between the satellites projected on the Earth's surface determines the geographical coordinates where the atmospheric parameters are given. Each one of these points is usually denoted as tangent point (TP). Successive perigees during the occultation form the line of tangent points (LTP). There is an uncertainty in the determination of the exact position of each TP position in geographical coordinates. TPs may be displaced away from the perigee along each ray path. This displacement is bounded between 25 km and 50 km in the 10-16 km and 16-35 km altitude intervals, respectively (Liou et al. 2007). This introduces uncertainties in localizing WA. The capability of this technique to detect GWs depends principally on the angle defined by LOS and wave surfaces. For example, surprisingly GW with horizontal wavelengths shorter than the horizontal resolution of GPS-ROs are frequently detected in the region considered. This happens because LOS directions and constant wave surfaces due to mountain waves (MWs)

have a predominant and nearly coincident North-South direction (de la Torre et al. 2006a).

The GWs activity has been usually quantified from GPS-RO Tprofiles, by calculating the mean specific potential energy (Ep) or the relative T variance content (a) in a vertical column of air C between altitudes z1 and z2:

where ST is the band-pass filtered Tperturbations between cutoffs at 3 km and 9 km, Tb is the background T, g is the gravitational acceleration, and N the buoyancy frequency. Due to the T behavior in the tropopause, the filtering process may lead to an overestimation of S T at some wavelengths (Schmidt et al. 2004). The lowest altitude limit is chosen above the tropopause, to avoid artificial contributions to the integral due to this effect. The potential energy could be inferred also from another occultation parameter like refractivity, which decreases monotonically with height. However, this decrease is nearly exponential, around two orders of magnitude from the lowest to the highest TP altitude, making it difficult to distinguish between the mean and perturbation values at different altitudes. Despite of the tropopause problem, it

(a) Ttopopause + lkm-35km, AxlOkm

(a) Ttopopause + lkm-35km, AxlOkm

2001 2002 2003 2004 2005 2006 2007 2001 2002 2003 2004 2005 2006 2007 2001 2002 2003 2004 2005 2006 2007

Fig. 1 a-c: Specific mean potential energy distribution, averaged between 1 km above the tropopause and 35 km, for different bandpass cut-offs. d-i: The same, for representative vertical columns consistent with the band-pass upper cutoffs selected: 10 km and 4 km, respectively (reproduced from de la Torre et al. (2006b))

2001 2002 2003 2004 2005 2006 2007 2001 2002 2003 2004 2005 2006 2007 2001 2002 2003 2004 2005 2006 2007

Fig. 1 a-c: Specific mean potential energy distribution, averaged between 1 km above the tropopause and 35 km, for different bandpass cut-offs. d-i: The same, for representative vertical columns consistent with the band-pass upper cutoffs selected: 10 km and 4 km, respectively (reproduced from de la Torre et al. (2006b))

is more adequate to use the T rather than refractivity, as its variations in the lower and middle atmosphere remain within the same order of magnitude.

Monthly global observations of WA between 2001 and 2006 reported in de la Torre et al. (2006b) revealed, in addition to general and specific features of energy distribution in the middle atmosphere (Fig. 1), the existence of singular extratropical locations with anomalously strong signatures. From each monthly tomographic latitude-longitude plot (not shown here), we selected two months that show intense WA in the region considered, during August and November 2001. A detailed insight among all the occultations registered in those periods, evidenced the influence in the mean of two intense events: August 30, 2001, 04:10 UTC and November 20, 2001, 03:58 UTC; hereinafter S1 and S2, respectively. In the following, we concentrate on the description of these events.

3 Case Studies: Two WA Events over Andes

3.1 Specific Features of GW Generation and Propagation

De la Torre et al. (2006b) performed an analysis of global distribution of WA in the upper troposphere and lower stratosphere between June 2001 and March 2006, using GPS-RO T profiles retrieved from the CHAMP satellite. A significant WA with respect to the remaining extra-equatorial regions in the Southern Hemisphere was detected in Mendoza, at the eastern side of the highest Andes Mountains (70° W to 65°W and 30°S to 40°S).

As it was pointed out by the authors, this region constitutes a natural laboratory where the known sources of GWs coexist: (i) Between October and March, frequent severe deep convection processes and intense hail storms take place. Waves throughout the full range of phase speeds, intrinsic frequencies, vertical and horizontal scales are generated. (ii) The Andes mountains represent a very important obstacle to the intense westerlies blowing from the Pacific Ocean, generating large amplitude GWs. This North-South barrier (tops around 7 km) generates mountain waves (MWs), whose phase surfaces are aligned nearly parallel to the mountains. The presence of an intense tropospheric jet allows for GWs propagation in the upper troposphere and stratosphere, because possible critical level filtering is avoided. (iii) This jet is observed above the highest orographic tops and its space and time variability may affect the geostrophic balance (de la Torre and Alexander 2005). As a consequence, possible generation of inertia gravity waves (IGWs) by geostrophic adjustment near the permanent jet is expected. This process may take place when the timescale of the wind evolution becomes comparable or shorter than the inertial period (around 1 day at 30°S). This perturbed flow, relaxes then to a new balanced state with redistribution of momentum, energy, and potential vorticity, with an additional radiation of excess energy as IGWs. In fact, downward/upward phase propagations above/below jets have been reported (Hirota and Niki 1985), in spite of the ignorance of the dynamical mechanism of wave emission (Plougonven et al. 2003).

3.2 Mesoscale Numerical Simulation and GWs Analysis

Mesoscale models can simulate realistic GW distributions in the troposphere and stratosphere and have been recently a major tool to study wave generation and propagation mechanisms (Zhang 2004). Mesoscale models can reveal detailed wave structures, energy sources, and maintenance mechanisms that are difficult to measure by satellite sensors. However, modeled GW properties and effects require observational verifications that are rarely available (Wu and Zhang 2004).

We performed simulations with the WRF (Weather Research and Forecasting) model during S1 and S2. In both cases, we employed three nested domains with effective horizontal grid spacing of 36 km, 12 km, and 4 km, respectively, and a time step equal to 30 s. The experiments were driven by assimilating lateral boundary conditions and sea surface temperatures from NCEP reanalysis. The simulations were initialized at least one day before the RO event in order to stabilize it. The physical parameterizations employed are described in Menendez et al. (2004). The results showed a reasonably good performance in reproducing various features of southern South America regional climatology. We recall that these simulations were performed with the MM5 model too, reproducing the same numerical results obtained with WRF. Figure 2 shows the topography in the highest resolution domain, for S1 and S2. The horizontal projections of LTPs and LOSs corresponding to each RO event are shown. It can be seen that the LTP corresponding to S1 is

Longitude

Fig. 2 Topography at the highest resolution domain for both simulations S1 and S2 and their corresponding horizontal projections of LTP and LOS. Observe that LTP corresponding to S1 is situated almost over the highest Andes Mountain, whereas for S2 it is situated approximately 200 km East of a lower part of the mountain range

Longitude

Fig. 2 Topography at the highest resolution domain for both simulations S1 and S2 and their corresponding horizontal projections of LTP and LOS. Observe that LTP corresponding to S1 is situated almost over the highest Andes Mountain, whereas for S2 it is situated approximately 200 km East of a lower part of the mountain range situated over the mountains, whereas S2 is situated, on average, at 200 km East of the mountains, over a plateau region. Note that in both cases, the respective LOSs (and LTPs) are close to parallel.

Typical westerlies are seen at and above 700 hPa during both events. An intense jet core with zonal speed greater than 50 m/s is seen in both simulations at 250 hPa. Figure 3 shows the jet core intensity variation for both events. It can be seen that the zonal wind speed, U, varies approximately 30% in a period shorter than the iner-tial (24 h) in both events. Probable IGWs radiated by geostrophic adjustment must then be considered here. It may be noted that the largest wind variation occurs just over the mountains. MWs generated at the Andes Range transfer energy upwards, decelerating the mean flow and possibly altering the geostrophic equilibrium.

We removed the background Tand wind components, to study ST and the zonal, meridional, and vertical velocity perturbations SU, SV, and SW. Figure 4 shows a typical MW with and around 50 km and 5 km, propagating from the troposphere to the lower stratosphere without finding any obstacle at the tropopause. As from cloud imagery we know that possible deep convection sources were absent during S1 and S2, the enhanced signatures registered by GPS RO could be explained by (i) the presence of MWs like this one, or instead, by (ii) longer waves originated a)

Lat S32.75

00 18 12

00UTC 29AUG

04:00UTC 30AUG 2001, Lat S32.75

57 54

51 I

48 fl

Lat S36,4

200 300 400 600

04:00UTC 30AUG 2001, Lat S32.75

57 54

51 I

48 fl

200 300 400 600

50 45 40 35

04:00UTC 20NQV 2001, Lat S36,4

06 00 18

12 06

00 18 12 06

00UTC 19NOV

Lat S36,4

04:00UTC 20NQV 2001, Lat S36,4

1000

50 45 40 35

Fig. 3 (a) and (c): U time and zonal variability, at constant latitude, for S1 and S2, respectively. The largest variability occurs over the mountain range in both simulations. (b) and (d): U vertical and zonal variability, at constant latitude, for S1 and S2, respectively. A jet with zonal speed greater than 45 m/s is seen at approximately 250 hPa in both simulations

50 45 40 35

50 45 40 35

Fig. 3 (a) and (c): U time and zonal variability, at constant latitude, for S1 and S2, respectively. The largest variability occurs over the mountain range in both simulations. (b) and (d): U vertical and zonal variability, at constant latitude, for S1 and S2, respectively. A jet with zonal speed greater than 45 m/s is seen at approximately 250 hPa in both simulations

1000

Fig. 4 a-b: U and SU vertical and zonal variability, at constant latitude, for S1. Note the wave constant phase surfaces due to the orographic forcing. (c) 3D view of the jet core (speed > 50 m/s). The Andes Range generates MWs and decelerates the mean flow, possibly altering the geostrophic balance

Fig. 4 a-b: U and SU vertical and zonal variability, at constant latitude, for S1. Note the wave constant phase surfaces due to the orographic forcing. (c) 3D view of the jet core (speed > 50 m/s). The Andes Range generates MWs and decelerates the mean flow, possibly altering the geostrophic balance in the radiation of the atmosphere during the restitution of geostrophic equilibrium after the departure induced by the MW.

Figure 5 shows 8 W and SU at 300 hPa at the closest simulation time step output to each event. A stationary wave pattern with horizontal Xh > 50 km along LOS, both during S1 and S2 are found in 8W and SU. The mesoscale waves coincide with the highest orographic tops, as well as constant phase surfaces quite parallel to topography, suggesting their topographic origin. Note that in these cases, due to the relative oblique orientation of LOS and constant wave phases, in spite of the short horizontal wavelengths revealed during the simulations, it may be possible for the RO technique to resolve MWs with horizontal wavelengths shorter than its horizontal resolution.

In Fig. 6 we show the continue Morlet wavelet transform (CWT) for SU and 8 V during both events for two representative latitudes, at 300 hPa and the closest time step output to each one. Two principal modes were found both in SU and 8V, longer and shorter than 100 km, respectively, and mostly located above the main mountains. One question arising here is whether the longer modes are due to the direct forcing of the mountains. To answer this, we recall that two important fundamental properties of GWs are (i) their phase front progression at right angles with group velocity (energy propagation) and (ii) their tendency to grow in amplitude a)

5W 300mb

5W 300mb

Longitude

Longitude

SW 300mb

Longitude

8U 300mb with ^Okm e-32

SW 300mb

I1'' 'A-' »'

*' > \

-35

1 ' „

Í

■. p, x

' ' ' i

de titu

-36

1 ,h

\ LTP

: M ¡V

-37

\los

-38

8U 300mb with ^Okm e-32

Longitude

Longitude

8U 300mb with

X^SOkm

-70 -69 -68 Longitude

8U 300mb with

J

Í» if If

y

\\ LTP

\

|

\los

\

-70 -69 -68 Longitude

[m/s]

4

2

0

-2

-4

L

-6

Fig. 5 SW and SU at 300 hPa at the closest simulation time step output to (a) S1 and (b) S2. A stationary wave pattern with Xh > 50 km along LOS, during the events are found in both variables with height, proportionally to the inverse square root of the exponentially decreasing air density. To identify internal waves in the atmosphere, it is necessary to know how the velocity components vary in space and time. Taking into account the Earth rotation effects, linear wave theory predicts an elliptic polarization relation between zonal and meridional velocity perturbation components. This means that the velocity vector rotates anticyclonically (counter-clockwise in the Southern Hemisphere) with time and hence also in space, as one moves in a direction opposite to the phase velocity (e.g., Gill 1982). Rotation effects are important in waves with horizontal scales greater than 100 km and they have no effect on shorter waves, which linear wave theory predicts a lineal polarization relation between SU and 8 V.

In the GWs literature, examples may be found where the polarization is analyzed from vertical regular radiosoundings, soundings from stratospheric balloons, etc.(e.g., de la Torre et al. 1996; Zhang et al. 2004). Nevertheless, GWs represent 3D structures without preferred symmetries, thus they can be observed in any direction or orientation. If the main wave source is at the ground and additional wave contributions from other sources are absent, the sense of rotation never changes. When a source is situated at a given altitude, energy is radiated at this level. In this case, the

U, lat=32.4S 04:00UTC 30AUG2001

U, lat=32.4S 04:00UTC 30AUG2001

3 50

100 200 300 400

Distance [km]

V, lat=32.4S 04:00UTC 30AUG2001

U, lat=36.5S 04:00UTC 20NQVG2001

3 50

100 200 300 400

Distance [km]

V, lat=32.4S 04:00UTC 30AUG2001

100 200 300 400

Distance [km]

100 200 300 400

Distance [km]

U, lat=36.5S 04:00UTC 20NQVG2001

200 300 400 Distance [km]

200 300 400 Distance [km]

V, lat=-36.5S 04:00UTC 20NOV2001

V, lat=-36.5S 04:00UTC 20NOV2001

3 50

100 200 300 Distance [km]

3 50

100 200 300 Distance [km]

Fig. 6 Morlet CWT for SU (above) and SV (below) for S1 (left) and S2 (right), at 300 hPa and the closest time step output to each event. Two principal modes were found both SU and SV. The origin of the horizontal axis coincides with the western limit of the domain (71° W)

sense of rotation must be different above and below it. In order to identify the main source of GWs we studied the sense of rotation of the perturbation velocity vectors (SU, S V) at different pressure levels, above and below the jet, along different paths: (i) at constant latitudes and (ii) parallel to the LOS. We applied two different methods to identify the principal modes of oscillation in both velocity components: (1) a non recursive bandpass filter and (2) a CWT wavelet transform. The CWT coefficient corresponding to a certain wavelength can be interpreted as a bandpass filter for this wavelength. From both filtering methods we observe the velocity vector for modes with wavelengths greater than 100 km rotating in the same sense above and below the jet along all paths. From these results, we conclude that IGWs do not stem from geostrophic adjustment and the major source must be topographic forcing.

3.3 Comparison of Observed and Simulated GW Activity

The RO bending angle is an integrated measure of the refractive index (and therefore T) in the atmosphere traversed by the optical ray. The contribution peaks at the perigee and decays exponentially away from it. Due to uncertainties in the determination the exact position of the perigee, the peak of the exponential decay does not always coincide with each TP. In some cases, a LOS traversing through wave packets away from a TP, may reveal a vertical Tprofile evidencing an apparent larger (or nonexistent) WA at the LTP locations, as it is the case during S2 (Fig. 7b). We must be careful to interpret the atmospheric region where a given RO event predicts intense WA. If we are interested only in the mean T profile, the consideration of a rectangular parallelepiped defined by the first and last TP would be enough. If we are interested in the WA associated with it, the proper interpretation must consider the region defined by the set of optical rays. The 3D contours corresponding to ±5T = 3.0 K for S1 and ±5T = 2.0 K S2 are shown in left panel of Fig. 7. LTPs and LOSs are included. The right panels show 5 T along the vertical planes defined by the LOSs' sets. Note the wave phase surfaces tilting westward, evidencing a downward-westward phase progression clearly corresponding to MWs. A first insight shows an intense WA in S1 close to the TP (as predicted by the corresponding RO); whereas for S2, there are only weak wave packets in the troposphere at approximately 100 km away from the tangent points. Note in Fig. 7b for S2, the a)

30 25

30 25

30 25 20

30 25 20

28 26 24

IT 22

-200 -150 -100 -50 0 50 100 150 200 Distance from tangent point [km]

-200 -150 -100 -50 0 50 100 150 200 Distance from tangent point [km]

-150 -100 -50 0 50 100 150 200 Distance from tangent point [km]

-150 -100 -50 0 50 100 150 200 Distance from tangent point [km]

Fig. 7 Sets of LOS corresponding to each tangent point (TP) for (a) S1 and (b) S2. The relative weighting of the contribution rises with decreasing distance to the LOS center (TP). The T perturbations in 3D contours corresponding to ±ST = 3.0 K for S1 and ±ST = 2.0 K for S2 are shown. The right panels show ST along the vertical planes defined by the LOSs' sets

partial penetration of LOSs into the high wave amplitude atmospheric region. Taking into account these two examples, in addition to the systematic GPS-RO uncertainties mentioned above, it appears that GPS-RO T data alone are not enough to quantify and locate accurately WA during single events. At most, they would provide a useful qualitative indication. This should be complemented with independent observations or with mesoscale simulations. On the other hand, it seems reasonable to draw statistical conclusions from the global WA distribution derived from GPS-RO measurements alone.

4 Conclusions

A previous global analysis of wave potential energy using GPS-RO Tprofiles in the period 2001-2006 revealed a considerable intense WA in the Mendoza (Argentina) region, in comparison with other non-equatorial areas. After examining WRF and MM5 results for two selected cases in the vicinity of the RO LTPs, we found intense activity only near to the mountains. A wavelet analysis led us to identify principal modes with two main horizontal wavelengths, clearly corresponding to mountain waves. A hodograph analysis performed from the bandpassed results and from the wavelet coefficients evidences that IGWs do not stem from geostrophic adjustment at jet levels, but the source seems to be the topographic forcing. One of the simulations does not show intense WA in the vicinity of the tangent points, even though that the GPS-RO T profile detects it. The GPS-RO technique is not by itself reliable enough to quantify and locate accurately WA of single events, but it may be considered as a useful tool to measure the global distribution of WA.

Acknowledgements Manuscript prepared under grants UBA X021 and CONICET PIP 5932. A. de la Torre and P. Alexander are members and P. Llamedo holds a fellowship of CONICET. The GFZ contribution was partially funded through DFG project GW-CODE (WI 2634/2-1), DFG priority program CAWSES SPP 1176. We acknowledge data provided by the NOAA-CIRES/Climate Diagnostics Center, Boulder (CO), from their website http://www.cdc.noaa.gov and GFZ Potsdam and JPL for making available CHAMP and SAC-C GPS RO data for our study.

References

Fritts DC, Alexander MJ (2003) Gravity wave dynamics and effects in the middle atmosphere. Rev

Geophys 41(1):1003, doi:10.1029/2001RG000106 Gill AE (1982) Atmosphere-Ocean Dynamics. Academic Press, San Diego London Hirota I, Niki T (1985) A statistical study of inertia-gravity waves in the middle atmosphere. J Met SocJpn 63:1055-1066

Kirchengast G (2004) Occultations for probing atmosphere and climate: Setting the scene. In: Kirchengast G, Foelsche U, Steiner AK (eds) Occultations for Probing Atmosphere and Climate, Springer-Verlag, Berlin Heidelberg New York, pp 1-8 Kursinski ER, Hajj GA, Schofield JT, Linfield RP, Hardy KR (1997) Observing the Earth's atmosphere with radio occultation measurements using the Global Positioning System. J Geophys Res 102(D19):23429-23465 Lindzen RS (1990) Dynamics in Atmospheric Physics. Cambridge University Press, Cambridge

Liou YA, Pavelyev AG, Liu SL, Pavelyev AA, Yen N, Huang CY, Fong CJ (2007) FORMOSAT-3/ COSMIC GPS radio occultation mission: Preliminary results. IEEE Trans Geosci Remote Sens 45(11):3813-3826, doi:10.1109/TGRS.2007.903365 Menendez CG, Cabre MF, Nunez M (2004) Interannual and diurnal variability of January precipitation over subtropical South America simulated by a regional climate model. CLIVAR Exch 29:1-3

Plougonven R, Teitelbaum H, Zeitlin V (2003) Inertia gravity wave generation by the tropospheric midlatitude jet as given by the Fronts and Atlantic Storm-Track Experiment radio soundings. J Geophys Res 108(D21):4686, doi:10.1029/2003JD003535 Schmidt T, Wickert J, Beyerle G, Reigber C (2004) Tropical tropopause parameters derived from GPS radio occultation measurements with CHAMP. J Geophys Res 109(D13105), doi:10.1029/2004JD004566 de la Torre A, Alexander P (1995) The interpretation of wavelengths and periods as measured from atmospheric balloons. J Appl Meteor 34(12):2747-2754 de la Torre A, Alexander P (2005) Gravity waves above Andes detected from GPS radio occultation temperature profiles: Mountain forcing? Geophys Res Lett 32(L17815), doi:10.1029/2005GL022959 de la Torre A, Teitelbaum H, Vial F (1996) Stratospheric and tropospheric wave measurements near the Andes mountains. J Atmos Terr Phys 58(5):521-530 de la Torre A, Tsuda T, Hajj G, Wickert J (2004) A global distribution of the stratospheric gravity wave activity from GPS occultation profiles with SAC-C and CHAMP. J Meteor Soc Jpn 82(1B):407-417

de la Torre A, Alexander P, Llamedo P, Menendez C, Schmidt T, Wickert J (2006a) Gravity waves above Andes detected from GPS radio occultation temperature profiles: Jet mechanism? Geo-phys Res Lett 33(L24810), doi:10.1029/2006GL027343 de la Torre A, Schmidt T, Wickert J (2006b) A global analysis of wave potential energy in the lower stratosphere derived from 5 years of GPS radio occultation data with CHAMP. Geophys Res Lett 33(L24809), doi:10.1029/2006GL027696 Wu DL, Zhang F (2004) A study of mesoscale gravity waves over North Atlantic with satellite observations and a mesoscale model. J Geophys Res 109(D22104), doi:10.1029/ 2004JD005090

Zhang F (2004) Generation of mesoscale gravity waves in upper-tropospheric jet-front systems.

J Atmos Sci 61(4):440-457 Zhang F, Wang S, Plougonven R (2004) Uncertainties in using the hodograph method to retrieve gravity wave characteristics from individual soundings. Geophys Res Lett 31(L11110), doi:10.1029/2004GL019841

New Applications and Advances of the GPS Radio Occultation Technology as Recovered by Analysis of the FORMOSAT-3/COSMIC and CHAMP Data-Base

A.G. Pavelyev, Y.A. Liou, J. Wickert, V.N. Gubenko, A.A. Pavelyev, and S.S. Matyugov

Abstact Comparative analysis of phase and amplitude variations of GPS radio-holograms allows one to separate the influence of the layered and irregular structures. A possibility exists to measure important parameters of internal waves: the intrinsic phase speed, the horizontal wind perturbations, and, under some assumptions, the intrinsic frequency as function of height in the atmosphere. A new technique was applied to measurements provided during CHAllenging Minisatellite Payload (CHAMP) and the Formosa Satellite-3/Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT-3/COSMIC) radio occultation (RO) missions. As an example of this approach, we establish the atmospheric origin of amplitude and phase variations in the RO signal at altitudes 10-26 km. We observed for the first time in the RO practice examples of internal wave breaking at altitudes between 38 km and 45 km. We obtained geographical distributions and seasonal dependence of atmospheric wave activity with global coverage within the years 2001-2003.

1 Introduction

Atmospheric gravity waves (GW) have been a subject of intense research activities in recent years because of their various effects and their major contributions to atmospheric circulation, structure, and variability (Fritts and Alexander 2003). Radiosonde and rocketsonde GW measurements, balloon soundings, radar observations, and lidar studies have been limited to ground-based sites (Fritts et al. 1988; Wilson et al. 1991; Eckermann et al. 1995; Steiner and Kirchengast 2000; Tsuda et al. 2004; Wang et al. 2005) mainly over specific land parts of the Northern and Southern Hemispheres.

Institute of Radio Engineering and Electronics of the Russian Academy of Sciences (IRE RAS),

Moscow, Russia e-mail: [email protected]

The radio occultation technology incorporates high-precision GPS radio signals at two frequencies (f1 = 1575.42 MHz and f2 = 1227.6 MHz) for the investigation of internal waves. It allows the analysis of phase and amplitude of radio waves after propagating through the atmosphere. Analysis of temperature variations found from RO phase data furnishes an opportunity to measure the GW's statistical characteristics in the atmosphere (Steiner and Kirchengast 2000; Tsuda et al. 2000; Tsuda and Hocke 2002; Tsuda et al. 2004). Of particular importance are new ways to investigate locations of the layered plasma structures in the ionosphere. Radio-holographic methods for the analysis of RO signals have the potential and capability for the research and simultaneous observation of atmospheric and ionospheric waves (Igarashi et al. 2000, 2001; Pavelyev et al. 2002, 2003, 2004; Liou et al. 2002, 2003, 2006). However, up to now the assumption of global spherical symmetry of the atmosphere and ionosphere is a cornerstone in the analysis of GPS RO measurements (Hajj et al. 2002; Wickert et al. 2004).

The aim of this paper is to introduce a new technique for estimating parameters of internal waves, to demonstrate the examples of direct observation and location of quasi-regular internal waves, and to analyze seasonal and geographical distributions of internal wave activity at different levels in the atmosphere using amplitude and phase variations in GPS occultation signals.

2 Radio Occultation Method

The scheme of the RO geometry is shown in Fig. 1. The point O is the center of the global spherical symmetry of the Earth's atmosphere and ionosphere. Radio waves emitted by the GPS satellite (point G) arrive at the receiver on board of the LEO satellite (point L) along the ray GTL, where T is the tangent point in the atmosphere. The results of registration which are 1-D radio-holographic images of the propagation medium consist of the phase path excesses @1(t) and @2(t) along the amplitudes A1(t) and A2(t) of the radio field as functions of time at two GPS frequencies. These variations are caused mainly owing to the medium influence at the tangent point T, where the refractivity gradient is perpendicular to the ray GTL. In the case of spherical symmetry the point T coincides with the perigee of ray GTL, where the distance from the center of spherical symmetry—point O is minimal and

Fig. 1 Key geometrical parameters for RO measurements

Fig. 1 Key geometrical parameters for RO measurements

O

equal to r0. The geographical coordinates of the ray perigee can be evaluated by use of orbital data of the GPS and LEO satellites. Analysis of RO data delivers the vertical profile of refractivity N(h) in the atmosphere and then vertical profiles of pressure p(h) and temperature T(h).

The projection of the point T on the Earth's surface determines the geographical coordinates of the RO region. The vertical velocity of the occultation beam path v± is about of 2 km/s. This value of v± is many times greater than those corresponding to the motion of layers in the atmosphere and ionosphere. Thus the RO radio-holograms record practically simultaneously the impact of the internal waves on the RO signal because the vertical displacement of a wave structure is negligible during the movement of the beam across it. However, the horizontal gradients in the atmosphere and ionosphere can disturb the spherical symmetry of the atmosphere and ionosphere (Wickert et al. 2004). Actually a local spherical symmetry can exist for inclined layered structures in the propagation medium. In the case of local spherical symmetry one can use the same relationships, which have been previously obtained for the case of global spherical symmetry (Pavelyev et al. 2002, 2004) with a change of the designation of the impact parameter from p to p' (Fig. 1). For simplicity we will not use the primes on p and O below.

In the case of local spherical symmetry with center at point O (Fig. 1) there are fundamental relations between the phase path excess @(p) (in m) and the refraction attenuation of radio waves X(p) (dimensionless), which characterizes the decreasing/increasing of the intensity of radio waves because of the influence of the refraction effect in the atmosphere (Pavelyev et al. 2002, 2004; Liou et al. 2006)

^(p) = L(p) + k(p) - Rq, L(p) = di + d2 + pf(p), (1)

R1 R2d1d2 sin 6

de dp

where k(p) is the main refractivity part of the phase path excess, f (p) = —dK(p)/dp is the refraction angle, 0(p) is the central angle, p, ps are the impact parameters of the ray trajectory GTL, and the line of sight GQL, respectively, R0, R1, R2 are the distances GL, OG, and OL, correspondingly, L(p) is the distance GABL. L(p) is a sum of two short lengths GA (d1), BL (d2), and arc AB, which is equal to the product pf (p). Because smallness of the refraction effects the distances d1, d2 are approximately equal to GQ and QL. According to Eq. (1) the phase path excess @(p) contains only one term k(p), which depends directly on the refractivity. This justifies the designation "main refractivity part" for k(p). The refraction angle f (p) is connected with the central angle 0 (Fig. 1):

0 0

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