Fabrizio Pelliccia *, Stefania Bonafoni, Patrizia Basili University of Perugia, Perugia, Italy

Transcription

1 2.6 COSMIC GPS RADIO OCCULAION: NEURAL NEWORKS FOR ROPOSPHERIC PROFILING OVER HE INERROPICAL OCEAN AREA Fabrizio Pelliccia *, Stefania Bonafoni, Patrizia Basili University of Perugia, Perugia, Italy Nazzareno Piericca University La Sapienza, Roma, Italy Vittorio De Cosmo Italian Space Agency, Roma, Italy Piero Ciotti University of L Aquila, L Aquila, Italy 1. INRODUCION Global Positioning System (GPS) raio-occultation (RO) is provie as a global souning technique for obtaining atmospheric profiles by integrating them in global moels for numerical weather preiction an for climate change stuies. he raio occultation system employs GPS receivers place on a Low-Earth Orbit (LEO) satellite to soun the Earth s troposphere an ionosphere evaluating the aitional elay affecting a raio signal when passing through the atmosphere ue to the refractivity inex magnitue an its variations (Gorbunov an Sokolovskiy 1993; Rius et al. 1998). GPS raio-occultations probe the atmosphere operating uner all-weather conitions because the GPS signal wavelength o not scatter by clous, aerosols, an precipitation, preserving a relatively high vertical resolution throughout the epth of the atmosphere associate with the limbviewing geometry. his technique is limite by the horizontal resolution ue to the Fresnel iffractionlimite pencil-shape sampling volume of each measurement: each one has a horizontal resolution of about 200 km in the irection along the occulte link an a resolution of 1 km or better in the cross-link an vertical irections (Kursinski et al. 1997). In this paper we have propose a retrieval metho base on neural networks to achieve atmospheric profiles from RO in wet conitions without using temperature profile at each GPS occultation from inepenent observations (i.e. raiosounings or ECMWF ata). We have traine three neural * Corresponing author aress: Fabrizio Pelliccia, Univ. of Perugia, Dept. of Electronic an Information Engineering, via G. Duranti 93, Perugia, Italy; fabrizio.pelliccia@iei.unipg.it networks with inputs consisting of refractivity profiles compute from the occultation parameters observe by the COSMIC (Constellation Observing System for Meteorology Ionosphere an Climate) Microsat Constellation satellites provie by the COSMIC Data Analysis an Archive Center (CDAAC) of Bouler (Colorao). he network outputs are the ry an wet refractivity profiles together with the ry pressure profiles obtaine from the contemporary European Centre for Meium-Range Weather Forecast (ECMWF) analysis ata. We have performe the neural network training an the following inepenent test over the entire ocean area between ropics by using ata on summer 2006, from July 17 to August 18. he output ecomposition of the refractivity components together with the estimation of the ry pressure allow to retrieve temperature an pressure of water vapor eluing the necessity to know the temperature profile from inepenent sources of information. 2. NEURAL NEWORK: INPU AND ARGE RERIEVAL GPS raio signals passing through the atmosphere are refracte ue to the vertical refractive profile: the overall effect of the atmosphere can be characterize by a total bening angle α, an asymptotic impact parameter a an a tangent raius r p (Kursinski et al. 1997). By consiering the assumption of local spherical symmetry, the refraction inex profile n can be retrieve from measurements of α as a function of a uring an occultation by using an Abel transformation as in (Fjelbo et al. 1971):

2 1 α( a ) n( rp ) = exp π 2 2 a a a rp r p (1) a where a rp = n(r p ) r p is the impact parameter for the ray whose tangent raius is r p. he refractivity profile use as input for the neural networks training an the successive inepenent test is then N=(n-1) he targets for the neural networks training an the successive valiation of the neural networks outputs were obtaine using geopotential, temperature, specific humiity an logarithmic surface pressure from ECMWF 91 moel levels analysis profiles (ECMWF website). From these profiles, the atmospheric refractivity N at microwave wavelength were compute by (Smith an Weintraub 1953): P P 5 P N = w w (2) 2 where P is the pressure of ry air in mbar, P w the partial pressure of water vapor in mbar, is the atmospheric temperature in Kelvin. o obtain, P an P w profiles given N, the aitional constraints of ieal gas an hyrostatic equilibrium laws are require, respectively as: P M Pw ( M w M ) ρ = + (3) R R 0 P ( r) = gρ( r) r (4) where ρ(r) is the air ensity in kg m -3, P=P +P w, M an M w are respectively the mean molecular mass of ry air an water vapor, R 0 is the universal gas constant, g the gravitation acceleration. Given N, we have a system of three equations an four unknowns (, P, P w an ρ) an therefore it is necessary to have an inepenent knowlege of one of the four parameters, usually the temperature, to solve the atmospheric profiling problem (Kursinski et al. 1997; Kursinski an Hajj 2001; Vespe et al. 2002). 2.1 Selection Of COSMIC GPS Raio Occultation An Corresponing ECMWF Data In this paper, we have collecte 1041 COSMIC GPS RO events provie by CDAAC (COSMIC website), covering the inter-tropical ocean area from July 17 to August 18, he COSMIC GPS RO an the corresponing ECMWF observations above the ocean area have been selecte on the basis of the lan/sea flag inclue 0 in the ECMWF ata, an co-locate by consiering a maximal interval of 1 hour an a maximal geographical coorinate istance of 0.5 between the terrestrial coorinates of the occultation points 1 an those provie in ECMWF ata. 3. NEURAL NEWORK: AMOSPHERIC PROFILING We have esigne three neural networks to solve the atmospheric profiling problem from GPS RO overcoming the constraint of temperature profile availability at each GPS occultation: the neural network preictors are the refractivity profiles N(r) provie by the RO technique using (1) an the targets are the corresponing ry N (r) an wet N w (r) refractivity profiles an the ry pressure profiles P (r) compute from ECMWF ata. N (r) an N w (r) are respectively the first an secon terms on the right-han sie of (2). We have performe the neural network training an the following inepenent test over the entire ocean area between ropics by using the available ata set of 1041 refractivity profiles on summer 2006, choosing ranomly, 937 profiles for the training an the remaining 104 for the inepenent test of the network, that represent 90% an 10% of the entire available ataset respectively. Since each profile has 689 fixe altitue levels, representing the atmosphere from 0.9 to 20 km, we have pre-processe the input an target features using Principal Component Analysis (PCA) by expaning the 689-level refractivity profiles on a basis of empirical orthogonal functions calle principal components (Smith an Woolf 1976). By using the PCA technique we have reuce the number of escriptive profile parameters by exploiting the correlation among values at ifferent altitues. We have use only 22 principal components for the total refractivity instea of the original 689 levels, representative of the 99.9% of the total variance of the original ata (Demuth et al. 2008). Concerning the neural network targets, the number of components for ry refractivity, wet refractivity an ry pressure profiles are 17, 20 an 10, respectively. We have consiere the profile ata set starting from 0.9 km above the Earth surface since approximately only the 50% of the GPS occultations reaches lower levels. 1 he occultation point is efine as the point on the Earth s surface to which the retrieve refractivity profile is assigne, locate uner the perigee point of the bene ray (Kuo et al. 2004)

3 3.1 Early Stopping Approach For the training session of the neural networks, we have applie the early stopping technique, useful for etermining the optimal number of training epochs. hen we have ivie the training ata set (937 events) in three subsets: the training subset use for the learning itself, the valiation subset an the test subset use to improve the ability of generalization of the neural network, by assigning them ranomly the 70% (655 events), the 15% (141 events) an the 15% (141 events) of the whole ata set, respectively. he consiere fee-forwar neural networks have been chosen among the possible combinations on the basis that they exhibit the lower root mean square (RMS) error compute comparing the network outputs of the test session with the corresponing ECMWF profiles, where the test session employs the 104 refractivity profiles not use in the training phase. he best neural network topologies in terms of performance for the ry refractivity, wet refractivity an ry pressure retrieval are reporte in able 1. he hien layers are characterize by tansigmoi transfer function while the output layers by linear transfer function. Instea of the stanar back-propagation, for a fast training, we use the Bayesan regularization process accoring to Levenberg-Marquart algorithm for a fast training (Hagan an Menhaj 1994). EARLY SOPPING PCA INPU HL OUPU N Dry N Wet P Dry we assume here an in the following as the true climatological variability. Consiering N estimate by the neural networks, i.e. the autotest result, the vertically average RMS error is 2.78 (N unit) while the corresponing vertically average RMS error of the refractivity profiles N obtaine from Abel transformation is 3.58 (N unit). he mean stanar eviation of the entire ECMWF atabase is 6.13 (N unit). N, N w an P retrieve as outputs of the neural networks, employing as input an inepenent set of 104 refractivity profiles N obtaine from Abel transformation, exhibit the profiles of RMS error (continuous shown in Figure 2, Figure 3 an Figure 4 respectively, superimpose to the corresponing ECMWF stanar eviation profiles (ashe. he RMS error is compute comparing the network outputs with the corresponing ECMWF profiles. he retrieve profiles using neural networks approach appear more consistent with the real state of the atmosphere with respect to the corresponing ECMWF atabase first guess. he choice to train the networks with three outputs is justifie by the necessity to retrieve atmospheric profiles overcoming the constraint of temperature profile availability at each GPS occultation, as require to solve the system of (2), (3), (4). Also, we have chosen to estimate the ry pressure P from the network instea of solving the ieal gas an hyrostatic equilibrium laws in ry conitions since the error introuce by the neural networks is significatively lower with respect to the one exhibite after the integration of the (4). able 1: Best neural network topologies name N Dry (for ry refractivity estimation), N Wet (for wet refractivity estimation) an P Dry (for ry pressure estimation): input, HL an output columns report the number of neurons for the input, hien layer an output, respectively 4. RESULS 4.1 Refractivity An Pressure Estimation By Neural Network As shown in Figure 1, the neural networks contribute slightly to reuce the RMS error compute between refractivity profiles N obtaine using Abel transformation, that are the inputs for the training of neural networks an the corresponing ECMWF N refractivity profiles, that Figure 1: Neural network autotest (937 occultations): profile of RMS error for N (continuous obtaine as output of the neural network training, profile of RMS error N from Abel transformation (otte an ECMWF stanar eviation profile (ashe

4 With the availability of N, N w an P, at first we can solve for temperature in a straightforwar way from the ry refractivity relation P N = (5) an then for partial pressure water vapor P w from the wet refractivity relation N P P = w w w (6) 2 Figure 2: Neural network inepenent test (104 occultations): profile of RMS error for N (continuous an ECMWF stanar eviation profile (ashe instea of solving the system of (2), (3), (4). In Figure 5 an Figure 6 the profiles of RMS error for respectively an P w (continuous are shown superimpose to the corresponing ECMWF stanar eviation profile (ashe. In able 2 the average RMS error for the estimate profiles an the corresponing mean ECMWF stanar eviation are shown. Figure 3: Neural network inepenent test (104 occultations): profile of RMS error for N w (continuous an ECMWF stanar eviation profile (ashe Figure 5: Neural network inepenent test (104 occultations): profile of RMS error for (continuous an ECMWF stanar eviation profile (ashe Figure 4: Neural network inepenent test (104 occultations): profile of RMS error for P (continuous an ECMWF stanar eviation profile (ashe 4.2 emperature An Pressure Water Vapor Estimation Figure 6: Neural network inepenent test (104 occultations): profile of RMS error for P w (continuous an ECMWF stanar eviation profile (ashe

5 Vertically Average RMS error Mean Stanar Deviation ECMWF Dry Refractivity 0.76 N-unit 1.21 N-unit Wet Refractivity 2.73 N-unit 6.34 N-unit Dry Pressure 1.61 mbar 2.55 mbar Wet Pressure 0.54 mbar 1.27 mbar emperature 1.53 K 2.22 K able 2: Neural network inepenent test (104 occultations): vertically average RMS error for estimate profiles an corresponing mean ECMWF stanar eviation 5. SUMMARY he results have shown goo performances of the neural networks using the principal component analysis for a fast an less expensive approach, exhibiting a fairly goo accuracy for temperature an partial pressure of water vapor profiles. he purpose of our analysis consists in showing the possibility to retrieve each atmospheric parameter inclue the wet ones only from RO refractivity, an then the ability to increase the atmospheric observations, integrating them successively in the accuracy moels, thanks to a wie spatial coverage of RO sounings on the Earth. he boun of this approach is that the informative contribution brought by RO sounings is in some way connecte to the necessary employment of the ECMWF atmospheric moel profiles as targets for the neural network training. he work has been sponsore by the ASI, Italian Space Agency. We wish to thank COSMIC Data Analysis an Archive Center (CDAAC) of Bouler (Colorao) for the availability of the occultation ata. REFERENCES COSMIC website. Available via No Max-Planck-Institut fur Meteorologie. Hamburg Hagan, M., Menhaj, M., 1994: raining feeforwar networks with the Marquart algorithm. IEEE ransactions on Neural Networks, Vol. 5, No. 6, pp Kuo, Y.H., Wee,.K., Sokolovskiy, S., Rocken, C., Schreiner, W., Hunt, D., Anthes, R.A., 2004: Inversion an error estimation of GPS Raio Occultation ata. J. Meteorological Society of Japan, Vol.82, N0. 1B, pp Kursinski, E.R., Hajj, G.A., Schofiel, J.., Linfiel, R.P., Hary, K.R., 1997: Observing Earth s atmosphere with raio occultation measurements using the Global Positioning System. J. Geophys. Res., vol. 102, N0 D19, pp Kursinski, E.R., Hajj, G.A., 2001: A comparison of water vapour erive from GPS occultations an global weather analyses. J. Geophys. Res., vol. 106, N0 D1, pp Rius, A., Ruffini, G., Romeo, A., 1998: Analysis of ionospheric electron ensity istribution from GPS/ME occultations. IEEE rans. Geosci. Remote Sensing, 36(2), Smith, E.K., Weintraub, S., 1953: he constants in the equation for atmospheric refractive inex at raio frequencies. Proc. IRE, vol.41, pp Smith, W.L., Woolf, H.M., 1976: he use of eigenvectors of statistical covariance matrices for interpreting satellite souning raiometer observations. J. Atmos. Sci., vol. 33, pp Vespe, F., Beneetto, C., Pacione, R., 2002: Water Vapor Retrieve by GNSS Raio Occultation echnique with no External Information?. Raio Occultation Science Workshop, Bouler, Colorao Demuth, H., Beale, M., Hagan, M., 2008: Neural network toolbox for use with Matlab, User s Guie v.6, he MathWorks ECMWF website. Available via Fjelbo, G., Kliore, A.J., Eshleman, V.R., 1971: he Neutral Atmosphere of Venus as Stuie. with the Mariner V Raio Occultation Experiments. Astron. J., 76, Gorbunov, M.E., Sokolovskiy, S., 1993: Remote sensing of refractivity from space for global observations of atmospheric parameters. Report