Data Assimilation into Ionospheric Models

Transcription

1 Data Assimilation into Ionospheric Models Bruno Nava Karl Franzens University Graz, Graz, Austria ICTP, Trieste, Italy Supervisor: Prof. H. Biernat Karl Franzens University Graz, Graz, Austria Advisor: Dr. Putz Karl Franzens University Graz, Graz, Austria Graz, 13 June 2012

2 Outline The ionosphere Chapman theory of ionospheric layer production The measurements The model Review of the techniques developed to update empirical models (mainly NeQuick) with experimental data Description Examples Validation

3 The Ionosphere The Ionosphere is the part of the atmosphere where free electrons exist in number sufficient to influence the propagation of radio waves. (It is a weakly ionized gas: <10-3 of the atmospheric molecules are ionized). To show how the electrons in the Ionosphere are produced by solar radiation, it is necessary to discuss the nature of the neutral atmosphere. The regions of the neutral atmosphere are named according to different parameters (e.g.: temperature, composition). The atmosphere are divided in a number of ʼspheresʼ and ʼpausesʼ, where the "pauses" are the boundaries between the ʼspheresʼ.

4 Atmospheric structure: temperature In the thermosphere the temperature strongly increases with height. The solar radiation in the UV band is absorbed due to dissociation of molecules like O2, N2, and NO and ionization of atomic O. In the mesosphere, above 50 km, the temperature decreases with altitude. The stratosphere above the troposphere has a positive temperature gradient due to heating from the ozone which absorbs the solar ultra-violet radiation that penetrates down to these altitudes. The troposphere is heated mainly by the ground, which absorbs solar radiation and re-emits it in the infra-red. The temperature decreases with height.

5 Atmospheric structure: temperature In the thermosphere the thermal conductivity increases with height. In the upper part of the thermosphere the thermal conductivity is so high that this region is kept nearly in an isothermal condition. The thermospheric temperature is of the order of K and it varies with the time of day and with solar activity.

6 Atmospheric structure: composition (a) solar min (b) solar max The homosphere: region below ~100 km altitude; turbulent mixing -> the relative concentrations of different molecular species are independent of height. The heterosphere: region above the homosphere; no turbulent mixing -> each molecular species behaves as if it were alone (diffusive equilibrium) -> the relative concentrations change with height. At higher altitudes light molecular species will dominate.

7 Formation of the Ionosphere The Ionosphere is created through the ionization of the atmospheric gases, mainly N2, O2 and O, by the extreme UV and X solar radiation. The density of the neutral atmosphere exponentially increases downwards. Since the photons are absorbed in the photoionization process, the radiation intensity decreases downwards. At some height a maximum of ion production (ionospheric layer) has to appear. Once formed, ions and electrons tend to recombine, react with other species and be affected by transport processes. By these processes neutral molecules or atoms are formed. This is described by the continuity equation: dn dt = q L (Nv) N = electron concentration q = production rate per unit volume L = loss rate per unit volume v = mean velocity of the electrons

8 Atmospheric Hydrostatic Equilibrium Equilibrium between gravity and pressure gradient Ideal gas law Suppose T, g independent of height with h = height n = molecule concentration m = molecule mass p = pressure T = temperature g = acceleration of gravity k = Boltzmannʼs constant H = (pressure) scale height

9 Solar radiation absorption Radiative transfer theory Variable change SUN I s χ h Integrate from above the atmosphere to altitude h to obtain the intensity I as a function of height I = intensity σ = absorption cross-section n = molecule concentration χ = solar zenith angle ds = element of path s dh = element of path h ds = cos(χ) dh H = scale height

10 Solar radiation absorption To obtain the Chapman formula for the ion production rate q we assume that: the atmosphere is composed of a single neutral species the absorption cross-section is constant (<=> monochromatic radiation) the atmosphere is horizontally stratified, isothermal and obeys the hydrostatic equation; H independent of height The intensity I as a function of height becomes:

11 Chapman Production Function With the previous assumptions becomes: q = the number of photo-electrons produced per unit volume per unit time (= ionization production rate) η = electrons produced by a unit of absorbed energy That, in terms of the rate of production qm at the peak, that occurs at height hm is: And in terms of the rate of production qm,0 at the peak for χ=0, that occurs at height hm,0 is:

12 Considering the continuity equation dn dt = q L (Nv) Chapman Layer Neglecting transport and considering that the electron are lost by recombination at a rate ~ αn 2 with α independent of height, at equilibrium (dn/dt = 0) we have: q = L = αn 2 Notice: the Chapman theory fully explains only the behavior of the E layer, not of the F region, because there the assumptions made are not valid. In any case this theory is an important reference for the study of ionized layers (Kelly 1989).

13 Layers of the ionosphere D region E region sporadic E F region F1 and F2 layers Topside

14 D Region It extends from 70 to 90 km height Under special conditions it might be present form 50 km In this region the electron density: increases quickly with height is very low during night-time its maximum is reached right after local noon during summer

15 E Region It extends from 90 to about 140 km It develops clearly after sunrise In this region the electron density reaches its maximum value: near the local noon in summer at about 110 km height

16 F Region It extends from 140 km upwards: During the day hours it is possible to distinguish two layers: F1 and F2, which are merging during the night. It shows a clear geographic variation with higher electron density values around 20 N and S of the dip equator. (Equatorial Anomaly)

17 F1 Layer It extends form about 140 to 200 km It is well developed especially during summer The maximum of electron density is between km, before noon in the equatorial region

18 F2 Layer It extends above the F1 layer The electron density maximum in this layer (NmF2) is in average between 250 and 350 km of height NmF2: reaches the minimum value between 4-6 LT reaches its maximum around local noon but also in the late afternoon or early evening depends on geomagnetic latitude reaches the highest values around 20 N and S of the dip equator is affected by geomagnetic activity

19 Topside Topside ionosphere is the region above the F2 maximum The electron density decreases with height reaching very low values at about km(plasmasphere)

20 Ionospheric measurements Remote sensing techniques Bottom-side soundings (ionosonde, from the ground, critical frequencies) Top-side soundings (ionosonde, satellite borne, critical frequency/ies) Ground based and space based Total Electron Content (TEC) measurements (GNSS) Incoherent scatter radar (from the ground, N profile) The Jicamarca Radio Observatory

21 Ionogram Ionospheric measurements Critical frequency: the frequency at which an e.m. wave just penetrates an ionospheric layer is known as the critical frequency of that layer. Frequency is related to the electron density by the simple relation: f=9 N f in Hz; N in m -3

22 Ionospheric measurements TEC: The total electron content (TEC) is the number of free electrons in a column of one square-metre cross-section along a given ray-path. TEC = N(s)ds

23 Ionospheric measurements GNSS signal propagation in the Ionosphere f = carrier frequency [Hz] TEC = Total Electron Content along the slant propagation path [m -2 ] n = electron concentration [m -3 ] Δt = (additional) time delay [s] with reference to propagation in a vacuum Δs = (additional) range delay [m] with reference to propagation in a vacuum -> range delay error due to the ionosphere -> if not corrected positioning error in GNSS single freq. applications Taking advantage of the 2 frequencies of the GPS, TEC can be estimated

24 Ionospheric models Theoretical (or first-principle) models In these models conservation (continuity, momentum, energy, etc.) equations are solved numerically as a function of spatial and time coordinates to calculate plasma densities, temperatures and flow velocities. These models require magnetospheric and atmospheric input parameters and their accuracy depend on the quality of the input data. They can be powerful tools to understand the physical and chemical processes of the upper atmosphere. Empirical and semi-empirical models These models are based on an analytical description of the ionosphere with functions derived from experimental data or adapted from physical models. In particular, the profilers can compute the electron concentration of the ionosphere as a function of height, using as experimental values of basic ionospheric characteristics as inputs.

25 The NeQuick 2 B. Nava, P. Coïsson, S. M. Radicella, "A new version of the NeQuick ionosphere electron density model", Journal of Atmospheric and Solar-Terrestrial Physics (2008), doi: /j.jastp

26 NeQuick 2 The NeQuick model is an ionospheric electron density model developed at the Aeronomy and Radiopropagation Laboratory of The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, and at the Institute for Geophysics, Astrophysics and Meteorology (IGAM) of the University of Graz, Austria. It is based on the DGR profiler proposed by Di Giovanni and Radicella [1990] and subsequently modified by Radicella and Zhang [1995] and is a quick run model particularly tailored for transionospheric propagation applications.

27 NeQuick 2 Further improvements have been implemented by Radicella and Leitinger [2001]. A modified bottomside has been introduced by Leitinger, Zhang, and Radicella [2005]. A modified topside has been proposed by Coïsson, Radicella, Leitinger and Nava [2006].

28 NeQuick 2 The model profile formulation includes 6 semi-epstein layers with modeled thickness parameters and is based on anchor points defined by foe, fof1, fof2 and M(3000)F2 values. These values can be modeled (e.g. ITU-R coefficients for fof2, M(3000)F2) or experimentally derived. NeQuick inputs are: position, time and solar flux; the output is the electron concentration at the given location and time. NeQuick package includes routines to evaluate the electron density along any ground-to-satellite ray-path and the corresponding Total Electron Content (TEC) by numerical integration.

29 NeQuick 2 formulation The model is represented by a sum of Epstein functions for the E, F1 and F2 layers: where

30 NeQuick 2 formulation with and is a function that ensures a fade out of the E and F1 layers layers in the vicinity of the F2 layer peak in order to avoid secondary maxima around hmf2.

31 NeQuick 2 formulation The model topside is represented by a semi-epstein layer with a height-dependent thickness parameter H: with

32 Peak heights NeQuick 2 formulation with

33 Thickness parameters NeQuick 2 formulation

34 NeQuick 2 formulation where and

35 NeQuick 2 formulation Critical frequencies and propagation factor

36 Data Assimilation Data assimilation is an analysis technique in which the observed information is accumulated into the model state by taking advantage of consistency constraints with laws of time evolution and physical properties ( newsevents/training/rcourse_notes/data_assimilation/ ASSIM_CONCEPTS/Assim_concepts2.html#962570). "Data assimilation is fundamentally a model specification and prediction technique that uses data to improve the fidelity of the model" (Bust, G. S., and C. N. Mitchell (2008), History, current state, and future directions of ionospheric imaging, Rev. Geophys., 46, RG1003, doi: /2006rg ).

37 Data Assimilation Empirical models like IRI and NeQuick have been developed as climatological models, able to reproduce the typical median condition of the ionosphere. For research purposes and practical applications, in order to pass from climate to weather, there is a need to have models able to reproduce the current conditions of the ionosphere. Considering that there is an increasing availability of experimental data even in real time (ground and space-based GPS, ionosondes), several assimilation schemes have been developed. They are of different complexity and rely on different kinds of data.

38 Assimilation schemes (example) Utah State University (USU) Global Assimilation of Ionospheric Measurements (GAIM) [Schunk et al., 2004] or the Jet Propulsion Laboratory (JPL)/University of Southern California (USC) Global Assimilative Ionospheric Model (GAIM) [Wang et al., 2004], for example, are based on assimilation of data originating from different sources and imply the use of first principle models. The Electron Density Assimilative Model (EDAM) [Angling and Khattatov, 2006] provides a means to assimilate ionospheric measurements into a background ionospheric model (that can be the IRI). Review paper: Bust, G. S., and C. N. Mitchell (2008), History, current state, and future directions of ionospheric imaging, Rev. Geophys., 46,RG1003, doi: /2006rg

39 Effective parameters In the case of NeQuick, the methods used to adapt the model to experimental data in order to retrieve the 3D electron density of the ionosphere are intended to be simple and quick. Therefore they rely on the use of effective parameters, that are defined on the bases of model (e.g. NeQuick) and the experimental data used (e.g. fof2 or TEC). One of the first effective parameter that has been proposed is the effective sunspot number (SSNe). This parameter valid for a set of fof2 observations has been defined as the SSN value that, when used as input to the URSI fof2 model, gives a weighted zero-mean difference between the observed and the modeled fof2 values.

40 Effective parameters IRI IG 12 ion52am.pdf T-index (The T index is an indicator of the highest frequencies able to be refracted from regions in the ionosphere). Klobuchar-Style Ionospheric Coefficients (Klobuchar-style alpha and beta coefficients best fitting VTEC data)

41 Basic concepts Model(s) features relevant to implement adaptation techniques. The models (like IRI, NeQuick) can be considered as profilers. The profile formulation is based on anchor points modeled in terms of ionosonde parameters (e.g. foe, fof1, fof2 and M(3000)F2). For a given epoch & ray-path the model TEC is a monotonic function of the solar activity index, that can be regarded as an effective ionization level parameter.

42 Adapting NeQuick model to vertical TEC maps

43 vtec map La Plata Lat. Lon. grid points: lat.=-90, 90 step 2.5 lon.=-180, 180 step 5

44 Reconstructed fof2 map Lat. Lon. grid points: lat.=-90, 90 step 2.5 lon.=-180, 180 step 5

45 At a given epoch vtec map data ingestion One vtec map Minimize the mismodelings vtecexp - vtecmod(az) i i Az (effective F10.7) grid Use NeQuick to reconstruct the 3D electron density of the ionosphere that reproduces the starting vtec map Reconstruct stec along any ray-path Reconstruct fof2 maps

46 vtec map ingestion scheme validation using LaPlata global vtec maps and manually scaled fof2 values hourly data for Apr (HSA) and Sep (LSA) have been used statistics on: ΔfoF2=foF2NeQ2-foF2exp Notice: validation is on stec calibration + mapping function + spherical harmonics expansion + ITU-R coeff + model formulation + vtec data ingestion technique.

47 Apr 2000 Location of the Ionosondes used for the validation

48 Sep 2006 Location of the Ionosondes used for the validation

49 Global statistics (effective F10.7) Apr Sep. 2006

50 Global statistics (daily f10.7) Apr Sep. 2006

51 Global statistics (R12) Apr Sep. 2006

52 From this statistics becomes evident that the best results are obtained with the use of the effective f10.7 (Az parameter).

53 The ingestion technique requires that the model vertical TEC has to match the experimental vertical TEC at any given location and time. Therefore when the retrieved fof2 are different from the ground truth values it can be said that NeQuick is not able to perfectly reproduce the experimental slab thickness. Weakness in the NeQuick slab thickness formulation

54 Global statistics (medians) Apr Effective F10.7 Sep. 2006

55 Statistics 3763 (Apr 2000)

56 Statistics AS00Q (Apr 2000)

57 Statistics 3763 (Sep 2006)

58 Statistics AS00Q (Sep 2006)

59 Validation statistics (HSA) global performance climate performance weather performance

60 Validation statistics (LSA) global performance climate performance weather performance

61 From the previous results becomes clear that the data ingestion allows NeQuick to follow also the weather like trend of the Ionosphere electron density Nava, B., S. M. Radicella, and F. Azpilicueta (2011), Data ingestion into NeQuick 2, Radio Sci., 46, RS0D17, doi: /2010rs

62 Remark

63 Adapting NeQuick model to experimental slant TEC data at a given location (For possible near real time applications)

64 stec data ingestion, single stat. At a given epoch One station, n experimental stec (n satellites) Minimize RMS of the TEC mismodelings as a function of (formally) F10.7 Az (effective F10.7) at the station, for the given epoch Use NeQuick to retrieve (locally) the 3D electron density of the ionosphere Reconstruct TEC along any Station-to-satellite ray-path Retrieve the fof2 values at the Station

65 Adapting NeQuick model to experimental slant TEC data at 6 given locations (Validation)

66 Stations & ionosondes locations GPS receivers Ionosondes Modip isolines

67 (6) Single station statistics (000405)

68 Adapting NeQuick model to experimental slant TEC data at several locations

69 stec data ingestion, multi stat. At a given epoch m stecexp (several stations & satellites) Minimize each mismodeling stecexp - stecmod(az) i i Scattered Az i Interpolate to get regularly spaced grid Use NeQuick to reconstruct the 3D electron density of the ionosphere Reconstruct TEC along any given ray-path Reconstruct any fof2 value (fof2 map)

70 Multiple station statistics (000405)

71 Using NeQuick model in a standard way (F10.7 input -> no adaptation)

72 Flux of the day statistics (000405)

73 The NeQuick adaptation to slant TEC data from multiple stations indicates again the effectiveness of the ingestion scheme to specify the 3D electron density of the Ionosphere, also in near-real-time Nava, B., S. M. Radicella, R. Leitinger, and P. Coïsson (2006), A near-real-time model-assisted ionosphere electron density retrieval method, Radio Sci., 41, RS6S16, doi: /2005rs

74 Remark Model is adapted to TEC but fof2 is not always adequately retrieved. The results of these studies have indicated that there is the need to further improve the model formulation in terms of slab thickness.

75 Adapting NeQuick model to experimental slant TEC and fof2 data at a given location (Use of slab thickness to constrain the NeQuick profile shape parameter)

76

77 Remarks The use of two effective parameters has been considered in order to use the ITUR coefficients to estimate fof2 and hmf2 in a region surrounding the ground station. In this way the peak parameter values can be estimated for a slant TEC computation.

78 Adaptation method validation Use JRO profiles to simulate the process of adapting NeQuick to GPS derived TEC and ionosonde peak parameters data. TEC and peak parameters are known from the profile. After model adaptation it is possible to compare profiles in order to evaluate the adaptation technique effectiveness.

79 Adaptation method validation Jicamarca Radio Observatory (JRO) location

80 Adaptation method validation Model: NeQuick

81 Adaptation method validation Model: NeQuick

82 Adaptation method validation Model: NeQuick

83 Adaptation method effectiveness In order to evaluate the adaptation technique effectiveness, the IRI model has been used instead of the NeQuick and the same data have been used for the adaptation. (Not so easy as in the case of NeQuick)

84 Adaptation method validation Model: IRI

85 Adaptation method validation Model: IRI

86 Adaptation method validation Model: IRI

87 These results indicate that the problems related to the slab thickness formulation of the models, can be overcome by the simultaneous ingestion of TEC and ionosonde-derived data D. Buresova, B. Nava, I. Galkin, M. Angling, S. M. Stankov and P. Coisson, "Data ingestion and assimilation in ionospheric models", Annals of Geophysics, VOL. 52, N. 3/4, June/August 2009.

88 Use of Radio Occultation data

89 The Onion Peeling algorithm TECk N1 Nk N3 dk,l rk rl rl-1

90 Radio Occultation data ingestion a) RO data inversion through specific algorithms Abel Inversion (bending angles). A simple way to invert RO data (only) in the Ionosphere is to apply the Onion Peeling algorithm. If additional data are available (e.g. TEC from ground GPS receivers), improved inversion techniques can be applied (e. g. variable separation). (Hernandez-Pajares M, Juan JM, Sanz J (2000); Improving the Abel inversion by adding ground data to LEO radio occultations in the ionospheric sounding, Geoph Res Lett 27(16): ).

91 Radio Occultation data ingestion b) Adaptation to electron density profile Using multiple effective parameters approach c) Direct TEC assimilation into a background model. EDAM NeQuick (first results)

92 RO geometry

93 Adapting NeQuick model to RO-derived slant TEC (corresponding to the LEO -> GPS link below the LEO orbit) First results

94 RO-derived TEC data ingestion At a given epoch One occultation event Use Onion Peeling algorithm to invert the RO data and obtain an electron density profile Use RO-derived hmf2 Using Dudeney formula & ITU-R coeff., minimize hmf2 mismodeling as a function of (formally) F10.7 Az_hmF2 (effective parameter related to hmf2)

95 RO-derived TEC data ingestion Using NeQuick with Az_hmF2 Minimize the RMS of the RO-derived TEC* mismodelings as a function of b2bot modulating factor and F10.7 * LEO -> GPS link below the LEO orbit Az_foF2 (effective parameter related to fof2) b2bot_mod Drive NeQuick with Az_hmF2, Az_foF2, b2bot_mod to retrieve the 3D electron density

96 NeQuick adaptation to RO TEC Ionosonde Onion-Peeling NeQuick

97 Least Square Estimation Best Linear Unbiased Estimator (BLUE)* First results y vector of observations xb background model state xa analysis model state H observation operator R covariance matrix of observation errors B covariance matrix of background errors slant TEC background electron density retrieved electron density crossing length in voxels e.g. bckg_tec = Hxb * ASSIM_CONCEPTS/Assim_concepts2.html#962570

98 Least Square Estimation The optimal least-square estimator (BLUE analysis) is defined by xa = xb + K (y - Hxb) K = BH T (HBH T + R) -1 K is called gain of the analysis

99 LS solution

100 LS solution

101 RO geometry <= prof. peak TUCU projections of the LEO -> GPS links below the LEO orbit tangent points of the LEO -> GPS links

102 The results shown indicate that the assimilation of radio occultation derived TEC data can improve the NeQuick capabilities to specify the 3D Ionosphere electron density

103 Conclusion Data ingestion into NeQuick improves substantially the model performance when it is used to provide 3D specifications of the electron density of the ionosphere. The adaptation to vtec maps improves the NeQuick capabilities to follow the day-to-day variability of the ionosphere. The studies carried out with JRO profiles have indicated that the simultaneous availability of TEC and fof2 (plus hmf2) data can be considered as a minimum requirement for the implementation of an effective electron density retrieval technique based on models adaptation to experimental data (RO-derived profiles included). The approach based on multiple parameters also allows to use ROderived TEC data to obtain still more realistic electron density values for the area of interest.

104 Acknowledgments The authors are grateful to FAA s WAAS Community; Cesar Valladares, Boston College; Leo McNamara of the AFRL; Francisco Azpilicueta Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata; K. Alazo of the Institute of Geophysics and Astronomy (IGA), Cuba; Marta Mosert, ICATE - CONICET; Rodolfo G. Ezquer, Universidad Tecnológica Nacional de Tucumán; the Center for Atmospheric Research of University of Massachusetts at Lowell for providing access to the digital ionogram database (DIDBase), and the Jicamarca Radio Observatory (JRO) group for providing the data used for the present work.

105 Very special thanks to Prof. R. Leitinger Prof. S.M. Radicella

106 Thank you for your attention