International Journal of Applied Engineering Research ISSN 0973-4562 Volume 8, Number 16 (2013) pp. 1937-1943 © Research India Publications http://www.ripublication.com/ijaer.htm

Ionospheric Electron Density Analysis using Empirical Orthogonal Functions
Bhagyasree Nimmagadda, A.L Siridhara, D.Venkata Ratnam Department Of ECE in affiliation to K L University K L University (KoneruLakshmaiah Education Foundation) Vaddeswaram, Andhra Pradesh, India. Email: dvratnam@kluniverity.in Abstract

Ionospheric electron density variations are more predominant error sources in precise positioning with Global Positioning System (GPS) based navigation systems over low latitude regions such as India and Brazil. spatial and temporal variability is more in this region due to Equatorial Ionospheric Anomaly (EIA), Spread F and ionospheric scintillations etc. Short and long term ionospheric changes such as the solar cycle, the annual and semiannual variations of the ionosphere needs to be investigated for improving reliable communication and navigation systems. In this paper, EOF analysis is used to investigate the spatial and temporal distribution of ionospheric electron density. An empirical model is implemented based on coefficients and basis functions obtained from the EOF analysis. It is evident from the results that the coefficients of EOF basis functions well signify the solar activity, diurnal variations of electron density. Keywords: GPS, EOF, TEC and IRI model

1. Introduction:
The EOF analysis is originally introduced into meteorology as a method for extracting

1938

Bhagyasree Nimmagadda et al

the dominant modes of spatial variability in meteorological fields such as Sea Level Pressure (SLP), sea surface temperature (SST), etc (Randall, et al., 2003). This is extensively used to represent meteorological and climatology data (Storch and Zwiers, et al., 2002 and 2004). It can also be used in acoustic tomography and ionospheric tomography. The (EOF) method can give the long term ionospheric changes such as the solar cycle, the annual and semiannual variations of the ionosphere (Baiqi Ningl, et al., 2007). The EOFs constructs the altitude profiles of ion concentration in their parameterized model of the ionosphere (Daniell, et al, . 1995). EOF is a method for analyzing the variability of a single field i.e. a field of only one scalar variable (Bjornsson, et al., 1997). The EOF method finds the spatial patterns of variability, their time variation, and gives a measure of the importance of each pattern (Lorenz, et al., 1956). The EOF analysis is used to find a relatively small number of independent variables (predictors: factors) which convey as much of the original information as possible without redundancy. The EOF analysis can be used to explore the structure of the variability within a data set in an objective way, and to analyze the relationships within a set of variables. The EOF analysis is called as principle component analysis. The EOFs with time series is represented as,

Zx, y, t    PCt  EOFx, y 
K 1

N

(1)

Where, Z(x, y, t) is the original time series and is a function of time (t) and space (x, y). EOF(x, y) is the spatial structures (x, y) of the major factors that can be account for the temporal variations of Z. PC (t) is the principle component and tells about the amplitude of each EOF varies with time.

2. International Reference Ionospheric (IRI) model
International Reference Ionosphere (IRI) model has been developed to model the ionosphere (Bilitza, 1990). This model would help to reduce the time delay error to a

Ionospheric Electron Density Analysis

1939

considerable extent. This model represent the properties of the ionosphere as accurately as possible as functions of geophysical indices with some statistical descriptions of their variability. It is widely used model of monthly mean ionosphere. From this, various parameters such as electron density, electron and ion temperature and the electron content of the ionosphere, etc. can be readily derived. TEC affects the GPS signals traversing the ionosphere. The ionospheric correction, which has to be applied to determine the user position correctly, is proportional to the TEC. Therefore several IRI teams are working on TEC deduced from measurements of the GPS satellite to update IRI model (Bilitza, 2001). The main purpose of IRI is to produce a reliable global reference model for the important ionospheric parameters such as electron density, ion composition etc. Important average values if input and output parameters of IRI 2007 parameters are tabulated in Table.1.

Table.1 Important input and output parameters of IRI 2007 model

IRI 2007 input parameters i)Year, ii)month, iii)Day, iv)Height, v)location, vi)local time and vii)sunspot number for magnetically quiet conditions in the altitude range from 60 to 2000 Km

IRI 2007 output parameters i)Electron density, ii)ratio of Ne, iii)F2 peak density, iv)Neutral Temperature, v)Ion

Temperature, vi)Electron Temperature Te, vii)TEC, viii)height, densities and plasma frequencies of various layers namely vertical F2, ion F1, drift, E and D, F

ix)Equatorial

x)Spread

probability, xi)Ratio of foF2 storm to foF2 quietion percentage of different ions namely O+, H+, He+, O2+, NO+, N+, Propagation factor M(3000)F2 xii)Bottomside thickness (B0), xiii)Bottomside_shape xiv)E-valley width, E-valley depth

1940
2000

Bhagyasree Nimmagadda et al

1500
Height (Km)

Date: 29 September 2009 Time: 14.00 Hrs(LT) 0 0 Location:(17.45 N, 78.35 )

1000

500

0

0

2

4

6

8
3

10

12 x 10

14
11

Electron density (el/m )

Fig.1 Electron density profile due to IRI 2007 model

IRI profiles can be derived for suitably chosen locations, hours, seasons and levels of solar activity. It is an empirical model based on the data from worldwide network of ionosonde stations, incoherent scatter radars and Alonette topside sounders and insitu measurements on several satellites and rockets (Bilitza, 1990). A typical electron profile derived from IRI 2007 is shown in Fig .1. The Electron density profile corresponds to 29th September, 2009, 14.00 at a location (17.450 N, 78.350 E).It can be observed from the figure that electron density reaches almost minimum (6.89x10^12 el/m3) at a height of 2000km.

3. Estimation of EOFs using IRI model
The main aim of EOFs is to find a new set of variables that capture most of the observed variance from the data through a linear combination of the original variables. In ionospheric region the function of the EOFs is to characterize the vertical profile of the ionosphere. The model based on EOF is used to minimize the ionospheric errors and used as a back ground profile. The empirical data of ionospheric electron densities in the vertical profile are obtained from the IRI model (Bilitza, 2001). The vertical ionospheric electron density profile N (h, t) is calculated

Ionospheric Electron Density Analysis

1941

from IRI by giving the date, time and location information of the GPS. The important steps for computing the EOFs are as follows: 1) Calculate the electron density profiles (N(ti, hj)) at different times ti(i=1, 2, …M) and heights hj(j= 1, 2, …N). Then, the vertical density profile matrix can be represented as,
 N t 1 , h 1   N t , h  2 1 N t, h     .....   N t M , h 1  N t 1 , h 2  N t 2 , h 2  ..... Nt M , h 2  .....  ..... N t 2 , h N     ..... ......  ..... N t M , h N  MxN Nt 1 , h N 

(2)

In matrix N(t, h), the row i ( i= 1, 2, ….M) represents the electron density values at different heights at the same time ti (i= 1, 2, … M) and the column j (j= 1, 2, … M) represents a time series of electron density samples at the same height hj(j= 1, 2, ….N). This form of organizing data in a matrix is called Smode analysis (Bjornsson and Venegas, 1997). 2) Calculate the mean value of each column matrix of N (t, h),

N h j  

1 M  Nt m , h j  M m 1

(3)

3) Calculate the covariance matrix (S),
SN
T

t, h  N t, h 

(4)

N t, h  is the data matrix with zero mean values.
4) Calculate the eigen vectors and eigen values of the covariance matrix. The eigen values of the covariance matrix are the EOFs. A typical day’s (29th September 2009, 14:00-16:00 hrs) electron density values due to IRI model are used for calculating EOF values. The electron density matrix is arranged in such a way that column represents time series and row represents different heights. The covariance of the matrix is computed. The estimated eigen values are 1.83e+022, 1.82e+021, 1.57e+018, 3.44e+017 and 2.03e+015. It is observed that the

1942

Bhagyasree Nimmagadda et al

largest eigen value corresponding to EOF #1 value is shown in Fig.2. The maximum EOF1 value is 0.92 and the minimum is -0.01 for the altitude range of 100 – 1000kms. The estimation of EOF values is one of the important steps in implementing function based ionospheric tomographic algorithm.

1000 900 800
Height(km)

Date: 29 September 2009 Time: 14.00 -16.00 Hrs(LT) 0 0 Location:(17.45 N, 78.35 )

700 600 500 400 300 200 100 -0.2 0 0.2 0.4 0.6 EOF1 values 0.8 1 1.2

Fig.2 Empirical orthogonal functions

4. Conclusions
In this paper, preliminary TEC analysis is carried out using EOFs. The EOFs possess the inherent characteristics of original data and the Eigen series. Ionospheric tomography model can be constructed by capturing the ionospheric irregularities effectively over the Indian region. In the tomographic technique, spherical harmonics and EOFs can be combined. The spherical harmonics and EOFs give the horizontal and vertical profile characteristics of the ionosphere. The spherical harmonic function ionospheric time delay model is successful implemented over the Indian region data (Venkata Ratnam and Sarma, 2011). Efforts towards development of ionosphere tomographic model are under progress. The EOF analysis would be immensely useful for analyzing vertical ionospheric profile.

Ionospheric Electron Density Analysis

1943

Acknowledgement
The above work has been carried out under the project entitled “Development of Ionospheric Forecasting models for Satellite based Navigation systems over the low latitude stations” sponsored by Department of Science and Technology, New Delhi, India, vide sanction letter No: SR/FTP/ETA-0029/2012, dated:08.05.12.

References
[1] Baiqi Ning, Zonghua Ding, , Weixing Wan, and Libo Liu, Automatic scaling of F2 layer parameters from Ionograms based on the empirical orthogonal function (EOF) analysis of ionospheric electron density, Earth Planets Space, 59, 51-58, 2007. [2] Bilitza, D. (1990), “International Reference Ionosphere 1990”, Rep. NSSDC/WDC-R&S 90-22, World Data for Rockets and Satell., Nat. Space Sci. Data Cent., Greenbelt, Md. [3] Bilitza, D. (2001), “International Reference Ionosphere 2000”, Radio Sci., 36(2), 261–275, doi:10.1029/2000RS002432. [4] Bjornsson H, S.A, Vergas, “ A Manual for EOF and SVD Analyses of Climate Data”, Department of Atmospheric and Oceanic sciences and Centre for climate and Global change Research, McGill University, February, 53, 1997. [5] Daniell, R. E., L. D. Brown, D. N. Anderson, M. W. Fox, P. H. Doherty, D. T. Decker, J. J. Sojka, and R. W. Schunk (1995), “Parameterized ionospheric model:A global ionospheric parameterization based on first principles models”, Radio Sci., 30, 1499–1510. [6] Lorenz, E. N. (1956), “Empirical orthogonal functions and statistical weather prediction”, Sci. Rep. 1, contract AF19 (604)1566, AFCRC-TN-57-256, Dep. Of Meteorol., Mass. Inst. of Technol., Cambridge. [7] Randall R. D, “Empirical Orthogonal Functions, Departement of AtmopshericScience, ColoradoUniversity, 2003(http://kiwi.atmos.colostate.edu/group/dave/pdf/EOFs.pdf. [8] Storch H. von and Zwiers, F.W., : “On the role of statistics in climate research. International Journal of Climatology:, 24, 665-680, 2004. [9] Storch, H. V., and F. W. Zwiers (2002), “Statistical Analysis in Climate Research”, Cambridge Univ. Press, Cambridge, UK. [10] D Venkata Ratnam, and A.D.Sarma, “Modelling of Low Latitude Ionosphere using GPS Data with SHF Model”, IEEE transactions on Geosciences and Remote Sensing, September, 2011. Digital Object Identifier: 10.1109/TGRS.2011.2163639.

1944

Bhagyasree Nimmagadda et al