3. Algorithm to remove aliasing and artifacts: Spatio-Periodic
Leveling Algorithm (SPLA)
To address the problem of aliasing in detecting ionospheric
perturbations caused by geomagnetic storms and to compute the
ionospheric perturbations free of signal aliasing, Shimna and Vijayan
(2020) proposed an algorithm called Spatio-Periodic Leveling (SPLA).
They also demonstrated that the SPLA is efficient in removing amplitude
aliasing, particularly from low elevation observations, and thereby
removes the need of applying elevation cut-off (Shimna and Vijayan,
2020). In this study, we show that the SPLA is also efficient in
removing artifacts, and inconsistencies in CIPs and TIPs caused by
polynomial misfits, and elevation dependent slant ray path in addition
to removing aliasing caused by unaccounted non-uniform spatial sampling.
In SPLA, ionospheric perturbations are computed as gradient Rate of TEC
(gROT) following a three-step process (Shimna and Vijayan, 2020):
Step 1: Impact of slant ray path is removed by converting the
leveled sTEC into vTEC (Eq. 2) along a leveled phase connected arc. ThevTEC at a given time t is mapped to the location of IPP.
The location of IPP (, ) is computed using elevation () and azimuth ()
angles subtended by the receiver R while tracking the satellite S.
(Klobuchar, 1987).
Geographic latitude of IPP is
– (4)
where is Earth angle , and is latitude of the GPS receiver.
Geographic longitude of IPP is
– (5)
where is azimuth angle; and is longitude of the GPS receiver.
Step 2: Computing rate of change of vTEC between two
consecutive IPPs separated by an observational epoch () (Eq. 1).
Step 3: Removing the influence of inter-IPP distance
(Δd ) from the rate of change of vTEC and computing the
spatiotemporal gradient at regular spatiotemporal intervals
– (6)
where R is receiver, S is satellite tracked by the receiver R, gROT is
spatiotemporal gradient measured in TECU km-1s-1 and Δd is inter-IPP distance.
Inter-IPP distance, Δd between two consecutive IPPs on a thin-shell
ionosphere at a height of 350 km is
– (7)
where ; is Radius of the Earth, is ionospheric shell height. , and are
in km.