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\begin{document}

\title{Application of VLF/LF databases in improving of Earth observations  and positioning by SAR and GNSS signals}

\author{\name Aleksandra Nina \email sandrast@ipb.ac.rs \\
       \addr Institute of Physics, University of Belgrade, Belgrade, Serbia
       \AND
       \name Giovanni Nico \email g.nico@ba.iac.cnr.it \\
       \addr Istituto per le Applicazioni del Calcolo (IAC), Consiglio Nazionale delle Ricerche (CNR), Bari, Italy}

%\editor{Leslie Pack Kaelbling}

\maketitle

\begin{abstract}
In this study we present one example of application of the  databases collected in low ionospheric monitoring by VLF/LF radio waves relevant for the Earth's observations and positioning by SAR and GNSS signals. We analyze contribution of the perturbed ionospheric D-region in propagation delay of this signals and the results of this analysis indicate the need for inclusion of this atmospheric layer in modeling of SAR/GNSS signal propagation. Keeping in mind that its influence is usually ignored in modeling of the ionospheric influence on satellite signals, this conclusion can be of high priority in preciously positioning, Earth's observations, analyses and emergency responses to changes caused by natural disasters and in many other areas of human activities. 
\end{abstract}

\begin{keywords}
  VLF/LF database, GNSS, SAR
\end{keywords}


\section{Introduction}

Information obtained in the Earth observations by satellites are very important in many areas of human activities.  Namely, positioning, displacements, navigation and timing play significant role in telecommunications, geodesy, all forms of transportation etc. In addition, many scientific studies  as well as analyses and emergency responses to changes caused by natural disasters are based on these measurements. Keeping in mind that many of these applications, primarily provided by the Global Navigation Satellite Systems (GNSS) and Synthetic Aperture Radar (SAR) interferometry, require high precision (less than 1 cm) knowledge of the signal propagation between satellite and Earth surface is required. Consequently, studies of different influences on these signals are of high priority. 

There are many sources which cause delay in satellite signal propagation. The largest contributions have the ionosphere and troposphere. For calculation of ionospheric influence it is necessary to know the total electron content (TEC) but its modelling is not trivial and due to lack of data needed for detail studies using methods are  based on different approximations. One of them which is usually used is neglecting the contribution of the ionospheric part below 90 km. This approximation is correct in quiet conditions but in the case of intensive disturbances in the low ionosphere it can causes significant errors in modeling of GNSS and SAR signal propagation properties. For this reason, it is necessary to have information about this ionospheric layer. 

One of the most important technique for the low ionospheric monitoring is based on very low and low frequency (VLF/LF) radio wave propagations. Here it is important to say that intensive disturbances in this atmospheric part are sudden and, in some cases, short time lasting and localized. Consequently, the necessary information requires continuous D-region observations at different geographical locations and with high time resolution.  In addition, to study rare sudden phenomena it is necessary to analyze long time periods. For these reasons the collected databases are big databases. They can reach several tens of GB/day or several TB/year. Consequently, some analyses based on these observations require applications of procedures relevant for big databases.   

In this work, we show an example of application of data collected in the D-region monitoring on spaceborne SAR and GNSS signals during strong perturbations. 

\section{Theory}
\label{sec:the}

Generally speaking, application of the databases collected in the low ionospheric observation for modelling of this atmospheric layer is needed for determination od the electron density time and space distributions. There are a few procedures for determination of the electron density from the data collected by the VLF/LF receiver. They are based on processing of values of amplitude values \citep{tho93}, phase \citep{ina07b} or both, amplitude and phase \citep{gru08}, and implementation of numerical models like the Long-Wave Propagation Capability LWPC \cite{fer98} or Modefinder/Modesearch \cite{mor76}. 

\begin{figure}
	\label{fig:sema}
	\centering
	\includegraphics[width=0.6\textwidth]{shema.png}
	\caption{\label{fig:Grid} Schematic representation of a database application in modeling of SAR/GNSS data.}
\end{figure}

One of the frequently used procedure for the low ionospheric studies (see for example \cite{baj15,nin11,nin12b,nin14}) is shown in schematic representation in Figure \ref{fig:sema}. This procedure has two parts: 1) comparison of databases with relevant modeled values by LWPC numerical code, and 2) analytical procedures for modeling different plasma parameters.

In the upper part of the presented scheme (above dashed line) it is presented a comparison of values of the signal amplitude and phase changes from the considered database ($\Delta A_{\rm {rec}}$ and $\Delta P_{\rm {rec}}$) and relevant values obtained by modeling of the VLF/LF signal propagation path by LWPC numerical code ($\Delta A_{\rm {rec}}$ and $\Delta P_{\rm {rec}}$). The result of this procedure is determination of time evolutions of the Wait's parameters $\beta$ and $H'$ \citep{wai64}, the input parameters for the following analytical procedure indicated in the bottom part of the given scheme.

In this work, the D-region delay is calculated by expression:

\begin{equation}
\label{eq::P}
\displaystyle P_{\rm{D}} = \alpha_{\rm{I}} {\rm{TEC_D}}/f^2.
\end{equation}
where $\alpha_{\rm{I}} = 40.3$ m$^{3}$s$^{-2}$ and the total electron content $TEC_{\rm{D}}=\int_{l_{\rm{D}}}N_{\rm{e}}dl_{\rm{D}}$ for the signal propagation path $l_{\rm{D}}$ in the D-region can be obtained from models of the electron density space and time distributions $N_{\rm{e}}$, and from determination of the GNSS/SAR signal propagation path which is determined by applying Snell's low on horizontal layers. 

The electron density $N_{\rm e}(h,t)$ (in m$^{-3}$) at fixed altitude $h$ (in km) is calculated from Wait's parameters estimated by fitting of data presented in \cite{tho05} by equation \cite{tho93}:

\begin{equation}
\label{eq::Ne}
N_{\rm e}(h,t) = 1.43\cdot10^{13}e^{-\beta(t)H'(t)}e^{(\beta(t)-0.15)h}.
\end{equation}



\section{Results and conclusions}

Here, we present an example of influence of the perturbed D-region on SAR signals which determination is based on  VLF data. We take $\beta$ and $H'$ which are determined in study of solar X-ray flare influences on the D-region (see \cite{tod16} and references therein) and consider frequencies of $f_1=$ 1.2 GHz and $f_2=$ 5.4 GHz which are relevant for the Earth observations with ALOS-2 or the future NISAR mission ($f_1$) and Sentinel-1 and Radarsat-2 ($f_2$).

Using the procedure given in Section \ref{sec:the} we obtained the propagation delays presented in Figure \ref{fig:graf}. The values for $\beta$ and $H'$ are  estimated for D-region disturbances induced by the X-ray flare of classes C5, M1 and M5. 

\begin{figure}
	\label{fig:graf}
	\centering
	\includegraphics[width=0.6\textwidth]{PD_teta_2D.eps}
	\caption{\label{fig:Grid}Propagation delay in the D-region as a function of the angle for frequencies 1.2 GHz (solid lines) and 5.4 GHz (dash lines) and different X-ray flare classes (C5 - the thinner lines, M1 - lines of medium thickness, M5 - the thickest lines).}
\end{figure}

In this graph, one can see that propagation delay significantly depends on the signal frequency and that increases with incident angle of the considered signals, $\Theta _0$ and the X-radiation intensity. Although, the estimated delay is smaller than 1 cm for C5 class X-ray flares, its values are significant for the analyzed M class X-ray flares which finally confirm the need for the inclusion of the ionospheric D-region part in modeling of the SAR signal propagations within intensive perturbed low ionosphere.

To conclude, the presented study points out one example of importance of the collected databases in low ionospheric monitoring by VLF/LF radio waves for practical applications relevant for SAR and GNSS signals. This conclusion can be of high priority in preciously positioning, Earth's observations, analyses and emergency responses to changes caused by natural disasters and in many other areas of human activities. 

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