Ionospheric Vertical Correlation Distances: Estimation From ISR Data, Analysis, and Implications For Ionospheric Data Assimilation

Forsythe, Victoriya V.; Azeem, Irfan; Crowley, G.; Themens, David R.

doi:10.1029/2020rs007177

Cited by 12 publications

(28 citation statements)

References 15 publications

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“…For retrieval of the electron density from VH data, only the vertical direction is considered, making it a 1‐D problem. Typically, to model the vertical component of the covariance matrix an assumption is used that the vertical correlations are represented by a Gaussian (Aa et al., 2015, 2016; Bust & Crowley, 2007; Bust & Datta‐Barua, 2014; Bust et al., 2001, 2004; Coker et al., 2001; Forsythe, Azeem, & Crowley, 2020; Forsythe et al., 2021; Yue et al., 2007, 2011). The construction of the error covariance matrix

\tilde{P}

can be separated into the construction of two matrices: the model variance matrix

\tilde{V}

and the vertical correlation matrix

{\overset{C}{true}}_{v e r}

.…”

Section: Data Assimilationmentioning

confidence: 99%

“…Each element of this matrix can be modeled as

{\overset{C}{true}}_{i j}^{v e r} = ({, \begin{matrix} cases \\ left \exp [- \frac{{false(z_{i} - z_{j} false)}^{2}}{{false(L_{1} false(z_{i}, λ_{i} false) false)}^{2}}], & left if z_{i} < z_{j} \\ left \exp [- \frac{{false(z_{i} - z_{j} false)}^{2}}{{false(L_{2} false(z_{i}, λ_{i} false) false)}^{2}}], & left if z_{i} > z_{j}, \\ left 1, & left if z_{i} = z_{j} \end{matrix})

where z is the height, λ is the magnetic latitude, L 1 and L 2 are functions of altitude and magnetic latitude, and subscripts i and j refer to the pairs of grid points. The vertical correlation lengths L 1 and L 2 depend on the geomagnetic latitude and height (Forsythe et al., 2021) and can be found at the data repository cited in (Forsythe et al., 2021). In the current study, the correlation lengths L 1 and L 2 were reduced by half because this showed more stable performance of the assimilation algorithm.…”

Section: Data Assimilationmentioning

confidence: 99%

“…The shape of the profile in the assimilative inversion is largely controlled by the model error covariance matrix P f which is described by Equation 9. The vertical correlation lengths model that provides L 1 and L 2 for a particular latitudinal region was derived based on the ISR data from five radars (Forsythe et al, 2021). It is, however, important to notice that this model does not include the information about the correlation of the E-region.…”

Section: Valley Regionsmentioning

confidence: 99%

“…Forsythe et al (2021) discussed in detail the construction of the vertical correlation matrix  ver C…”

mentioning

confidence: 99%

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Data Assimilation Retrieval of Electron Density Profiles From Ionosonde Virtual Height Data

et al. 2021

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In the ionosphere the electromagnetic wave has to pass through the ionized medium which decreases the group velocity of the radio pulses, making the propagation speed less than the free-space speed of light c. This makes the VH h′ greater than the true height h. A certain procedure, known as true height analysis, needs to be applied in order to recreate the true height electron density profile N e (h) from the VH data.Two of the most commonly used true height inversion algorithms are POLynomial ANalysis (POLAN) (Titheridge, 1988) and NhPC (Reinisch et al., 2005;Reinisch & Xueqin, 1983), with the latter being a component of the Automatic Real-Time Ionogram Scaler with True height (ARTIST) software that is widely used in the ionospheric research community. Both algorithms determine the true height using polynomial analysis. POLAN expresses each ionospheric layer in terms of sixth-order overlapping polynomials, whereas the NhPC algorithm describes the layers in terms of shifted Chebyshev polynomials. Both algorithms model the transition in the valley region between E and F layers. Additionally, some ionosonde operators employ the Autoscala algorithm (Pezzopane et al., 2010) which is based on image recognition and parametrization of empirical curves. This paper describes a new method for the electron density profile retrieval from VH measurements using data assimilation. Data assimilation methods incorporate observations into models, providing a description of the system that is optimally consistent with both the model and data. The components that are necessary to build a data assimilation model include a background model, the observations, the observation operator that maps the observations to the model state, and an optimization method that gives an optimal analysis by incorporating the observations into the model. Numerous ionospheric data assimilation methods Abstract A new method is developed to retrieve electron density profiles from a raw virtual height ionosonde traces. A Kalman filter is used for the assimilative inversion scheme together with the newly developed data-driven vertical covariance model. The detailed mathematical formalism for the derivation of the Jacobian that takes into account the effect of the magnetic field is presented. The incoherent scatter radar measurements from Arecibo observatory are employed as the known truth to simulate the virtual height data. The results show that the data assimilative inversion technique accurately retrieves the vertical structure of the ionospheric density at the bottom side of the profile and reconstructs the vertical and temporal small-scale density variations. A comparison with the results obtained by the POLynomial ANalysis (POLAN) inversion algorithm is presented. The assimilative inversion systematically outperforms the accuracy of the POLAN algorithm, on average reducing the percent errors in the electron density by half. Additionally, the simultaneous data ingestion is compared to the sequential assimilation of the virtual height data. FORSYTHE ET AL.

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\tilde{P}

can be separated into the construction of two matrices: the model variance matrix

\tilde{V}

and the vertical correlation matrix

{\overset{C}{true}}_{v e r}

.…”

Section: Data Assimilationmentioning

confidence: 99%

“…Each element of this matrix can be modeled as

{\overset{C}{true}}_{i j}^{v e r} = ({, \begin{matrix} cases \\ left \exp [- \frac{{false(z_{i} - z_{j} false)}^{2}}{{false(L_{1} false(z_{i}, λ_{i} false) false)}^{2}}], & left if z_{i} < z_{j} \\ left \exp [- \frac{{false(z_{i} - z_{j} false)}^{2}}{{false(L_{2} false(z_{i}, λ_{i} false) false)}^{2}}], & left if z_{i} > z_{j}, \\ left 1, & left if z_{i} = z_{j} \end{matrix})

Section: Data Assimilationmentioning

confidence: 99%

Section: Valley Regionsmentioning

confidence: 99%

“…Forsythe et al (2021) discussed in detail the construction of the vertical correlation matrix  ver C…”

mentioning

confidence: 99%

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Data Assimilation Retrieval of Electron Density Profiles From Ionosonde Virtual Height Data

et al. 2021

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“…Many investigations have explored the spatial correlation distances of the ionosphere. For example, horizontal correlation distances have been studied using TEC data (Forsythe, Azeem, & Crowley, 2020; Gail et al, 1993; Klobuchar et al, 1995; Shim et al, 2008; Yue et al, 2007), and vertical correlation distances have been investigated using Incoherent Scatter Radar (ISR) data (Forsythe, Azeem, Crowley, & Themens, 2020; Yue et al, 2007). To the best of our knowledge, no previous investigations have examined in detail the temporal ionospheric correlation or the relaxation parameter.…”

Section: Introductionmentioning

confidence: 99%

The Global Analysis of the Ionospheric Correlation Time and Its Implications for Ionospheric Data Assimilation

et al. 2020

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Ionospheric correlation time is an important parameter that contains information about the temporal variability, structures, and dynamics of the ionosphere. This parameter is also important in forecasting of the ionospheric state. Ionospheric data assimilation algorithms employing empirical background models, such as Ionospheric Data Assimilation Four‐Dimensional (IDA4D), apply Gauss‐Markov approximation for the propagation of temporal updates from one time stamp to the next. In this process, the relaxation parameter, or the correlation time, determines to what degree the projected state depends on the background model and analysis density. An ad hoc approach is usually applied to choose this user‐defined parameter. This paper focuses on the estimation of the ionospheric correlation time using high temporal resolution global ionospheric maps (GIMs). It is found that the correlation time changes significantly with latitude. The longest correlation time is observed in the equatorial region, whereas the shortest correlation time is observed at high latitudes and in the polar cap regions. The global distribution of the correlation time exhibits seasonal variation and depends on the solar flux conditions. The correlation time at the equatorial and mid‐latitude regions increases with increasing solar and geomagnetic activity, whereas the correlation time at high‐latitude regions decreases. The results of this study can be directly applied to improve ionospheric data assimilation models.

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Evaluation of the New Background Covariance Model for the Ionospheric Data Assimilation

et al. 2021

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This paper presents the evaluation of the recently developed covariance model for the Ionospheric Data Assimilation Four-Dimensional (IDA4D) technique. The ionospheric data are generated using the Observation System Simulation Experiment Tool from the known ionospheric state produced by the physics-based Thermosphere-Ionosphere-Mesosphere Electrodynamics General Circulation Model. Several experiments are conducted to assess performance of IDA4D with data-driven vertical and horizontal covariance matrices. We show that the vertical part of the covariance model plays the most important role because it preserves the vertical structure of the F-region density layer and helps to correct a tomographic issue that arises when the slant total electron content is assimilated along the intersecting rays. The results show that the new covariance model improves the fidelity of IDA4D algorithm, making it more suitable for the regional assimilation with dense ground-based Global Positioning System data coverage.FORSYTHE ET AL.

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Ionospheric Vertical Correlation Distances: Estimation From ISR Data, Analysis, and Implications For Ionospheric Data Assimilation

Cited by 12 publications

References 15 publications

Data Assimilation Retrieval of Electron Density Profiles From Ionosonde Virtual Height Data

Data Assimilation Retrieval of Electron Density Profiles From Ionosonde Virtual Height Data

The Global Analysis of the Ionospheric Correlation Time and Its Implications for Ionospheric Data Assimilation

Evaluation of the New Background Covariance Model for the Ionospheric Data Assimilation

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