A framework for estimating spherical vector fields using localized basis functions and its application to SuperDARN data processing

Abstract

A technique for estimating a plasma drift velocity distribution in the ionosphere is presented. This technique is based on a framework for representing a global vector field on a sphere by using a set of localized basis functions which is newly derived as a variant of the spherical elementary current system (SECS). A vector field on a sphere can be divided into its divergence-free (DF) component and curl-free (CF) component. The DF and CF components can then be represented by weighted sums of the DF and CF vector-valued basis functions, respectively. While the SECS basis functions have a singular point, the new basis functions do not diverge over a sphere. This property of the new basis function allows us to achieve robust prediction of the drift velocity at any point in the ionosphere. Assuming that the ionospheric plasma drift velocity has no divergence, its distribution can be represented by a weighted sum of the DF basis functions. The proposed technique estimates the ionospheric plasma drift velocity distribution from the SuperDARN data by using the DF basis functions. Since there are some wide gaps in the spatial coverage of the SuperDARN, an empirical convection model is combined with the framework based on the new basis functions. It is demonstrated that the proposed technique is useful for the estimation and modeling of the ionospheric plasma velocity distribution.

Data‐Driven Basis Functions for SuperDARN Ionospheric Plasma Flow Characterization and Prediction

“…(2018) and Nakano et al. (2020). These techniques each contrast with ours in a similar manner, in that they rely on additional measurement information to complete the SuperDARN data coverage.…”

“…For Thomas and Shepherd (2018) and Nakano et al. (2020), this information is climatological averages of the flow for different solar wind states, while Gjerloev et al. (2018) relied on a principal component regression of the flow history onto geomagnetic indices.…”

“…Our primary motivation in describing our technique is to create an alternative to the "Map Potential" method for obtaining the global plasma flow pattern, introduced by Ruohoniemi and Baker (1998), and further improved by Thomas and Shepherd (2018). Recently, several additional alternative infill solutions have been proposed, for example, by Gjerloev et al (2018) and Nakano et al (2020). These techniques each contrast with ours in a similar manner, in that they rely on additional measurement information to complete the SuperDARN data coverage.…”

“…For Thomas and Shepherd (2018) and Nakano et al (2020), this information is climatological averages of the flow for different solar wind states, while Gjerloev et al (2018) relied on a principal component regression of the flow history onto geomagnetic indices. Conversely, our infill solution is entirely self-consistent, and to our knowledge is the only SuperDARN imputation which requires only SuperDARN data.…”

Local Mapping of Polar Ionospheric Electrodynamics

“…We note that there are other options for representing electric fields or plasma flow in a regional grid: Nakano et al. ( 2020 ) presented an analysis technique for ionospheric plasma convection that uses basis functions similar to SECS, but without a singularity at the pole. Nicolls et al.…”