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Abstract Data assimilation methods often also employ the same discrete dynamical model used to evolve the state estimate in time to propagate an approximation of the state estimation error covariance matrix. Four‐dimensional variational methods, for instance, evolve the covariance matrix implicitly via discrete tangent linear dynamics. Ensemble methods, while not forming this matrix explicitly, approximate its evolution at low rank from the evolution of the ensemble members. Such approximate evolution schemes for the covariance matrix imply an approximate evolution of the estimation error variances along its diagonal. For states that satisfy the advection equation, the continuity equation, or related hyperbolic partial differential equations (PDEs), the estimation error variance itself satisfies a known PDE, so the accuracy of the various approximations to the variances implied by the discrete covariance propagation can be determined directly. Experiments conducted by the atmospheric chemical constituent data assimilation community have indicated that such approximate variance evolution can be highly inaccurate. Through careful analysis and simple numerical experiments, we show that such poor accuracy must be expected, due to the inherent nature of discrete covariance propagation, coupled with a special property of the continuum covariance dynamics for states governed by these types of hyperbolic PDE. The intuitive explanation for this inaccuracy is that discrete covariance propagation involves approximating diagonal elements of the covariance matrix with combinations of off‐diagonal elements, even when there is a discontinuity in the continuum covariance dynamics along the diagonal. Our analysis uncovers the resulting error terms that depend on the ratio of the grid spacing to the correlation length, and these terms become very large when correlation lengths begin to approach the grid scale, for instance, as gradients steepen near the diagonal. We show that inaccurate variance evolution can manifest itself as both spurious loss and gain of variance. 

Low Earth orbit (LEO) radio occultation|radio occultations (RO) constellations can provide global electron density profiles (EDPs) to better specify and forecast the ionosphere‐thermosphere (I‐T) system. To inform future RO constellation design, this study uses comprehensive Observing System Simulation Experiments (OSSEs) to assess the ionospheric specification impact of assimilating synthetic EDPs into a coupled I‐T model. These OSSEs use 10 different sets of RO constellation configurations containing 6 or 12 LEO satellites with base orbit parameter combinations of 520 or 800 km altitude, and 24° or 72° inclination. The OSSEs are performed using the Ensemble Adjustment Kalman Filter implemented in the data assimilation (DA) Research Testbed and the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIEGCM). A different I‐T model is used for the nature run, the Whole Atmosphere Model‐Ionosphere Plasmasphere Electrodynamics (WAM‐IPE), to simulate the period of interest is the St. Patrick's Day storm on March 13–18, 2015. Errors from models and EDP retrieval are realistically accounted for in this study through distinct I‐T models and by retrieving synthetic EDPs through an extension Abel inversion algorithm. OSSE assessment, using multiple metrics, finds that greater EDP spatial coverage leading to improved specification at altitudes 300 km and above, with the 520 km altitude constellations performing best due to yielding the highest observation counts. A potential performance limit is suggested with two 6‐satellite constellations. Lastly, close examination of Abel inversion error impacts highlights major EDP limitations at altitudes below 200 km and dayside equatorial regions with large horizontal gradients and low electron density magnitudes. 

This work introduces a new, compactly supported correlation function that can be inhomogeneous over Euclidean three‐space, anisotropic when restricted to the sphere, and compactly supported on regions other than spheres of fixed radius. This function, which we call the Generalized Gaspari–Cohn (GenGC) correlation function, is a generalization of the compactly supported, piecewise rational approximation to a Gaussian introduced by Gaspari and Cohn in 1999 and its subsequent extension by Gaspariet alin 2006. The GenGC correlation function is a parametric correlation function that allows two parameters and to vary, as functions, over space, whereas the earlier formulations either keep both and fixed or only allow to vary. Like these earlier formulations, GenGC is a sixth‐order piecewise rational function (fifth‐order near the origin), while the coefficients now depend explicitly on the values of both and at each pair of points being correlated. We show that, by allowing both and to vary, the correlation length of GenGC also varies over space and introduces inhomogeneous and anisotropic features that may be useful in data assimilation applications. Covariances produced using GenGC are computationally tractable due to their compact support and have the added flexibility of generating compact support regions that adapt to the input field. These features can be useful for covariance modeling and covariance tapering applications in data assimilation. We derive the GenGC correlation function using convolutions, discuss continuity properties relating to and and its correlation length, and provide one‐ and two‐dimensional examples that highlight its anisotropy and variable regions of compact support. 

Abstract. This paper presents a new technique to derive thermospheric temperature from space-based disk observations of far ultraviolet airglow. The technique, guided by findings from principal component analysis of synthetic daytime Lyman–Birge–Hopfield (LBH) disk emissions, uses a ratio of the emissions in two spectral channels that together span the LBH (2,0) band to determine the change in band shape with respect to a change in the rotational temperature of N2. The two-channel-ratio approach limits representativeness and measurement error by only requiring measurement of the relative magnitudes between two spectral channels and not radiometrically calibrated intensities, simplifying the forward model from a full radiative transfer model to a vibrational–rotational band model. It is shown that the derived temperature should be interpreted as a column-integrated property as opposed to a temperature at a specified altitude without utilization of a priori information of the thermospheric temperature profile. The two-channel-ratio approach is demonstrated using NASA GOLD Level 1C disk emission data for the period of 2–8 November 2018 during which a moderate geomagnetic storm has occurred. Due to the lack of independent thermospheric temperature observations, the efficacy of the approach is validated through comparisons of the column-integrated temperature derived from GOLD Level 1C data with the GOLD Level 2 temperature product as well as temperatures from first principle and empirical models. The storm-time thermospheric response manifested in the column-integrated temperature is also shown to corroborate well with hemispherically integrated Joule heating rates, ESA SWARM mass density at 460 km, and GOLD Level 2 column O/N2 ratio. 

Abstract FORMOSAT-3/COSMIC (F3/C) constellation of six micro-satellites was launched into the circular low-earth orbit at 800 km altitude with a 72-degree inclination angle on 15 April 2006, uniformly monitoring the ionosphere by the GPS (Global Positioning System) Radio Occultation (RO). Each F3/C satellite is equipped with a TIP (Tiny Ionospheric Photometer) observing 135.6 nm emissions and a TBB (Tri-Band Beacon) for conducting ionospheric tomography. More than 2000 RO profiles per day for the first time allows us globally studying three-dimensional ionospheric electron density structures and formation mechanisms of the equatorial ionization anomaly, middle-latitude trough, Weddell/Okhotsk Sea anomaly, etc. In addition, several new findings, such as plasma caves, plasma depletion bays, etc., have been reported. F3/C electron density profiles together with ground-based GPS total electron contents can be used to monitor, nowcast, and forecast ionospheric space weather. The S4 index of GPS signal scintillations recorded by F3/C is useful for ionospheric irregularities monitoring as well as for positioning, navigation, and communication applications. F3/C was officially decommissioned on 1 May 2020 and replaced by FORMOSAT-7/COSMIC-2 (F7/C2). F7/C2 constellation of six small satellites was launched into the circular low-Earth orbit at 550 km altitude with a 24-degree inclination angle on 25 June 2019. F7/C2 carries an advanced TGRS (Tri Gnss (global navigation satellite system) Radio occultation System) instrument, which tracks more than 4000 RO profiles per day. Each F7/C2 satellite also has a RFB (Radio Reference Beacon) on board for ionospheric tomography and an IVM (Ion Velocity Meter) for measuring ion temperature, velocity, and density. F7/C2 TGRS, IVM, and RFB shall continue to expand the F3/C success in the ionospheric space weather forecasting. 

Abstract The largest obstacle to managing satellites in low Earth orbit (LEO) is accurately forecasting the neutral mass densities that appreciably impact atmospheric drag. Empirical thermospheric models are often used to estimate neutral densities but they struggle to forecast neutral densities during geomagnetic storms when they are highly variable. Physics‐based models are thus increasingly turned to for their ability to describe the dynamical evolution of neutral densities. However, these models require observations to constrain dynamical state variables to be able to forecast mass densities with adequate fidelity. The LEO environment has scarce neutral state observations. Here, we demonstrate, in simulated experiments, a reduction in orbit errors and neutral densities using a physics‐based, data assimilation approach with ionospheric observations. Using a coupled thermosphere‐ionosphere model, the Thermosphere Ionosphere Electrodynamics General Circulation Model, we assimilate Constellation Observing System for Meterology, Ionosphere, and Climate electron density profiles (EDPs) derived from radio occultation (RO) observations. We use the EDPs to directly update neutral states, improving errors for neutral temperature by 70% and neutral winds by 20%. Updated neutral temperature and neutral winds additionally improve helium composition errors by 60% and 40%, respectively. Improved neutral density estimates correspond to a reduction in orbit errors of 1.2 km over 2 days, a 70% reduction over a no‐assimilation control, and a 29 km improvement over 9 days. This study builds on the results of our earlier work to further develop and demonstrate the potential of using a vast and growing RO data source, with a physics‐based model, to overcome our limited number of neutral observations.