The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The Electric and Magnetic Field Instrument and Integrated Science (EMFISIS) investigation on the NASA Radiation Belt Storm Probes (now named the Van Allen Probes) mission provides key wave and very low frequency magnetic field measurements to understand radiation belt acceleration, loss, and transport. The key science objectives and the contribution that EMFISIS makes to providing measurements as well as theory and modeling are described. The key components of the instruments suite, both electronics and sensors, including key functional parameters, calibration, and performance, demonstrate that EMFISIS provides the needed measurements for the science of the RBSP mission. The EMFISIS operational modes and data products, along with online availability and data tools provide the radiation belt science community with one the most complete sets of data ever collected.

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The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) on RBSP

The NASA Radiation Belt Storm Probes (RBSP) mission addresses how populations of high energy charged particles are created, vary, and evolve in space environments, and specifically within Earth’s magnetically trapped radiation belts. RBSP, with a nominal launch date of August 2012, comprises two spacecraft making in situ measurements for at least 2 years in nearly the same highly elliptical, low inclination orbits (1.1×5.8 RE, 10∘). The orbits are slightly different so that 1 spacecraft laps the other spacecraft about every 2.5 months, allowing separation of spatial from temporal effects over spatial scales ranging from ∼0.1 to 5 RE. The uniquely comprehensive suite of instruments, identical on the two spacecraft, measures all of the particle (electrons, ions, ion composition), fields (E and B), and wave distributions (d E and d B) that are needed to resolve the most critical science questions. Here we summarize the high level science objectives for the RBSP mission, provide historical background on studies of Earth and planetary radiation belts, present examples of the most compelling scientific mysteries of the radiation belts, present the mission design of the RBSP mission that targets these mysteries and objectives, present the observation and measurement requirements for the mission, and introduce the instrumentation that will deliver these measurements. This paper references and is followed by a number of companion papers that describe the details of the RBSP mission, spacecraft, and instruments.

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Science Objectives and Rationale for the Radiation Belt Storm Probes Mission

Resonant diffusion curves for electron cyclotron resonance with field-aligned electromagnetic R mode and L mode electromagnetic ion cyclotron (EMIC) waves are constructed using a fully relativistic treatment. Analytical solutions are derived for the case of a single-ion plasma, and a numerical scheme is developed for the more realistic case of a multi-ion plasma. Diffusion curves are presented, for plasma parameters representative of the Earth's magnetosphere at locations both inside and outside the plasmapause. The results obtained indicate minimal electron energy change along the diffusion curves for resonant interaction with L mode waves. Intense storm time EMIC waves are therefore ineffective for electron stochastic acceleration, although these waves could induce rapid pitch angle scattering for ≳ 1 MeV electrons near the duskside plasmapause. In contrast, significant energy change can occur along the diffusion curves for interaction between resonant electrons and whistler (R mode) waves. The energy change is most pronounced in regions of low plasma density. This suggests that whistler mode waves could provide a viable mechanism for electron acceleration from energies near 100 keV to above 1 MeV in the region outside the plasmapause during the recovery phase of geomagnetic storms. A model is proposed to account for the observed variations in the flux and pitch angle distribution of relativistic electrons during geomagnetic storms by combining pitch angle scattering by intense EMIC waves and energy diffusion during cyclotron resonant interaction with whistler mode chorus outside the plasmasphere.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JA01740

Relativistic theory of wave‐particle resonant diffusion with application to electron acceleration in the magnetosphere

https://ntrs.nasa.gov/api/citations/20110005631/downloads/20110005631.pdf

Adaptive numerical algorithms in space weather modeling

Waves and Acceleration of Relativistic Particles (WARP) is a constellation mission proposed to European Space Agency in response to Call for proposals for Cosmic Vision 2015-2025 D/SCI/DJS/SV/val/21851 It is designed for detailed and comprehensive studies of the plasma physical processes leading to acceleration, transport and loss of relativistic electrons in the outer radiation belt of the Earth's inner magnetosphere WARP consists of four identical spacecraft in a relatively tight tetrahedron constellation on a nearly equatorial orbit with an apogee altitude of about 36000 km and perigee of 6000 km In order to fulfill its scientific objectives all spacecraft are equipped with a comprehensive suite of fields and particle instrumentation with a strong European heritage The spacecraft and the model payload instruments have very high technology readiness The satellites are suggested to be launched from Kourou with Soyuz Fregat 2B WARP can be realized as an M-class ESA-only mission with the total cost to ESA being 275 Meuros, including a contingency of 50 Meuro Instruments are assumed to be PIprovided and selected through an open AO process

/pdf/waves-and-acceleration-of-relativistic-particles-warp-58oifc3tbs.pdf

Waves and acceleration of relativistic particles (WARP)

Frequency-Dependent Modulation of Whistler-Mode Waves by Density Irregularities During the Recovery Phase of a Geomagnetic Storm

[1] Plasma wave observations on Voyager, Ulysses, and Galileo have shown that whistler-mode hiss at frequencies below one kHz is continuously present in the extended Io torus of Jupiter. Cyclotron resonant energies at frequencies below 1 kHz are extremely high (typically > MeV), and the Jovian resonant electron flux is too low to cause significant local wave amplification. We consequently explore the possibility that Jovian hiss could be generated elsewhere, and then propagate into the torus to form the observed hiss band. Based on previous studies of the properties and excitation region of Jovian chorus emissions, we demonstrate that whistler-mode waves originating as discrete chorus emissions in the tenuous region from 10 to 15 RJ can refract and propagate inwards into the dense Io torus and there merge into a band of low-frequency hiss. This proposed mechanism for the origin of Jovian hiss is analogous to the formation of plasmaspheric hiss at Earth.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008GL034636

Richard B. Horne

Papers

Waves and acceleration of relativistic particles (WARP)

Frequency-Dependent Modulation of Whistler-Mode Waves by Density Irregularities During the Recovery Phase of a Geomagnetic Storm

Origin of Jovian hiss in the extended Io torus

地球,木星と土星の放射線環境における放射線帯電子とホイスラーモード・コーラス波との間のジャイロ共鳴相互作用:比較研究

Implementation of the digital wave-processing experiment