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Data assimilation aims to blend incomplete and inaccurate data with physics-based dynamical models. In the Earth's radiation belts, it is used to reconstruct electron phase space density, and it has become an increasingly important tool in validating our current understanding of radiation belt dynamics, identifying new physical processes, and predicting the near-Earth hazardous radiation environment. In this study, we perform reanalysis of the sparse measurements from four spacecraft using the three-dimensional Versatile Electron Radiation Belt diffusion model and a split-operator Kalman filter over a 6-month period from 1 October 2012 to 1 April 2013. In comparison to previous works, our 3-D model accounts for more physical processes, namely, mixed pitch angle-energy diffusion, scattering by Electromagnetic Ion Cyclotron waves, and magnetopause shadowing. We describe how data assimilation, by means of the innovation vector, can be used to account for missing physics in the model. We use this method to identify the radial distances from the Earth and the geomagnetic conditions where our model is inconsistent with the measured phase space density for different values of the invariants mu and K. As a result, the Kalman filter adjusts the predictions in order to match the observations, and we interpret this as evidence of where and when additional source or loss processes are active. The current work demonstrates that 3-D data assimilation provides a comprehensive picture of the radiation belt electrons and is a crucial step toward performing reanalysis using measurements from ongoing and future missions.
Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model
(2019)
In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate.
New wave frequency and amplitude models for the nightside and dayside chorus waves are built based on measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. The corresponding 3D diffusion coefficients are systematically obtained. Compared with previous commonly-used (typical) parameterizations, the new parameterizations result in differences in diffusion rates that depend on the energy and pitch angle. Furthermore, one-year 3D diffusive simulations are performed using the Versatile Electron Radiation Belt (VERB) code. Both typical and new wave parameterizations simulation results are in a good agreement with observations at 0.9 MeV. However, the new parameterizations for nightside chorus better reproduce the observed electron fluxes. These parameterizations will be incorporated into future modeling efforts.
Current algorithms for the real-time prediction of the Kp index use a combination of models empirically driven by solar wind measurements at the L1 Lagrange point and historical values of the index. In this study, we explore the limitations of this approach, examining the forecast for short and long lead times using measurements at L1 and Kp time series as input to artificial neural networks. We explore the relative efficiency of the solar wind-based predictions, predictions based on recurrence, and predictions based on persistence. Our modeling results show that for short-term forecasts of approximately half a day, the addition of the historical values of Kp to the measured solar wind values provides a barely noticeable improvement. For a longer-term forecast of more than 2 days, predictions can be made using recurrence only, while solar wind measurements provide very little improvement for a forecast with long horizon times. We also examine predictions for disturbed and quiet geomagnetic activity conditions. Our results show that the paucity of historical measurements of the solar wind for high Kp results in a lower accuracy of predictions during disturbed conditions. Rebalancing of input data can help tailor the predictions for more disturbed conditions.
The Kp index is a measure of the midlatitude global geomagnetic activity and represents short-term magnetic variations driven by solar wind plasma and interplanetary magnetic field. The Kp index is one of the most widely used indicators for space weather alerts and serves as input to various models, such as for the thermosphere and the radiation belts. It is therefore crucial to predict the Kp index accurately. Previous work in this area has mostly employed artificial neural networks to nowcast Kp, based their inferences on the recent history of Kp and on solar wind measurements at L1. In this study, we systematically test how different machine learning techniques perform on the task of nowcasting and forecasting Kp for prediction horizons of up to 12 hr. Additionally, we investigate different methods of machine learning and information theory for selecting the optimal inputs to a predictive model. We illustrate how these methods can be applied to select the most important inputs to a predictive model of Kp and to significantly reduce input dimensionality. We compare our best performing models based on a reduced set of optimal inputs with the existing models of Kp, using different test intervals, and show how this selection can affect model performance.
Storm Time Depletions of Multi-MeV Radiation Belt Electrons Observed at Different Pitch Angles
(2019)
During geomagnetic storms, the rapid depletion of the high-energy (several MeV) outer radiation belt electrons is the result of loss to the interplanetary medium through the magnetopause, outward radial diffusion, and loss to the atmosphere due to wave-particle interactions. We have performed a statistical study of 110 storms using pitch angle resolved electron flux measurements from the Van Allen Probes mission and found that inside of the radiation belt (L* = 3 - 5) the number of storms that result in depletion of electrons with equatorial pitch angle alpha(eq) = 30 degrees is higher than number of storms that result in depletion of electrons with equatorial pitch angle alpha(eq) = 75 degrees. We conclude that this result is consistent with electron scattering by whistler and electromagnetic ion cyclotron waves. At the outer edge of the radiation belt (L* >= 5.2) the number of storms that result in depletion is also large (similar to 40-50%), emphasizing the significance of the magnetopause shadowing effect and outward radial transport.
Modeling and observations have shown that energy diffusion by chorus waves is an important source of acceleration of electrons to relativistic energies. By performing long-term simulations using the three-dimensional Versatile Electron Radiation Belt code, in this study, we test how the latitudinal dependence of chorus waves can affect the dynamics of the radiation belt electrons. Results show that the variability of chorus waves at high latitudes is critical for modeling of megaelectron volt (MeV) electrons. We show that, depending on the latitudinal distribution of chorus waves under different geomagnetic conditions, they cannot only produce a net acceleration but also a net loss of MeV electrons. Decrease in high-latitude chorus waves can tip the balance between acceleration and loss toward acceleration, or alternatively, the increase in high-latitude waves can result in a net loss of MeV electrons. Variations in high-latitude chorus may account for some of the variability of MeV electrons.
Electron acceleration at Saturn due to whistler mode chorus waves has previously been assumed to be ineffective; new data closer to the planet show it can be very rapid (factor of 104 flux increase at 1 MeV in 10 days compared to factor of 2). A full survey of chorus waves at Saturn is combined with an improved plasma density model to show that where the plasma frequency falls below the gyrofrequency additional strong resonances are observed favoring electron acceleration. This results in strong chorus acceleration between approximately 2.5 R-S and 5.5 R-S outside which adiabatic transport may dominate. Strong pitch angle dependence results in butterfly pitch angle distributions that flatten over a few days at 100s keV, tens of days at MeV energies which may explain observations of butterfly distributions of MeV electrons near L = 3. Including cross terms in the simulations increases the tendency toward butterfly distributions. Plain Language Summary Radiation belts are hazardous regions found around several of the planets in our Solar System. They consist of very hot, electrically charged particles trapped in the magnetic field of the planet. At Saturn the most important way to heat these particles has for many years been thought to involve the particles drifting closer toward the planet. This paper adds to the emerging idea at Saturn that a different way to heat the particles is also possible where the heating is done by waves, in a similar way to what we find at the Earth. We use recent information from the Cassini spacecraft on the number and location of particles and also of the waves strength and location combined with computer simulations to show that a particular wave called chorus is excellent at heating the particles where the surrounding number of cold particles is low.
Pitch Angle Scattering of Sub-MeV Relativistic Electrons by Electromagnetic Ion Cyclotron Waves
(2019)
Electromagnetic ion cyclotron (EMIC) waves have long been considered to be a significant loss mechanism for relativistic electrons. This has most often been attributed to resonant interactions with the highest amplitude waves. But recent observations have suggested that the dominant energy of electrons precipitated to the atmosphere may often be relatively low, less than 1 MeV, whereas the minimum resonant energy of the highest amplitude waves is often greater than 2 MeV. Here we use relativistic electron test particle simulations in the wavefields of a hybrid code simulation of EMIC waves in dipole geometry in order to show that significant pitch angle scattering can occur due to interaction with low-amplitude short-wavelength EMIC waves. In the case we examined, these waves are in the H band (at frequencies above the He+ gyrofrequency), even though the highest amplitude waves were in the He band frequency range (below the He+ gyrofrequency). We also present wave power distributions for 29 EMIC simulations in straight magnetic field line geometry that show that the high wave number portion of the spectrum is in every case mostly due to the H band waves. Though He band waves are often associated with relativistic electron precipitation, it is possible that the He band waves do not directly scatter the sub-megaelectron volts (sub-MeV) electrons, but that the presence of He band waves is associated with high plasma density which lowers the minimum resonant energy so that these electrons can more easily resonate with the H band waves.
Models of ring current electron dynamics unavoidably contain uncertainties in boundary conditions, electric and magnetic fields, electron scattering rates, and plasmapause location. Model errors can accumulate with time and result in significant deviations of model predictions from observations. Data assimilation offers useful tools which can combine physics-based models and measurements to improve model predictions. In this study, we systematically analyze performance of the Kalman filter applied to a log-transformed convection model of ring current electrons and Van Allen Probe data. We consider long-term dynamics of mu = 2.3 MeV/G and K = 0.3 G(1/2) R-E electrons from 1 February 2013 to 16 June 2013. By using synthetic data, we show that the Kalman filter is capable of correcting errors in model predictions associated with uncertainties in electron lifetimes, boundary conditions, and convection electric fields. We demonstrate that reanalysis retains features which cannot be fully reproduced by the convection model such as storm-time earthward propagation of the electrons down to 2.5 R-E. The Kalman filter can adjust model predictions to satellite measurements even in regions where data are not available. We show that the Kalman filter can adjust model predictions in accordance with observations for mu = 0.1, 2.3, and 9.9 MeV/G and constant K = 0.3 G(1/2) R-E electrons. The results of this study demonstrate that data assimilation can improve performance of ring current models, better quantify model uncertainties, and help deeper understand the physics of the ring current particles.