Information theoretical approach to discovering solar wind drivers of the outer radiation belt

textabstractThe solar wind-magnetosphere system is nonlinear. The solar wind drivers of geosynchronous electrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutual information (CMI), and transfer entropy (TE). These information theoretical tools can establish linear and nonlinear relationships as well as information transfer. The information transfer from solar wind velocity (Vsw) to geosynchronous MeV electron flux (Je) peaks with a lag time of 2 days. As previously reported, Je is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed at least partly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 h, suggesting that the MeV electron loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 h. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics is investigated using windowed TE. When the data are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identified between Je(t + 2 days) versus Vsw(t).

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title: Data‐derived forecasting model for relativistic electron intensity at geosynchronous orbit
abstract: In this paper we present a data-derived model of relativistic electron flux at geosynchronous orbit. The model is driven by multiple solar wind and magnetospheric inputs and combines the deterministic approach of nonlinear dynamics with conditional probability consideration. The model is used for one-day predictions of daily flux maxima for the years 1995–2000. The deterministic part of the model yields average prediction efficiency of 0.77 and linear correlation coefficient of 0.89. It identifies solar wind velocity and SymH index as most relevant input parameters. The probabilistic part of the model quantifies the risks of deviations from deterministic predictions as a function of average solar wind and magnetosphere conditions.  2720 Magnetospheric Physics: Energetic particles, trapped; 2722 Magnetospheric Physics: Forecasting; 2730 Magnetospheric Physics: Magnetosphere— inner; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; 3220  Nonlinear dynamics.  Ukhorskiy, A. Y., M. I. Sitnov, A. S. Sharma, B. J. Anderson, S. Ohtani, and A. T. Y. Lui (2004), Data-derived forecasting model for relativistic electron intensity at geosynchronous orbit,  L09806,

title: Radiation belt electrons respond to multiple solar wind inputs
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title: On the influence of solar wind conditions on the outer-electron radiation belt
abstract: The dependence of outer-radiation belt electron fluxes upon solar wind velocity and density is investigated using the OMNI solar wind database and LANL-GEO geosynchronous satellites for a period spanning over 20 years. Two dimensional probability distribution functions (PDF) of the flux-solar wind velocity (Vsw) and flux-solar wind density are calculated for electron energies in the 10's of keV to MeV range. The PDF's are normalized by Vsw and density and reveal new distinct relationships. Triangle-shaped flux-Vsw distributions become non-linear PDF's, and the most probable flux increases with Vsw. The only significant saturation of fluxes observed with an increase in Vsw occurs for the lower energy electron fluxes (31.7 keV). The low energy fluxes exhibit a positive correlation with solar wind density, while mid-to-high energy electron fluxes are anti-correlated with density. The maximum probability in the PDF's depends upon both velocity and density, the probability is higher for larger Vsw, and the maximum probability is larger for a given Vsw than for density. The results indicate that Vsw may be more important for determination of fluxes than density, especially for periods of high Vsw if suitable mixed delay times are applied to each solar wind parameter. It is shown that the source population of relativistic electrons of tens of keV exhibit a 2-D normalized flux-Vsw PDF, which is strikingly similar to that of the relativistic electrons. The findings support a model whereby solar wind velocity drives convective transport of source and seed electrons, to the inner magnetosphere, where local acceleration and subsequent radial diffusion is responsible for the enhanced fluxes. The results of this study also indicate that, statistically, ULF waves driven by dynamic pressure variations may act as a significant cause of loss for electrons in the 100's of keV to MeV range.

title: Using the NARMAX approach to model the evolution of energetic electrons fluxes at geostationary orbit
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title: Effect of solar wind density on relativistic electrons at geosynchronous orbit
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title: Solar wind and magnetospheric conditions leading to the abrupt loss of outer radiation belt electrons
abstract: The trapped radiation belt electron population is maintained through a competition between multiple source and loss processes occurring within the magnetosphere and driven by the solar wind. In this research we have concentrated on the solar wind and the magnetospheric conditions that lead to the loss of electrons through abrupt energetic electron flux dropouts. We have focused on times when there is only a moderate level of geomagnetic activity, since the magnetospheric response during these conditions is expected to be far less complex than during large geomagnetic storms. We have found that under certain circumstances the radiation belt electrons are remarkably sensitive to the onset of southward IMF and to solar wind dynamic pressure increases. The onset of southward IMF is found to be sufficient to cause the flux dropouts, while increases in solar wind pressure are not necessary but are likely to enhance the loss when they occur in conjunction with southward IMF, as is often the case. It is not clear if an increase in solar wind pressure in the absence of southward IMF is sufficient to cause a flux dropout. The radiation belt fluxes can decrease by more than an order of magnitude with the onset of only minor geomagnetic activity. The level of solar wind forcing (as estimated by the epsilon parameter) and of geomagnetic activity (as estimated by AE, Dst, and the local magnetic field inclination at geosynchronous orbit) responsible for the flux loss is intermediate between lower levels of activity that create localized, adiabatic variations in the flux and large geomagnetic storms that result in both loss and acceleration. The dropout events examined here occurred after one or more days of quiet geomagnetic conditions, which we suggest preconditioned the magnetosphere to be highly sensitive to the onset of new activity. Although it is not known which specific conditions within the magnetosphere lead to this extreme sensitivity of the relativistic electrons, the time periods identified here are ones where the electron loss processes appear to operate in relative isolation of the acceleration processes.

title: Prediction of relativistic electron flux at geostationary orbit following storms: Multiple regression analysis
abstract: Many solar wind and magnetosphere parameters correlate with relativistic electron flux following storms. These include relativistic electron flux before the storm; seed electron flux; solar wind velocity and number density (and their variation); interplanetary magnetic field Bz, AE and Kp indices; and ultra low frequency (ULF) and very low frequency (VLF) wave power. However, as all these variables are intercorrelated, we use multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Using 219 storms (1992–2002), we obtained hourly averaged electron fluxes for outer radiation belt relativistic electrons (>1.5 MeV) and seed electrons (100 keV) from Los Alamos National Laboratory spacecraft (geosynchronous orbit). For each storm, we found the log10 maximum relativistic electron flux 48–120 h after the end of the main phase of each storm. Each predictor variable was averaged over the 12 h before the storm, the main phase, and the 48 h following minimum Dst. High levels of flux following storms are best modeled by a set of variables. In decreasing influence, ULF, seed electron flux, Vsw and its variation, and after-storm Bz were the most significant explanatory variables. Kp can be added to the model, but it adds no further explanatory power. Although we included ground-based VLF power from Halley, Antarctica, it shows little predictive ability. We produced predictive models using the coefficients from the regression models and assessed their effectiveness in predicting novel observations. The correlation between observed values and those predicted by these empirical models ranged from 0.645 to 0.795.

title: Kp forecast models
abstract: Magnetically active times, e.g., Kp > 5, are notoriously difficult to predict, precisely the times when such predictions are crucial to the space weather users. Taking advantage of the routinely available solar wind measurements at Langrangian point (L1) and nowcast Kps, Kp forecast models based on neural networks were developed with the focus on improving the forecast for active times. To satisfy different needs and operational constraints, three models were developed: (1) a model that inputs nowcast Kp and solar wind parameters and predicts Kp 1 hour ahead; (2) a model with the same input as model 1 and predicts Kp 4 hour ahead; and (3) a model that inputs only solar wind parameters and predicts Kp 1 hour ahead (the exact prediction lead time depends on the solar wind speed and the location of the solar wind monitor). Extensive evaluations of these models and other major operational Kp forecast models show that while the new models can predict Kps more accurately for all activities, the most dramatic improvements occur for moderate and active times. Information dynamics analysis of Kp suggests that geospace is more dominated by internal dynamics near solar minimum than near solar maximum, when it is more directly driven by external inputs, namely solar wind and interplanetary magnetic field (IMF).

title: Data based quest for solar wind‐magnetosphere coupling function
abstract: The NARMAX (Nonlinear Autoregressive Moving Average with eXogenous inputs) modeling based approach is used to identify the relations for Solar wind Magnetosphere Coupling Functions in order to identify the one with the best Dst index forecasting abilities. It is argued that the Error Reduction Ratio which is a cornerstone concept in the NARMAX system identification methodology is more appropriate for such nonlinear system as the terrestrial magnetosphere than correlation function analysis which has often been used in the past. It is shown that the identified relationships for coupling functions are proportional to , where is the clock angle, and not to as was suggested in earlier studies. It is shown that the factor appears naturally within the analytical model of Kan and Lee (1979) as the dependence on the clock angle.

title: Predictive Space Weather: An information theory approach
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title: Mutual information functions versus correlation functions
abstract: This paper studies one application of mutual information to symbolic sequences: the mutual information functionM(d). This function is compared with the more frequently used correlation functionΓ(d). An exact relation betweenM(d) andΓ(d) is derived for binary sequences. For sequences with more than two symbols, no such general relation exists; in particular,Γ(d)=0 may or may not lead toM(d)=0. This linear, but not general, independence between symbols separated by a distance is studied for ternary sequences. Also included is the estimation of the finite-size effect on calculating mutual information. Finally, the concept of “symbolic noise” is discussed.

title: A Definition of Conditional Mutual Information for Arbitrary Ensembles
abstract: Shannon's mutual information for discrete random variables has been generalized to random ensembles by R. L. Dobrushin, M. S. Pinsker, and others. Dobrushin also proposed a rather indirect and not very intuitive definition of conditional mutual information which has the additional shortcoming of requiring the existence of certain regular conditional probability measures. In this note we propose a new definition of conditional mutual information for arbitrary ensembles which is simple, intuitive, and completely general. We show that our definition and Dobrushin's both result in the same quantity when the latter is defined. We also derive several important properties of conditional mutual information.

title: The energy spectrometer for particles (ESP): Instrument description and orbital performance
abstract: The ESP detector is functionally described, along with the pertinent orbital and spin properties of the spacecraft that supports it. The phoswiched plastic/BGO scintillators sensor design, electronic implementation, and resulting data types are recounted, and the ground calibration procedures are reported. Several illustrative examples of data are given, including the solar proton event of 29 September 1989, and the nearly periodic episodes of high relativistic electron flux that are associated with solar coronal holes which have been a dominant feature of the space weather over the past few years. 2 refs., 10 figs., 1 tab.

title: Estimation of the Information by an Adaptive Partitioning of the Observation Space
abstract: We demonstrate that it is possible to approximate the mutual information arbitrarily closely in probability by calculating the relative frequencies on appropriate partitions and achieving conditional independence on the rectangles of which the partitions are made. Empirical results, including a comparison with maximum-likelihood estimators, are presented.

title: Generalized redundancies for time series
abstract: Extensions to various information-theoretic quantities (such as entropy, redundancy , and mutual information) are discussed in the context of their role in nonlinear time series analysis. We also discuss \linearized" versions of these quantities and their use as benchmarks in tests for nonlinearity. Many of these quantities can be expressed in terms of the generalized correlation integral, and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics (such as the BDS and Green-Savit statistics). Further, numerical estimation of these quantities is found to be more accurate and more eecient when the the correlation integral is employed in the computation. Finally, we consider several \local" versions of these quantities, including a local Kolmogorov-Sinai entropy, which gives an estimate of variability of the short-term predictability.

title: The Choice of a Class Interval
abstract: (1926). The Choice of a Class Interval.  21, No. 153, pp. 65-66.

title: Flux enhancement of the outer radiation belt electrons after the arrival of stream interaction regions
abstract: The Earth's outer radiation belt electrons increase when the magnetosphere is surrounded by the high-speed solar wind stream, while the southward interplanetary magnetic field (IMF) is also known as an important factor for the flux enhancement. In order to distinguish the two different kinds of solar wind parameter dependence statistically, we investigate the response of the outer belt to stream interaction regions (SIRs). A total of 179 SIR events are identified for the time period from 1994 to 2005. We classify the SIR events into two groups according to the so-called “spring-toward fall-away” rule: IMF sector polarity after the stream interface is toward in spring or away in fall (group A) and vice versa (group B). According to the Russell-McPherron effect, groups A and B have a significant negative and positive offset of the IMF Bz after the stream interface, respectively. Comparing groups A and B by superposing about the stream interface, only IMF Bz dependence can be obtained because the other solar wind parameters change in the same manner. As a result, the greatest flux enhancement is found in the highest-speed streams with a southward offset of the IMF Bz, indicating that only the solar wind speed by itself is not a sufficient condition for the large flux enhancement. It is also found that the large flux enhancement tends to be associated with weak geomagnetic activities with minimum Dst of about −50 nT on average, implying that the existence of intense magnetic storms is not essential for the flux enhancement.

title: Solar cycle changes, geomagnetic variations, and energetic particle properties in the inner magnetosphere
abstract: The causes and effects of geospace variability during recent years have been studied using coordinated measurements from an international constellation of Sun–Earth spacecraft. Particular emphasis is placed on long-term, homogeneous data sets from recent NASA spacecraft missions. It is found that even for modest geomagnetic storms, radiation belt electron fluxes can be rapidly enhanced within the Earth's inner magnetosphere. Remote-sensing solar data identify the eruptive or recurrent coronal features that produce the upstream drivers that, in turn, cause episodes of intense geomagnetic activity. Continuous solar wind data allow study of the principal drivers of magnetospheric acceleration processes. The Earth's radiation belts and inner magnetosphere show pronounced differences in their characteristics as the interplanetary magnetic field and solar wind properties change over the 11-year solar cycle. Solar coronal holes produce regular, recurrent solar wind streams, almost invariably enhancing highly relativistic electrons when solar wind speeds exceed 500 km/s. These phenomena are characteristic of the several-year approach to solar minimum. This contrasts with major geomagnetic disturbances associated with aperiodic coronal mass ejections that occur most frequently around solar maximum. As a practical consequence of Sun–Earth connection events, it is found that many adverse space weather episodes have contributed significantly to spacecraft operational anomalies and failures. We discuss how present and future space missions can address International Living With a Star (ILWS) goals and improve space weather forecasts.

title: Strong electron acceleration in the Earth's magnetosphere
abstract: Electron data are examined over long periods in the outer zone of electron trapping (L ≳ 3). Energetic particle detectors at geostationary orbit and onboard the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) satellite show evidence of strong electron acceleration in Earth's outer radiation belts. Data are studied according to L-value and are compared with concurrent solar wind and geomagnetic conditions. Evidence is presented of a strong correlation between high-speed solar wind speeds and the occurrence of high energy electrons in the Earth's outer radiation belts. Thus, high-speed solar wind streams apparently drive the acceleration of electrons throughout the outer zone on time scales of days. The processes by which electrons are accelerated to high energies (E>1 MeV) are found to consist of two temporally distinct steps. The first involves prompt, relatively modest, acceleration of many electrons during magnetospheric substorms. The second step involves higher energy acceleration of a portion of the substorm electrons throughouth the outer trapping region on a time scale of days.

title: Evolution of electron fluxes in the outer radiation belt computed with the VERB code
abstract: Three-dimensional simulations of the dynamics of outer radiation belt electrons with the recently developed Versatile Electron Radiation Belt (VERB) code are presented. Simulations are preformed for an idealized storm with geomagnetic activity–dependent wave amplitudes that are parameterized as a function of the level of geomagnetic activity. Numerical experiments using the VERB code with various scattering processes (pitch angle diffusion, radial diffusion, and energy diffusion) indicate that diffusive processes are strongly coupled with each other and that they all should be included in realistic simulations of the radiation belts. We show that during storms, inward radial diffusion can produce significant accelerations to relativistic energies, while pitch angle scattering and energy diffusion produce a decrease and an increase in fluxes, respectively. We show that in the presence of high-latitude and low-latitude chorus, peaks in the radial profile of phase space density are formed between L of 4 and 6 during the recovery phase of a storm and are later smoothed by radial diffusion. Sensitivity experiments show that geomagnetic control of wave intensities plays a controlling role in the dynamics of radiation belt electrons. Numerical simulations indicate that electrons of 10–100 keV near geosynchronous orbit can reach MeV energies in the heart of the radiation belts by combined radial diffusion and in situ acceleration. We present two scenarios of acceleration of the plasma sheet electrons: (1) in the range of hundreds of keV by means of radial diffusion and (2) in the range of tens of keV by means of radial diffusion combined with local acceleration.

title: Relativistic electrons in the outer radiation belt: Differentiating between acceleration mechanisms
abstract: Many theoretical models have been developed to explain the rapid acceleration to relativistic energies of electrons that form the Earth's radiation belts. However, after decades of research, none of these models has been unambiguously confirmed by comparison to observations. Proposed models can be separated into two types: internal and external source acceleration mechanisms. Internal source acceleration mechanisms accelerate electrons already present in the inner magnetosphere (L < 6.6), while external source acceleration mechanisms transport and accelerate a source population of electrons from the outer to the inner magnetosphere. In principle, the two types of acceleration mechanisms can be differentiated because they imply that different radial gradients of electron phase space density expressed as a function of the three adiabatic invariants will develop. Model predictions can be tested by transforming measured electron flux (given as a function of pitch angle, energy, and position) to phase space density as a function of the three invariants, μ, K, and Φ. The transformation requires adoption of a magnetic field model. Phase space density estimates have, in the past, produced contradictory results because of limited measurements and field model errors. In this study we greatly reduce the uncertainties of previous work and account for the contradictions. We use data principally from the Polar High Sensitivity Telescope energetic detector on the Polar spacecraft and the Tsyganenko and Stern [1996] field model to obtain phase space density. We show how imperfect magnetic field models produce phase space density errors and explore how those errors modify interpretations. On the basis of the analysis we conclude that the data are best explained by models that require acceleration of an internal source of electrons near L* ∼ 5. We also suggest that outward radial diffusion from a phase space density peak near L* ∼ 5 can explain the observed correspondence between flux enhancements at geostationary orbit and increases in ULF wave power.

title: Timescale for radiation belt electron acceleration by whistler mode chorus waves
abstract: Electron acceleration inside the Earth's magnetosphere is required to explain increases in the ∼MeV radiation belt electron flux during magnetically disturbed periods. Recent studies show that electron acceleration by whistler mode chorus waves becomes most efficient just outside the plasmapause, near L = 4.5, where peaks in the electron phase space density are observed. We present CRRES data on the spatial distribution of chorus emissions during active conditions. The wave data are used to calculate the pitch angle and energy diffusion rates in three magnetic local time (MLT) sectors and to obtain a timescale for acceleration. We show that chorus emissions in the prenoon sector accelerate electrons most efficiently at latitudes above 15° for equatorial pitch angles between 20° and 60°. As electrons drift around the Earth, they are scattered to large pitch angles and further accelerated by chorus on the nightside in the equatorial region. The timescale to accelerate electrons by whistler mode chorus and increase the flux at 1 MeV by an order of magnitude is approximately 1 day, in agreement with satellite observations during the recovery phase of storms. During wave acceleration the electrons undergo many drift orbits and the resulting pitch angle distributions are energy-dependent. Chorus scattering should produce pitch angle distributions that are either flat-topped or butterfly-shaped. The results provide strong support for the wave acceleration theory.

title: Geotail observations of the Kelvin‐Helmholtz instability at the equatorial magnetotail boundary for parallel northward fields
abstract: For several hours on March 24, 1995, the Geotail spacecraft remained near the duskside magnetotail boundary some 15 RE behind the Earth while the solar wind remained very quiet (V=330 km s−1, n=14–21 cm−3) with a very steady 11-nT northward magnetic field. Geotail experienced multiple crossings of a boundary between a dense (n= 19 cm−3), cool (Tp=40 eV), rapidly flowing (V=310 km s−1) magnetosheath plasma and an interior region characterized by slower tailward velocities (V=100 km s−1), lower but substantial densities (n=3 cm−3) and somewhat hotter ions (220 eV). The crossings recurred with a roughly 3-min periodicity, and all quantities were highly variable in the boundary region. The magnetic field, in fact, exhibited some of the largest fluctuations seen anywhere in space, despite the fact that the exterior magnetosheath field and the interior magnetosphere field were both very northward and nearly parallel. On the basis of an MHD simulation of this event, we argue that the multiple crossings are due to a Kelvin-Helmholtz instability at the boundary that generates vortices which move past the spacecraft. A determination of boundary normals supports Kelvin-Helmholtz theory in that the nonlinear steepening of the waves is seen on the leading edge of the waves rather than on the trailing edge, as has sometimes been seen in the past. It is concluded that the Kelvin-Helmholtz instability is an important process for transferring energy, momentum and particles to the magnetotail during times of very northward interplanetary magnetic field.

title: Dawn‐dusk asymmetries, ion spectra, and sources in the northward interplanetary magnetic field plasma sheet
abstract: During periods of northward IMF, plasma sheet ions often have two components: hot (magnetospheric origin) and cold (magnetosheath origin). The temperatures of the cold-component ions are ∼30–40% higher in the dawn sector compared to the dusk sector, implying the dawnside magnetosheath ion heating of ∼30–40%. As a result, the magnetosheath ions are less distinguishable from the hot-component ions, which have lower temperatures on the dawnside, leading to a higher occurrence of the ions having (apparent) one-component distribution. As the duration of the hourly averaged IMF being northward (Δt) increases from 1 to 10 hours, the occurrence of two-component ions increases from 65% to 83% in the dusk flank, but in the dawn flank it remains relatively stable at around 45%. In contrast, the occurrence of ions best characterized by kappa (κ) distribution increases from 25% to 35% in the dawn flank whereas in the dusk flank it remains relatively insensitive to Δt (10%). The occurrence of a one-component Maxwellian distribution appears to be most pronounced in the region of the plasma sheet close to the midnight meridian, and these ions appear to be characteristic of the nominal plasma sheet (hot component) ions. The densification of the plasma sheet, as Δt increases, mainly results from the influx of the magnetosheath ions. However, the cooling of the plasma sheet ions can be attributed not only to the influx of the cold magnetosheath ions but also to the cooling of the nominal plasma sheet ions. The dawn-dusk asymmetries observed in the cold magnetosheath ion profiles should provide constraints that can help determine the roles of various proposed magnetosheath ion entry mechanisms.

title: Steady magnetospheric convection and stream interfaces: Relationship over a solar cycle
abstract: Recently, an association between steady magnetospheric convection (SMC) events and solar wind stream interfaces (SI) was discovered. SMC occurrence tends to peak 0.5–1 day after a stream interface encounters the Earth, while a minimum in SMC events is seen 3–1.5 days before an SI arrives. We investigate whether this relationship holds throughout an entire solar cycle and find that during the declining phase, the relationship is consistent with previous results, while during the rising phase, no association is seen. Conditions during SMCs associated with stream interfaces are compared to unassociated SMCs, and we find differences from previous observations but consistencies with poststream interface conditions. We find that the Russell-McPherron geoeffectiveness of the solar wind stream and increased solar wind–magnetosphere coupling in the declining phase contribute to the observed association. Since SMCs usually begin with a substorm, and substorm occurrence increases both after a stream interface and during the declining phase of the solar cycle, we suggest that the increased number of substorms contributes to the higher probability of an SMC occurring during this period. The question of why coupling is greater, and why substorms occur more frequently during the declining phase, remains to be answered.

title: A comprehensive high‐throughput analysis of substorms observed by IMAGE magnetometer network: Years 1993–2003 examined
abstract: The annual and yearly variation of the substorm activity during a complete solar cycle, from year 1993 to year 2003, has been examined. Almost 6000 substorms were identified by an automated search engine. The identification method was found to be robust and applicable to all activity levels. To examine the long-term (annual, yearly, and solar cycle) variability in the substorm occurrence rate, we formed a measure called the substorm number. The substorm number and peak amplitude were found to only weakly follow the Sun's activity measured by a sunspot number. During the years of sunspot maxima in the solar cycle 23, the Northern Hemisphere auroral region was only moderately active. The largest substorm numbers and peak amplitudes were found during the declining solar cycle phases when the interplanetary high-speed streams hit the Earth. We found out that the substorms last longer during the least active season (i.e., summer months) and during the least active years (e.g., 1997 and 2001). Furthermore, the substorm number and peak amplitude show much larger values for winter than for summer, which may be partly due to the fact that the maximum southward component of the interplanetary magnetic field (B south ) occurs in February and the minimum occurs in June.

title: Substorm probabilities are best predicted from solar wind speed
abstract: Most measures of magnetospheric activity – including auroral power (AP), magnetotail stretching, and ring current intensity – are best predicted by solar wind-magnetosphere coupling functions which approximate the frontside magnetopause merging rate. However radiation belt fluxes are best predicted by a simpler function, namely the solar wind speed, v. Since most theories of how these high energy electrons arise are associated with repeated rapid dipolarizations such as associated with substorms, this apparent discrepancy could be reconciled under the hypothesis that the frequency of substorms tracks v rather than the merging rate – despite the necessity of magnetotail flux loading prior to substorms. Here we investigate this conjecture about v and substorm probability. Specifically, a continuous list of substorm onsets compiled from SuperMAG covering January 1, 1997 through December 31, 2007 are studied. The continuity of SuperMAG data and near continuity of solar wind measurements minimize selection bias. In fact v is a much better predictor of onset probability than is the overall merging rate, with substorm odds rising sharply with v. Some loading by merging is necessary, and frontside merging does increase substorm probability, but nearly as strongly as does v taken alone. Likewise, the effects of dynamic pressure, p, are smaller than simply v taken by itself. Changes in the solar wind matter, albeit modestly. For a given level of v (or Bz), a change in v (or Bz) will increase the odds of a substorm for at least 2 h following the change. A decrease in driving elevates substorm probabilities to a greater extent than does an increase, partially supporting external triggering. Yet current v is the best single predictor of subsequently observing a substorm. These results explain why geomagnetically quiet years and active years are better characterized by low or high v (respectively) than by the distribution of merging estimators. It appears that the flow of energy through the magnetosphere is determined by frontside merging, but the burstiness of energy dissipation depends primarily on v.

title: A coronal hole and its identification as the source of a high velocity solar wind stream
abstract: X-ray images of the solar corona, taken on November 24, 1970, showed a magnetically open structure in the low corona which extended from N20W20 to the south pole. Analysis of the measured X-ray intensities shows the density scale height within the structure to be typically a factor of two less than that in the surrounding large scale magnetically closed regions. The structure is identified as a coronal hole.Since there have been several predictions that such a region should be the source of a high velocity stream in the solar wind, wind measurements for the appropriate period were traced back to the Sun by the method of instantaneous ideal spirals. A striking agreement was found between the Carrington longitude of the solar source of a recurrent high velocity solar wind stream and the position of the hole.Solar wind bulk velocity and photospheric magnetic field data from the period 1962–1970 indicate the possible extension of the result to the interpretation of long term variations in the wind pattern.

title: Compressions and Rarefactions in the Solar Wind' Vela 3 J. T. GosLInG, A. J. HUN)HAUSEN, AND V. Pzzo
abstract: Large non-shock-associated proton density enhancements in the solar wind observed by the Vela 3 satellites have been studied by a superposed epoch analysis. The enhancements typically represent a threefold increase above the nominal average density of 7 protons cm−3, are short lived (of ∼1-day duration), and are followed by an extended period (∼4 days) of depressed densities (≈5 protons cm−3). Associated with the 25 enhancements studied are large positive velocity and proton temperature gradients arising from low-speed (≈335 km sec−1) cool (∼4 × 104 °K) flows. At times there is also a very sharp shift in the flow direction associated with the density enhancement, the flow swinging briefly several degrees to the east ahead of the enhancement and then several degrees to the west on its trailing edge. The total average event, i.e., compression and rarefaction, represents a net proton particle flux increase of about 24% over the nominal average value of 2.5 × 108 protons cm−2 sec−1. Of the 25 events studied, 17 occur within 1 day of the passage of an interplanetary field sector boundary. The space-time profiles of these events compare favorably with nonlinear models of a hot fast solar-wind stream simultaneously overtaking a cold slow-moving stream ahead while outrunning slower-moving plasma behind. The heating associated with the compression at the leading edge of the high-speed stream appears to account for about one-half of the temperature rise found there. Although there is some evidence for a small coronal density signal associated with these events, the major density variations can best be interpreted as the result of a spatial rearrangement of material within the solar wind in transit from the sun to the earth. The measurements are consistent with the viewpoint that low solar-wind speeds frequently originate above the coronal magnetic loops joining photospheric regions of opposite polarity and high speeds originate in the diverging-field interstreamer regions.

title: A case study of transient event motion in the magnetosphere and in the ionosphere
abstract: We present a case study of the magnetospheric and ionospheric response to a series of repetitive (7–8 min) solar wind dynamic pressure and interplanetary magnetic field (IMF) strength variations generated at the bow shock. During a period of duskward and antisunward IMF orientation, the magnetospheric and ionospheric observations indicate transient events moving dawnward and duskward away from a point of origin at or after local noon. In contrast, during a subsequent period of dawnward and antisunward IMF orientation, the observations indicate events moving duskward away from a point of origin at or prior to 0900 LT. We consider explanations in terms of pressure pulse driven riplets on the magnetopause or directly driven bursts of antiparallel merging.

title: Observations of discrete, global magnetospheric oscillations directly driven by solar wind density variations
abstract: In this paper we present six events in which both the time series and the spectral content of solar wind number density fluctuations and magnetospheric magnetic field observations were highly correlated for intervals ranging from a few to twelve hours. The fluctuations were periodic and occurred at discrete frequencies which often matched the f = 1.3, 1.9, 2.6, and 3.4 mHz oscillations that have been attributed to global magnetospheric MHD cavity and/or waveguide modes. We also observed significant power in the sub-mHz region, with frequencies as low as f = 0.1 mHz. We show that these fluctuations were first observed in the solar wind, far upstream from the Earth, and argue that the convected density perturbations slowly alter the size of the magnetospheric cavity leading to the appearance of multiple, discrete magnetospheric oscillations. We argue that for these events the discrete frequencies were an inherent property of the solar wind and were not related to a possible cavity or waveguide mode of the magnetosphere. We then show that the density fluctuations, when converted into length scales, organize into scale sizes of L = 23, 30, 45, and 80–100 RE. Finally, we speculate on a possible solar source for the periodic solar wind structures.

title: Solar wind driving of magnetospheric ULF waves: Field line resonances driven by dynamic pressure fluctuations
abstract: Several observational studies suggest that solar wind dynamic pressure fluctuations can drive magnetospheric ultralow‐frequency (ULF) waves on the dayside. To investigate this causal relationship, we present results from Lyon‐Fedder‐Mobarry (LFM) global, three‐dimensional magnetohydrodynamic (MHD) simulations of the solar wind–magnetosphere interaction. These simulations are driven with synthetic solar wind input conditions where idealized ULF dynamic pressure fluctuations are embedded in the upstream solar wind. In three of the simulations, a monochromatic, sinusoidal ULF oscillation is introduced into the solar wind dynamic pressure time series. In the fourth simulation, a continuum of ULF fluctuations over the 0–50 mHz frequency band is introduced into the solar wind dynamic pressure time series. In this numerical experiment, the idealized solar wind input conditions allow us to study only the effect of a fluctuating solar wind dynamic pressure, while holding all of the other solar wind driving parameters constant. We show that the monochromatic solar wind dynamic pressure fluctuations drive toroidal mode field line resonances (FLRs) on the dayside at locations where the upstream driving frequency matches a local field line eigenfrequency. In addition, we show that the continuum of upstream solar wind dynamic pressure fluctuations drives a continuous spectrum of toroidal mode FLRs on the dayside. The characteristics of the simulated FLRs agree well with FLR observations, including a phase reversal radially across a peak in wave power, a change in the sense of polarization across the noon meridian, and a net flux of energy into the ionosphere.

title: Outward radial diffusion driven by losses at magnetopause
abstract: Loss mechanisms responsible for the sudden depletions of the outer electron radiation belt are examined based on observations and radial diffusion modeling, with L*-derived boundary conditions. SAMPEX data for October–December 2003 indicate that depletions often occur when the magnetopause is compressed and geomagnetic activity is high, consistent with outward radial diffusion for L* > 4 driven by loss to the magnetopause. Multichannel Highly Elliptical Orbit (HEO) satellite observations show that depletions at higher L occur at energies as low as a few hundred keV, which excludes the possibility of the electromagnetic ion cyclotron (EMIC) wave-driven pitch angle scattering and loss to the atmosphere at L* > 4. We further examine the viability of the outward radial diffusion loss by comparing CRRES observations with radial diffusion model simulations. Model-data comparison shows that nonadiabatic flux dropouts near geosynchronous orbit can be effectively propagated by the outward radial diffusion to L* = 4 and can account for the main phase depletions of outer radiation belt electron fluxes.

title: Explaining sudden losses of outer radiation belt electrons during geomagnetic storms
abstract: Geomagnetic storms driven by the solar wind can cause a dramatic drop in the flux of high-energy electrons in the Earth’s outer Van Allen belt. Analysis of data obtained during such an event by three different sets of spacecraft suggests that these electrons are directed into space rather than lost to the atmosphere.

title: Storm time evolution of the outer radiation belt: Transport and losses
abstract: During geomagnetic storms the magnetic field of the inner magnetosphere exhibits large-scale variations over timescales from minutes to days. Being mainly controlled by the magnetic field the motion of relativistic electrons of the outer radiation belt can be highly susceptible to its variations. This paper investigates evolution of the outer belt during the 7 September 2002 storm. Evolution of electron phase space density is calculated with the use of a test-particle simulation in storm time magnetic and electric fields. The results show that storm time intensification of the ring current produces a large impact on the belt. In contrast to the conventional Dst effect the dominant effects are nonadiabatic and lead to profound and irreversible transformations of the belt. The diamagnetic influence of the partial ring current leads to expansion of electron drift orbits such that their paths intersect the magnetopause leading to rapid electron losses. About 2.5 hr after the storm onset most of the electrons outside L = 5 are lost. The partial ring current pressure also leads to an electron trap in the dayside magnetosphere where electrons stay on closed dayside drift orbits for as long as 11 hours. These sequestered electrons are reinjected into the outer belt due to partial recovery of the ring current. The third adiabatic invariant of these electrons exhibits rapid jumps and changes sign. These jumps produce localized peaks in the L*-profile of electron phase space density which have previously been considered as an observable indication of local electron acceleration.

title: Long‐term variations in solar wind velocity and radiation belt electrons
abstract: In this paper we analyze the relationship between yearly variations in MeV radiation belt electron fluxes and solar wind velocity (Vsw). We find that the long-term trends have properties that are important for physical understanding of solar wind-magnetosphere coupling processes and, potentially, for improvements of short-term space weather forecasts. A statistical analysis of solar wind velocity shows that years with high average solar wind velocity are not high simply due to a larger number of days with high Vsw. Rather the entire distribution (median and percentiles) shifts along with the mean Vsw. Similar behavior is seen in the MeV geosynchronous electron fluxes. By subtracting out a 365 day running average baseline, we show that the distribution of log fluxes around the mean is remarkably stable from year to year within a solar cycle and from one solar cycle to another. In contrast, the long-term trends in the baseline show significant changes from year to year and from one solar cycle to another suggesting that solar wind coupling to radiation belt fluxes is not constant but varies over long, as well as short, time scales. In some epicycles, the mean flux is strongly dependent on Vsw while in others the dependence is weak. Similarly, a given average Vsw may produce high average fluxes in one epicycle and low average fluxes in another. Future study of these epicycles and the relative variations within them may improve both physical understanding of solar wind-magnetosphere coupling and space weather forecasting.

title: Solar wind control of Pc5 pulsation power at geosynchronous orbit
abstract: We statistically study the solar wind control of Pc5 magnetic pulsations at geosynchronous orbit. Solar wind conditions are quantified with the use of proton measurements at L1 from the ACE spacecraft that are propagated to the bow shock nose. In addition to the solar wind velocity, Vsw, density, Nsw, and dynamic pressure, Psw, we also consider the dynamic pressure variance in the Pc5 band, VarPsw. Pc5 pulsation parameters are derived from the GOES 8 magnetic field measurements at geosynchronous orbit at ∼10° magnetic latitude. The pulsations are quantified by three parameters: Sy, total power of the azimuthal magnetic field component in the 1.6- to 6.7-mHz Pc5 band; Sz, total power of the field-aligned (compressional) component in the same band; and Stor, the azimuthal power of narrow-band Pc5 oscillations attributed to the fundamental toroidal standing Alfven waves. All parameters are computed in non-overlapping 1-h time windows and then used in linear correlation analysis. We find that all pulsation parameters are positively correlated with Psw and VarPsw with a correlation coefficient of up to ∼0.7 on the dayside. While the correlation of pulsation parameters with the solar wind velocity and density is also positive, the correlation coefficients are smaller. We discuss three mechanisms relevant to the observed Psw and VarPsw control of pulsation power: (1) solar wind-forcing of magnetic pulsations (breathing mode); (2) Psw control of the magnetopause-satellite distance, which results in the Psw dependence of the amplitude of surface waves observed at the satellite; and (3) coupling of impulsively excited fast mode waves to toroidal standing Alfven waves.