William Liu

Bio: William Liu is an academic researcher from Canadian Space Agency. The author has contributed to research in topics: Ionosphere & Solar wind. The author has an hindex of 4, co-authored 7 publications receiving 102 citations.

The Dynamic Magnetosphere

Abstract: Part I Solar Wind-Magnetosphere Interaction 1. The Magnetopause, its Boundary Layers and Pathways to the Magnetotail 2. Quantifying Energy Transfer at the Magnetopause 3. Long-period ULF Waves Driven by Periodic Solar Wind Disturbances Part II Magnetotail Dynamics 4. Magnetotail Dynamics: Survey of Recent Progress 5. Physical Processes for Magnetospheric Substorm Expansion Onsets 6. Cluster Observations of Plasma Bubbles, BBFs and Their Wakes 7. A Statistical Study of Pressure Changes in the near-Earth Magnetotail Associated With Substorm Expansion Onsets 8. Categorization of the Time Sequence of Events Leading to Substorm Onset Based on THEMIS All-Sky Imager Observations Part III Inner Magnetospheric Processes 9. Dynamic Inner Magnetosphere: A Tutorial and Recent Advances 10. Self-Consistent Simulations of Plasma Waves and their Effects on Energetic Particles 11. Topology of High-Latitude Magnetospheric Currents 12. Detection of Dynamical Complexity Changes in Dst Time Series Using Entropy Concepts and Rescaled Range Analysis Part IV Waves and Turbulence in Magnetosphere-Ionosphere Coupling 13. Magnetospheric ULF Waves: A Review 14. ULF Waves in the Topside Ionosphere: Satellite Observations and Modeling 15. Evidence for a Multi-Scale Aurora Part V Ionospheric Driver of the Magnetosphere 16. Influences of the Ionosphere, Thermosphere and Magnetosphere on Ion Outflows 17. Heavy Ion Energization, Transport, and Loss in the Earth's Magnetosphere 18. Data Assimilation Models: A 'New' Tool for Ionospheric Science and Applications Part VI Extraterrestrial Magnetospheres 19. Large-Scale Structure in the Magnetospheres of Jupiter and Saturn 20. Lunar Plasma Environment Index

Nonlinear Geophysics: Why We Need It

Abstract: Few geoscientists would deny that effects are often sensitively dependent on causes, or that their amplification is commonly so strong as to give rise to qualitatively new “emergent” properties, or that geostructures are typically embedded one within another in a hierarchy. Starting in the 1980s, a growing number felt the need to underline the absolute importance of such nonlinearity through workshops and conferences. Building on this, the European Geosciences Union (EGU) organized a nonlinear processes (NP) section in 1990; AGU established a nonlinear geophysics (NG) focus group in 1997; and both unions began collaborating on an academic journal, Nonlinear Processes in Geophysics, in 1994.

Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

Abstract: The magnetosphere undergoes a transition from a dipole-like to taillike structure in the antisunward direction. In this region, Alfven ballooning instability has been considered as a leading candidate to be responsible for the onset and expansion phase of observed impulsive substorms. We apply the generalized Ohm's law in isotropic Hall-MHD equations and study the effect of heat flux on the ballooning modes under substorm circumstances. The set of partial differential equations is obtained for a general ballooning dispersion relation from which all classical Alfven waves and fundamental ballooning modes are recovered, e.g., the decoupled shear Alfven and magnetosonic modes, the classical ballooning instability in incompressible plasmas. In the absence of the heat flux, the ballooning mode is featured by the coupling of the two modes by the superposition of the independent Hall effect and the independent plasma inhomogeneity effect. By contrast, heat flux exerts its influence on the ballooning mode by updating the coefficients of the terms in the dispersion relation. The results expose that the growth rate (γBM) has two branches. If kp is β free, one branch shifts versus β, while the other branch is damped substantially by the heat flux, leading to a more stable ballooning mode; if kc is β free, one branch shifts little versus β, but the other one has higher γBM driven by the heat flux, leading to a more unstable ballooning mode.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Abstract: 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 Upgraded CARISMA Magnetometer Array in the THEMIS Era

Abstract: This review describes the infrastructure and capabilities of the expanded and upgraded Canadian Array for Realtime InvestigationS of Magnetic Activity (CARISMA) magnetometer array in the era of the THEMIS mission. Formerly operated as the Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) magnetometer array until 2003, CARISMA capabilities have been extended with the deployment of additional fluxgate magnetometer stations (to a total of 28), the upgrading of the fluxgate magnetometer cadence to a standard data product of 1 sample/s (raw sampled 8 samples/s data stream available on request), and the deployment of a new network of 8 pairs of induction coils (100 samples per second). CARISMA data, GPS-timed and backed up at remote field stations, is collected using Very Small Aperture Terminal (VSAT) satellite internet in real-time providing a real-time monitor for magnetic activity on a continent-wide scale. Operating under the magnetic footprint of the THEMIS probes, data from 5 CARISMA stations at 29–30 samples/s also forms part of the formal THEMIS ground-based observatory (GBO) data-stream. In addition to technical details, in this review we also outline some of the scientific capabilities of the CARISMA array for addressing all three of the scientific objectives of the THEMIS mission, namely: 1. Onset and evolution of the macroscale substorm instability, 2. Production of storm-time MeV electrons, and 3. Control of the solar wind-magnetosphere coupling by the bow shock, magnetosheath, and magnetopause. We further discuss some of the compelling questions related to these three THEMIS mission science objectives which can be addressed with CARISMA.

A study of geomagnetic storms

Abstract: Twenty-one geomagnetic storm events during 1966 and 1970 were studied by using simultaneous interplanetary magnetic field and plasma parameters. Explorer 33 and 35 field and plasma data were analyzed on large-scale (hourly) and small-scale (3 min.) during the time interval coincident with initial phase of the geomagnetic storms. The solar-ecliptic Bz component turns southward at the end of the initial phase, thus triggering the main phase decrease in Dst geomagnetic field. When the Bz is already negative, its value becomes further negative. The By component also shows large fluctuations along with Bz. When there are no clear changes in the Bz component, the By shows abrupt changes at the main phase onet. On the small-scale behavior of the magnetic field and electric field (E=-VxB) studied in details for the three events, it is found that the field fluctuations in By, Bz and Ey and Ez are present in the initial phase. These fluctuations become larger just before the main phase of the storm begins. In the largescale behavior field remains quiet because the small scale variations are averaged out.

Substorm and magnetosphere characteristic scales inferred from the SuperMAG auroral electrojet indices

Abstract: [1] A generalization of the traditional 12-station auroral electrojet (AE) index to include more than 100 magnetometer stations, SME, is an excellent predictor of global auroral power (AP), even at high cadence (1 min). We use this index, and a database of more than 53,000 substorms derived from it, covering 1980–2009, to investigate time and energy scales in the magnetosphere, during substorms and otherwise. We find, contrary to common opinion, that substorms do not have a preferred recurrence rate but instead have two distinct dynamic regimes, each following a power law. The number of substorms recurring after a time Δt, N(Δt), varies as Δt−1.19 for short times ( 3 hours). Other evidence also shows these distinct regimes for the magnetosphere, including a break in the power law spectra for SME at about 3 hours. The time between two consecutive substorms is only weakly correlated (r = 0.18 for isolated and r = 0.06 for recurrent) with the time until the next, suggesting quasiperiodicity is not common. However, substorms do have a preferred size, with the typical peak SME magnitude reaching 400–600 nT, but with a mean of 656 nT, corresponding to a bit less than 40 GW AP. More surprisingly, another characteristic scale exists in the magnetosphere, namely, a peak in the SME distribution around 61 nT, corresponding to about 5 GW precipitating AP. The dominant form of auroral precipitation is diffuse aurora; thus, these values are properties of the magnetotail thermal electron distribution. The characteristic 5 GW value specifically represents a preferred minimum below which the magnetotail rarely drops. The magnetotail experiences continuous loss by precipitation, so the existence of a preferred minimum implies driving that rarely disappears altogether. Finally, the distribution of SME values across all times, in accordance with earlier work on AE, is best fit by the sum of two distributions, each normal in log(SME). The lower distribution (with a 40% weighting) corresponds to the characteristic quiet peak, while the higher value distribution (60% weighting) is an average over the characteristic substorm peak and the subsequent prolonged recovery.