The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

/pdf/riemann-manifold-langevin-and-hamiltonian-monte-carlo-254effw0xm.pdf

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

The International Reference Ionosphere (IRI) is the international standard for the specification of ionospheric densities and temperatures. It was developed and is being improved-updated by a joint working group of the International Union of Radio Science (URSI) and the Committee on Space Research (COSPAR). A new version of IRI is scheduled for release in the year 2000. This paper describes the most important changes compared to the current version of IRI: (1) an improved representation of the electron density in the region from the F peak down to the E peak including a better description of the F1 layer occurrence statistics and a more realistic description of the low-latitude bottomside thickness, (2) inclusion of a model for storm-time conditions, (3) inclusion of an ion drift model, (4) two new options for the electron density in the D region, and (5) an improved model for the topside electron temperatures. The outcome of the most recent IRI Workshops (Kuhlungsborn, 1997, and Nagoya, 1998) will be reviewed, and the status of several ongoing task force activities (e.g., efforts to improve the representation of electron and ion densities in the topside ionosphere and the inclusion of a plasmaspheric extension) will be discussed. A few typical IRI applications will be highlighted in section 6.

/pdf/international-reference-ionosphere-2000-zhazhxmwus.pdf

International Reference Ionosphere 2000

The Dual Auroral Radar Network (DARN) is a global-scale network of HF and VHF radars capable of sensing backscatter from ionospheric irregularities in the E and F-regions of the high-latitude ionosphere. Currently, the network consists of the STARE VHF radar system in northern Scandinavia, a northern-hemisphere, longitudinal chain of HF radars that is funded to extend from Saskatoon, Canada to central Finland, and a southern-hemisphere chain that is funded to include Halley Station, SANAE and Syowa Station in Antarctica. When all of the HF radars have been completed they will operate in pairs with common viewing areas so that the Doppler information contained in the backscattered signals may be combined to yield maps of high-latitude plasma convection and the convection electric field. In this paper, the evolution of DARN and particularly the development of its SuperDARN HF radar element is discussed. The DARN/SupperDARN network is particularly suited to studies of large-scale dynamical processes in the magnetosphere-ionosphere system, such as the evolution of the global configuration of the convection electric field under changing IMF conditions and the development and global extent of large-scale MHD waves in the magnetosphere-ionosphere cavity. A description of the HF radars within SuperDARN is given along with an overview of their existing and intended locations, intended start of operations, Principal Investigators, and sponsoring agencies. Finally, the operation of the DARN experiment within ISTP/GGS, the availability of data, and the form and availability of the Key Parameter files is discussed.

DARN/SUPERDARN : A global view of the dynamics of high-latitude convection

A numerical simulation study of the thermospheric winds produced by auroral heating during magnetic storms, and of their global dynamo effects, establishes the main features of the ionospheric disturbance dynamo. Driven by auroral heating, a Hadley cell is created with equatorward winds blowing above about 120 km at mid-latitudes. The transport of angular momentum by these winds produces a subrotation of the mid-latitude thermosphere or westward motion with respect to the earth. The westward winds in turn drive equatorward Pedersen currents which accumulate charge toward the equator, resulting in the generation of a poleward electric field, a westward E × B drift, and an eastward current. When realistic local time conductivity variations are simulated, the eastward mid-latitude current is found to close partly via lower latitudes, resulting in an ‘anti-Sq’ type of current vortex. Both electric field and current at low latitudes thus vary in opposition to their normal quiet-day behavior. This total pattern of disturbance winds, electric fields, and currents is superimposed upon the background quiet-day pattern. When the neutral winds are artificially confined on the nightside, the basic pattern of predominantly westward E × B plasma drifts still prevails on the nightside but no longer extends into the dayside. Considerable observational evidence exists, suggesting that the ionospheric disturbance dynamo has an appreciable influence on storm-time ionospheric electric fields at middle and low latitudes.

The ionospheric disturbance dynamo

The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

The past four years have seen important advances in our understanding of global ionospheric electrodynamics and of ionospheric irregularities. The accumulation of ionization drift measurements by radar and satellite have led to the development of quantitative global electric field models. Extensive ground- and satellite-based magnetic field measurements have given improved information about electric currents. Quantitative models of high-latitude ionospheric electrical conductivities have been produced. Theoretical modeling efforts have given us the capability of inferring unknown electrodynamic parameters from measured quantities on a global basis, and allow us to assess quantitatively the influence of ionospheric electric fields and currents on the ionospheric plasma and on the neutral atmosphere. Ionospheric irregularities have also been extensively studied by both experimental and theoretical means in recent years, but are treated only very briefly in this report, with the reader referred to more comprehensive review articles for further information.

Ionospheric electrodynamics and irregularities: A review of contributions by U.S. scientists from 1979 to 1982

A two-dimensional pole-to-pole numerical model with background solstitial winds has been used to study the global dynamical response of the thermosphere to high-latitude energy inputs associated with a model geomagnetic storm. This model storm has four distinct pulses of heat input over a 12-h period. The thermospheric wave response to the sustained part of the storm heat input consists in the establishment of a global meridional circulation that is initiated in about 3 to 4 hours after storm commencement and never quite reaches steady state in the simulation. The main purpose of this study is to investigate the interaction between the disturbances and the mean meridional flow associated with the storm. It is shown that this interaction can be represented in terms of an induced circulation. This induced circulation is forced by the transient nature of the eddy flux convergences (divergences) of heat and momentum. The equivalent temperature changes due to the induced circulation are one-third to o...

Wave–Mean Flow Interaction in the Storm-Time Thermosphere: A Two-Dimensional Model Simulation

Recent advances in numerical algorithms for estimating ionospheric electric fields and currents from groundbased magnetometer data are reviewed and evaluated. Tests of the adequacy of one such algorithm in reproducing large-scale patterns of electrodynamic parameters in the high-latitude ionosphere have yielded generally positive results, at least for some simple cases. Some encouraging advances in producing realistic conductivity models, which are a critical input, are pointed out. When the algorithms are applied to extensive data sets, such as the ones from meridian chain magnetometer networks during the IMS, together with refined conductivity models, unique information on instantaneous electric field and current patterns can be obtained. Examples of electric potentials, ionospheric currents, field-aligned currents, and Joule heating distributions derived from ground magnetic data are presented. Possible directions for future improvements are also pointed out.

Estimation of Electric Fields and Currents from Ground-Based Magnetometer Data

A new technique is presented to estimate electric fields and currents in a localized region of the high-latitude ionosphere by combining two magnetogram-inversion algorithms. This paper describes the concept and practical procedures of the method as well as the first results of our efforts in which this new scheme is applied to northern Scandinavia, computing the ionospheric parameters on a small scale. Examining latitudinal profiles of these parameters and precipitating particles, it is found that the region of the most intense precipitation in the morning sector is located equatorward of the region of the strongest electric field. To evaluate the relative importance of ionospheric and magnetospheric effects, the field-aligned current is divided into two components: (∇Σ) · E and Σ∇ · E. These two components give often the opposite directions in the resultant field-aligned currents. The relative strength of the two components appears to vary considerably with latitude.

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Regional estimation of electric fields and currents in the polar ionosphere

Plasma drift and particle measurements from the DMSP spacecraft for the three Geospace Environmental Modeling (GEM) campaign periods (January 27–29, March 28–29, and July 20–21, 1992) have been used to study the relationship between the plasma convection reversal and the poleward boundary of the diffuse auroral zone characterized by hard electron precipitation with energies greater than 0.45 keV. This boundary, named the hard auroral precipitation boundary (or the HAP boundary) in this paper, is often regarded as the ionospheric footprint of the boundary between the central plasma sheet (CPS) and the boundary plasma sheet (BPS). By examining simultaneous ion drift and particle measurements from about 500 satellite passes we find that the large-scale plasma flow in the morning and evening sectors changes its direction within the auroral oval at the HAP boundary. However, exceptions are found in the early morning sector between 0300 and 0600 MLT, where the convection reversal is sometimes (in 30% of the DMSP crossings) displaced poleward relative to the HAP boundary. It is shown that the shape of the region bordered by the HAP boundary can be roughly represented by a circle, whose size is influenced by the IMF Bz component. There is roughly a linear correlation between the diameter of this circle and the cross-polar-cap potential drop, with the best correlation coefficient of 0.65 for winter season. Our study suggests that the HAP boundary corresponds to the magnetospheric boundary between the quasi-dipolar region and the region with more stretched field lines, and the source of the region 1 field-aligned current is located near the HAP boundary. A By-dependent shift of the HAP boundary with respect to the noon-midnight meridian is also found. In the northern hemisphere, the shift is dawnward for positive By and duskward for negative By in the southern hemisphere, the shift is opposite to that in the northern hemisphere.

/pdf/relationship-of-the-ionospheric-convection-reversal-to-the-1ga1201abe.pdf

Arthur D. Richmond

Papers

Ionospheric electrodynamics and irregularities: A review of contributions by U.S. scientists from 1979 to 1982

Wave–Mean Flow Interaction in the Storm-Time Thermosphere: A Two-Dimensional Model Simulation

Estimation of Electric Fields and Currents from Ground-Based Magnetometer Data

Regional estimation of electric fields and currents in the polar ionosphere

Relationship of the ionospheric convection reversal to the hard auroral precipitation boundary