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.

A new simulation model of upper atmospheric dynamics is presented that includes self-consistent electrodynamic interactions between the thermosphere and ionosphere. This model calculates the dynamo effects of thermospheric winds, and uses the resultant electric fields and currents in calculating the neutral and plasma dynamics. A realistic geomagnetic field geometry is used. Sample simulations for solar maximum equinox conditions illustrate two previously predicted effects of the feedback. Near the magnetic equator, the afternoon uplift of the ionosphere by an eastward electric field reduces ion drag on the neutral wind, so that relatively strong eastward winds can occur in the evening. In addition, a vertical electric field is generated by the low-latitude wind, which produces east-west plasma drifts in the same direction as the wind, further reducing the ion drag and resulting in stronger zonal winds.

A thermosphere/ionosphere general circulation model with coupled electrodynamics

The NCAR thermospheric general circulation model (TGCM) is extended to include a self-consistent aeronomic scheme of the thermosphere and ionosphere. The model now calculates total temperature, instead of perturbation temperature about some specified global mean, global distributions of N(²D), N(4S) and NO, and a global ionosphere with distributions of O+,NO+, O2+, N2+, N+, electron density, and ion temperature as well as the usual fields of winds, temperature and major composition. Mutual couplings between the thermospheric neutral gas and ionospheric plasma occur at each model time step and at each point of the geographic grid. Steady state results for this first Eulerian model of the ionosphere, are presented for solar minimum equinox conditions. The calculated thermosphere and ionosphere global structure agrees reasonably well with the structure of these regions obtained from empirical models. This suggests that the major physical and chemical processes that describe the large-scale structure of the thermosphere and ionosphere have been identified and a self-consistent aeronomic scheme, based on first principles, can be used to calculate thermospheric and ionospheric structure considering only external sources.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/GL015i012p01325%4010.1002/%28ISSN%291944-8007.GRL40

A coupled thermosphere/ionosphere general circulation model

The equations of ionospheric electrodynamics are developed for a geomagnetic field of general configuration, with specific application to coordinate systems based on Magnetic Apex Coordinates. Two related coordinate systems are proposed: Modified Apex Coordinates, appropriate for calculations involving electric fields and magnetic-field-aligned currents; and Quasi-Dipole Coordinates, appropriate for calculations involving height-integrated ionospheric currents. Distortions of the geomagnetic field from a dipole cause modifications to the equations of electrodynamics, with distortion factors exceeding 50% at some geographical locations. Under the assumption of equipotential geomagnetic-field lines, it is shown how the field-line-integrated electrodynamic equations can be expressed in two dimensions in magnetic latitude and longitude, and how the height-integrated and field-aligned current densities can be calculated. Expressions are derived for the simplified calculation of magnetic perturbations above and below the ionosphere associated with the three-dimensional current system. It is shown how the base vectors for the Modified Apex coordinate system can be applied to map electric fields, plasma-drift velocities, magnetic perturbations, and Poynting fluxes along the geomagnetic field to other altitudes, automatically taking into account changes in magnitude and direction of these vector quantities along the field line. Similarly, it is shown how Quasi-Dipole coordinates are useful for expressing horizontal ionospheric currents, equivalent currents, and ground-level magnetic perturbations. A computer code is made available for efficient calculation of the various coordinates, base vectors, and related quantities described in this article.

Ionospheric Electrodynamics Using Magnetic Apex Coordinates.

This paper describes a novel procedure for mapping high-latitude electric fields and currents and their associated magnetic variations, using sets of localized observational data derived from different types of measurements. The technique provides a formalism for incorporating simultaneously such different classes of data as electric fields from radars and satellites, electric currents from radars, and magnetic perturbations at the ground and at satellite heights; the technique also uses available statistical information on the averages and variances of electrodynamic fields. The technique provides a more rigorous way of quantitatively estimating high-latitude electric field and current patterns than other methods and has a capability to quantify the errors in the mapped fields, based on the distribution of available data, their errors, and the statistical variances of the fields. The technique is illustrated by an application to a substorm which was analyzed by Kamide et al. (1982) by an earlier technique.

Arthur D. Richmond

Papers

The ionospheric disturbance dynamo

A thermosphere/ionosphere general circulation model with coupled electrodynamics

A coupled thermosphere/ionosphere general circulation model

Ionospheric Electrodynamics Using Magnetic Apex Coordinates.

Mapping electrodynamic features of the high-latitude ionosphere from localized observations: technique