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.

Joule Heating in the Thermosphere

Effects of high-latitude forcing uncertainty on the low-latitude and midlatitude ionosphere

The assimilative mapping of ionospheric electrodynamics (AMIE)-derived ionospheric field-aligned current patterns during the ninth Coordinated Data Analysis Workshop substorm event have been mapped to the magnetospheric equatorial plane, using the data-based magnetospheric magnetic field model [Tsyganenko, 1995]. We find that at the onset of the substorm expansion phase, a pair of field-aligned currents emerges about 8 RE tailward of the Earth, near the x axis. This pair of field-aligned currents is consistent with the substorm current wedge model; it lines up in the east–west direction across the near–Earth tail current and has the sense of the nightside region 1 current, i.e., flowing into the ionosphere on the east side and out of the ionosphere on the west side. The ionospheric counterpart of the substorm wedge currents in the midnight sector, on the other hand, has a northeast-to-southwest alignment. During the expansion phase, the substorm wedge currents intensify and expand in spatial size; however, their peaks remain nearly at the same location in the equatorial magnetosphere, about 8 RE tailward from the Earth. We also find that the intensification of the substorm wedge currents during the expansion phase is accompanied by the intensification of the region 2-sense currents located closer to the Earth, and the boundary between the region 2 and substorm wedge currents lies around x = −6 RE.

/pdf/mapping-of-the-ionospheric-field-aligned-currents-to-the-1ii2qmjpad.pdf

Mapping of the ionospheric field‐aligned currents to the equatorial magnetosphere

[1] Large-scale currents in the ionosphere are driven by a variety of sources, including neutral winds, gravity, and plasma pressure gradients. While the stronger daytime wind-driven currents have been extensively studied, gravity and diamagnetic currents in the ionosphere have received very little attention but can have substantial effects even during the night. With the availability of a new generation of magnetic field models based on high-accuracy satellite magnetic measurements, it becomes increasingly important to account for these smaller current systems. In this work, we use the stand-alone NCAR TIEGCM electrodynamics solver along with empirical density, wind, and temperature inputs to model the global current systems caused by gravity and diamagnetism in the F region ionosphere and calculate their magnetic perturbations. These results allow us for the first time to visualize the global structure of these currents and quantify their magnetic perturbations. We find a significantly higher gravity-driven current during the night than one would expect from the lower conductivity which is primarily due to a Pedersen current driven by polarization charges in the predawn sector. We find some discrepancies between the diamagnetic perturbation and a theoretical prediction which could be a result of magnetic tension due to the curvature of the geomagnetic field lines. These results will allow geomagnetic field modelers to account for these important current systems and create more accurate models. This work will also be crucial in analyzing ionospheric magnetic field measurements from upcoming satellite missions such as Swarm.

/pdf/the-ionospheric-gravity-and-diamagnetic-current-systems-jcgiogn298.pdf

The ionospheric gravity and diamagnetic current systems

Magnetograms of ground-based geomagnetic variation are a useful, yet cumbersome data source for substorm studies. In this study geomagnetic variations from 52 northern hemisphere observatories are used to create magnetic potential contour plots representing so called “equivalent ionospheric current” systems. Contour plots of 10 isolated and storm-time substorms for 26 – 28 March 1976 demonstrate the dynamic behavior of the westward and eastward electrojets in the auroral zone. Substorms may be ordered by the preferred longitude of the dominant westward electrojet during their main phase and fall into three categories, morning, evening and midnight, which may occur simultaneously or independently. During recovery of these ten substorms the westward electrojet is always in the morning sector.

Arthur D. Richmond

Papers

Joule Heating in the Thermosphere

Effects of high-latitude forcing uncertainty on the low-latitude and midlatitude ionosphere

Mapping of the ionospheric field‐aligned currents to the equatorial magnetosphere

The ionospheric gravity and diamagnetic current systems

Magnetic Substorm Characteristics Described by Magnetic Potential Maps for 26 – 28 March 1976