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.

Equatorial electrojet and regular daily variation SR—III. Comparison of observations with a physical model

Ionospheric Electrodynamics Modeling

The relationship between the structure of the equatorial anomaly and the strength of the equatorial electrojet

[1] The National Center for Atmospheric Research Thermosphere-Ionosphere-Electrodynamics General Circulation Model (NCAR TIE-GCM) is employed to quantify the influence of Joule heating at different altitudes on the neutral temperature and density at 400 km for solar minimum and maximum conditions. The results show that high-altitude Joule heating is more efficient than low-altitude heating in affecting the upper thermosphere. Most of the Joule heating is deposited under 150 km, and the largest Joule heating deposition per scale height happens at about 125 km, independent of solar activity. However, the temperature and density changes at 400 km are largest for heat deposited at ∼140 km for solar minimum and ∼263 km for solar maximum. The timescale for the thermospheric response varies with the altitude of heating. Joule heating deposited at lower heights needs more time to conduct upward, and it takes more time for the thermosphere at 400 km to approach a steady state. A simple one-dimensional model is utilized to explain how the amplitude and characteristic timescale of the upper-thermosphere response to Joule heating depends on the height of heat input. The characteristic response timescale for heat deposited around 135 km is ∼6 hours, while that for heat deposited around 238 km is ∼0.5 hours. The initial temperature response at 400 km to the high-altitude heating is much stronger than the response to the low-altitude heating, but the responses become comparable after about 4 days.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2012JA017885

Height distribution of Joule heating and its influence on the thermosphere

[1] A new quantitative empirical model of the high-latitude forcing of the thermosphere, which is the first empirical model with an electric field variability component consistent with the average electric field, is used with the NCAR-TIEGCM to investigate the influence of the electric field variability on the Joule heating, neutral temperature and density. The electric field variability increases the Joule heating by more than 100%, and significantly improves the agreement between the total Joule heating and integrated Poynting flux, while the horizontal distributions of the height-integrated Joule heating and the Poynting flux have some detailed differences in the polar cap and nightside regions. Including the electric field variability into the energy calculation results in significant changes in the neutral temperature and density. At 400 km, it causes a 120 K polar average temperature increase and the corresponding percentage difference of density is close to 30%.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008GL036916

Arthur D. Richmond

Papers

Equatorial electrojet and regular daily variation SR—III. Comparison of observations with a physical model

Ionospheric Electrodynamics Modeling

The relationship between the structure of the equatorial anomaly and the strength of the equatorial electrojet

Height distribution of Joule heating and its influence on the thermosphere

Impact of electric field variability on Joule heating and thermospheric temperature and density