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Ionosphere

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Full-Text Articles in Physical Sciences and Mathematics

Deep Learning Applications On Ionospheric Studies, Yang Pan Jan 2024

Deep Learning Applications On Ionospheric Studies, Yang Pan

Physics Dissertations

Machine learning techniques, particularly deep learning techniques, have been vigorously pursued to tackle space physics problems and achieved some impressive results recently. The growth of deep learning technologies in different domains enables innovative solutions to those problems compared to conventional methods. Filling data gaps in instrumental observations is among the demanding issues, which benefits space physicists to study ionospheric phenomena with complete data coverage. Global total electron content (TEC) and regional ionospheric electron density (Ne) are among important physical parameters in ionospheric studies. Due to the limited coverage of global navigation satellite system (GNSS) ground receivers and sporadic …


Relation Between Solitary Wave Occurrence And Solar Wind Parameters During The Kelvin-Helmholtz Instability, Tyler Workman Aug 2023

Relation Between Solitary Wave Occurrence And Solar Wind Parameters During The Kelvin-Helmholtz Instability, Tyler Workman

Physics Theses

The Kelvin-Helmholtz instability (KHI) is an important mechanism whereby the solar wind transports energy and momentum into the magnetosphere. One unresolved topic is the role of kinetic phenomena and turbulence in mediating this energy transport. Previous studies hypothesized that the prevalence of electrostatic solitary waves, an artifact of kinetic turbulence, decreased along the flanks as the instability grew. These previous studies had been conducted using 3 KHI events. For this study, we test the hypothesis and further investigate how these solitary waves affect the local plasma with an expanded list of 15 KHI events. A combination of solar wind data …


The Time-Dependent Ionospheric Model Using A Tec-Driven Servo: An Investigation Of The Capabilities And Limitations, Jenny Rebecca Whiteley Aug 2023

The Time-Dependent Ionospheric Model Using A Tec-Driven Servo: An Investigation Of The Capabilities And Limitations, Jenny Rebecca Whiteley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The ionosphere is a region of the atmosphere with a high density of electrons. These electrons affect the behavior of any electromagnetic wave that passes through the ionosphere. Communication and geolocation systems, such as traditional radio and Global Positioning Systems, depend on emitted electromagnetic signals being picked up by a receiver. The presence of the ionosphere affects the behavior of the signal and the quality of the service. Hence, the interactions between electromagnetic waves and the ionosphere provide a major motivation to understand, research, and successfully model and predict the ionosphere and its physical phenomena. This study focused on determining …


Model And Observation Comparisons Of Ionospheric Current Systems, Tre'shunda James May 2023

Model And Observation Comparisons Of Ionospheric Current Systems, Tre'shunda James

Physics Dissertations

The interaction between the dynamically changing solar wind and Earth’s magnetosphere results in several different current systems. The most relevant to space weather are the Birkeland currents, a.k.a field-aligned currents (FACs), that couple the magnetosphere to the ionosphere. These currents flow into and out of the ionosphere and are closed through the ionosphere by the horizontally flowing eastward and westward electrojets. This FAC-electrojet current system is responsible for some of the most beautiful and detrimental space weather impacts. The aurora borealis (or northern lights) in the Northern Hemisphere and aurora australis (or southern lights) in the Southern Hemisphere are displays …


Validation Of Bottom-Up Gnss Radio Occultation Method To Measure D- And E-Region Electron Density, Dylan J. Shaver Mar 2023

Validation Of Bottom-Up Gnss Radio Occultation Method To Measure D- And E-Region Electron Density, Dylan J. Shaver

Theses and Dissertations

An in-depth validation of a new bottom-up approach using GNSS Radio Occultation (GNSS-RO) data to generate electron density profiles in the D- and E-region ionosphere. This comparison was completed using daytime ionosonde profiles when sporadic-E (Es) was not present, and corresponding FIRI profiles. The average GNSS-RO profile is a few kilometers higher in altitude than the ionosonde profiles at the minimum frequency, f min. When the ionosonde profiles are shifted so that the altitudes match at f min, they are in good agreement up to the E-region peak altitude, hmE. Below f min, the …


Multifrequency Scintillation In The Polar Caps, Tate Colby Dec 2022

Multifrequency Scintillation In The Polar Caps, Tate Colby

Doctoral Dissertations and Master's Theses

In the ionosphere, plasma density structures with scales sizes ranging from a few centimeters to hundreds of kilometers are capable of modifying the phase and amplitude of a radio signal in a rapid random manner in a process called scintillation. The Coherent Electromagnetic Radio Tomography (CERTO) and the Canadian High Arctic Ionospheric Network (CHAIN) are two different networks of scintillation receivers, each with a station in Resolute Bay, Canada. CERTO measures amplitude and phase signals in VHF and UHF while CHAIN measures amplitude and phase signals in the L-band. Through these measurements we can calculate the scintillation indexes, S_4 and …


Feasibility Of Fireball Trail Detection Using Ground-Based Gps Receivers, Ian R. Moffett Mar 2022

Feasibility Of Fireball Trail Detection Using Ground-Based Gps Receivers, Ian R. Moffett

Theses and Dissertations

The feasibility of using GPS data to detect fireballs is analyzed by first modeling the fireball’s trail diffusion and plasma chemistry to get a resulting ion density profile of the trail over time. The signal perturbation caused by the fireball trail is simulated for a ground receiver using an analytic solution for diffraction from a Gaussian lens. Five cases were modeled with varying initial peak ion densities and altitudes taken from fireball and reentry vehicle data. This paper shows that it is feasible to detect a fireball trail using GPS if the fireball has a sufficiently high initial ion density, …


Comparing Twins Ion Temperature Maps With Mms, Ampere, And Themis Observations During July 26, 2017 Reconnection Event, Isabella M. Householder Jan 2022

Comparing Twins Ion Temperature Maps With Mms, Ampere, And Themis Observations During July 26, 2017 Reconnection Event, Isabella M. Householder

Honors Theses and Capstones

The solar wind releases a constant stream of ionized particles into space which causes complex behaviors to occur within Earth’s magnetosphere. These disruptions can initiate magnetic reconnection and cause flow reversal of ions in the magnetotail. Two flow reversal events were locally detected by the Magnetospheric Multiscale Mission (MMS) on July 26, 2017 at 0700 UT and 0730 UT. The Two Wide-Angle Imaging Neutral-Atom Spectrometers (TWINS) provide a global measurement of heated signatures of the magnetic field and detected an increase in ion temperature during these reconnection events without the presence of a geomagnetic storm. Active Magnetosphere and Planetary Electrodynamics …


Ionospheric F-Layer Dipole Flute Instability Effects On Electromagnetic Scattering In A Magnetohydrodynamic Plasma, Andrew J. Knisely Nov 2021

Ionospheric F-Layer Dipole Flute Instability Effects On Electromagnetic Scattering In A Magnetohydrodynamic Plasma, Andrew J. Knisely

Theses and Dissertations

The ionosphere has significant impact on radio frequency (RF) applications such as satellites, over-the-horizon radar, and commercial communication systems. The dynamic processes effecting the behavior of the ionic content leads to a variety of instabilities that adversely affect the quality of RF signals. In the F-layer ionosphere, flute instability persists, appearing as two radial regions of high and low density perturbations elongated along the earth's geomagnetic field lines. The sizes of flute structures are comparable to the wavelengths in the high frequency spectrum. The objective is to characterize the high frequency scattering of an incident field by developing a 3D …


A Comparison Of Sporadic-E Occurrence Rates Using Ionosondes And Gps Radio Occultation Measurements, Rodney A. Carmona Jr. Mar 2021

A Comparison Of Sporadic-E Occurrence Rates Using Ionosondes And Gps Radio Occultation Measurements, Rodney A. Carmona Jr.

Theses and Dissertations

Sporadic-E (Es) occurrence rates from Global Position Satellite radio occultation (GPS-RO) measurements have shown to vary by nearly an order of magnitude between studies, motivating a comparison with ground-based measurements. In an attempt to find an accurate GPS-RO technique for detecting Es formation, occurrence rates derived using five previously developed GPS-RO techniques are compared to ionosonde measurements over an eight-year period from 2010-2017. GPS-RO measurements within 170 km of a ionosonde site are used to calculate Es occurrence rates and compared to the ground-truth ionosonde measurements. Each technique is compared individually for each ionosonde site and then combined to determine …


Impendance Probe Payload Development For Space-Based Joint Service Collaboration, Brian T. Kay Mar 2021

Impendance Probe Payload Development For Space-Based Joint Service Collaboration, Brian T. Kay

Theses and Dissertations

Collaborations utilizing small spacecraft in near earth orbit between the U. S. Coast Guard Academy (CGA), Naval Research Lab (NRL), the U. S. Naval Academy (USNA), and the Air Force Institute of Technology (AFIT) have initiated scientific and engineering space-based experiments. Sourced opportunities like the VaSpace ThinSat missions have provided a platform for payload, sensor, and experiment development that would have otherwise been resource prohibitive. We have constructed an impedance probe payload derived from the existing ‘Space PlasmA Diagnostic suitE’ (SPADE) mission operating from NASA’s International Space Station. Currently both space and laboratory plasmas are investigated with AC impedance measurements …


Validation Technique For Modeled Bottomside Ionospheres Via Ray Tracing, Kevin S. Burg Mar 2020

Validation Technique For Modeled Bottomside Ionospheres Via Ray Tracing, Kevin S. Burg

Theses and Dissertations

A new method for validating ionosphere models using High Frequency (HF) angle of arrival (AoA) data is presented. AoA measurements from a field campaign held at White Sands Missile Range, New Mexico, USA in January 2014 provide the actual elevation angle, azimuth and group delay results from 10 transmitter-receiver circuits. Simulated AoAs are calculated by ray tracing through the electron density profiles predicted from the ionosphere models hosted by NASA's Community Coordinated Modeling Center: IRI-2016, USU-GAIM, GITM, CTIPe, TIE-GCM, and SAMI3. Through the implementation of metrics including Mean Absolute Error, Prediction Efficiency, Correlation Coefficient, and others, we are able to …


Localized Effects Of Hurricane Michael (2018) On Total Electron Content, Joanna E.S. Williams Mar 2020

Localized Effects Of Hurricane Michael (2018) On Total Electron Content, Joanna E.S. Williams

Theses and Dissertations

Understanding the connection between terrestrial and space environments is an emerging field of study that can significantly improve operational weather forecasting. In particular, it is well known that tropical cyclones (TCs) and thunderstorms can initiate gravity waves that generate fluctuations in the total electron content (TEC) of the ionosphere. These perturbations can deteriorate and delay the transmission of high-frequency (HF) communications, such as emergency services, amateur radio, and aviation. This study investigates changes in TEC according to the number of lightning ashes and the rainfall rates associated with Hurricane Michael (2018). A composite analysis will be performed using the GOES …


One-Dimensional Kinetic Particle-In-Cell Simulations Of Various Plasma Distributions, Richard N. Vanderburgh Jan 2020

One-Dimensional Kinetic Particle-In-Cell Simulations Of Various Plasma Distributions, Richard N. Vanderburgh

Browse all Theses and Dissertations

A one-dimensional kinetic particle-in-cell (PIC) MATLAB simulation was created to demonstrate the time-evolution of various plasma distributions. Building on previous plasma PIC programs written in FORTRAN and Python, this work recreates the computational and diagnostic tools of these packages in a more user- and educational-friendly development environment. Plasma quantities such as plasma frequency and species charge-mass ratios are arbitrarily defined. A one-dimensional spatial environment is defined by total length and number and size of spatial grid points. In the first time-step, charged particles are given initial positions and velocities on a spatial grid. After initialization, the program solves for the …


Using Natural Phenomena To Study The Ionosphere, Joseph Benjamin Malins Nov 2019

Using Natural Phenomena To Study The Ionosphere, Joseph Benjamin Malins

Physics & Astronomy ETDs

This dissertation explores novel techniques for observing the ionosphere using natural signals. The ionosphere is a region of plasma hundreds of kilometers above the Earth that affects communication and remote sensing applications across the world. Traditional techniques for observing the ionosphere involve using man made radio signals, either to reflect the signal at HF frequencies or to pass several signals through the ionosphere and compare the difference the ionosphere makes in the signals. However, such techniques are limited by the ability of equipment to produce these signals and by the numerous laws and regulations governing transmission of signals in the …


Non-Linear Magnetosphere-Ionosphere Interactions At High Latitudes, Beket Tulegenov Aug 2019

Non-Linear Magnetosphere-Ionosphere Interactions At High Latitudes, Beket Tulegenov

Doctoral Dissertations and Master's Theses

Non-linear, 3D electromagnetic coupling between the ionosphere and magnetosphere is investigated in this dissertation. The study is based on a non-linear, 3D, reduced magnetohydrodynamic model describing interaction between dispersive Alfven waves and the nightside high-latitude ionosphere. Results are presented from a numerical study of small-scale, intense magnetic field-aligned currents observed in the vicinity of the discrete auroral arc by the Magnetosphere-Ionosphere Coupling in the Alfven Resonator (MICA) sounding rocket launched from Poker Flat, Alaska, on 19 February 2012. The goal of the MICA project was to investigate the hypothesis that such currents can be produced inside the ionospheric Alfven resonator …


Microcontroller Differential Gps To Subtract Signal Delay Due To Ambient Free Electrons In The Ionosphere, Diana Jane Swanson Jun 2019

Microcontroller Differential Gps To Subtract Signal Delay Due To Ambient Free Electrons In The Ionosphere, Diana Jane Swanson

Physics

The goal of this project is to create a Global Positioning System (GPS) receiver that is more precise than one GPS receiver on its own. The technique is to take the difference between a GPS receiver’s measured position and its actual position, then use radio frequency (RF) communication to send that differential value to another microcontroller GPS receiver. This differential value will be added to the measured second location to get a more accurate position for the second GPS receiver, thus creating a differential GPS.


Planar Ion Probe For Low-Latitude Ionosphere/Thermosphere Enhancements In Density Cubesat Mission, Liam Owen Gunter Apr 2019

Planar Ion Probe For Low-Latitude Ionosphere/Thermosphere Enhancements In Density Cubesat Mission, Liam Owen Gunter

Doctoral Dissertations and Master's Theses

One of the crucial measurements for characterizing any space weather event is absolute plasma density and plasma density fluctuations, both spatially and temporally. Langmuir probes are the oldest and most proven instruments for these in-situ measurements. This thesis enumerates the development of a miniaturized low-noise Langmuir probe intended for a dual CubeSat mission to study equatorial temperature and wind anomaly in the Earth’s ionosphere.

The Langmuir probe instrument developed is of a planar geometry and fix biased in the ion saturation region, i.e. negative w.r.t. spacecraft chassis. Operating the Langmuir probe in the ion saturation region avoids excessive spacecraft charging …


Global Ionosonde And Gps Radio Occultation Sporadic-E Intensity And Height Comparison, Joshua Y. Gooch Mar 2019

Global Ionosonde And Gps Radio Occultation Sporadic-E Intensity And Height Comparison, Joshua Y. Gooch

Theses and Dissertations

A global, multi-year comparison of low and mid-latitude COSMIC GPS radio occultation (RO) sporadic-E (Es) plasma frequency and altitude and Digisonde blanketing frequency (fbEs) and altitude within 150 km and 30 minutes of each other. RO methods used to estimate the intensity of the Es layer include the scintillation index S4, total electron content (TEC) with both a constant and variable Es cloud thickness, and an Abel transform. The S4 and TEC with varying thickness techniques both under-represent the fbEs values while the TEC with constant thickness and Abel transform better estimate Digisonde fbEs values. …


Modeling High-Altitude Nuclear Detonations Using Existing Ionospheric Models, Sophia G. Schwalbe Mar 2019

Modeling High-Altitude Nuclear Detonations Using Existing Ionospheric Models, Sophia G. Schwalbe

Theses and Dissertations

One threat to the United States is a nuclear weapon being detonated at high altitude over the country. The resulting electromagnetic pulse (EMP) could devastate the nation. Despite its destructive nature, the response of the ionosphere to such an event is poorly understood. This study assesses if existing ionospheric models, which are used to nowcast and forecast ionospheric changes, can be used to model the response to a high-altitude nuclear detonation (HAND). After comparing five ionosphere models, the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM) was selected and modified to incorporate an array of F10.7 indices to serve as a proxy for …


The Response Of Ionosphere And Thermosphere To The High Latitude Energy Deposition, Yang Lu Dec 2018

The Response Of Ionosphere And Thermosphere To The High Latitude Energy Deposition, Yang Lu

Physics Dissertations

The ionosphere and thermosphere are the important regions in the Earth upper atmosphere. They represent the ionized and neutral particles, respectively. The main external energy sources in those regions are solar radiation and geomagnetic energy due to the solar wind-magnetosphere interaction. The neutral particles are ionized by solar radiation on the dayside. Meanwhile, the energy deposition from the magnetosphere is also critical at high latitudes. The energy source at high latitudes depends on whether the local magnetic field line is closed or not. In the polar cap region where it is connected to open magnetic field line, the main energy …


Impacts Of Anisotropy, Wave Heating, And Neutral Winds On High-Latitude Ionospheric Dynamics, Meghan R. Burleigh Aug 2018

Impacts Of Anisotropy, Wave Heating, And Neutral Winds On High-Latitude Ionospheric Dynamics, Meghan R. Burleigh

Doctoral Dissertations and Master's Theses

Significant amounts of ionospheric plasma can be transported to high altitudes (ion upflow) in response to a variety of plasma heating and uplifting processes such as DC electric fields and precipitation. Once ions have been lifted to high altitudes, transverse ion acceleration by broadband ELF waves can give the upflowing ions sufficient energy for the mirror force to propel these ions to escape into the magnetosphere (ion outflow). In order to accurately examine the connection between upflow and outflow processes, a new two dimensional, anisotropic fluid model is developed.

The new model, named GEMINI-TIA, is based on a Bi-Maxwellian distribution …


Impacts Of Sub-Auroral Polarization Streams On High Frequency Operations As A Function Of Modeled Particle Energy Flux, Nathan D. Smith Mar 2018

Impacts Of Sub-Auroral Polarization Streams On High Frequency Operations As A Function Of Modeled Particle Energy Flux, Nathan D. Smith

Theses and Dissertations

Space weather events can cause irregularities within the ionosphere; in particular, this research examines sub-auroral polarization streams (SAPS), as their accompanying irregularities and effects can degrade high-frequency (HF) signal propagation. It is known that the strongest westerly current drifts delineating SAPS are associated with a deep ionospheric trough, which in turn contaminates HF data with clutter from the non-standard ionosphere. Having a methodology to track and identify these occurrences on current computational architecture would provide operators enhanced situational awareness in knowing to expect degradation in HF processes. This study has discovered a weak, yet significant, exponentially decaying correlation between maximum …


Characterizing Coseismic Ionospheric Disturbance For Surface-Rupturing Earthquakes, Rebekah Faith Lee Dec 2017

Characterizing Coseismic Ionospheric Disturbance For Surface-Rupturing Earthquakes, Rebekah Faith Lee

Boise State University Theses and Dissertations

Coseismic ionospheric disturbances (CID) are commonly identified using global navigation space system (GNSS) satellites. Little research, however, has focused on using total electron content (TEC) observations to characterize acoustic sources on Earth's surface. For this thesis, I investigate the applicability of an analytical method to invert the TEC for the acoustic wave. The inversion is based on the modeling of a transfer function. Deconvolving the TEC by the transfer function gives the acoustic wave. Inverting for the acoustic wave in this way would remove phase differences in the TEC created by atmospheric-ionospheric coupling. I test the assumption in the model …


Altitudinal Variability Of Quiet-Time Plasma Drifts In The Equatorial Ionosphere, Debrup Hui May 2015

Altitudinal Variability Of Quiet-Time Plasma Drifts In The Equatorial Ionosphere, Debrup Hui

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In the modern world, we increasingly depend on space-based systems for our communication, positioning, and navigation systems. These systems depend on electromagnetic waves propagating through the ionosphere. The ionosphere is the medium in the upper atmosphere where, due to presence of the charged atomic and molecular particles and electrons collectively known as plasma, it influences the traveling electromagnetic waves following laws of electrodynamics. Improved models for predicting space weather conditions require improved knowledge of the drifts of these plasmas in the ionosphere. This study is focused on climatology of the altitudinal variations of these plasma drifts in the equatorial latitudes. …


Ion-Cyclotron Resonance Heating Of O+ In The Topside Ionosphere And Mapping Outflows To The Magnetosphere, Anthony W. Pritchard Sep 2014

Ion-Cyclotron Resonance Heating Of O+ In The Topside Ionosphere And Mapping Outflows To The Magnetosphere, Anthony W. Pritchard

Doctoral Dissertations and Master's Theses

This thesis considers the heavy ion dynamics due to ion-cyclotron resonance energization processes that take place in the turbulent region of the Earth’s topside, high latitude ionosphere. We simulate the impact of this transverse heating process upon energies and velocity distribution functions of outflowing oxygen ions (O+) in the approximate altitude range of 800 km to 15,000 km. To do so most effectively, we use a single particle tracing model that precisely reproduces the small-scale wave-particle interaction of broadband extremely low frequency (BBELF) waves with the ions’ cyclotron motions, leading to the upward acceleration of ions in type-II ion outflows …


Mapping Of The Quasi-Periodic Oscillations At The Flank Magnetopause Into The Ionosphere, Emily R. Dougal Nov 2013

Mapping Of The Quasi-Periodic Oscillations At The Flank Magnetopause Into The Ionosphere, Emily R. Dougal

Doctoral Dissertations and Master's Theses

We have estimated the ionospheric location, area, and travel time of quasi-periodic oscillations originating from the magnetospheric flanks. This was accomplished by utilizing global and local MHD models and Tsyganenko semi-empirical magnetic field model on multiple published and four new cases believed to be caused by the Kelvin-Helmholtz Instability. Finally, we used auroral, magnetometer, and radar instruments to observe the ionospheric signatures. The ionospheric magnetic latitude determined using global MHD and Tsyganenko models ranged from 58.3-80.2 degrees in the northern hemisphere and -59.6 degrees to -83.4 degrees in the southern hemisphere. The ionospheric magnetic local time ranged between 5.0-13.8 hours …


A 3-D Model Of The Auroral Ionosphere, Yishi Lee Jun 2013

A 3-D Model Of The Auroral Ionosphere, Yishi Lee

Doctoral Dissertations and Master's Theses

A new 3-D model of the high latitude ionosphere is developed to study the coupling of the ionosphere with the magnetosphere and neutral atmosphere. The model consists of equations describing conservations of mass, momentum and energy for the six ionospheric constituents (O+, NO+, N+2 , O+2 , N+ and e-) and an electrostatic potential equation. This 3-D model is used to examine interrelated processes of ion heating, plasma structuring due to perpendicular transport, ion upflow, molecular ion generation, and neutral wave forcing. It is first validated by comparisons with a 2-D model, which uses similar mathematical and numerical approaches, and …


Simultaneous Multi-Angle Measurements Of Plasma Turblence At Haarp, Naomi Watanabe Jul 2012

Simultaneous Multi-Angle Measurements Of Plasma Turblence At Haarp, Naomi Watanabe

Master's Theses and Doctoral Dissertations

We report the results from a recent series of experiments employing the HAARP HF transmitter to generate and study strong Langmuir turbulence (SLT) in the interaction region of overdense ionospheric plasma. Diagnostics included the Modular UHF Ionospheric Radar (MUIR) sited at HAARP, the Super DARN-Kodiak HF radar, and HF receivers to record stimulated electromagnetic emissions (SEE). Short pulse, low duty cycle experiments demonstrate control and suppression of artificial field-aligned irregularities (AFAI). This allows the isolation of ponderomotive plasma turbulence effects. For the first time, plasma line spectra measured simultaneously in different spots of the interaction region displayed marked but contemporaneous …


Verification Of Global Assimilation Of Ionospheric Measurements Gauss Markov (Gaim-Gm) Model Forecast Accuracy, Paul H. Domm Sep 2011

Verification Of Global Assimilation Of Ionospheric Measurements Gauss Markov (Gaim-Gm) Model Forecast Accuracy, Paul H. Domm

Theses and Dissertations

GAIM-GM is an operational Kalman filter data assimilation model of the ionosphere that can assimilate data from GPS total electron content (TEC), ionosonde electron density profiles, and satellite based in situ electron densities. The Air Force Weather Agency (AFWA) uses GAIM-GM to specify and forecast the ionosphere. An in depth investigation into the accuracy of these forecasts has not been completed. GAIM-GM output obtained from four cases run from combinations of geomagnetic and solar activity was used to determine GAIM-GM forecast accuracy. Forecast accuracy was determined through the use of a skill score as well as other statistical tools to …