John Retterer

Air Force Research Laboratory



1. Model Content

The PBMOD ionospheric model is a system of Physics Based MODels that describes the three-dimensional time-dependent evolution of the low-latitude ionosphere on several different spatial scales: globally it provides the plasma density and composition at altitudes between 90 and 2000 km; at finer scales it describes the development of fluid plasma turbulence within this region and the resulting radio scintillation. The numerical model of the ambient (global scale) ionosphere yields density distributions for electrons and several ion species (O+, H+, and NO+, O2+, N2+) as a function of latitude, longitude, and altitude on a prespecified spatial grid at specified times. The system also includes models that evaluate the growth rate for the generalized Rayleigh-Taylor instability, perform evolutionary calculations of the self-consistent nonlinear development of equatorial low-density plasma plumes/bubbles, and perform a phase-screen calculation to estimate the strength of amplitude and phase scintillation of radio signals passing through the turbulent structure.


Numerous physical and chemical processes are contained in the model, including field-aligned diffusion, cross-field electrodynamic drifts, thermospheric winds, ion production due to EUV radiation, chemical and other collisional processes.  The model uses the IGRF geomagnetic field model for an accurate depiction of the Earth's magnetic-field geometry.  Depending on the inputs, the global ionospheric model can describe different solar cycle, seasonal, and daily variations. It can describe the low-latitude effects of geomagnetic storm dynamics.


Built to be the forecast model in the C/NOFS (Communication and Navigation Outage Forecast System) Data Center, a demonstration of a potential operational system, the models employ robust numerical techniques, and are designed to be fault-tolerant of data dropouts and noise in the ingested data from the satellite and other sensors.  (One implementation of the model has been providing climatology-based forecasts of UHF and L-band scintillation every six hours since 2008 for the Space Environment Technologies CAPS web site, with the only outages being those of the host computer.)  The models have been validated with in-situ satellite data (CHAMP, DMSP, C/NOFS), ionosonde data, Jicamarca ISR data, JASON vertical TEC data, and SCINDA scintillation data.



2. Model uncertainties and limitations


2.1 To a large extent, the reliability of the calculated ionospheric parameters depends on the accuracy to which the global inputs have been specified. The ambient ionospheric model is particularly sensitive to the equatorial electric field (including both penetration and dynamo fields), but also depends on thermospheric winds, neutral densities, plasma temperatures, and plasma production rates.

2.2  The plasma plume model depends on the parameters in 2.1, and is additionally dependent on the choice of ‘seed’ or initial perturbation for plume development.

2.3  The structuring of the plasma in the turbulent plumes does not feed back into the ambient model.

2.4 A Beowulf-class supercomputer (i.e., multiple processors) is needed for global simulations.


3. Basis of the model


3.1  The ambient plasma density model calculates the O+ and H+ densities by solving the coupled ion momentum and continuity equations numerically using a Crank-Nicholson implicit finite differencing technique along closed geomagnetic fields lines near the geomagnetic equator, in a code originally developed by D. N. Anderson in 1973 (LOWLAT).  The flux tubes are allowed to convect through the neutral atmosphere in directions perpendicular to B as a consequence of electric-field drift.  The three-dimensional nature of the model is obtained by following many flux tubes of plasma while keeping track of their positions at all times. The model includes the effects of production by solar EUV radiation, loss through charge exchange with the neutral atmosphere and transport by E x B drift, ambipolar diffusion, and momentum exchange with the neutral atmosphere through collisions.  The density of the molecular ions NO+ , O2+, and O2+  are calculated under the chemical equilibrium assumption that production equals loss, without transport effects.  Electric fields and plasma temperatures are specified a priori, and are not calculated self-consistently.


3.2 The transport model for the mesoscale plumes requires the simultaneous solution of the nonlinear continuity and momentum equations with electric fields calculated self-consistently using the principle of current continuity.  Transport processes parallel and perpendicular to the geomagnetic field are treated separately using an operator-splitting technique, with the LOWLAT algorithm from the ambient code for parallel transport, and a flux-corrected transport algorithm for the perpendicular motion.  An Eulerian grid, typically of an altitude range of 1000 km and a similar East-West extent, defines the grid in the plane of the geomagnetic equator; transport along each field line is described down to altitudes of 90 km at the ends.  From an initial, arbitrary density perturbation, the evolution of the F-region plasma is followed self-consistently, allowing low-density plasma plumes or bubbles to develop if the plasma is unstable to interchange instabilities.   Numerous diagnostics, including snapshots of density and velocity, irregularity spectra, and airglow depletion images are available.


3.3 The phase-screen calculation of the strength of radio scintillation relies on spectra of the total electron content integrated along the signal ray path through the turbulent ionosphere; extrapolation down to the Fresnel wavelength (sub-km) regime relevant for scintillation is necessary.  The simple asymptotic behavior of amplitude scintillation when irregularities are strong permits extrapolation of the phase-screen result into a more general description.



4. Model Input Parameters


The ionospheric model requires several inputs.  The main global inputs are the neutral densities, temperatures, and winds; the magnetospheric and equatorial electric field distributions and histories; the plasma temperatures; the plasma production rate; and the seed perturbation for the plume calculation. Typically, empirical or statistical models are used for these inputs. For storm simulations, the temporal variation of the magnetospheric and atmospheric inputs must be specified.  Simple scalings with the interplanetary electric field (as provided by the solar-wind parameters measured by the sensors on the ACE satellite or forecast by a solar-wind model) can provide a rough estimate of the penetration field and thermospheric energy input in storm events.  Alternatively, the model can be driven by parameters obtained from a run of TIEGCM, the NCAR general circulation model, or another thermospheric model.  Additionally, since PBMOD was designed as the ionospheric forecast model for the C/NOFS program, in-situ or other measurements can also be used to specify or constrain the variation of the driving parameters of the model.



5. Publication References


5.1 "Assimilative Modeling of the Equatorial Ionosphere for Scintillation Forecasting: Modeling with Vertical Drifts," J. Geophys. Res., 110, A11307, (2005) (J. M. Retterer, D. T. Decker, W. S. Borer, R. E. Daniell, and B. G. Fejer)

5.2 “Physics-based forecasts of equatorial radio scintillation for C/NOFS,” Space Weather Journal, 3, S12C03, (2005) (J. M. Retterer)

5.3 “Forecasting Low-Latitude Radio Scintillation with 3-D Ionospheric Plume Models: I. Plume Model”, J. Geophys. Res., doi:10.1029/2008JA013839, (2010) (J. M. Retterer)

5.4 “Forecasting Low-Latitude Radio Scintillation with 3-D Ionospheric Plume Models: II. Scintillation Calculation”, J. Geophys. Res., doi:10.1029/2008JA013840, (2010) (J. M. Retterer)

5.5 “Solar wind drivers for low-latitude ionosphere models during geomagnetic storms”, J. Atmos. Solar-Terr. Phys., doi:10.1016/j.jastp.2009.07.00,3 (2010), (J. M. Retterer and M. C. Kelley)

5.6Guide to reference and standard ionosphere models”, American Institute of

Aeronautics and Astronautics, ANSI/AIAA publication G-034-2011.



6. Dates of Development, Authors, and Sponsors:


6.1 Dates of Development

1997: D. N. Anderson LOWLAT code (1973) adapted for low-latitude ionosphere.

1998: Two-dimensional plasma bubble code written.

2001: PBMOD system concept organized.

2002: IGRF geomagnetic field model incorporated.

2004: Three-dimensional plasma bubble code developed.

2008: Coupling to TIEGCM.

2010: Coupling to solar-wind models


6.2 Author: John M. Retterer (john.retterer@hanscom.af.mil or john.retterer@gmail.com).


6.3 Sponsors:  AFRL, AFOSR, NASA.