Problems associated with uncertain parameters and missing physics for long-term ionosphere-thermosphere forecasting



[1] Data assimilation models like the Utah State University (USU) Global Assimilation of Ionospheric Measurements (GAIM) models use physics-based models of the ionosphere, ionosphere-plasmasphere, or thermosphere and a Kalman filter as a basis for assimilating a diverse set of measurements. With a sufficient amount of data and with multiple data types, the data assimilation models can provide reliable specifications and near-term forecasts. However, for long-term forecasts (5 days or longer) stand-alone or coupled physics-based models are needed. Unfortunately, the various physics-based models contain several uncertain parameters and processes as well as missing physics. Further complications arise for coupled physics-based models because of coupling issues and error propagation from model to model. Some of the problems are associated with the magnetosphere and lower atmosphere drivers, the adopted set of physics-based equations, the parameterization of physical processes, the values adopted for the transport coefficients, the numerical techniques used, the spatial and temporal resolutions adopted, and the uncertainties in the initial and boundary conditions. Examples of the type of problems the space weather community faces in its attempt at long-term ionosphere-thermosphere forecasting are given.

1. Introduction

[2] It is well known that the near-Earth space environment can vary markedly from day-to-day and from hour-to-hour, particularly during geomagnetic storms and substorms. Strong variations can occur at all latitudes, longitudes and altitudes, and they can occur over a wide range of spatial and temporal scales. Unfortunately, the daily and hourly variations that occur in the ionosphere-thermosphere system can have a detrimental effect on numerous military and civilian operations and systems. They can affect High-Frequency (HF) communications, Over-The-Horizon (OTH) radars, GPS navigation systems, surveillance, electric power grids, ocean drilling operations, deep space tracking, the FAA's Wide Area Augmentation System (WAAS) system, and satellite lifetimes. Because of society's increasing reliance on advanced technology, there is a need for long-term ionosphere-thermosphere (I-T) forecasts so that the operators affected by space weather disturbances can mitigate potential problems. Recently, the length of the forecast that is needed has been increased from 3 to 5 days, and the focus of this study is to elucidate some of the difficulties associated with achieving this goal.

2. Thermosphere-Ionosphere Environment

[3] In order to provide forecasts that the applications community can use in routine operations, the forecasts must describe the real environment. Specifically, the forecasts cannot just describe large-scale ionosphere-thermosphere features (e.g., time-dependent climatology). Typically, the I-T system contains mesoscale (100–1000 km) and small-scale (10–100 km) density structures and these structures drift from region to region and evolve with time. At high latitudes, the mesoscale plasma structures include tongues of ionization, aurora and boundary blobs, theta aurora, Sub-Auroral Ion Drift (SAID) events, propagating plasma patches (Figure 1a), and sun-aligned polar cap arcs (Figure 1b). At middle and low latitudes, there are Storm Enhanced Density (SED) ridges (Figure 1c) and equatorial plasma bubbles (Figure 1d). Examples of mesoscale neutral density/wind structures include the cusp neutral fountain, propagating atmospheric holes, and supersonic neutral winds. These mesoscale and small-scale structures have a significant impact on numerous systems and operations, and if their presence is not included in a forecast, the forecast may be of limited value.

Figure 1.

Examples of I-T plasma density structures. (a) Propagating plasma patches over Greenland during a southward Interplanetary Magnetic Field (IMF) configuration [Fukui et al., 1994]. (b) Sun-aligned polar cap arcs over Greenland for a northward IMF [Valladares et al., 1994]. (c) A SED over the United States during a geomagnetic storm [Schunk et al., 2005]. (d) A radar signature of equatorial spread-F and plasma bubbles [Hysell and Burcham, 1998].

3. Forecasting Tools

[4] Physics-based global models are useful for describing the dynamic evolution of the near-Earth space environment, and hence, they are good candidates for forecasting. With this approach, transport equations (continuity, momentum, energy, etc.) are solved numerically in 3-dimensions as a function of time in order to obtain the evolution of the relevant densities, flow velocities and temperatures. To date, physics-based global models have been developed for the thermosphere, ionosphere, plasmasphere, polar wind, exosphere, and magnetosphere, and over the years, there have been various levels of global model coupling in the near-Earth space environment. More recently, Sun-to-Earth coupled global models have been developed via the CISM and the Space Weather Modeling Framework programs. Also, global ionosphere-thermosphere models that couple to lower atmospheric models are now available. Some representative references includeBailey and Balan [1996], Barakat and Schunk [1984], Burns et al. [1995], Crowley et al. [1989], Fedder et al. [1995], Fuller-Rowell et al. [1996], Huba et al. [2008], Ma and Schunk [1995], Millward et al. [1996], Raeder [1999], Richards and Torr [1996], Ridley et al. [2006], Roble [1996], Schunk [1988], Rasmussen and Schunk [1988], Schunk and Sojka [1989, 1997], Schunk et al. [1997], Siskind et al. [2007], Sojka [1989], and Tóth et al. [2005].

[5] Possible forecasting schemes based on physics-based global models can include data driven, data assimilation and coupled models. Using the ionosphere as an example, a data driven model is one where the inputs (solar, magnetosphere and/or lower atmosphere) are obtained from measurements and they are used to drive the physics-based ionosphere model. With data assimilation models, ionospheric measurements and the output of the physics-based model are combined to obtain a reconstructed ionospheric state, and depending on the technique, it is also possible to obtain the self-consistent ionospheric drivers (neutral densities, winds, and electric fields). With coupled global models, the drivers (inputs) needed by one model are obtained from other global physics-based models. If the physics and chemistry in the physics-based global models were accurate, then the output of the global models would be reliable. Unfortunately, there are uncertain parameters and missing physics in all of the physics-based global models and this impacts both short-term and long-term forecasts.

4. Specifications and Short-Term Forecasts

[6] Specifications and short-term forecasts are best accomplished with data assimilation models. This is true because the data driven and coupled model approaches probably will not get the current state correct due to the uncertain parameters and missing physics in the physics-based models. If a physics-based model is run forward in time starting from an incorrect specification, then the short-term forecast will be wrong.

[7] An example of the value of a physics-based data assimilation model is shown inFigure 2. The figure is a snapshot from a regional run of the Utah State University (USU) Global Assimilation of Ionospheric Measurements-Gauss-Markov (GAIM-GM) data assimilation model for the large magnetic storm that occurred on November 20–21, 2003 [Scherliess et al., 2004, 2006, 2011; Schunk et al., 2004a, 2004b, 2005]. Ground Total Electron Content (TEC) measurements from 332 GPS receivers covering the U.S. and Canada were assimilated in the GAIM-GM model. More than 2000 slant TEC values were assimilated every 15 min. Bottom-side electron density profiles from the ionosondes at Dyess and Eglin Air Force bases were also assimilated.Figure 2 shows a snapshot at 20 UT on day 324. Figure 2(top) shows a snapshot of the output from the background, physics-based, Ionosphere Forecast Model (IFM) [Schunk et al., 1997] (no data assimilation), the Figure 2(middle) shows the GAIM-GM TEC reconstruction, andFigure 2(bottom) shows the measured TEC plotted at 350 km (slant TEC converted to the vertical). A ridge of Storm Enhanced Density (SED), which extends from Florida to the Great Lakes, is clearly evident in the data and is reproduced by the GAIM-GM data assimilation model.

Figure 2.

The output from the USU GAIM Gauss-Markov data assimilation model for the magnetic storm that occurred on November 20–21, 2003. (top) The TEC distribution obtained from the physics-based IFM (no data assimilation), (bottom) the measured TEC at the 350 km pierce point (slant TEC converted to the vertical), and (middle) the GAIM-GM reconstruction, where the slant TECs were assimilated into the IFM. The snapshot is for day 324 in 2003 at 2000 UT. FromSchunk et al. [2005].

[8] The physics-based model (IFM) does not reproduce the SED feature and yields TEC values outside of the SED region that are too high. This erroneous output is a result of missing physics in the IFM. Specifically, the SED is a result of high-latitude electric fields that penetrate to the middle-low latitude region [Foster et al., 2005; Heelis et al., 2009] and these penetrating electric fields are not included in the IFM. Likewise, the thermosphere model used in the IFM (MSIS [Hedin, 1987]) does not properly describe the large O/N2depletions that occur in major magnetic storms, and this is why the TECs obtained from the IFM are too large. Nevertheless, the data available for the storm period were sufficient to overcome the shortcomings in the IFM, and as a consequence, the GAIM-GM model was able to provide a reliable specification of the current state of the ionosphere over the United States.

[9] With a reliable ionospheric specification, a short-term forecast can now be made. One can just run the physics-based model forward in time starting from this specification. It may also be possible to estimate the temporal variation of the magnetospheric inputs and then run the physics-based model forward in time. Other schemes are possible, and an extensive validation effort is needed to determine which scheme is best for the different geographical regions and for different geomagnetic conditions.

5. Long-Term Forecasts With Coupled Global Models

[10] Long-term reliable forecasts are probably best accomplished with coupled, physics-based, global models that extend from the Sun's surface to the Earth's surface. Unfortunately, however, the current global models are not advanced enough to provide reliable elements for a Sun-to-Earth chain of models, and error propagation from model to model is a serious issue.

[11] The problem with coupled global models can be illustrated with the aid of the NCAR Thermosphere-Ionosphere Nested Grid (TING) model and the USU GAIM-GM data assimilation model [Jee et al., 2007, 2008]. The NCAR TING model was run in its “standard” coupled mode (S_TING) for the period April 1–4, 2004, which contained both quiet and disturbed periods. The USU GAIM-GM data assimilation model was run for the same period using slant TEC from ground receivers, bottom-side Ne profiles from ionosondes, and in situ Nedensities along DMSP satellite orbits. The ionosphere obtained from the TING model was significantly different from that obtained from the GAIM-GM model, particularly during disturbed times. The GAIM-GM ionosphere is expected to be more reliable than the TING ionosphere because it was based on data. Therefore, the TING model was rerun with the GAIM-GM ionosphere supplied to it at each TING time step in order to see the effect on the thermosphere of using a different ionosphere (G_TING). There were large neutral wind, temperature, and composition differences when the GAIM-GM ionosphere was used.Figure 3shows a snapshot of neutral temperature distributions during a disturbed time. When the GAIM-GM ionosphere was used to drive the TING model (G_TING), the neutral temperatures increased by as much as 40% (409 K) in a large region in the northern hemisphere.

Figure 3.

Snapshot of the neutral temperature distributions (middle) from the TING coupled physics-based model (S_TING) and (top) from the TING thermosphere driven by the GAIM ionosphere (G_TING). (bottom) The percentage difference of the neutral temperature distributions (G_TING – S_TING). The pressure level z = 2 corresponds to about 300 km. The results are for day 95 in 2004 at 00:00 UT. FromJee et al. [2008].

[12] The conclusion is that if one of the coupled global models does not produce accurate results, then unreliable results may be obtained from other global models in the modeling chain. For a modeling chain that extends from the Sun-to-Earth, all of the elements in the chain have problems because of uncertain parameters and missing physics.

6. Uncertain Parameters and Missing Physics

[13] The problems with coupled global models is that they are usually based on relatively simple mathematical formulations, the spatial and temporal resolutions are coarse, many of the parameters in the models are uncertain, the coupling between the models is approximate or incomplete, and there is missing physics in all of the global models. A few examples are given for the ionosphere-thermosphere models in the following paragraphs.

[14] Figure 4is a schematic diagram of the processes that affect ion outflow at high latitudes. Most of these processes have been included in ionosphere-polar wind simulations [Barakat and Schunk, 2006], but the continual loss of plasma due to the polar wind is not taken into account in the global ionosphere-thermosphere models. Typically, a breathing boundary condition is adopted at the upper boundary in these global models, which means that plasma can flow through the boundary but what flows up eventually flows back down. However, the continual loss of plasma at high latitudes in both the northern and southern hemispheres is significant and should have an appreciable effect on the ionosphere-thermosphere system. The global models need to be modified to account for this process if reliable forecasts are desired.

Figure 4.

Schematic diagram showing the processes that affect ion outflow from the ionosphere at high latitudes. From Schunk and Sojka [1997].

[15] Figure 5is a schematic diagram of another process that is not included in global ionosphere-thermosphere models. As the polar wind H+ and O+ ions flow upwards (designated by i in Figure 5), they can undergo charge exchange reactions with the background thermal and energetic neutrals, thereby creating up-flowing Hs and Os stream neutrals (designated by n in Figure 5) [Gardner and Schunk, 2004, 2005]. The Hs stream neutrals have sufficient energy to escape, but the Osstream neutrals do not have sufficient energy to escape and fall back on the ionosphere-thermosphere system. This effect is not included in the current global models, but the exact effect that this process has on the global models has not been fully elucidated.

Figure 5.

Schematic diagram showing the creation of streaming charge exchange neutrals (Hs and Os; designated by n) created from up-flowing H+ and O+ ions (designated by i). The Hs neutrals have sufficient energy to escape. The Osneutrals do not escape and provide for a neutral rain on the ionosphere-thermosphere system. FromGardner and Schunk [2005].

[16] The third example of missing physics is also connected with the polar wind. As the polar wind plasma flows up and out of the topside ionosphere, it interacts with the overlying polar rain. The energy gained by the polar wind electrons from the hot polar rain electrons is subsequently conducted down into the underlying ionosphere, thereby raising the ionospheric electron temperature [Schunk et al., 1986]. This elevated electron temperature then affects the ion temperature and plasma densities. Figure 6provides a snapshot of recent Time-Dependent Ionosphere Model (TDIM) simulations of the effect of downward electron heat flows into the high-latitude ionosphere [David et al., 2011]. Results are shown for solar minimum, winter, and quiet magnetic conditions, and the snapshot corresponds to 0500 UT. Three topside electron heat flow (QT) values were adopted in three separate simulations, and the largest value is consistent with values deduced from measurements [Bekerat et al., 2007]. For the largest downward electron heat flow, NmF2 can change by up to a factor of 10 in some regions of the polar cap. This effect is not included in the current global models.

Figure 6.

Comparison of plasma parameters from three ionosphere simulations with different downward electron heat flows into the ionosphere (QT). The simulations were for solar medium (F10.7 = 160), winter (day 357), and quiet (Kp = 2) conditions. The plasma parameters are noted on the right and the downward heat flow values are (left) 0, (middle) 0.5 and (right) 1.5 × 1010 eV cm−2 s−1. From David et al. [2011] (with permission).

[17] There are numerous uncertain parameters in the global ionosphere-thermosphere models, including chemical reaction rates, photo-ionization rates, collision frequencies, diffusion coefficients, viscosity coefficients, thermal conductivities, etc. One of the most important uncertain parameters is the O+- O collision frequency, and it will be used as an example of the effect that an uncertain parameter can have on the ionosphere. Global ionosphere-plasmasphere simulations were conducted using the standard O+- O collision frequency and then these simulations were repeated with the O+- O collision frequency multiplied by a factor of 2 [Jenniges, 2011; Jenniges et al., 2010]. The results of the two simulations were subtracted so the effect of the factor of 2 uncertainty could be clearly seen. The simulations were conducted with the Ionosphere-Plasmasphere Model (IPM) [Schunk et al., 2004a, 2004b; Scherliess et al., 2004]. One of the geophysical conditions considered was solar minimum, December solstice, and low magnetic activity. For this case, Figure 7 shows snapshots of the percentage differences in electron density distributions (factor of 2 run – factor of 1 run) at selected local times. The Ne differences are shown as a function of altitude and latitude for 0° east longitude. The greatest differences occur in the equatorial region, where an electron density difference of more than a factor of 2 can occur. Increasing the O+- O collision frequency by a factor of 2 above its default value leads to enhanced electron densities at night (04 – 08 LT) in and above theF region and decreased electron densities below the F region. With an enhanced O+- O collision frequency, the upward wind-induced plasma drift is increased and this acts to decrease the electron densities below theF region. This upward transport of plasma, coupled with the slower rate of downward diffusion (due to the enhanced collision frequency) accounts for the elevated electron densities in the F region. Therefore, the uncertainty in the O+- O collision frequency is a serious problem for accurate forecasting using coupled global models.

Figure 7.

Snapshots of the differences in electron density distributions due to differences in the O+- O collision frequency (factor of 2 – factor of 1). The Ne differences are shown at selected local times as a function of altitude and latitude for 0° east longitude. The geophysical conditions are for solar minimum, December solstice, and low magnetic activity. From Jenniges [2011] (with permission) and Jenniges et al. [2010].

7. Summary and Discussion

[18] Disturbances in the Ionosphere-Thermosphere (I-T) system can have detrimental effects on military and civilian operations and systems, and therefore, both short-term and long-term (5-day) forecasts are needed. Reasonable short-term forecast can probably be achieved with physics-based data assimilation models, where the data assimilation model provides the specification and the physics-based model provides the short-term forecast. Work in this area has only just begun.

[19] Long-term I-T forecasts, on the other hand, require physics-based, global, coupled ionosphere-thermosphere models and work in this area is proceeding. However, we have shown that “the current, physics-based, global Ionosphere-Thermosphere models are not adequate for long-term forecasting.” This is true because the physics-based I-T models contain uncertain parameters and missing physics. Additional problems arise because of I-T model coupling issues, error propagation from model to model, the uncertainty associated with magnetosphere and lower atmosphere drivers, the adopted set of physics-based equations, the parameterization of physical processes, the values adopted for the transport coefficients, the numerical techniques used, and the spatial and temporal resolutions adopted. Examples have been presented in the previous sections that demonstrate the current I-T models are not adequate for long-term forecasting. Hence, global I-T models will not provide reliable long-term forecasts unless a significant effort is devoted to improving the existing ionosphere and thermosphere models.

[20] The problem with global I-T models was clearly elucidated in recent community-wide efforts to compare global physics-based models, including various combinations of stand-alone and coupled ionosphere, thermosphere, plasmasphere, and electrodynamics models. In the Equatorial PRIMO effort (T.-W. Fang et al., Comparative studies of theoretical models in the equatorial ionosphere, submitted toModeling the Ionosphere-Thermosphere System, Geophysical Monograph Series, AGU, Washington, D. C., 2012), 12 different models were compared for the same conditions in order to see how well the models reproduced the Equatorial Ionization Anomaly (EIA). Typically, the spread in model results was more than a factor of 2 and as large as a factor of 5. In general, the performance of the coupled models was worse than the stand-alone models; the coupled models had difficulty in describing the latitudinal variation of the EIA. There was also a CEDAR challenge for a systematic quantitative comparison of physics-based I-T models with observations; 8 global models were evaluated [Shim et al., 2011]. No model ranked the best. The physics-based I-T models displayed significant differences from each other and from the data at most times and locations.

[21] Numerous applications that are relevant to radio science depend on reliable I-T forecasts. Single-frequency GPS receivers are adversely affected by the ionosphere and this is relevant to navigation and geo-location applications. If I-T forecast model predictions produce electron density enhancements and depletions in the wrong place, then the accuracy of the GPS receivers will be seriously degraded. Also, if the ionospheric density gradients are wrong (e.g., too steep, too shallow, or in the wrong place), HF communications and OTH radar propagation paths can be significantly affected. Therefore, as noted above, reliable long-term I-T forecasts are needed and this will require a significant improvement in the existing physics-based, global, coupled ionosphere-thermosphere models.


[22] This research was supported, in part, by NSF grant AGS-0962544 and ONR grant N00014-09-1-0292 to Utah State University.