Using data from 75 ionosonde stations and 43 storms, and based on the knowledge gained from simulations from a physically based model, we have developed an empirical ionospheric storm-time correction model. The model is designed to scale the quiet time F region critical frequency (foF2) to account for storm-time changes in the ionosphere. The model is driven by a new index based on the integral of the ap index over the previous 33 hours weighted by a filter obtained by the method of singular value decomposition. Ionospheric data were sorted as a function of season and latitude and by the intensity of the storm, to obtain the corresponding dependencies. The good fit to the data at midlatitudes for storms during summer and equinox enable a reliable correction, but during winter and near the equator, the model does not improve significantly on the quiet time International Reference Ionosphere predictions. This model is now included in the international recommended standard IRI2000 [Bilitza, 2001] as a correction factor for perturbed conditions.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 The ionospheric behavior during quiet conditions is well known and efficiently modeled by the International Reference Ionosphere (IRI; Bilitza ). However, knowledge of the ionospheric response during geomagnetic storms and related process remains incomplete. Currently no empirical storm-time correction algorithm shows significant improvement over climatological reference models such as the IRI. To predict and model the ionospheric response during storms is therefore a high priority.
 There have been several attempts to simulate the storm-time response of the thermosphere and ionosphere using theoretical models [e.g., Crowley et al., 1996] and Parameterized Ionospheric Models (PIM; Daniell et al. ). The reviews by Prölss , Fuller-Rowell et al. , and Buonsanto  provide a reasonably comprehensive account of the current understanding. What have been noticeably lacking are the parallel developments of empirical ionospheric storm models that can take advantage of the recent advances. Mendillo  used midlatitude TEC data to look at storm-time templates based on analysis of a number of storms from a single station, but he did not try to link the template to a storm index. The design of the empirical model presented here relies on the theories developed by Prölss  and extended by Fuller-Rowell et al. .
 This theory suggests that long-lived negative storm effects are due to regions in which the neutral composition is changed. The neutral “composition bulge” is produced through heating by the magnetospheric energy input at auroral levels, causing upwelling of air that can then be moved to middle latitudes by nighttime equatorward winds and brought into the dayside as the Earth rotates. The prevailing summer-to-winter circulation, which transports the molecular rich gas to mid and low latitudes in the summer hemisphere over a day or two following the storm, explains the seasonal dependence. In the winter hemisphere poleward winds restrict the equatorward movement of the bulge. Consequently, the altered environment in summer depletes the F region midlatitude ionosphere to produce a negative phase, while in winter midlatitude a decrease in molecular species, associated with downwelling, persists and produces the characteristic positive storm. The seasonal migration of the bulge is superimposed on the diurnal oscillation driven by the normal diurnal variation of the meridional wind [Fuller-Rowell et al., 1994].
 There are, however, a number of physical processes operating during a storm that can result in changes in the ionosphere. At high latitude the direct action of the magneto-sources on plasma transport, by the convective electro field, and in ion production, by auroral particles precipitation, can at times dominate the plasma structure. Even here the present results suggest that an underlying consistent trend occur in all seasons. Lack of data is often a problem at high latitudes due to the disruption of the ionosonde radio signal by auroral absorption. Changes in the neutral wind during a storm also directly impact the ionosphere, as well as being the conduit through which neutral composition changes can occur. Wind surges, by gravity waves, and changes in the global circulation can both push plasma to a different altitude driving increases or decreases in plasma density. Electro field can strip away plasma a high midlatitudes and can penetrate to low latitudes.
 The ionospheric response to all of the physical processes are very difficult to capture and understand even with a complex physical model, and are even more difficult to capture in a simple empirical model as is attempted here. The details of the ionospheric response to a particular storm therefore are unique due to the many physical processes involved and due to the complexity of the driving processes from the magnetosphere. However, there are underlying trends in the response that can be captured, and provide a useful first step in characterizing the ionosphere response to storms in a relatively simple way.
 The most widely used empirical model is the IRI, an empirical standard model of the ionosphere, initially based on all available data from 1950 to 1975 and updated periodically. For a given location, time and date, IRI describes the electron density, electron temperature, ion temperature, and ion composition in the altitude range from about 50 km to about 2000 km; as well as the total electron content (TEC). It provides monthly averages in the non-auroral ionosphere for magnetically quiet conditions [Rawer et al., 1978]. The latest version of the IRI (IRI2000; Bilitza ) includes the STORM model as the correction for perturbed conditions.
2. Data Sources
 Because the strong seasonal dependence of the ionospheric response, rather than divide the data in solstice and equinoxes, we grouped the storms in five seasonal bins, including an intermediate season between winter or summer solstices (peak solstices) and the equinox. (Figure 3 shows the specific features of the ionospheric response for every season, where it is possible to see, mainly in the winter intermediate, that the particular response in the intermediate seasons differs from the corresponding “peak” solstice.)
 Tables 1a–1c and Table 2 show the data used in this study. Tables 1a–1c show the storms included, and the maximum Dst value for each one. The storms were sorted as a function of season, such that 7 storms occurred during the equinoxes (February 21 to April 21, and August 21 to October 21); 11 storms occurred during peak solstices (May 21 to July 21, and November 21 to January 21), and 7 storms during the previously described intermediate periods; between summer (winter) and equinoxes (January 21 to February 21, and October 21 to November 21), and, in the opposite hemisphere, between winter (summer) and equinoxes (April 21 to May 21, and July 21 to August 21).
|1||June 05, 1981||N||S||−119|
|2||June 10, 1982||N||S||−137|
|3||July 11, 1982||N||S||−325|
|4||November 22, 1982||S||N||−197|
|5||December 07, 1982||S||N||−106|
|6||December 15, 1982||S||N||−106|
|7||January 07, 1983||S||N||−213|
|8||June 10, 1983||N||S||−127|
|9||January 02, 1984||S||N||−86|
|10||December 08, 1987||S||N||−102|
|11||January 12, 1988||S||N||−147|
|1||July 23, 1981||N||S||−226|
|2||July 22, 1982||N||S||−155|
|3||February 04, 1983||S||N||−183|
|4||May 2, 1983||N||S||−86|
|5||November 09, 1983||S||N||−82|
|6||November 13, 1984||S||N||−141|
|7||July 26, 1987||N||S||−60|
|1||October 11, 1981||−113|
|2||October 20, 1981||−192|
|3||March 01, 1982||−211|
|4||April 10, 1982||−137|
|5||September 06, 1982||−289|
|6||September 22, 1982||−210|
|7||March 02, 1983||−167|
|Station||Code||Geomagnetic Latitude||Geomagnetic Longitude|
|1||Resolute Bay||RB974||83.2 N||292.9 E|
|2||Churchill||CH958||68.7 N||324.9 E|
|3||Kiruna||KI167||65.1 N||116.4 E|
|4||Sodankyla||SO166||63.6 N||120.8 E|
|5||Lycksele||LY164||62.5 N||111.7 E|
|6||Providenya Bay||PD664||59.9 N||237.1 E|
|7||Arkhangelsk||AZ163||58.7 N||129.1 E|
|8||Norilsk||NO369||58.6 N||165.7 E|
|9||Uppsala||UP158||58.3 N||106.9 E|
|10||Nurmijarvi||NU159||57.7 N||113.5 E|
|11||Ottawa||OT945||56.4 N||352.7 E|
|12||Leningrad||LD160||56.1 N||118.3 E|
|13||JuliusruhRugen||JR055||54.3 N||99.7 E|
|14||Slough||SL051||54 N||84.4 E|
|15||De Bilt||DT053||53.5 N||90.5 E|
|16||Kaliningrad||KL154||53 N||106.4 E|
|17||Lannion||LN047||52 N||80.1 E|
|18||Dourbes||DB049||51.7 N||88.9 E|
|19||Yakutsk||YA462||51.2 N||194.8 E|
|20||Magadan||MG560||50.9 N||211.6 E|
|21||Podkamennaya||TZ362||50.8 N||165.4 E|
|22||Miedzeszyn||MZ152||50.5 N||105.7 E|
|23||Moscow||MO155||50.4 N||123.2 E|
|24||Gorky||GK156||50.2 N||127.7 E|
|25||Poitiers||PT046||49.2 N||83 E|
|26||Wallops Is||WP937||49.2 N||353.9 E|
|27||Boulder||BC840||48.9 N||318.7 E|
|28||Sverdlovsk||SV256||48.5 N||139.6 E|
|29||Kiev||KV151||47.1 N||113.3 E|
|30||Graz||GZ146||46.7 N||98.1 E|
|31||Tomsk||TK356||46 N||160.6 E|
|32||Novosibirsk||NS355||44.2 N||158.9 E|
|33||Point Arguello||PA836||42.3 N||302.4 E|
|34||Rome||RO041||42.3 N||93.2 E|
|35||Irkutsk||IR352||41.2 N||175.5 E|
|36||Karaganda||KR250||40.3 N||149.8 E|
|37||Khabarovsk||KB548||38.1 N||201.3 E|
|38||Novokazalinsk||NK246||37.6 N||139.6 E|
|39||Tbilisi||TB142||36.2 N||123.2 E|
|40||Wakkanai||WK545||35.5 N||207.3 E|
|41||Alma Ata||AA343||33.5 N||151.9 E|
|42||Tashkent||TQ241||32.3 N||145.2 E|
|43||Ashkhabad||AS237||30.4 N||134.5 E|
|44||Akita||AK539||29.8 N||206.8 E|
|45||Kokubunji||TO535||25.7 N||206.7 E|
|46||Maui||MA720||21.2 N||269.6 E|
|47||Yamagawa||YG431||20.6 N||199.1 E|
|48||Ouagadougou||OU012||16.2 N||71.6 E|
|49||Okinawa||OK426||15.5 N||196.9 E|
|50||Taipei||TP424||13.8 N||190.9 E|
|51||Manila||MN414||3.6 N||191.1 E|
|52||Huancayo||HU91K||0.7 S||355.2 E|
|53||Vanimo||VA50L||12.3 S||212.5 E|
|54||Tahiti||TT71P||15.2 S||284.4 E|
|55||Darwin||DW41K||22.9 S||202.7 E|
|56||Johannesburgo||JO12O||27.2 S||92.8 E|
|57||La Reunión||LR22J||27.4 S||121.5 E|
|58||Townsville||TV51R||28.5 S||220.4 E|
|59||Capetown||CT13M||33.1 S||81.2 E|
|60||Norfolk Is||NI63_||34.5 S||244.6 E|
|61||Brisbane||BR52P||35.4 S||228.3 E|
|62||Port Stanley||PSJ5J||40.6 S||10.3 E|
|63||Camden||CN53L||42 S||227.6 E|
|64||Mundaring||MU43K||43.2 S||187.7 E|
|65||Canberra||CB53N||43.7 S||225.7 E|
|66||Salisbury||SR53M||44.4 S||213.9 E|
|67||Christchurch||GH64L||47.7 S||253.5 E|
|68||Hobart||HO54K||51.4 S||225.9 E|
|69||Argentine Is||AIJ6N||54 S||4.4 E|
|70||Campbell Is||CI65K||57.1 S||254.4 E|
|71||Kerguelen||KG24R||57.4 S||129.9 E|
|72||Syowa Base||SW16R||69.9 S||79.2 E|
|73||Mawson||MW26P||73.3 S||105.1 E|
|74||Terre Adelie||DU56O||75.3 S||232.4 E|
|75||Scott Base||SQ67Q||78.8 S||294.1 E|
 Table 2 shows the names, geomagnetic coordinates and codes of the ionosonde stations used in our study. With this group of stations, latitudes from 83.2 N (Resolute Bay) to 78.8 S (Scott Base) are covered with a reasonable latitudinal and longitudinal resolution, in an attempt to include all the characteristic ionospheric responses for different locations.
 In this analysis, foF2 hourly values for each site were used for a 5 days period for each storm (120 values). For the input to the model we use the time history of the geomagnetic index ap. All data was obtained from the NGDC Ionospheric Digital Database cd-rom and from the NGDC Space Physics Interactive Data Resource (http://spidr.ngdc.noaa.gov/)
3. Empirical Model
 Recent investigations have provided some insight and understandings to some of the expected dependencies in the ionospheric response to geomagnetic activity [Rodger et al., 1989; Fuller-Rowell et al., 1996]. The results indicate that the ionosphere responds to long-lived thermospheric composition changes.
 Based on this knowledge, a model taking into account the prior history of the geomagnetic index ap was designed [Araujo-Pradere and Fuller-Rowell, 2000]. Such design includes the regional dependence in the migration of the composition bulge by the diurnal wind field, and also includes an optimum shape of the ap index filter (to weight the time history of the input), and a non-linear dependence of the integral of the ap and the ionospheric response. Including all the features, the algorithm that describes the empirical model is given by Fuller-Rowell et al. :
where Φ = (foF2observed/foF2monthly mean), X(t0) = ∫F(τ)P(t0 − τ)dτ, and F(τ) is the filter weighting function of the ap index, P, over the 33 previous hours (Figure 1). The coefficients a0, a1, a2 and a3 have been adjusted to fit the non-linear relationship between the ionospheric response and the integral of the geomagnetic index ap.
 The analysis by Rodger et al.  showed a strong local time signature with a variation of about 40% in NmF2, but we have been unable to show such a strong dependence in the present analysis, so, at this point in the development of the empirical algorithm, we have not included the local time dependence represented by coefficient a4 in equation (1).
 The optimum shape and length of the filter shown in Figure 1 was obtained by the singular value decomposition method, minimizing the mean square difference between the filter input (ap index) and filter output (Φ, ionospheric ratios). Detman and Vassiliadis  presented a good discussion of this technique. The filter was constructed from mid latitude data only. Ideally, separate filters are required in all latitudes and seasonal conditions, but the approach was not feasible due to the limited size of the data sample at high and low latitudes.
 The dashed line in Figure 1 is the actual output of the numerical method, and the full line is the fit used in the empirical model. The ap values have a negative weight in the first hour, possibly due to the penetration effects of the electric field. During the next six hours there is a sharp peak that could be the consequences of the time-dependent response of the wind field to the gravity wave propagation. Finally, from the 7th hour to the 33rd hour, we suggest this is the effect of the development of a composition bulge. In general, this implies that, at midlatitudes the ionosphere is dependent on geomagnetic or auroral activity that occurred up to 33 hours before the time that is being observed.
 Figure 2 shows the equivalence between the Dst index and the integral of the ap index. The correlation between the two indexes of 0.78 was largest when the integral of ap was lagged by 4 hours with respect to Dst. The physical significance of this delay is not clear.
 Although not a perfect correlation, the relationship is reasonably linear, and enables the new index to be related to the more widely available and more familiar measure of the magnitude of a storm, the Dst index. This plot was obtained using the Dst and the ap values corresponding to all the storms listed in Tables 1a–1c. Note that Dst is not intended as a replacement of the integral of the ap index.
 The composition theory implied a seasonal-latitudinal dependence in the ionospheric response. To accommodate this dependence the model is designed to capture the changing response through the year and over latitude. With this objective, the data has been divided in high (60–80), low (0–20), and two mid latitude bins (20–40, 40–60); and for solstices, equinox, and intermediate seasons.
 In Figure 3, the results of sorting all the data by season and latitude is presented. The X axis corresponds to the integral of the ap index (input) and the Y axis corresponds to the ionospheric ratios, Φ = foF2obs/foF2mm (output). Here, the data shows a consistent negative response in summer midlatitudes, while in the winter hemisphere the response is not so well defined, showing a boundary around 40°. The consistent response in summer is likely due to the prevailing summer-to-winter circulation. In the winter hemisphere, theory suggests a boundary exists in the prevailing circulation and in the composition response. Such a boundary also exists in the sorted data producing a negative phase in latitudes greater than 40°, while in lowest latitudes a decrease in molecular species, associated with downwelling, persists and produce the characteristic positive storm.
 Another important difference between summer and winter hemispheres is the variability in both sets of data. Summer hemisphere and equinox mid latitudes show a very coherent behavior, with the variability band around the fit following the negative phase, while the winter hemisphere shows a high dispersion around the fit. In each panel a polynomial cubic fit to the data has been determined to provide the set of coefficients “a0,” “a1,” “a2,” and “a3” required in equation (1).
 In general, the storm time ionospheric behavior at equinox is close to that at summer, with a well defined tendency for a negative phase, i.e. lower values than monthly mean for perturbed conditions.
 Figure 4 shows the “goodness of fit,” i.e. a measure of how well the chosen model dependencies fit the data, presented in the same format as Figure 3 (separation by latitude and seasons). In each panel the root-mean square-error (RMSE) between the original data and the empirical model fit to the data is shown as a function of the integral of the power. Also shows, for comparison, are the equivalent profiles when using climatology (in this case the monthly mean).
 The summer hemisphere shows a significant reduction in RMSE, compared with the climatology, while the winter hemisphere does not show an improvement.
 Using equation (1), and the results presented in Figure 3, a program has been constructed in FORTRAN 77, to obtain the scaling factor, under perturbed conditions, for correcting the storm-time effects in the ionosphere. This correction has now been included in the International Reference Ionosphere, IRI 2000 [Bilitza, 2001]. It is feasible for the correction to be used in other quiet time climatological ionospheric model.
 The program uses as input an array of 13 values of the 3-hourly ap index. The last value in the array will contain the ap at the Universal Time (UT) of interest; the 12th value will contain the 1st three hourly interval preceding the time of interest, and so on to the first ap value at the earliest time.
 For a user-prescribed location in geographical or geomagnetic coordinates, and the day of the year (doy), the program selects the four closest points to the doy and location of interest, two to define the seasons and two to define the latitudes, and makes a weighted linear interpolation to obtain the best value for the point of interest, checking in each pass if the input data, day of the year, UT, and coordinates are within the limits.
 As output, the program gives the Correction Factor (CF) used to scale the IRI or any other quiet time reference (QT), using the expression:
Running the program for one full year, in five-day steps, and for the integral of a power from 500 to 6000 (steps of 500), we obtained the picture shown in Figure 5, for different values of geomagnetic latitude.
 The upper portion of Figure 5 corresponds to the southern hemisphere, and the lower to the northern hemisphere. Each plot was calculated for one latitudinal point, and for all seasons. X axis is the day of the year (doy), Y axis the integral of ap, and Z axis the modeled ratio of foF2.
 It is possible to observe several features in Figure 5. The deepest negative phases, in summer, are in the Polar Regions, where the composition bulge (the physical cause of the long-lived negative phase) is very well defined. Related to the same causes, there is a negative phase in winter high latitudes (greater than 40°) while in lowest latitudes, where the bulge doesn't reach, a decrease in molecular species, associated with downwelling, persists and produces the characteristic positive storm.
 Because of the lack of observations and the poor understanding of the different low-latitude physical processes involved, the correction model is not expected to capture the response near the equator. This will be the subject of a further study, after physical understanding of the low latitude storm-time response has matured.
 We have implemented a real time operational test version of the STORM model (http://sec.noaa.gov/storm/), using as input the hourly determination of ap over the previous 3 hours given by the USAF Hourly Magnetometer Analysis Reports (http://sec.noaa.gov/ftpdir/forecasts/MA/oldMAhr.txt). In this case the model uses the last 33 values of the hourly estimated ap affected by the filter in Figure 1, so the model output is updated every hour. An example of the operational test version of STORM can be seen in Figure 6, where the output of the model for the Bastille Day storm is shown. Araujo-Pradere and Fuller-Rowell  extensively tested the prediction of the model for this particular storm.
 In order to avoid the running of the model for quiet conditions, we have imposed the condition that a storm correction is only made if the filtered ap exceeds 200, i.e.,
For this case, the use of the monthly mean, or any other quiet time reference (CF = 1), is adequate.
 The condition imposed, a filtered ap of 200, is equivalent to a steady Kp of 2+ or ap of 8 over the previous 33 hours. From Figure 2 this corresponds to a Dst greater than −15 nT.
 The empirical storm-time correction model has been tested on many periods [Fuller-Rowell et al., 2001; Araujo-Pradere and Fuller-Rowell, 2002] but only a twenty-five day interval toward the end of 1997, between November 12 and December 6 is shown here. This storm, November 22/23, 1997, was not part of the study, so it is an independent test of the new algorithm.
 Figure 7 shows the ionospheric response, and the empirical model prediction, for the significant disturbance that occurred on November 22/23, 1997. The left Y axis of the two upper panels correspond to the foF2 ratio, while the right Y axis is the integral of ap for the previous 33 hours.
 The disturbance can be seen in the lower panel as a large increase shown by the ap index, and by the corresponding integral of ap (in the upper panels), coinciding with the ionospheric response at two sites in similar latitudes but in different hemispheres, Rome in the northern winter midlatitudes (41.9N, 12.52), and Grahamstown, SA, in the southern summer midlatitudes (33.3S, 26.5).
 At Rome, the ionospheric response is positive, consistent with expectations in winter midlatitudes (a not well defined composition bulge, and a decrease in molecular species, associated with downwelling). At Grahamstown, the ionospheric F region decreases, again consistent with expectations in summer midlatitudes (a very well defined composition bulge). In both cases, the empirical model captures the direction of the change, and the magnitude is particularly good in summer, and for the peak of the storm as expressed by the integral of ap.
 From the examples shown it is clear that the empirical model improves the prediction of the IRI model for summer conditions, mainly for deep negatives phases, reaching up to 50% improvement for the summer example in Grahamstown.
 For winter conditions, the example in Figure 7 indicates only a slight improvement over climatology, consistent with the more general result from Figures 3 and 4 that winter storm-time corrections are more challenging.
 A more comprehensive validation of the model is detailed in a companion paper [Araujo-Pradere and Fuller-Rowell, 2002].
7. Summary and Conclusions
 The goal of this work was to capture the global ionospheric response to a geomagnetic storm in a simple empirical model. Due to the complexity of the system and the many physical processes involved, this task is far from trivial. This complexity has hindered progress in understanding the balance between the various processes, including the production and transport at high latitudes, the effect of the coupling of the ionosphere to changes in winds and composition of the neutral atmosphere, and the impact of electrodynamics. A full understanding of the global system has yet to be realized but over the last few years sufficient knowledge has been acquired to make the first step in the development of an empirical model.
 Guided by the emerging physical understanding of the system the current empirical model was developed by sorting ionospheric data as a function of season, in five separate intervals, and in four geomagnetic latitude regions. Data from 75 ionospheric stations and 43 separate geomagnetic storms were used to cover the range of latitudes and seasons. In each seasonal/latitudinal bin, the change in the ionospheric F region peak critical frequency (ratio to the monthly mean) was recorded as a function of the intensity of the storm. A new index was developed to characterize the intensity of the storm by integrating the previous 33 hours of ap, weighted by a filter. The output of the model provides a simple correction to the quiet time F-region peak critical frequency due to the storm.
 The initial validation study indicates that the output from the empirical storm-time correction model provides a significant improvement in equinox and summer, but in winter no quantitative improvement can be demonstrated. This model has been included in the new International Reference Ionosphere (IRI2000, Bilitza ) in an effort to include a dependence on geomagnetic activity within this climatological model. A more comprehensive validation study is required and will be presented in subsequent paper.