Ionospheric climatology and variability from long-term and multiple ...

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, A06328, doi:10.1029/2006JA012206, 2007

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Ionospheric climatology and variability from long-term and multiple incoherent scatter radar observations: Climatology in eastern American sector Shun-Rong Zhang1 and John M. Holt1 Received 6 December 2006; revised 9 April 2007; accepted 12 April 2007; published 29 June 2007.

[1] Ionospheric climatology and variability studies are conducted using long-term

incoherent scatter radar (ISR) observations from seven sites around the world. These studies result in an empirical model system, the ISR Ionospheric Model (ISRIM), which represents local and regional ionospheric climatology and variability of the ionosphere. This paper addresses some new climatological features revealed by the model for latitudes spanning 18–70°N over the eastern American sector. The latitudinal change of the F2-layer electron density exhibits a clear depletion near Millstone Hill latitudes when solar activity is median or low, accompanied by a Te enhancement, and electron density peaks at 10° both to the north and south of Millstone Hill. Possible explanations are discussed. We also characterize several types of variation in plasma temperatures in this region, including ion temperature elevation for quiet conditions in the auroral zone and electron temperature increases toward higher latitudes. Citation: Zhang, S.-R., and J. M. Holt (2007), Ionospheric climatology and variability from long-term and multiple incoherent scatter radar observations: Climatology in eastern American sector, J. Geophys. Res., 112, A06328, doi:10.1029/2006JA012206.

1. Introduction [2] Studies of the ionospheric climatology and variability have been pursued by many prior workers. Recently, some emphasis has been placed on annual and seasonal climatology and variability. Effects of the neutral composition and longitudinal variations of the auroral oval were discussed by Rishbeth [1998] to address the upper atmospheric circulation contributions to semiannual ionospheric changes. Mendillo et al. [2005] presented a study of the global ionospheric asymmetry in the total electron content and uncovered a similar behavior in the neutral composition. Balan et al. [1998] and Kawamura et al. [2002] discussed the springautumn asymmetry at the middle and upper atmosphere (MU) radar site and effects of the neutral wind. Zhang et al. [2005] revealed annual ionospheric changes versus height from long-term observations of chains of ISRs highlighting their evolution with latitude and longitude. On the other hand, ionospheric F2 region variability on a temporal scale much less than monthly or seasonally, especially during quiet magnetic conditions, is considered to be more likely connected to phenomena in the lower atmosphere, including acoustic, tidal, and planetary waves, as well as meteorological processes. See Forbes and Zhang [1997], Forbes et al. [2000], Rishbeth and Mendillo [2001], Altadill and Apostolov [2001], Mendillo et al. [2002], Lasˇtovicˇka [2006], and Rishbeth [2006] for some recent publications.

1 Haystack Observatory, Massachusetts Institute of Technology, Westford, Massachusetts, USA.

Copyright 2007 by the American Geophysical Union. 0148-0227/07/2006JA012206$09.00

[3] It is noted that most prior studies of ionospheric climatology and variability are based on F2 peak parameters, the E peak density, and TEC. As one of the most powerful ground-based instruments for probing the Earth’s upper atmosphere, an incoherent scatter radar (ISR) directly measures the ionospheric electron density Ne, electron and ion temperatures Te and Ti, and line-of-sight ion velocity over a broad height range. Since the development of ISRs in the 1960s, long-term observational data sets have been accumulating for various ISR sites around the world. Among the existing nine operational ISRs, over 30 years worth of data in modern digital form are available from Arecibo and Millstone Hill radars and over 7 years worth of data are available for the Svalbard radar; data from other sites, including the St. Santin radar, which was closed in 1986, the Sondrestrom radar in Greenland, EISCAT radars in Tromsø and Svalbard, and Shigaraki MU radar in Japan encompass at least one solar cycle [see Zhang et al., 2005]. Long-term ISR observations provide an extremely valuable data source for addressing significant aspects of ionospheric climatology and variability. The advantages of using such data lies in the broad height range afforded by the radar and the variety of parameters it produces, facilitating synthetic investigations of the relevant ionospheric processes. [4] The main purpose of our research is to characterize the climatology and variability of the ionosphere for multiple parameters based on data from multiple ISRs, with emphases on latitudinal variations for regional climatological features and on height changes for local variability features. We note that (1) The subauroral-auroral ionosphere is very dynamical experiencing complex impacts from the magnetosphere, plasmasphere, and thermosphere. Background or baseline ionospheric specification, i.e., the quan-

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ZHANG AND HOLT: ISRS BASED IONOSPHERIC CLIMATOLOGY

tified climatology, is the basis of understanding space weather effects. This present work has resulted in such an ISR-based ionospheric specification system, the Incoherent Scatter Radar Model (ISRIM). It provides various changes of the local ionosphere as well as of the regional ionosphere, especially the subauroral-auroral ionosphere over Eastern America where space weather could have some important social impacts. (2) These models can reveal features that might be smeared out by global models. In this paper we focus our scientific discussions on some new climatological features in the broad latitude span of 18– 70°N, as revealed in the model. As long-term multiple-ISR data sets are used, we are able to have an insight into these features from various aspects, e.g., electron density depletion above Millstone Hill which undergoes clear seasonal, solar activity, and height variations. Also, on the basis of data from both Millstone Hill and Sondrestrom radars, this paper offers an ISR perspective of baseline ionospheric heat properties over the subauroral-auroral area where various heating processes take place. [5] We will first describe the technique of processing ISR long-term data sets for quantifying the ionospheric climatology. Further detailed discussions about the method, i.e., the local ISRIM as well as its extension to the regional ISRIM, are given in Appendix A. In the subsequent section we present climatology results and address regional features of the subauroral ionosphere during quiet conditions. A summary of this study is given in the last section.

2. Modeling Method and Data [6] The method we are using to process the long-term ISR data is associated with constructing the ISRIM system and is detailed in Appendix A. Here we only highlight some key features. [7] The ISR data from each site are binned by month and local time with 3-month and 1-hour bin sizes. In this initial step of data binning, we assume a linear variation between any two consecutive altitude nodes (i.e., piecewise-linear variation over the entire height range), and the constant and linear coefficient in the linear equation for each height segment can be calculated. Each constant and linear coefficient is further assumed to be linear in the solar activity index F107 and magnetic activity index 3-hourly ap. A sequential least squares fit to the solar and magnetic activity dependence and to the piecewise-linear function for altitude dependence is then performed, generating coefficients for the constant, F107, and ap terms. Here F107 is an average between the daily F107 index and the 81-day running average of the daily F107 centering at the current day (see Appendix A) [Richards et al., 1994]. The initial binning results are then represented by a three-dimensional (3-D) basis with a cubic B-spline function to give twice-differentiable height variations, and harmonics with 12-, 6-, and 4month periodicities for seasonal changes and with 24-, 12-, 8-, and 6-hour periodicities for local time changes. This process is applied to Ne, Te, and Ti for each ISR site and results in local climatological models of the ISRIM. [8] Regional ISRIMs are created based primarily on local ISRIMs. For the eastern American regional ISRIM, individual local ISRIMs for Sondrestrom (67°N geodetic), Millstone Hill (42.5°N, geodetic), and Arecibo (18°N,

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geodetic) are combined, together with information from regional observations made by Millstone Hill MISA radar’s wide coverage scans over 32– 55°N. We use a 4-D basis function to fit the data (coefficients), generating changes with latitude, height, local time, and season. It contains a cubic B-spline basis for latitudinal changes between 18 and 70°N, a cubic B-spline basis for height variations over 100– 600 km, and harmonics with 12- and 6-month periodicities for seasonal changes and with 24-, 12-, 8-, and 6-hour periodicities for local time changes. [9] All ISR data were obtained from the Madrigal database (http://www.openmadrigal.org) developed at MIT Haystack Observatory. Up to December 2004, the number of experiments for Svalbard (operational since 1996) is over 600, for Sondrestrom (operational since 1983) the number is over 1000, for the EISCAT Tromsø (operational since 1981) the number is over 1200 (over 900 for the UHF radar), for Millstone Hill (operational since 1960) the number is over 1000 experiments, for St. Santin (operational during 1963– 1987) the number is about 100 experiments, for Shigaraki (operational since 1986) the number is about 200 experiments, and for Arecibo (operational since 1963) the number is over 100 experiments. Each ISR experiment covers typically 3– 7 days, though a calibration run can be as short as a few hours during 1 day. There were also 30-day experiments for some sites. At high latitudes there are relatively fewer data in summer than in other seasons. St. Santin has the fewest data but they are nearly equally distributed with month. Outside the polar and auroral areas there are much more data in the F region than in the E region where the ionosphere is, however, less variable and more easily characterized.

3. Electron Density Depletion at Millstone Hill [10] Some comparisons between the local ISRIM climatology and the IRI, a global ionospheric model [Bilitza, 2001], were made for local noon [Zhang et al., 2007a, 2007b]. It was found that for Ne there is generally good agreement between the two models in terms of the shape of the profile in the topside. In the bottomside the ISRIM Ne model tends to give more F1 region ionization and a wider F region. Agreement between the two models is better in equinox and summer than in winter, where the topside Ne decreases toward higher altitude at a rate higher for the ISRIM profile than for the IRI profile. For Ti, good agreement between the two models prevails over most sites with Millstone Hill and St. Santin being excellent. [11] Holt et al. [2002] reported briefly regional features of the ionosphere near Millstone Hill; Zhang et al. [2005] reported the annual and semiannual development of the ionosphere local to the seven ISR sites. Here we focus on changes in 18– 70°N in the Eastern American longitude sector. 3.1. Depletion Characteristics [12] Figure 1 is a regional ISRIM representation of the day number (seasonal) variation in Ne at noon for above the F2 peak. Similar to results shown by Zhang et al. [2005], well defined Ne semiannual components occur above the F2 peak at Arecibo with higher densities in spring than in autumn. The semiannual component also appears at Mill-

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Figure 1. Monthly variations of the noon time electron density at 450 km from 20° to 70°N in the Eastern American sector for median solar activity and quiet magnetic activity conditions. stone Hill and at Sondrestrom. It is noted that Ne is generally higher in autumn than in spring in the bottomside and at the F2 peak and above Ne is higher in spring than in autumn. There exists the spring-autumn asymmetry. The most striking feature, however, is the latitudinal density minimum near Millstone Hill. The southern peak is located near 30°N persistently over the year but strongest in spring. The northern peak is at 55°N, also persistently over the year but weaker in later summer and earlier autumn. The northern peak at noon is likely 5 –10° southward of the Northern Hemisphere auroral zone during quiet magnetic activity (see, e.g., http://www.sec.noaa.gov/pmap/ index.html for a routine auroral monitoring based on the

Figure 2. Height variations of the F2 region electron density at noon from 20° to 70°N in the Eastern American sector in winter for median solar activity and quiet magnetic activity conditions.

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Figure 3. Local time variations of the total electron content between 200 and 600 km from 20° to 70°N in the Eastern American sector in winter for median solar activity and quiet magnetic activity conditions. NOAA POES satellite). So what is shown beyond this peak toward the north is the so-called main trough, and the location of this peak is most likely very close to the ionospheric footprint of the plasmapause. [13] The height-latitude variation of the midday electron density, as shown in Figure 2, indicates that the south and north density peaks are present throughout the entire F2 region. At the bottomside, electron density at latitudes to the south of Millstone Hill is greater than that to the north and vice versa at the topside. In fact, the F2 peak height increases with latitude and reaches the highest at about 57°N. The local time evolution of the south and north density peaks is shown in Figure 3 where the integrated ionospheric electron content calculated from the regional ISRIM between 200 and 600 km is given. Again, the electron density depletion at Millstone Hill occurs throughout the whole day. The region of high electron density, as shown in the figure in bright colors which are centered near local noon, tends to shrink toward high latitudes. This is not simply due to the solar irradiation change with latitude since similar plots (not shown here), but for other seasons when the north is illuminated more (or the daylight hours are longer) than in the south, show a similar trend. [14] Results shown in Figures 1 to 3 are for median solar activity. The Ne depletion around Millstone Hill tends to disappear with increasing solar activity. As shown in Figure 4 (Figure 4a for the F2 peak density), this is because of the larger response to the solar activity change over Millstone Hill than over the surrounding areas, especially 10° to the north where the plasmapause footprint is likely located and the corresponding electron density is less changeable. [15] An independent data source, GPS observations of the total electron content (TEC), confirms the type of latitudinal variations shown in Figure 3. Global TEC data processed at MIT Haystack Observatory [Rideout and Coster, 2006] were extensively used for studies of ionospheric features

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activity, the GPS TEC depletion appears to be insignificant: on 17 December 2001 the 81-day F107 average was 232 units; the GPS TEC (not shown here) peaks around 40°N and no pronounced deep depletion occurs as TEC increases toward 40°N and decreases afterward with a slightly higher decrease rate for 55– 65°N. [16] One of the consequences of the electron density depletion is the enhancement of electron temperature, because of the well known anticorrelation between them [see Bilitza, 1975; Schunk and Nagy, 1978; Zhang and Holt, 2004; Zhang et al. [2004]. Figure 6 is the same as Figure 1 but for Te at 450 km altitude. The annual and semiannual variation exhibits clearly two minima in equinox at lower latitudes (indicating predominant semiannual components), and a single peak in summer at higher latitude (indicating a predominant annual component). The transition from double minima to a single peak takes place at latitudes of a few degrees southward of Millstone Hill. It can be seen that the midday Te tends to be higher at Millstone Hill than at surrounding areas both to the north and south throughout the year and is highest in summer corresponding exactly to the lowest Ne. To the north (except at the highest latitude), Te is lower, especially in winter. To the south, Te reaches minima in equinox. Therefore regional ISRIM results of Ne and Te for around Millstone Hill are consistent and support to each other. 3.2. Discussion [17] The midlatitude electron density in the F2 region is strongly controlled by the O/N2 ratio, where O acts as the major neutral target of photoionization, and N2 acts to cause O+ loss through recombination. The term O/N2 cosc may be

Figure 4. Solar activity dependence of the electron density latitudinal variation for 1100 LT in winter in the eastern American using quiet magnetic conditions, showing (a) the F2 peak density and (b) the F2 peak height. The F107 values are changed from 95 to 225 units at 20 units interval. The highest lines in both panels (highest F2 peak density and height) are for F107 = 225 and the lowest lines are for F107 = 95. during magnetic storms [Foster et al., 2002]. Figure 5 shows the daytime TEC in the Millstone Hill longitude for low solar activity (with an 81-day average F107 index of 88 units) in a winter day, 18 December 2005. The line and circles with error bars are for 1600 UT (LT = UT 4.8 hour), and error bars are standard deviations around the bin averages. The crosses are for 1500 UT and dots are for 1700 UT. Bin sizes are ±1.5 hour in time, ±2.5° in longitude, and ±2° in latitude. The variation pattern of the depletion over Millstone Hill and double peaks in the north and south are similar to that shown in the regional ISRIM results. However, in other winter cases with high solar

Figure 5. GPS TEC observations of the latitudinal profile at 1500, 1600, and 1700 UT on 18 December 2005 for the Eastern American sector. The 81-day average F107 index was 88 units. The line and circles with error bars are for 1600 UT, and error bars are standard deviations around the bin averages. The crosses are for 1500 UT and dots are for 1700 UT. Bin sizes are ±1.5 hour in time, ±2.5° in longitude, and ±2° in latitude. LT = UT 4.8 hour.

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Figure 6. Same as Figure 1 but for Te. used to represent the combined effect of O/N2 and solar zenith angle c changes. Of course, c changes with season and latitude. Figure 7 shows latitudinal profiles of midday O/N2 cosc for 290°E longitude in winter, summer, and autumn under median solar activity and quiet magnetic activity conditions. O and N2 are calculated for a constant pressure level of 1.5 107 mb (282 – 305 km) from the NRLMSIS model [see Hedin, 1987; Picone et al., 2002]. It can be seen that O/N2 cosc values in winter and summer start to be separated at around 50°N. Toward lower latitudes, O/N2 cosc is lower in summer than in winter, causing the so-called winter anomaly. O/N2 cosc is larger at equinox than either summer or winter; at the lowest latitude, O/N2 cosc is well above that in winter, causing a very clear semiannual variation. Of course, an exact evaluation of the composition effect on the F2 peak density requires consideration of the layer height which undergoes solar cycle, seasonal, diurnal, and latitudinal changes, and the transportation effect can be of great significance, especially near the low and high ends of our latitude span. [18] The composition/solar zenith effects shown in Figure 7 do not directly explain the density depletion around Millstone Hill. To investigate possible effects of dynamical processes, such as winds and local electric fields, we can examine changes in the F2 peak height, hmax. Figure 4b displays the F2 peak height change with latitude in winter for various F107 indices from 95 (dashed line) to 225 (thick solid line). For low solar activity, hmax ascends with latitude until at around 57°N where it starts to descend, i.e., the F2 layer is highest at 57°N. This also occurs in summer (not shown), where the F2 peak height is high at the lowest latitude and decreases to a minimum over Millstone Hill, but the highest hmax remains at 57°N. Therefore although at the fixed pressure level of 1.5 107 mb, O/N2 cosc decreases with increasing latitude, due to the F2 peak height maximizing at 57°N, the peak density tends to be high as a result of the lower loss rate, caused by the exponential reduction of N2 toward the higher altitude. Consequently, the elevation of the peak height by around 25 km from the level for Millstone Hill seems to have canceled or even dominated the effect of O/N2 cosc

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reduction at a fixed pressure level with latitude. This is shown in Figure 7 where the crosses stand for the ratio at the height of the F2 peak. With increasing solar activity, less increases are seen near 57°N relative to Millstone Hill, yielding a smaller hmax difference between the two locations. [19] Now the question reduces to reasons for the peak height elevation associated with upward ion drifts to the north of Millstone Hill. The daytime neutral winds are normally poleward which pushes the ions downward along the filed lines. So weaker poleward winds or reversed (equatorial) winds would be needed if one ascribes the hmax variation to winds. This seems to be unlikely in the context of global atmospheric circulation; one would have to resort to the local circulation. Alternatively, eastward electric fields could also move the ions up across the field lines, but why are the electric fields more important at 55°N? Are they of magnetosphere origin? These are some of the questions that remain to be answered. [20] Other than winds and electric fields, another possibility is associated with local thermal expansion effects. These will lift the balance height near the F2 peak established between chemical loss and diffusion [Rishbeth et al., 1978], since thermal expansion gives rise to the neutral concentration increase and therefore leads to a larger loss rate. The balance then settles at higher altitudes where the diffusion rate is higher. The expansion could also alter the local circulation by adding an equatorial flow toward Millstone Hill. This flow is against the regular (background) poleward flow during the day so that the overall meridional wind speed is reduced, causing a higher hmax. [21] The regional ISRIM does show an ion temperature 200°K higher near 55°N than that at Millstone Hill (not shown here), an indication of thermal expansion in the neutral temperature. Possible explanations for the temperature increase include the so-called subauroral ion drifts (SAID) or subauroral red (SAR) arcs events [Mendillo et

Figure 7. Latitudinal profiles of midday O/N2cosc calculated for a constant pressure level of 1.5 107 mb (2820– 305 km) in the eastern American sector using the NRLMSIS model with F107 = 135 and ap = 15. The crosses represent midday values calculated for the height of the F2 peak in winter.

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Figure 8. Latitudinal and local time variations of ion temperature at 200 km in winter for F107 = 135 and ap = 15. The solid lines are equipotential lines of high-latitude convection derived from Millstone Hill and Sondrestrom long-term observations. The convection is for winter with By and Bz negative. The bottom blue and red bars are dusk and dawn potential values, so the total length of the two bars is the cross polar cap potential drop. al., 1987; Foster et al., 1994] that are a nighttime phenomenon and geomagnetic disturbance associated. Further work is needed to clarify the exact mechanism, but this is beyond the scope of this paper.

4. Plasma Temperatures [22] Thermal properties of the subauroral-auroral ionosphere, which are associated with a variety of interactions among the neutrals, ions, and electrons, are another interesting subject for this climatological study. Figure 8 shows a dial plot of Ti at 200 km in winter for median solar activity and quiet magnetic activity conditions. This altitude is near the lower limit for which the Millstone Hill ISR can make measurements over a wide range of altitudes. The coordinates are apex latitude and apex local time. In the American longitude sector, apex latitude is roughly 10° higher than the geodetic latitude. Superimposed on the plot is the convection pattern derived from Millstone Hill and Sondrestrom long-term ISR observations which was described by Zhang et al. [2007a, 2007b] but is used only as a reference here. The convection corresponds to winter conditions with both IMF By and Bz negative. [23] Ti is higher during the day than at night and reaches a maximum 2 – 3 hours after noon. This corresponds to the

afternoon thermal bulge in the neutral atmosphere. The decrease from lower latitudes toward Millstone Hill is not surprising because of the solar zenith angle effect on neutral atmospheric heating. As the latitude increases to around apex latitude 70°, Ti increases again. This zone of high Ti is coincident with the equatorial part of the convection cells. Further poleward, Ti decreases slightly. It can be seen that Ti in this zone is at least 100°K higher than in the surrounding area for quiet conditions we are considering. At night the ion temperature elevation is very remarkable. This case is for winter when it is dark throughout the day for apex latitude 65°, so the solar heating is largely neglectable. The high Ti, however, is likely due to the auroral heating. At this altitude of 200 km, precipitating auroral particles can heat the atmosphere and produce the green emission. On the dayside, however, the auroral zone Ti is more than 150°K higher than on the nightside despite less frequently auroral heating and absence of direct solar heating. Therefore it seems that the dayside magnetospheric particle precipitation plays a role. [24] The electron temperature has very different characteristics. Figure 9 is similar to Figure 8 but for Te at 450 km in summer. Te is high during daytime hours at high latitudes. The morning enhancement appears around 0800

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Figure 9. Same as Figure 8 but for Te in summer at 450 km. apex local time over the entire latitude range. The enhancement becomes more pronounced with increasing latitude. As pointed out previously [see, e.g., Schunk and Nagy, 1978; Oyama et al., 1996; Otsuka et al., 1998; Zhang and Holt, 2004; Zhang et al., 2004], the enhancement is associated with rapid solar heating in the morning when electron density has yet to be built up as a major cooling mechanism. The latitudinal change is more likely related to the general decreasing trend of background Ne with increasing latitude. It is interesting to note that even though the Sun always rises in this summer case at very high latitudes, cosc changes by 30 – 50% from 0600 LT to 0800 LT. Such changes can still produce the pronounced morning enhancement. The daytime elevated Te occurs near Millstone Hill and has discussed in section 3.1. Again, Te is clearly high in the auroral zone even for an altitude of 450 km.

5. Summary [25] Ionospheric climatology and variability studies are conducted using long-term incoherent scatter radar (ISR) observations from seven sites around the world. These studies result in an empirical model system, the ISR Ionospheric Model (ISRIM), which describes local and regional ionospheric climatology and variability of the ionosphere. This paper deals with the climatology for latitudes spanning 18– 70°N in the eastern American sector. The latitudinal change of the F2-layer electron density exhibits a clear depletion near Millstone Hill latitudes when solar activity is

median or low, with peaks of electron density at 10° both to the north and the south. It tends to disappear, especially in winter, when solar activity is high. GPS TEC data in winter yield similar results. This depletion is also evidenced as a Te enhancement. Various possible explanations are explored. In particular, neutral composition effects do not seem to directly explain the depletion, although they are responsible for much of what is seen in our electron density climatology, such as the winter anomaly and the semiannual changes that vary with latitudes. [26] We have also characterized some variations in plasma temperatures in this region. Ion temperature in winter for quiet conditions is at least 100°K higher in a zone around apex latitude 70° than in the surrounding area. This elevated ion temperature seems to be a signature of auroral activity. Electron temperature tends to increase with latitude, with a high elevation near Millstone Hill where there is a depletion in Ne. [27] This paper focuses on some regional features of the ionosphere in the eastern American sector; variability results are discussed in an accompanying paper.

Appendix A: ISRIM [28] The ISRIM comes from a system that dealt with Millstone Hill incoherent scatter radar local and regional observations collected using the radar’s 68 m zenith antenna and 46 m steerable antenna. As described by Holt et al. [2002], this earlier system used a binning and fitting

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technique to sort and construct the climatology of the radar’s directly measured parameters. Measurements were separated into bins according to local time, altitude, and the day of year (to represent seasonal variations), and also to the geodetic latitude for regional modeling. For regional modeling, the bin size was 1° from 32° to 55° geographic latitude and 50 km from 200 to 600 km. For local modeling, in each bin, the dependencies on solar and magnetic activity are determined through a sequential least squares fit based on Givens transforms [Gentleman, 1973] to the equation: P ¼ b0 þ b1 f þ b2 a þ b3 f a

where P is either Ne, Te, or Ti, the bs are fitting coefficients, and f = (F107 135)/135 and a = (Ap 15)/15 are the normalized F107 and Ap indices. F107 is the previous day’s 10.7 cm solar flux index, and Ap is the 3-hourly equivalent range index Ap for the previous 3 hours. Here b 3 in the last term, representing cross-term effects between solar and magnetic activities, turns out to be very small in most cases and therefore this term is neglected in our later studies. [29] Zhang et al. [2005] described an updated system specifically for local models at each of the ISR sites. The main difference from that in the work of Holt et al. [2002] is the size of the data bin, the treatment of height variations including the selection of the height nodes, and smoothing methods. In brief, the data for each site were binned by month and local time with 3-month and 1-hour bin sizes. With an assumption of a linear variation between any two consecutive altitude nodes (piecewise-linear function over the entire height range), these constant and linear coefficient terms for such piecewise-linear height variations were calculated. These constants and coefficients were assumed to be linear in the solar activity index F107 and magnetic activity index 3-hourly ap. A sequential least squares fit to the solar and magnetic activity dependence and, unlike Holt et al. [2002], to the piecewise-linear function for altitude dependence was then performed, generating coefficients for the constant, F107, and ap terms for each of the 12 (monthly bins) 24 (hourly bins) = 288 bins and each of the altitude nodes. To further smooth diurnal and seasonal variations, a 3 (month) 3 (hour), median filter in season and local time to the coefficients was used. Lastly, a cubic B-spline was fit to give twice-differentiable height variations, a feature very useful for height gradient calculations. [30] It is noted that in the earlier step of data binning, using the piecewise-linear function has some advantages over using simply averaging for binning. The piecewiselinear function approach leads to better determined bin/node values by considering contributions from the neighboring points weighted by the distance from the node. If we were using a simpler approach of averaging over an altitude bin, for instance, height variations within a bin would be neglected. A1. ISRIM Local Climatology [31] The ISRIM consists of models for the ionospheric climatology and variability. It provides local models of Ne, Te, and Ti for each of the following ISR sites: Svalbard (78.1°N, 16.0°E; geodetic coordinates, the same hereafter), Sondrestrom (67.0°N, 309.0°E), Tromsø (69.6°N, 19.2°E), Millstone Hill (42.6°N, 288.5°E), St. Santin

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(44.6°N, 2.2°E), Arecibo (18.3°N, 293.2°E), and Shigaraki (34.8°N, 136.1°E). [32] The local models for the climatology and variability adopt an algorithm very similar to that described above for Zhang et al. [2005]. The same data binning scheme and the same technique for dealing with height variations are used. However, two major differences exist: (1) the ISRIM is now using a different solar F107 index. This is to accommodate concerns about the ionospheric saturation in responding to increases in the daily F107 index that occur in TEC and NmF2 data [see Balan et al., 1994; Richards et al., 1994; Liu et al., 2003; Liu et al., 2004; Lei et al., 2005] and ionospheric temperatures [Zhang and Holt, 2002]. Such a saturation was explained as the effect of the nonlinear correlation between the EUV flux and the daily F107 index, and other factors may be at work as well [see Richards, 2001; Liu et al., 2003]. A new F107 index, F107p, is often used [e.g., Richards et al., 1994; Lei et al., 2005] to efficiently overcome the nonlinear effect of the daily index while still using the readily accessible 10.7 cm flux index. F107p is the average between the daily F107 and the 81-day running average calculated for the current day being at the center, and is used in developing the ISRIM. (2) The ISRIM is a fully analytical model. Earlier versions are largely bin models with a linear variation between bins. Zhang et al. [2005] applies a cubic B-spline to the binning results for height variations, thus giving analytical and smooth height variations. For the ISRIM the binning results are represented by the same cubic B-spline to give twice-differentiable height variations and by harmonics with 12-, 6-, and 4- month periodicities for seasonal changes and with 24-, 12-, 8-, and 6-hour periodicities for local time changes. [33] The broad height coverage is an important feature of ISR measurements. Figure A1 shows an example for Millstone Hill on how we implement the representation of the height variation described above. The circles, crosses, and dots on both panels are relevant points for height profile modeling. The two smaller panels on the right zoom in details for two altitude ranges, 100 – 160 km and 200 – 350 km. The horizontal positions of these points (log10(Ne) in this example) are for illustration purposes only. What is meaningful for this plot is the height of these points. Actual height nodes vary among the radar sites due to each radar’s specific configurations and measurement modes, and were given by Zhang et al. [2005]. Circles are the original binning nodes; corresponding physical parameter (such as Ne) values at the node, and linear coefficients for piecewiselinear function, expressed as constant, F107, and ap terms, are all from the sequential least squares fit. The solid line across them represents such a piecewise-linear variation. Values for these nodes are to be used for the last-step least squares fitting of variations in time, seasonal, and height using cubic B-splines and harmonics. In fact, it is not values for these nodes (circles) but the values for the crosses that go into the final fitting. Each segment between two nodes can be broken into four equal parts in height, and the use of two heights at these quarter-points (crosses) neighboring one height node maintains better the curvature or the height gradient around a node if the height variation around the node is a second-order polynomial. [34] Cubic B-spline breakpoints are shown as dots. The number of breakpoints is 12 and the number of B-splines is

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Figure A1. Nodes and basis function used for the height variation representation. On the left panel, the blue curves are the cubic B-splines used for construction the height variation. They are shifted by 10 units for a better view. The circles, crosses, and dots on both panels are relevant points for height profile modeling. The two smaller panels on the right zoom in details shown on the left panel for two altitude ranges, 100 – 160 km and 200 – 350 km. Circles are the original binning nodes; the solid line across them represents a linear variations. The crosses represents the height of the quarter points between the two nodes. the dots are the cubic B-spline breakpoints. See text for more discussions. 14 for Millstone Hill. They are 9 – 11 for other sites. On the left panel, the blue curves are the cubic B-splines used for constructing the height variation (shifted by 10 units for a better view of the entire figure). In handling the profile shape generated by the cubic B-spline basis near the upper and lower boundaries, where unrealistic large change may occur, we set third and second partial derivatives of the basis to zero so that there is only a linear change between the boundary and the breakpoint next to it. The cubic Bspline basis function has the useful feature of being twicedifferentiable. This enables an appropriate height gradient determination for applications such as plasma diffusion velocity calculations in order to deduce thermosphere meridional winds from the ISR parameters. A2. Regional ISRIM [35] Local ISRIM climatology and variability is a 3-D model with seasonal, local time, and height variations controlled by solar and magnetic activity. With the addition of latitudinal variations, the regional ISRIM is a 4-D system. Three sets of such regional models have been created: [36] 1. Millstone Hill regional ISRIM makes use of the data from Millstone Hill radar’s steerable antenna latitudinal coverage from about geodetic 32– 55°. Holt et al. [2002] reported the binning and fitting method and results; now these bin coefficient data are fitted to a 4-D basis function

with a cubic polynomial for latitudinal variations, cubic Bsplines for height variations, and harmonics with 12- and 6-month periodicities for seasonal changes and with 24-, 12-, and 8-hour periodicities for local time changes. [37] 2. Eastern American regional ISRIM connects bin/ node coefficient data from sites in the American chain, namely, Sondrestrom, Millstone Hill, and Arecibo. Various modes of measurements at Sondrestrom can provide up to about 5° latitudinal span between geodetic 65– 70°N for Eand F-region measurements below 600 km. Millstone Hill radar covers geodetic 55 – 32°N. Using the beam swing technique, the long-term Arecibo data span 1° in latitude centering at 18.3°N. Therefore these ISR data cover approximately 18– 70°N, with gaps between 55° and 65°N and 19° and 32°N. To represent the latitudinal variation, our 4-D basis function contains a cubic B-spline basis for latitudinal changes between 18° and 70°N. Having data both to the north and south of Arecibo and Sondrestrom, we can better determine the latitudinal gradient near the two ends of the latitudinal span. Other parts of the 4-D basis function include the cubic B-spline for height variations, and harmonics with 12- and 6-month periodicities for seasonal changes and with 24-, 12-, 8-, and 6-hour periodicities for local time changes. The latitudinal breakpoints for the splines are 19, 35, 42, 56, 68°, and the height breakpoints are 100, 125, 150, 190, 230, 275, 350, 450,

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600 km. As a result, there are 4455 4-D basis function coefficients for each of the three geophysical terms. [38] The original observational data are not actually used in fitting the 4-D basis function, as it would take huge computational resource to handle them; however, it is more practical to use binned coefficient results. In the local ISRIM we fit bin coefficient data to the 3-D basis function. Here we fit bin coefficient data from each site to the 4-D basis function. Bin coefficients for both the north and the south of each ending site (Arecibo and Sondrestrom) are obtained using the same method used for creating bin coefficients of Arecibo and Sondrestrom local models, as described in section 2.1. Therefore Arecibo and Sondrestrom each contributes three sets of local bin coefficient data to the fitting, i.e., the overhead bin, the north bin, and the south bin. At Millstone Hill, the regional bin coefficient data obtained previously by Holt et al. [2002] are used, in addition to the local bin coefficient data. Accordingly, three (Arecibo) + one (Millstone Hill) + three (Sondrestrom) = seven sets of local bin coefficient data and one set of Millstone Hill regional bin coefficient data are included in the fitting. The altitude range is 100 – 600 km, although the local ISRIM for Millstone Hill is up to 1000 km. The E-F1 region results rely heavily on the seven local bin sets of local bin coefficients; Millstone Hill regional bin coefficient data start from an altitude of 200 km. For each of the seven sets, the number of bin coefficients for each of the three geophysical terms (constant, F107, and Ap terms) is the product of altitude bin number (17), local time bin number (24), monthly bin number (12), or 4896. The Millstone Hill regional bins amount to 23 (latitude) 9 (altitude) 24 4 (season) = 19872 for one geophysical term. As we can see, the overall amount of the bin coefficients and the number of the basis function coefficients are still significant but are not too difficult to be handled with modern computers. The three sites span about 11° in longitude with Millstone Hill in the east and Sondrestrom in the west; therefore the longitudinal variation is neglected. [39] 3. Western European regional ISRIM is a trial version for the European sector between 45° and 78°N, as only local measurements from three sites, Svalbard, Tromsø, and St. Santin, are included. The 4-D basis function is the same as we use for the above American regional ISRIM, except that the latitudinal variation has to be reduced to be a third-order polynomial. The longitudinal variation of the sites, from 2° to 19°E, is ignored. [40] Acknowledgments. We thank the members of the Haystack Observatory Atmospheric Sciences Group for assembling and maintaining the Madrigal Database. GPS TEC data were from Madrigal database; we thank Anthea Coster for her help with GPS TEC data processing. This research was supported by NSF Space Weather grant ATM-0207748. Observations and research at the Sondrestrom, Millstone Hill and Arecibo incoherent scatter radars are supported by the US National Science Foundation. [41] Zuyin Pu thanks the reviewers for their assistance in evaluating this paper.

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J. M. Holt and S.-R. Zhang, Haystack Observatory, Massachusetts Institute of Technology, Route 40, Westford, MA 01886, USA. (jmh@haystack. mit.edu; [email protected])

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