Response of the thermosphere to Joule heating and particle precipitation

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005ja011274, 2006 Response of the thermosphere to Joule heating and particle precipitation G. R. Wilson, 1 D. R. Weimer, 1 J. O. Wise, 2 and F. A. Marcos 2 Received 17 June 2005; revised 16 May 2006; accepted 26 May 2006; published 19 October [1] We have used output from the Weimer Joule heating model (2005) and the Air Force High Accuracy Satellite Drag Model (HASDM) to study the response of the thermosphere to Joule heating. Our study period of 15 January to 29 June 2001 contains a number of large and small magnetic storms during which thermospheric heating events occurred. We find that a new Joule heating model (Weimer, 2005), combined with the energy input provided by precipitating particles (NOAA/TIROS hemispheric power index), can supply more than enough energy to account for the change in total thermospheric internal and gravitational potential energy during magnetic storms. In the smaller storm heating events the energy input is about equally divided, with Joule heating only slightly dominant over particle precipitation. In the larger events, Joule heating clearly dominates. We find that the thermosphere responds globally in just 3 6 hours to an increase in energy input. Citation: Wilson, G. R., D. R. Weimer, J. O. Wise, and F. A. Marcos (2006), Response of the thermosphere to Joule heating and particle precipitation, J. Geophys. Res., 111,, doi: /2005ja Introduction [2] Some of the energy supplied to the magnetosphere from the solar wind is dissipated by deposition into the atmosphere via particle precipitation and Joule heating. The consequences of this are increases in the electrical conductivity and heating of the ionosphere and thermosphere, which can cause both to expand upward. The upward expansion of the ionosphere can lead to enhanced ion outflow while the expansion of the thermosphere increases satellite drag. It is typically observed that Joule heating dominates particle precipitation in terms of the amount of energy delivered to the atmosphere [Ahn et al., 1983a; Chun et al., 2002]. In order to understand the dynamics of the ionosphere/thermosphere it is important to understand the Joule heating process and the electrodynamics of the highlatitude ionosphere which gives rise to it. [3] The local Joule heating rate (j. E) can be written Q J ðhþ ¼ s P ðþe h ½? þ uðþb h Š 2 ð1þ where s P (h) is the local Pedersen conductivity as a function of height (h), E? is the convection electric field, u(h) is the neutral wind and B is the ambient magnetic field. Radar measurements of E region electron density profiles and plasma drifts can be used to estimate s P (h) and E? [Vickrey et al., 1982]. Since the contribution from the neutral wind is small at high latitudes it is often approximated or ignored. Such local measures of Joule heating have been used to 1 ATK Mission Research, Nashua, New Hampshire, USA. 2 Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, Massachusetts, USA. Copyright 2006 by the American Geophysical Union /06/2005JA build statistical relationships between the rate and location or level of auroral or magnetic activity (see Foster et al. [1983] for an example using AE-C data). [4] Most efforts to find the global Joule heating rate rest on solving a height integrated version of (1), which ignores neutral winds (S P E? 2 ), that is integrated over the whole high-latitude region. In this equation S P is the height integrated Pedersen conductivity. Kamide et al. [1981] demonstrates how the electric field can be found using ground magnetometer data and Kamide et al. [1982] illustrates the whole process for data from the International Magnetospheric Study (17 19 March 1978) using six magnetometer chains. These data must be combined with a model of the high-latitude pattern of S P to complete the calculations. An obvious drawback to this technique is the fact that the conductivity pattern can differ significantly from the model during storm events [Ahn et al., 1983a]. [5] An approach that improves on that of Kamide et al. [1981], called the assimilative mapping of ionospheric electrodynamics (AMIE) technique [Richmond and Kamide, 1988], combines data from ground magnetometers, satellites and radar to estimate the global pattern of electric potential, currents and conductivities. In areas devoid of data, statistical models are used. Over the last 16 years this technique has been widely used and greatly improved in terms of the data assimilation and mathematical methods. It has been used, for example, to study Joule heating rates [Richmond et al., 1990] and storm time magnetospheric convection [Chen et al., 2003]. [6] In order to make the global Joule heating rate a more accessible quantity there have been efforts to correlate it with magnetic indices. The first efforts used the auroral electrojet indices AE (or AU/AL) [Ahn et al., 1983b; Baumjohann and Kamide, 1984]. This is a natural association given that much of the Joule heating results from the 1of9

2 dissipation of the electrojet currents. More recently it has been shown that the global Joule heating rate provided by AMIE correlates well with the polar cap index PC [Chun et al., 1999]. This index correlates well with the polar cap potential and in turn the merging electric field (V x jb T jsin n q/2, n = 2 4) [Troshichev et al., 1996]. The pattern of highlatitude Joule heating produced by AMIE also correlates well with PC [Chun et al., 2002]. As PC increases from 3 to8, the Joule heating region shifts from dayside at high latitudes to auroral latitudes on the dawn and dusk flanks. [7] A new approach to finding the Joule heating rate has just been introduced [Weimer, 2005, hereinafter referred to as W05]. The approach uses satellite data (from DE2) to statistically determine both the electric potential pattern and the parallel current magnetic deflection pattern as a function of upstream solar wind and interplanetary magnetic field conditions, and the tilt of the Earth s dipole. The two patterns are combined to calculate the Poynting flux into the ionosphere which is equivalent to the Joule dissipation rate. One advantage of this approach is that it does not require knowledge of the conductivities to find the Joule heating rate. [8] In this paper we will examine the response of the thermosphere to Joule heating by comparing the energy gains of the thermosphere to energy supplied by Joule heating as given by W05. This work constitutes a test of W High Accuracy Satellite Drag Model [9] To know what the global thermosphere is doing during a Joule heating event we use output from the High Accuracy Satellite Drag Model (HASDM) developed by the Air Force Space Battlelab to improve its satellite orbit prediction ability [Storz et al., 2002]. The dynamic calibration atmosphere (DCA) portion of the model [Casali and Barker, 2002] is based on a near real-time correction to the Jacchia density model [Jacchia, 1970]. Tracking data from 75 calibration satellites (inclinations of 20 to 100, perigees of 190 to 900 km attitude) are used to spatially adjust the inflection and exospheric temperatures of the temperature profile used in the Jacchia model. These temperature profiles are used to solve the hydrostatic and diffusion equations to obtain density profiles. A new global density distribution from 90 to 1000 km altitude is generated every 3 hours. This time interval is set by the Jacchia model s use of the Ap index and is about twice the orbital period of the calibration satellites. The model does not have sufficient spatial resolution to discern features such as the auroral zone but it can accurately determine global thermospheric changes as was demonstrated by its ability to predict orbits for test satellites that were not part of the set used to construct the model [Casali and Barker, 2002]. [10] During the development of the HASDM the time interval of 15 January to 29 June 2001 was used as a test case. As an example of the output of this model Figure 1 shows Northern Hemisphere densities at 450 km altitude during the initial phase of the magnetic storm of 31 March to 2 April Since the basic latitude/local time structure of the thermosphere is fixed by the Jacchia model representation there is no apparent auroral oval in these plots even though it is very likely that the density increases apparent in these plots begins there. A more meaningful comparison with the HASDM output should involve a global parameter that represents the state of the thermosphere. Thus we obtain a quantity called the thermospheric potential energy (TPE) by performing the following integration Z TPE ¼ r m F g dv: In equation (2) r m is the thermospheric mass density, F g is the gravitational potential (whose zero reference level (r o ) can be set arbitrarily) and dv is a volume element. This integral includes the spherical volume that starts at some lower altitude (z o ) and extends to infinity. [11] Since we are interested in heating events the real quantity of interest is the change in TPE which can be expressed Z DTPE ¼ Dr m F g dv: ð3þ The function Dr m gives the difference between the mass distribution at the beginning and end of the heating time interval. Dr m will be positive at the higher altitudes which gain mass and negative at low altitudes which lose it. In order to get the correct value for DTPE we should choose a value of z o such that Dr m = 0 for all z < z o. [12] HASDM cannot describe Dr m below 200 km altitude because of the lack of satellite data there. In all of the HASDM output used in this paper Dr m > 0 for altitudes above 200 km. Therefore we cannot do the full integration of equation (3) to find DTPE, but we can find a quantity call DTPE 200 (subscript indicates the value of z o ), which is the change in gravitational potential energy for the thermosphere above 200 km altitude. The question is, can DTPE 200 serve as a useful measure of DTPE? [13] In view of some of the extreme situations imaginable, one may be tempted to answer the previous question no. Consider one extreme where the thermosphere is heated but Dr m is only nonzero below 200 km. In that case DTPE 200 = 0 and tells us nothing about the change in the energy content of the atmosphere. In another extreme situation where Dr m is only negative below 200 km and positive above, DTPE 200 > DTPE. If results in nature ranged fully between these two extremes then DTPE 200 would not have much value since it would not correlate with the energy input to the atmosphere. [14] To address this point we did a series of numerical experiments with the Jacchia [1970] model varying the level of solar activity and the magnitude of the increase in Ap. We allowed F 10.7 to vary from a value of 70 to 320 and simulated the heating by allowing Ap to increase from 5 to values of 20 to 320. We experimented with the behavior of DTPE as a function z o and r o and found that the value calculated for DTPE was insensitive to r o when z o was at or below 100 km altitude. For z o = 200 km, however, DTPE depended on the choice of r o. This is due to the fact that as Ap changes (for fixed F 10.7 ) the mass of the atmosphere above 100 km altitude changes little while above 200 km it changes a great deal. As r o is moved below 200 km the value of DTPE 200 increases. We then calculated the fraction ð2þ 2of9

3 Figure 1. Northern Hemisphere HASDM mass densities at 450 km altitude for the indicated times. of the potential energy change for the atmosphere above 100 km (DTPE 100 ) that was given by the change that occurred above 200 km (DTPE 200 ). We found that as F 10.7 or the size of the Ap jump increased, this fraction increased. Using a value of 100 km for r o we found that the ratio DTPE 200 /DTPE 100 ranged from a low of 0.5 to a high of 0.74 as F 10.7 was varied from 124 to 274 for all changes in Ap. This range of values for F 10.7 is significant since it is the same as that of our study interval (15 January to 30 June, 2001). On the basis of these results we say that DTPE DTPE 100 for the level of solar activity that applies to our study. [15] Errors in the satellite tracking data and the HASDM output lead to fluctuations of TPE 200 that are not geophysical. To estimate this error level we took six 2 3 day intervals where the solar input (as measured by the EUV flux and F10.7) was nearly constant, the magnetospheric energy input rates (as measured by the W05 and the NOAA/ TIROS hemispheric power index) were very small (<100 GW), and the curve for TPE 200 versus time was nearly horizontal. For each interval we found the average value of TPE 200 and its variance. The variances ranged from a low value of J to a high value of J. The average variance was J. Given typical values for TPE 200 of about J our uncertainty in TPE 200 is then about 2%. [16] Figure 2c shows TPE 200 for the interval from day 70 to day 130 of 2001 with the zero of F g set at 100 km. Additional environmental data are contained in Figure 2. Figure 2a shows data from the SOHO/SEM instrument which monitors solar EUV emissions. Figure 2b shows F 10.7, and Figure 2d shows the Ap index. Figure 2 suggests that long-term variations in TPE 200 (timescale of 10 days) correlate with long-term variations in solar EUV output while short-term increases in TPE 200 (less than 1 day) correlate well with increases in magnetic activity but not with abrupt increases in solar EUV output. [17] To quantify these assertions we took TPE 200 for the whole time interval (180 days) and removed the lowfrequency baseline. This baseline was found by computing the running average and variance of TPE 200 using a 90 hour sliding bin and then subtracting four times the variance from the average. We tested the correlation between the highfrequency (DTPE 200 = TPE 200 -baseline) and low-frequency (Ba = baseline) components of TPE 200 with the Ap index. The correlation coefficient between the concurrent value of Ap and DTPE 200 is 0.63 and for Ba it is When previous values of Ap (back 3, 6, 9, 12, 15 hours) are tested for correlation with Ba the correlation coefficient remains at about 0.32 while for DTPE 200 the correlation coefficient first increases to 0.74 at 3 and 6 hours and then drops to 0.67, 0.56 and When the concurrent plus the previous 3 values of Ap are averaged, the correlation with DTPE 200 is a maximum at Clearly, the high-frequency component of TPE 200 correlates well with magnetospheric activity, especially when the recent past is taken into consideration. We next tested the correlation of Ba and DTPE 200 with energy input as measured by the W05 Joule heating model. Figure 2. Environmental data for the stormy spring equinox period of 2001 (11 March to 10 May): (a) SOHO/SEM measurements of solar EUV emissions in the and nm bands, (b) F 10.7, (c) TPE 200 from the HASDM, and (d) the Ap index. 3of9

4 into the atmosphere. Here DB is the magnetic field perturbation produced by the field-aligned currents. The local Poynting flux matches the local, height integrated, Joule heating rate in the limit that the transfer of mechanical energy is negligible [Weimer, 2005]. W05 can find the local and global Joule heating rates as a function of upstream interplanetary magnetic field (IMF) and solar wind parameters (B Y,B Z,n,jV X j) and dipole tilt angle without a direct knowledge of ionospheric conductivities. [19] As is often the case with empirical models that produce results from an averaged data set, this model tends to smooth out actual variations. The result is that the electric field predicted by the model can be smaller than the actual field because the smoothing of the data tends to reduce potential gradients. Another issue is the range of parameter space sampled by the data set used to construct the model. For example, the maximum IMF magnitude in the DE-2/ IMP-8/ISEE-3 database is 15 nt. It is possible, then, that extending the model to situations where the IMF is more intense could give erroneous results if the model does not handle polar cap potential saturation properly. However, tests of the model with large IMF (30 nt) indicate that the model appears to perform satisfactorily in this regime [Weimer, 2005]. Figure 3. Plots of the advected and 15 min averaged ACE/ MFI and ACE/SWE data for the magnetic storm interval of 29 March to 3 April (a) Magnitude of the GSM Y Z component of the IMF, (b) IMF clock angle, (c) solar wind density, and (d) magnitude of the x component of solar wind velocity. These quantities are used as inputs for the Weimer Joule heating model. The correlation coefficient between the output of W05 (integrated over the three hours appropriate to TPE 200 ) and Ba is 0.21 and for DTPE 200 is Integrating the global joule heating rate further into the past improves the correlation with DTPE 200 significantly (0.85 after 11.5 hours) but Ba only marginally (0.31 after 24 hours). We next tested the correlation of the SOHO/SEM nm photon flux with Ba and DTPE 200. The correlation coefficient of the SEM flux (integrated over the three hours appropriate to TPE 200 ) with Ba is 0.68 and with DTPE 200 is Integrating the SEM flux into the past improves the correlation with Ba (0.75 after 4 days) but does not improve the correlation with DTPE Weimer Joule Heating Model [18] W05 is based on the Weimer electric potential model originally developed in the mid nineties [Weimer, 1996]. Recently, the same technique has been adapted to finding a magnetic potential whose gradient gives the magnetic perturbations produced by field-aligned currents [Weimer, 2001]. Combining the two gives the downward Poynting flux S ¼ E DB=m o ð4þ 4. Comparison of Joule Heating Rate With Thermospheric Potential Energy Content [20] As a first case we show a close-up comparison for the large magnetic storm of 31 March to 2 April 2001 in Figures 3 and 4. Figure 3 shows the time-shifted (by advection only) and averaged (15 min) IMF and solar wind parameters (from ACE) that serve as inputs to W05. The quantity plotted in Figure 3a is not the magnitude of the total IMF but is just the magnitude of the GSM Y and Z components of the IMF. C.A. is the IMF clock angle in the GSM Y Z plane. The sudden commencement of this storm occurred on 31 March (day 90) driven by an increase in the dynamic pressure and an intensification of the IMF. Note the two main IMF intensifications during day 90. [21] Figure 4d shows the W05 global Joule heating rate for the same 5 day interval shown in Figure 3. This value combines the heating rate from both the northern and southern high-latitude regions (jmlatj 45 ). Note the similarity of the two main peaks with the peaks in jbj of Figure 3a (day UT and day UT). The dotted curve in Figure 4d is the global (northern and southern) energy input to the atmosphere carried by precipitating particles and is derived from NOAA/TIROS data [Foster et al., 1986] (NOAA/TIROS hemispheric power index). Figures 4a and 4b give the same solar parameters as are plotted in Figure 2. Figures 4a and 4b demonstrate that the change seen in TPE 200 in Figure 4e cannot be attributed to a sudden increase in solar EUV output. Figure 4c gives the polar cap index for this time interval. This parameter has been shown to be a reliable indicator of the level of Joule heating [Chun et al., 2002]. Figures 4c and 4d show that the increase in TPE 200 is closely associated with an increase in geomagnetic activity and its associated Joule heating and particle precipitation. They also illustrate that the thermosphere can respond 4of9

5 about the middle of day 101 (11 April) and peaked early on day 102 (12 April). As Figure 5 illustrates this event is driven by an increase in the magnitude of the IMF. From day UT to day UT TPE 200 increased by about J. The particle and Joule heating energy inputs for the same interval are J and J respectively. Together they supply about 5.5 times the energy needed to account for the change in TPE 200. [24] One thing that is apparent in Figures 4 and 6 is that the shape of the TPE 200 curve is similar to the shape of the Joule heating curve, in spite of the fact that these two curves are the product of data sets which are entirely independent. Figures 7 and 8 show two additional examples in the same format as Figures 4 and 6. In Figure 7 the Joule heating interval is intense (>1000 GW) but brief (<6 hours) and the interval of elevated TPE 200 is also brief (9 hours) and lags by about 3 hours (the time resolution limit of HASDM). In Figure 8 the Joule heating interval is less intense ( GW) but of longer duration (30 hours). The interval of elevated TPE 200 is of the same duration and again is shift by about 3 hours. [25] Table 1 lists 25 thermospheric heating events (with a significant increase in TPE 200 ) identified for the interval of 15 January to 29 June The time intervals listed in Table 1 start shortly before the heating events begin (increase in TPE 200 and energy input) and carry through to the peak value of TPE 200. We do this so that we can find the maximum DTPE 200 for the event. The precipitating particle and Joule heating energy input are then integrated over the same time interval. DTPE 200 and these integrated Figure 4. For the magnetic storm of 31 March to 1 April 2001: (a) solar flux of EUV photons in the nm and nm bands as measured by the SEM instrument on SOHO, (b) F 10.7, (c) polar cap index, (d) global Joule heating rate from the Weimer model and the global precipitating particle energy input rate as given by the NOAA/TIROS hemispheric power index, and (e) gravitational potential energy of the thermosphere above 200 km altitude as determined by the HASDM. (F g = 0 at 100 km altitude.) The dotted curve is equation (5) fit to these data. (See Table 2 for fit parameters.) globally in just a few hours to the increased energy input that accompanies intervals of enhanced magnetic activity. [22] The information in Figure 4 can be used to make a quantitative comparison between the energy input to the atmosphere and the change in energy content of the thermosphere. Between day UT and day UT, TPE 200 increased by about J. During this same time interval particle precipitation supplied about J and Joule heating supplied about J. Together these two sources supply 7.9 times the energy needed to account for the change seen in Figure 4e. [23] Figures 5 and 6 show another thermospheric heating event that occurred during the second largest magnetic storm of the January June 2001 study period (11 13 April 2001). The formats of Figures 5 and 6 are the same as those of Figures 3 and 4. In this event TPE 200 began increasing at Figure 5. Same format as Figure 3 but for the 9 14 April 2001 storm interval. 5of9

6 DTPE 200 and the Joule heating energy input suggests that Joule heating is the dominant energy source. The fact that these two quantities correlate well with each other strongly suggests that DTPE 200 is a useful measure of the total energy change of the thermosphere. [27] One way to better compare the energy inputs with the changes in TPE 200 is to account for losses during the heating event. To that end we have fit the following equation to the TPE 200 curves for some of our events (including those of Figures 4, 6, 7, and 8) dtpe 200 =dt ¼ a EUV þ b ðj þ PÞ c TPE 200 ð5þ In equation (5) EUV is the flux of solar photons in the 0.1 to 50 nm wavelength range, J is the Joule heating rate, and P is the energy input rate from precipitating particles. a, b, and c are constants for a given event adjusted to provide the best fit. The dotted curves in Figures 4e, 6e, 7e, and 8e are equation (5) fit to the TPE 200 data for those four events. Table 2 contains the values for a, b, and c for all events that were fit. The constant a (units of J cm 2 ) is the product of the disk area of the Earth, the mean energy of a solar EUV photon, and the fraction of that energy converted to gravitational potential energy. Parameter b (unitless) is the Figure 6. Same format as Figure 4 but for the 9 14 April 2001 storm interval. energy inputs are listed in Table 1 for each event. On average the combined inputs of W05 and the NOAA/TIROS hemispheric power index supply about 9 times the energy needed to account for the change in TPE 200. The results of Table 1 also suggest that the ratio of Joule heating to precipitating particle energy input increases with the severity of the event. For DTPE J the average ratio is 3.2. For DTPE 200 < J the average ratio is 2.4. The average length of one of the thermospheric heating events (the time interval from where TPE 200 begins to rise to when it returns to its previous level) is about 19 hours. [26] Figure 9 plots the values of DTPE 200 from Table 1 versus the Joule energy input (Figure 9a), the particle energy input (Figure 9b), and both together (Figure 9c). The dashed lines in Figures 9a 9c are least squares fits to the points. The slopes of these lines are (Figure 9a), (Figure 9b), and (Figure 9c), respectively. The slope of the line in Figure 9c forms the basis of our conclusion that the combined energy input of W05 and particle precipitation (NOAA/TIROS hemispheric power index) provides 9 times the energy needed to account for the change in the thermospheric gravitational potential energy above 200 km altitude. Figures 9a 9c also include the coefficient giving the correlation between DTPE 200 and the size of the energy input. The higher correlation between Figure 7. Same format as Figure 4 but for the April 2001 storm interval. 6of9

7 needed fraction of the precipitating particle and Joule heating energy input that contributes to the detected (above 200 km) potential energy increase, while c (units of s 1 )is the exponential energy loss decay constant. [28] The values of b in Table 2 indicate that even when energy loss is taken into account the precipitating particle and Joule heating energy sources provide about 6 times more energy than is needed to account for the increases in TPE 200 seen in Figures 4e, 6e, 7e, and 8e. The average value of c in these events corresponds to a cooling time constant of about 14 hours. Figure 8. Same format as Figure 4 but for the April 2001 storm interval. 5. Comparison of TPE 200 With the Total Thermospheric Energy Content [29] In this paper we have discussed the changing of the thermospheric energy content in terms of only one component: the gravitational potential energy of the thermosphere above 200 km altitude or TPE 200. As discussed in paragraph 14, we estimate that under the level of solar activity in our study interval and for the value chosen for r o, changes in TPE 200 under represent the change in the gravitational potential energy of the whole thermosphere by up to a factor of 2. [30] For the case of a planar, isothermal atmosphere, where r o = z o, the gravitational potential energy of equation (2) reduces to NkT. N is the total number of molecules in the portion of the atmosphere under consideration and T is the temperature. If this portion of the atmosphere is large enough so that N does not change during the heating event then the total change in thermospheric gravitational potential energy (DTPE) is given by NkDT. The change in the internal energy of the thermosphere is given by 3/2 to 5/2 times NkDT depending on whether the thermosphere is composed predominately of atomic or diatomic constituents. The change in the total energy of the Table 1. The 2001 Thermospheric Heating Events Start, DOY:UT End, DOY:UT DTPE 200,10 15 J Particle, J Joule, J PþJ DTPE200 Joule/Particle 101: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : of9

8 thermosphere (DTPE + 3/2NkDT to DTPE + 5/2NkDT) is then given by 5/2 to 7/2 times NkDT. For the preceding to be the case the value for z o used in equation (3) must be low enough so that N remains constant during a heating event. On the basis of our Jacchia model experiments we know that this condition is satisfied if z o = 100 km. Using the results in paragraph 14 we can then say that 0:74 NkDT DTPE 200 0:5 NkDT ð6þ since DTPE = DTPE 100 = NkDT. Therefore NkDT = 1.35 to 2.0 times DTPE 200 so the change in the total energy of the thermosphere is then between 3.4 and 7 times DTPE 200. In our analysis above we showed that the combination of energy inputs from particle precipitation and Joule heating supplied about 6 9 times the energy needed to account for DTPE 200. Given the simplified nature of our analysis here it appears that these two sources supply more than enough energy to account for thermospheric heating during magnetic storms. 6. Conclusions [31] We conclude from the results shown in Figure 2 that during storm times, short timescale (1 2 days) variations in the structure of the thermosphere are controlled by variations in magnetospheric energy inputs (Joule heating and Figure 9. Plots of the values of DTPE 200 from Table 1 versus (a) the Joule energy input, (b) the particle energy input, and (c) both together. Table 2. Fit Parameters for Equation (5) Event Interval, DOY a b c particle precipitation) and not by variations in the solar EUV energy input. Our study interval (15 January to 29 June 2001) contains a number of large and small, short-term thermospheric heating events that are clearly associated with magnetospheric activity. In the smaller events the energy input is about equally divided between Joule heating and particle precipitation. In the larger storm events, Joule heating dominates. [32] Previous models of the Joule heating process tended to underestimate the heating rate as demonstrated by the difficulty of matching results from first principle thermospheric models to empirical models [Codrescu et al., 1995]. Such a comparison likely understates the deficiency of the Joule heating model because the averaging done to construct the empirical thermosphere model tends to down play true thermospheric variability. Codrescu et al. [1995] and Rodger et al. [2001] propose that including small-scale fluctuations in the electric field or the conductivity could lead to a 20 60% increase of the Joule heating rate. However, the existence of an inverse correlation between the height integrated Pedersen conductivity and the magnitude of the electric field [Evans et al., 1977] argues that small-scale fluctuations may not add much to the energy transfer rate associated with Joule heating. [33] In this study we have examined the ability of a new Joule heating model (W05) to account for the response of the thermosphere during storm time Joule heating events. By using the HASDM we can incorporate in our study the more extreme mass redistributions that occur in nature compared to what would be given by an averaged empirical model. We find that the energy supplied by particle precipitation (NOAA/TIROS hemispheric power index) and Joule heating (W05) can account for the total change in the internal and gravitational potential energy of the thermosphere implied by the HASDM results. This study did not try to account for Poynting flux energy that is converted to the energy of bulk motion of the ionosphere and thermosphere [Vasyliûnas and Song, 2005]. [34] At present the response of the thermosphere and the resulting changes in satellite drag can only be determined after geomagnetic storms by the tracking of calibration satellites. Our results indicate that it should be possible to use IMF measurements in conjunction with an empirical Joule heating model to make advance predictions of the thermospheric expansion and the resulting orbit perturbations. [35] Acknowledgments. This work was supported by Air Force SBIR contract F C-0012 to ATK Mission Research and by the National Aeronautics and Space Administration under contract NASW issued through the Living with a Star Program. 8of9

9 [36] Arthur Richmond thanks Francis K. Chun and Alan Rodger for their assistance in evaluating this paper. References Ahn, B.-H., R. M. Robinson, Y. Kamide, and S.-I. Akasofu (1983a), Electric conductivities, electric fields and auroral particle energy injection rate in the auroral ionosphere and their empirical relations to the horizontal magnetic disturbances, Planet. Space Sci., 31, 641. Ahn, B.-H., S.-I. Akasofu, and Y. Kamide (1983b), The Joule heat production rate and the particle energy injection rate as a function of the geomagnetic indices AE and AL, J. Geophys. Res., 88, Baumjohann, W., and Y. Kamide (1984), Hemispherical Joule heating and the AE indices, J. Geophys. Res., 89, 383. Casali, S. J., and W. N. Barker (2002), Dynamic calibration atmosphere (DCA) for the High Accuracy Satellite Drag Model (HASDM), paper AIAA presented at AIAA/AAS Astrodynamics Specialist Conference, Am. Inst. of Aeronaut. and Astronaut., Monterey, Calif. Chen, M. W., M. Schulz, G. Lu, and L. R. Lyons (2003), Quasi-steady drift paths in a model magnetosphere with AMIE electric field: Implications for ring current formation, J. Geophys. Res., 108(A5), 1180, doi: / 2002JA Chun, F. K., D. J. Knipp, M. G. McHarg, G. Lu, B. A. Emery, S. Vennerstrøm, and O. A. Troshichev (1999), Polar cap index as a proxy for hemispheric Joule heating, Geophys. Res. Lett., 26, Chun, F. K., D. J. Knipp, M. G. McHarg, J. R. Lacey, G. Lu, and B. A. Emery (2002), Joule heating patterns as a function of polar cap index, J. Geophys. Res., 107(A7), 1119, doi: /2001ja Codrescu, M. V., T. J. Fuller-Rowell, and J. C. Foster (1995), On the importance of E-field variability for Joule heating in the high-latitude thermosphere, Geophys. Res. Lett., 22, Evans, D. S., N. C. Maynard, J. Trøim, T. Jacobsen, and A. Egeland (1977), Auroral vector electric field and particle comparisons: 2. Electrodynamics of an arc, J. Geophys. Res., 82, Foster, J. C., J.-P. St.-Maurice, and V. J. Abreu (1983), Joule heating at high latitudes, J. Geophys. Res., 88, Foster, J. C., J. M. Holt, R. G. Musgrove, and D. S. Evans (1986), Ionospheric convection associated with discrete levels of particle precipitation, Geophys. Res. Lett., 13, 656. Jacchia, L. G. (1970), New static models of the thermosphere and exosphere with empirical temperature profiles, Spec. Rep. 313, Smithson. Astrophys. Observ., Washington, D. C. Kamide, Y., A. D. Richmond, and S. Matsushita (1981), Estimation of ionospheric electric fields, ionospheric currents, and field-aligned currents from ground magnetometer records, J. Geophys. Res., 86, 801. Kamide, Y., et al. (1982), Global distribution of ionospheric and fieldaligned currents during substorms as determined from six IMS meridian chains of magnetometers: Initial results, J. Geophys. Res., 87, Richmond, A. D., and Y. Kamide (1988), Mapping electrodynamic features of the high-latitude ionosphere from local observations: Technique, J. Geophys. Res., 93, Richmond, A. D., et al. (1990), Global measures of ionospheric electrodynamic activity inferred from combined incoherent scatter radar and ground magnetometer observations, J. Geophys. Res., 95, Rodger, A. S., G. D. Wells, R. J. Moffett, and G. J. Bailey (2001), The variability of Joule heating, and its effects on the ionosphere and thermosphere, Ann. Geophys., 19, Storz, M. F., B. R. Bowman, and Maj. J. I. Branson (2002), High accuracy Satellite Drag Model (HASDM), Paper AIAA presented at AIAA/AAS Astrodynamics Specialist Conference, Am. Inst. of Aeronaut. and Astronaut., Monterey, Calif. Troshichev, O., H. Hayakawa, A. Matsuoka, T. Mukai, and K. Tsuruda (1996), Cross polar cap diameter and voltage as a function of PC index and interplanetary quantities, J. Geophys. Res., 101, 13,429. Vasyliunas, V. M., and P. Song (2005), Meaning of ionospheric Joule heating, J. Geophys. Res., 110, A02301, doi: /2004ja Vickrey, J. F., R. R. Vondrak, and S. J. Matthews (1982), Energy deposition by precipitating particles and Joule dissipation in the auroral ionosphere, J. Geophys. Res., 87, Weimer, D. R. (1996), A flexible IMF dependent model of high-latitude electric potentials having space weather applications, Geophys. Res. Lett., 23, Weimer, D. R. (2001), Maps of ionospheric field-aligned currents as a function of the interplanetary magnetic field derived from Dynamics Explorer 2 data, J. Geophys. Res., 106, 12,889. Weimer, D. R. (2005), Improved ionospheric electrodynamic models and application to calculating Joule heating rates, J. Geophys. Res., 110, A05306, doi: /2004ja F. A. Marcos and J. O. Wise, Air Force Research Laboratory, Space Vehicles Directorate, Hanscom Air Force Base, MA 01731, USA. D. R. Weimer and G. R. Wilson, ATK Mission Research, 589 West Hollis Street, Suite 201, Nashua, NH 03062, USA. (gordonr.wilson@atk.com) 9of9