Global Joule heating index derived from thermospheric density physics-based modeling and observations

Transcription

1 SPACE WEATHER, VOL. 10,, doi: /2011sw000724, 2012 Global Joule heating index derived from thermospheric density physics-based modeling and observations Mariangel Fedrizzi, 1,2 Tim J. Fuller-Rowell, 1,2 and Mihail V. Codrescu 3 Received 31 August 2011; revised 19 December 2011; accepted 26 December 2011; published 1 March [1] The primary operational impact of upper atmospheric neutral density variability is on satellite drag. Drag is the most difficult force to model mainly because of the complexity of neutral atmosphere variations driven by solar UV and EUV radiation power, magnetospheric energy input, and the propagation from below of lower atmosphere waves. Taking into account the self-consistent interactions between neutral winds, composition, ion drifts, and ionization densities, first-principles models are able to provide a more realistic representation of neutral density than empirical models in the upper atmosphere. Their largest sources of uncertainty, however, are the semiannual variations in neutral density and the magnitude, spatial distribution, and temporal evolution of the magnetospheric energy input. In this study, results from the physics-based coupled thermosphere-ionosphere-plasmasphere electrodynamics (CTIPe) model and measurements from the CHAMP satellite are compared and used to improve the modeled thermospheric neutral density estimates. The good agreement between modeled and observed densities over an uninterrupted yearlong period of variable conditions gives confidence that the thermosphere-ionosphere system energy influx from solar radiation and magnetospheric sources is reasonable and that Joule heating, the dominant source during geomagnetically disturbed conditions, is appropriately estimated. On the basis of the correlation between neutral density and energy injection, a global time-dependent Joule heating index (JHI) is derived from the relationship between Joule heating computed by the CTIPe model and neutral density measured by the CHAMP satellite. Preliminary results show an improvement in density estimates using CTIPe JHI, demonstrating its potential for neutral density modeling applied to atmospheric drag determination. Citation: Fedrizzi, M., T. J. Fuller-Rowell, and M. V. Codrescu (2012), Global Joule heating index derived from thermospheric density physics-based modeling and observations, Space Weather, 10,, doi: /2011sw Introduction [2] The growing importance of monitoring satellites and tracking debris has been highlighted since the first accidental hypervelocity collision of two intact spacecraft in February The collision occurred at an altitude of 790 km [NASA, 2009], leaving pieces of debris that have been gradually separated into different orbital planes around the Earth, threatening other satellites for the next few decades. Since 1957, more than 25,000 artificial space debris have been cataloged, many of which have naturally decayed into the lower atmosphere [Koskinen et al., 2001]. 1 Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, Colorado, USA. 2 Also at NOAA Space Weather Prediction Center, Boulder, Colorado, USA. 3 NOAA Space Weather Prediction Center, Boulder, Colorado, USA. Currently, the U.S. Space Surveillance Network (SSN) tracks over 20,000 man-made objects larger than 10 cm in size, which are known as the catalogued population. Debris between 1 cm and 10 cm (approximately 500,000), referred to as the lethal population, are the most concerning as they cannot be tracked or cataloged and can cause catastrophic damage when colliding with a satellite. Objects smaller than 1 cm (approximately 135 million measuring from 1mm to 1cm, and many more smaller than 1 mm (N. L. Johnson, personal communication, 2010)) that could disable a satellite upon impact (but can be defeated by physical shields) are termed the risk population [Crowther, 2003]. The consequences of a spacecraft collision with debris can range from performance degradation to failure and satellite fragmentation. In low Earth orbit (LEO), debris as small as a few millimeters in diameter can puncture unprotected fuel lines and damage sensitive components, while debris smaller than 1 mm in Copyright 2012 by the American Geophysical Union 1of13

2 diameter can erode thermal surfaces and damage optics [National Research Council (NRC), 1995]. [3] Orbit propagation models are used to determine the location of space objects in the relatively near-term (typically over a period of a few days or less) for purposes of collision avoidance or re-entry predictions, and also to make long-term predictions (typically over a period of years) about the debris environment [e.g., NRC, 1995; Koskinen et al., 2001; Lathuillere et al., 2001; Crowther, 2003; Fukushige et al., 2007]. Both short- and long-term propagation models must take into account the various forces acting on space objects in Earth s orbit, such as atmospheric drag, solar radiation pressure, gravitational perturbations by the Sun and the Moon, and irregularities in the gravitational field of the Earth. Since accurate orbit propagation models that include all forces acting on an orbiting object can be very computation intensive, most models take into account only the forces that strongly affect the space objects in particular orbital regions. The primary forces acting on a space object in lower orbits (below 800 km) are atmospheric drag and gravitational attraction of the Earth; for space objects in higher orbits, solar and lunar gravitational influences become more important factors. Small pieces of debris can also be affected by solar radiation pressure, plasma drag and electrodynamic forces [Koskinen et al., 2001]. [4] The largest uncertainty in determining orbits for satellites operating in low Earth orbit is the atmospheric drag [Marcos et al., 2006; Doornbos, 2007]. Drag is the most difficult force to model mainly because of the complexity of neutral atmosphere variations driven by solar radiative power, magnetospheric energy inputs, and the propagation from below of lower atmosphere waves. Neutral density models used routinely in orbit determination applications are mainly empirical (e.g., COSPAR International Reference Ionosphere (1972), NASA MET [Owens et al., 2000], and DTM models [Bruinsma et al., 2003], MSIS-class models [Hedin, 1987, 1991; Picone et al., 2002], Jacchia thermospheric models [Jacchia, 1977, and references therein], and Jacchia-Bowman models [Bowman et al., 2008a, 2008c]). These models are based on historical observations to which parametric equations have been fitted, representing the known thermospheric variations with local time, latitude, season, solar and geomagnetic activity. Changes in solar and geomagnetic activity are represented by their proxies F10.7 and geomagnetic indices (Ap or Kp) with model specific combinations of lag-times, interpolation, and smoothing applied. In Jacchia- Bowman 2006 (JB2006 [Bowman et al., 2008a]) and 2008 (JB2008 [Bowman et al., 2008c]) models, additional solar indices based on orbit-based sensor data are used for the solar irradiances in the extreme (EUV) and far (FUV) ultraviolet wavelengths, and geomagnetic storm effects are modeled in JB2008 using the Disturbance Storm Time (Dst) index as the driver of global density changes [Bowman et al., 2008a, 2008c]. [5] One of the main limitations of empirical models in representing the global neutral atmosphere structure is their difficulty to capture the inherent time dependence of the atmospheric response during geomagnetic activity. Empirical models are driven by traditional geomagnetic indices, which are not able to correctly specify the magnitude of the magnetospheric forcing and follow its time dependence [e.g., Moe and Moe, 2011]. The use of scalar geomagnetic indices to describe the varying heating distributions is insufficient, and small inconsistencies in the heating location and magnitude can lead to vastly different conclusions since the upper atmosphere is strongly externally driven [Fuller- Rowell et al., 2009]. Unlike empirical models, physics-based models have the capability to describe the time-dependent evolution of neutral density, especially in long-duration geomagnetic storm events [Fuller-Rowell et al., 1999, 2006, 2009]. [6] During active conditions, the first order response to magnetospheric energy injection is thermospheric heating and thermal expansion of the neutral atmosphere gas, giving rise to an increase in density at a given altitude. In addition, the uneven expansion of the thermosphere due to the high-latitude heating produces pressure gradients that generate strong neutral winds and waves flowing equatorwards. The divergent effect of these winds drives an upwelling of molecular rich thermospheric gas from lower altitudes, enhancing the molecular species in the upper thermosphere. Changes in neutral composition affect the scale height of the atmosphere, which modulates the impact of the heating and thermal expansion on neutral density at low-altitude orbits [e.g., Fuller-Rowell et al., 1994; Kim et al., 2006; Leietal., 2010]. Divergent and convergent wind fields also drive adiabatic heating and cooling, which can further modulate the spatial distribution of the neutral density response to the heating. Recent studies showing an increase in neutral density during geomagnetic storms include Rhoden et al. [2000], who have found high-latitude density increases by as much as 134% in response to an increase in the Kp index from 1 to 6 when analyzing atmospheric density measurements near 200 km from the Satellite Electrostatic Triaxial Accelerometer (SETA) experiment. Liu and Lühr [2005] identified density enhancements up to 800% measured by the Challenging Minisatellite Payload (CHAMP) satellite at approximately 400 km altitude during three geomagnetic superstorms occurring in October and November Bruinsma et al. [2006] also found density increases in the order of % measured by CHAMP and GRACE satellites in the km height region in response to the November 2003 geomagnetic storm. Lei et al. [2010] reported pronounced density enhancements between 200 and 300% observed by CHAMP satellite during the main phase of the November 2004 storm. [7] Taking into account the self-consistent interactions between neutral winds, composition, ion drifts, and ionization densities, first-principle models are able to provide a realistic representation (of the type of improvements physics-based modeling can provide) of neutral density in the upper atmosphere if the magnitude, spatial distribution, and temporal evolution of the magnetospheric sources can be defined with sufficient accuracy [Fuller-Rowell et al., 1999; Fuller-Rowell and Solomon, 2010]. In this study, results from the self-consistent physics-based coupled thermosphere-ionosphere-plasmasphere electrodynamics model 2of13

3 (CTIPe [Fuller-Rowell et al., 1996; Millward et al., 1996]) are used along with CHAMP neutral density satellite observations [Sutton et al., 2005; Sutton, 2011] to show how the model captures the orbit-averaged daily space weather and the yearlong climatology not only in a qualitative but in a quantitative way. In addition, preliminary results on the establishment of a relationship between high-latitude Joule heating and the neutral density response is presented. For the current analysis, model results and satellite measurements orbit averages are used since comparisons along the orbit would accentuate details of the structures and shorttime scales, which are irrelevant in the Joule heating and neutral density relationship derivation process. [8] Section 2 presents an overview of CTIPe model, followed by a brief description of CHAMP satellite mission in section 3. Comparisons between CHAMP neutral density observations and CTIPe model results are presented in section 4. In section 5, the neutral density response to magnetospheric energy sources during a moderate geomagnetic storm is analyzed. Initial results on the development of a Joule heating index derived from the relationship between CTIPe Joule heating and CHAMP neutral density are presented in section 6. A summary is provided in section CTIPe Model [9] The coupled thermosphere-ionosphere-plasmasphere electrodynamics (CTIPe) model is a global, three-dimensional, time-dependent, nonlinear, self-consistent model that solves the momentum, energy, and composition equations for the neutral and ionized atmosphere. CTIPe has evolved from the union of three physical models. The first is a global, nonlinear, time-dependent neutral thermospheric code developed by Fuller-Rowell and Rees [1980, 1983]. The second is a mid- and high-latitude ionospheric convection model developed by Quegan et al. [1982]. These first two components were initially coupled self-consistently and are known as the Coupled Thermosphere-Ionosphere Model (CTIM) [Fuller-Rowell et al., 1996]. CTIM was further extended by including a third component, a plasmasphere and low latitude ionosphere [Millward et al., 1996], to produce CTIP. Later the electrodynamics was solved self-consistently with the neutral dynamics and plasma components. The electrodynamic calculation was developed by Richmond and Roble [1987] and was included in the CTIP model by Millward et al. [2001], resulting in the creation of CTIPe. The global atmosphere in CTIPe is divided into a series of elements in geographic latitude, longitude, and pressure. The latitude resolution is 2, the longitude resolution is 18, and each longitude slice sweeps through local time with a 1 min time step. In the vertical direction, the atmosphere is divided into 15 levels in logarithm of pressure from a lower boundary of 1 Pa at 80 km to more than 500 km altitude [Fuller-Rowell et al., 2002]. The magnetospheric input is based on the statistical models of auroral precipitation and electric fields described by Fuller-Rowell and Evans [1987] and Weimer [2005], respectively. The auroral precipitation is keyed to the hemispheric power index (PI), based on the TIROS/ NOAA auroral particle measurements, and has been available since the mid 1970s. The PI index runs from 1 to 10 to cover very quiet to storm levels of geomagnetic activity; the relationship between PI and K p is described by Foster et al. [1986]. The Weimer electric field model is keyed to the solar wind parameters impinging the Earth s magnetosphere. The input drivers include the magnitude of the interplanetary magnetic field (IMF) in the y-z plane, together with the velocity and density of the solar wind. The new version of the Weimer model accommodates a realistic saturation of the magnetospheric potential for high solar wind velocities and magnetic field. The (2,2), (2,3), (2,4), (2,5), and (1,1) propagating tidal modes are imposed at 80 km altitude [Fuller-Rowell et al., 1991; Müller-Wodarg et al., 2001] with a prescribed amplitude and phase. Realistic tidal forcing is required for the quiet time dynamo, which is disturbed by the storm-time wind field and conductivity changes. CTIPe uses time-dependent estimates of nitric oxide (NO) obtained from Marsh et al. [2004] empirical model based on Student Nitric Oxide Explorer (SNOE) satellite data rather than solving for minor species photochemistry self-consistently. Solar heating, ionization and dissociation rates, and their variation with solar activity are specified by Solomon and Qian [2005] solar EUV energy deposition scheme for upper atmospheric general circulation models. 3. CHAMP Satellite [10] The German satellite CHAMP (Challenging Minisatellite Payload) was launched in July 2000 into a polar orbit (87.3 inclination) at 456 km altitude. Drifting in local time, CHAMP covered all local time sectors in about 130 days. The project plan included a 5-year mission duration to study the gravity and magnetic fields of the Earth, with a secondary goal of studying the upper atmosphere. The thermospheric density observations were inferred from measurements taken by a highly sensitive triaxial accelerometer on board the spacecraft [e.g., Lühr et al., 2004; Bruinsma et al., 2004; Sutton et al., 2005; Sutton, 2011]. Nine years after its launch, the orbital altitude has gradually decreased to about 311 km (Franz-Heinrich Massmann, private communication, 2009), ending its mission by natural atmospheric re-entry in September 2010 [GeoForschungsZentrum (GFZ), 2010]. As a result of the satellite s long life span, almost a full solar cycle of neutral density measurements containing information at unprecedented levels of detail and coverage are available for thermospheric studies. 4. Model/Data Comparisons [11] In this section, one year of neutral density simulations from CTIPe are compared with CHAMP satellite observations during The predominantly quiet to moderate geomagnetic conditions during that year are ideal to assess the capability of the CTIPe model in specifying the upper atmosphere s climatology and day-to-day- 3of13

4 Figure 1. (a) Comparison of orbit-averaged observed (CHAMP) and modeled (coupled thermosphere-ionosphere-plasmasphere electrodynamics (CTIPe)) neutral density at 400 km altitude during the year (b) Scatterplot and linear regression between observations and model results for the same period. An identity line (dashed line) is drawn as a reference. Results from the statistical analysis are correlation coefficient (R) = 0.73, root-mean square errors (RMSE) = 0.31, bias = 0.23, and standard deviations (SD) = variability, and to identify areas that require improvement in the model. Model/data comparisons are performed through time series, and evaluation of correlation coefficients (R), root-mean square errors (RMSE), biases, and standard deviations (SD). The correlation coefficient is a measure of the degree of linear relationship between two variables; root mean square error is a quadratic scoring rule which measures the average magnitude of the error (i. e., the difference between values predicted by a model and the values actually observed); the bias determines whether results are consistently too high or too low relative to a given actual value of the measured or estimated variable; the standard deviation measures the dispersion of a set of data from its mean value. In this study, the ratios between modeled and measured density are used in the statistical analysis, in a similar way as done by Marcos et al. [2006]. [12] Figure 1a shows a comparison between orbit-averaged CHAMP observations normalized to 400 km of altitude and CTIPe neutral density during the year CTIPe results are interpolated to the same altitude, latitude, and longitude as the satellite before the orbit average is applied. The black and orange lines represent the orbit averages of density for CHAMP and CTIPe, respectively. The model was able to follow the observations with quite high fidelity at solstice, but its density values are lower during months around equinox. Particularly, the model is underestimating the semi-annual variation in neutral density. The semi-annual variation is characterized by a six-month periodicity with density maxima in April and October, soon after equinoxes [e.g., Bowman et al., 2008b]. At low solar activity, when solar rotation modulation of EUV flux is small, the semi-annual variation is the main source of density (and satellite drag) change in the upper thermosphere [Fuller-Rowell et al., 1997]. The agreement between model and observations is also illustrated by the scatterplot and the linear regression presented in Figure 1b. An identity line (i.e., a y = x line) is drawn as a reference. Results from the statistical analysis show R = 0.73, RMSE = 0.31, bias = 0.23, and SD = 0.21, indicating that model results underestimate the measurements. It is clear that the semi-annual variation in density observations is not captured by the model. [13] There are various mechanisms that could contribute to the semi-annual variation in neutral density, such as the seasonal variation in eddy diffusivity in the upper mesosphere and lower thermosphere regions due to gravity wave breaking [Qian et al., 2009], and the thermospheric spoon mechanism associated with the global scale interhemispheric circulation at solstice [Fuller-Rowell, 1998]. The former mechanism is not included in the model, and it is possible that a combination of its effects and various others listed by Qian et al. [2009] could be responsible for the semi-annual variation in density. This is still an open question, and further investigation is required to understand the seasonal processes in the upper atmosphere. [14] The main purpose of this study is to simulate the model response to short-period variations in geomagnetic activity during the year. To accommodate this goal the disagreement between CTIPe and CHAMP caused by the semi-annual effect has been removed by introducing a semi-annual variation in electric field small-scale variability. Electric fields can directly change Joule heating by varying the ion convection at high-latitudes [Deng and Ridley, 2007]. An increase in Joule heating raises the neutral temperature, which enhances the neutral density at constant heights. According to Codrescu et al. [1995, 2000], electric field variability changes the distribution of Joule heating significantly, and can introduce interhemispheric 4of13

5 Figure 2. (a) Same as in Figure 1a, but the seasonal variation in the electric field small scale variability is now included in the model simulation. (b) Scatterplot and linear regression between observations and model results for the same period. An identity line (dashed line) is drawn as a reference. Results from the statistical analysis are R = 0.88, RMSE = 0.17, bias = 0.017, and SD = asymmetries. CTIPe model simulation results showing the inclusion of a seasonal variation in the electric field small-scale variability are presented in Figure 2a. As in Figure 1a, the black and orange lines represent the orbit averages of density for CHAMP and CTIPe, respectively. There is a significant improvement in the agreement with satellite observations. During more active conditions the model slightly overestimates measurements at times, possibly due to the uncertainty in the magnitude and spatial distributions of the magnetospheric electric field and auroral precipitation. Including just a semi-annual variation of this source does not capture all the intraannual variability. For instance, CTIPe density values relative to CHAMP are still lower around March equinox. However, enough of the long-term variation has been modeled to enable the dependence on the geomagnetic response to be investigated. As mentioned earlier, this method is not the only way to eliminate the unmodeled semi-annual variation, but serves the current purpose. Figure 2b shows the scatterplot and the linear regression between observations and model for this new simulation. Results from the statistical analysis are: R = 0.88, RMSE = 0.17, bias = 0.017, and SD = 0.17, which is a significant improvement on the previous statistics, largely by decreasing the bias associated with the unmodeled semiannual variation. We expect more detailed tuning of the intraannual variability would improve the correlation further, but the agreement is sufficient for the current analysis. 5. Partitioning of Energy [15] The improved agreement between model and observations suggests that the amount of energy influx from solar radiation and magnetospheric sources deposited into the atmosphere is reasonably accurate, enabling the model to be used to estimate the rate of energy influx from those sources. As an example, a numerical simulation showing the response of neutral density to a moderate geomagnetic storm is presented in Figure 3. The highlatitude heat input caused thermal expansion of the neutral atmosphere, increasing the mass density at constant heights during the disturbed conditions. The neutral density enhancement was observed by CHAMP satellite on January 7 8, and CTIPe model was able to follow the observations quite well (Figure 3a). Figure 3b shows the auroral particle energy, which can directly heat the neutral thermosphere via collisions, with indirect contributions from ionization and excitation processes [Olson and Moe, 1974]. Accounting for the majority of energy input into the ionosphere/thermosphere system, the integrated Joule heating in the Northern and Southern hemispheres are presented in Figures 3c and 3d, respectively. Joule heating, calculated as the scalar product of the current and electric field, is a term used to describe the Ohmic production of heat that occurs as the charged particles drifting in response to the electric field collide with the neutral particles of the resistive medium [Palmroth et al., 2005]. In addition to Joule heating, kinetic energy (Figure 3e) is injected by the action of the ion drag. Above 100 km altitude, collisions between ions and neutrals tend to drag neutral gas in a similar convection pattern to that of the ions. If the two were to match, Joule heating would drop to zero, but other forces controlling the neutral gas, such as Coriolis, viscosity, and inertia, restrict the neutrals from following the ions exactly. Acceleration of the neutrals in the direction of the ions therefore tends to modulate the magnitude and spatial distribution of Joule heating [e.g., Thayer et al., 1995; Richmond and Thayer, 2000]. While Joule and auroral particle heating increase the temperature of the upper atmosphere during geomagnetic storms, the enhanced 5.3 mm infrared radiative emission from excited 5of13

6 Figure 3. Thermospheric neutral density and partitioning of energy during a moderate geomagnetic storm in January Shown is (a) a comparison between CHAMP neutral density measurements and CTIPe numerical simulation results at 400 km altitude. Also shown are (b) estimates of auroral power, (c and d) Joule heating in the Northern and Southern hemispheres, (e) kinetic energy deposition, and (f) nitric oxide infrared cooling rates. NO is responsible for cooling the thermosphere [e.g., Mlynczak et al., 2005; Dobbin and Aylward, 2008; Lu et al., 2010]. Figure 3f shows the time history of the NO radiative cooling in the Northern hemisphere from the CTIPe model simulation. NO cooling peaks between 150 and 200 km altitude, and is the main heat loss mechanism controlling the recovery of neutral temperature and density to geomagnetic activity, in addition to downward heat conduction [e.g., Roble et al., 1987; Maeda et al., 1992]. [16] These results are in general agreement with previous studies in the literature showing that some of the energy supplied to the magnetosphere from the solar wind during geomagnetic storms is dissipated by deposition into the atmosphere via auroral particle precipitation and Joule heating, the latter being generally the dominant source [e.g., Sharber et al., 1998; Lu et al., 1995; Chun et al., 2002; Wilson et al., 2006; Fuller-Rowell and Solomon, 2010]. 6of13

7 Figure 4. Shaping filter resulting from the cross correlation between 2007 neutral density residuals (CHAMP minus quiet time JB2008) and 2007 CTIPe Joule heating. Knipp et al. [2004] showed that Joule power alone (not accounting for small-scale variability of the electric field, which could add considerably to the Joule power) exceeded the combined particle and solar EUV power during 13 extreme events of the solar cycles According to Fuller-Rowell and Solomon [2010], the total global Joule power can be greater than the combined solar UV and EUV radiation during typical storms that are not extreme, such as the storm case presented in Figure 3. Joule power transfers energy to the neutral gas at nearly 100% efficiency [Thayer and Semeter, 2004], therefore even moderately elevated Joule power values can compete with solar power as the dominant heating mechanism in the upper atmosphere [Knipp et al., 2004]. [17] Although Joule heating is a fundamental parameter in the energy transfer processes between solar wind and magnetosphere-ionosphere-thermosphere system during geomagnetic disturbances, its continuous global monitoring has been difficult. Various authors have been able to estimate Joule heating from geomagnetic indices derived from rocket-borne instrumentation, incoherent scatter radar, and ground-based and satellite magnetometer measurements [Baumjohann and Kamide, 1984, and references therein; Anderson et al., 1998]. Single station observations can only provide Joule heating rates integrated over a small area [Baumjohann and Kamide, 1984], and ground network observations can be difficult during highly disturbed periods because the auroral oval expands equatorward of the observation sites [Anderson et al., 1998]. Another method for calculating Joule heating is the assimilative mapping of ionospheric electrodynamics (AMIE) procedure [Richmond and Kamide, 1988; Richmond et al., 1990; Richmond, 1992], which combines data from ground magnetometers, satellites and radar. Although this technique has been improved over the last two decades in terms of the data assimilation and mathematical methods, it has limitations in obtaining accurate estimates of energy inputs to the upper atmosphere [Richmond et al., 1998]. Taking advantage of the near real-time availability of the polar cap (PC) index, Chun et al. [1999, 2002] showed that PC can be used as a proxy measurement of the hemispheric integrated Joule heating rate into the domain of spatial variations. In their study, AMIE was used to derive Joule heating, which is underestimated during strong storms. Knipp et al. [2004, 2005] have addressed that concern by including the Dst index as an additional fit parameter to improve Joule power estimates. Fixed statistical maps of the electric potential pattern derived from satellite and radar measurements [e.g., Foster, 1983; Heppner and Maynard, 1987] and analytical expressions of the electric potential distributions [e.g., Heelis et al., 1982] also have been used to determine Joule heating rates. These studies have steadily evolved to more advanced computer models that can reproduce the statistical patterns for arbitrary solar wind conditions [Weimer, 2005, and references therein]. Magnetohydrodynamic (MHD) models of the magnetosphere [e.g., Wiltberger et al., 2004; Palmroth et al., 2005; Li et al., 2011] have been used to estimate Joule heating. These models seem to be able to better handle extreme conditions that are not well represented in empirical electric field models. 6. Relationship Between CTIPe Joule Heating and CHAMP Neutral Density [18] Since CTIPe is able to follow the CHAMP neutral density response with reasonable fidelity, it is now possible to explore the use of Joule heating estimated by the model as an alternative index for the neutral density response. In this study, an index based on CTIPe Joule heating is derived. This index is obtained from the relationship between yearlong time series of CTIPe Joule heating and CHAMP neutral density observations during The seasonal and solar cycle influences in the CHAMP neutral density observations are removed, so that residual neutral density variations are primarily due to geomagnetic activity. This is achieved by subtracting the quiet time density from the satellite density measurements. The quiet time density is obtained from the empirical model JB2008, assuming no variation from geomagnetic activity, i.e., Ap and Dst are set to zero. Orbit averages (1.5 h) for CHAMP, quiet time JB2008, and Joule heating are used in this process. [19] The neutral density signature is a cumulative, or integrated, response to Joule heating. How far in the past Joule heating impacts density depends on the recovery timescale of the thermosphere, which is controlled largely by vertical heat conduction and NO cooling. Therefore, the correlation of neutral density with Joule heating over the previous 4 days is examined using a temporal resolution of 90 min, which corresponds to roughly one CHAMP orbit. The cross-correlation as a function of time lag is shown in Figure 4. The maximum cross-correlation is found at about 8 h, beyond which the correlation gradually decreases, approaching zero after a lag of about 3 days. This implies that magnetospheric energy sources up to 3 days before 7of13

8 Figure 5. Scatterplot and linear regression between 2007 CHAMP observations and the new absolute density estimated from Joule heating index (JHI) using 2007 CTIPe Joule heating with 2007 shaping filter applied, added to quiet time JB2008. An identity line (dashed line) is drawn as a reference. Results from the statistical analysis are R = 0.92, RMSE = 0.10, bias = 0.01, and SD = are affecting the neutral density at the current time. It also implies that the recovery time is about 3 days from NO cooling and downward heat conduction, which is consistent with the recovery time scales presented by Maeda et al. [1992]. The correlation analysis in Figure 4 provides the filter shape by which to scale the time series of Joule heating to best match the CHAMP neutral density. [20] The shaping filter in Figure 4 contains the information relating time-dependent geomagnetic activity to the atmospheric response. Using this information, it is possible to obtain estimates of neutral density residuals from CTIPe Joule heating values. This can be done through a convolution procedure, which determines a system s output (density residuals) from knowledge of the input (Joule heating) and the system s impulse response (shaping filter). By convolving CTIPe Joule heating with the shaping filter, the result is a new parameter representing the integral of the product of the two functions. This new parameter is named Joule heating index (JHI). A linear regression between JHI and the observed density residuals (CHAMP minus quiet time JB2008) is then used to produce the new density residuals derived from JHI. Finally, the new absolute values of neutral density are obtained by adding the density residuals derived from JHI to the quiet time JB2008 neutral density. The improvement in density estimates using this method is presented in Figure 5, which shows the correlation between CHAMP observations and the new density derived from JHI. The statistical analysis results are R = 0.92, RMSE = 0.10, bias = 0.01, Figure 6. Scatterplot and linear regression between 2007 CHAMP observations and density estimated from 2008 Jacchia-Bowman empirical model. An identity line (dashed line) is drawn as a reference. Results from the statistical analysis are R = 0.90, RMSE = 0.16, bias = 0.06, and SD = and SD = This technique also improves the neutral density calculated by JB2008 empirical model using the Dst index. The correlation between CHAMP observations and JB2008 density is presented in Figure 6, where R = 0.90, RMSE = 0.16, bias = 0.06, and SD = [21] A true test of the JHI is to develop the filter from one year and apply it to another. The 2005 yearlong CTIPe Joule heating and CHAMP neutral density measurements are used to obtain this new filter according to the process described above. Figure 7 presents the 2005 shaping filter showing the maximum of cross-correlation at about 5 h. Figure 7. Shaping filter resulting from the cross correlation between 2005 neutral density residuals (CHAMP minus quiet time JB2008) and 2005 CTIPe Joule heating. 8of13

9 Figure 8. Scatterplot and linear regression between 2007 CHAMP observations and the new absolute density estimated from JHI using 2007 CTIPe Joule heating with 2005 shaping filter applied, added to quiet time JB2008. An identity line (dashed line) is drawn as a reference. Results from the statistical analysis are R = 0.95, RMSE = 0.09, bias = 0.007, and SD = The convolution of 2007 CTIPe Joule heating with the 2005 shaping filter generates a new set of JHI values. The linear regression is then used to obtain the new density residuals derived from JHI, which are added to the 2007 quiet time JB2008 neutral density to produce the absolute neutral density. The correlation between CHAMP observations and the density derived from this JHI is shown in Figure 8, and the statistical analysis results are: R = 0.95, RMSE = 0.09, bias = 0.007, and SD = 0.09, showing the best results so far. A summary of the neutral density comparison results is presented in Table 1. [22] To illustrate how neutral density calculated by the models and derived from CTIPe Joule heating compare to satellite observations, a two-month time series of neutral density including a moderate geomagnetic storm is presented in Figure 9. During the entire year 2007, the maximum level of geomagnetic activity was below Kp = 6. All four lines are orbit averaged neutral density at 400 km altitude: the black line are CHAMP observations, the orange line represents CTIPe neutral density, the light blue line is JB2008 neutral density, and the green line corresponds to the new density estimated using the 2007 CTIPe Joule heating convolved with the 2005 shaping filter and added to the quiet time density from JB2008. The line showing density estimated using the 2007 CTIPe Joule heating convolved with the 2007 shaping filter is very close to the 2005 shaping filter case, so it was not shown to avoid confusion from too many lines. Although the new density underestimate at times the storm-time density enhancements observed by CHAMP, they are following the satellite measurements quite well. The agreement between satellite observations and densities estimated from CTIPe Joule heating is very dependent on the accuracy of the spatial distribution and magnitude of the Joule heating source. [23] The procedure described in this section is also performed for the 2005 data set. The correlation between 2005 CHAMP observations and the neutral density derived from JHI obtained through the convolution of 2005 CTIPe Joule heating with the 2005 shaping filter is However, when applying the 2007 shaping filter to the same Joule heating, the correlation decreased to 0.83, which is possibly due to a couple of factors. First, the year 2005 was significantly more active geomagnetically than 2007 (and the average density was about twice as high). Therefore, the 2007 filter does not contain representative information regarding large storm events, and may not correctly specify the neutral density during more disturbed conditions. Second, satellite orbit determination algorithms revealed events with poorly specified enhanced neutral density in year 2005, according to Knipp et al. [2011]. These authors reported studies unable to reproduce local dayside Joule heating rates measured by a Defense Meteorological Satellite (DMSP) spacecraft during large IMF B y conditions, including the Joule heating produced from Weimer s [2005] statistical patterns. Electric fields from Weimer [2005] are used in the computation of CTIPe Joule heating. 7. Summary [24] Joule heating is a fundamental parameter in the energy transfer processes between the solar wind and the magnetosphere-ionosphere-thermosphere system. Joule heating is particularly important during geomagnetically disturbed times when the total global Joule power can be greater than the combined solar UV and EUV radiation absorption even during typical storms that are not Table 1. Summary of Neutral Density Comparisons for 2007 CHAMP Versus Correlation Coefficient (R) Root-Mean-Square Error (RMSE) Bias Standard Deviation (SD) CTIPe JB JB2008 quiet + density residuals using 2007 shaping filter JB2008 quiet + density residuals using 2005 shaping filter of13

10 Figure 9. Two-month time series comparison of CHAMP observations with neutral density calculated by CTIPe physics-based model, JB2008 empirical model, and the new density derived from CTIPe Joule heating. All four lines are orbit averaged neutral density at 400 km altitude: the black line is CHAMP observations, the orange line represents CTIPe neutral density, the light blue line is JB2008 neutral density, and the green line corresponds to the new density estimated using the 2007 CTIPe Joule heating convolved with the 2005 shaping filter and added to the quiet time density from JB2008. extreme. This work presents preliminary results on the establishment of a relationship between high-latitude Joule heating and the neutral density response in the thermosphere. Joule heating calculated by CTIPe physicsbased model and neutral density measured by the CHAMP satellite are used to establish the relationship. When model results and observations are in good agreement, the model can be used to estimate the rate of energy influx from magnetospheric sources. [25] The model does not self-consistently capture the full semi-annual variation in density, underestimating the observations during equinox. An improvement in model/ data agreement was obtained by introducing a seasonal variation in the electric field small-scale variability in CTIPe, which increased Joule heating at equinox, and raised the neutral temperature and density at constant heights. The seasonal variation introduced in the model is consistent with electric field variability observations. [26] The global monitoring of Joule heating has been difficult. Joule heating provided by CTIPe model driven by solar wind and interplanetary magnetic field data is able to specify the magnitude of the magnetospheric forcing and follow its time dependence. The relationship between CTIPe Joule heating and neutral density satellite observations contains the information relating time-dependent geomagnetic activity to the atmospheric response. This information is captured in a Joule heating index that can improve neutral density estimates in empirical models. In the year 2007, for instance, the correlation and standard deviation between CHAMP observations and neutral densities computed by Jacchia-Bowman 2008 empirical model at 400 km altitude are, respectively, 0.90 and These numbers have improved to 0.95 and 0.09, when comparing satellite observations with neutral density values computed using CTIPe Joule heating index. This analysis will be extended to a full solar cycle of observations and model simulations. [27] Having the capability to forecast Joule heating would be ideal. Currently, it is possible to obtain Joule heating from CTIPe about min ahead of real-time, as solar wind and IMF input parameters are provided by the Advanced Composition Explorer (ACE) spacecraft. CTIPe model results are generated using the latest version of the code running automatically at ctipe/ [Codrescu et al., 2012]. In the future, solar wind and magnetosphere models may be able to predict important external drivers for thermosphere-ionosphere models, so a few hours to a few days forecast of the Joule heating index and therefore neutral density would be possible. [28] Quantifying and understanding the dependence of Joule heating on various geomagnetic conditions is relevant due to its effects on operational systems. Joule heating is the dominant heating mechanism affecting the neutral density during disturbed conditions. Knowing its magnitude and spatial distribution is important for the accuracy of neutral density specification and atmospheric drag determination. [29] Acknowledgments. Funding for this research was provided by the AFOSR MURI NADIR project. The authors would like to thank Eric Sutton of the Air Force Research Laboratory for providing neutral density data from the CHAMP satellite, and Bruce Bowman of the Air Force Space Command for assistance with JB2008 empirical thermospheric density model runs. 10 of 13

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