Height-dependent energy exchange rates in the high-latitude E region ionosphere

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, , doi: /2013ja019195, 2013 Height-dependent energy exchange rates in the high-latitude E region ionosphere L. Cai, 1 A. T. Aikio, 1 and T. Nygrén 1 Received 4 July 2013; revised 6 September 2013; accepted 21 October 2013; published 15 November [1] The statistical properties of the altitude profiles of the different energy transfer rates in the auroral ionosphere are studied by using the European Incoherent Scatter radar measurements in Tromsø (67 ı cgmlat). Aikio et al. (2012) found that during active conditions, winds reduce the height-integrated Joule heating rates in the evening but enhance them in the morning. Here we show that the reduction in the evening takes place close to and above the peak altitude of Joule heating, so that the Joule heating peak descends from the Pedersen conductivity maximum at 120 km down to about 115 km. Values close to the peak are reduced also in the morning, but the positive effect by winds above the peak makes the net effect positive. The altitude range where the electromagnetic energy of magnetospheric origin is converted to the mechanical energy of the neutrals is only km wide in the E region and shows a clear magnetic local time variation. Model calculations are made to study the effect of the angle between the wind and electric field directions on the energy transfer rates and to explain the observed features. Citation: Cai, L., A. T. Aikio, and T. Nygrén (2013), Height-dependent energy exchange rates in the high-latitude E region ionosphere, J. Geophys. Res. Space Physics, 118, , doi: /2013ja Introduction [2] The flow and conversion of electromagnetic energy from or to other forms of energy and the related Joule heating are the key processes in the coupling between the magnetosphere and the ionosphere-thermosphere system, which have been studied theoretically [Cole, 1962, 1971; Cowley, 1991; Vasyliunas and Song, 2005; Strangeway, 2012], with simulations [e.g., Thayer et al., 1995; Lu et al., 1995; Deng and Ridley, 2007; Deng et al., 2008], and by using observations [e.g., Brekke and Rino,1978;Thayer, 1998a,1998b;Fujii et al., 1998, 1999; Thayer, 2000; Thayer and Semeter, 2004; Aikio and Selkälä, 2009; Aikio et al., 2012]. Many works have estimated the height-integrated and global Joule heating rates based on magnetic indices [e.g., Ahn et al., 1983; Foster et al., 1983; Chun et al., 1999; Tanskanen et al., 2002; Østgaard et al., 2002] and empirical models [e.g., Weimer, 2005; McHarg et al., 2005]. [3] The electromagnetic (EM) energy exchange rate between the plasma and the electromagnetic field can be described using the Poynting s theorem [Cowley, 1991; Thayer and Vickrey, 1992]. In a quasi steady state, the conversion of EM energy to other forms is equal to the divergence of the Poynting vector. The EM energy exchange rate can further be partitioned between the Joule heating and the mechanical energy transfer rate. The Joule heating calculated in the frame of reference of the neutral atmosphere has 1 Department of Physics, University of Oulu, Oulu, Finland. Corresponding author: L. Cai, University of Oulu, Oulu, Finland. (lei.cai@oulu.fi) American Geophysical Union. All Rights Reserved /13/ /2013JA been shown to be mostly frictional heating due to relative motion of ions and neutrals, and the resulting thermal energy is distributed both to the neutrals and ions increasing their temperature [e.g., Thayer and Semeter, 2004;Vasyliunas and Song, 2005]. In the absence of spatial gradients, the mechanical work done on neutrals will go to the bulk-flow kinetic energy of the neutral air. [4] Motion of the neutral gas is an integral element in the different energy exchange rates. Thayer [2000] showed in a statistical study that a reduction in the electromagnetic energy exchange rate by neutral winds takes often place when the conductivity-weighted wind has a component in the E B direction. However, the role of the neutral winds in the energy exchange processes is still poorly known, partly because reliable measurements of the neutral wind in the thermosphere are sparse. [5] When the neutral winds are neglected, the EM energy exchange rate becomes equivalent to the Joule heating rate. In addition, the height distribution of the Joule heating rate then depends solely on the Pedersen conductivity profile. [6] For calculation of the altitude profiles of energy exchange rates, simultaneous measurements of electric fields, conductivity profiles, and neutral wind profiles with sufficient temporal and height resolution are needed. The incoherent scatter radar provides a comprehensive way to measure the key parameters in the ionosphere and to estimate the neutral winds in the E region [e.g., Brekke et al., 1994; Thayer, 1998a; Fujii et al., 1998, 1999; Heinselman and Nicolls, 2008; Nygrén et al., 2011]. However, since neutral wind determination requires either tristatic observations at several preselected altitudes (only available from the European Incoherent Scatter (EISCAT) radar) or multiple-beam direction experiments, very few

2 studies on height-resolved energy exchange rates have been made: Thayer [1998a, 1998b] studied two events, Fujii et al. [1998] studied one event, and Fujii et al. [1999] conducted a statistical study based on 28 day measurements. These will be discussed in section 5. [7] Recently, Aikio et al. [2012] presented statistical results of height-integrated energy exchange rates based on EISCAT beam-swing experiments. It was found that the maximum of the EM energy input took place in the evening sector, but due to the effect of winds, the Joule heating rate reached a maximum in the morning sector. For quiet conditions, the neutral wind was the major source of Joule heating. During active conditions, winds increased the Joule heating rates in the morning but reduced them in the evening. Up to 20% of the EM energy exchange rate was converted to the mechanical energy of the neutrals in the afternoon-evening sector during medium and high activity conditions. [8] It is important to elucidate the altitude profiles of energy exchange rates, since those have an effect on the 3-D electrodynamics, neutral dynamics, ion-neutral chemistry, and possible atmospheric gravity wave generation [e.g., Richmond, 1978]. In this paper, the altitude-dependent energy exchange rates from the data used in Aikio et al. [2012] (hereafter ACN12) will be studied. We will show the statistics on the Hall and Pedersen conductivity profiles, the altitude profiles of energy exchange rates, and neutral winds by grouping them in three Kp index intervals and eight magnetic local time (MLT) regions. The observations are interpreted by utilizing simple model calculations, which illustrate the role of the angle between the electric field and the wind direction as well as the magnitudes of the electric field and the wind. We will show which altitude regions are responsible for the effects reported in ACN Measurements and Data Analysis [9] In this study, the ionospheric parameters were measured by the EISCAT UHF incoherent scatter radar in Tromsø (geographic: ı N, ı E and corrected geomagnetic: ı N, ı E). Two long runs of the Common Programme 2 (CP2) experiment were used, which were during 6 30 September 2005 and November The CP2 experiment is a scan in four beam directions, for which the azimuth-elevation angle pairs are (180 ı,90 ı ), (185 ı,77 ı ) parallel to B, (166 ı,64 ı ),and(133 ı,62 ı ).The measurement in each direction lasts about 60 s, antenna moves during 30 s, and the cycle takes 6 min. [10] The data base is the same one as in ACN12, and the data analysis is similar, with two small modifications. First, as input to the NRLMSISE-00 model, actual activity indices are used. Second, we have used even more strict criteria to remove outliers of neutral wind results. We will give the basic information of the data analysis below. For more detailed explanation, see ACN12. [11] The calculation of the Pedersen and Hall conductivities is based on the standard equations [Brekke and Hall, 1988; Moen and Brekke, 1990]. The electron densities from EISCAT and model ion-neutral and electron-neutral collision frequencies are used as input. For collision frequency calculations [Brekke and Hall, 1988], the densities of the neutral constituents and the neutral temperature are taken from the NRLMSISE-00 model [Picone et al., 2002]. We use the actual F10.7, F10.7a, andap indices as input to the model. The time resolution of the conductivities is 90 s, and the height resolution is 1 km. In the calculation of standard deviations, only the electron density errors are taken into account. [12] The most probable values of the electric field and the neutral wind with error estimates are calculated by means of stochastic inversion [Nygrén et al., 2011]. The time resolution for the electric field is the radar cycle time, 6 min, and the neutral wind is calculated at 12 min steps with 24 min resolution. Eight height ranges for the neutral wind are used: 80 90, , , , , , , and km. We use the method described in Nygrén et al. [2012] to improve the neutral wind estimation. In addition, we discard neutral wind results exceeding a given altitude-dependent limit using the following criteria: 200 m/s at km, 400 m/s at km, 800 m/s at km, and 1500 m/s at km. The selected threshold values reflect the fact that at high latitudes, wind magnitudes increase with altitude above about 120 km [e.g., Kwak and Richmond, 2007]. [13] The energy exchange rates of interest are the EM energy transfer rate q EM = j E, the Joule heating rate q J = j (E + u B), and the mechanical energy transfer rate q m = u (j B), wherej is the current density, E is the electric field, u is the neutral wind velocity, and B is the magnetic field. The values of q EM are positive at those altitudes where the EM energy is deposited in the ionosphere. If the ionosphere is a generator of EM energy, q EM is negative. The Joule heating rate corresponds to the ion-neutral frictional heating rate in most conditions. Since Joule heating describes energy dissipation, it is always positive. Positive q m means that mechanical work is done on neutrals, and negative q m means that neutral wind is doing work. In the absence of spatial gradients, the mechanical work done on neutrals will go into the bulk-flow kinetic energy of the neutral air, as discussed by Vasyliunas and Song [2005]. For details of the different energy rates, see ACN12. The three energy exchange rates obey the equation 7370 q EM = q J + q m. (1) Hence, if the magnetosphere is providing EM energy into the ionosphere, it can be distributed between Joule heating and mechanical work on the neutral wind. [14] The energy exchange rates can be expanded as follows q EM = P E 2 + P E (u B)+ H B u E = q E + q P + q H, (2) and q J = P E 2 +2 P E (u B)+ P (u B) 2 = q E +2 q P + q u, (3) q m = P E (u B) P (u B) 2 + H B u E = q P q u + q H. (4) In the equations above, P and H are the Pedersen and Hall conductivities, q E is equal to the Joule heating rate in the absence of neutral wind, and the quantities q P, q H,andq u are called the Pedersen, Hall, and wind terms, respectively. The altitude variation of q E is determined only by the height profile of the Pedersen conductivity since medium-scale

3 Figure 1. Statistical profiles of the Pedersen conductivity within 3 h MLT sectors for (top) low, (middle) medium, and (bottom) high geomagnetic activity conditions. Thick lines are median values, and the lower and upper quartiles are shown by shaded colours.the parameter = H / P is the ratio of height-integrated conductivities. electric fields map at a constant value within the studied altitude range. The wind term q u depends on the Pedersen conductivity and wind altitude profiles. The Pedersen and Hall terms depend on the respective conductivity profiles, the angle between E and u as well as the electric field and wind magnitudes. These terms will be studied in section 4 to understand the role of the different parameters in energy exchange rates. [15] The conductivity profiles have 90 s time resolution, and the electric field and the neutral wind are interpolated linearly according to the times of conductivity profiles. Consequently, the time resolution for the calculated energy exchange rates is 90 s, and the height resolution is 1 km for altitudes from 80 to 180 km. 3. Statistical Results [16] In the statistical study, the altitude profiles of the median values of all the parameters are grouped into 3 h MLT sectors and three geomagnetic activity conditions. The sectors are 00 03, 03 06, 06 09, 09 12, 12 15, 15 18, 18 21, and MLT. The geomagnetic activity conditions are represented by three 3 h Kp index intervals: Kp: 0 2 (low), Kp: (medium), and Kp > 5 (high) The average number of the profiles in the 3 h MLT sectors is 1300 for low, 1250 for medium, and 800 for high activity conditions. In addition to median (50% percentile) values, we have calculated the lower (25%) and upper (75%) percentiles for the parameters. We use the median instead of the mean as a measure of central tendency to avoid a bias caused by outliers or nonnormal distribution of parameter values Hall and Pedersen Conductivities [17] The altitude profiles of the Pedersen (red curves) and Hall (black curves) conductivities are shown in Figure 1. In the daytime, the conductivities depend on the solar radiation and the solar zenith angle [Schlegel, 1988; Senior, 1991]. At night, the conductivities may be increased due to particle precipitation. Hence, the peak values increase with enhanced geomagnetic activity (from top to bottom). Pedersen conductivity profiles are less affected by geomagnetic activity than Hall conductivity profiles. When going from low to medium and finally to high activity conditions, the MLT region of maximum conductivities shifts from to and finally to MLT. The peak altitude of the Pedersen conductivity stays all the time close to 120 km, while the peak altitude of the Hall conductivity decreases from 113 to 102 km with increasing activity.

4 magnetic activity in the morning and premidnight sectors. At MLT, does not increase with increasing activity, although the peak conductivities grow. This suggests that the number flux of precipitating electrons increases, but the characteristic energy remains the same. Our results are in agreement with the previous studies [Roble and Rees, 1977; Wallis and Budzinski, 1981; Hardy et al., 1985] showing that precipitating particles in the morning sector are more energetic than in the evening sector. A statistical study by the CHAMP satellite data showed that, in the equinox and winter seasons, the maximum values of are located in the morning sector and increase with enhanced geomagnetic activity [Juusola et al., 2007]. The MLT dependence of in our study is in accordance with that result. However, the values by Juusola et al. [2007] stayed always below 2, but even the 3 h averages in this study go up to 3. Figure 2. Profiles of the northward (black) and eastward (red) neutral winds with 1 limits as error bars. The times of the individual profiles are (a) 09 September :14 UT, (b) 18 September :56 UT, (c) 18 November :50 UT, and (d) 13 September :40 UT. [18] ACN12 showed that Tromsø was located in the auroral oval at MLT during low, MLT during medium, and MLT during high activity conditions. In the oval region, the electron density depends on the differential energy flux of precipitating particles. The shift of peak conductivities from the midnight to the morning sector suggests that the precipitating flux of energetic particles increases and reaches its maximum at a later MLT time with increasing geomagnetic activity at 67 ı cgmlat. The statistical study by Newell et al. [2009] showed that the energy flux is dominated by monoenergetic aurorae in the evening sector, whereas diffuse aurorae take place in the morning sector. The diffuse auroral region, which contains the highest energy flux, intensifies, widens in MLT, and expands equatorward with increasing solar wind driving. Hence, it is possible that the observed shift of peak conductivities to later MLT at Tromsø is related to the equatorial expansion of the auroral oval in the morning sector. [19] In Figure 1, the height-integrated Hall to Pedersen conductivity ratio = H / P is also given for the median profiles within MLT. Its maximum values are 1.8 at MLT for low, 2.7 at MLT for medium, and 3.0 at MLT for high activity conditions. The conductance ratio can be used as a proxy for the characteristic energy of precipitating particles [e.g., Vickrey et al.,1981;robinson et al., 1987]. The observations indicate that the characteristic energy of precipitating electrons increases with increasing 3.2. Neutral Winds and Electric Fields [20] The neutral winds have been estimated between 80 and 180 km for the calculation of the energy exchange rates. Before showing the statistical results, we present some typical profiles of the analysed neutral wind with the error estimates in Figure 2 for evening and morning, low and high activity conditions. As discussed in section 2, the wind height gates are 10 km wide, except for the uppermost height gate that extends from 150 to 180 km. Because the ion-neutral collision frequency decreases exponentially with altitude, the standard deviations for the uppermost gates are the largest in all cases. The smallest errors are found in the height gates centered at 105 and 115 km [see also Nygrén et al., 2011]. Linear interpolation is adopted between the centers of the range gates. We assume that the wind velocity is constant between the center point and the upper limit of the uppermost range gate, and the same approach is used for the lowest range gate. Points where the analysis has failed are replaced by linear interpolation. [21] Figure 3 shows the median altitude profiles of the eastward (red curves) and northward (black curves) components of the estimated neutral wind. Typically, the magnitude of neutral winds increases greatly with altitude. In the evening sector, neutral winds have a strong westward and a northward component above km at MLT for low activity conditions and at MLT for medium and high activity conditions. Below these altitudes, the wind rotates to an eastward direction, and the rotation to a southward direction takes place at the same or lower altitudes. [22] In the premidnight sector at MLT, the neutral wind magnitudes are smaller. The winds typically have a westward component above 105 km and a southward component, which has a strong altitude variation. [23] In the morning sector, the southward component dominates above about 110 km, except at MLT during high activity conditions, when the westward component is larger in the topmost part of the profiles. During late morning at MLT, the zonal component is at all activity levels mostly eastward above 105 km. However, in the early morning at MLT, the zonal component can be eastward or westward. [24] Wind magnitudes are smaller in the daytime. They typically have a northward component, and the zonal component usually points in the westward direction with a strong altitude variation. 7372

5 Figure 3. The median profiles of neutral winds with the north component (black) and the east component (red) in the same format as Figure 1. [25] We have compared the main characteristics of the winds with some published measurements and models [e.g., Kwak and Richmond, 2007], and the results are in a general accordance of wind directions at 66.6 ı geomagnetic latitude, even though the high-altitude winds are not well known. [26] The radar data are also used for determining the electric fields. The median values of the electric field magnitude at different activity levels and MLT sectors are shown in Table 1. The electric field characteristics are discussed in detail in ACN12. The calculated neutral winds, together with the electric fields and conductivity profiles, are used below in calculating the profiles of the energy rates Electromagnetic Energy Exchange Rates [27] Figure 4 shows the altitude profiles of the electromagnetic energy exchange rate q EM (red curves) given by equation (2). For comparison, we show the altitude profiles of q E (black curves), which are equal to q EM in the absence of neutral winds. The q E profiles have similar shapes and peak altitudes as P, but they are multiplied by the square of the electric field. [28] The median values of the EM energy exchange rates are almost always positive, indicating that the magnetosphere is the source of EM energy and the ionosphere acts as a sink at all altitudes. The peak altitude of q EM remains close to 120 km, regardless of MLT and activity level, just like the peak altitude of q E does. Almost all of the EM energy is deposited above 100 km. [29] During low activity conditions, the EM energy input is very small and the maximum q EM is observed in the MLT sector, where the convection electric field maximizes (see Table 1). [30] During medium activity conditions, significant increase of q EM appears from 15 to 06 MLT. The q EM profiles have two maxima, at and MLT, with a local minimum at MLT. The premidnight minimum Table 1. The Median Values of the Electric Field Magnitude in mv/m Kp Kp: Kp: Kp > MLT

6 Figure 4. Statistical profiles of q EM (red) and q E (black) in the same format as Figure 1. is associated with the location of the Harang discontinuity region. The evening maximum corresponds to a maximum in electric field within the auroral oval (Table 1). Evening and morning peak values of median profiles are close to 0.1 W/m 3, but the peak value of the upper quartile in the evening sector 0.28 W/m 3 is greater than that in the morning sector 0.22 W/m 3. [31] During high activity conditions, the evening maximum of q EM appears at MLT with the peak values of 0.3 W/m 3 and 0.65 W/m 3 for the median and upper quartile profiles, respectively. The peak values are about 1.5 times that of the morning maximum at MLT. The evening maximum corresponds to a maximum in electric field within the auroral oval (Table 1). [32] In the evening sector, large electric fields take place both in the auroral and subauroral regions. According to ACN12, the MLT sector during medium activity conditions and the MLT sector during high activity conditions represent subauroral latitudes. The peak values of q EM at these subauroral latitudes even exceed those in the corresponding premidnight (21 00 MLT) sectors within the auroral oval. [33] Neutral winds can reduce or enhance q EM in comparison with q E. These effects are visible in medium and high activity conditions. Reduction of q EM takes place mainly above 120 km and is more pronounced in the evening than in the morning. At lower altitudes, neutral winds typically 7374 slightly enhance the EM energy deposition. The transition altitude from a reduction to an enhancement is mostly close to the peak of q E. The reduction is larger and operates over a wider altitude range than the enhancement does, which produces narrower profiles and lower peak altitudes for q EM in the evening sector. The net effect is that the height-integrated EM energy exchange rates Q EM are decreased by neutral winds in the evening sector. [34] The decrease of q EM above about 120 km is in accordance with the observations by the Sondrestrom radar at 73 ı cgmlat [Thayer and Semeter, 2004]. However, the larger decrease in the evening sector than in the morning sector found in this study is opposite to the observations by the Sondrestrom radar, which show a larger reduction in the morning sector [Thayer, 2000]. The disagreement may be caused by the latitudinal difference, since both the local electric field and the neutral wind depend on latitude. [35] Negative EM energy exchange rates never take place in the median profiles, but the lower quartile in the high activity conditions at MLT shows small negative values above 140 km indicating that the ionosphere may also act as a generator of EM energy Mechanical Energy Transfer Rates [36] The altitude profiles of the mechanical energy transfer rate q m are shown in Figure 5. In the low activity

7 Figure 5. Statistical profiles of q m in the same format as Figure 1. conditions, the q m profiles are mostly negative indicating that neutral winds do work. Only the upper quartile between 110 and 130 km in the MLT sector shows positive values indicating that at those altitudes winds are a load (and gain some kinetic energy). [37] In the medium activity conditions, neutral winds still do work at high altitudes. The most pronounced negative values are observed in the MLT sector with a minimum value of 0.08 W/m 3 at about 145 km. However, neutral winds become a load at lower altitudes with a maximum in the MLT sector between 110 and 130 km. The peak values are 0.03 W/m and 0.1 W/m for the median and upper quartile profiles, respectively. We can compare the respective q m and q EM values according to equation (1) to see that about 30 % of EM energy goes to the neutral wind at the peak altitude. Small positive values of the median q m are also observed in the mid-e region between 21 and 06 MLT. [38] In high activity conditions, the mechanical energy transfer rates are negative in the upper parts of the profiles, much like during low and medium activity. The strongest negative values are encountered in the morning sector with the steepest minimum of 0.1 W/m 3 at a height of 145 km at MLT. The transition altitude from negative to positive q m depends greatly on MLT [39] Positive values of q m are observed within a limited altitude range. The width of the positive band for median curves during high activity conditions is about 30 km at the evening maximum and 20 km at the morning maximum. The peak value of 0.05 W/m 3 for the median profile appears at MLT between 110 and 140 km. About 15% of EM energy goes to the neutral wind at the peak altitude. In the premidnight sector, the median curve stays negative or near zero. In the morning sector, the maximum appears at MLT between 105 and 125 km, where about 10% of EM energy goes to the neutral wind at the peak altitude Joule Heating Rates [40] Figure 6 shows the altitude profiles of the Joule heating rate q J (red curves) and q E (black curves). During low activity conditions, Joule heating rates are small. Neutral winds increase Joule heating above the peak height of q E, producing q J peaks at about 145 km. [41] In the case of medium activity, q J is also greater than q E in the upper parts of the profiles. The evening maximum of q J is observed at MLT, but the peak value for the median profile is reduced by about 25% in comparison with q E due to neutral winds. In the morning sector, the neutral wind has no effect on Joule heating below 120 km, but at higher altitudes, neutral winds increase Joule heating. As a

8 Figure 6. Statistical profiles of q J (red) and q E (black) in the same format as Figure 1. result, q J in the MLT sector has two peaks, at 120 and 145 km. [42] During high activity conditions, the evening maximum appears at MLT, with the peak values of 0.26 W/m 3 and 0.59 W/m 3 for the median and upper quartile profiles, respectively. However, at the peak altitude of q E, Joule heating rates are reduced by 20% in comparison with q E due to neutral winds. The largest reduction takes place in the MLT sector, where the peak value is reduced by 45%. The morning maximum is observed at MLT with two peaks. The lower peak is close to the altitude where q EM has a maximum and it is decreased by about 20% in comparison with q E. The higher peak at 145 km is produced by neutral winds (see Figure 5 and note the different scale). Neutral winds increase Joule heating at high altitudes. [43] Neutral winds have a different effect on q J in the morning and evening sectors. In the morning sector, winds increase q J over abroad altitude range, and hence, Q J > Q E. In the evening sector, winds decrease q J over a broad altitude range. For the evening maximum at MLT, q J is decreased between 115 and 160 km. As a result, the peak altitude of q J is lowered from 120 km to 115 km, and the q J profile becomes narrower than the q E profile. When integrated over altitudes, Q J < Q E at MLT during medium activity conditions and at MLT during high activity conditions. One effect of neutral winds is to make 7376 Q J larger in the morning sector than in the evening sector (see ACN12). 4. Interpretation and Discussion 4.1. Model Calculations [44] In this section, we will show by model calculations how different energy exchange rates depend on the relative magnitudes of the neutral wind and the electric field as well as on the angle between the wind and the electric field. The model calculations will be used to interpret the observational results shown in the earlier sections. [45] Equations (2) (4) show that the energy transfer rates q EM, q J,andq m can be expressed as sums of the terms q E, q u, q P,andq H. In addition, as shown in Appendix A, all the energy transfer rates in equations (2) (4) can be expressed as a product of q E = P E 2 and functions that depend only on three parameters: r = u? B/E, = H / P,and. Here u? is the neutral wind component perpendicular to B, and hence, r is equal to the ratio of the neutral wind velocity and the maximum plasma drift velocity perpendicular to the geomagnetic field. The parameter is the ratio of Hall and Pedersen conductivities. The parameter is the angle between the electric field and the perpendicular component of neutral wind, increasing from zero with clockwise

9 Altitude (km) σ H /σ P (L) (M) (H) (L) (M) (H) Figure 7. Selected altitude profiles of the median Hall-to- Pedersen conductivity ratio taken from Figure 1. Solid lines correspond to MLT and dashed lines to MLT. Low activity level (L, Kp: 0 2 ) is denoted by green, medium (M, Kp: ) by blue, and high (H, Kp > 5 ) by red. lines are again the zero boundaries. This plot can now be interpreted using Figures 7 and 8. The q E term (Figure 8) gives a positive background, which is uniform in but has a maximum close to 120 km in altitude. The q P term (Figure 9, left column) gives a maximum at = 90 ı and at 120 km, whereas the q H term (Figure 9, right column) gives a larger maximum at =0 ı and at 110 km. The sum of the terms produces a broad tilted maximum region of q EM,which bulges downward to its lowest altitudes at =0 ı. Negative values are centered at 180 ı,andwhenr 6 1, they can be found only at low altitudes. The largest negative values in the bottom are obtained at 105 km, and they are produced by the Hall term. Negative values indicate that neutral winds are a generator of EM energy. Even for very small values of r, the winds are a generator at 95 km, when = 180 ı (see Appendix A). [50] The dashed white lines for q EM indicate the angles for which q EM is equal to q E. Between the dashed lines in the middle of the panels, neutral winds enhance the EM energy deposition above q E. rotation from the electric field direction when viewed along the geomagnetic field. Hence, = 90 ı when u k E B. [46] In the model calculations, the neutral wind magnitude is set to 200 m/s, and the electric field magnitudes are 5, 10, 20, and 50 mv/m. As a result, r obtains values 2, 1, 0.5, and 0.2. The conductivity ratio = H / P depends on altitude. Figure 6 shows the altitude profiles of for time intervals MLT and MLT and the three activity levels. This figure indicates that is rather insensitive to magnetic activity or MLT, and therefore, we have chosen to use the median profile of the medium activity conditions at MLT. [47] Figure 8 shows the altitude profiles of the electric field term q E (the left column) and the wind term q u (the right column) as a function of and for different values of r. Although these terms are independent of, this presentation is used in order to allow comparison with the other terms. The q E values increase with the decreasing ratio r = u? B/E. Both of the q E and q u altitude profiles have the same shape as the P profile that peaks at about 120 km. [48] The Pedersen term q P and the Hall term q H are shown in Figure 9. The boundaries between the positive and negative values (q P,H =0) are marked by the dash-dotted lines. The Pedersen term has a maximum at =90 ı, which means that u B points in the same direction as the electric field. The Hall term has a maximum when the neutral wind and the electric field point in the same direction. Since constant neutral wind magnitude is used in the calculations, the peaks of the q P and q H profiles are determined by the respective conductivity profile peaks. An interesting feature is that, with increasing electric field (decreasing r), q P peaks bulge upward, while q H peaks bulge downward. [49] The left column in Figure 10 shows the electromagnetic energy transfer rate q EM = q E +q P +q H. The dash-dotted Figure 8. The altitude profiles of the terms (left) q E and (right) q u as function of the angle between the wind velocity u? and the electric field E. This angle is defined to increase clockwise from the direction of E when viewed in the direction of B. TheE B direction is hence = 90 ı. The values of u? and E for calculating r = u? B/E are u? = 200 m/s, E =5, 10, 20, and 50 mv/m. 7377

10 equal to the E B drift velocity. This is shown by the dash-dotted line in the panel r = 1 for = 90ı (see also Appendix A). [53] Figure 11 (right) shows the difference between qj and qe, which is equal to 2qP +qu. The wind term produces asymmetry, so that the angular region of Joule heating values increased above qe is always larger than the region where values have decreased below qe. In Appendix A, we show that winds decrease Joule heating when u? < 2E cos /B, where is the angle between u and the E B direction Statistics of the Angle  [54] In order to compare the model calculations with the observations, we have created the distributions of at various magnetic local times, altitudes, and magnetic activity levels. For this purpose, we have taken 5ı wide bins in and calculated the normalized number of samples in each bin k (k = 1, 2,..., 72) at each altitude gate h. Hence, Nkh = nkh, nmax,h (5) where nkh is the number of samples within the kth bin and nmax,h is the maximum value of nkh at the altitude gate h. Figure 9. The altitude profiles of (left) the Pedersen term qp and (right) the Hall term qh in the same format as Figure 8. The dash-dotted lines show the contour where qp = 0 (first column) and qh = 0 (second column). [51] The right column in Figure 10 shows the mechanical work term qm = qp qu + qh. Now the negative of the wind term gives a weak uniform negative background. The negative of the Pedersen term gives a maximum at = 90ı at a height of 120 km, whereas the Hall term gives a larger maximum at = 0ı at a height of 110 km. The sum of the terms produces a maximum region of qm tilted in the opposite sense in comparison with qem. The maximum region has again its lowest altitudes at = 0ı. When r is increased from 0.2, the range of giving positive qm gets narrower in the high altitudes, and when r = 2, positive qm are found only below 120 km in height. If r would be further increased, winds would remain as a load at an altitude of 95 km (altitude of max ) for = 0ı up to r 37 (see Appendix A). [52] The left column in Figure 11 shows the Joule heating rate term qj = qe + 2qP + qu. Both qe and qu give a positive background for all values of, and thus, the angular variation of qj is produced by the Pedersen term. Hence, a minimum in Joule heating is obtained at the angle of 90ı, corresponding to winds in the E B direction. A maximum is found at 90ı, when winds are antiparallel to E B. Naturally, Joule heating increases with increasing electric field, i.e., with decreasing r. Zero value of Joule heating can only be obtained when the wind velocity is Figure 10. The altitude profiles of the terms (left) qem and (right) qm in the same format as Figure 8. The dash-dotted lines show the contour where qem = 0 (first column) and qm = 0 (second column), and white dashed lines show the contour where qem = qe. 7378

11 Figure 11. The altitude profiles of (left) the Joule heating term q J and (right) the difference between q J and q E in the same format as Figure 8. The dash-dotted lines show the contour where q J =0(first column) and q J q E =0(second column). This is done separately for each altitude gate, MLT sector and activity level. The resulting distributions are shown in Figure 11. [55] The clear structures in Figure 11 indicate that, within certain MLT sectors, the variation of the angle between the electric field and neutral wind directions is limited throughout the data set. At low activity level, the broad distributions reflect mainly the fact that the direction of the weak electric field is variable. [56] In the evening sector at high altitudes, above km, the distribution of has a narrow peak between 90 ı and 45 ı at MLT for low and at MLT for medium and high activity conditions, suggesting that neutral winds have a large E B component. Close to the altitude of 110 km, the wind has a strong shear within about 10 km altitude range and below 105 km, 90 ı. The broadening of the distributions at MLT most probably results from the fact that the Harang discontinuity is encountered within this time sector. [57] In the morning sector, the distribution of the angle is scattered for low and medium activity conditions, and there is a clear change from low to high activity conditions. During low activity, 180 ı at high altitudes at MLT indicating that wind direction is opposite to the electric field direction. In medium activity conditions, the winds have an E B component above 110 km at MLT. In high activity conditions, the distribution of the angle becomes rather narrow especially at MLT. Below 160 km, the winds start to turn in the E B direction and 90 ı below 100 km Interpretation of Statistical Results [58] In this section, we will discuss some of the main features in the statistical properties of q EM, q m,andq J in the light of the model calculations Electromagnetic Energy Exchange Rates [59] As discussed in section 3.3 and shown in Figure 4, the EM energy exchange rates q EM are reduced by neutral winds above about 120 km. The effect is most pronounced in the evening sector during high activity conditions. By looking at Figure 12, we can see that for Kp > 5 in the evening sector, the transition altitude of 120 km corresponds to the altitude where the wind direction changes. Above 120 km, the angle is distributed around 45 ı, which corresponds to a reduction of q EM according to model calculations: The white dashed lines in Figure 10 show that at high altitudes, q EM < q E for 2 [ 180 ı,0 ı ] and at 120 km for 2 [ 180 ı, 45 ı ] or 2 [135 ı, 180 ı ]. Below about 120 km, the distribution of the angle corresponds to an enhancement of q EM. Since wind magnitudes increase with altitude (Figure 3), the effect of reduction at high altitudes is larger than the effect of enhancement at low altitudes Mechanical Energy Transfer Rates [60] The altitude profiles of mechanical energy transfer rates q m in Figure 5 show both positive and negative values. Mechanical energy transfer rates are always negative at altitudes higher than 140 km for all activity levels. The model calculations in Figure 10 show that, when r >1, q m is negative above about 120 km for all angles. At these altitudes, the magnitude of the estimated neutral wind (Figure 3) is large, and the parameter r is generally greater than 1, which explains the negative values of q m in Figure 5. In addition, these values decrease with increasing geomagnetic activity, which is due to the increase of the electric field magnitude in the Pedersen term in equation (4). [61] Negative values of q m are also observed within the MLT sector between the altitudes of about 100 and 115 km, when the activity is high. In these conditions, the electric field is large (Table 1), and the neural wind velocity is small, which leads to a small value of r. Thus, the case is similar to r =0.2or r =0.5in Figure 10. Figure 12 shows that, typically, 90 ı < < 180 ı. Thus, in accordance with the observations, Figure 10 gives negative values of q m in these conditions. [62] The bands of q m > 0 are observed in the evening and morning sectors for medium and high activity conditions (see Figure 5), which are located below km. The upper boundaries of the bands are clearly defined by the sign change of q m, whereas the lower boundaries correspond to a decrease of positive q m values. In the evening sector, above km, the angle is distributed around 45 ı (Figure 12). For r =2, this angle corresponds to positive values below 118 km, and for r = 1, the transition altitude ascends to 130 km (Figure 10). Hence, the transition altitude is determined by parameter r, which is the altitude- 7379

12 Figure 12. The angle between the wind velocity u? and the electric field E are shown by a normalized number of samples as a function of the geomagnetic activity (rows) and MLT sectors (columns). The value = 90ı corresponds to the E B direction. dependent ratio of the wind magnitude to the electric field term E/B. The maximum altitude of the upper boundary of positive qm takes place in the MLT sector for Kp > 5, where the electric field has a maximum. [63] For high activity conditions, the lower boundaries of the positive band at MLT and MLT take place at an altitude of 100 and 110 km, respectively. At these altitudes, r 0.2 and positive values correspond to 2 [ 90ı, 90ı ] (Figure 10). In Figure 12, the wind direction shows a shear from 45ı toward 90ı at these altitudes, and it is stronger in the MLT sector. The qm values for angles smaller than but close to 90ı are significantly reduced in comparison with the values for = 45ı. Hence, the lower boundary is determined by the shear in the wind direction. [64] In the morning sector, the altitude profiles of are different from the evening sector (Figure 12). However, the upper boundary of the positive band of qm is determined by the altitude-dependent r since is distributed between 90ı and 0ı. The lower boundary is again determined by the change in wind direction, but now approaches 90ı at low altitudes, where qm values are significantly reduced. [65] The peak altitude of qm is at about km in the evening sector but within km in the morning sector. The effect is caused by the different Hall conductivity profiles in the evening in comparison with the morning sector: Hall conductivities peak at lower altitudes and have higher magnitudes in the morning sector (Figure 1). The model calculations shown in Figures 8 11 are made utilizing the evening sector conductivity profiles as discussed earlier. Hence, the peak altitude for the Hall term qh (shown in Figure 9) in qm would be located at a lower altitude and would have a larger value for the morning sector. While there is a small effect in the statistics, this illustrates that during hard particle precipitation, the qm profiles would have higher peak values and would extend to lower altitudes in any MLT sector. Note that qj does not include the Hall term Joule Heating Rates [66] As seen in section 3.5, the Joule heating rates can be reduced or enhanced by neutral winds in comparison with qe at different altitudes. In the evening sector, the reduction always takes place around the peak of qe during medium and high activity, extending to altitudes of km. [67] Figure 11 and Appendix A show that qj < qe only when r < 2. The range of giving qj < qe does not depend on altitude when r is fixed. At low values of r, this range varies between 180ı and 0ı, but with increasing r, this range gets more narrow and completely disappears at r = 2. [68] Figure 12 shows that, in the evening sector, 90ı < < 45ı in the height region above km. Therefore, the condition qj < qe is valid up to altitudes where r = 2. At high altitudes, where r increases, the Joule heating rate is enhanced by neutral winds. The transition altitude gets the highest value of 160 km at MLT for high activity conditions, since the maximum of electric field takes place there maintaining small values of r at high altitudes. At altitudes below 115 km, qj is slightly larger than qe, 7380

13 which is associated with the neutral wind shear making the angle >0. [69] In the morning sector, neutral winds start to increase the Joule heating rates already above km because r > 2. The most pronounced reduction by neutral winds takes place at km in the MLT sector for high activity conditions. The electric field has a morning maximum within this MLT region, and hence, r <1. In addition, the angle 2 [ 90 ı, 45 ı ], which corresponds to q J < q E according to the model calculation. 5. Discussion [70] Only few observational studies of the heightdependent energy exchange rate profiles have been conducted. Thayer [1998a] studied two events during moderate to strong geomagnetically active conditions with the Sondrestrom incoherent scatter (IS) radar. The first one showed that the height-integrated Joule heating rate was reduced in the evening sector and enhanced in the morning sector by winds, which is in accordance with the statistical results by ACN12. The evening sector electric field maintained a northward direction throughout the event. Near 16 MLT, Joule heating was reduced by neutral winds in the upper E region and increased in in the lower E region below about 117 km. This was associated with a rotating wind direction. In the morning sector, the positive enhancement by the wind came from the upper E region. These results are in agreement with the results in the present paper. [71] Thayer [1998a] found that the influence of the neutral wind from 90 to 140 km was significant. Reductions of 40% and enhancements even up to 400% were observed. He also concluded that, during directional changes in the electric field, the neutral winds tended to enhance the Joule heating rate, while directionally steady electric fields resulted in an overall reduction of the Joule heating rate. [72] Fujii et al. [1999] studied energy exchange rates using EISCAT CP1 measurements at four altitudes: 101, 109, 117, and 125 km. The peak altitudes for the EM energy exchange rate and the Joule heating rate were observed at 117 km at the peak altitude of the Pedersen conductivity. The effect of neutral wind on the height profiles of q EM and q J were not separately studied in that work. [73] In the present paper, we find that the peak altitude of the Joule heating rate is different from that of the Pedersen conductivity maximum. We observe that, in the evening sector, the effect of the neutral winds in Joule heating is to lower its peak altitude by 5 km, as well as to decrease its peak magnitude by 15 45% and to narrow its thickness. In the morning sector, the profiles are flattened so that the peak magnitude is somewhat decreased while values above the peak are increased. The EM energy exchange rate profiles are less affected by winds, but they also become somewhat narrower in the evening sector. [74] Most of the magnetospheric EM energy is deposited into Joule heating, but a part of it may go to mechanical work. The region where the winds are a load (q m >0) is limited in altitude, and one such example of the positive band of q m is shown in Figure 4 of ACN12. The statistical results of this paper indicate that in the evening sector, the region of q m > 0 is situated in the middle of the E region with 7381 the peak altitude close to km. A weaker positive band is observed also in the morning sector, but in the premidnight sector MLT, the median profiles of q m are negative at all altitudes, indicating that winds are rather a source of energy than sink. The upper and lower boundaries of q m >0have a clear MLT variation. In the evening sector, the altitude of the upper boundary is mainly determined by the magnitude of the ratio between the neutral wind velocity and the electric field. Strong electric fields increase the altitude of the upper boundary. The lower boundary is determined by the rotation in the wind direction. The same factors determine the altitude region of the positive band in the morning sector. [75] The results shown in the present work indicate that neutral winds play a crucial role in distributing the magnetospheric energy in the ionosphere. The high-altitude magnetospheric convection electric field may act as an energy source accelerating the neutral atmosphere [e.g., Zhang and Shepherd, 2000]. Indeed, one can see that the wind magnitude and direction significantly change with increasing magnetic activity. This is quite clear in the morning sector where the wind directions change and their distribution becomes less scattered when the geomagnetic activity is increasing. In the evening sector, the neutral wind direction is more stationary at all activity levels, and there, the acceleration is not so clearly seen. This result is similar to the general observation that neutral winds in the evening sector tend to follow the plasma E B direction [see Kwak and Richmond, 2007, and references therein]. [76] With the IS radar technique, it is not possible to estimate the F region winds, and hence, it is not possible to estimate EM energy exchange or Joule heating rates in the F region. However, due to the controlling effect by the Pedersen conductivity profile, the F region energy exchange rates are much smaller than in the E region. Using the global thermosphere ionosphere electrodynamics general calculation model, which includes F region winds, Deng et al. [2008] estimate the effects of Joule heating in the E and F regions. Due to the exponential decrease of density with altitude, heatinginthef region per unit mass is larger or comparable to heating in the E region. The absolute change of neutral temperature is largest in the F region, but the relative change in temperature is of the same order in the E and F regions. Deng et al. [2011] show how a sudden enhancement in Joule heating produces an acoustic wave that propagates from the E region to the F region. However, Joule heating above 150 km is the primary source for large vertical winds and an increase in the F region neutral density at 300 km and higher altitudes. Also, Carlson et al. [2012] predict large density enhancements and vertical winds near 400 km due to plasma flow shears and large electric fields. [77] In this paper, we use the calculated total electric field, which in some cases may compose of a magnetospheric electric field plus a polarization electric field. Amm et al. [2013] show that the polarization effect (described by the Cowling efficiency) may significantly decrease Joule heating. 6. Summary and Conclusions [78] We have studied the statistical properties of the altitude profiles of the electromagnetic energy exchange rate, the Joule heating rate, and the mechanical energy