We have developed a new beam configuration for monostatic incoherent scatter (IS) radars at high latitudes in order to estimate the vertical component of the neutral wind velocity in the lower thermosphere (from 100 to 120 km). This method has been applied to experiments with the Sondrestrom IS radar, Greenland, on 5 and 8 March 2004. The measurement and the analysis methods provide various temporal and altitudinal structures of the vertical neutral wind velocity with amplitude of a few tens of meters per second at 3 km height resolution. This paper also demonstrates how to evaluate assumptions adopted in calculations of the vertical neutral wind velocity using experimental data on 5 and 8 March 2004. Caution should be exercised in inferring effects of variations in the thermospheric density or the ion-neutral collision frequency in association with vertical thermospheric motions, in particular above 112 km.
 The vertical motions in the lower thermosphere at high latitudes pose various important questions concerning, for example, the momentum transfer in association with atmospheric wave breaking, effects of the thermospheric constituent mixture on chemical reactions, and the energy budget as a part of the magnetosphere-ionosphere-thermosphere coupled system. Our understanding on the lower thermospheric vertical motions is inadequate to consistently explain the experimental data from Fabry Perot Interferometers (FPI) [Price and Jacka, 1991; Price et al., 1995; Smith and Hernandez, 1995] and incoherent scatter (IS) radars [Kofman et al., 1996; Oyama et al., 2005].
 Vertical neutral wind velocities measured with the FPI technique at a wavelength of 557.7 nm, corresponding to principal auroral emission altitudes around 110 km, at the South Pole station show a predominantly diurnal variation with average amplitude of 10 m s−1 [Smith and Hernandez, 1995]; by contrast lower thermospheric tides predicted with a classical tidal theory suggest that the vertical component has amplitudes of the order of centimeters per second [Kato, 1980; Forbes, 1995]. Statistics on the vertical ion velocity measured with the vertical beam of the European Incoherent Scatter (EISCAT) Tromsø UHF radar for geomagnetically quiet summer conditions show that magnitudes of the hourly mean velocity are at most a few meters per second at 100 km level where the ion velocity is generally equal to the neutral wind velocity [Oyama et al., 2005]. These differing results are derived using data measured at different locations and seasons with different techniques; it is therefore important to optimize the experimental methods, particularly because the errors are often comparable with measured values.
 Experimental data from FPI and IS radar for geomagnetically disturbed conditions indicate that there is often an unexpected level of large amplitudes in the lower thermospheric vertical motions compared with predictions from thermospheric models, even though those models take into account reasonable ionospheric conditions for the electric field and the electron density to calculate the Joule heating rate and the ion momentum drag [Walterscheid et al., 1985; Sun et al., 1995; Shinagawa et al., 2003].
 The objective of this paper is to introduce a new IS radar beam configuration suitable to estimate the vertical component of the neutral wind velocity in the polar lower thermosphere with minimal errors; this is applicable to monostatic radars. While derivation of the horizontal component with the IS radar has been conducted during the last three decades [Rino et al., 1977; Nozawa and Brekke, 1995, 1999], the conventional beam configurations should not be applied simply to derive the vertical component because the method is subject to significantly larger errors in the vertical component than the calculated speed [see Nozawa and Brekke, 1995, Figure 4]. Furthermore, some beam configurations used previously necessarily assume no vertical neutral wind velocities. We have conducted experiments with the Sondrestrom IS radar (67°N, 309°E, 73° magnetic latitude) on 5 and 8 March 2004 using the newly developed beam configuration, which is explained in section 2 together with the mathematical approach to derive the vertical neutral wind velocity. Section 3 presents initial results from the experiments. Section 4 explains how to evaluate assumptions for calculations of the vertical neutral wind velocity using data on 5 and 8 March 2004.
2. Mathematical Approach and Methodology to Be Employed
2.1. Derivation of the Vertical Neutral Wind Velocity
 The neutral wind velocity is derived from the steady state ion momentum equation neglecting ambipolar diffusion [Rino et al., 1977; Nozawa and Brekke, 1995, 1999]. This assumption is acceptable at E region heights because statistics using EISCAT radar data suggest that the ion diffusion velocity along the magnetic field line is considerably smaller than the observed field-aligned ion velocity below 230 km [Oyama et al., 2003].
where U, V, B, and E are vectors of the neutral wind velocity, the ion velocity, the magnetic field, and the electric field, respectively, B is magnitude of the magnetic field, Ωi is the ion gyrofrequency, and νin is the ion-neutral collision frequency, which is calculated using data from the Mass Spectrometer Incoherent Scatter (MSIS) model [Hedin, 1991]. The vertical component of U or Uz is written as
2.2. Beam Configuration
 We optimize a beam configuration to reduce estimated error values of the vertical neutral wind velocity. Figure 1 shows a schematic drawing of the antenna position selected for the experiments with the Sondrestrom IS radar. The experiments were conducted from 1202 to 2031 UT (UT = LT + 3 hours) and from 1159 to 2028 UT on 5 and 8 March 2004, respectively, using short and long pulses (pulse lengths are 20 and 320 μs, respectively), which provide the height resolution of 3 km in the E region and 42 km in the F region, respectively. The configuration consists of three beam positions; geographical zenith, along the magnetic field line (azimuth: 140°, elevation: 80°), and other direction (azimuth: 50°, elevation: 75°; hereinafter referred to as east beam). It takes about 10 min for one sequence with 3 min integration time at individual three antenna positions, and the value of D1 and D2 are a few tens of kilometers at E region heights.
 One of characteristics in the selected beam configuration is the coordinate system. The x and y axes are directed to the geomagnetic southward and eastward, respectively, and the z axis is directed to the geographical zenith. Under this coordinate system, the geomagnetic field vector in the northern hemisphere can be expressed as
where I is the magnetic dip angle (80° at the Sondrestrom site). This equation shows that the y component of B or By is zero thus the second term in the parentheses of equation (2) is zero. This in turn indicates that it is not necessary to estimate Vx because the vertical and east beams are enough to estimate the other terms in equation (2) under the assumption of uniform spatial and temporal structures in the ionosphere for one beam sequence. While the Sondrestrom IS radar was periodically directed up the magnetic field line for the March 2004 experiments, data from this beam will be used for the additional objective to determine effects of the vertical neutral wind velocity on the field-aligned ion motion. This latter study is beyond the scope of this paper and may be reported in future. The vertical neutral wind velocity determination actually needs only two beams, vertical and east.
 The optimum elevation angle of the east beam is determined considering the value of D2 and the error of Uz, which is estimated with error propagation analyses using the measurement uncertainty of the ion velocity. The measurement uncertainty is estimated through the IS spectrum fitting procedure with a theoretical function. The estimated error of Uz decreases with lowered elevation angle values because the east beam is directed closer to the horizontal in that case which then provides better estimation of the y component of the ion velocity, Vy; however, the value of D2 increases with smaller values of the elevation angle. The errors normalized by the measurement uncertainty of the ion velocity and the value of D2 are tabulated in Table 1. In this error calculation, we assume that the measurement uncertainty is independent of the radar antenna beam direction. We also assume that the ratio of the ion gyrofrequency to the ion-neutral collision frequency is unity, which corresponds to a height about 120 km. Thus the normalized error in Table 1 is representative for that height. Since the frequency ratio decreases exponentially with decreases in height, the normalized error is decreased compared to values in Table 1 when going down to lower heights. Measurement uncertainties of the lower ionospheric ion velocity integrated for 3 min with the Sondrestrom IS radar usually have values about 10 m s−1 for sunlit conditions. Statistics of the vertical ion velocity in the lower ionosphere suggest that IS radars frequently detect speeds in excess of 20 m s−1 even for geomagnetically quiet conditions [Oyama et al., 2005]. In the case of elevation angles smaller than 75°, Table 1 shows that the normalized error of Uz is smaller than 2 thus the error of Uz can be smaller than 20 m s−1 when the measurement uncertainty of the ion velocity is 10 m s−1. This error estimation suggests that we can select the elevation angle up to 75°. Specifically, the elevation angle that provides the normalized error of 2 is 79°. Since pointing information of the Sondrestrom IS radar antenna can be specified to 0.01° resolution, and the 4° difference (= 79° − 75°) is larger than the antenna beam width (0.5°), we may select 79° as the elevation angle; however, such detail determination will be unnecessary because the measurement uncertainty of the ion velocity is variable depending on the electron density or the ionospheric conditions.
Table 1. Elevation Angle Dependences of the Error of Uz and the Value of D2 at 100, 120, and 300 km Heightsa
Elevation Angle of the East Beam
The error values are normalized by the measurement uncertainty of the ion velocity assuming that the measurement uncertainty is independent of the beam direction. The ratio of the ion gyrofrequency to the ion-neutral collision frequency is unity in this calculation, which corresponds to a height of about 120 km.
(Error of Uz)/(measurement uncertainty of V)
D2 at 100 km, km
D2 at 120 km, km
D2 at 300 km, km
 The values of D2 for the elevation angle of 75° at E and F region heights are about 30 and 80 km, respectively. While assumption of the uniform spatial structure in such distance has been adopted conventionally for estimation of the ion velocity vector with the monostatic IS radar, we should assess the validity of the assumption for each experiment.
 The x and z components of electric field are derived using the ion velocity measured with the long-pulse code in the F region (in this paper, at 298 and 309 km for the vertical and the east beams, respectively) assuming that the E × B force drives motions of ions and electrons at that height.
3. Initial Results With the New Beam Configuration
3.1. Results From 5 March 2004
Figure 2 shows temporal variations in the H component of the geomagnetic field measured with the Greenland Magnetometers of the Danish Meteorological Institute. To determine the offset curve at each site, data in two 24-hour segments for geomagnetically quiet conditions, 6 and 7 March 2004 (daily Ap at both dates is 3, and the minimal and maximal Kp indexes are 0 and 2, respectively) are averaged at each time (20 s resolution) then the running average method with 2-hour boxcar window is applied to the averaged temporal variations. The deviation at Kullorsuaq (KUV) cannot be determined from 0400 to 2323 UT because of data gaps on 6 March. Here we show twelve individual measurements along the west coast of Greenland. Data from the Sondrestrom IS radar site is denoted as STF in Figure 2. The experiment has been conducted for geomagnetically quiet conditions, although magnetometers show small positive and negative excursions from 16 to 1800 UT; in particular at poleward sides from STF.
Figure 3 shows temporal variations in the x and z component of electric field, Ex (solid circles) and Ez (open circles), respectively, and color-coded height-time profiles of the electron density, the electron temperature, and the ion temperature. Ex is equal to −Ez tan I in the coordinate system illustrated in Figure 1. To make the color-coded height-time profiles we use data obtained from the three beams. Ex has smaller magnitudes before 1630 UT than 10 mV m−1. At 1706 UT, magnitude of Ex increases to 23 mV m−1 then remains about 10 mV m−1 except just before the end of the experiment. The electron density shows significant enhancements at the first half of the experiment because of particle precipitation; but obvious depressions in the E region electron density coincide with the electric field increase around 1700 UT. The electron and ion temperatures in the E region do not show remarkable variations during the experiment. Ionospheric parameters above 100 km before 1700 UT are available with relatively good quality, although those after 1700 UT are sometimes not available below 100 km because of the sudden E region disappearance.
 The measurement uncertainty in the velocity data is estimated through the IS spectrum analysis fitting with a theoretical function. Figure 4 shows temporal variations in the measurement uncertainty of the ion velocity along the vertical and the east beams (solid and open circles, respectively) from 100 to 118 km. In general there are few differences between two measurement uncertainties at each height. The measurement uncertainties in this height region remain approximately constant before 1700 UT at about 10 m s−1 independent of height; by contrast they gradually increase with time after 1700 UT. The onset when the measurement uncertainty begins to increase varies with height. Increased measurement uncertainties are relevant to electron density decreases as shown in Figure 3.
Figure 5 shows temporal variations in the vertical component of the neutral wind velocity calculated from 100 to 118 km. The error bars are estimated using the measurement uncertainties shown in Figure 4 with error propagation analyses. Since vertical neutral wind velocities at 97 km and below are sparse because of low signal-to-noise ratio, and the speeds at 121 km and above are frequently smaller than the estimated errors, these velocities are not plotted in Figure 5. One can identify various oscillations with significantly larger amplitudes than the estimated errors. These oscillations consist of various complicated structures such as small correlations among adjacent heights, and significant vertical shears. Large amplitudes after 1900 UT may not be significant because of relatively large error values.
3.2. Results From 8 March 2004
Figure 6 shows temporal variations in the H component of the geomagnetic field. The base line at each site is defined with the same way with Figure 2. The data indicate geomagnetically quiet conditions not only over the Sondrestrom site (STF) but also at poleward and equatorward sites. The x component of electric field, Ex, shown in Figure 7a, has smaller magnitudes before 1600 UT then remains constant at about −12 mV m−1 till the end of the experiment. The E region electron density around 1200 UT shows enhancements due to particle precipitation. The electron density in this height region gradually decreases with time. The electron and ion temperatures in the E region do not show notable variations for the experiment interval. Ionospheric data below 100 km are sparse because of low electron density and signal-to-noise ratio for the experiment interval. These temporal variations in the electron density directly affect measurement uncertainties of the ion velocity. We also compare the measurement uncertainties from two individual IS radar beams (the vertical and the east beams) in a similar manner as was done for the 5 March experiment (not shown here). The magnitudes and the temporal variations are similar to the 5 March experiment case, except at 100 km. Values at 100 km show obvious fluctuations with relatively large magnitudes (up to 35 m s−1) compared with values at the other heights.
Figure 8 shows temporal variations in the vertical neutral wind velocity from 100 to 118 km. The velocities at 97 km and below and at 121 km and above are not shown in Figure 8 for the same reason as in the 5 March case. While vertical neutral wind velocities at 100 km are sparse because of low data quality, one can identify various fluctuations with significantly larger amplitudes than the estimated errors. Magnitudes do not always increase with height. For example, from 1500 to 1700 UT, the vertical neutral wind velocity at 109 km shows three wavelike structures with amplitudes of a few tens of meters per second; by contrast the velocity at 112 km shows considerably smaller amplitudes than those at 109 km for this time interval. While temporal variations at each height show frequently sinusoidal structures, these oscillations are not always in phase among adjacent heights. Of particular interest is the vertical shear. Vertical neutral wind velocities from 1713 to 1834 UT at 112 km have negative or downward velocity from −30 to −35 m s−1, although those at 115 km have positive or upward velocity from 42 to 57 m s−1. While strong horizontal wind shears at E region heights have been reported using data from chemical releases [Larsen, 2002, and references therein] and IS radar [Johnson and Virdi, 1991; Salah et al., 1991; Salah, 1994; Azeem and Johnson, 1997; Fujiwara et al., 2004], there are few publications reporting vertical shears in the vertical neutral wind velocity at auroral E region heights. These are interesting subjects for future works.
 The previous section shows that the vertical neutral wind velocity estimated from Sondrestrom IS radar data measured on 5 and 8 March 2004 from 100 to 118 km fluctuates with larger amplitudes than the estimated errors, and that there are notable vertical shears in the vertical neutral wind velocity. While those smaller error values suggest that the measurement and analysis methods employed here are able to be applied to calculations of the vertical neutral wind velocity in the polar lower thermosphere, we should evaluate the assumptions used for the calculations. Furthermore, we discuss effects of the MSIS model data on calculations of the vertical neutral wind velocity because vertical motions may cause significant modulations in the thermospheric density and therefore the ion-neutral collision frequency. The other topic in this section concerns the difference between vertical ion and neutral wind velocities. It is important to evaluate upper heights where the relative velocity is negligible thus Vz is equal to Uz. The vertical neutral wind velocity at lower heights may be estimated with better time resolutions using successive measurements of the vertical IS radar beam.
4.1. Assumption of the Uniform Spatial and Temporal Structures
 We evaluate the assumption of uniform spatial and temporal structures in the ionosphere using the electron density and the electron and ion temperatures measured with two individual IS radar beams, namely the vertical and the east beams. While these ionospheric parameters are not used to calculate the vertical neutral wind velocity according to equation (2), they may be used to evaluate the uniform structure.
Figure 9 shows height profiles of hourly means for the electron density (Figure 9a), the electron temperature (Figure 9b), and the ion temperature (Figure 9c) from 100 to 300 km for the experiment on 5 March 2004. The statistical method used here is shown in Appendix A. We have compared the nonaveraged height profiles derived with each beam before making the averaged profiles. Since conclusions are the same for the averaged case, we will not show comparisons using individual measurements. While the distance between two beams is 26.8 (80.4) km at 100 (300) km as shown in Table 1, the height profiles in the E and F regions do not show significant differences between two beams except the ion temperature for the last one hour, 1950 UT (i.e., averages from 1900 to 2000 UT); the ion temperature from the east beam is higher than that from the vertical beam by about 100 K at F region heights. It is evident that the assumption of uniform spatial and temporal structures in the ionosphere is valid except for the last one hour.
 The ion temperature in the transition region between E and F regions has relatively large statistical standard deviations than those in the other height region. This may not be critical for evaluating the assumption because variations in the ion composition ratio, might be due to mixture associated with vertical thermospheric motions, are not taken into account for IS spectrum analysis, although the ion temperature in this height region is considerably sensitive to the ion composition ratio [Oyama et al., 2004, and references therein]. To evaluate the assumption in the E-F transition region, the ion temperature may not be suitable.
 Hourly mean height profiles of the measured ionospheric parameters for the 8 March experiment do not show significant differences between two beams for the experiment interval, although the ion temperature in the E-F transition region also shows relatively large statistical standard deviations than in the other height region (not shown here).
 Effects of the horizontal inhomogeneity of horizontal neutral wind velocity on the vertical wind derivation should be also discussed. As a rough estimation, we consider the horizontal velocity difference by 30 m s−1 between the zenith and off-vertical IS beams. Since the elevation angle of the oblique IS beam is 75°, contribution of the velocity difference to the line-of-sight ion velocity is 7.8 m s−1. This value can be regarded as the maximum uncertainty caused by the assumed velocity difference, thus 1σ is much smaller than this level. Figure 4 shows the measurement uncertainty of ion velocity, which is larger than 7.8 m s−1 level for the experiment. This suggests that the spatial inhomogeneity effects on the vertical wind derivation are smaller than effects of the measurement uncertainty.
4.2. Effects of the Ion-Neutral Collision Frequency in Association With Vertical Thermospheric Motions
 The vertical thermospheric motions must affect the thermospheric density and therefore the ion-neutral collision frequency, which is necessary to calculate the vertical neutral wind velocity as shown in equation (2). While the ion-neutral collision frequency in this paper is calculated using data from the MSIS model, departures from the averaged values given from the MSIS model should be expected from vertical winds. In this section, we investigate effects of thermospheric density variations resulting from vertical motions.
 Specifically, we cannot precisely determine how large effects of the modified thermospheric density in association with the vertical motions are, even if the vertical neutral wind velocity is derived with the IS radar. This is because the ion-neutral collision frequency is a function of the vertical neutral wind velocity. Therefore it is inconclusive to use the calculated vertical neutral wind velocity itself to estimate the effects of thermospheric density variations. The available method may be to assume plausible vertical neutral winds, calculating thermospheric density variations resulting from the vertical motions then recalculating the vertical neutral wind velocity substituting the modified thermospheric density. Calculations for the various ionospheric conditions can allow us to estimate the maximum deviations from the original velocity derived with the MSIS values.
 We next assume two height profiles of the lower thermospheric density modified by upward and downward neutral wind velocities as shown in Figure 10. The vertical neutral wind speeds assumed here are 0 m s−1 at 100 km, and gradually increase with height reaching upward and downward speeds about 50 m s−1 around 120 km. Note that these height profiles are not responsible for the calculated vertical neutral wind velocity. In this calculation, we assume that the whole lower thermosphere is lifted up or dragged down, namely no divergence/convergence in association with horizontal thermospheric motions. Neutral gas temperature variations due to adiabatic cooling/heating in association with vertical thermospheric motions are not important for the vertical neutral wind calculation (The reason for this will be explained in Appendix B). In the case where these vertical neutral wind velocities flow for 5 min, the neutral density at 121 km increases by 134% of the original MSIS model value for upward velocity case, and decreases by 52% of it for downward velocity case (see Figure 10a). These variations are not unreasonable as experimental information suggests that there are factor of two changes in the MSIS density between geomagnetically quiet and disturbed days [Richards and Wilkinson, 1998]. The ion-neutral collision frequency is recalculated using the modified thermospheric density as shown in Figure 10b.
 We next calculate the vertical neutral wind velocity using two types of the modified ion-neutral collision frequency. Figure 11 shows temporal variations in the original vertical neutral wind velocity (same as Figure 5) together with the modified vertical neutral wind velocities for the upward and downward wind cases on 5 March 2004. Top (bottom) point of the vertical bar at each time shows the modified vertical neutral wind velocity for the upward (downward) wind case shown in Figure 10. Below 109 km, modifications of the ion-neutral collision frequency do not affect significantly the vertical neutral wind calculations. Above 112 km, differences between original and recalculated vertical neutral wind velocities increase during enhancements of the electric field, for example, around 1700 UT (see Figure 3). While the differences are smaller or comparable with amplitudes of the vertical neutral wind velocity, these never exceed estimated error values of the vertical neutral wind velocity. Similar results are found for the 8 March experiment case (not shown here).
 Statistics on the difference between original and recalculated vertical neutral wind velocities (the recalculated velocity minus the original velocity) are shown in Figure 12. The statistical method is shown in Appendix A. Figure 12 shows height profiles of the mean differences for upward (solid circle) and downward (open circle) wind cases together with the statistical standard deviation (not error values). For the downward wind case, magnitudes of the mean difference and the statistical standard deviation are smaller than 5 and 7 m s−1, respectively, increasing with height except for the 116–118 km level on 8 March. These values are smaller than estimated errors of the vertical neutral wind velocity at each height. Therefore for the downward wind case possible effects of the thermospheric density variations on the vertical neutral wind velocity calculation are not significant below 118 km.
 For the upward wind case, the effects appear to be insignificant below 110 km; however caution may be exercised above that level. While the mean differences above 112 km for the 8 March experiment are at most 4 m s−1, which is considerably smaller than estimated errors of the vertical neutral wind velocity, in the case of the 5 March experiment, the mean difference increases with height above 112 km reaching to 11 m s−1 at 118 km. The statistical standard deviations for both dates are sometimes significantly larger than estimated errors of the vertical neutral wind velocity. These large statistical standard deviations denote that calculations of the vertical neutral wind velocity above 112 km are considerably sensitive to variations in the ion-neutral collision frequency and therefore the thermospheric density.
4.3. Temporal Variations in the Relative Velocity Between Uz and Vz
 This section discusses contributions of the second term in the right-hand side of equation (2) to the calculated vertical neutral wind velocity. This discussion allows us to determine the upper height where the ion velocity is equal to the neutral wind velocity. To do so, we use data in Figure 13, which shows temporal variations in the relative velocity between vertical neutral wind and ion velocities, Uz − Vz. Calculations of the relative velocity provide more effective information to determine the upper height rather than normalization of the second term by some values such as the observed vertical ion velocity. This is because the normalized value can be infinite when the denominator is very small.
 The relative velocities in this height region before 1630 and 1600 UT on 5 and 8 March, respectively, have initial small amplitudes and later increase after these times due to the electric field increases. Below 106 km, the relative velocities do not deviate significantly from 0 m s−1 for the experiment interval. These small deviations suggest that ions are dragged by neutrals through collisions below that height. This is consistent with results from Oyama et al. ; they derive 103 km as the upper height where we can assume the ion velocity corresponds to the neutral wind velocity. The height difference of 3 km (i.e., 106–103 km) may be attributed to more disturbed conditions in the case of Oyama et al.  than geomagnetic conditions in this paper according to magnetometer data. The relative velocity at 109 km also has small deviations from 0 m s−1 before the electric field enhancements. Therefore ions at 109 km are also significantly dragged by neutrals through collisions for the small electric field periods, although effects of the electric field become more important after the electric field enhancements.
 The relative velocity at 112 km for the 5 March experiment shows significant deviations from 0 m s−1 from 1200 to 1400 UT. For the 8 March experiment the relative velocity at 112 km shows small deviations from 0 m s−1 for the small electric field period. Above 118 km, the relative velocities for both experiments fluctuate with significantly large amplitudes.
 The upper height where the ion velocity is equal to the neutral wind velocity is 106 km for both experiments; however this height may increase up to the 112 km level for the small electric field periods.
5. Summary and Conclusions
 In this paper, we present application of a new beam configuration for monostatic IS radars to estimate the vertical neutral wind velocity in the lower thermosphere at high latitudes. This beam configuration was tested with the Sondrestrom IS radar on 5 and 8 March 2004. Both experiments were conducted at local daytime for geomagnetically quiet conditions. We are able to derive the vertical neutral wind velocity from 100 to 118 km at 3 km height resolution and about 10 min time resolution. The estimated errors of the vertical neutral wind velocity are usually smaller than vertical neutral wind speeds. The vertical neutral wind velocities show various temporal variations with amplitudes larger than a few tens of meters per second, and sometimes also show remarkable vertical shears.
 Two assumptions are applied for the vertical neutral wind calculation; uniform spatial and temporal structures in the ionosphere for one IS beam sequence, and availability of the thermospheric density from the MSIS model to calculate the ion-neutral collision frequency. The paper demonstrates how to evaluate these assumptions using data from the March experiments. For both experiments, assumption of the uniform ionospheric structure is valid except from 1900 to 2000 UT on 5 March 2004; however, caution should be exercised in inferring effects of variations in the thermospheric density or the ion-neutral collision frequency in association with vertical thermospheric motions, in particular above 112 km.
 The relative velocity between vertical neutral wind and ion velocities are calculated using data from the March experiments. Below 106 km, the relative velocities do not deviate significantly from 0 m s−1 for the experiment intervals. These small deviations suggest that ions and neutrals are closely coupled through collisions. Above that height, the relative velocities sometimes show significant deviations from 0 m s−1 depending on the electric field magnitude.
 The beam configuration proposed in this paper can be applied for geomagnetically active conditions by decreasing the integration time at individual antenna positions in order to satisfy the assumptions required for application of the technique. Applications at other IS radar facilities at middle and low latitudes are in principle possible. However, we may need careful analyses about effects of vertical component of the E × B drift on the vertical neutral wind velocity, although the electric field at middle and low latitudes is in general smaller than that at high latitudes.
Appendix A:: Statistical Analysis Method
 We have developed a statistical analysis using a weighting function from the measurement uncertainty γi, being a value associated with data Xi, derived from the IS spectrum analysis. The mean value can be expressed with equation (A1) where N is the gross data number to be used for the statistics:
 The estimated weighted variance or standard deviation squared is given by
Appendix B:: Effects of the Thermospheric Temperature Variations Through Adiabatic Cooling/Heating Process in Association With Vertical Thermospheric Motions
 We calculate the temperature change due to vertical motions assuming the adiabatic lapse rate of −0.0096 K m−1. First we assume that the vertical speed of 50 m s−1 flows for 10 min. This speed can be sometimes seen in Figures 5 and 8. The temperature decrease (increase) is 288 K for the upward (downward) wind case. This temperature change is comparable or larger than the general lower thermospheric temperature. The vertical motion at 50 m s−1 for 10 min results in 30 km departure, which might be unrealistic because the calculated vertical neutral wind velocities are frequently out of phase among adjacent heights in the lower thermosphere. This suggests that air parcels may not move vertically over 3 km, corresponding to the height resolution of the IS radar. If the air parcel is dragged up/down by 3 km, the temperature change is 28.8 K. We here calculate the vertical neutral wind velocity with temperature change of 28.8 K.
 The vertical neutral wind velocity is recalculated using observed IS radar data and MSIS model values except for the neutral gas temperature, which is increased/decreased by 28.8 K from the MSIS value when calculating the ion-neutral collision frequency. Mean differences between original and recalculated vertical neutral wind velocities and the statistical standard deviations are less than 0.3 and 0.4 m s−1, respectively, from 100 to 118 km for the 5 and 8 March experiments. These values are considerably smaller than amplitudes of the calculated vertical neutral wind velocity and the estimated error values. We thus conclude that adiabatic cooling/heating of 28.8 K does not affect the vertical neutral wind calculation significantly.
 The Sondrestrom Research Facility is operated by SRI International under cooperative agreement ATM-9813556 with the U.S. National Science Foundation and in cooperation with the Danish Meteorological Institute.