The techniques used to process the MF-radar data and develop a gravity wave climatology are common in the literature (see Vincent and Fritts, 1987; Dowdy et al., 2007). This thesis models its method on that found in Hibbins et al. (2007). However, it should be noted that while theHibbins et al.(2007) study bins the radar data at two-minute resolutions, this was not done in this study in order to reduce the computational overhead of the method.
Initially, the radar data was placed into 26 bins from 70 - 96km, the data region dic- tated by the radar data acquisition and high signal-to-noise ratio. All winds greater than
Figure 4.1: The wave periods present in the radar wind data in 2007. The dashed line is the 99% significance level.
100ms−1 were discarded at this point in order to remove the occasional artificially large
wind measurement due to errors in the FCA algorithm. (Chapter 3.2.1). Note that while there is some radar wind data below 70km, the very weak D-region during the polar night means that the data availability is too low to be of use. The last height bin was selected to be 96km; above this altitude, ionisation becomes increasingly strong and electromagnetic effects become important (Fraser, 1984b). These electromagnetic effects mean that the as- sumption that the diffraction pattern observed by the radar moves due to the neural wind is likely to be violated. Furthermore, as height increases above 90km, very strong reflections from the E-region of the ionosphere can contaminate winds measurements, producing false winds (Hocking, 1997; Namboothiri et al., 1993)
Long period waves, such as the diurnal, semidiurnal and terdiurnal waves, often dominate the velocity field and therefore need to be removed to obtain wind perturbations from gravity waves alone. This was done by least square fitting a set of known period waves to the data and then removing them from each height bin. The periods of the waves to be fit were determined using a Lomb-Scargle periodogram (Figure 4.1). This gave strong peaks at 12 and 24h, and a weaker peak at 8h. These periods correspond to the diurnal, semi-diurnal and terdiurnal waves which would be expected to be present in this region.
Because the strength of the long period waves vary over time, the least squares fitting was performed over a five-day sliding window, applied to hourly average winds in order to reduce the effect of noise and speed up the computation. If the hourly mean was comprised of fewer than four data points, it was discarded. If less than 24 data points made up the data for the five-day sliding window (20% of the maximum possible data), then there were also considered to be too few data points for reliable removal of the long period waves. As such,
4.2. Methodology 29
Figure 4.2: Example of radar gravity wave energy quality control
the day in the centre of a given five-day sliding window was not considered in the analysis. The equation used in the least squares fitting routine used in this analysis to remove the long period waves is shown below
y = Acos(−ω24t) +Bsin(−ω24t) +Ccos(−ω12t) +Dsin(−ω12t)
+Ecos(−ω8t) +Fsin(−ω8t) +Gt+H) (4.1)
where ω24, ω12, ω8 are the frequencies of the diurnal wave, semi-diurnal and terdiurnal
waves respectively;GtandH are the linear trend and DC offset; A−H are the least squares fit parameters. For example Acos(−ω24t) +Bsin(−ω24t) makes up the diurnal wave.
Each five day window the waveform of the long period waves was reconstructed from the least squares fit parameters and then subtracted from the radar data. The variance of the residual was then taken giving u02 and v02. It was assumed that this variance was due to
gravity waves and some noise component. An additional quality control step was performed at this point to ensure that there were at least three data points in each least squares fitting set (per hour), and that they were less than two standard deviations away from a 15-day sliding mean over of the variance. Assuming a lognormal distribution, the variances were then reduced to daily means, which served to mitigate the effect of any white noise present.
The kinetic energy per unit mass is given by:
Ekm =
1 2(u
02+v02) (4.2)
Taking the mean of the Ekm across a set of years yielded the gravity wave climatology
Figure 4.3: Averaging the gravity wave kinetic energy for each height bin and year. It was particularly important to consider the quality of the MF-radar data, as the MF- radar had undergone a substantial upgrade early in 2004. The upgrade involved a change to the radar control and data acquisition (Baumgaertner et al., 2006). This resulted in a significantly higher rate of data acquisition: in early 2004, the usual time between sampling periods was around eight minutes, while in early 2005 the system was collecting data at one set per minute. To test the effect of the upgrade, the gravity wave field was calculated for each year from 1985 to 2008, averaged across the whole year for each height bin taken. Figure 4.3 shows that after 2005 there was a large increase in the mean kinetic energy per unit mass, particularly at higher altitudes. For this reason, the final gravity wave climatology was generated using only data from 2005 to 2008.
In order to ensure that the climatology produced over such a short timespan was repre- sentative, an additional climatology was produced for the period from 1985 to 2004. While the magnitudes of gravity wave structures could be expected to differ because of the radar data acquisition upgrade, a broad similarity in the structures themselves would add credence to the 2005 to 2008 climatology.
Lastly, the data between 2005 and 2008 was checked for any obvious anomalies that were not removed by the usual quality control methods. This was done by calculating the gravity wave climatology and checking each height bin for variations between years. Figure 4.4 shows an anomalous section of data in 2006 from the 4th of June to the 29th of July. As this anomaly was present at all altitudes, it was manually removed.