MF radar spaced antenna experiment: wind variance vs. record length

Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 181–191

www.elsevier.nl/locate/jastp

MF radar spaced antenna experiment: wind variance vs. record length Chris Meek ∗ , Alan Manson Institute of Space and Atmospheric Studies, University of Saskatchewan, 116 Science Pl., Saskatoon, Canada S7N 5E2 Received 1 September 1999; accepted 30 November 1999

Abstract Because of the relatively wide transmitter antenna beamwidths at medium frequency (MF), measurements are expected to represent an integration over space as well as time. For historical (and practical) reasons, the normal record lengths at Saskatoon have been ∼ 5 min (4.5 – 4.8 min). This is approximately the Brunt–Vaisala (B–V) period, equivalent to 1 cycle of the shortest expected gravity wave (GW) period, so some GW energy may be lost by averaging. In addition the GW oscillations may add “noise” to the measured wind or even prevent a successful analysis, which assumes stationary statistics. On the other hand, if the spatial averaging has removed those waves contributing to high-frequency uctuations in wind, then reducing the record length increases the noise level rather than giving us more information regarding these GW. This paper describes two multiple record length experiments performed with the Saskatoon MF radar. Conclusions are that in the fall, below say 80 km, there is an inverse relationship between wind variance and record length, as would be expected from elementary statistics if the variance were strictly analysis noise. Presumably, this is because GW amplitudes are negligible here. In the summer, short period GW contribute signi cantly to the variance from 60 to 100 km. If we assume a form for the (unknown) GW spectrum, e.g. −5=3 log–log slope (VanZandt, 1982), then measurements with dierent record lengths can be used to separate the analysis noise and GW parts of this variance. Finally, the small amount of 90 s record wind data examined does not reveal obvious coherent features at short periods which are not also seen in 5 min records. On the other hand, their spectra do enhance some features which are less obvious in those of 5 min data, and interestingly, no apparent c 2001 Elsevier Science Ltd. All rights reserved. change is seen in spectral slope at the B–V frequency. Keywords: MF radar; FCA; Wind variance

1. Introduction GW play a dominant role in determining the dynamical and physical state of the atmosphere, especially at mesospheric heights, e.g. Fritts (1989). All general circulation models (GCMs) must incorporate GW eects in some reasonably realistic fashion, before their global wind and temperature elds are in any way physically appropriate (McLandress, 1998). However, there must be useful global observations of these waves to use as input to the GCMs, either directly or for use as a diagnostic against the characteristics of the model. ∗

Corresponding author. E-mail address: [email protected] (C. Meek).

Given that, there is remarkably little available to us on the global GW characteristics. The MF radars have played a very valuable role in building up this database. The radars can provide frequency spectra (10 min–10 h have been used typically), wind variances in the form of “ovals” which provide the predominant directions of GW propagation, and climatologies of variances in various GW spectral bands providing height and time information with monthly resolution (60 –100 km). Papers include Manson and Meek (1988, 1993), Thorsen and Franke (1998), and Nakamura et al. (1993). In most recent papers, we have provided GW spectra for stations from Christmas Island (2◦ N) to TromsH (70◦ N) (Manson et al., 1999), with considerable spatial resolution in the Canadian prairies (Manson et al., 1997). These studies have demonstrated important Doppler eects upon the

c 2001 Elsevier Science Ltd. All rights reserved. 1364-6826/01/$ - see front matter PII: S 1 3 6 4 - 6 8 2 6 ( 0 0 ) 0 0 1 4 8 - 6

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spectra, with important latitudinal dierences between equatorial and mid=high latitudes. Seasonal-latitudinal variations have been demonstrated. As always with such radar and optical studies great care has to be used to distinguish between ionospheric= geophysical noise and the high-frequency GW contributions to spectra and to other data presentations such as the “ovals”. This paper addresses these issues in detail, and provides a promising method for de ning these noise levels in a quantitative fashion. Spaced antenna analysis for wind velocities involves the nding, among other parameters, of time lags, tmax , for the peaks in the lagged cross correlations between signal sequences from dierent antennas. The lag step depends on the amount of raw signal integration and pulse repetition rate (prf): the more integration, the better the signal-to-noise ratio, but the worse the lag-time resolution. If raw data are recorded, these parameters can be varied for re-analysis, but the volume of data required for representative long term statistics is prohibitive. In real-time analysis, parameters are usually xed in any particular system. The main criterion for data selection, after signal-to-noise level (S=N), is the normalized time discrepancy (NTD). For a moving pattern of the type assumed by full correlation analysis (FCA, Briggs, 1984), the sum of the tmax taken around a closed path in the receiver antenna array should theoretically be zero (e.g. Meek et al., 1979). The NTD is just this sum divided by the sum of |tmax |. Acceptance criteria in our analysis are based on xed NTD levels. Since small tmax are related (but not directly in the FCA) to high speeds, then an analysis with a smaller lag step (more accurate determination of the tmax ) is more likely to result in small NTD, resulting in a potential data selection bias. Of course, a smaller lag step means less signal integration, and thus a poorer S=N ratio, so there is a trade-o here. Early analysis (1978–1988) at Saskatoon used noncoherent receivers, and because of micro-computer (and budget) limitations at that time, changed each fading signal sample to a single bit: 1 if above the mean, 0 otherwise. Our early coherent system analysis also used bit-amplitudes. Because of the resulting digitization noise, records shorter than 5 min were not attempted. The latter length is of the order of one cycle at the highest frequency expected (the B–V frequency), and so we could not accurately characterize the high-frequency end of the GW spectrum with these systems. When we began continuous full amplitude analysis in 1997, examination of the analysis noise versus record length became feasible. Studies to determine the shortest record length yielding an acceptable analysis noise must have been done by others, but there do not seem to be any published reports. This may be because, although the dierence lter concept is very valuable, maybe essential, in estimating data quality (i.e. noise level), it is not widely used (or maybe not widely known) in the MF radar eld.

May (1988) has made a detailed investigation of the causes of random errors in FCA wind values, but here we just try to estimate them without reference to their sources. The argument for estimating analysis noise in the presence of GW is that as records are made shorter and shorter relative to the B–V period, the eect of a change in wind due to GW on the measured wind variance for a given wind record becomes small, and what remains is analysis noise. A simple representation of the mean square velocity difference, 2 , for a xed time dierence,
T , is 2 2 = N2 (V; Tav ; h) + GW (
T; Tav ; h);

(1)

where Tav is the record length. The noise term, N2 , above includes potential dependences on speed, V , more important at high speeds because of increased relative errors in measuring the tmax as their values are reduced (although as mentioned above, the “true velocity” found by the FCA is not directly related to the tmax ), on the record length, Tav , for statistical averaging reasons, and on height because of changes in scattered signal characteristics. In the GW variance term, the
T represents the dierence lter response (see next section), and the Tav the reduction due to integration over short period wind variations. Both of these depend on the GW spectrum, which is presumably a function of height and time=season. Another similar in uence, very dicult to estimate, especially on a record-by-record basis, is the area over which the signal is averaged. This depends on the transmitter antenna beamwidth and aspect sensitivity of the scatterers, and we will refer to this area as the eective eld of view, E-FOV. The latter should be related to pattern scale which is determined by the FCA, but that scale may be in uenced by, for example, the receiver antenna spacing. The height parameter accounts for the expected GW amplitude increase with height (in the absence of saturation or critical layers). We note that Eq. (1) may not be strictly valid if N2 depends directly on V , because then the GW contribute to the noise term. However in this paper we are concerned with high-frequency GW, whereas most of V , evidenced by power vs. frequency spectra with negative slopes, is due to low-frequency components (e.g. mean wind, tides). 1.1. Dierence ÿlter Our pre-recorded raw data consist of variable length runs of only several hours each, because of this and because of gaps due to writing and copying errors spectral analysis is not suitable for estimating high-frequency variance. Consequently, a dierence lter has been employed. The dierence lter is applied by convolving the sequence (1; −1) with the data sequence. The mean-square value of the resulting sequence represents the integrated power after ltering. The power gain of such a high-pass lter, found by taking the Fourier transform of (1; −1), is p(f) = 2 − 2 cos(2f
T ):

(2)

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Thus, there is a maximum in power gain of 4 at the Nyquist frequency (period = 2
T ). The main advantage of a difference lter is that it is not aected by gaps; a disadvantage is that it has a wide bandwidth. For example Meek et al. (1985) show that if the original spectrum has a log–log slope of −5=3; a
T = 5 min dierence lter has a signi cant response to periods a little greater than ∼1 h. Hereafter we will refer to this band as 10 –100 min, although there is also a signi cant contribution from shorter periods. The above gain response must be multipled by another term since the original data employed in the time dierence lter have actually been pre- ltered by the non-negligible record length, Tav . If we assume that the result of a long record is the same as a time average (with equal weight, e.g. signal strength) of distributed instantaneous measurements, then the ltering eect of a time average on the power spectrum is  2 sin(fTav ) p(f) = : (3) fTav (This equation was stated incorrectly, without the square, in Meek et al. (1985).) 1.2. System biases When comparing the FCA results from dierent analyses we must consider potential sources of bias. A good discussion of these is given by Holdsworth (1999). In the present case of wind variance, we are mainly concerned with speed biases. These depend on parameters such as radio frequency (RF) signal-to-noise level (S=N) and correlation lag step time. A low S=N causes a bias to low speeds on average. We do not usually correct for this bias because it involves some loss of data if re-analysis fails, and the results may be noiser in some cases when it succeeds, since correction involves scaling the cross correlation values upwards, closer to 1. A factor which directly aects S=N is the amount of coherent signal integration done. This noise bias is usually only signi cant at the lowest 2 or 3 heights, and is not expected to signi cantly aect the results presented here. Better lag time resolution means more accurate tmax (but usually goes along with reduced signal integration). This means that smaller tmax , and thus larger speeds are more liable to pass the NTD criterion. 1.3. Data All data come from the antenna arrays described in Meek and Manson (1992). The transmitter antenna, which de nes the eld of view, is a square 4 × 4 array on a 12  spacing grid. The height resolution is 3 km (20 s pulse). A zenith angle distribution for a very small amount of data, found by interferometry and Doppler sorting, was shown by Meek et al. (1986). Here the majority of the echoes occurred at zenith angles of ¡ 15◦ , a sample area of ∼ 40 km in diameter.

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Fig. 1. Structure of raw data recording used in o-line analysis, which was done on the full 4.5 min records as well as the 2.2 and 1.1 min subdivisions.

Adams et al. (1989) found that their aspect sensitivity was related to height: quite strong below ∼85 km (±6◦ from the direction of maximum returns), but isotropic above (viz., the E-FOV just depends on the transmitter antenna beam pattern.). Jones and Thiele (1991) estimated a spread of ±2◦ in zenith below 80 km and ±4◦ above. Usable estimates of the E-FOV are very dicult, if not impossible, to make because it likely depends on factors such as GW (through strati ed layer tilting), and turbulence (causing isotropic scatter), which themselves may depend on height, season, and local geography, for example. 1.3.1. O-line analysis The recorded raw data consist of many short (mostly summer) daytime runs of 2– 4 h each, over 1989 and 1990. These were taken from the “raw data port” on our regular real-time wind analysis system. Fig. 1 shows a schematic of the original time sequence format. Each record comprises 512 time samples of fading signal covering 4.5 min. In the present work these have been used whole (4.5 min) and also subdivided into halves (2.2 min) and quarters (1.1 min). The correlation analysis lag step and maximum lag are the same for all sequence lengths. All our o-line analyses employ data with the same amount of integration and lag step in order that the S=N remain constant. Just the sequence length is changed. 1.3.2. Real-time data Actual record lengths in these data are 88 s and 4:8 min, but will usually be referred to hereafter as 90 s and 5 min. These data sets come from two simultaneously running real-time receiver=analysis systems which are independent, except that both sample the same receiver antenna array through the use of RF power splitters. Several data sets are available: fall 1997, fall 1998, late winter 1999 and summer 1999 (the latter was cut short by a power failure and re at

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Fig. 2. RMS dierences for Tav = 1:1 min records at dierent time separations,
T , for (mostly) summer 1989=1990 daytime data. All plotted points are based on more than 100 original values.

the radar site, caused by lightning). The 90 s data employ half the integration of the 5 min data, and have half the lag step (and twice the number of lags). 1.4. Paper outline The paper is organized as follows. For the o-line raw data we rst x Tav at 1:1 m and vary the time dierence. Then we x the time dierence
T at 5 min and vary the record length (Tav =1:1; 2:2; 4:5 min). We repeat the latter analysis for the simultaneous real-time analysed data (90 s; 5 min) for four data sets, but use both
T = 4:5 and 6 min since 5 min separation is not available for the 90 s data.
T =90 s for Tav = 90 s data is also included for comparison. To see whether higher time-resolution data show features we would not see with 5 min data, we compare time sequences and spectra. All dates in this paper are given as day numbers where January 1 = day 1. 2. Results from o-line analysis 2.1. Eect of varying
T at constant T Fig. 1 shows the raw data format and the record subdivisons used here. A variety of time dierences is available, especially for the 1:1 min subdivisions. RMS dierences, p
VN2 +
VE2 , using 1:1 m-length records with varying spacing are shown in Fig. 2 for summer data. These have been done for four 9 km layers (each comprising 3 original heights). Note the increase in RMS dierence (except at 76 –82 km) as the time dierence passes 300 s. Since the maximum response of the dierence lter is at a period of 2
T , this suggests that the shortest GW periods are between 5 and 10 min.

Also shown in Fig. 2 are the RMS dierences from two time sequence models. Both consist of sequences of random values with a time step of 30 s. These numerical models have been generated by specifying the desired amplitude spectrum, in this case a constant slope on a log(amplitude) vs. log(frequency) scale, while the phase is made random for each frequency component. This spectrum is inverted to get the time sequence representation to which the time dierence lter can be applied. Model-A has a −5=3 slope log–log spectrum, with zero power at periods less than 5 min, viz., just what is expected from real data, with one dierence — there is no noise. Model-B is similar to Model-A, except the spectral slope is zero. The absolute power scales of these models are arbitrary. This means that it is legitimate to scale them by a factor to match the shape of the real data, although the present scale for Model-A seems to be a reasonably good match to the data. The oset is of more interest than the scale, as it represents analysis noise. If we assume the real data follow a −5=3 slope log–log spectrum and slide the Model-A curve up to t the 58–64 km data, its intercept at
T = 0 gives the variance due to analysis noise (for a 1:0 m record), which is approximately 82 m2 =s2 . Since from elementary statistics the variance of a dierence is equal to the sum of the variances for each term, we conclude that√ the analysis noise for a measurement in the lowest layer is 32 or ∼ 6 m=s. The unexpected feature in Fig. 2 is the similarity of data slopes in dierent height layers, viz., the GW component does not appear to change with height. This suggests that the GW are always saturated. Model-A is expanded in Fig. 3 as a function of record separation and length for future reference. Note that the contour labels refer to units of squared velocity, but the scale is arbitrary. This gure allows record overlap for completeness (but no overlapping record dierences are used in this paper). It can be seen that record separation is more important than record length in the GW contribution to wind dierence variance. Note that the spectrum only has to have the assumed form (e.g. log–log slope of −5=3 here), over the response band of the lowest frequency dierence lter used, say periods less than 2 h for the present study. 2.2. Five minutes dierences using Tav = 1:1; 2:2; 4:5 min Two analysis runs were done. In the rst each 5 min record had to have a 4:5 min and at least one 1:1 min wind value (Run #1) and in the second, a 4:5 min and at least one 2:2 min value (Run #2). Thus the two Tav = 4:5 min data sets are slightly dierent, and both are shown. Fig. 4 shows mean-square dierences vs. height for 5 min dierences using record lengths Tav = 4:5; 2:2 and 1:1 min. The variances of 5 min dierences for the 2.2 and 1:1 min data, at 79 km for example, are approximately 1.5 and 2.5 times the 4:5 min variance; and at 94 km, 2 and 4.6. The former height (and other heights) shows signi cantly smaller variances than would be expected from simple averaging

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2.2, and 4:5 min, we see that the variance increases should be ∼ 1:3 and ∼ 1:4, respectively. The measured data fall between these two expectations, and so the inference is that even for these relatively small time dierences, both analysis noise and GW are contributing. It is tempting to use our noise and GW expectations to solve for their separate contributions to the measured mean-square dierences. We have succumbed to this temptation. 2 the GW Let N2 represent the analysis noise, and GW 5 min-dierence variances for the 4:5 min records. Then for 79 km (Fig. 4) for Tav = 4:5 min: 2 N2 + GW = 140 m2 =s2 ;

(4)

for Tav = 2:2 min: 2 2N2 + 1:3GW = 200 m2 =s2

Fig. 3. Model-A is a −5=3 log–log slope power spectrum with no power at periods shorter than 5 min. The variance of dierences in the corresponding time sequence versus record length (data are averaged) and separation is shown. The units on contours represent squared velocity, but the scale is arbitrary. Record overlap is allowed.

Fig. 4. Mean square 5 min dierences for o-line analysis of (mostly) summer 1989=1990 daytime data. Record lengths Tav = 4:5; 2:2, and 1.1 min are used. Two sets of 4.5 min values exist because the 4:5=2:2 and 4:5=1:1 min analysis runs had slightly dierent selection criteria.

statistics, viz., a two- and four-fold increase respectively, while 94 km is the only height which even approximately meets expectations (and heights above this are probably total re ection E-region). However, if we look at a xed record separation of 5 min in Fig. 3 for record lengths of 1.1,

(5)

and for Tav = 1:1 min 2 4N2 + 1:4GW = 330 m2 =s2 :

(6)

In the latter two equations the GW term is multiplied by a factor ¿ 1 because there is less averaging of the GW. Since these equations have one degree of freedom a least-squares t could be used, but for the present we will solve pairs of equations in turn. The 4.5 and 2:2 m equations give N2 and 2 GW = 26 and 114 m2 =s2 , the 4.5 and 1:1 min equations, 56 and 88 m2 =s2 , respectively (as before variances per measured wind value are half of these). Precise results are not expected because our model may not accurately re ect the actual analysis noise dependence on record length or the real GW spectrum, but it is clear that at this height and season, 10 –100 min GW are the dominant contributor to measured wind variance. We will now outline the least-squares t method which will be employed after we have introduced the rest of the data. As before we will let 2 be the measured mean-square dierence for record length Tav and separation
T; a be the analysis noise variance part (relative to Tav = 1 min), and b be the scale by which the model value (from Fig. 3) must be multiplied to give the GW contribution to the variance (recall that we are assuming a −5=3 log–log slope in the model). Then i2 = a

1 + bG(Tavi ;
Ti ); Tavi

(7)

where, for data point i , the value of the function G is found from Fig. 3 for the particular value of Tav and
T . This is a linear equation in a and b, so the standard least-squares solution applies. After b has been found, the dierence lter variance for a particular Tav and
T can be found by reading the value from Fig. 3 and multiplying it by b, e.g. we are particularly interested in our normal wind data, for which Tav and
T are 4:8 and 5 min, respectively.

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Fig. 5. Daytime height variation of measured mean-square wind dierence for various record lengths and separations. The inset legend has the format x(y) where x is the record length (Tav ) and y is the separation (
T ). The two lefthand panels are for the fall season, the top right is late winter, and bottom right, summer. Local noon is near 19UT.

3. Five minutes vs. 90 s data The intent is to compare 5 min dierences with both data sets, but this time step is not available with 90 s data, so 4.5 and 6 min dierences are calculated. Fig. 5 shows the comparisons on daytime data (10 –15 CST) over a periods of a week or more. Ninety seconds dierences for 90 s data are added to the plot. The fall data (Fig. 5, both LH panels) closely agree with our expectations for analysis noise, viz., the
T = 4:5 and 6 min for Tav =90 s variances are approximately three times larger than that for Tav = 5 min at the lower height (but the

factor decreases with height, probably because GW contributions are becoming signi cant). Since the equinoxes are known to have small variances at low heights, which is presumed to indicate seasonal minimum in GW activity (Meek et al.,1985; Manson and Meek, 1993), this provides some justi cation for the tacit assumption made throughout this paper that the analysis-noise part of the wind variance varies inversely as record length. The late winter data at the lower heights (Fig. 5, bottom RH panel) show a smaller increase in variance with shorter records, while summer (Fig. 5, top RH panel) shows the smallest increase.

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We conclude that short period GW, ∼ 10–100 min, are not an important part of the wind variance in the fall at lower heights, say below ∼ 80 km, they are slightly more important in late winter, and very signi cant in summer at all mesospheric heights. The next section gives a more quantitative picture.

4. Analysis noise and GW variance for all wind dierence data Eq. (7) has been applied to the 5 available data sets separately. In the t, the required values of G were scaled from Fig. 3. The results are shown in Table 1. This table lists the values a=4:8 and 8b (where 8 is the Tav = 4:8 min;
T = 5 min value from Fig. 3), which are the estimated analysis noise variance and GW variance parts, respectively, of a 5 min dierence of 4:8 min records — our normal operating parameters. The fall 1997 and fall 1998 results are quite similar, viz., analysis noise dominates below about 80 km. In winter the GW are more signi cant, beginning to exceed the noise at 64 km. The two summer data sets are somewhat contradictory. Summer 1999 data in Table 1 or Table 2 show GW dominance at all heights, while 89=90 shows a more equal (and more variable) variance distribution between noise and GW. The latter nding agrees with the discussion of Fig. 2, in which it was mentioned that the GW did not appear to be increasing with height. The height variation of the 89=90 noise and GW components in Table 1 are seen to be more erratic than those of summer 1999 data, possibly because the former data set is about one-quarter the size of the latter in terms of number of dierences available. The other main dierence between the data sets is the mixture of
T and Tav used in the least-squares t. More data are required to see whether this apparent contradiction is explained by normal, say year to year, data variability. We re-iterate that the accuracy of these results depends on the GW power spectrum which we must guess, and on the assumption that noise variance varies inversely with record length. The spectra to be presented in the next section all have slopes shallower than −5=3. This is typical for Saskatoon data, especially in summer and at low heights (Manson et al., 1997). In order to see how strongly the results depend of the choice of model slope, we have re-analysed the data for a spectral slope of −0:8, and it is shown in Table 2. Comparison of Tables 1 and 2 show that the noise and GW variances are insensitive to the model slope. As a nal comment, it appears that there is nothing to prevent us from using the same theory for a single record length at two or more time separations, e.g. Tav = 5 min;
T = 5 and 10 min, viz., routine data rather than specialized runs. This would open up a very large data set for analysis.

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5. Comparison of time sequences for 5 min and 90 s records From the foregoing discussion, it appears that summer is the best time to look for short period GW. Consequently, we have plotted time sequences of 90 s northward wind data from July 5, 1999 (day 186) for 6 h around local noon (13 CST), which are shown in Fig. 6. A long period (∼ 2:5 h) oscillation can be seen at the greatest heights. Many uctuations are seen with time scales less than 10 m, which is the smallest measurable period with our normal 5 min spacing, but unlike those in VHF radar data (narrow beam, e.g. Bowhill, 1983) they do not appear to be coherent at adjacent heights. The latter nding is typical for the 90 s data, and for short periods in general in our MF wind data, and may indicate that there are usually multiple waves in our relatively large eld of view. Taylor et al. (1995, their Fig. 2). show an example of this in all-sky optical measurements. A study by Waltersheid et al. (1999) concludes that ducting of short period gravity waves is common, so that a VHF radar because of its relatively narrow beam may see just one, while we see a mixture. Fig. 7 compares northward 4.8 m and the same latter 90 s wind data. In general the 90 s data look like a noisy version of the 5 min data, however, as we found earlier (Table 1, summer 1999 column), at least half this “noise” can be attributed to short period GW. 6. Comparison of spectra for 5 min and 90 s records The spectral analysis is similar to that of Zhan et al. (1996). Brie y, we require greater than 50% data existence at more than half the heights in a layer; the mean is removed; data are linearly detrended; gaps are lled by linear interpolation; then the time sequence is tapered with a cosine window (hanning, Blackman and Tukey, 1959). For 5 min data, we use 10.7 h sequences (128 points) starting at 9 CST. Originally we tried to break this 10.7 h interval into 3128 point 90 s data sequences (each 3.2 h), but found puzzling large dierences between 5 min data and 90 s data spectra at periods of several hours except in summer. Since the eect was not apparent in summer, when the tidal oscillations at Saskatoon are small, we assume this is an artifact of the linear detrending, created when the original data had oscillations with periods much longer than 3.2 h. To avoid these problems, we changed to 426 point 90 s data sequences (10.7 h). Unfortunately, it turns out that the percentage data continuity is worse than the 5 min data, resulting in fewer sequences meeting the 50% existence criterion. This is undoubtedly a result of increased noisiness, due to shorter records, of the correlations used in the FCA method leading to more record rejection by the NTD criterion. We will not go into a detailed discussion of spectra here, but restrict ourselves to a cursory comparison of the 5 min and 90 s data average spectra. What we expect to see, given our model in Eq. (7), is a signi cant dierence between 90 s

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Table 1 Least-squares t estimates of analysis noise, N, and GW parts of
T = 5 min dierence variance assuming Tav = 4:8 min. A −5=3 log–log spectral slope model was assumed. The “summer 89=90” t used all data plotted in Figs. 2 (but single heights here) and 4. The N column value is twice the variance of a single 5 min wind measurement, while the GW represents the total GW variance in the ∼ 10–100 min period band Height (km)

Summer 89=90 (m2 =s2 ) N GW

Fall 1997 (m2 =s2 ) N GW

Fall 1998 (m2 =s2 ) N GW

Winter 1999 (m2 =s2 ) N GW

Summer 1999 (m2 =s2 ) N GW

58 61 64 67 70 73 76 79 82 85 88 91 94

— — — 41 53 49 60 78 90 91 129 70 105

— 28 25 25 25 50 41 52 47 61 74 55 76

22 23 26 26 30 34 35 38 51 53 63 77 110

31 31 36 35 38 43 40 35 59 63 83 94 113

— 12 23 36 51 68 80 89 77 76 88 97 114

— — — 46 73 103 64 46 69 102 80 165 103

— 16 16 10 14 37 24 35 75 57 121 159 168

5 12 7 16 20 26 34 36 73 83 119 189 279

23 20 23 41 42 64 60 49 66 106 146 209 212

— 44 45 73 83 105 109 136 120 106 106 106 202

Table 2 As in Table 1, but a spectral model with a log–log slope of −0:8 was used Height (km)

Summer 89=90 (m2 =s2 ) N GW

Fall 1997 (m2 =s2 ) N GW

Fall 1998 (m2 =s2 ) N GW

Winter 1999 (m2 =s2 ) N GW

Summer 1999 (m2 =s2 ) N GW

58 61 64 67 70 73 76 79 82 85 88 91 94

— — — 40 51 46 54 71 86 86 126 54 94

— 27 23 24 23 48 38 48 41 56 62 44 64

22 21 26 25 28 31 32 34 44 47 54 61 87

29 29 34 32 34 37 36 31 54 55 70 75 96

— 9 20 30 43 58 70 77 66 67 81 82 95

— — — 35 56 79 58 48 59 85 64 156 98

— 16 18 9 14 34 26 38 75 58 126 156 163

5 12 7 15 21 27 35 38 76 82 118 190 278

24 21 23 40 43 66 57 50 66 106 147 213 211

Fig. 6. An example of summer daytime 90 s data: northward wind component.

— 44 44 73 84 106 110 138 122 106 101 169 208

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Fig. 7. Comparison of 5 min (thick line) vs. 90 s (thin line) summer daytime data over a 6 h period.

Fig. 8. Average daytime spectra for northward wind component, 98:054 – 067 (winter 1999), 55 –73 km, for 5 min (thick, 84 spectra averaged) and 90 s (thin, 38 spectra averaged) data. The thin straight line indicates a −5=3 slope.

and 5 min data spectra at the highest frequencies, because here the spectral power is low enough for the extra 90 s data noise to make a dierence. At the low frequencies where powers are high we expect the eect of such additive noise to be negligible. Fig. 8 shows the average northward component spectra for the lower mesosphere winter 1999 data set. Note that there fewer 90 s than 5 min spectra, 38 as compared to 84, contributing to the average. The average northward and eastward component (not shown) spectra are similar overall. Our high-frequency expectation, mentioned previously, is met, but at low frequencies there is still a signi cant difference in power. It is likely that this latter dierence is at least partly due to linear interpolation, because the extra 90 s data gap lling with a linear function should increase the low-frequency content at the expense of the high. Another factor is that because RF signal increases with height, there are liable to be fewer gaps at greater heights, and so a greater acceptance of data. Thus, the eective height for the 90 s spectrum is liable to be larger, and, because of that, have a larger GW component than the 5 min. The median of the height distributions for 90 s and 5 min spectra used in this winter 1999 average were found to be virtually identical, but in the fall 1998 data to be presented shortly, the 90 s median height is ∼ 2 km greater than that of the 5 min data.

It is interesting that no sudden drop in power, or even slope change, is seen near the B–V period (∼ 5 min). This may be due to Doppler shifting of observed GW periods as proposed by Hines (1991), or turbulence with a scale larger than the E-FOV. In addition there is probably some smearing of the spectra due to gaps in the original sequence, although the general eect of linear interpolation (Zhan et al., 1996) is a reduced high-frequency content. In the case of Doppler shifting, a stronger eect is expected when the GW and background winds are large, as in summer, and this may be the cause of the reduced spectral slope at the lower heights then. However Manson et al. (1997), after an inspection of monthly mean Saskatoon spectra concluded that there was no consistent slope variation related to the background wind, although the summer spectral densities at high frequencies were found to depend on the strength of the background wind. Also, Doppler shifting would also have to apply during the weaker winds in the fall, where the high-frequency spectra presented later here show negligible change in slope as the frequency passes the B–V period. Fig. 9 shows summer data, upper height layer, for the northward component. Here the numbers of spectra are almost the same (5 min: 84 vs. 90 s: 76 spectra), and so it is likely that the eective height layers are equivalent. Both spectral powers are larger than in winter. Presumably, this is the increase in GW that was found in the 5 min dierence

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Fig. 9. As in Fig. 8 but for the 99:180 –193 (summer 1999) 76 –91 km layer (5 min: 84 spectra and 90 s: 76 spectra).

Fig. 10. As in Fig. 8 but for 98:251–265 (fall 1998) for the 76 –91 km layer, northward component (5 min: 87 spectra, 90 s: 44 spectra).

study, and probably this covers up the noise to a large extent, leading to a smaller dierence between 90 s and 5 min spectra. The corresponding spectra for the east component are virtually identical to those presented. Finally Figs. 10 and 11 show upper mesosphere fall 1998 data for North and East wind components. As in the winter 1999 data, the number of original 90 s spectra (44) is much smaller than for the 5 min data (87), and as mentioned above, the eective height for the 90 s spectra is greater than that for the 5 min spectra. It is interesting that the feature seen in both north and east component 90 s spectra at ∼ 35 min period is not very visible in the 5 min spectra; only the east component has a hint of it. It is not clear why this is so, since 5 min integration should not signi cantly reduce the amplitude of a 35 min wave, but it suggests that these shorter records, although noisier, can contain valuable information. 7. Conclusions We have tried to estimate MF radar FCA wind variance by comparing mean-squared wind dierences for varying record lengths and separations. There is clear evidence that wind variance is inversely related to record length, but it is not always the linear relationship that would be expected from simple statistics; and there is some dependence on season. We have invoked GW contributions to explain these ndings. For this latter analysis we only need to assume the

Fig. 11. As in Fig. 10 (same height layer and season), but for the eastward component.

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slope of the log–log GW spectrum at short periods, say less than 2 h, and we need to assume that wind variance varies inversely with record length. The method presented of separating analysis noise and high-frequency GW appears to be applicable to our routine data (single record length) although we have not made a direct comparison yet. A potential advantage is that assumptions about the dependence of analysis noise on record length are not required. We also compared time sequences and average daytime spectra to investigate whether new features can be seen using 90 s sampling that are obscured by 5 min sampling. The time sequences did not show such features, and we concluded that because of our wide beam width we may be averaging over dierent wave motions. On the other hand, the fall 1998 average 90 s data spectra (Figs. 10 and 11) did show clear peaks at ∼35 min period in both North and East components, which were not obvious in the 5 min data spectra. An interesting feature in all spectra for 90 s records (Nyquist period 3 min) is that they do not change character, e.g. slope, at the B–V period (∼ 5 min). The desire to investigate this region of the spectrum was the major factor behind the decision to try very short records. Acknowledgements The nancial support of the Natural Sciences and Engineering Research Council and the Atmospheric Environment Service, both of Canada, is gratefully acknowledged. The University of Saskatchewan, through the Institute of Space and Atmospheric Studies, has also supported this work. References Adams, G.W., Brosnahan, J.W., Johnson, R.E., 1989. Aspect sensitivity of 2.66-MHz radar returns from the mesosphere. Radio Science 24, 127–132. Blackman, R.B., Tukey, J.W., 1959. The Measurement of Power Spectra. Dover Publications, New York, 190pp. Bowhill, S.A., 1983. Pulse stuttering as a remedy for aliased ground backscatter. In: Handbook for MAP, Vol. 9. SCOSTEP Secr., University of Illinois, Urbana, pp. 122–123. Briggs, B.H., 1984. The analysis of spaced sensor records by correlation techniques. In: Handbook for MAP, Vol. 13. SCOSTEP Secr., University of Illinois, Urbana, pp. 166 –186. Fritts, D.C., 1989. A review of gravity wave saturation processes, eects, and variability in the middle atmosphere. Pure Applied Geophysics 130, 343–371. Hines, C.O., 1991. The saturation of gravity waves in the middle atmosphere, Part II, Development of Doppler-spread theory. Journal of the Atmospheric Sciences 48, 1360–1379. Holdsworth, D.A., 1999. In uences of instrumental eects upon the full correlation analysis. Radio Science 34, 643–655. Jones, K.L., Thiele, D.L., 1991. Further observations of the structure of the D-region using a 1.98 MHz steerable-beam radar. Journal of Atmospheric and Terrestial Physics 53, 89–97. Manson, A.H., Meek, C.E., 1988. Gravity wave propagation characteristics (60 –120 km) as determined by the Saskatoon MF

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