Evaluation of wind profiles from the NERC MST radar , Aberystwyth , UK

This study quantifies the uncertainties in winds measured by the Aberystwyth Mesosphere–Stratosphere– Troposphere (MST) radar (52.4 ◦ N, 4.0 W), before and after its renovation in March 2011. A total of 127 radiosondes provide an independent measure of winds. Differences between radiosonde and radar-measured horizontal winds are correlated with long-term averages of vertical velocities, suggesting an influence from local mountain waves. These local influences are an important consideration when using radar winds as a measure of regional conditions, particularly for numerical weather prediction. For those applications, local effects represent a source of sampling error additional to the inherent uncertainties in the measurements themselves. The radar renovation improved the signal-tonoise ratio (SNR) of measurements, with a corresponding improvement in altitude coverage. It also corrected an underestimate of horizontal wind speeds attributed to beam formation problems, due to pre-renovation component failure. The root mean square error (RMSE) in radar-measured horizontal wind components, averaged over half an hour, increases with wind speed and altitude, and is 0.8–2.5 m s −1 (6–12 % of wind speed) for post-renovation winds. Pre-renovation values are typically 0.1 m s −1 larger. The RMSE in radial velocities is< 0.04 m s−1. Eight weeks of special radar operation are used to investigate the effects of echo power aspect sensitivity. Corrections for echo power aspect sensitivity remove an underestimate of horizontal wind speeds; however aspect sensitivity is azimuthally anisotropic at the scale of routine observations ( ≈ 1 h). This anisotropy introduces random error into wind profiles. For winds averaged over half an hour, the RMSE is around 3.5 % above 8 km, but as large as 4.5 % in the mid-troposphere.

sive refurbishment of the system in 2011.
The Aberystwyth MST radar (Vaughan, 2002; Table 1) operates at a frequency of 46.5 MHz and can use any of 17 beam directions between zenith angles 0 • and 12 • .
The Doppler Beam Swinging (DBS) technique combines measurements from at least three beams to quantify three-dimensional winds, with more beams improving accu-15 racy and precision (e.g. Weber et al., 1992;Adachi et al., 2005;Cheong et al., 2008;Srinivasa Rao et al., 2008). A three-beam profiler uses one vertical and two off-vertical beams (pointing at orthogonal azimuths). The radial velocity (V r ) measured by an offvertical beam may be decomposed into components of the vertical velocity (w) and the horizontal velocity along the beam's azimuth (H φ ) (Eq. 1, where θ is the off-vertical 20 zenith angle, and φ is the azimuth, of the beam).
V r (φ) = H φ sin θ + w cos θ (1) w is measured directly by the vertical beam, with the two off-vertical beams measuring orthogonal values of H φ each. Eq. (2) relates H φ to the cartesian wind components u 25 and v (eastward and northward components respectively).
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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cancels vertical velocity components (w cos φ in Eq. 1), leaving only the horizontal component (Eq. 3).
A five-beam system (one vertical beam and four off-verticals) uses the same approach 5 as a three-beam setup. Multiple vertical beam measurement are made in a cycle, and Eq.
(1) is used to calculate H φ for each off-vertical. Values from opposing beams are averaged to reduce errors. The DBS method assumes temporal and spatial homogeneity of the wind field across the beams, which may be separated by several kilometres in the lower stratosphere.
Where there are rapid changes in vertical velocity, vertical beam measurements may not represent the average background airflow. These discrepancies propagate through Eqs. (1)-(3), into the horizontal winds (Weber et al., 1992;Adachi et al., 2005). Cheong et al. (2008) examined the homogeneity across a DBS sampling area, using a coherent imaging radar. They concluded that the assumption of homogeneity was invalid 15 at short (i.e. single-cycle) observation times. Such effects can be reduced with temporal averaging, but this can remove some of the genuine structure in the horizontal flow (Weber et al., 1992), particularly during the passage of fronts (for example, Luce et al. (2001b) showed poor agreement between radiosonde and radar winds measured around a warm front). Inhomogeneity across the sampling area becomes increasingly 20 likely with altitude, as beam separation increases. For example, the horizontal separation between opposing 6 • beams (routinely used by the radar in this study) is 4.2 km at a range of 20 km.
The uncertainty in winds is also affected by the strength of the signals received by the radar. These decrease with range above the tropopause, and the signal processing 25 algorithm struggles to accurately identify the clear-air signal where the signal-to-noise ratio (SNR) is small (Weber and Wuertz, 1990;Luce et al., 2001b;Srinivasa Rao et al., 2008). 4592 launch site, and may not sample the same volume as the radar. Weber and Wuertz (1990) and Srinivasa Rao et al. (2008) compared radiosonde and radar winds, and noted an increase in wind velocity differences with height, however they were unable to separate the potential effects of radiosonde drift.
At VHF, the effects of anisotropic scatter must also be considered, since the strength 10 of backscatter at angles closer to the vertical is usually enhanced (Luce et al., 2001a), causing the effective pointing angle of off-vertical beams to move closer to the zenith. Horizontal winds will be underestimated if the effective pointing angle θ eff is not used in Eqs.
(1)-(3). For the Aberystwyth radar, θ eff is calculated using the following formula (Hocking et al., 1986): where θ is the intended pointing zenith angle of the beam, and Θ is the beam's oneway e −1 half-width. ϑ s indicates the degree of aspect sensitivity (Hocking et al., 1986) and is defined as follows (Hooper and Thomas, 1995) using echo powers, P (θ), from 20 two beams at zenith angles θ 1 and θ 2 : ϑ s approaches zero for specular reflectors, and is around 4-5 • or greater for isotropic scatterers, where vertical beam echo powers are compared with off-vertical mea-25 surements (Hocking and Hamza, 1997). Hocking et al.'s (1986)  SOUSY radar showed a rapid fall-off of echo power with angles close to the zenith, followed by a slower decrease at larger angles. This implies that different values of ϑ s apply at different beam zenith angles. The same result has been found with measurements from the Aberystwyth MST radar (Hooper and Thomas, 1995). Aspect sensitivity tends to be strongest at the tropopause and in the lower strato-5 sphere (Hocking et al., 1986(Hocking et al., , 1990Luce et al., 2001a), though strong aspect sensitivity has been observed throughout the free troposphere during, and after, the passage of synoptic fronts (Hooper and Thomas, 1995;Kawano and Fukao, 2001). It is likely that corrugated sheets of constant refractive index are responsible for the anisotropic echoes typically observed at VHF frequencies (Luce et al., 2001a). Equation (4), how-10 ever, assumes that sheets are smooth, and some studies suggest that correcting winds for aspect sensitivity may not improve measurements. Hocking et al. (1990) found that corrections for effective pointing angle were not needed to get close agreement between horizontal winds measured at different beam zeniths. Kawano and Fukao (2001) directly measured the arrival angle of echoes under conditions of aspect sensitivity, 15 using spatial interferometry, and found that these were distributed about the intended 10 • pointing angle, rather than biased towards the vertical. We return to this point in Sect. 3. Quantifying aspect sensitivity may also be complicated by an azimuthal dependence of echo power. Worthington et al. (1999b) created maps of aspect sensitivity, using both 20 the MU radar in Japan, and the NERC MST radar at Aberystwyth (used in this study). They showed that the peak in echo power can be displaced from the zenith, and that displacement direction was correlated with the direction of wind shear. Echo power anisotropy can extend to large off-vertical zenith angles (Worthington et al. (1999a), measuring with the MU and Aberystwyth radars, found aspect sensitivity at zenith angles of 30 • and 12 • respectively).
Several studies have sought to quantify the various uncertainties in winds derived from the Aberystwyth MST radar. Thomas et al. (1997)  that the radar underestimated horizontal wind velocities by 4-5 %, and that aspect sensitivity corrections were necessary to remove the bias. However, they also reported that correction actually degraded the correlation at some altitudes, and had no effect at others, when sonde profiles were considered individually. Hooper et al. (2008) compared Aberystywth radar and radiosonde winds to wind fields from the global run of 5 the Met Office's Unified Model (see also Hooper et al., 2013b). They noted a systematic overestimate of radar wind speeds below 10 km, and an underestimate above; the magnitude of the bias was less than 1 m s −1 . The RMS difference in consecutive 30 min averages of horizontal wind speeds showed an increase with altitude, from 2 m s −1 at 2 km, to 3 m s −1 at 15 km. RMS differences above 15 km increased significantly, as SNR 10 reduced. A surprising result from long-term VHF radar measurements is that average vertical velocities are often non-zero. Such profiles have been measured with many different instruments, including the Aberystwyth radar (Worthington et al., 2001). To achieve conservation of mass, mean vertical velocities are expected to be negligible, how-15 ever typical profiles measured at Aberystwyth show downward motion in the midtroposphere (peaking at more than −4 cm s −1 ), and upward velocities in the lower stratosphere (peaking at 2 cm s −1 ). Worthington et al. (2001) reviewed the potential causes of such measurements, which included persistent vertical velocities observed around jet streams and streaks; false measurements associated with tilted aspect sen-20 sitive layers; and false measurements associated with gravity waves. The authors concluded that local mountain waves are the only mechanism capable of explaining all of the cases examined at Aberystwyth. Under such a model, the phases of mountain waves above the radar are not random. This skews long-term averages of vertical velocity towards the dominant mountain wave pattern. Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | winds than previous studies, given the proximity of the sondes to the radar. We also re-examine the effects of aspect sensitivity corrections, using eight weeks of special observations that measured on 17 different beams. The next section introduces the radar and radiosonde measurement techniques, and analysis methods; Sect. 3 discusses the results; and the conclusions are presented in Sect. 4.

2 Radar and radiosonde measurements
The NERC MST radar ( Radial and horizontal wind components are calculated using the radar's routine signal processing software (version-3, Hooper et al., 2008). This uses a variety of selfconsistency checks, including for radial and for time continuity, in order to quality-control the data. For each 6 • off-vertical beam, the corresponding horizontal wind component is derived from Eq. (1) using the vertical beam dwell that is closest in time. The off-5 vertical angle is initially assumed to be 6.0 • . The horizontal components for complementary beams are then averaged, however they are flagged as unreliable if they differ by more than 10 m s −1 . For each cycle, θ eff is derived from Eqs. (4) and (5)  . Radiosonde winds are averaged over 300 m height intervals, corresponding to the radar's pulse length, and are used to calculate the systematic difference between 20 radar and radiosonde horizontal winds. Radial velocities from opposing beams can be combined to give vertical velocity (w c , Eq. 6), assuming homogeneity of the wind field across the beams. The difference with directly measured vertical velocities (w d , from the vertical beam) gives a measure of the random errors in radar winds that arise from inhomogeneity across the beams (Eq. 7, Aspect sensitivity corrections are automatically applied to horizontal winds by the V3 processing algorithm. The effective pointing angle is calculated with Eq. (4), using the 5 average echo power of all 6 • zenith beams, and the 4.2 • zenith, 252.5 • azimuth beam.
Where beams with different zenith angles are compared in this study, velocities and echo powers have been linearly interpolated to the range gates of the 6 • zenith beams, to account for differences in sampling altitudes.
3 Results and discussion 10

Biases
The impact of the radar renovation is illustrated in Fig. 1, which shows the systematic difference between radiosonde and MST radar horizontal wind speed. Before renovation, the radar under-estimated horizontal wind speed at nearly all altitudes (Fig. 1a).
Post-renovation speeds, corrected for aspect sensitivity, show no overall difference 15 ( Fig. 1d), but wind speed is over-estimated below 10 km, and under-estimated above (Fig. 1b). The post-renovation profile has the same pattern as that presented by Hooper et al. (2008), who calculated mean wind speed differences between V3 winds and the Met Office Global Model, between July 2006 and January 2007. The origin of this altitude dependence is discussed shortly. Their is a striking anti-correlation between radar-radiosonde wind speed differences (post-renovation) and vertical velocities measured by the radar (Fig. 3). This suggests that horizontal winds above the radar are influenced by mountain waves: because ra-15 diosondes drift from the radar site (shown by the flight tracks in Fig. 4) they measure a different phase of the mountain waves, thus introducing the horizontal wind speed differences in Fig. 3a.
The pattern of mountain waves, and hence average vertical velocities, are expected to change with wind direction, because the terrain around Aberystwyth is inhomoge-20 neous. Figure 5a shows average vertical velocity profiles from 30 months of measurements, binned according to the 2 km wind direction. (2 km winds have been chosen as a measure of low-level winds that could drive mountain waves; Worthington, 1999.) Westerly winds occur 49 % of the time (approximately 617 000 profiles), with an average vertical velocity profile like that of the special operation period. (Note that westerlies 25 dominate the special operation period, and radar-sonde comparisons.) Southerly (24 % -299 000 profiles) and northerly (18 % -223 000 profiles) winds are associated with smaller average vertical velocities, with magnitudes roughly half those of the westerly profile. Finally, average vertical velocities during easterly winds (9 % -119 000 profiles) 4599 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | are similarly around half the strength of the westerly profile below 10 km, but tend to zero above. The tendency towards zero can be explained by changes in winds with height. Figure 5b shows that easterly winds at the surface persist up to an altitude of 8 km, and then gradually back to northerlies over the next 5 km; there then follows a sharp backing to westerlies over less than a kilometer. This backing through 180 • is 5 a critical layer, through which the mountain waves cannot propagate, hence the nearzero vertical velocities above 10 km. Pavelin and Whiteway (2002) presented a case study of such critical level filtering above the Aberystwyth radar site.
Finally, further evidence of mountain wave activity can be seen as the average vertical velocity profiles change with wind speed. Figure 6 shows the westerly vertical The profiles in Figs. 5 and 6 are averages over 30 months, and the patterns for individual cases will depend on the exact wind direction, wind speed, and stability of the atmosphere. Attempting to decompose such effects, and assess their impact on 20 horizontal winds, is beyond the scope of this study; however, it is clear that horizontal winds have a strong dependence on local conditions, particularly low level wind speed and direction.

Root Mean Square Errors
The random error in radial wind measurements is assessed by comparing vertical and 25 complementary beam observations (Eq. 7). Radar-sonde comparisons cannot be used because sondes drift from the radar site (Fig. 4), and do not sample the local conditions above the radar. The RMS difference of complementary beam radial winds increases with both wind speed and altitude (Fig. 7, where values have also been projected into the horizontal, assuming a beam zenith of 6 • ). The altitude dependence is related to the radar's signal to noise ratio, as well as the greater horizontal separation of the beams with height. At low SNR, the probability of detecting the clear-air signals is reduced, so the number of 5 reliable beam pairs decreases toward the top of the profile. (The definition of SNR used in this study is the ratio of peak signal power spectral density to noise.) The marked improvement in post-renovation SNR (around 5 dB below 13 km, and 2-4 dB above; Fig. 8) provided more occasions where measurements from both beams in a pair were available to calculate the RMS differences in Fig. 7. For practical application, an approximation to these profiles is given in Appendix A. Hooper et al. (2008) presented RMS difference profiles of radar and model winds 20 which show the same trends presented here, however the magnitude of their differences are much larger. This is attributed to the comparison method: the model comparison includes any systematic differences between the radar and the model, as well as differences between the (effective) spatial resolution of the two techniques, and the local effects identified in the previous section. Hooper et al. also calculated RMS 25 differences between consecutive 30 min averages of horizontal winds. That comparison includes any temporal changes in the background wind. In contrast our approach effectively quantifies the level of consistency between winds measured on opposing beams, removing sampling effects from different instruments, and contributions from scales larger than those of interest. However, one factor that Fig. 7 does not include (and which the Hooper et al. study does) is the effect of erroneous aspect sensitivity corrections, which is discussed next.

Aspect sensitivity corrections
Routine wind profiling with the Aberystwyth radar uses only one 4.2 • zenith beam to cal-5 culate aspect sensitivity. Azimuthal anisotropy of echo power therefore has the potential to introduce discrepancies into corrections. Average power maps at 2.5 km height intervals, derived from the special operation measurements, are shown in Fig. 9. At most altitudes the echo power is largely azimuthally isotropic, though 7.5 km echo powers are skewed towards larger zeniths in the south-west direction (the star symbol in each 10 map indicates the 4.2 • beam used for aspect sensitivity calculations). Effective pointing angles derived from the average power maps using one and four 4.2 • beams are similar (Fig. 10a). In contrast, there are significant differences between the one-and four-beam approaches when echo powers are averaged over only one hour (Fig. 11); at these time scales the single 4.2 • beam measurements are not representative of 15 the average echo power, because of azimuthal anisotropy. Routine aspect sensitivity correction uses only one beam, and so introduces this random error into corrected horizontal winds. (Note that these one-hour averages span six cycles of measurementsthe same number as a half-hour average during the routine observations used in previous sections.) The RMS difference between the effective pointing angles derived from 20 one, and all four, 4.2 • beams is shown in Fig. 10b, for the period of special operation. The corresponding wind speed uncertainty (top axis in Fig. 10b) is around 3.5 % above 8 km, but is as large as 4.5 % in the mid-troposphere. This uncertainty is additional to that discussed in the previous section, and further quantified in the appendix.

4 Conclusions
We have examined the uncertainties in winds quantified by the NERC MST radar, before and after its renovation in March 2011. The radar underestimates wind speed at almost all altitudes before the renovation, and there is a complex pattern of biases in radial winds that suggests a problem with beam formation (generating unintended 5 pointing angles). After renovation there is no overall bias. The upgrade improved the altitude coverage of the radar, and random errors in wind velocities decreased. Long-term patterns in vertical velocities are shown to be strongly correlated with radar-radiosonde differences. Our results support the conclusions of Worthington et al. (2001), that the radar is sampling local mountain waves. This is an important consid-10 eration when using radar winds as a measure of regional conditions, particularly when assimilating winds for numerical weather prediction. Many other VHF radars record non-zero vertical velocities over long time periods. The horizontal wind effects recorded here may extend to those instruments too.
Altitude and wind speed both affect the random error in wind velocities. Post-15 renovation horizontal velocities have RMS errors ranging from 0.6 m s −1 in low wind speeds (10-15 m s −1 ) and at low altitudes (below 5 km), to greater than 2.5 m s −1 at 20 km. Faced with such a range, the practice of quoting a single value for wind velocity uncertainty is clearly inadequate. Where the radar is used as a measure of regional winds the systematic differences identified by the radiosonde comparison, and quan-20 tified by Hooper et al. (2008), will also be significant. The RMS random error in radial winds is < 0.04 m s −1 . Aspect sensitivity corrections remove the overall bias in horizontal winds, but also contribute to the random error. The correction for 6 • zenith angle beams is largely constant throughout the troposphere and lower-most stratosphere (up to 15 km), and 25 corresponds to a horizontal wind speed increase of 5-6 %. At the time scales used for routine wind profiling (≈ 1 h), aspect sensitivity is azimuthally anisotropic. Routine wind profiling uses fewer beams than the special operation period examined in this study.
Here we present a simple formula to approximate the random errors in horizontal winds presented in Sect. 3.3. Random errors are estimated with Eq. (7), and profiles for different wind speeds are shown in Fig. 7. A cubic least squares fit to each RMS profile has been made. The shape of the fits vary with year and wind speed. A single curve shape is used to approximate all of the error profiles; it is expressed by Eq. (A1a), and constants a-c in Table 2. x corresponds to the height (h) of observations in km (Eq. A1b); the height offset (h off ) is an adjustment to account for the step change in errors following the renovation. Changes in random errors with wind speed (U) are implemented by Eq. (A1c); g off is another offset to account for the pre-/post-renovation step change. Variables and constants are summarised in Table 2. Equation (A1a) is 15 plotted with the corresponding random error profiles in Fig. 12. Note that horizontal winds corrected for aspect sensitivity will include the additional uncertainty detailed in Sect. 3.3 (3.5 % of wind speed in the lower stratosphere and near the tropopause, and up to 4.5 % in the free troposphere). [131][132][133][134][135][136][137][138][139][140][141][142][143][144]1986. 4593, 4594 Hocking, W. K., Fukao, S., Tsuda, T., Yamamoto, M., Sato, T., and Kato, S.: Aspect sensitivity of stratospheric VHF radio-wave scatterers, particularly above 15 km altitude, Radio Sci., 25,[613][614][615][616][617][618][619][620][621][622][623][624][625][626][627]1990. 4594 Hooper, D. and Thomas, L.: Aspect sensitivity of VHF scatterers in the troposphere and strato-   Comparison of wind speeds measured by the MST radar, and 75 and 52 radiosonde launched from the Aberystwyth radar site, pre-and post-renovation respectively. (a) Average radar-radiosonde wind speed differences at different altitudes, before the renovation. Negative differences correspond to radar speeds smaller than radiosonde speeds. The grey shading shows the standard error. Radar winds have been corrected for aspect sensitivity.   Fig. 1b, but showing radar-radiosonde wind speed bias corrected for aspect sensitivity (black line) and un-corrected (grey line). Error shading has not been included to aid interpretation; the standard error for both curves is as Fig. 1b. (  5a, but showing the 2 km westerly winds, decomposed into different 2 km wind speeds (shown   Pre-renovation Post-renovation nly results for every third height gate between 4 and 9 km are shown, to aid interpretation. Fig. 11. Effective pointing angles derived from eight weeks of special radar operation, using all 4.2 • zenith beams (x axis), and the 252.5 • azimuth 4.2 • beam (y axis). The grey dots are pointing angles from hourly averages, and the pluses are averages over the whole eight weeks of operation. The solid line traces the 1 : 1 points. Only results for every third height gate between 4 and 9 km are shown, to aid interpretation. 4620