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Before discussing the statistical analysis, we first show several examples of the comparisons made. Figure 1 shows five comparisons of ws, wd, u and v measurements taken from observations in January, April, July and October 2012. The agreements were generally very good in each example.
3.1. Characteristics and preliminary comparisons of horizontal wind measurements from the MST radar system and the radiosondes
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We start the preliminary comparison from the basic characteristics of the time-height plots of ws, wd, u and v for the year 2012.
Figure 2 shows that the spatial and temporal distributions of ws, wd, u and v obtained from the MST radar system and the radiosondes were generally highly consistent. The horizontal winds were weaker throughout the height range 3-25 km from June to August, but were stronger in January and February (Figs. 2a and b). Apart from during the summer, the horizontal wind directions were mainly in the range 225°-315° at heights of 3-25 km. In June, July and August, the wind directions showed a significant shift in the vicinity of 18 km height, turning from low-level westerly winds into high-level easterly winds (Figs. 2c and d). This is clearly seen in the time-height distribution plots of u (Figs. 2e and f). In addition, westerly winds were observed in the lower layers and easterly winds in the upper layers in May and September at around 20 km height. The zonal wind speed in winter can reach >60 m s-1. The distribution of v is more complex. The winds in early July were mainly northerly, whereas southerly winds dominated in late July. As August proceeded, southerly and northerly winds appeared alternately in the height range 5-15 km (Figs. 2g and h).
In addition to the detailed characteristics of the time-height distribution, the wind characteristics also showed obvious seasonal variations. We therefore carried out further analyses of the seasonal mean distribution of ws, wd, u and v with height for both instruments (Fig. 3).
Figure 3a shows that the average horizontal wind speed was at a maximum in winter, followed by spring and autumn, and at a minimum in summer. The height range of the maximum wind speed in each season was about 10-15 km. The seasonal mean wind speeds measured by the radiosonde in this height range were larger than the MST radar observations in each season.
Figure 3b shows that the horizontal wind directions clearly shifted from west to east during summer in the height range 18-22 km. Figure 3c clearly shows the shift in direction from a westerly to an easterly wind and that the wind speed was <5 m s-1 from 18 to 22 km. The meridional winds were light with speeds close to 0 m s-1 at 18-22 km in summer (Fig. 3d). This meets the definition of a quasi-zero wind layer at about 20 km; the zonal winds turn from westerly below this layer to easterly above this layer and the meridional winds are all light at this time. The height range 18-22 km in summer is therefore referred to as a quasi-zero wind layer.
Figure 4 shows the analysis of the monthly mean ws, wd, u and v distributions with height. The trends in the monthly mean profiles for ws, wd, u and v measured by the Beijing MST radar system and the radiosonde were basically the same. Figures 4b and d show the wind shift in each month more specifically. In May and September, the months of transition from spring to summer and summer to autumn, there was a wind shift in the height range 18-22 km. The wind direction during June to September also changed rapidly with height at about 5 km altitude.
3.2. Statistical analysis
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After the preliminary analysis of the wind characteristics measured by the MST radar system and the radiosondes above, the seasonal and monthly characteristics of the horizontal winds were also obtained. Next, comparisons were undertaken in a statistical sense, and made contrastive analysis as a whole. Figures 5 and 6 show scatterplots and the linear least-squares fits of ws, wd, u and v. We then calculated the correlation coefficient, mean difference, mean absolute difference, standard deviation of difference and standard deviation of absolute difference for ws, wd, u and v measured by the two instruments, and show the results below.
3.2.1. Scatterplots and linear least-squares fits
Figure 5 shows that the slopes of the least-squares fit lines for ws, wd, u and v were 0.94, 0.89, 0.96 and 0.83, respectively. Good consistencies were found for u and ws. However, the distribution of scatter points for wd was widely dispersed (Fig. 5b) when we considered whether the wind speed affected the consistency of the wind direction. Figure 6 therefore shows a scatterplot of the wind direction at different wind speeds and its least-squares fit.
By comparing Fig. 5b and Fig. 6, it is obvious that most of the more dispersed points in Fig. 5b correspond to wind speeds <5 m s-1. When the wind speed was between 5 and 10 m s-1, the slope of the least-squares fit line for wind direction increased to 0.95. The slope reached 0.97 at wind speeds >10 m s-1. We therefore concluded that there was poor consistency between the wind directions obtained using the MST radar and radiosonde measurements at smaller wind speeds. It is understandable that in a situation of lower wind speeds, any small error in both u and v will reflect a larger error in wind direction.
3.2.2. Results of statistical comparison
Table 3 shows the results of the statistical comparison made using the correlation coefficient, mean difference (MST radar minus radiosonde), mean absolute difference, standard deviation of difference and standard deviation of the absolute difference for values of ws, wd, u and v obtained by the MST radar system and the radiosondes.
The correlation coefficient for u (0.98) was the highest, followed by ws (0.97) and wd (0.92); the correlation coefficient for v (0.90) was the lowest, but was still fairly high. The values of ws and u showed better agreement than those of wd and v.
The absolute differences for ws, u and v were all about 2.5 m s-1. The mean difference and standard deviation of the difference for wd were 0.77° and 24.86°, respectively.
The mean differences for u and v were -0.32 and -0.25 m s-1, respectively. This is close to the results of a previous study, in which values of -0.58 m s-1 for u and -0.78 m s-1 for v were observed in a study comparing the Indian Gadanki MST radar system with measurements from a radiosonde launched about 90 km from the radar site using unedited data in the height range 3.6-18 km (Kishore et al., 2000). Other previously reported results of the mean difference include values of -0.37 m s-1 for u and 0.1 m s-1 for v (Weber et al., 1990) and -0.66 m s-1 for u and -0.71 m s-1 for v (Weber and Wuertz, 1990); the detailed comparison information is given in Table 1.
The standard deviations of the difference for u and v were 3.33 and 3.58 m s-1, respectively. This is also close to, and in the range of, the results of previous studies. For example: 3.65 m s-1 for u and 3.06 m s-1 for v with 657 data pairs covering the height range 1.83-16.73 km (Weber et al., 1990); 2.98 m s-1 for u and 3.02 m s-1 for v with 6480 data pairs covering the height range 3.6-18 km (Kishore et al., 2000); and 4.60 m s-1 for u and 4.67 m s-1 for v with 18,173 data pairs covering height range 3-10 km (Weber and Wuertz, 1990).
The standard deviation of the difference for ws (3.37 m s-1) was smaller than the 3.6 m s-1 observed in a previous comparison study between the ALWIN MST radar system and radiosonde (launched from the radar site) measurements in the height range 2-8 km reported by (Engler et al., 2008). However, it was larger than the 2.6 m s-1 observed in the comparison study between the Japanese MU radar system and radiosonde (launched 30 km east of the radar site) measurements in the height range 2-20 km (Luce et al., 2001). The value is in the range 2-4 m s-1 observed in the comparison study between the CLOVAR VHF radar system and radiosonde (launched within 400 m of the radar site) measurements in the height range 2-7 km (Belu et al., 2001).
The results in this study cover a larger height range of 3-25 km with 15 210 data pairs. Given that the SNR of the MST radar system in the upper heights is lower, the uncertainty of the data for horizontal winds obtained at particular heights is increased. Therefore, considering that we made the comparisons over a larger height range, our standard deviation of the difference for u, v and ws was relatively good. The statistical analysis was followed by further comparative analyses with respect to the profiles and as a function of height.
3.3. Comparison of profiles
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The correlation coefficient and mean difference of the profiles for ws, wd, u and v measured by the Beijing MST radar system and radiosonde were analyzed to investigate the consistency of the profiles, and the probability distributions are shown in Fig. 7.
Figure 7a shows that the correlation coefficients for the ws and u profiles in the range 0.9-1 represented 88% and 91% of the total, respectively. For wd, correlation coefficients in the ranges 0.9-1 and 0.8-0.9 had percentages of 50% and 25%. The correlation coefficients in the range 0.9-1 for the v profiles accounted for 22%. The percentage of correlation coefficients for the v profiles in the ranges 0.8-0.9 and 0.7-0.8 were 25% and 21%, respectively.
Figure 7b shows that the mean difference in the ws, u and v profiles in the range -1 to 0 m s-1 accounted for the highest proportion, with values of 42%, 43% and 38%, respectively. The second highest percentage of the mean differences for the ws, u and v profiles were in the range 0-1 m s-1, with values of 28%, 32% and 28%, respectively. The mean difference in the wd profiles was mainly in the range 0-5°, with a percentage of 46%. A total of 22% of the wd profiles had a mean difference in the range -5° to 0°.
These analyses showed a good agreement between profiles. The profiles for u showed the highest consistency, followed by those for ws, which were only a little lower than u, then wd; the profiles for v showed the lowest consistency. These results agree with the overall statistical analyses and may be related to the fact that the values of v were small and the sign changed along the profiles. With respect to the wind direction, this may be related to the shift in the wind directions in a certain month and at a certain height because the fact that the two instruments take samples at different times and in different spaces may lead to a larger difference. Further detailed in-depth analyses were therefore carried out.
3.4. Comparisons as a function of height for each season and over the whole year
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Comparisons were made as a function of height for each season and over the whole year with respect to the correlation coefficient, mean difference and standard deviation of difference for ws, wd, u and v observed by the Beijing MST radar system and the radiosondes (Fig. 8).
Figure 8a shows that the whole year correlation coefficients of ws at all heights were >0.9. At heights above 18 km, however, the correlation coefficients of ws were relatively lower in the summer. This is explained by the existence of the quasi-zero wind layer around 18-22 km during summer with low mean wind speeds above 18 km (Fig. 3a). In addition, the SNR at heights above 18 km was also small in summer (Fig. 9a). The rate of acquisition of MST radar data and the percentage of comparison data pairs of the two instruments above 18 km were also lower in summer than in other seasons (Fig. 9b). The rate of data acquisition is defined as the percentage of effective detection points in a total detection time during a certain period of time. The percentage of comparison data pairs for the two instruments represents the percentage of data pairs available for comparison in the whole set of data pairs.
Figure 8b shows that the annual average difference in ws between the Beijing MST radar system and the radiosondes was about -2 to 2 m s-1 at each height. At around 19 km height, the annual mean difference was at a maximum of 2 m s-1. The seasonal mean profiles showed that the mean differences were large at a height of 18-20 km in spring and summer, which was related to the presence of the quasi-zero wind layer. The mean difference was -2 m s-1 at about 12 km because the height region of 10-12 km corresponded to the area of maximum wind speed. The mean difference was also about -2 m s-1 at a height of 6 km and the winter mean profile showed large absolute values around 5 km as a result of the wind speed increasing rapidly near 5 km height in winter (Fig. 3a).
The annual mean difference was positive above 15 km, but negative below 15 km. This means that the wind speeds measured by the Beijing MST radar system were larger than the radiosonde observations above 15 km and smaller below 15 km. Figure 10a clearly shows that the annual mean position of the radiosondes is west of the Beijing MST radar system below 14 km, and east of the MST radar system above 14 km. The annual mean distance between the MST radar system and the radiosonde was smallest at a height of about 13 km (Fig. 10c), which corresponded to an annual mean difference of about 1 m s-1.
Figure 8c shows that the annual average of the standard deviation of the difference between the value of ws measured by the Beijing MST radar system and the radiosonde was about 2.5 m s-1 in the height range 3-10 km, except at a height of around 5-6 km, where it was 3 m s-1 on account of the rapid increase in wind speed in winter. It was about 3-4.2 m s-1 at 10-15 km and at a maximum near 12 km, corresponding to the height region for the maximum wind speed. The annual average standard deviation of difference was about 2.8 m s-1 in the height range 15-23 km.
The mean difference and standard deviation of difference for ws in winter were -1 to 1 m s-1 and about 3 m s-1, respectively, in the height range 10-20 km (Figs. 8b and c). However, Fig. 10a shows that the mean position of the radiosonde balloon above 10 km was east of the MST radar site and that it drifted far away at greater heights. The mean distance between the radiosonde balloon and the MST radar site was 5 km at a height of 10 km; this distance was 40 km at a height of 15 km and 70 km at a height of 20 km (Fig. 10c). This indicated that the distance between the MST radar site and the radiosonde balloon did not affect the consistency of ws measured by the two instruments in winter, and that it was related to the characteristics of the horizontal wind in winter. Figures 3 and 4 show that the wind direction remained at about 270° and that the mean wind speed was >20 m s-1 in winter at a height of 10-20 km. Because the weather systems in winter usually have long temporal and large spatial scales with a homogeneous horizontal distribution, the two instruments were within the same relatively homogeneous region of the weather system despite the large distance between them, leading to a good agreement in the measurements. Similar results were obtained for the zonal wind u as for ws (Figs. 8g-i).
Figure 8d shows that the correlation coefficient of the whole year for wd measured by the MST radar system and radiosondes was almost >0.9 at each height except near 18 and 5 km, which had the lowest value of 0.8. The correlation coefficient in autumn was lower around 5 km, which was related to the rapid change in wind direction with height near 5 km in autumn (Fig. 3b). Figures 8e and f show that the annual mean difference and standard deviation of difference for wd measured by the two instruments were larger at heights of around 18 and 5 km as a result of the rapid change in wind direction with height during summer, and in the transition months from spring to summer and from summer to autumn, at these heights.
Figure 8j shows that the correlation coefficients for v for the whole year were about 0.9 at heights below 15 km, then decreased rapidly in the height range 15-20 km, and were about 0.6 above 20 km. This was related to the absolute values of v decreasing with height and approaching 0 m s-1 (Fig. 3d). Figure 8k shows that the annual mean difference in v at all heights was about -2 to 1 m s-1. The mean difference in v measured by the MST radar system and radiosonde were positive at heights below 10 km and negative above 10 km height. At the height of about 19 km, the mean difference in v in summer was larger, which was related to the change in wind direction. Figure 8l shows that the standard deviation of the difference in v obtained by the two instruments was larger at heights of around 12 and 18 km. This was attributed to the alternation of southerly and northerly wind directions from late July to August in the height range 12-14 km (Figs. 2g and h), and the change in wind direction near 18 km during summer and the related transition month.