BMeteorologische Zeitschrift, PrePub DOI /metz/2017/0858

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1 BMeteorologische Zeitschrift, PrePub DOI /metz/2017/ The authors Traffic Meteorology Application of spectral decomposition of LIDAR-based headwind profiles in windshear detection at the Hong Kong International Airport Tsz-Chun Wu 1 and Kai-Kwong Hon 2 1 The Hong Kong University of Science and Technology, Hongkong, China 2 Hong Kong Observatory, Hong Kong, China (Manuscript received February 22, 2017; in revised form June 10, 2017; accepted June 29, 2017) Abstract In aviation, rapidly fluctuating headwind/tailwind may lead to high horizontal windshear, posing potential safety hazards to aircraft. So far, windshear alerts are issued by considering directly the headwind differences measured along the aircraft flight path (e.g. based on Doppler velocities from remote-sensing). In this paper, we propose and demonstrate a new methodology for windshear alerting with the technique of spectral decomposition. Through Fourier transformation of the LIDAR-based headwind profiles in 2012 and 2014 at arrival corridors 07LA and 25RA of the Hong Kong International Airport (HKIA), we study the occurrence of windshear in the spectral domain. Using a threshold-based approach, we investigate performance of single and multiple channel detection algorithms and validate the results against pilot reports. With the receiver operating characteristic (ROC) diagram, we successfully demonstrate feasibility of this approach to alert windshear by showing a comparable performance of the triple channel detection algorithm and a consistent hit rate gain (07LA in particular) of 4.5 to 8 % in quadruple channel detection against GLYGA, which is the currently operational algorithm in HKIA. We also observe that some length scales are particularly sensitive to windshear events which may be closely related to the local geography of HKIA. This study serves to open a new door for the methodology of windshear detection in the spectral domain for the aviation community. Keywords: aviation meteorology, windshear, LIDAR, spectral decomposition 1 Introduction In aerodynamics, headwind blowing in the opposite direction to aircraft motion is responsible for generating lift. Rapidly fluctuating headwind/tailwind poses potential hazards to aviation safety due to the sudden change in lift. The intended flight path of aircraft may therefore be deflected, during take-off or landing in particular. Significant low level horizontal windshear events are capable of causing difficulties in control. Timely and accurate alerting of windshear is therefore important for pilots to take appropriate corrective actions. According to the convention in international civil aviation, sustained headwind change of 15 knots (Fig. 1) ormoreatanaltitude below 1600 feet within three nautical miles from the runway threshold, which marks the beginning and ending of the space designated for landing and take-off, is classified as significant low-level windshear (ICAO, 2005). For the rest of this paper, windshear will be used exclusively to refer to the horizontal shear along the landing and take-off paths of an aircraft, unless otherwise stated. Following the established practice in provision of alerts to aviation users, the magnitude of such windshear will be expressed in terms of velocity difference (in knots). Corresponding author: Kai-Kwong Hon, Hong Kong Observatory, 134A Nathan Road, Tsim Sha Tsui, Hong Kong SAR, China, kkhon@ hko.gov.hk Figure 1: An example of headwind profile. Low-level windshear is defined as a sustained headwind change of 15 knots or more at an altitude below 1600 feet within three nautical miles from the runway threshold according to international civil aviation. The Hong Kong International Airport (HKIA) is situated next to the mountainous Lautau Island with peaks over 900 m above the sea level and valleys as low as 400 m (Fig. 2). Due to the complex terrain, the airflow is disrupted, resulting in non-uniform wind field which DOI /metz/2017/ The authors Gebrüder Borntraeger Science Publishers, Stuttgart,

2 2 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles Meteorol. Z., PrePub Article, 2017 Figure 2: Top: Schematic diagram of terrain (contoured at elevation of 100 m) and meteorological instruments by HKO (refer to legend) in the vicinity of the Hong Kong International Airport. Bottom: Coloured contours of the terrain (units in m). may give rise to high windshear. On average, about 70 % of the windshear reported by pilots at HKIA are contributed by the terrain-induced windshear. The remaining 30 % of windshear events could be associated with sea breezes, squall lines, microbursts, and low level jets. On average, 0.2 % of flights report experiencing significant windshear at HKIA. The Hong Kong Observatory (HKO) provides operational windshear and turbulence warning service at HKIA in accordance with international practice (ICAO, 2007). Apart from alerts issued by aviation forecasters subjectively, automated alerts are generated by the Windshear and Turbulence Warning System (WTWS) (Lau, 2000; Lee, 2004; Shun et al., 2004). As part of

3 Meteorol. Z., PrePub Article, 2017 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles 3 the WTWS, a network of anemometers around HKIA and Lantau peaks with the Anemoneter-based Windshear Alerting Rules (AWARE) and Hilltop algorithm allow detection of windshear at a fixed distance, especially those brought by sea breeze. In additional to anemometers and weather buoys, the Terminal Doppler Weather Radar (TDWR) is employed in covering windshear events caused by thunderstorm-induced microburst and gust (Wilson and Wakimoto, 2001) based on a pioneering study conducted by Fujita (1978). However, since over 90 % of the windshear events are reported on non-rainy days, headwind profiles from TDWR are not always available. To cater for windshear events under clear-air conditions, HKO introduced the Doppler light detection and ranging (LIDAR) in 2002 for operational windshear alerting at HKIA (Shun and Chan, 2008). During the period 2002 to 2016, the Windtracer LIDAR manufactured by Lockheed Martin was in use at HKIA. In addition to conventional fixedelevation (PPI) scans, each glide path is scanned using a specialised method where the azimuthal and elevation angles of the scanners are adjusted simultaneously to cover the slanted plane enclosing the glide paths. The radial wind velocity data can be then obtained by LIDAR at variable distances and used to generate the headwind profile. The resulting headwind profiles have a radial resolution of about 100 m and are updated once every one to two minutes, which is capable of resolving low level windshear features with spatial and temporal scale of hundreds of meters and tens of seconds respectively. The headwind profile is analyzed by the glide path scan windshear alerting algorithm (GLYGA), which is responsible for identifying headwind ramps, or sudden changes, after the method of Jones and Haynes. Further details of the GLYGA algorithm and its implementation at HKIA can be found in Shun and Chan (2008). Several detection algorithms based on the LIDAR wind data at HKIA have been studied recently. For instance, the use of GLYGA alone demonstrated skills in nearly all the runway corridors with 70 % hit rate and reasonable alert duration (Chan et al., 2006). On top of it, usage of gradient of LIDAR-measured headwind, or the LIDAR-based F-factor, in windshear alerting at HKIA was studied in Chan et al. (2010a,b). Thecombined use of LIDAR-based F-factor and GLYGA was found capable in capturing about 87 to 90 % of windshear in HKIA upon appropriate choices of thresholds. In 2014, this method was advanced by applying different smoothing algorithms on the LIDAR-based F-factor and able to reach a percentage of detection (PoD) of 86 % and a percentage of time on alert (PoTA) of 12 % (Lee and Chan, 2014). Although performance gain has been demonstrated in the above methods, none of them show a consistent and significant improvement against GLYGA alone. In this paper, we present a new methodology in windshear alerting through investigating the spectral components of the headwind profile. One of the possible means is to Fourier transform the profiles, which is a common technique in signal processing. Calculations are performed for two arrival corridors of North Runway in HKIA (07LA and 25RA) for 2012 and Through a threshold-based approach, alerts are generated and compared with the reported windshear by aircraft pilots during take-off or landing. Alerts are generated using a threshold-based approach and validated against reported windshear by aircraft pilots during takeoff or landing. The length scale dependency of the windshear events is explored in spectral domain. The rest of the paper is organized as follows: Section 2 gives a review of Fourier transform and demonstrates some examples of the transformed headwind profile; Section 3 describes the single channel and multichannel approaches to detect windshear and the performance of them; the results are then discussed in Section 4. Finally, our conclusion is presented in Section 5. 2 Calculation of the power of spectral components To decompose a wind speed profile into different spectral components, a number of methods are available, with Fourier transform being the most standard and common one. Here, the technique of discrete Fourier transform is employed to decompose the headwind profile into sinusoidal (or complex exponential) components of different wavelengths. The headwind profile v(x) is a function of the distance. The wind speed data v n are sampled by LIDAR at equally spaced points x n = nδx. The spacing Δx depends on the resolution of the headwind profile, Δx = 100 m in HKIA for example. Mathematically, the Fourier transformation of the headwind profile can be written as N 1 ṽ kn = v n e ik n x n=0 (2.1) where ṽ kn is a complex number containing information of the amplitude and phase of a sinusoidal component, v n is the n th headwind data point, x is distance, k n = 2π/λ n = 2πn/NΔx is the wavenumber, and N is the total number of data points in a 1-minute headwind profile. The headwind profile is now transformed to into the spectral (or wavenumber) domain from the spatial domain. In practice, the algorithm of fast Fourier transform (Cooley and Tukey, 1965) is employed for faster computation. It is interesting to investigate the power spectrum of the headwind profile. The power of the sinusoid component with wavenumber k n can be readily obtained from the transformed data by the well-known Parseval s theorem, P kn = 1 N ṽ k n 2 (2.2) However, observed turbulence in general follows the Kolmogorov s 5/3 law, which states that the energy distribution of turbulent fluid follows a power law

4 4 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles Meteorol. Z., PrePub Article, 2017 (a) (b) Figure 3: Examples of headwind profiles and the corresponding power spectrum in the presence and absence of windshear respectively. When the wind speed is steady, the power of nearly all the components is not significant. Meanwhile, if the fluctuation of the wind speed is large, some of the components in the spectral domain show noticeable power, with a dominating wavenumber of k n = 22 km 1. E(k) k 5/3 (Kolmogorov, 1941). We thereby introduce a normalization factor kn 5/3 to the power spectrum for a fair comparison, namely ṽ kn = 1 N k5/3 n ṽ kn 2 (2.3) To demonstrate the transformation, two headwind profiles are elected from 05-Mar-2014 and 28-Mar-2014 respectively as depicted in Fig. 3. For the former one (Fig. 3(a)), there is no significant change in headwind/tailwind and the power spectrum is not very interesting. For the latter one (Fig. 3(b)), the headwind/tailwind keeps fluctuating and a windshear ramp is noted, leading to a windshear. Transforming into the spectral domain, some of the components showed a considerable amplitude (k n = 22 km 1 λ = 0.3km).Theresponse in the spectral domain suggests that some spatial components contribute more to windshear events. Consequently, it is interesting to study the effectiveness of alerting windshear by setting thresholds for some of the windshear-sensitive channels with wavenumber k n. 3 Performance on alerting of windshear Following the method discussed in the previous section, headwind profiles in years 2012 and 2014 over the mostly used arrival runway corridors, 07LA and 25RA, of HKIA are used to generate the power spectrum. The headwind profiles available from LIDAR have a line of sight resolution of 100 m and cover a distance up to 6 8 km (or 3 4 nautical miles) from the respective runway threshold. A threshold-based approach is then employed to trigger an alert once the power of the selected wavenumber channel(s) exceeds the predetermined threshold(s). Each alert is valid for one minute only. For simplicity, the performance of single channel detection is first investigated. It is then trivial to generalize to multi-channel detection approach. 3.1 Single channel detection A particular channel with wavenumber ˆk 1 is first chosen. The power spectrum time series for ˆk 1 is then examined. In case there is no data point with k 1 = ˆk 1 at time t, we linearly interpolate the power of the two nearest neighbors. A windshear alert is issued if the power of channel ˆk 1 exceeds the threshold T 1,i.e.Pˆk 1 T 1. These alerts are then compared with the pilot reports of windshear at 07LA and 25RA received by HKIA. In year 2012 and 2014, the total number of windshear reported at 07LA and 25RA were 417 and 397 respectively (at 07LA and 25RA). An event of windshear is marked as hit if its time of occurrence falls within a 5 min interval when a spectral-domain-based alert is valid. To assess the overall skill level of the spectral-domain-based alert, we construct the receiver operating characteristic (ROC) diagram by applying thresholds ranging from 0 to 60, with a step size of 4. The vertical axis and horizontal axis of the ROC diagram correspond to the Percentage of Detection (PoD) and Percentage of Time on Alert (PoTA). Their definitions are as follows: No. of hits PoD = 100 % (3.1) Total no. of pilot reports Alert duration PoTA = Total length of time investigated 100 % (3.2)

5 Meteorol. Z., PrePub Article, 2017 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles 5 (a) (b) (c) (d) Figure 4: The ROC diagram for the one channel detection algorithm using the headwind profiles in 2012 (a), (b) and 2014 (c), (d) at runway corridors 07LA and 25RA in HKIA. Data points are obtained using a threshold based approach. Different colors correspond to different channels and the black cross refers to the performance of GLYGA, which is currently operational in HKIA. The insets magnify the portion of data points near the GLYGA point for easier comparison. Due to maintenance of LIDAR, the PoD and PoTA do not reach 100 %. Note that some channels are more sensitive to windshear events and lie closer to the performance of GLYGA. The skillfulness of an algorithm is dictated by the proximity to the top-left corner by convention, meaning a high hit rate with a short alert duration. Note that due to the maintenance of LIDAR, both the PoD and PoTA do not reach 100 % due to a lack of headwind data. As shown in Fig. 4, ROC curves for channels ˆk 1 = 1, 2,..., 30km 1 are generated and indicated by different colors. The black cross represents the performance of the currently operational algorithm, GLYGA, as depicted in Section 1. The portion of data points near GLYGA are enlarged in the inset for easier comparison. All the channels demonstrate positive skills as indicated by their concavity. For the same alert duration as GLYGA, the hit rate of GLYGA is higher than that of the single channel detection approach, indicating the single channel detection approach has much room for improvement compared to GLYGA. Although none of the channels outrun GLYGA, channels with ˆk 1 = 3, 4, 7 km 1

6 6 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles Meteorol. Z., PrePub Article, 2017 wavenumber k { k n } where k n is the wavenumber we are interested in. We issue a windshear alert at time t whenever the power in the selected channels exceeds their corresponding threshold T {T n }. This idea can be expressed more compactly as If Pˆk 1 T 1 Pˆk 2 T 2, then alert a windshear at time t. (3.3)... Pˆk n T n All the windshear alerts therefore appear in a n- dimensional statistical sample space. Figure 5: The original (a) and the filtered (b) headwind profile on 29 March 2012 (0602 UTC) when a windshear was present (the shadowed region). For the filtered profile (b), only components with wavenumbers ranging from 1 to 7 km 1 are plotted. Although the Fourier components with wavenumber exceeding 7 km 1 are filtered in (b), the essential features of the windshear can still be reflected. (λ = 0.9, 1.6, 2.1 km) demonstrated a larger extent to the top-left corner, suggesting that the rapid change of headwind speed in windshear events may be manifested by the components with length scales ranging from one to two kilometers. The sensitivity of the windshear events to this length scale range can be visualized by filtering the components with wavenumber larger than 7 km 1.Forexample, on 29 March 2012 (0602 UTC), a windshear was reported by pilots and the headwind profile at that time is showninfig.5a. Removing the undesired Fourier components in the spectral domain, it can be seen that the essential features of the windshear can still be captured by the sensitive channels (Fig. 5b). Owing to the sensitivity of these channels and their positive skills, it is interesting to further examine this algorithm and search for possible improvements. In order to cut the number of false alarm for the same hit rate (or increase the hit rate for the same alert duration), more constraints have to be imposed for alert issuing algorithm. A possible way is to generalize the single channel detection approach to the multichannel ones. The existence of windshear-sensitive channels suggests the flexibility of detecting windshear through applying thresholds to those particular channels in the multichannel detection approach. 3.2 Multi-Channel detection The methodology of multi-channel detection is similar to the single channel case. Instead of selecting one channel, we explore the power spectrum time series with The performance of this method can be studied by the ROC diagram in a similar manner. The threshold range applied is the same as that in single channel detection. In fact, the single channel detection approach is just a special case of the n-channel one. The condition for single channel detection can be recovered by setting T 2 = T 3 =...= T n = 0. As a result, the performance of n-channel case should be at least as good as the single channel approach if we try out all the combinations of the n-channel. Moreover, since we are now applying more constraints, the alert duration and hence the PoTA is expected to decrease and can potentially out-perform GLYGA. To illustrate the effectiveness of the algorithm as the number of channels used for detection increases, ROC diagrams for triple-channel and quadruple-channel approach are constructed, as shown in Fig. 6 and 7. For triple channels approach, only combinations of channels with sensitive wavenumbers ˆk i = 3, 4, 7, 18, 23, 27 km 1 are selected. Similar to the single channel approach, the performance of this algorithm is examined through comparing its performance with GLYGA by considering the headwind data at the runway corridors 07LA and 25RA in 2012 and 2014 (Fig. 6). For the corridor 07LA, considerable improvement is shown in both 2012 and For the same alert duration (PoTA), or the same false alarm rate, around 4.5 % and 0.5 % gain in PoD against GLYGA are noted in 2012 and 2014 respectively. Although the performance of 25RA is less superior to GLYGA in 2014 with a 5 % loss in PoD for the same PoTA, positive skill level is still obtained. To search for potential improvement in PoD gain, the performance of quadruple channel approach is further studied. The methodology is analogous to that described above. Combinations of four sensitive channels are chosen and their ROC curves are shown in Fig. 7. Asignificant enhancement in the PoD gain is demonstrated is this approach. Comparing with GLYGA, the corridors 07LA and 25RA show a gain of approximately 6 % and 8 % respectively in 2012 while a gain of about 5 % and 1 % respectively is noticed in Although the PoD gain for 25RA in 2014 is relatively small in contrast to other cases, the gain is 6 % greater than that in the

7 Meteorol. Z., PrePub Article, 2017 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles 7 (a) (b) (c) (d) Figure 6: The ROC diagram for the triple channel detection algorithm using the headwind profiles in 2012 (a), (b) and 2014 (c), (d) at runway corridors 07LA and 25RA in HKIA. The data points are obtained by using a similar manner as in Fig. 4. Different colors represent different combinations of channels (any three out of ˆk i = 3, 4, 7, 18, 23, 27 km 1 ). triple channel approach. The improvement is expected as more constraints are imposed. It can be predicted that further increase in gain is possible for all the cases when more channels are selected. The performance of the PoD gain against GLYGA of the corridors 07LA and 25RA in 2012 and 2014 can be summarized by Table 1. Even though there are performance gains in 2012 and 2014, it is still rather premature to conclude that the new algorithm can generate more precise warnings due to variation in meteorological conditions and quality of pilot reports. Further studies with more years of data are required before putting this algorithm into practice. Table 1: The gain/loss in PoD against GLYGA by using the spectraldomain-based alerts in 2012 and 2014 at runway corridors 07LA and 25RA in HKIA. Gain/Loss in PoD against GLYGA (For the same PoTA) Triple channel Quadruple channel detection detection LA +4.5 % +6 % 25RA +0.5 % +8 % LA +4 % +5 % 25RA 5% +1%

8 8 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles Meteorol. Z., PrePub Article, 2017 (a) (b) (c) (d) Figure 7: The ROC diagram for the quadruple channel detection algorithm using the headwind profiles in 2012 (a), (b) and 2014 (c), (d) at runway corridors 07LA and 25RA in HKIA. The data points are obtained by using a similar manner as in Fig. 4. Two combinations of channels are studied, including ˆk i = 3, 4, 7, 23 km 1 and ˆk j = 3, 4, 18, 27 km 1. 4 Discussion 4.1 Feasibility of the spectral method Through spectral decomposition, one can investigate the contribution of components with different length scales. In the currently operational approach, focus is put on capturing windshear events with a headwind change which exceeds a pre-determined threshold (15 knots traditionally) in real space in which all the spectral components add up to yield the headwind profile. Although some information of length scale is incorporated in this approach, through checking the size of windshear ramps for example, the prescribed threshold remains unchanged. In contrast, in the spectral domain, one can apply varying intensity thresholds across different channels, which is physically equivalent to simultaneously applying different thresholds in real space to wind features with different spatial scales. Since windshear events are more sensitive to some particular characteristics of headwind as shown in Section 3.1, it is rea-

9 Meteorol. Z., PrePub Article, 2017 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles 9 sonable to apply varying threshold to different components of different length scales. The superior skill level demonstrated in Section 3.2 of the proposed method demonstrates the feasibility of such an approach. 4.2 Windshear-sensitive length scales Typical windshear events have a length scale between 0.4 km to 4 km. Through Fourier transformation, contribution of components with wavelength of 1 2 km to windshear events remain robust over 2012 and 2014 as studied in Section 3.1. The high sensitivity of these length scales might be induced by the complex terrain on Lantau Island. From the coloured contours of Fig. 2, it could be seen that the major peaks on Lantau Island (immediately to the south of HKIA) are of horizontal length scales similar or smaller than HKIA, whose runways stretch over a distance of about 3.8 km. The gaps between those peaks would be even narrower in length. It is known that when wind blows overs a mountain, disturbances propagate and mountain lee waves can be formed due to a periodic change in temperature, atmospheric pressure and orographic height. A recent study by Chan and Hon (2016) has even reported observation and simulation results of mountain waves with subkilometre wavelength at HKIA. Although it is not possible to pinpoint the formation mechanism of individual windshear-related features using only 1-dimensional headwind profiles, nor is the LIDAR able to directly observe thermodynamical parameters of the atmosphere (such as temperature, humidity and stability), the contribution of possible mountain waves, particularly near the high wave number end of the spectral components discussed above, could not be ruled out. 4.3 Possible improvements In the current paper, the ROC curves are generated by applying different thresholds for different channels. Some of the data points are found to outperform GLYGA, with a gain of PoD between 4 8 %. Nonetheless, there is still much room for improvement for this approach before putting it into practice. For example, further researches are required to figure out the optimal threshold for each channel. On the other hand, it is worthwhile to investigate the feasibility of the spectral method by decomposing the headwind profile with non-sinusoidal basis. Although Fourier transformation is a common and well-known technique, owing to the transient and sporadic nature of the low-level windshear, the use of sinusoidal basis which possesses certain wavelengths may not be capable of capturing all the features of windshear events. A possible alternative is to use wavelet transformation, with Morlet wavelets as basis for example, such that suitable resolution in wavenumber and distance can be adjusted and the distance at which windshear occurs can be determined. It would be interesting to study the spectrogram through wavelet transformation and further examine the occurrence of windshear in spectral domain. Finally, the alerting methodology is relatively simple: only single, triple and quadruple channel detection with a few sets of channel combinations are studied in the spectral domain. Possible advancement includes, for example: to explore the union of spectral-based alerts and rules for existing ground-based or remote-sensing instruments in alerting windshear; to choose five, or more, channels for detection; to apply post-processing to LIDAR headwind profiles to simulate aircraft response (e.g. Robinson, 1990; Chan, 2012) before transforming them into the spectral domain. 5 Conclusion In aviation meteorology, issuing timely and accurate windshear alerts is essential for aviation safety. Based on LIDAR measurements, over minutes of headwind profiles along the runway corridors 07LA and 25RA in 2012 and 2014 have been analyzed in this paper. The headwind profiles are available at a line-of-sight resolution of 100 m at 1 minute interval. Conventionally, a windshear warning is issued once a sustained and significant change of headwind speed is noticed in real space. In this paper, we propose a detection algorithm through decomposing the headwind profiles into components of different length scales by spectral decomposition, Fourier transformation in particular, since wind disturbances should have preferred spatial scales. With a threshold-based approach, single and multiple (up to quadruple) channel detection for windshear are studied using ROC diagrams. For single channel detection, the simplest case, although the performance of our algorithm is not better than GLYGA which is the currently operational one, positive skills are demonstrated. Meanwhile, some of the channels are found to be more sensitive to windshear as indicated by the proximity to the top-left corner. After band filtering high wavenumber channels, the headwind profile is still capable to capture the essential characteristics of the original profile. This suggests windshear events for aircraft are more sensitive to some particular wind features and hence invites further studies of the multi-channel detection algorithm for the sensitive channels. Multi-channel approach is then explored and found to have improved performance compared with the single channel one. The performance of the triple channel detection is comparable with yet not better than GLYGA for some cases. On the other hand, a consistent performance gain ranging from 4.5 to 8 % is attainable over GLYGA, 07LA especially, through the quadruple channel detection algorithm. It is hoped that the advancement of this methodology can further improve the windshear alerting performance. Although cases have been constructed and shown to outperform GLYGA, further works are required to explore the optimal channel combination and thresholds for each channel for better detection performance. Apart from that, to better understand the cause of windshear, further scientific studies are required to figure out the relation between windshear-sensitive length scales and the

10 10 T.-C. Wu & K.-K. Hon: Application of spectral decomposition of LIDAR-based headwind profiles Meteorol. Z., PrePub Article, 2017 geographical structure near the airport. Other possible future works include examining the feasibility of spectral decomposition for windshear alerting using other basis and combining this algorithm with rules for existing ground-based or remote-sensing instruments. Acknowledgement The authors would like to thank P.W. Chan for his support of the research study. C.M. Li and S.H. Chong are gratefully acknowledged for their assistance in coding efforts. The authors also thank the two anonymous reviewers for their useful suggestions and detailed reading of the manuscript. References Chan, P.W., 2012: Application of LIDAR-based F-factor in windshear alerting. Meteorol. Z. 21, , DOI: / /2012/0321. Chan, P.W., K.K. Hon, 2016: Performance of super high resolution numerical weather prediction model in forecasting terrain-disrupted airflow at the Hong Kong International Airport: case studies. Meteror. Apps. 23, Chan, P.W., C.M. Shun, K.C. Wu, 2006: Operational LIDARbased System for Automatic Windshear Alerting at the Hong Kong International Airport. 12th Conference on Aviation, Range, & Aerospace Meteorology, American Meteorological Society, Atlanta, GA, USA. Chan, P.W., C.M. Shun, M.L. Kuo, 2010a: Latest Developments of Windshear Alerting Services at the Hong Kong International Airport. 14th Conference on Aviation, Range, and Aerospace Meteorology, American Meteorological Society, Atlanta, Georgia, USA. Chan, P.W., K.K. Hon, D.K. Shin, 2010b: Combined Use of Headwind Ramps and Gradients Based on LIDAR Data in the Alerting of low-level Windshear/Turbulence. 14th Conference on Mountain Meteorology. Amer. Meteor. Soc., 30 August 3 September 2010, Olympic Valley, CA, USA. Cooley, J.W., J.W.Tukey, 1965: An Algorithm for the Machine Calculation of Complex Fourier Series. Math Comput 19, Fujita, T.T., 1978: Manual of downburst identification for project Nimrod. Satellite and Mesometeorology. Research Paper 156, Dept. of Geophysical Sciences, University of Chicago. ICAO, 2005: Manual on Low-level Wind Shear and Turbulence, 1 st Edition. International Civil Aviation Organization, Montreal, Canada. ICAO, 2007: Meteorological Service for International Air Navigation: Annex 3 to the Convention on International Civil Aviation, 16 th Edition. International Civil Aviation Organization, Montreal, Canada. Kolmogorov, A.N., 1941: Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Doklady Acad Sci. USSR 31, Lau, S.Y., 2000: Wind shear and turbulence detection and warning at the Hong Kong International Airport. In: Proceedings of Working Group on Training, The Environment and New Developments (TREND), Commission for Aeronautical Meteorology, October 2000, Hong Kong, China. World Meteorological Organisation, Geneva, Switzerland. Lee, O.S.M., 2004: Enhancement of the Anemometer-based system for wind shear detection at the Hong Kong International Airport. In: Proceedings of 8th Meeting of the Communications/Navigation/Surveillance and Meteorology Sub- Group (CNS/MET/SG/8) of APANPIRG, July 2004, Bangkok, Thailand. International Civil Aviation Organisation, Montreal, Canada. Lee, Y.F., P.W. Chan, 2014: LIDAR-based F-factor for wind shear alerting. Meteorol. Appl. 21, 86 93, DOI: /met Robinson, P.A., 1990: The modelling of turbulence and downbursts for flight simulators. University of Toronto Institute for Aerospace Studies, Report 339. Shun, C.M., 2004: Wind shear and turbulence alerting at Hong Kong International Airport. WMO Bull. 53, Shun, C.M., P.W. Chan, 2008: Applications of an Infrared Doppler Lidar in Detection of Wind Shear. J. Atmos. Ocean. Technol. 25, , DOI: /2007JTECHA Shun, C.M., S.Y. Lau, C.M. Cheng, O.S.M. Lee, H.Y. Chiu, 2004: LIDAR Observations of Wind Shear Induced by Mountain Lee Waves. 11th Conference on Mountain Meteorology and MAP Meeting 2004, Mount Washington Valley, NH, USA, June Wilson, J.W., R.M. Wakimoto, 2001: The Discovery of the Downburst: T.T. Fujita s Contribution. Bull. Amer. Meteor. Soc. 82, 49 62, DOI: / (2001)082<0049:TDOTDT>2.3.CO;2.