Determining planetary boundary layer height by micro-pulse lidar 1 with validation by UAV measurements

Abstract


INTRODUCTION
The planetary boundary layer (PBL), or atmospheric boundary layer (ABL), is part of the troposphere directly influenced by surface forcing (Stull, 1988).To investigate the structure of the PBL, vertically-resolved observations from remote sensing technologies, such as high towers, balloons, lidar, wind profilers etc., are widely used (Hellmann et al., 1915;Peppler, 1921;Mildner, 1932;Davis et al., 2000;Lewis et al., 2013).Aerosol lidar is a mainstream technology which using aerosol as tracer to illustrate PBL structure and further apply to air quality study.
Micro-Pulse Lidar (MPL) is a ground-based, autonomous and compact remote sensing technology used for aerosol and thin cloud vertical profiling throughout the atmosphere (Spinhirne, 1993;Welton et al. 2002).MPL is highly sensitive to aerosol scattering and utilizes dual-polarization elastic-backscatter lidar, based on Rayleigh and Mie scattering theory.MPL retrieves the aerosol scattering coefficient, translatable to a mass concentration or often to the normalized relative backscatter (NRB) signal, and illustrates the aerosol distribution clearly at distinguishable levels up to 25 km under ideal conditions, especially at daytime when the signalto-noise ratio is the highest (He et al., 2012).MPL also provides volume depolarization ratio data, a measurement of aerosol symmetry (Flynn et al, 2007).Aerosols within the PBL are usually capped by an inversion layer, while significantly lower aerosol concentrations are observed in the free troposphere.Therefore, the intensity of the lidar backscatter signals reduce significantly from the top of the PBL to the free troposphere, and these dramatic changes are used to estimate the planetary boundary layer height (PBLH) (Gaudio et al., 2015).
MPL data are widely used to determine the PBLH because of its ability to monitor aerosol backscatter and vertically profile at a high temporal resolution.To this end, several groups have developed a variety of PBLH retrieval techniques from the lidar NRB/ backscatter signals (Davis et al., 2000;Lucchese and Mitra, 2001;Brooks, 2003;Müller et al., 2010;Bravo-Aranda et al., 2017;Li et al., 2017), with most of the methods able to capture general trends in the convective daytime PBL development.Although, lidar is best suited to determine daytime PBLH (i.e.mixing layer height), certain nighttime conditions are still suitable for this type of analysis, including stable nocturnal conditions.However, due to residual layers and near-field measurement limitations, resolving nocturnal PBLH trends still has a high associated uncertainty.For instance, Li et al. (2007) found that the gradient method and idealized backscatter method, both lidar methods for PBLH determination, were suitable in high signal-to-noise ratio conditions, but failed at low signal-to-noise ratio conditions whether in the daytime or nighttime.Thus, there is significant room to improve the existing algorithms for optimizing daytime determinations and realizing nighttime determinations.Other retrieval methods include combining WCT (wavelet covariance transform) (Berkoff et al., 2003;Bravo-Aranda et al., 2017) and basic image analysis techniques to remove the influence of clouds and residual layers, which has correlated well with sounding observations and modelled PBLH from GEOS-5 (The Goddard Earth Observing System Model, Version 5) (Lewis et al., 2013).However, different forms of wavelet analysis, for example, Haar wavelet and Mexican Hat wavelet, have been found to be highly dependent on different initial values or different initial amplitudes.
Determination of PBLH is dependent on retrieval methods affected by geophysical locations, of which the optimal method is still debated in the literature.Therefore, the objective of this study is to develop retrieval techniques suitable for PBLH detection in densely populated subtropical locations.In contrast to previous studies using the NRB for PBLH retrieval, we used the depolarization ratio (δ) for PBLH retrieval as has been done in a few recent studies.De Tomasi et al. ( 2011) used δ to discuss how the PBL differences between a continental area to a coastal area.Bravo-Aranda et al. (2017) used wavelet analysis to compare with PBLH derived from lidar depolarization ratio and microwave radiometer data, and found the former was consistently shallower during the daytime, but at nighttime there was better agreement.The δ is the ratio of the cross-polarized NRB signals and the total (both cross-polarized and co-polarized) NRB signals, and its value implies particle shapes or nonsphericity of particles.In addition, using δ to tracing the PBLH, is a useful parameter to distinguish between aerosol types such as dust, anthropogenic, and fresh/aged aerosols.Under a well-mixing PBL condition, locally assembled particles populate within PBL with similar δ values.The MPL measurements provide useful information with a high temporal and special resolution which independently confirms the PBLH estimation.Furthermore, in this study, UAV (unmanned aerial vehicle) is utilized as an independent PBLH determination method and validation for the lidar methods.PBL development characteristics are dependent on geophysical location.The purpose of this study is to find retrieval techniques suitable for PBLH detection in densely populated subtropical locations; this paper focuses primarily on retrieval methods suitable over urban areas in East Asia.This article is organized as follows.Descriptions of the experiment and PBLH determination methods are described in methods section.Results comparing several PBLH determination methods and validation by UAV observation are presented in results and discussion section.
Finally, conclusions and future prospects are presented in last section.

Experiment and Instrumentation
We carried out this experiment nearby the Taiwan CWB (Central Weather Bureau) sounding station in Banqiao, New Taipei City from June 21 -September 19, 2017 (Fig. 1).The total population of New Taipei City is nearly four million, and Banqiao is the most populous district (Fig. 1(a)).Banqiao is located on flat terrain near the western boundary of the Taipei basin (Fig. 1(b)), which also includes much of Taipei City, the capital.The southwest monsoon prevails in the summer-months, but primarily the weather in New Taipei City is affected by the basin's topography.Furthermore, the mountains around the Taipei basin lock the hot air mass near the surface, and therefore the temperature is usually higher than the surrounding area, enhancing the heat island effect.As a result, the main source of pollution in Banqiao during the summertime is from local anthropogenic emissions.Days without influence from long-range transport were chosen in order to test the PBLH retrieval methods under only local influence and compared across similar conditions.Observational data from MPL and UAV were used in this study, and aerosol layers at different heights were distinguished through lidar observation profiles.During the long-range transport or transboundary events, the NRB signal or the depolarization ratio of this layer will be higher than the surrounding air mass and remain aloft.
Our MPL system was manufactured by Sigma Space Corporation (now Droplet Measurement Technologies), and the specifications are shown in Table 1.For the experiment, the MPL was installed at the Banqiao sounding station.We programmed the MPL for a vertical resolution of 75 meters and temporal resolution of 1 minute.Routine maintenance was carried out following the guidance of MPLNET (The NASA Micro-Pulse Lidar Network), including monthly dark count and after-pulse calibrations.However, instead of using the operational data provided by MPLNET, the raw data were processed locally based on Welton et al (2002) and our Level 1 data, including NRB and volume depolarization ratio (δ), followed the methods described by the previous studies (Welton et al., 2002;Flynna et al., 2007;Welton et al., 2018).
In this study, we used MPL observations and UAV measurements to characterize the structure of the PBL including the location of the PBL top.The UAV measurements were used as a general validation of the MPL-derived PBLH determination methods over the denoted area.In summertime, the PBLH can easily reach above 2 km at noon, therefore, we chose the Sky-surfer X8 (X-UAV) fixed-wing drone with a maximum height of 4 -5 km, and flight time of 1 -2 hours with a max payload about 200 g.Throughout the experiment (Ke et al., 2018), the UAV was equipped with a Windsond system (Sparv Embedded AB Company) to measure meteorological parameters, including pressure, temperature, and relative humidity (RH), from which potential temperatures (θ) were calculated to construct the vertical profiles and characterize the PBL structure.The UAV was flown from a site ~2 km north of the sounding station.Before the experiment, quality assessments of the UAV sensors quality assessments were conducted by intercomaprison with a meteorological standard Vaisala RS41 radiosonde launched simultaneously from the Banqiao sounding station, as reported in our previous publication (Ke et al., 2018).We have analyzed the radiosonde data, along with UAV observations in determining PBL height in a previous publication (Ke et al., 2018).The results showed that the UAV system successfully delineated the low-level (0-3 km) atmospheric profile with parameters (temperature, RH, and pressure) in good agreement with the data observed by meteorological radiosondes and MPL, especially for the daytime PBL when the discontinuous layer is associated with an inversion layer easily observed by sounding data.The intercomparison revealed good correlations of temperature (r > 0.999) and relative humidity (r > 0.95) between the two measurements (Fig.

PBLH determined by Gradient method
The gradient method has been applied to determine PBLH in several studies (Boers et al., 1984;Senff et al., 1996).We apply the method to both the volume depolarization ratio from MPL observation and potential temperature from UAV measurements.The gradient method is based on the following differential Eq. ( 1) where B(z) is some range-dependent atmospheric variable (e.g.volume depolarization ratio or potential temperature in this study), dz is the vertical resolution of the atmospheric variable, and is the first derivative of B(z).The maximum g(z) is the position at the top of the PBL.
Based on the meteorological conditions in the Taipei basin in summer, we assumed that aerosols are mostly distributed beneath the PBL top, thus MPL gradient observation data was used to calculate the PBLH.Considering that the maximum amplitude range of the PBLH should be less than 210 m when using the gradient method (Noonkester et al., 1974;Flamant et al., 1997), the data were averaged for 5 minutes before the gradient calculation.Also, because of near-field limitation (Campbell et al., 1982;Berkoff et al., 2003) we removed the data under 225 m agl (above ground level).In addition, we chose cases on relatively clean days without any long-range transport or transboundary events and with low surface PM2.5 concentrations.On these days, it is assumed aerosols were only contributed by local emissions and thus, the range of depolarization ratio could be more easily distinguished.There is usually an inversion layer just above the PBL, so we monitored this with the potential temperature calculated from UAV measurements and compared to the MPL observations.

PBLH determined by δ -threshold method
Most locally emitted aerosols originate at the surface.When there is less mixing with transboundary aerosols, PBL aerosols in the Taipei basin are assumed to have similar optical and microphysical properties throughout the PBLH.Thus, we used the volume depolarization ratio  , 1982;Müller et al., 2010;Baars et al., 2016), while the Cabannes line suggests a δp of approximately 0.004 for pure molecular signal (Young, 1982).
According to our measurements in the Taipei basin, δv values between 0.028 and 0.032 were considered representative of urban aerosol and used in this study, while any value lower was considered a primary molecular lidar return, thus indicating the free troposphere and delineation of the PBL top.Different sources of aerosol are associated with different depolarization ratio, thus, the threshold may change case by case.

PBLH determined by Haar Wavelet Covariance Transform
Wavelet covariance transform (WCT) is a general transform process used to study the characteristics of conditional sampling techniques (Gamage et al., 1993;Senff et al., 1996).WCT has been applied to many scientific research studies (Davis et al., 2000;Brooks et al., 2003) because it can emphasize the magnitude in the signal gradient.WCT is based on Eq. ( 2) where f(z) is the signal (e.g.lidar volume depolarization ratio profile in our study), z is altitude, zt and zb are the top and bottom of the lidar volume depolarization ratio profile, respectively, and h is the mother function of Haar wavelet.We used Haar wavelet (h) defined by Eq. ( 3).The size of h is determined by zm the position at which is h centered (translation function), and ∆h, the amplitude or spatial scale.This technique uses different combinations of zm and ∆h to arrive at the best results.The location of the maximum value of Wf indicates the altitude of the PBLH.

PBLH determined by Hybrid Image Processing: clustering data by color labeling
Image processing has been used recently in many science and technology applications, including self-driving automobiles, UAVs, artificial intelligence and machine learning.Also, the image processing technique has been applied to find PBLH.Lolli et al. (2011) used the 2D-Sobel algorithm (Sobel et al., 1968) to obtain a gradient image and the PBLH profile by retrieved the range-corrected backscatter signals profile (Lolli et al., 2011).Lewis et al. (2013) used the Canny edge detection algorithm (Canny, 1986) to identify the upper and lower bounds of PBL top features in the Wavelet Covariance Transform (WCT) image (Lewis et al., 2013).Vivone et al.
(2020) applied the Morphological Image Processing Approach (MIPA) which performances more stable than the other benchmarking methods and shows a fast running time (Vivone et al., 2020).
Our study combines several image processing methods and algorithms into a Hybrid Image Processing method that can detect PBLH and also reduce the noise within the MPL data.
The Hybrid Image Processing method enhances the character of the data through clustering and clearly reveals the diurnal changes.First, we split the depolarization ratio image (Fig. 4(a)) into its three RGB channels (R for red, G for green, and B for blue), and then chose two of the channels to de-saturate and give the best contrast which emphasized the region we need easily (i.e. the area beneath PBL top).Next, we applied a Gaussian filter (Deng and Cahill, 1993) to smooth the color transition and reduce noise.To further decrease noise, we then set up a bi-level threshold (Lucchese and Mitra, 2001) to create a pure black and white image (Fig. 4(b)).
The final and most important step in our image processing is to use the Image Region Segmentation method (Ester et al., 1996) and group the color blocks by neighboring distance relations.In Fig. 4(c), the MPL depolarization ratio profile has been separated into two colors, green and pink, allowing us to easily omit any outliers, consisting of the green points and some higher pink points.The green points represent the noise which is removed, and the pink area represent the aerosols within the PBL.

RESULTS AND DISCUSSION
To emphasize the performance of algorithm testing, it is necessary consider cases without too many clouds, a residual layer, or transported pollutants.Due to the rare use of lidar for PBLH determination over subtropical locations, we were seeking to develop the retrieval techniques suitable to these areas for only the best of conditions.Thus, we chose cases less influenced by clouds and transportation events, to ensure the algorithm performed well.Cloudy conditions may be heavily influenced from transported air masses and not dominated by local atmospheric thermodynamics convection, also the boundaries of clouds are difficult to clarify clearly, this may lead unreliable results during PBL detection.Two periods of MPL observations were selected: June 23 -26, 2017 (Case 1) and August 29, 2017 (Case 2).The meteorological conditions during both periods were suitable for us to do the algorithm testing.The average visibility of these two cases was 20.75 km and 23.07 km, with an average temperature of 30.3 °C and 30.6 °C, and relative humidity of 71.8 % and 66.2 %, respectively.The air quality was fairly clean for a populated area, with mean PM2.5 concentrations of 11.0 μg m -3 and 6.9 μg m -3 , respectively, lower than Taiwan's EPA daily average air quality standard (35.0 μg m -3 ).

Combining the Gradient and δ-threshold methods and comparing to the WCT
The PBLH retrieval results for Case 1 are shown in Fig. 5.During noontime, clouds contaminated the signal as indicated by the high noise level of δ above the PBL.The results of the Gradient method (Fig. 5(a)) demonstrate that the PBLH estimation was affected by cloud contaminated signals between 11:00 to 14:00, and resulted in an unstable fluctuation.In contrast to the Gradient method, the PBLH retrieved by the δ-threshold method (Fig. 5(b)) shows a more stable daytime pattern than from the Gradient method, indicating the δ-threshold method is less sensitive to and more reliable during the presence of clouds.The δ-threshold method reduces the effect from the clouds around noontime.For the nighttime retrievals, the Gradient method yielded a lower and smoother PBLH compared to the δ-threshold method, suggesting residual layer aerosols may cause the overestimation of nighttime PBLH by the δ-threshold method.
Considering the pros and cons of these two methods, we combined them, applying the gradient method results at nighttime (20:00-07:00) and the δ-threshold method results during daytime (07:00 to 20:00), and arrived at a more reasonable solution (Fig. 5(c)).
Continuing with the Case 1 analysis, the Haar wavelet transform exhibited a less noisy retrieval of daytime PBLH (Fig. 6) and was smoother than the results in Fig. 5, but the nighttime PBLH from the Haar wavelet transform was on average 200 meters higher than in the combination result (Fig. 5(c)).The higher nighttime PBLH could be due to a more homogenous aerosol distribution than in daytime, creating difficulties for the Haar wavelet transform method to detect the maximum change of each signal profile.In conclusion to the Case 1 analysis, the Gradient method outperformed the other two methods under nighttime conditions, while the δthreshold and Haar wavelet methods proved more reliable for the daytime.

Comparison of PBLH evolution from retrievals and UAV measurements
Two-hour routine UAV measurements were only available for Case 2 in this study and thus  2).
Fig. 7 shows the PBLH retrievals by the combination of the Gradient method and δ-threshold method combination, the Haar wavelet transform, the hybrid image processing, and seven profiles from UAV observations.The method combination was suitable when the PBL had clear development and the asymmetric aerosol distribution decreased with increasing height.However, the δv features show larger variability which might be associated with a turbulent boundary layer in this case.The performance of the Gradient method during nighttime largely failed, showing large PBLH variations, while the δ-threshold method showed unreasonably low PBL heights during the daytime (Fig. 7(a)).In addition, the Haar wavelet transform performed better than the previous two methods (Fig. 7(b)), capturing not only the nocturnal boundary layer but also the convective boundary layer during the daytime.The PBLH of each method during the UAV flight time is reported in Table 2.The UAV-derived PBLH was similar to the hybrid image processing result most of the time.The largest differences between them were at 06:00 and 12:00, representing sunrise and local noon, time period and near the peak of active convection.
Table 2 also lists the PBLH difference between each retrieval method and UAV measurements at each flight time on August 29.It shows that the results from these algorithms underestimated the UAV-derived PBLH most of the time.Both the Haar wavelet transform and Hybrid image processing performed well, with the latter was consistently closer to the UAV PBLH results.The PBLH difference between UAV measurements and the Hybrid image processing were 308 and 128 meters at 06:00 and 12:00, respectively.The UAV-derived PBLH is based on observation parameters representing the meteorological state of the atmosphere, while MPL observes the aerosol vertical distribution, thus, the PBLH determinations may not always agree.Uncertainties in the UAV data may have increased with turbulence and influenced the meteorological parameters and thus PBLH estimation.Moreover, the discrepancies between the MPL and UAV methods may be due to complex vertical mixing which can occur during these transition times.
For example, the significant changes in solar heating and transportation emissions can introduce variability into the retrievals in the morning hours; at noontime, the boundary between the PBL top and free atmosphere can be more unstable due to solar heating and cloud thermodynamic processes.In this case, we found that cloud dissipation happened around 12:00, which indicates the structure of the inversion layer is breaking up, implying the PBLH retrievals may have greater uncertainty.

CONCLUSIONS
In this study, we used three common algorithms (i.e., the Gradient method, the δ-threshold method, and the Haar wavelet transform), and one new algorithm (the hybrid image processing) to determine the planetary boundary layer height (PBLH) based on aerosol lidar data and compared these results to our observations using a UAV.The experiment was carried out in a subtropical city (New Taipei City, Taiwan) in the summer of 2017.Two cases were selected and studied to understand the effectiveness of using different PBLH retrieval methods and their suitability for the subtropical meteorological conditions.
Our results show that combining the Gradient method and the δ-threshold method can produce better results than using only one of the methods.However, using these two methods may not always be the optimal choice.In general, the performance of the Haar wavelet transform in both cases is better than the PBLH detected by the Gradient method or the δ-threshold method.In Case 2, the Haar wavelet showed a better performance than the combined method on a low pollution day.For the PBLH comparison, in Case 2, the temperature inversions monitored by the UAV observation profiles were most consistent with the hybrid image processing method.The vertical aerosol distribution variability caused PBLH discontinuities on both the Gradient method and δthreshold method.The result of hybrid image processing is consistent with the position of the inversion in the UAV observation.In addition, we must acknowledge the limitations of our study.
First of all, our discussions are limited to clean and cloud-free conditions which do not fully represent the gamut of real cases.Second, cloud boundary needs to be more clearly defined.
Third, different sources of aerosol are associated with different depolarization ratios; thus, the threshold may change on a case-by-case basis.Finally, at high aerosol concentrations, the boundary between long-range transport or transboundary aerosol and local emissions becomes ambiguous.
The Hybrid Image Processing showed good performance of retrieving PBLHs, and UAV provided a suitable validation technique to verify continuous atmospheric boundary layer observations.Although the novel hybrid image processing technique proved to be highly functional in one scenario, other methods still proved useful under other circumstances (e.g.different times of day, different environmental conditions), and it is suggested that more cases covering more conditions should be analyzed with the suite of retrieval techniques described here and with support of UAV.
2).However, a larger difference was observed during the daytime flight suggesting uneven radiation heating of the sensors.Another comparison was made for UAV with Windsond sensor versus balloon with Vaisala RS41 was conducted on August 22 and August 25, 2017 during the measurement period (Fig. 3).To note, the Windsond and Vaisala flight paths were different after launch in this case.The meteorology parameter profiles include air temperature, dew point temperature and RH.Although the flight paths diverged, the results again highlight the reliability of the UAV profile observations, especially for determining the PBLH (~ 920 hPa on August 22, 2017 and ~ 850 hPa on August 25, 2017).

(
δv) to describe diurnal PBLH change.δv is provided by the new type-4 polarized MPL systems and can be used to describe the aerosol shape(Flynn et al., 2007).The volume depolarization ratio by MPL is the ratio of the cross-polarized NRB signals and the total (both cross-polarized and co-polarized) NRB signals.From the measurement principle, MPL cannot determine the particle depolarization ratio (δp) directly.Other studies have tabulated the relationship between aerosol types and δp, where urban aerosol is associated with a δp of approximately 0.04, dust with a δp approximately 0.3, and other polluted air masses (e.g.biomass burning, sea-salt) are associated with different values (Young Finally, selected the tip points from the pink area, which indicate the PBLH (Fig. 4(d), light gray points), and applied them back into the original depolarization ratio image (e.g.shown by magenta dots in Fig. 7(c)).