Turbulence Analysis in Long‐Range‐Transported Saharan Dust Layers With Airborne Lidar

In this study, turbulent properties of long‐range‐transported Saharan dust layers are investigated for the first time using airborne backscatter and water vapor lidar measurements. This is achieved via the utilization of spectral signal decomposition to the collected lidar data. Additionally, measurements by dropsondes are analyzed in detail. The presented measurements were conducted during the Next‐Generation Aircraft Remote Sensing for Validation Studies II in boreal summer 2016 upstream Barbados. An analysis of two case studies shows that the derived mesoscale turbulence cascades inside the transported dust layers follow the predicted slopes for turbulence of −5/3. The turbulent nature of the Saharan air layers (SALs) is additionally indicated by small Richardson numbers, which are derived from data collected by launched dropsondes. These presented results also fortify the hypothesis that turbulence inside dust layers helps to keep large mineral dust particles aloft for a longer time, so that they can still be found after long‐range transport.


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in the Caribbean (Bagnold, 1941). In addition to in situ observations, complementary lidar measurements were performed during the Saharan Mineral Dust Experiments SAMUM-I (Freudenthaler et al., 2009) and SAMUM-II (Groß et al., 2011) as well as the SALTRACE (Groß et al., 2015) project. Except for the expected decrease in SAL optical thickness, no significant differences in optical properties of SALs were observed. This was also the case for measurements conducted during NARVAL-II  which supports the hypothesis of an undisturbed dust transport. Moreover, observations of dust particle size distributions in the Caribbean show a nearly unchanged mean particle size compared to the distributions that are measured near source regions (e.g., Sunnu et al., 2008).
In recent years, several studies aimed at unraveling the processes behind decelerated dust sedimentation rates and soon two major mechanisms emerged to be potentially responsible, that is, SAL vertical mixing generated by radiative heating (Gasteiger et al., 2017;Gutleben et al., 2020) or electrostatic levitation of the dust particles (Nicoll et al., 2010;Renard et al., 2018). Studies that tried to explain the reduced fall speed of large dust particles via electrostatic levitation focused on investigations of relative dust particle polarities compared to the atmospheric electric fields. However, up to now, the electrostatic effect is not quantified for long-range particle transport inside SALs and further research is needed (van der Does et al., 2018). Gasteiger et al. (2017) used an integrated model and measurement approach to investigate particle settling processes during SAL advection. They conjectured that daytime convective mixing within the SAL could be the main driver for particle mixing and would allow dust particles with diameters larger than 20 m E  to arrive in the Caribbean. However, radiative heating effects from dust particles alone could not explain vertical mixing inside the SALs.
Recently, airborne lidar measurements indicated enhanced water vapor mass mixing ratios in SAL-altitudes compared to the dry and dust-free surrounding troposphere . It was found that the shapes and magnitudes of the radiative heating profiles in regions influenced by long-range-transported SALs are mainly governed by water vapor absorption and emission and not by aerosol radiative effects (Gutleben et al., 2020). Associated water vapor radiative cooling with altitude can induce static instability, promote mixing processes and can help large dust particles to remain inside the dust layers during transport. Additionally, as a consequence of radiative cooling, the confining inversions at the top and the bottom of the SALs are maintained.
Up to now, turbulent and dynamic processes in and around long-range-transported SALs have never been investigated as such analyses usually require highly resolved in situ measurements of the wind components. However, previous studies have shown that spectral decomposition of lidar return signals can be utilized to remotely study the dynamics and turbulent features of cirrus clouds or propagating gravity waves (e.g., Demoz et al., 1998;Reichert et al., 2019;Wang & Sassen, 2008). Wang and Sassen (2006); Wang and Sassen (2008) for instance, analyzed the dynamical structure of cirrus mammatus and cirrus uncinus clouds by applying spectral methods on measurements from a ground-based backscatter lidar and a W-Band radar. They demonstrated that measured lidar-backscatter can be directly linked to the content of the cirrus itself, that is, to particle concentrations. Under additional assumption of Taylor's frozen turbulence hypothesis (Taylor, 1935), they spectrally analyzed fluctuations in measured backscatter coefficients. Their derived spectra of power spectral density (PSD E ) of the measured backscatter perturbations were interpreted as proxies for the distribution of turbulent kinetic energy (TKE E ) in the air mass and could thus be related to wave motions and turbulence.
Motivated by these findings, this study focuses for the first time on the investigation of dynamical and turbulent processes in regions affected by long-range-transported SALs by means of airborne lidar remote sensing, spectral signal decomposition and dropsonde measurements. Airborne backscatter and water vapor lidar measurements during NARVAL-II are analyzed with the goal to study variations in the backscattered signal using power spectra. In this way, mesoscale turbulent processes as well as the dynamics in a SAL-influenced atmosphere can be uncovered and studied. An extensive investigation of data collected by dropsondes complements the spectral analysis. This contributes to a better understanding of long-range dust transport.
The paper is structured as follows. Section 2 gives an overview of the used lidar instrument, the conducted field campaign as well as the utilized methods for the analysis of atmospheric turbulence. In Section 3, the 3 of 11 main findings of the analysis are presented by means of representative case studies. Results are summarized and conclusions from the performed analysis are drawn in Section 4.

The WALES Lidar Instrument
In this study, measurements of the airborne lidar system WALES (Water Vapor Lidar Experiment in Space; Wirth et al., 2009) are spectrally analyzed. WALES combines two lidar techniques that are well suited for aerosol and cloud remote sensing, that is, the water vapor differential absorption lidar (DIAL) technique and the depolarization-sensitive high spectral resolution lidar technique (HSRL; Esselborn et al., 2008). The DIAL module of WALES operates at four wavelengths in the 935 nm absorption band of water vapor and enables highly sensitive measurements of water vapor mass concentrations ( m E r ) that cover the whole extent of the troposphere. Needed narrow-band wavelength operation around the water vapor absorption band is guaranteed using injection-seeded optical parametrical oscillators (Mahnke et al., 2007) together with potassium titanyl phosphate acting as nonlinear material. In addition to the DIAL capability, depolarization sensitive HSRL measurements at 532 nm allow direct measurements of particle extinction coefficients, particle linear depolarization ratios (532) p E  and the backscatter ratios 532 E R ‖ between the total and the molecular backscatter coefficients. The most important performance parameters and a detailed instrument description can be found in Wirth et al. (2009). WALES measurements are temporally and spatially averaged for noise reduction. This results in horizontal resolutions of ∼3 km for DIAL measurements and 0.2 km for HSRL measurements at typical aircraft speed. The vertical resolution amounts to 150 and 15 m, respectively. For DIAL measurements, uncertainties are estimated to be smaller than 5%, as pulses are repeated at the very high rate of 200 Hz (Kiemle et al., 2008). Measurement uncertainties of 5% for 532 E R ‖ and 10%-16% for (532) p E  have to be considered as well.

The NARVAL-II Field Campaign With the HALO Research Aircraft
The main objective of the NARVAL-II research campaign was to explore subtropical atmospheric circulation patterns and to study the formation and evolution of clouds during boreal summer 2016. The summer months also mark the peak-season of transatlantic dust-transport to the Caribbean (Prospero & Lamb, 2003). As a result, it was possible to design research flights to regions covered by long-range-transported Saharan dust. This enabled an in-depth investigation of the SALs and their properties Gutleben et al., 2020). During NARVAL-II the WALES instrument was operated in a downward-looking setup aboard HALO (High Altitude and Long Range research aircraft; Krautstrunk & Giez, 2012). HALO has a ceiling altitude of E 15 km and can cover distances of up to E 12,000 km. During the period of NARVAL-II in August 2016, HALO was based on the island of Barbados at the Grantley Adams International Airport .
In this study, mesoscale turbulent structures in SALs and their environment are investigated on the basis of lidar data collected during the research flights on August 12 and 19, 2016 (RF3 and RF6). As dropsondes were launched at a high frequency during those flights, collected meteorological data complements the lidar-measurements. RF3 and RF6 were specifically designed to lead over a long-range-transported SALs over the North Atlantic Ocean where measured total column aerosol optical depths (AODs; Figure 1) took values around 0.3 (RF3) and E 0.4 (RF6). As the flights also aimed for studying mesoscale tropospheric vertical motions using dropsondes , flight tracks were designed to contain circular patterns.

Lidar-and Dropsonde-Based Turbulence Analysis
is an important measure in fluid-dynamics and turbulence-analysis. It represents the part of kinetic energy in a flow, that is associated with eddies and waves. In classical physics, kinetic energy k E E is given by only with the turbulent perturbations of the mean wind components (u  2 , v  2 , w 2 ). For an atmospheric flow, it can be expressed as follows,

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In this equation, E g is the gravitational acceleration and Θ E is potential temperature. The greater E Ri, the lower the chance for turbulence to be generated. According to stability theory, E Ri even has to be smaller than a critical value of 1/4 for the formation of turbulence (e.g., Turner, 1973). In this study, an analysis of E Ri using dropsonde data additionally aims for resolving turbulent regions in the lidar profiles.
This study for the first time expounds a lidar-based analysis of atmospheric turbulence and dynamics in regions affected by long-range-transported Saharan dust layers. The backscattered power in a certain range interval of WALES lidar measurements can be interpreted to be a proxy for variations of aerosol and concentrations in the dust layer, as it is directly linked to variations of particle concentrations. In this way, turbulent eddies can be reconstructed from time series of backscatter and water vapor measurements and conclusions on the dynamics and the turbulence in desired atmospheric regions can be drawn.
Here, perturbations of 532 E R ‖ and m E r are spectrally decomposed to periodograms of PSD E using the Lomb-Scargle-method, for unevenly spaced observations (Lomb, 1976;Scargle, 1982). Such spectral analyses of spatially resolved measurements are performed to detect dominant length scales in signal variability and, consequently, the distribution of energy as a function of eddy length. The derived spectral slopes of the power spectra correspond to the turbulent activities in these regions. To obtain the needed perturbations for calculations in the respective signals, the mean values of the time series are subtracted from the individual measurements according to Reynolds averaging: Here, R 532 and r m represent the mean components of the backscatter and water vapor measurements and R 532  and r m  are the respective fluctuating parts.

Results
To evaluate turbulent processes inside long-range-transported SALs and the subjacent marine boundary layer (MBL), two 1-h-lidar data sets (550 and 590 km length) collected in the framework of the NARVAL-II research flights RF3 and RF6 are analyzed. Figure 2 gives an overview of the measurement situations and the meteorological conditions derived from dropsondes during that flights (14 dropsondes each).
During both flights, measurements of (532) p E  exhibit typical values for transported mineral dust of approximately 30% E . In the course of RF6 a distinct SAL, which ranged from 2.7 to 4.0 km altitude and was well-separated from the MBL below (0.0-1.7 km), was observed. In contrast, the SAL observed during RF3 (1. ) compared to the atmosphere below and above (see also Gutleben, Groß, Wirth, Emnde, & Mayer, 2019;Gutleben et al., 2020). During both flights, the SALs represented decoupled layers as wind speeds and directions differed from the ones in the surrounding regions. While wind speeds during RF3 were considerably higher in the SAL (20 E 25 kt [10.0 E  12.5 m s −1 ]) than above and below, they were weaker in the SAL (5 E 10 kt [2.5 E 5.0 m s −1 ]) than above and below during RF6. In addition, wind directions during RF6 differed (winds from north-west) from the ones in the MBL below (easterly winds). In both cases, the SAL was confined by inversions. During RF6 a total of three inversions could be detected in vertical measurements of temperature (T), Θ E and Θ e E . One was located at the top of the MBL (1.7 km) and the other two confined the SAL at its top (4.0 km) and bottom (2.7 km). The bottom inversion of the SAL during RF3 merged with the trade wind inversion below. Hence, only two inversions were observed on August 12, 2016. Both SALs were observed to represent neutrally stratified layers (Θ E and Θ e E are constant with height) and should have therefore been well mixed.
To spot turbulent regions in the observed vertical columns by dropsondes, squared Brunt-Väisälä frequencies, as well as derived wind shears and Richardson numbers are investigated in detail (Figure 3). Both observed scenes are characterized by small 2 E N in SAL regions ( ). This supports the hypothesis that the SALs represent decoupled atmospheric layers. 2 E N to E G, the Richardson number E Ri, also shows smallest values inside the respective SALs. Greatest E Ri is found at their top and bottom. These findings highlight that the SALs must be well mixed in their interior and that they are delimited at their top and bottom.To study the turbulent and dynamical processes in these SAL-influenced atmospheres in more detail, lidar power spectra for four different altitude ranges are calculated for both observed scenes, that is, inside the MBL as well as inside, below and above the pronounced SALs (Figure 4)

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At highest levels in both scenes, above the SALs, the 532 E R ‖ -spectra flatten and take values between 1 / 6 E  and 1 E  . These spectra have to be interpreted very carefully, as the signal to noise ratio is small because of the lack of aerosol. Consequently, the derived slopes get flattened. However, Richardson numbers at these altitudes point toward the suppression of turbulence and great static stability. Slopes in the spectra of m E r are steeper since filaments of water vapor convective outflow at these altitudes were captured.

Summary and Conclusion
This study for the first time substantiated that spectral analyses of airborne lidar measurements can be employed to study mesoscale turbulence in regions affected by long-range-transported Saharan mineral dust layers. The analysis of two case studies shows that the SALs are vertically well mixed layers. An analysis of Brunt-Väisälä frequencies and Richardson numbers highlights that the SALs represent decoupled layers that are delimited by statically stable regions at their confining top and bottom. Inside the SALs, Richardson numbers take values around 0.25 -an indication that turbulence can potentially evolve. ; Gutleben et al. (2020) expected turbulence inside the SAL form derived differential vertical radiative heating rates. The results in this work, shows that mesoscale turbulent features inside the observed SALs are well established and endorse their presumption.
A spectral analysis of variations in the backscattered signals are interpreted as proxies for variations of TKE E , as was already shown in previous studies concentrating on turbulent structures of cirrus clouds (Demoz et al., 1998;Wang & Sassen, 2006). Derived power spectra of both lidar backscatter ratio and water vapor mass mixing ratio indicate well-established turbulence cascades from larger toward smaller eddies inside SALs. The slopes of both spectra follow the predicted slopes of −5/3 for fully developed mesoscale turbulence. At altitudes below and above the SALs the slope of the cascade are flatter, thus pointing toward less developed dynamics and a clear separation from turbulent effects inside the SALs.
The observed findings also fortify the hypothesis that turbulence inside SALs helps to keep large mineral dust particles with diameters of several tens of microns aloft for a longer time and counteracts gravitational settling effects.