atmosphere

Article Evaluation of and Low Stratus Microphysical Properties Derived from In Situ Sensor, Cloud Radar and SYRSOC Algorithm

Jean-Charles Dupont 1,*, Martial Haeffelin 2, Eivind Wærsted 3 ID , Julien Delanoe 4, Jean-Baptiste Renard 5, Jana Preissler 6 ID and Colin O’Dowd 6

1 Institut Pierre-Simon Laplace, École Polytechnique, UVSQ, Université Paris-Saclay, 91128 Palaiseau, France 2 Institut Pierre Simon Laplace, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau, France; [email protected] 3 Laboratoire de Météorologie Dynamique, École Polytechnique, Université Paris-Saclay, 91128 Palaiseau, France; [email protected] 4 Laboratoire Atmosphères, Milieux, Observations Spatiales/UVSQ/CNRS/UPMC, 78280 Guyancourt, France; [email protected] 5 LPC2E-CNRS/Université d’Orléans, 3A Avenue de la Recherche Scientifique, 45071 Orléans, France; [email protected] 6 Centre for Climate and Air Pollution Studie, National University of Ireland, Galway H91 CF50, Ireland; [email protected] (J.P.); [email protected] (C.O.) * Correspondence: [email protected]

 Received: 15 March 2018; Accepted: 23 April 2018; Published: 2 May 2018 

Abstract: The microphysical properties of low stratus and fog are analyzed here based on simultaneous measurement of an in situ sensor installed on board a tethered balloon and active remote-sensing instruments deployed at the Instrumented Site for Atmospheric Remote Sensing Research (SIRTA) observatory (south of Paris, France). The study focuses on the analysis of 3 case studies where the tethered balloon is deployed for several hours in order to derive the relationship between liquid water content (LWC), effective radius (Re) and cloud droplet number concentration (CDNC) measured by a light optical aerosol counter (LOAC) in situ granulometer and Bistatic Radar System for Atmospheric Studies (BASTA) cloud radar reflectivity. The well-known relationship Z = α × (LWC)β has been optimized with α  [0.02, 0.097] and β  [1.91, 2.51]. Similar analysis is done to optimize the relationship Re = f(Z) and CDNC = f(Z). Two methodologies have been applied to normalize the particle-size distribution measured by the LOAC granulometer with a visible extinction closure (R2  [0.73, 0.93]) and to validate the LWC profile with a liquid water closure using the and Temperature Profiler (HATPRO) microwave radiometer (R2  [0.83, 0.91]). In a second step, these relationships are used to derive spatial and temporal variability of the vertical profile of LWC, Re and CDNC starting from BASTA measurement. Finally, the synergistic remote sensing of (SYRSOC) algorithm has been tested on three tethered balloon flights. Generally, SYRSOC CDNC and Re profiles agreed well with LOAC in situ and BASTA profiles for the studied fog layers. A systematic overestimation of LWC by SYRSOC in the top half of the fog layer was found due to fog processes that are not accounted for in the cloud algorithm SYRSOC.

Keywords: fog; cloud radar; microphysical properties

1. Introduction Accurate forecasts of atmospheric conditions resulting in low , particularly on short timescales, have become an important issue [1–24]: Fog and low clouds often cause a strong reduction

Atmosphere 2018, 9, 169; doi:10.3390/atmos9050169 www.mdpi.com/journal/atmosphere Atmosphere 2018, 9, 169 2 of 19 of visibility, thus affecting various types of transport systems such as car, air and ship traffic, and the financial and human costs are comparable to those of tornadoes and storms [9]. Low visibility during fog events is a result of complex radiative, turbulent and microphysical processes as well as interactions between the atmospheric boundary layer (ABL) and the underlying surface [5–27]. The mechanisms of fog formation, development and dissipation are very complex and have been extensively studied with a series of numerical simulations and comprehensive observational programs including in situ measurements [9]. From the numerical modelling point of view, meteorological models usually lack accuracy due to poor horizontal [18] and vertical [25] resolutions, and inadequacies in microphysical parametrizations [9]. To explore the parameterization of microphysical processes in fog, it is essential to observe the spatial and temporal variations of key microphysical parameters related to fog, cloud droplet number concentration (CDNC), liquid water content (LWC), and effective radius (Re). Fog drop size distribution (DSD) is undoubtedly an important parameter for describing various fog types and the lifecycle stages of fog. All the key microphysical parameters are affected by DSD when fog develops [16]. Fog drop-size distributions pertain to various types with spatial and temporal variations [26], and even at different heights of fog layers, fog drop size distributions vary due to inhomogeneous microphysical structures in fog [28]. The variability of fog drop-size distributions is incurred by the combined effects of microphysical processes, such as nucleation, activation, growth, gravitational setting, turbulent mixing, and macro conditions such as wind and radiative fluxes [17]. Unfortunately, few data are available concerning LWC in fog events, as well as for single fog lifecycle stages. Balloon-borne systems are also unsuitable for continuous spatial and temporal measurements of the vertical fog structure. One possible solution comprises frequency-modulated continuous wave technique (FMCW) cloud radars that could provide continuous but indirect LWC measurements in a high temporal resolution [2–16]. Reliable Z-LWC relationships for fog events are paramount to retrieving LWC profiles from radar reflectivity: existing procedures use empirically-derived static relationships [7–22], and some are more advanced accounting for additional instrumentation such as a ceilometer [3] or microwave radiometer [14]. However, assumptions about the shape of the droplet-size distribution lead to inaccuracies in retrieved Z-LWC because Z is proportional to the sixth moment of the DSD (in Rayleigh approximation, valid for small drops i.e., for fog) while LWC is proportional to the third moment of the DSD. The objective of this study is (1) to derive microphysical property profiles from radar reflectivity, (2) to quantify the accuracy of retrievals with an in situ granulometer, and (3) to evaluate an algorithm to derive cloud-layer microphysical properties, the synergistic remote sensing of clouds (SYRSOC) algorithm [15]. In Section2, we describe the instrumental setup of the intensive observational periods (IOP) carried out at the Instrumented Site for Atmospheric Remote Sensing Research (SIRTA) observatory, the dataset available for the four case studies, and the SYRSOC algorithm used in this study. Section3 shows the parametric relationship used to derive the microphysical properties starting from radar reflectivity. In Section4, the vertical profiles of microphysical properties such as LWC, Re and CDNC derived in Section3 are compared to in situ sensor and SYRSOC output data.

2. Observational Dataset and Synergistic Remote Sensing of Clouds (SYRSOC) Algorithm

2.1. Intensive Observational Periods (IOP) and Three Tethered Balloon Flights SIRTA is a French national observatory dedicated to studying clouds, aerosols, dynamics and thermodynamics in the boundary layer and the free . The SIRTA observatory is a mid-latitude site (48.7◦ N, 2.2◦ E) located in a semi-urban area, on the Saclay plateau 25 km south of Paris [10]. Table1 describes the active and passive remote-sensing instruments and the main in situ sensors deployed at the SIRTA site for the IOP and used in this study. These IOP correspond to 6 January 2015, 19 December 2016, 3 January 2017 and 17 February 2017. On the three first dates, a tethered balloon carrying an optical particle counter was deployed to document fog and low-stratus microphysical properties, while Atmosphere 2018, 9, 169 3 of 19

duringAtmosphere the fog 2018 on, 9 17, x FOR February PEER REVIEW 2017 the balloon was not used and measurements were only3 of taken 18 at 4 m . All instruments were set up in an area covering less than 1 km2. All times are universal 2 time (UT)than and1 km all. All times are are universal above ground time (UT) level and (agl). all altitudes Figure 1are shows above a ground time series level of (agl). the Figure cloud radar1 reflectivityshows (coloreda time series panel) of and the tetheredcloud radar balloon reflectivi (blackty markers)(colored panel) path for and 3 Januarytethered 2017balloon between (black 10:00 markers) path for 3 January 2017 between 10:00 and 17:00. Fog thickness reaches 300 m at 10:30 and and 17:00. Fog thickness reaches 300 m at 10:30 and maximum altitude reached by the tethered balloon maximum altitude reached by the tethered balloon is 250 m around 11:00. During this event we is 250performed m around 2 11:00.different During flights, thisone eventduring we the performedmorning (between2 different 10:15 flights and 13:00),, one and during one thebetween morning (between15:00 10:15 and 16:45. and 13:00), and one between 15:00 and 16:45.

TableTable 1. Active 1. Active and and passive passive remote remote sensing sensing instrumentsinstruments and and the the in-situ in-situ sensors sensors deployed deployed at the at the InstrumentedInstrumented Site Site for Atmosphericfor Atmospheric Remote Remote Sensing Sensing ResearchResearch (SIRTA) (SIRTA) site site and and used used for for this this study. study.

Type of Type of Name Parameters Sampling Uncertainty Instrument Name Parameters Sampling Uncertainty Instrument Bistatic Radar System Bistatic Radar System for Reflectivity, Doppler for Atmospheric Reflectivity, Doppler Atmospheric Studies velocity, cloud top 12 s 0.5 dBZ, 0.2 m/s Studies (BASTA) cloud velocity, cloud top 12 s 0.5 dBZ, 0.2 m/s (BASTA) cloud radar height radar (95 GHz) height Remote- (95 GHz) Humidity and Remote-sensingsensing Humidity and Temperature Temperature Profiler LiquidLiquid water water path path instrumentsinstruments Profiler (HATPRO) 5 min5 min LWPLWP ± 20± g/m²20 g/m 2 (HATPRO) microwave (LWP)(LWP) microwave radiometer radiometer CL31 Ceilometer Cloud Cloud base base heigh heightt 1 min 1 min 7.5 m 7.5 m CHM15K Ceilometer Cloud Cloud base base height height 1 min 1 min 7.5 m 7.5 m Degreane DF320 HorizontalHorizontal visibility visibility 1 min1 min ±10–25%±10–25% diffusometer (km)(km) at 4 at m 4 magl agl Particle-size In situ Particle-size In situ sensors Light optical aerosol distributiondistribution for for 1 min1 min sensors Light optical aerosol counter counter (LOAC) particlesparticles ranging ranging from from SamplingSampling (LOAC) granulometer granulometer 0.2 to0.2 50 to µm 50 (inµm 2.5 2.5L/min L/min diameter)(in diameter)

FigureFigure 1. Cloud 1. Cloud radar radar reflectivity reflectivity and and tetheredtethered balloon balloon path path on on 3 January 3 January 2017. 2017.

2.2. Remote-Sensing Instruments and In Situ Sensor 2.2. Remote-Sensing Instruments and In Situ Sensor A Degreane DF320 diffusometer (Degreane, La Garde, France) was operated near the ground (4 Am Degreaneagl). The instrument DF320 diffusometer provides horizontal (Degreane, visibility La Garde,range and France) particle was extinction operated at 550 near nm, the with ground (4 m agl10–25%). The uncertainty instrument [6]. provides horizontal visibility range and particle extinction at 550 nm, with 10–25% uncertaintyThe cloud base [6]. height and the cloud top height were derived from the CL31 (Vaisala, Vantaa, TheFinland) cloud or baseCHM15K height ceilometer and the (Lufft, cloud Berlin, top height Germany) were backscatter derived signal from theand CL31the BASTA (Vaisala, 95 GHz Vantaa, Finland)Doppler or CHM15K cloud radar ceilometer developed (Lufft, by the Berlin, LATMOS Germany) laboratory, backscatter respectively signal [2]. and The the ceilometer BASTA and 95 GHz radar blind zones are 15 m and 40 m, with vertical resolutions of 15 m and 12.5 m, respectively. This Doppler cloud radar developed by the LATMOS laboratory, respectively [2]. The ceilometer and radar zone corresponds to the altitude without information on lidar backscatter or radar reflectivity and blind zones are 15 m and 40 m, with vertical resolutions of 15 m and 12.5 m, respectively. This zone Doppler velocity. The cloud radar is operated in a vertically pointing mode and uses the frequency corresponds to the altitude without information on lidar backscatter or radar reflectivity and Doppler velocity. The cloud radar is operated in a vertically pointing mode and uses the frequency modulated Atmosphere 2018, 9, 169 4 of 19 Atmosphere 2018, 9, x FOR PEER REVIEW 4 of 18 continuousmodulated wave continuous approach wave at 95 approach GHz. Its at bi-static 95 GHz. configuration Its bi-static configuration allows us to allows reduce us theto reduce blind zonethe comparedblind zone to mono-static compared to radar. mono-static The 3.2 radar. mm wavelengthThe 3.2 mm wavelength gives a clear gives advantage a clear advantage compared compared to classical meteorologicalto classical meteorological radar in term radar of sensitivity in term of for sensitivity equivalent for equivalent antenna size antenna and emitted size and power, emitted the power, cloud radarthe is cloud perfectly radar suited is perfectly for the suited characterization for the charac of microphysicalterization of microphysica properties ofl properties fog and stratus of fog above and 40 mstratus height, above while 40 them height, CL31 while or CHM15K the CL31 ceilometer or CHM15K is totallyceilometer attenuated is totally when attenuated the fog when thickness the fog is morethickness than some is more tens than ofmeters. some tens The of sensitivitymeters. The ofsensitivity the radar of isthe estimated radar is estimated to be at aboutto be at− about40 dBZ −40 at 1 kmdBZ for at a temporal1 km for a resolutiontemporal resolution of 12 s and of 12.512 s mand range 12.5 m resolution range resolution [2]. [2]. TheThe Humidity Humidity and Temperatureand Temperature Profiler (RPG-HATPRO,Profiler (RPG-HATPRO, Radiometer Radiometer Physics Gmbh, Physics Meckenheim, Gmbh, Germany)Meckenheim, water vaporGermany) and water oxygen vapor multi-channel and oxygen microwave multi-channel profiler, microwave installed profiler, at SIRTA installed site since at FebruarySIRTA 2010, site since provides February time series2010, provides of the liquid time water series path of the when liquid fog water or clouds path occur,when andfog or integrated clouds occur, and integrated water vapor on the total column of the atmosphere. water vapor on the total column of the atmosphere. The Light Optical Aerosol Counter (LOAC) is a compact optical counter/sizer to perform The Light Optical Aerosol Counter (LOAC) is a compact optical counter/sizer to perform measurements of liquid and solid particles at ground level and under all kinds of balloons in the measurements of liquid and solid particles at ground level and under all kinds of balloons in the troposphere and in the [20]. Particles are collected and are injected through a laser beam troposphere and in the stratosphere [20]. Particles are collected and are injected through a laser beam by a pumping system. LOAC is characterized by a sampling rate around 2.5 L/min through a tube of by a8 pumpingmm in diameter system. and LOAC 20 cm is characterizedin lengths. Measuremen by a samplingts of the rate light around scattered 2.5 L/min by the through particles a tubeare of 8performed mm in diameter at two scattering and 20 cm angles. in lengths. The first Measurements one is around of 12°, the and light is scatteredalmost insensitive by the particles to the ◦ arerefractive performed index attwo of the scattering particles; the angles. second The one first is around one is 60° around and is 12strongly, and sensitive is almost to the insensitive refractive to ◦ theindex refractive of the index particles. of the By particles; combining the measurements second one isat aroundthe two 60angles,and it is is strongly possible sensitiveto retrieve to the the refractiveconcentrations index of thefor 19 particles. size classes By combining between 0.2 measurements µm and 50 µm at thein diameter two angles, and it to is estimate possible tothe retrieve main thetypology concentrations of the forparticles 19 size (droplets, classes betweencarbonaceous, 0.2 µ mmineral and 50 particles,µm in diameter salts) when and the to estimatemedium theis mainrelatively typology homogeneous. of the particles This (droplets, typology carbonaceous,is based on calibration mineral charts particles, obtained salts) in when the laboratory the medium [21]. is relativelyThe homogeneous. LOAC sensor Thiscalibration typology procedure is based follows on calibration the standard charts calibration obtained inof an the optical laboratory counter, [21]. i.e.,The the LOAC particle sensor size calibrationis controlled procedure but not the follows number. the Latex standard beads, calibration which are of perfect an optical transparent counter, i.e.,spheres, the particle have sizebeen is used controlled for diamet buter not calibration the number. below Latex2 µm. beads,For the whichcalibration are in perfect the 5–45 transparent µm size spheres,range, have different been usednatures for diameterof irregular calibration grains belowhave 2beenµm. Forused: the glass calibration beads in(quite the 5–45 irregular),µm size range,carbonaceous different natures particles, of irregulardust sand grains of several have beentypes, used: ashes glass and beadssalts. Figure (quite irregular),2 shows an carbonaceous example of particles,particle-size dust sanddistribution of several measured types, with ashes the and LOAC salts. sensor Figure on2 3 shows January an 2017 example at 10:00 of and particle-size 11:00. At distribution10:00, LOAC measured is at the with ground the LOAC during sensor the fog on event 3 January with 2017more atthan 10:00 50 andparticles 11:00. bigger At 10:00, than LOAC 10 µm is at thewhereas ground at during11:00, LOAC the fog sensor event reaches with morethe top than of the 50 fog particles layer with bigger only than one 10tenthµm of whereas particles at larger 11:00, than 10 µm. LOAC sensor reaches the top of the fog layer with only one tenth of particles larger than 10 µm.

Figure 2. Particle-size distribution derived from LOAC sensor on 3 January 2017 at 10:00 and 11:00 Figure 2. Particle-size distribution derived from LOAC sensor on 3 January 2017 at 10:00 and 11:00 UT. UT.

Atmosphere 2018, 9, 169 5 of 19

The uncertainty for total concentrations measurements is ±20% when concentrations are higher than 5 particles cm−3 (for a 10-min integration time). The uncertainties in size calibration are ±0.025 µm for particles smaller than 1 µm, and 10% for greater particles. The measurement accuracy of submicron particles is reduced when the concentration of particles >3 µm exceeds a few particles cm−3. In the case of measurements inside a thick fog, several particles are present in the laser beam at the same time and the concentrations can be underestimated. Corrective coefficients have been established to tentatively correct from this effect and to retrieve the relative distribution of the particles. Nevertheless, this procedure becomes inaccurate for the highest concentrations; it is then necessary to normalize also the results with the total number of particles estimated from independent measurements. The following part presents a possible method to normalize the particle-size distribution by comparing it to the optical extinction measured with the diffusometer.

2.3. Visible Extinction Normalisation for Light Optical Aerosol Counter (LOAC) Validation The particle-size distribution in ambient conditions is measured by the LOAC sensor and used to derive the extinction coefficient σloac. The measured size distribution, according to Mie applicable to spherical droplet particles allows us to derive σloac as the following equation:

Dmax πD2 σ = N Q (1) loac ∑ 4 D ext(m,D) Dmin where Qext is the Mie extinction efficiency factor depending on the particle size D and the refractive index m. As for [6], we assume m = 1.33 for particles larger than 2 µm and m = 1.48 − 0.01i for particles smaller than 2 µm (derived from an AERONET sun photometerDmin equals to 0.1 µm and Dmax = 50 µm. D corresponds to mean diameter for the LOAC sensor and ND is the particles concentration for each size D. The extinction coefficient σDF is here derived from the measured horizontal visibility (DF320 measurement) according to the Koschmieder equation [12]:

− ln(VC) σ = (2) DF Visi where VC is the visual contrast defined here as 5%, and Visi is the horizontal visibility measured by the DF320 diffusometer [6]. Some visible extinction comparisons have been undertaken to compare extinction coefficient derived from LOAC sensor and measured by DF320 diffusometer (Figure3 for collocated measurement at 4 m agl. Figure3 on the left shows a time series of extinction coefficient derived from Equations (1) and (2). The black line corresponds to diffusometer data and the red line to LOAC processing. Fog occurs between 05:30 and 07:00. The following table shows slope (normalization factor), and correlation coefficient for four experimental closures in visible extinction according to the relationship as in Figure3 on the right. We note a significant difference for the normalization factor that can be explained by some physical phenomena. First, during the foggy situation considered on 6 January 2015 the temperature was about −1 ◦C with perhaps some ice crystal that can induce very important scattering inside the LOAC optical chamber leading to an overestimation of the optical extinction compared to true visibility measured by DF320 diffusometer. This explains why the slope between the LOAC extinction coefficient and the diffusometer extinction coefficient was 8.2 (Table2). For 17 February 2017, the slope is equal to 4.2 according to very high number of particles larger than 10 µm about 110 #/cm3 compared to 35 or 55 #/cm3 for 3 January 2017 and 19 December 2016, respectively. We had some problems with the electronic card for this IOP because of a water leak in the electronic box several days before. So, for this IOP the relative size distribution is biased toward the largest droplets leading to an overestimation of the calculated visible extinction (Equation (1)). For 19 December 2016 and 3 January 2017, the slope Atmosphere 2018, 9, 169 6 of 19 is 0.59 and 0.92, respectively, for an average visibility of 500 m and 180 m. Additional explanation is providedAtmosphere in Section 2018, 9, x3.5 FOR. PEER REVIEW 6 of 18

Figure 3. Time series of extinction coefficient derived from LOAC granulometer and DF320 Figurediffusometer 3. Time ( seriesleft) and of scatter extinction plot of coefficientLOAC extinction derived coefficient from versus LOAC DF320 granulometer extinction coefficient and DF320 diffusometerfor 19 December (left) and 2016 scatter (right plot). of LOAC extinction coefficient versus DF320 extinction coefficient for 19 December 2016 (right). Table 2. Coefficients used to normalize the LOAC cloud droplet number concentration (CDNC) compared to visible extinction derived from DF320 diffusometer for the four case studies at 4 m agl. Table 2. Coefficients used to normalize the LOAC cloud droplet number concentration (CDNC) Average Average Average CDNC Average Normalization compared to visible extinctionSlope derived# fromρ DF320Temp. diffusometer Wind Speed for the four(#/cm case3) studies atVisibility 4 m agl. Procedure (°C) (m/s) Total, and >10 µm (m) Average Average Average CDNC Average Normalization6 January 2015 8.2 86 0.93 −1.2 2.2 840/40 670 Slope # ρ Temp. Wind Speed (#/cm3) Visibility Procedure19 December 2016 0.59 76 0.88 3.4 0.5 465/55 500 (◦C) (m/s) Total, and >10 µm (m) 3 January 2017 0.92 157 0.73 0.9 1.8 930/35 180 6 January17 February 2015 2017 * 8.2 4.2 86 450.93 0.83 −1.2 7.6 2.2 1.1 840/40 270/110 320670 19 December 2016 0.59 76 0.88 3.4 0.5 465/55 500 * This case study is used in this part solely because the LOAC was fixed at the ground next to the 3 January 2017 0.92 157 0.73 0.9 1.8 930/35 180 17 Februarydiffusometer, 2017 * and4.2 we did 45 not deploy 0.83 the tethered 7.6 balloon; 1.1# corresponds to 270/110the sample for each day. 320 * This case study is used in this part solely because the LOAC was fixed at the ground next to the diffusometer, and we2.4. did SYRSOC not deploy Algorithm the tethered balloon; # corresponds to the sample for each day. SYRSOC is an algorithm for the calculation of microphysical cloud-property profiles from 2.4. SYRSOCcollocated Algorithm cloud radar, ceilometer or lidar, and microwave radiometer data. In this study, SYRSOC used backscatter signal from the CHM15k (Lufft) and CL31 (Vaisala) ceilometers to detect the cloud SYRSOC is an algorithm for the calculation of microphysical cloud-property profiles from base. Reflectivity from BASTA cloud radar was used to detect the cloud top and to calculate cloud collocateddroplet cloud number radar, concentration ceilometer or(CDNC) lidar, andcombined microwave with information radiometer from data. the In other this instruments. study, SYRSOC From used backscatterthe HATPRO signalfrom microwave the CHM15k radiometer (Lufft) (RPG, and Sectio CL31n (Vaisala) 2.2), liquid ceilometers water path to detect(LWP) thewas cloud used. base. ReflectivityTemperature from BASTA profiles cloud were radarderived was from used in to situ detect mast the measurements, cloud top and assuming to calculate an cloudadiabatic droplet numbertemperature concentration decrease (CDNC) with height. combined Under with the information assumption fromof a mono-modal the other instruments. cloud droplet From size the HATPROdistribution microwave of single-layer radiometer purely (RPG, liquid Section water 2.2 clouds,), liquid profiles water of pathRe and (LWP) LWC waswere used.calculated Temperature from profilesCDNC, were which derived is the from primary in situ output mast of measurements, SYRSOC. Further assuming details on an SYRSOC adiabatic were temperature given by [15] decrease and with height.[19]. Under the assumption of a mono-modal cloud droplet size distribution of single-layer For this study, an entrainment factor has been introduced to take into account entrainment of purely liquid water clouds, profiles of Re and LWC were calculated from CDNC, which is the primary dry air at the cloud top. The entrainment factor is calculated for the top 30% of the cloud, replicating output of SYRSOC. Further details on SYRSOC were given by [15] and [19]. the shape of the measured reflectivity profile. The ratio of radar reflectivity at each height bin to radar Forreflectivity this study, at 30% an entrainmentfrom the cloud factor top is has calculated. been introduced This height to dependent take into accountfactor is entrainmentthen multiplied of dry air at theto the cloud CDNC top. profile The entrainmentto produce more factor realistic is calculated shapes offor the theCDNC top profile, 30% of and the subsequently cloud, replicating of Re the shapeand of the LWC measured profiles. reflectivity profile. The ratio of radar reflectivity at each height bin to radar reflectivityThis at 30% is the from first thetime cloud SYRSOC top ishas calculated. been applied This to heightfog layers. dependent The cloud factor base in is any then fog multiplied layer is to the CDNCat ground profile level. to produce However, more BASTA realistic has a shapes blind ofzone the in CDNC the lowest profile, 40 andm and subsequently a height range of Re of and LWC profiles.incomplete overlap of outgoing radiation and receiver field of view from 40 m to 240 m [2]. ThisReflectivity is the first below time 240 SYRSOC m will be has reduced been applieddue to th tois fogeffect. layers. However, The cloud LWP of base the in whole any fogcolumn layer is is at measured by HATPRO. In case of fog, much of the liquid water will be located in the lowest 240 m. ground level. However, BASTA has a blind zone in the lowest 40 m and a height range of incomplete overlap of outgoing radiation and receiver field of view from 40 m to 240 m [2]. Reflectivity below Atmosphere 2018, 9, 169 7 of 19

240 m will be reduced due to this effect. However, LWP of the whole column is measured by HATPRO. In case of fog, much of the liquid water will be located in the lowest 240 m. The weak reflectivity would be causing SYRSOC to produce unrealistically high CDNC values and, consequently, very small Re. Therefore, BASTA reflectivity was corrected in the height range of 120–240 m using a near-field correction proposed by [23]. Below 120 m, reflectivity was assumed constant.

3. Liquid WaterAtmosphere Content 2018, 9, x FOR (LWC), PEER REVIEW Effective Radius (Re) and Cloud Droplet Number Concentration7 of 18 (CDNC) RetrievalsThe weak reflectivity would be causing SYRSOC to produce unrealistically high CDNC values and, consequently, very small Re. Therefore, BASTA reflectivity was corrected in the height range of 120– 3.1. Pairing of240 Radar m using and a near-field In Situ Observationscorrection proposed Along by the[23]. Flight Below Path120 m, reflectivity was assumed constant.

In Section3. Liquid3, we Water derive Content the microphysical (LWC), Effective properties Radius (Re) such and Cloud as liquid Droplet water Number content Concentration (LWC), effective radius (Re) and(CDNC) cloud Retrievals droplet number concentration (CDNC) measured by the LOAC granulometer from BASTA cloud radar reflectivity (Z). We compare LWC, Re, CDNC and Z along the tethered 3.1. Pairing of Radar and In Situ Observations Along the Flight Path balloon path. We consider 2 min average data of LOAC along the balloon path and we determine the identical time andIn Section altitude 3, we bins derive for BASTAthe microphysical measurements. properties We such used as liquid the 12.5 water m content vertical (LWC), resolution of effective radius (Re) and cloud droplet number concentration (CDNC) measured by the LOAC BASTA andgranulometer the closest gatefrom BASTA to the averagecloud radar altitude reflectivity of LOAC(Z). We compare during LWC, the averaging Re, CDNC and period. Z along the tethered balloon path. We consider 2 min average data of LOAC along the balloon path and we 3.2. Dopplerdetermine Cloud Radar the identical Reflectivity time and (Z)–LWC altitude Relationshipbins for BASTA measurements. We used the 12.5 m vertical resolution of BASTA and the closest gate to the average altitude of LOAC during the averaging Theoreticalperiod. relationships between cloud radar reflectivity and LWC have been developed and [7–22] proposed a relationship of the form: 3.2. Doppler Cloud Radar Reflectivity (Z)–LWC Relationship  −  β Theoretical relationships betweenZ mm 6cloudm 3 radar= αre×flectivityLWC and LWC have been developed and (3a) [7–22] proposed a relationship of the form:

Z Zmm m dBZ =α×LWC−log 10(α) (3a) 10 β LWC = 10 (3b) (3b) LWC = 10 During the three tethered balloon flights, LWC is measured by the LOAC sensor and Z is measured by the BASTA cloudDuring radar.the three Figure tethered4 showsballoon flights, the relationship LWC is measured between by the LOAC LOAC liquidsensor and water Z is content measured by the BASTA cloud radar. Figure 4 shows the relationship between LOAC liquid water and BASTAcontent reflectivity and BASTA for thereflectivity three for tethered the three balloon tethered balloon flights flights (black (black markers markers for for 19 December December 2016, blue markers2016, for blue 3 Januarymarkers for 2017 3 January and 2017 red and markers red markers for for 6 January 6 January 2015). The The LWC LWC ranges ranges between between 0.01–0.7 g/m0.01–0.73 for theg/m period3 for the period of reflectivity of reflectivity increase increase from from −58.558.5 to to−16.5− 16.5dBZ. dBZ.

Figure 4. Relationship between liquid water content (LWC) measured with the LOAC sensor and Figure 4. Relationshipradar reflectivity between measured liquid with water BASTA content for the (LWC)three case measured studies (black with markers the LOAC for 19 sensorDecember and radar reflectivity measured2016, blue markers with for BASTA 3 January for 2017 the and three red markers case studies for 6 January (black 2015). markers for 19 December 2016, blue markers for 3 January 2017 and red markers for 6 January 2015).

Atmosphere 2018, 9, 169 8 of 19

Equation (3) derives a linear relationship between reflectivity in dBZ and the logarithm of LWC, which appears to agree well with the observations within each case study (Figure4). It therefore allows us to deriveAtmosphereα and 2018,β 9, coefficientsx FOR PEER REVIEW by the least square method. Statistical results are presented in8 Tableof 18 3 (ρ is the correlation factor). For our study, α ranges from 0.044 to 0.097 and β from 1.91 to 2.51 with an average reflectivityEquation ranging(3) derives from a linear−33.4 relationship to −22.7 dBZbetween leading reflectivity to a LWC in dBZ ranging and the from logarithm 0.07 to of 0.19 LWC, g/m 3, respectively.which appears The total to sampleagree well for with this the experiment observations is almost within 186each 5-min-periods case study (Figure and 4). each It therefore correlation factor isallows bigger us thanto derive 0.74. α and β coefficients by the least square method. Statistical results are presented in Table 3 (ρ is the correlation factor). For our study, α ranges from 0.044 to 0.097 and β from 1.91 to Table2.51 3.withParametrical an average coefficient reflectivity to ranging optimize from Equation −33.4 (3)to − with22.7 ZdBZ measured leading withto a LWC cloud ranging radar and from LWC 0.07 3 measuredto 0.19 g/m by LOAC, respectively. sensor alongThe total the tetheredsample for balloon this expe flight.riment is almost 186 5-min-periods and each correlation factor is bigger than 0.74. Average Z Average LWC Equation (3) α β # ρ Table 3. Parametrical coefficient to optimize Equation (3)(min, withmax) Z measured (dBZ) with(min, cloud max) radar (g/m3 )and LWC measuredAtlas, 1954by LOAC sensor alon0.048g the tethered2 / balloon flight. / /

Sauvageot and Omar, 1987 0.030 1.7 / 0.67 //Average Z Average LWC (min, Equation (3) α β # ρ Fox and Illingworth, 1997 0.012 1.16 / 0.82 (min,// max) (dBZ) max) (g/m3) Atlas, 1954 0.048 2 / −38.4 / 0.07 / Flight 1. 6 January 2015 0.020 1.91 62 0.79 Sauvageot and Omar, 1987 0.030 1.7 / 0.67 (−57.5, −25.1) / (0.03, 0.26) / Fox and Illingworth, 1997 0.012 1.16 / 0.82 / / −27.7 0.19 Flight 2. 19 December 2016 0.049 2.06 43 0.88 −38.4 0.07 Flight 1. 6 January 2015 0.020 1.91 62 0.79 (−48.5, −19.8) (0.02, 0.35) (−57.5, −25.1) (0.03, 0.26) −25.1 0.1 Flight 3. 3 January 2017 0.097 2.51 81 0.74 −27.7 0.19 Flight 2. 19 December 2016 0.049 2.06 43 0.88 (−43.4, −11.5) (0.01, 0.85) (−48.5, −19.8) (0.02, 0.35) −25.1 0.1 Flight 3. 3 January 2017 0.097 2.51 81 0.74 The variability of the relationship between LWC and Z is analyzed(−43.4, −11.5) and discussed(0.01, 0.85) in Section 3.6.

3.3. Z–Re RelationshipThe variability of the relationship between LWC and Z is analyzed and discussed in Section 3.6.

Fox3.3. and Z–Re Illingworth Relationship (1997) have developed a best linear fit with the following form to link the reflectivityFox Z and and the Illingworth effective (1997) radius have Re: developed a best linear fit with the following form to link the reflectivity Z and the effective radius Re: Z(dBZ) = γ × log 10(Re) + δ (4) ZdBZ = γ ×log10Re +δ (4) (Z(dBZ)−δ)/γ Re =Re10 = 10⁄ (5) (5) DuringDuring the three the tetheredthree tethered balloon balloon flights, flights, effective effective radius radius is measuredis measured with with the the LOAC LOAC sensor sensor and Z correspondsand Z corresponds to reflectivity to reflectivity measured measured with the BASTAwith the cloud BASTA radar. cloud Figure radar.5 shows Figure the 5 shows relationship the betweenrelationship the effective between radius the and effective the reflectivity radius and the for reflectivity each tethered for each balloon tethered flight. balloon flight.

Figure 5. Relationship between effective radius (Re) measured with the LOAC sensor and radar Figure 5. Relationship between effective radius (Re) measured with the LOAC sensor and radar reflectivity measured with BASTA for the three case studies (black markers for 19 December 2016, reflectivityblue markers measured for 3 with January BASTA 2017 forand thered threemarkers case for studies6 January (black 2015). markers for 19 December 2016, blue markers for 3 January 2017 and red markers for 6 January 2015).

Atmosphere 2018, 9, 169 9 of 19

We applied the same method as for Equation (3) to derive γ and δ coefficients by the least square method and we present the result in Table4. For our study, γ ranges from 52.60 to 69.2, δ from −80.7 to −94.2, and effective radius Re ranges from 3.6 to 5.7 µm. For this experiment, the reflectivity range between −57.5 and −11.5 dBZ.

Table 4. Parametrical coefficient to optimize Equation (5) to derive Re with Z measured with the cloud radar and by the LOAC sensor along the tethered balloon flight.

Average Re * Average Z Average Re Equation (4) γ δ (min, max) # ρ (min, max) (min, max) (µm) (dBZ) (µm) Fox and Illingworth, 2007 40.9 −64.2 4 / / / / 3.6 −38.4 4.9 Flight 1. 6 January 2015 65.0 −74.2 62 0.74 (1.1, 4.9) (−57.5, −25.1) (0.8, 8.6) 5.7 −27.7 6.8 Flight 2. 19 December 2016 52.0 −69.2 43 0.86 (2.1, 7.2) (−48.5, −19.8) (1.1, 9.4) 4.3 −25.1 5 Flight 3. 3 January 2017 69.2 −80.7 81 0.78 (1.7, 9.5) (−43.4, −11.5) (0.8, 12.6) * Measured by the LOAC sensor.

The variability of the relationship between LWC and RE is analyzed and discussed in Section 3.6.

3.4. Cloud Droplet Number Concentration (CDNC) The combination of Equations (3a) and (4) allows the estimation of the CDNC with the following equation: LWC = CDNC 4 3 (6) 3 π × ρl × Re where ρl is the volumic mass of the liquid water and Re is the effective radius of the drops. For our study, CDNC measured by the LOAC sensor (noted * in Table5) ranges from 54–108 cm −3. CDNC derived from the BASTA cloud radar data and Equation (6) ranged from 65–133 cm−3.

Table 5. Cloud droplet number concentration (CDNC) derived with Equation (6) for LWC and Re derived from Equations (3) and (5).

CDNC * Average Z Average CDNC Equation (4) (#/cm3) (min, max) (dBZ) (min, max) (#/cm3) −33.4 113 Flight 1. 6 January 2015 108 (−52.5, −20.1) (95, 166) −22.7 65 Flight 2. 19 December 2016 58 (−43.5, −14.8) (62, 97) −25.1 133 Flight 3. 3 January 2017 154 (−43.4, −11.5) (5, 155) * Measured by LOAC sensor. Atmosphere 2018, 9, 169 10 of 19

3.5. Liquid Water Closure According to Equation (3), we can derive the liquid water content (LWC) and so derive the liquid water path (LWP) according to Equation (7).

ZdBZ(z) −log 10(α) Z CTH Z CTH 10 β LWP = LWC(z)dz = 10 dz (7) Atmosphere 2018, 9, x FOR PEER REVIEWCBH CBH 10 of 18

For the two first flights, the HATPRO microwave radiometer retrieved LWP and hence it is For 6 January 2015, slope equals to 0.75, intercept is −0.7 g/m² and correlation coefficient is 0.83 possible to compare the integrated LWC derived from BASTA cloud radar and Equation (7) (Figure6). for 46 10-min samples. For 19 December 2016, slope equals to 0.95, intercept is +23 g/m² and For 6 January 2015, slope equals to 0.75, intercept is −0.7 g/m2 and correlation coefficient is 0.83 correlation coefficient is 0.91 for 35 10-min samples. This offset has been a posteriori corrected because for 46 10-min samples. For 19 December 2016, slope equals to 0.95, intercept is +23 g/m2 and correlation we have observed an offset of 23 g/m² for HATPRO LWP retrieval by comparison with a clear sky coefficient is 0.91 for 35 10-min samples. This offset has been a posteriori corrected because we have period some hours before the formation of the cloud, so this value has been subtracted before the observed an offset of 23 g/m2 for HATPRO LWP retrieval by comparison with a clear sky period some analysis. hours before the formation of the cloud, so this value has been subtracted before the analysis.

FigureFigure 6. 6.Liquid Liquid water water path path derived derived from Equationfrom Equation (7) versus (7) liquidversus water liquid path water measured path bymeasured HATPRO by microwaveHATPRO radiometermicrowave (MWR).radiometer (MWR).

The discrepancies of this relationship between LWP derived from Equation (7) and LWP The discrepancies of this relationship between LWP derived from Equation (7) and LWP measured measured by HATPRO microwave radiometer is directly linked with the validity of Equation (3) and by HATPRO microwave radiometer is directly linked with the validity of Equation (3) and will be will be discussed in the following Section 3.6. discussed in the following Section 3.6.

3.6.3.6. Discussion Discussion on on the the Validity Validity of of these these Relationships Relationships

3.6.1.3.6.1. Impact Impact of of Aspiration Aspiration Efficiency Efficiency InIn this this part part we we discussdiscuss thethe validity of of each each rela relationshiptionship depending depending on on the the capacity capacity of ofthe the in situ in situand and remote-sensing remote-sensing instrument instrument to characterize to characterize cloud cloud microphysics microphysics in fog in fog layers. layers. In InTables Tables 3–5,3– 5we, weshow show thethe range range of of variability variability for for Z Z measured measured by by the the cloud radar BASTABASTA butbut alsoalso for for LWC, LWC, Re Re and and CDNCCDNC derived derived with with Equations Equations (3), (3), (5) (5) and and (6), (6), respectively. respectively. The The main main limitation limitation of of this this method method is is the the tendencytendency of of the the LOAC LOAC sensor sensor to to collect collect the the biggest biggest droplets, droplets, which which lead lead to to drizzle and and . precipitation. ForFor the the three three tethered tethered balloon balloon flights, flights, we we observed observed reflectivity reflectivity ranges ranges between between−58 −58 and and− 6−6 dBZ dBZ andand 98% 98% of of data data with with Z < Z− 15< − dBZ15 dBZ (the (the final final 2% correspond 2% correspond to the to flight the onflight 6 January on 6 January 2015 around 2015 12:00around). The12:00). value The of Z value = −15 of dBZ Z = corresponds −15 dBZ corresponds to the limit betweento the limit the sedimentationbetween the sedimentation and drizzle characterized and drizzle bycharacterized bigger droplets by ofbigger several droplets hundreds of several of micrometers hundreds [ 11of ].micrometers These biggest [11]. drops These cannot biggest be collecteddrops cannot by thebe LOACcollected sensor by the due LOAC to the sensor low inlet due flowto the of low about inlet 2.5 flow L/min; of about the aspiration2.5 L/min; the efficiency aspiration is near efficiency 0 for theseis near types 0 for of these particles. types of particles. To better understand the impact of drizzle and dynamics on the droplet collection by the LOAC sensor, we apply the [8] methodology to derive the aspiration efficiency (AE) of a thin sampler in calm air and low velocity. For the test, we consider a temperature around 283.15 K, atmospheric pressure of 1013 hPa, particle volumic pass of 1000 kg/m3 with an inlet tube diameter of 8 mm with a sampling rate of 2.5 L/min. We quantified the relationship between the aspiration efficiency and the particle size ranging from 1–300 µm (Figure 7). We tested the sensitivity (1) to the external wind direction compared to the inlet, noted WDI; (2) to external wind speed compared to the inlet flow, noted inlet-relative wind speed (WSI); and (3) to the angle of inlet attack from the vertical, noted inlet angle of attack from the vertical (AIV).

Atmosphere 2018, 9, 169 11 of 19

To better understand the impact of drizzle and dynamics on the droplet collection by the LOAC sensor, we apply the [8] methodology to derive the aspiration efficiency (AE) of a thin sampler in calm air and low velocity. For the test, we consider a temperature around 283.15 K, atmospheric pressure of 1013 hPa, particle volumic pass of 1000 kg/m3 with an inlet tube diameter of 8 mm with a sampling rate of 2.5 L/min. We quantified the relationship between the aspiration efficiency and the particle size ranging from 1–300 µm (Figure7). We tested the sensitivity (1) to the external wind direction compared to the inlet, noted WDI; (2) to external wind speed compared to the inlet flow, noted inlet-relative wind speed (WSI); and (3) to the angle of inlet attack from the vertical, noted inlet angle of attack from the verticalAtmosphere (AIV). 2018, 9, x FOR PEER REVIEW 11 of 18

Figure 7. Sensitivity test on aspiration efficiency versus particle diameter for several configurations Figureof 7. inlet-relativeSensitivity testwind on direction aspiration (WDI) efficiency and speed versus (WSI), particle and angle diameter of inlet for attack several from configurations the vertical of inlet-relative(AIV). wind direction (WDI) and speed (WSI), and angle of inlet attack from the vertical (AIV).

For a lowFor a wind low wind speed speed of about of about 1 m/s 1 m/s and and an an inlet inlet orientedoriented to to the the vertical vertical (AIV (AIV = 0°, = 0blue◦, blue curve), curve), the droplet settling velocity drives the aspiration efficiency reaching 350% for particle size of 300 µm. the droplet settling velocity drives the aspiration efficiency reaching 350% for particle size of 300 µm. The aspiration efficiency is quasi constant at 100% until 100 µm. When the inlet angle of attack from The aspiration efficiency is quasi constant at 100% until 100 µm. When the inlet angle of attack from the vertical (AIV) equals 90° (horizontal tube, green curve), AE is 100% until 20 µm to reach 19% for ◦ µ the verticalparticle (AIV) size of equals 300 µm: 90 gravitational(horizontal settling tube, greencompetes curve), with AEinlet is aspiration 100% until and 20 LOACm to sensor reach is 19% for particleunable size to collect of 300 particlesµm: gravitational bigger than 500 settling µm. For competes an inlet withturned inlet away aspiration from the wind and LOAC(cyan curve), sensor is unablethe to aspiration collect particles efficiency bigger reaches than 0%500 for dropletµm. For size an of inlet 23 µm. turned When away the inlet from isthe faced wind to an (cyan external curve), the aspirationwind around efficiency 4 m/s reaches(black curve), 0% for the droplet aspiration size ofefficiency 23 µm. Whenincreases the from inlet 100% is faced (for toa anparticle external wind arounddiameter 4 of m/s 1 µm) (black to 370% curve), at 80 the µm; aspiration the external efficiency wind forces increases the particles from to 100% be collected (for a particle by the LOAC diameter of 1 µm)sensor. to 370% At the at opposite 80 µm; the extreme, external for winda similar forces exte thernal particles wind speed to be of collected 4 m/s with by an the angle LOAC of 90° sensor. At therelative opposite to extreme,the external for wind, a similar the aspiration external windefficiency speed drops of 4very m/s quickly with an to angle0% for of10 90µm.◦ relative to the Given these aspiration efficiency dependencies on wind direction, and that wind direction external wind, the aspiration efficiency drops very quickly to 0% for 10 µm. relative to inlet will vary a lot as the LOAC is turning and moving in the air, which curve we are on Given these aspiration efficiency dependencies on wind direction, and that wind direction relative will change with time and cause biases that are difficult to correct for. However, improvements to to inletthe will measurement vary a lot as setup the LOACcould reduce is turning this bias. and movingFor example, in the the air, inlet which tube curvecould webe made are on to will always change with timepoint and into cause the wind biases using that a arewind difficult vane. to correct for. However, improvements to the measurement setup could reduce this bias. For example, the inlet tube could be made to always point into the wind using a3.6.2. wind Variability vane. of Droplet-Size Distribution Figure 8 shows the particle-size distribution measured with LOAC sensor for the 19 December 2016, 3 January 2017 and 6 January 2015 along the tethered balloon path. We note a similar peak around 10 µm and a droplet distribution width depending on the case study, i.e., around 300, 100 and 30 #/cm3/µm at 30 µm of diameter for 19 December 2016, 3 January 2017, and 6 January 2015 respectively. This size distribution will have an impact on the aspiration efficiency of the in situ granulometer. The shape of the size distribution is also important for the theoretical Z-LWC relationship itself, because the LWC is much less sensitive to the biggest droplets than the reflectivity is. The variability of the size distribution during the fog life cycle therefore has an important impact on the Z-LWC [16]. In [26], using in situ measurements at 2 m, authors found important variability in the size distribution both between fog events and during the lifecycle of each event. Therefore, they recommended measurement of the size distribution continuously near the surface as well as vertical profiles in order to obtain more data.

Atmosphere 2018, 9, 169 12 of 19

3.6.2. Variability of Droplet-Size Distribution Figure8 shows the particle-size distribution measured with LOAC sensor for the 19 December 2016, 3 January 2017 and 6 January 2015 along the tethered balloon path. We note a similar peak around 10 µm and a droplet distribution width depending on the case study, i.e., around 300, 100 and 30 #/cm3/µm at 30 µm of diameter for 19 December 2016, 3 January 2017, and 6 January 2015 respectively. This size distribution will have an impact on the aspiration efficiency of the in situ granulometer. The shape of the size distribution is also important for the theoretical Z-LWC relationship itself, because the LWC is much less sensitive to the biggest droplets than the reflectivity is. The variability of the size distribution during the fog life cycle therefore has an important impact on the Z-LWC [16]. In [26], using in situ measurements at 2 m, authors found important variability in the size distribution both between fog events and during the lifecycle of each event. Therefore, they recommended measurement of the size distribution continuously near the surface as well as vertical profiles in order Atmosphere 2018, 9, x FOR PEER REVIEW 12 of 18 to obtain more data.

Figure 8. Particle size distribution measured with LOAC for 19 December 2016, 3 January 2017 and 6 Figure 8. Particle size distribution measured with LOAC for 19 December 2016, 3 January 2017 and January 2015 along the tethered balloon path. 6 January 2015 along the tethered balloon path.

3.6.3. Variability of Parametrical Relationships and Impact on Profiles 3.6.3. Variability of Parametrical Relationships and Impact on Profiles To evaluate the importance of the impact of the case-to-case variability of the empirical To evaluate the importance of the impact of the case-to-case variability of the empirical relationships, we can compare the fits from each of the three case studies on the same data. Figure 9 relationships, we can compare the fits from each of the three case studies on the same data. Figure9 shows the parametrical relationships between LWC (left) or Re (right) measured with LOAC sensor shows the parametrical relationships between LWC (left) or Re (right) measured with LOAC sensor and cloud radar reflectivity for the different case studies. For a reflectivity around −40 dBZ (−20 dBZ) and cloud radar reflectivity for the different case studies. For a reflectivity around −40 dBZ (−20 dBZ) LWC ranges from 0.03 and 0.06 g/m3 (from 0.2 to 0.7 g/m3). The validity of the LWC-Z relationship, LWC ranges from 0.03 and 0.06 g/m3 (from 0.2 to 0.7 g/m3). The validity of the LWC-Z relationship, is −50 to −15 dBZ for Z and 0.01 to 1 g/m3 for LWC; for Re-Z relationship, Re ranges from 1 to 11 µm is −50 to −15 dBZ for Z and 0.01 to 1 g/m3 for LWC; for Re-Z relationship, Re ranges from 1 to 11 µm and Z from −50 to −15 dBZ. and Z from −50 to −15 dBZ.

Figure 9. Parametrical relationship between LWC (right) or Re (left) and reflectivity for these three tethered balloon flights and previous studies (Atlas, 1954, Sauvageot and Omar, 1987, and Fox and Illingworth, 1997).

Figure 10 shows the vertical profiles of LWC, Re and CDNC for 19 December 2016 between 08:00 and 09:00 derived from Equations (3b), (5) and (6). Red curves correspond to coefficients adjusted using the data from 6 January 2015, the black curve using data from 19 December 2016, and the blue curve using data from 3 January 2017. The maximum difference between each model corresponds to the reflectivity maximum at 300 m agl. The LWC difference reaches 0.17 g/m3 (max at 0.28 g/m3 and min at 0.11 g/m3), the Re difference reaches 2.3 µm (max at 6.2 µm and min at 3.9 µm), and the CDNC difference reaches 300 #/cm3 (max at 500 #/cm3 and min at 200 #/cm3). For this case study, the liquid

Atmosphere 2018, 9, x FOR PEER REVIEW 12 of 18

Figure 8. Particle size distribution measured with LOAC for 19 December 2016, 3 January 2017 and 6 January 2015 along the tethered balloon path.

3.6.3. Variability of Parametrical Relationships and Impact on Profiles To evaluate the importance of the impact of the case-to-case variability of the empirical relationships, we can compare the fits from each of the three case studies on the same data. Figure 9 shows the parametrical relationships between LWC (left) or Re (right) measured with LOAC sensor and cloud radar reflectivity for the different case studies. For a reflectivity around −40 dBZ (−20 dBZ) LWC ranges from 0.03 and 0.06 g/m3 (from 0.2 to 0.7 g/m3). The validity of the LWC-Z relationship, is −50 to −15 dBZ for Z and 0.01 to 1 g/m3 for LWC; for Re-Z relationship, Re ranges from 1 to 11 µm andAtmosphere Z from2018 −50, 9to, 169 −15 dBZ. 13 of 19

FigureFigure 9. 9.ParametricalParametrical relationship relationship between between LWC LWC (right (right) or) orRe Re (left (left) and) and reflectivity reflectivity for for these these three three tetheredtethered balloon balloon flights flights and and previous previous studies studies (Atlas, (Atlas, 1954, 1954, Sauvageot Sauvageot and and Omar, Omar, 1987, 1987, and and Fox Fox and and Illingworth,Illingworth, 1997). 1997).

FigureFigure 10 10 shows shows the the vertical vertical profiles profiles of ofLWC, LWC, Re Re and and CDNC CDNC for for 19 19 December December 2016 2016 between between 08:00 08:00 andand 09:00 09:00 derived derived from from Equations Equations (3b), (3b), (5) (5) and and (6). (6). Red Red curves curves correspond correspond to tocoefficients coefficients adjusted adjusted usingusing the the data data from from 6 January 6 January 2015, 2015, the the black black curv curvee using using data data from from 19 19 December December 2016, 2016, and and the the blue blue curvecurve using using data data from from 3 January 3 January 2017. 2017. The The maximu maximumm difference difference between between each each model model corresponds corresponds to to 3 3 thethe reflectivity reflectivity maximum maximum at at 300 300 m m agl. agl. The The LWC LWC difference difference reaches reaches 0.17 0.17 g/m g/m 3(max(max at at 0.28 0.28 g/m g/m and3 and min at 0.11 g/m3), 3the Re difference reaches 2.3 µm (max at 6.2 µm and min at 3.9 µm), and the CDNC Atmospheremin at 0.11 2018 g/m, 9, x FOR), the PEER Re differenceREVIEW reaches 2.3 µm (max at 6.2 µm and min at 3.9 µm), and the13 CDNC of 18 3 3 3 differencedifference reaches reaches 300 300 #/cm #/cm (max3 (max at at500 500 #/cm #/cm and3 and min min at at200 200 #/cm #/cm). For3). For this this case case study, study, the the liquid liquid waterwater closure closure with with the the HATPRO HATPRO microwave radiometer described in Section Section 3.53.5 allowsallows us us to to validate validate thethe LWC LWC profile profile fitted fitted for the corresponding day (19(19 DecemberDecember 2016).2016).

Figure 10. Vertical profiles of LWC, Re and CDNC for 19 December 2016 between 08:00 and 09:00, Figure 10. Vertical profiles of LWC, Re and CDNC for 19 December 2016 between 08:00 and 09:00, derived from Equations (3b), (5) and (6) for the 3 pairs of fitted parameters. derived from Equations (3b), (5) and (6) for the 3 pairs of fitted parameters. 4. Comparison and Discussion of Two Stratus-Fog Events 4. Comparison and Discussion of Two Stratus-Fog Events 4.1. Vertical Profiles of Microphysical Properties on 6 January 2015 4.1. Vertical Profiles of Microphysical Properties on 6 January 2015 On 6 January 2015, a tethered balloon flight was performed during 6 h of a stratus-fog event as On 6 January 2015, a tethered balloon flight was performed during 6 h of a stratus-fog event as shown in Figure 11. 2D-color corresponds to the radar reflectivity and the black curve is the tethered shown in Figure 11. 2D-color corresponds to the radar reflectivity and the black curve is the tethered balloon trajectory (altitude versus coordinated universal time (UTC)). This 6-h flight is characterized balloon trajectory (altitude versus coordinated universal time (UTC)). This 6-h flight is characterized by two periods: one before 12:00 and one after 13:00, separated by one precipitation event. by two periods: one before 12:00 and one after 13:00, separated by one precipitation event.

Figure 11. Time series of cloud radar reflectivity on 6 January 2015 and tethered balloon flight trajectory in cloud layer (black markers).

In Figure 12, we show vertical profiles of liquid water content, effective radius and cloud droplet number concentration derived from LOAC (dark green), BASTA (orange), and SYRSOC algorithm (purple). For BASTA, we distinguish the coincident measurement with LOAC (dashed line), and the complete sampling during the period (solid line). LWC and Re are derived from BASTA with Equations (3) and (5) with corresponding coefficient in Tables 3 and 4. We consider a first period between 09:00 and 10:00, when only one cloud layer was present and the SYRSOC algorithm was applied. During this period, a complete ascent and descent between the surface and almost 300 m agl has been undertaken with the tethered balloon.

Atmosphere 2018, 9, x FOR PEER REVIEW 13 of 18 water closure with the HATPRO microwave radiometer described in Section 3.5 allows us to validate the LWC profile fitted for the corresponding day (19 December 2016).

Figure 10. Vertical profiles of LWC, Re and CDNC for 19 December 2016 between 08:00 and 09:00, derived from Equations (3b), (5) and (6) for the 3 pairs of fitted parameters.

4. Comparison and Discussion of Two Stratus-Fog Events

4.1. Vertical Profiles of Microphysical Properties on 6 January 2015 On 6 January 2015, a tethered balloon flight was performed during 6 h of a stratus-fog event as shown in Figure 11. 2D-color corresponds to the radar reflectivity and the black curve is the tethered balloonAtmosphere trajectory2018, 9 ,(altitude 169 versus coordinated universal time (UTC)). This 6-h flight is characterized14 of 19 by two periods: one before 12:00 and one after 13:00, separated by one precipitation event.

FigureFigure 11. 11.TimeTime series series of cloudcloud radar radar reflectivity reflectivity on 6 Januaryon 6 January 2015 and 2015 tethered and balloon tethered flight balloon trajectory flight trajectoryin cloud in layercloud (black layer markers). (black markers).

In FigureIn Figure 12, 12we, weshow show vertical vertical profiles profiles of of liquid liquid water content, content, effective effective radius radius and and cloud cloud droplet droplet numbernumber concentration concentration derived derived from from LOAC LOAC (dark (dark green), BASTABASTA (orange), (orange), and and SYRSOC SYRSOC algorithm algorithm (purple).(purple). For BASTA, For BASTA, we wedistinguish distinguish the the coincide coincidentnt measurement measurement with with LOAC LOAC (dashed line),line), andand the completethe complete sampling sampling during during the period the period (solid (solid line). line). LWC LWC and and Re areare derived derived from from BASTA BASTA with with EquationsEquations (3) and (3) and (5) (5)with with corresponding corresponding coefficient coefficient inin TablesTables3 and3 and4. We4. We consider consider a first a periodfirst period betweenbetween 09:00 09:00 and and 10:00, 10:00, when when only only one one cloud cloud layer waswas present present and and the the SYRSOC SYRSOC algorithm algorithm was was applied.applied. During During this this period, period, a complete a complete ascent ascent and and descent between between the the surface surface and and almost almost 300 m300 agl m agl hasAtmosphere beenhas been undertaken 2018 undertaken, 9, x FOR with PEER with theREVIEW the tethered tethered balloon. balloon. 14 of 18

FigureFigure 12. 12. VerticalVertical profile profile of LWCLWC( left(left),), Re Re (middle (middle), CDNC), CDNC (right (right) derived) derived from from LOAC, LOAC, BASTA, BASTA, and andSYRSOC SYRSOC algorithm algorithm between between 09:00 09:00 and 10:00and on10:00 6 January on 6 January 2015. Error 2015. bars Error on SYRSOCbars on profilesSYRSOC indicate profiles indicatestandard standard deviation deviation of the mean of the over mean the over 1-h period. the 1-h period.

Vertical profiles show a good agreement of CDNC in the center of the cloud. Re from SYRSOC agrees well with the BASTA profile, ranging from 4–8 µm. LOAC Re is lower, ranging from 2–5 µm. Large differences were found for LWC with an increase between cloud base height and cloud top height from 0.1–0.4 g/m3 for SYRSOC algorithm, whereas LOAC and BASTA retrievals do not reach 0.2 g/m3 During the 14:00 to 16:00 period shown in Figure 13, SYRSOC CDNC and Re profiles agreed very well with LOAC measurements in the lower half of the fog layer, where LOAC profiles were available. For BASTA, we distinguish the coincident measurement with LOAC (dashed orange line), and the complete sampling during the period (solid orange line). Both BASTA profiles overestimate Re and underestimate CDNC, compared to LOAC. BASTA LWC matches LOAC LWC very well for coincident measurements. The average BASTA LWC profile for the whole period is slightly higher, as is the SYRSOC LWC. Besides, there is an increasing difference with height, of the BASTA and SYRSOC LWC, above the cloud center.

Figure 13. Vertical profile of LWC (left), Re (middle), CDNC (right) derived from LOAC, BASTA, and SYRSOC algorithm between 14:00 and 16:00 on 6 January 2015. Error bars on SYRSOC profiles indicate standard deviation of the mean over the 2-h period.

Atmosphere 2018, 9, x FOR PEER REVIEW 14 of 18

Figure 12. Vertical profile of LWC (left), Re (middle), CDNC (right) derived from LOAC, BASTA, and SYRSOC algorithm between 09:00 and 10:00 on 6 January 2015. Error bars on SYRSOC profiles indicate standard deviation of the mean over the 1-h period. Atmosphere 2018, 9, 169 15 of 19 Vertical profiles show a good agreement of CDNC in the center of the cloud. Re from SYRSOC agrees well with the BASTA profile, ranging from 4–8 µm. LOAC Re is lower, ranging from 2–5 µm. Vertical profiles show a good agreement of CDNC in the center of the cloud. Re from SYRSOC Large differences were found for LWC with an increase between cloud base height and cloud top agrees well with the BASTA profile, ranging from 4–8 µm. LOAC Re is lower, ranging from 2–5 µm. height from 0.1–0.4 g/m3 for SYRSOC algorithm, whereas LOAC and BASTA retrievals do not reach Large differences were found for LWC with an increase between cloud base height and cloud top height 0.2 g/m3 from 0.1–0.4 g/m3 for SYRSOC algorithm, whereas LOAC and BASTA retrievals do not reach 0.2 g/m3. During the 14:00 to 16:00 period shown in Figure 13, SYRSOC CDNC and Re profiles agreed During the 14:00 to 16:00 period shown in Figure 13, SYRSOC CDNC and Re profiles agreed very verywell well with with LOAC LOAC measurements measurements in the lowerin the halflower of thehalf fog oflayer, the fog where layer, LOAC where profiles LOAC were profiles available. were available.For BASTA, For BASTA, we distinguish we distinguish the coincident the coinciden measurementt measurement with LOAC with (dashed LOAC orange (dashed line), orange and theline), andcomplete the complete sampling sampling during during the period the (solidperiod orange (solid line).orange Both line). BASTA Both profiles BASTA overestimate profiles overestimate Re and Reunderestimate and underestimate CDNC, CDNC, compared compared to LOAC. to BASTA LOAC. LWC BASTA matches LWC LOAC matches LWC LOAC very well LWC for very coincident well for coincidentmeasurements. measurements. The average The BASTAaverage LWC BASTA profile LWC for prof theile whole for the period whole is slightly period higher,is slightlyasis higher,the as SYRSOCis the SYRSOC LWC. Besides, LWC. thereBesides, is an there increasing is an difference increasing with difference height, of with the BASTA height, and of SYRSOCthe BASTA LWC, and SYRSOCabove the LWC, cloud above center. the cloud center.

Figure 13. Vertical profile of LWC (left), Re (middle), CDNC (right) derived from LOAC, BASTA, Figure 13. Vertical profile of LWC (left), Re (middle), CDNC (right) derived from LOAC, BASTA, and andSYRSOC SYRSOC algorithm algorithm between between 14:00 14:00 and 16:00 and on16:00 6 January on 6 January 2015. Error 2015. bars Error on SYRSOC bars on profilesSYRSOC indicate profiles indicatestandard standard deviation deviation of the mean of the over mean the over 2-h period. the 2-h period.

4.2. Vertical Profiles of Microphysical Properties on 19 December 2016 On 19 December 2016, another tethered balloon flight was performed between 06:00 and 08:00 but a second cloud layer at 1 km prevented the use of the SYRSOC algorithm, which requires single-layer clouds or fog. During this period, we compared the LWC calculated from LOAC (derived with droplet size distribution) and derived from BASTA reflectivity and Equation (3). We obtained a slope of 0.89, and intercept of 0.04 with a correlation factor about 0.78. After this 2-h period, the upper layer cloud stopped and SYRSOC profiles could be obtained. SYRSOC output are shown in Figure 14 (purple line) for comparison with coincident BASTA retrievals (orange line). Atmosphere 2018, 9, x FOR PEER REVIEW 15 of 18

4.2. Vertical Profiles of Microphysical Properties on 19 December 2016 On 19 December 2016, another tethered balloon flight was performed between 06:00 and 08:00 but a second cloud layer at 1 km prevented the use of the SYRSOC algorithm, which requires single- layer clouds or fog. During this period, we compared the LWC calculated from LOAC (derived with droplet size distribution) and derived from BASTA reflectivity and Equation (3). We obtained a slope of 0.89, and intercept of 0.04 with a correlation factor about 0.78. After this 2-h period, the upper layer cloudAtmosphere stopped2018, 9and, 169 SYRSOC profiles could be obtained. SYRSOC output are shown in Figure16 of 19 14 (purple line) for comparison with coincident BASTA retrievals (orange line).

FigureFigure 14. 14. VerticalVertical profile profile of of LWC LWC ( (leftleft),), Re Re ( middle),), CDNCCDNC (right(right),), derived derived from from BASTA, BASTA, and and SYRSOCSYRSOC algorithm algorithm between between 08:00 08:00 and and 09:00 09:00 on 19 DecemberDecember 2016.2016. ErrorError bars bars on on SYRSOC SYRSOC profiles profiles indicateindicate standard standard deviation deviation of of the the mean mean over over the 1-h1-h period.period.

ForFor this this period period we notenote a a good good agreement agreement of LWCof LWC up to up the to center the center of the cloud,of the where cloud, the where BASTA the BASTALWC profileLWC profile starts decreasing starts decreasing towards towards the cloud the top, cloud but thetop, SYRSOC but the LWCSYRSOC further LWC increases, further reaching increases, reaching0.35 g/m 0.353 near g/m cloud3 near top. cloud BASTA top. retrievals BASTA showretrievals a peak sh aroundow a peak 300 m around agl of 0.2 300 g/m m3 ,agl decreasing of 0.2 g/m to 3, decreasinga value of to 0.02 a g/mvalue3 atof 500 0.02 m g/m agl.3 The at 500 shape m ofagl. the The Re profile shapeis of well the represented Re profile byis well SYRSOC, represented but there by SYRSOC,is an offset but of there about is 2–4 an µoffsetm from of theabout BASTA 2–4 Reµm profile. from the The BASTA BASTA ReRe profileprofile. reaches The BASTA its maximum Re profile of reaches6 µm atits around maximum 300 mofagl. 6 µm At at the around same altitude, 300 m agl. SYRSOC At the Re same is 10 altitude,µm. On theSYRSOC other hand,Re is SYRSOC10 µm. On theCDNC other ishand, much SYRSOC smaller CDNC than BASTA is much CDNC smaller in the than center BASTA of the CDNC cloud (100in the #/cm center3 for of SYRSOC the cloud and (100 #/cm2003 #/cmfor SYRSOC3 for BASTA and 200 retrievals). #/cm3 for BASTA retrievals).

4.3.4.3. Discussion Discussion of ofSYRSOC SYRSOC Results Results TheThe cloud cloud base base in in any any fog fog layer layer is is at at ground ground level. However, asas stated stated before, before, BASTA BASTA has has a blinda blind zone in the lowest 40 m and a height range of incomplete overlap of outgoing radiation and receiver zone in the lowest 40 m and a height range of incomplete overlap of outgoing radiation and receiver field of view from 40 m to 240 m [2]. In the case of 19 December 2016, the cloud top was around 500 m. field of view from 40 m to 240 m [2]. In the case of 19 December 2016, the cloud top was around 500 That means nearly half of the fog depth was affected by reduced reflectivity. The fog layer observed m. That means nearly half of the fog depth was affected by reduced reflectivity. The fog layer in the morning of 6 January 2015 was less than 300 m deep. In this case, nearly the whole layer was observed in the morning of 6 January 2015 was less than 300 m deep. In this case, nearly the whole affected. Radar reflectivity was corrected from 120 m to 240 m. Below 120 m, reflectivity was assumed layer was affected. Radar reflectivity was corrected from 120 m to 240 m. Below 120 m, reflectivity constant, using an average value. This correction introduced a discontinuity in the profiles at 120 m. was assumedThe three constant, studied using periods an revealedaverage limitationsvalue. This of correction SYRSOC, introduced but also ways a discontinuity of improving in the the profilesalgorithm. at 120 Performance m. in fog was improved by correcting for the near field behavior of the cloud radar.The Anthree overall studied improvement periods revealed of SYRSOC limitations was the implementation of SYRSOC, but of an also entrainment ways of factor,improving taking the algorithm.into account Performance entrainment in offog dry was air atimproved the cloud by top, corr causingecting a for more the realistic near field shape behavior of the LWC of the profile, cloud radar.decreasing An overall at the improvement cloud top. However, of SYRSOC this was did the not implementation fully account for of deviations an entrainment in the BASTAfactor, taking and intoSYRSOC account LWC entrainment profiles. of An dry overestimation air at the cloud of LWCtop, causing by SYRSOC a more in realistic the top half shape of theof the fog LWC layer profile, was decreasingobserved at in the all casescloud studied top. However, here. SYRSOC this did produces not fully the account linear LWCfor deviations increase expected in the BASTA in water and clouds, modified at the top by the entrainment factor. However, the shape of the LWC profile in

fog depends on the phase in the fog lifecycle: formation phase, mature phase and dissipation phase. LWC gradients in fog can be positive, quasi-null or negative. This depends on a number of factors, like evaporation at the cloud top, precipitation or sedimentation at the cloud base, evaporation at the cloud base, and temperature and humidity gradients above the fog top. As the fog thickness is limited Atmosphere 2018, 9, 169 17 of 19 to some hundreds of meters, those competitive processes have a significant impact on the LWC profile throughout the fog layer. None of these factors are taken into account in SYRSOC, which explains differences between LOAC/BASTA and SYRSOC profiles, not only of LWC, but also of CDNC and Re.

5. Conclusions The robust dataset developed at the SIRTA site during three intensive operational periods when a tethered balloon was deployed allows us to derive vertical profiles of the low stratus and fog microphysical properties based on almost 200 5-min-periods. A methodology has been applied to normalize and validate the particle size distribution measured with the LOAC granulometer: a visible extinction closure has been undertaken by comparing the extinction coefficient measured by a diffusometer and derived from Mie theory applied to measured particle-size distribution. Correlation factors range from 0.73 to 0.93 for a dataset composed of more than 200 5-min-periods. As explained in Sections 2.3 and 3.5, the aspiration efficiency (i.e., 0% up to 350%) and the correlation between the “true” visible extinction and “measured particle-size distribution” (i.e., 0.59 up to 8.2) is correlated with the wind speed and wind direction relative to the inlet axis. A first relationship between the LWC (measured with the LOAC granulometer) and the Doppler Z dBZ −log 10(α) 10 cloud radar reflectivity (noted Z) has been established for our dataset: LWC = 10 β and, α ranges from 0.020 to 0.097 and β from 1.91 to 2.51 with an average reflectivity ranging from −33.4 to −22.7 dBZ leading to a LWC ranging from 0.07 to 0.19 g/m3. A second relationship between effective radius (Re) and Doppler cloud radar reflectivity has also been established, Re = 10(Z(dBZ)−δ)/γ with γ ranging from 52.0 to 69.2, δ from −69.2 to −80.7, for an effective radius Re ranging from 3.6 to 5.7 µm. The cloud droplet number concentration is deduced from these 2 equations, and average CDNC ranges from 13 to 113 cm−3. In the fourth section, we applied the SYRSOC algorithm to three fog periods when the tethered balloon was deployed and we compared the LWC, CDNC and Re vertical profiles. Overall, the SYRSOC CDNC and Re profiles agreed well with either LOAC in situ, or BASTA profiles, or both. An overestimation of LWC by SYRSOC in the top half of the fog layer was observed in all of the cases studied here. This is due to dominant processes in fog layers which are not accounted for in the cloud algorithm SYRSOC. The experiments carried out in this study confirm that the relationship between Z and LWC varies importantly from one fog event to another and that more continuous in situ measurements of the vertical profile of fog microphysics are needed. The amount of data from such measurements currently available is very limited, mainly because the tethered balloon measurements need to be carried out manually. One way to gain more continuous measurements would be to lift the instrument with an automatized drone rather than a balloon. This would allow not only measurement to be automated, but also the sensor to be kept more still in the air and to ensure that the air inlet always points in the direction of the wind, which we found in this paper to be an important issue to address in order to improve the quality of the retrievals.

Author Contributions: E.W. contributed in the experiments with the tethered balloon. J.D. and J.-B.R. analyzed the data on BASTA cloud radar and LOAC granulometer, respectively. J.P. and C.O. did the SYRSOC numerical simulations. J.-C.D. and M.H.designed and performed the experiment, analyzed the data and wrote the paper. Acknowledgments: The authors would like to thank the technical and computer staff of the SIRTA Observatory for taking the observations and making the data set easily accessible. The authors would like to acknowledge Meteo-France for providing CL31 data, the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 654109 for ACTRIS TransNational Access funding of Jana Preißler, and the Irish Environmental Protection Agency for her fellowship (2015-CCRP-FS.24). Conflicts of Interest: The authors declare no conflict of interest. Atmosphere 2018, 9, 169 18 of 19

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