Interactive comment on “ Evaluating the capabilities and uncertainties of droplet measurements for the fog droplet spectrometer ( FM-100 ) ”

Abstract. Droplet size spectra measurements are crucial to obtain a quantitative microphysical description of clouds and fog. However, cloud droplet size measurements are subject to various uncertainties. This work focuses on the error analysis of two key measurement uncertainties arising during cloud droplet size measurements with a conventional droplet size spectrometer (FM-100): first, we addressed the precision with which droplets can be sized with the FM-100 on the basis of the Mie theory. We deduced error assumptions and proposed a new method on how to correct measured size distributions for these errors by redistributing the measured droplet size distribution using a stochastic approach. Second, based on a literature study, we summarized corrections for particle losses during sampling with the FM-100. We applied both corrections to cloud droplet size spectra measured at the high alpine site Jungfraujoch for a temperature range from 0 °C to 11 °C. We showed that Mie scattering led to spikes in the droplet size distributions using the default sizing procedure, while the new stochastic approach reproduced the ambient size distribution adequately. A detailed analysis of the FM-100 sampling efficiency revealed that particle losses were typically below 10% for droplet diameters up to 10 μm. For larger droplets, particle losses can increase up to 90% for the largest droplets of 50 μm at ambient wind speeds below 4.4 m s−1 and even to >90% for larger angles between the instrument orientation and the wind vector (sampling angle) at higher wind speeds. Comparisons of the FM-100 to other reference instruments revealed that the total liquid water content (LWC) measured by the FM-100 was more sensitive to particle losses than to re-sizing based on Mie scattering, while the total number concentration was only marginally influenced by particle losses. Consequently, for further LWC measurements with the FM-100 we strongly recommend to consider (1) the error arising due to Mie scattering, and (2) the particle losses, especially for larger droplets depending on the set-up and wind conditions.


Introduction
The cloud droplet size distribution is one of the key parameter for a quantitative microphysical description of clouds (e.g.Pruppacher and Klett, 1997).It plays an important role for the radiative characteristic of the cloud and is, for example needed to describe the anthropogenic influence (Gunn and Philips, 1957;Twomey, 1977) and the cloud lifetime effect (Albrecht, 1989;Rosenfeld and Lensky, 1998).Moreover, the knowledge of droplet size distribution is crucial for a better understanding of the onset of precipitation (Gunn and Philips, 1957;Stevens and Feingold, 2009) as well as the occult deposition input of clouds to vegetation, which is known to be a relevant component in the hydrological budget of tropical mountain cloud forests (Bruijnzeel et al., 2005;Eugster et al., 2006).At this stage, there are two different approaches of measuring cloud droplet sizes: in-situ measurements using optical instruments on aircrafts or ground based stations (e.g.Knollenberg, 1981;Baumgardner, 1983;Baumgardner et al., 2003) and inverse retrieval techniques based on remote sensing measurements from satellites (e.g.Bennartz et al., 2011;Kokhanovsky and Rozanov, 2012).Although in-situ measurements have intrinsic difficulties, they are considered to be the best available method for measuring cloud droplets (Miles et al., 2000).The basic working principle for the size detection used in these devices is forward scattering of light, which was first mathematically solved by Gustav Mie (Mie, 1908).The first commercial available optical instrument for in-situ droplet measurements was build in the 1970s (Pinnick and Auvermann, 1979).The instruments have been developed further and their performance has been strongly improved in terms of precision and automatization since then.Today, a variety of instruments based on forward scattering are in use: the Forward Scattering Spectrometer Probe (FSSP; capable of measuring hydrometeors with diameters D = 2 to 50 µm, e.g.Pinnick and Auvermann, 1979), the Cloud Droplet Probe (CDP; Model CDP-100, D = 2 to 50 µm, e.g.McFarquhar et al., 2007), the Cloud and Aerosol Spectrometer -also with Depolarization CAS-DPOL -(CAS and CAS-DPOL; D = 0.5 to 50 µm, Baumgardner et al., 2011), the Cloud Particle Spectrometer with Depolarization (CPSD; D = 0.5 to 50 µm, Baumgardner et al., 2011), the Small Ice Detectors (SID model 1 and 2; D = 2 to 140 µm, Baumgardner et al., 2011) and the Fog Monitor 100 (FM-100; D = 2 to 50 µm, e.g.Burkard et al., 2002).Using light scattering interferometry, cloud droplets can also be measured in size, for example with the Phase Doppler Interferometer (PIP; 1 to 1000 µm, Baumgardner et al., 2011).However, for realistic operations a reasonable upper-bound was found to be D ≈ 100 µm (Chuang et al., 2008).Furthermore, imaging techniques can be used to capture the cloud's particle images.Beyond others, a Cloud Particle Imager (CPI; SPEC Inc. Model 230X, Connolly et al., 2007) can be deployed to observe and record real-time CCD images (8-bit, gray-scale 1024 × 1024 pixels with a pixel resolution of 2.3 µm) of the ice particles and supercooled droplets with D = 10 to 2300 µm present in the clouds.From these images, the ice crystal number and mass concentration can be determined.The two main groups are passively ventilated instruments, which are mainly installed on aircrafts (e.g.Lance et al., 2010) and actively ventilated instruments, which are mainly used for ground based or tower based measurements (e.g.Burkard et al., 2002;Eugster et al., 2006).In-situ measurements are very challenging due to various difficulties recently discussed for aircraft devices by Lance et al. (2010) and Baumgardner et al. (2011) and for the FSSP in general by Baumgardner (1983) and Baumgardner et al. (1992).
In this paper, we will focus on the Fog Monitor 100 (DMT FM-100, Droplet Measurement Technologies, Boulder, CO, USA), which is a ground based instrument with an active ventilation.We will present a detailed error analysis of two topics influencing the droplet measurements of this device: droplet sizing precision and particle losses.The question whether Mie scattering could be responsible for special features in measured droplet size distribution, for example causing false bimodal size distributions is a common known problem for optical particle counters (e.g.Jaenicke, 1993;Baumgardner et al., 2010).In a first step, we will therefore evaluate how Mie scattering could influence the droplet size spectra collected with the FM-100 and propose a new procedure to reprocess already measured data.Second, we will evaluate droplet losses during sampling with the FM-100, and in a third step, apply both corrections to cloud droplet spectra collected during the CLACE 2010 (the CLoud and Aerosol Characterization Experiment 2010) campaign, performed at the Jungfraujoch (JFJ) in the Swiss Alps.Based on these campaign data, we will provide recommendations on how to improve the measurement quality in future instrument deployments with the FM-100.This is to the best of our knowledge the first work not only mentioning the errors but also proposing a suitable correction procedure, which can be applied to the data after sampling.
The paper is structured such that we first present the measurement site as well as the FM-100 and the instruments used for validation (Sect.2) which is followed by a methodology section (Sect.3), focusing on the proposed sizing and particle loss corrections as well as the implementation of both corrections for the data collected at the JFJ (Sect.4).Finally, we will end with a discussion of the effects of the proposed corrections and provide recommendations how to improve the measurement quality in future instrument set-ups.

Instrumentation and site
The study to validate and compare the FM-100 with other instruments was performed in the frame of CLACE 2010, which took place at the Jungfraujoch (JFJ, 46 • 32 N, 7 • 59 E) situated in the Bernese Alps at 3580 m a.s.l., Switzerland (Fig. 1).Several intensive cloud characterization experiments have been conducted there for many years at different times of the year (e.g.Mertes et al., 2007;Verheggen et al., 2007;Cozic et al., 2008;Targino et al., 2009;Kamphus et al., 2010;Zieger et al., 2012).The aerosol measurements performed at the JFJ are part of the Global Atmosphere Watch (GAW) program of the World Meteorological Organization since 1995 (Collaud Coen et al., 2007).Long term studies have been conducted at the site, which indicated that the station is in clouds approximately 40 % of the time throughout the year (Baltensperger et al., 1998).CLACE 2010 took place in June-August 2010 (temperature range: −11 to 11 • C) and its main aims were to obtain an in-depth chemical, optical and physical characterization of the aerosols at the JFJ as well as to investigate the interaction of aerosol particles with cloud droplets for improving the understanding of the aerosol direct and indirect effects.by the user.Channel thresholds and diameters are provided by the manufacturer for 10, 20, 30 and 40 channels, but can be defined by the user as well.Simultaneously, the temperature as well as the sampled air volume is measured.A sketch of the working principle of the FM-100 is shown in Fig. 2. A pump pulls ambient air through the wind tunnel of the instrument.First, the droplets reach the sizing region, where they pass a laser beam (wavelength λ = 658 nm).The light which is scattered forward within approximately 3 • to 12 • from the beam direction is collected and directed to an optical splitter and then to a pair of photodetectors.These collectors translate the scattered radiance into a voltage pulse.Under the assumption that there are no saturation effects, the pulse height is proportional to the scattered light intensity.For correct sizing one needs to assure that the detected particle was inside the depth of field (DOF) of the instrument, which is the uniform power region of the laser.To qualify a particle for sizing (meaning that the voltage from the sizer is saved for further processing) the two photodetectors are needed.The scattered light is split by the prism, such that one third is directed to the sizer and two thirds to the qualifier.The qualifier only records radiance that passed the optical mask in front of the detector.If the scattering particle was inside the DOF, the scattered signal of the qualifier exceeds the scattering signal of the sizer.For qualified particles the sizer voltage is directly proportional to the scattered radiance into the solid angle with an inner opening angle of 3 • to 4 • and an outer opening angle of around 12.0 • to 12.6 • (see Fig. 2).The scattered radiance is described by the scattering cross section, which can be calculated using Mie theory (Mie, 1908).The exact values of the scattering angles needed for the Mie calculations differs among instruments.Additionally, they depend on where exactly the particle passes the laser beam (Lance et al., 2010).They need to be derived from glass bead cal- ibrations followed by Mie calculations to find the solid angle that fits best to the calibration results (D. Baumgardner, Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de Mexico, Mexico City, Mexico, personal communication, 2010).They are therefore one of the sources of uncertainty of the FM-100 that will be addressed in this paper.For further details on the electronic part of the FM-100, we refer to Droplet Measurement Technologies (2011).
Behind the sizing region there is a pitot tube measuring the air speed in the tunnel.The air speed (which is the traveling velocity of the droplets) is needed in order to determine the sample volume to infer number concentrations and liquid water content per volume from the measured droplet numbers.Technical specifications are summarized in Table 1.
A series of parameters can be derived from the measured droplet number size distribution such as total droplet number concentration (N FM ), and total liquid water content (LWC FM ).In this work we will use N FM (cm −3 ) which is defined as and the LWC FM (in mg m −3 ) which is calculated based on the assumption that the droplets are spherical: where i max is the number of channels used, ρ H 2 O is the density of water in kg m −3 , D i the geometric mean diameter of each channel in µm, and n i the droplet number concentration per channel in cm −3 as derived from the sizer signal.The FM-100 has been used in several ground based studies so far especially as part of an eddy covariance system to quantify fog water deposition fluxes in tropical mountain cloud forests (e.g.Eugster et al., 2006;Holwerda et al., 2006;Beiderwieden, 2007;Beiderwieden et al., 2008;Schmid et al., 2010), in temperate ecosystems (Burkard et al., 2002;Thalmann, 2002;Burkard, 2003), and deposition fluxes in rather arid areas (Westbeld et al., 2009).It has also been used as a single instrument for microphysical studies of fog (Gonser et al., 2011;Liu et al., 2011) and compared to other devices (Holwerda et al., 2006;Schmid et al., 2010;Frumau et al., 2011).Most of the presented work used the channel configuration defined by the manufacturer in order to translate the voltage to a droplet size; while Niu et al. (2010) used the 20 channel configuration, which is the one that is used by the manufacturer to calibrate the instrument, some of the authors (Burkard et al., 2002;Eugster et al., 2006;Beiderwieden, 2007;Beiderwieden et al., 2008;Westbeld et al., 2009;Frumau et al., 2011) used the 40 channel configuration in order to obtain a better resolved size distribution.A different approach was taken by Gonser et al. (2011) -which is one of the most recent publications -who defined their own 23 channel sizes and widths by using Mie curves prior to sampling.Such a procedure has already been suggested earlier for the FSSP (Pinnick et al., 1981;Dye and Baumgardner, 1984).Nevertheless, this has not been the standard procedure for the FM-100 so far.Here, we will propose a similar procedure that can be applied after sampling.
The FM-100 was installed on the NW corner of the upper terrace of the observation platform (Sphinx station, Fig. 1) and the inlet was turned into the mean wind direction (323 • ) as was expected for June/July conditions based on a dataset from MeteoSwiss from 1990 to 2009.For the second part of the campaign, the device was inclined and a horizontal angle of 293 • and a vertical angle of −25 • were chosen in order to account for the pronounced upwind aspiration at this site.

Aerosol inlets
For the collection of aerosols an interstitial and a total inlet were installed at a fairly undisturbed place on the roof of the observation laboratory at the Jungfraujoch (Fig. 1).The interstitial inlet was installed for collecting particles smaller than 2 µm.It uses an aerodynamic size discriminator without heating (Henning et al., 2002).Thus, all non-activated particles pass this inlet.The total inlet samples all particles smaller than 40 µm at wind speeds up to 20 m s −1 (Weingartner et al., 1999).Hence, the heated total inlet samples cloud droplets and non-activated (interstitial) aerosols.The condensed water on the cloud droplets and aerosols is evaporated by heating up the total inlet to +20 • C (Henning et al., 2002).

PVM-100: Particulate Volume Monitor
The Particulate Volume Monitor (PVM-100, Gerber Scientific Instruments Inc.) is an open path optical instrument that   , 2011).Cloud droplets (blue dots) are pulled through the wind tunnel at constant speed (True Air Speed = TAS) and pass the laser beam.The scattered light (red) from the particle is directed through the optical system and then detected by the qualifier and sizer.The inner and outer opening angle depend on the individual instrument and the position where exactly the droplet passed the laser beam.
measures the light scattered in the forward direction of all abundant particles in the sample volume.A detailed description can be found in Gerber (1991) and Arends et al. (1994).The PVM-100 was installed on the eastern side of the sphinx roof (Fig. 1).Based a PVM-100 intercomparison during an earlier campaigns, we do not expect any considerable differences in the LWC measurements due to the different locations at the building.The PVM-100 needs calibration in order to translate the scattering signal into an LWC.The instrument was periodically calibrated with a calibration disk provided by the manufacturer.Particles with a diameter of 3 to 45 µm are taken into account and the calibration is valid for an LWC range from 0.002 to 10 g m −3 and a measurement accuracy of 15 % (Allan et al., 2008).The LWC measured by the PVM is hereafter referred to as LWC PVM .

Dew point hygrometer
The PVM-100 as well as the FM-100 both measure the LWC of a cloud using a similar optical method.In order to get another estimate of the LWC that is independent of potential problems associated with light scattering techniques, we computed the condensed water content (CWC) of the cloud with a simple thermodynamic method based on the following assumptions: First, we assume that the cloud is liquid (no ice crystals).So the CWC is equivalent to the LWC of the cloud.Second, we assume that the water vapor pressure can be described by the ideal gas law, which is fulfilled for atmospheric conditions.Third, the cloud is saturated (= relative humidity 100 %).The first criterion is fulfilled in warm fog events, which we select via a temperature threshold of 0 • C for our analysis.By taking the ambient temperature measured by the SwissMetNet station (operated by MeteoSwiss) the corresponding saturation vapor pressure for water can be calculated during cloud events.Using the ideal gas law equation and under the assumption of 100 % RH the water content in the vapor phase can be deduced (VWC).Simultaneously, we measured the dew point temperature with a high accuracy dew point hygrometer (Dewmaster, Edgetech West Wareham, Massachusetts, USA; precision ±0.1 • C) after the ambient air has passed a heated inlet.Thus, the air reaching the dew point hygrometer contains all the water present in the ambient air (i.e. the evaporated droplets and gas phase).Hence, by calculating the equilibrium pressure at the dew point we can deduce the total amount of water (TWC) of the ambient air parcel using the ideal gas law.The CWC of the ambient air parcel is then: CWC = TWC − VWC.

Scanning Mobility Particle Sizer (SMPS)
Behind both inlets Scanning Mobility Particle Sizer (SMPS) systems were used to measure the number size distributions of the total and the interstitial aerosol between 17 and 900 nm (dry) diameter (Verheggen et al., 2007).The SMPS system behind the total inlet consisted of a Differential Mobility Analyzer (DMA, TSI 3071) and a condensation particle counter (CPC, TSI 3022A).The other SMPS system behind the interstitial inlet consisted of a DMA (TSI 3071) and a CPC (TSI 3775).During cloud-free conditions the response of the total and interstitial inlets should be identical.The interstitial size spectrum was corrected towards the total spectrum by a size-dependent correction factor for the small systematic difference in concentration between the two inlets (interstitial up to 25 % lower than total for particles smaller than 30 nm, concentrations within 5 % for larger particles), as particle losses were expected to be higher in the interstitial inlet, due to a longer residence time in the sampling line.The integration of the respective distribution gives the total number concentration of the total (N tot ) or non-activated aerosols (N int ).The difference (N tot-int ) is the number concentration of the cloud droplets and can be compared to the number concentration of cloud droplets measured by the FM-100.The methodological accuracy of the SMPS number size distributions was ± 10 % in concentration for particle diameters larger than 20 nm and ± 20 % for smaller particles, respectively.Based on the cross-comparison of the two SMPS systems, the precision in N tot-int (= N cr for number concentration of cloud residuals later on) was estimated to be ± 50 cm −3 .

Ultrasonic anemometer
The wind field around the FM-100 has an important influence on the data quality of the FM-100.Therefore, a HS ultrasonic anemometer (Gill Ltd., Solent, UK) was installed at 1.7 m away from the FM-100.The ultrasonic anemometer was run together with the FM-100 using an in-house data acquisition software (Eugster and Plüss, 2010) recording data at 12.5 Hz.Thus, microphysical processes can be studied at a high temporal resolution.3 Methods: sizing and counting corrections for the FM-100

Corrections for the size detections of the FM-100 due to Mie theory
In order to deduce the size of each droplet from the measured signal, the scattering cross section (see Fig. 3; Mie curves are shown in gray) needs to be inverted.As this curve is highly non-monotonic, this is not a trivial task.This is an inherent problem of all types of optical particle counters as seen by many previous studies (e.g.Pinnick et al., 1981;Dye and Baumgardner, 1984;Rosenfeld et al., 2012).The manufacturer solved this problem as follows: the Mie curves were smoothed (by applying a running average) to an extent that yielded a monotonic function and then attributed four different channel ranges to it: 10, 20, 30 and 40 (D.Baumgardner, personal communication, 2010).So the user can decide whether to use 10, 20, 30 or 40 channels.This procedure does not account for sizing ambiguities, i.e. a particle with a diameter of around 3 µm has a similar scattering cross section as a particle with a diameter of around 8 µm.With this default configuration, the signal of both the 3 and the 8 µm particle are interpreted as a particle of 5 µm.In Fig. 3, the pink boxes show the 40 channels that have been deduced in the described way for the used FM-100.The default channels varied between 0.19 µm (first channel) and 2.13 µm in channel width with a mean value of 1.21 µm (see Table 2 for more details).We will refer to these channels later on using the term default channels (with geometric mean diameters D dft ), and the LWC derived from this configuration we will be referred to as LWC dft .Throughout this text we will use the following terms: each channel is defined by a lower and an upper margin for the pulse amplitude, which we will later on refer to b low and b up (see Fig. 3 for details).b up − b low will be referred to as "channel height", i.e. with the term "channel width", we refer to the droplet diameter range that is covered by this channel.
In the next section, we suggest two approaches on how to take the Mie curve variations for sizing into account: one by using channels that are wide enough to cover the Mie variations (Sect.3.1.1)and another to obtain a new size dis-tribution by redistributing the measured counts per channel (Sect.3.1.2).

Widening of the size bins of the FM-100 and error calculations
Redefining channel limits as well a combining channels to remove the ambiguity in sizing has been suggested for different optical particle counters by previous studies (e.g.Pinnick et al., 1981;Dye and Baumgardner, 1984).However, to the extend of our knowledge, none of them proposes overlapping channels (as presented in this section) or the use of a stochastic approach (next section) in order to retrieve the droplet size distribution from the measured signal.
The procedure to derive new channels is as follows: in a first step we made Mie calculations for the optical system using an algorithm further developed from Mätzler (2002) which in turn is based on the work by Bohren and Huffman (1983).The derivation of the scattering cross section as well as detailed calculations can be found in the corresponding literature (e.g., Mie, 1908;Van de Hulst, 1981;Bohren and Huffman, 1983;Liou, 2002).The inner and outer angles of the scattering cone (see Fig. 2) were not clearly determined during manufacturing of the FM-100 (= instrumentation uncertainty) and hence needed to be estimated via glass bead calibrations.Additionally, these angles also depend on where exactly the droplet passes the laser beam (= spatial uncertainty).We therefore did several Mie calculations starting with a cone with an inner opening angle of 3 • and an outer opening angle of 12 • .By increasing the angles stepwise by 0.1 • to 4 • for the inner angle and 12.6 • for the outer angle, we obtained a set of Mie curves that represents the scattering cross sections of the droplets including instrumental and spatial uncertainty (see Fig. 3; the maximum and minimum of this Mie curve set are shown in dark gray).We then translated this Mie band into a voltage as it is done in the FM-100 electronics by assuming a linear relationship between scattered light intensity and voltage signal and setting the scattering cross section of a 50 µm particle equal to 4096 mV (D.Baumgardner, personal communication, 2010).In a second step, we used the Mie band to reassign new droplet diameters to each of the channels.In the following we will use the values for channel 5 for illustration (inset Fig. 3).As the FM-100 only determines whether a particle was detected in a certain channel while the exact light scattering signal is not recorded, we had to keep the channel boundaries b low (149 mV) and b up (192 mV) as they were configured during the measurements.Hence, for each channel we searched the lowest droplet diameter that still yielded a voltage signal within the height of the respective channel.b low intersects the Mie band at different diameters D low (= 3.32 to 3.66 µm and 4.86 to 5.22 µm and 6.48 to 7.50 µm, see inset Fig. 3 for details).The minimum of the set of D low is the minimum diameter of this channel (D min = min {D low } = 3.32 µm).Similarly, the maximum diameter D max corresponding to this channel was derived by taking the maximum of the set of D up (D max = max D up = 9.84 µm).From the geometric mean (D geo = 6.27 µm) of the minimum and the maximum, we then obtained the new droplet diameter to be assigned to this channel.We then repeated this procedure for all other channels.By doing this we obtained three monotonic curves that can be easily inverted and used to evaluate the signal: the geometric mean curve, as a mean estimate for the size distribution, the minimum and the maximum as a lower and upper estimate for the size distribution, respectively.In that way the channels (later on referred to as Mie channels) became wider and therefore overlap, with channel width varying from 1.44 µm to 6.52 µm with a mean channel width of 4.21 µm (see Table 2 for more details).However, the differences of the geometric means (D dft , black bar in the pink boxes for the default channels, and D geo green crosses for the Mie channels in Fig. 3) between the two configurations was always smaller than 1.32 µm (see Table 2).Out of the maximum 40 channels, 21 channels were smaller with the default channel configuration than the Mie channel configuration and 19 channels were wider.This way of translating the voltage signal has the advantage that it also provides the uncertainty of the droplet sizes associated with the Mie scattering, but at the expense of clear channel separation.The LWC derived using the mean channels will hereafter be referred to as LWC geo , the one us-ing the maximum curve as LWC max and the one using the minimum curve as LWC min .

Retrieving a new droplet size distribution using probability density functions
With the method above it is possible to retrieve an appropriate maximal error assumption for the LWC.However, the FM-100 was mainly designed for measuring droplet size distributions.The question arises on how to retrieve a size distribution for channels which overlap.In this section we therefore present a new method on how size distributions that account for Mie scattering can be deduced from measured distributions.We consider this new approach to be the best way of dealing with the Mie uncertainties with respect to overlapping channels.Due to the channel overlap an adequate size distribution could be achieved by redistributing the number counts per channel over an adequate channel width.For this purpose we had a closer look at the channels, which were defined in the previous section.The procedure will be explained in the following using channel 5 as an example (Fig. 4c and f).Channel 5 ranged from D min = 3.32 µm to D max = 9.84 µm (see Fig. 3 inset).The Mie band of channel 5 was not uniformly distributed along the channel width (Fig. 4c), e.g.droplets between 3.64 µm and 4.86 µm as well as between 8.04 µm and 9.12 µm did not produce a scattering signal that fell into this channel height.On the other hand, droplets between 6.76 µm and 7.48 µm covered the entire channel height with their scattering signal.So if a scattering signal between 149 and 192 mV is detected, it is more likely that it came from a droplet that has a size between 6.76 µm and 7.48 µm than 3.64 µm and 4.86 µm.To account for this, we calculated a probability density function based on the Mie band that represents the contribution of each droplet size to the scattering signal within the channel.It includes the assumption that each scattering cross section within the Mie band is equally probable, which we consider to be a reasonable first approximation.For the redistribution, the measured number concentration was multiplied with the normalized probability density function leading to a stochastic assumption of the droplets that could have produced the according scattering signal.The procedure was as follows: First, discrete probability density functions (PDF i (D)) for each channel (i) were deduced from the Mie band.Each channel was divided in D R = 0.02 µm intervals from D min to D max .For each diameter D, the percentage of the Mie band relative to the pulse amplitude height (b up − b low ) of the channel was calculated: This resulted in a curve from D min to D max , which was 1 if the pulse covered the entire channel height.Second, this discrete probability density function was normalized (Fig. 4c to f) such that Third, the amount of droplets measured per channel N i was redistributed from D min to D max based on the normalized probability density function.This was done for every channel leading to a discrete droplet number distribution n * with a resolution of D R = 0.02 µm: In order to account for uncertainties (such as the equally probable Mie band or slightly different opening angles), a new droplet size distribution based on bins with the same size D should be retrieved (n PDF,aµm refers to channels with bin size D = a µm).The liquid water content based on this method will be referred to as LWC PDF,aµm .This procedure was applied to one minute mean values of the collected cloud droplet spectra from CLACE 2010.

Particle losses
While measuring droplets, one is facing the problem that cloud droplets are rather heavy and therefore are influenced by their inertia and gravity.Hence, depending on their size and volume, they do not necessarily follow exactly the same trajectories as gas molecules would.This means that there is a potential for particle losses during sampling from ambient air (sampling efficiency, η smp (D)) and during transport through the system (transport efficiency, η tsp (D)).One way of assessing this issue is to simulate particle transport through a system using computational fluid dynamics (CFD).Another approach is to use experimentally and theoretically derived formulas for different loss mechanisms within the different tube sections in order to calculate the overall efficiency.As CFD calculations are very time-consuming, we will therefore use the second approach for particle losses in the FM-100 as a first estimate.
In general, the efficiency η is the fraction of the number concentration of droplets downstream of the loss mechanism and the droplet number concentration upstream.The fraction of particle losses is then 1 − η.The product of the sampling and the transport efficiency is the inlet efficiency η tot , which describes the performance of the sampling device (von der Weiden et al., 2009).Sometimes the efficiencies are named differently, (e.g. in Brockmann, 2011).Nevertheless, throughout this text we will adhere to terms used by von der Weiden et al. ( 2009): In general, different particle loss mechanisms contribute to the losses in the two parts of the measurement system.An overview of the different mechanisms was given, e.g. by von der Weiden et al. (2009).Here, we will only discuss the mechanisms which are relevant for the FM-100 (see Fig. 5 for illustration): aspiration losses η asp , transmission losses η trm , sedimentation losses η grav inside the FM-100, losses due to eddy formation η turb inside the FM-100, and inertial losses in the contraction η cont .In the following we shortly introduce sampling and transport losses and refer to the Appendix A for a detailed presentation of the used formulas.

Sampling losses
During ideal sampling conditions, the sampling is isoaxial and isokinetic (Brockmann, 2011).Isoaxial means that the sampling inlet has no inclination with respect to the surrounding wind direction.The term isokinetic sampling indicates that the sampling speed (U ) is equal to the surrounding wind speed (U 0 ).If the sampling speed is smaller than the ambient wind speed, the term sub-kinetic sampling is used, while for U > U 0 the term super-kinetic sampling is used.It will be used in the following for the turbulent as well as for the laminar regime as it has been done by others before (von der Weiden et al., 2009;Brockmann, 2011).Values for the FM-100 geometry are given in Table 1.Detailed description of the formulas of the particle loss mechanisms are given in Appendix A.
Both regimes need to be taken into account when setting up an inlet system and where and how to position the instrument (Brockmann, 2011).One way of addressing the isoaxial sampling is to put the instrument onto a turntable and letting it continually turn into the main wind direction as done by Vong (1995), Kowalski et al. (1997), Kowalski (1999), Wrzesinsky (2000), Burkard et al. (2002), Thalmann (2002), Burkard (2003), Eugster et al. (2006), andHolwerda et al. (2006).Nevertheless, these procedures do not assure isokinetic sampling conditions.Westbeld et al. (2009) and Liu et al. (2011) also installed the FM-100 in a fixed position for the entire measurement campaign.They established a quality criterion, by only accepting data as good data if the horizontal wind direction does not differ by a certain degree from the actual inlet orientation.Westbeld et al. (2009) used ± 30 • of the hourly mean wind direction and Liu et al. (2011) used ± 7 • for this criterion.However, a clear justification why they chose these angles was not given.Instead of excluding any data immediately, we suggest to calculate the sampling efficiency for the FM-100 in order to estimate the losses and correct for those.The sampling efficiency η smp is defined as the fraction of particles of interest (for the FM-100: the droplets), which reach the sampling probe from the surrounding air and successfully penetrate into the transport tubing.In general, the sampling efficiency itself consists of two different contributions: The aspiration efficiency η asp is the ratio of the number concentration of particles that enter the sampling probe cross section to the number concentration of particles in the ambient air (von der Weiden et al., 2009;Brockmann, 2011).
For the FM-100 we calculate the aspiration efficiency for the three different velocity regimes: (1) calm air (surrounding wind velocity U 0 < 0.5 m s −1 ), (2) slow moving air (0.5 m s −1 ≤ U 0 ≤ 2.18 m s −1 , which corresponds to a velocity ratio R v = U 0 /U of up to 0.5; with inlet velocity U ), and (3) moving air (velocity ratio R v = 0.5 to 2) and different angle regimes.Details on the used formulas are given in the Appendix A1.
The transmission efficiency (η trm ) is the ratio of particle concentration exiting the inlet to the particle concentration just past the inlet face (formulas are given in the Appendix A2).

Transport losses η tsp (D)
In contrast to the sampling losses, the transport losses do not depend on the flow conditions outside the sampling device.The transport losses are described by the transport efficiency of the tubing system which is the ratio of the number concentration of particles leaving the tubing system divided by the particles entering the tubing system.As different loss mechanisms happen in the transport system, the overall transport efficiency of a tubing system is the product of the all particle loss mechanisms for all tubing sections (Brockmann, 2011): where η sec,mech are the different loss mechanisms per section.
In the FM-100 there is a two-part tubing section: the contraction zone of 16 cm length and the wind tunnel with constant diameter with a length of 10 cm (see Fig. 5).For both parts we calculated transport losses due to sedimentation η grav and turbulent inertial deposition η turb as well as inertial losses in the contraction part η cont .Detailed formulas are given in the Appendix A3.

Application of the corrections for particle losses to the FM-100
The described efficiencies were calculated numerically from the minimal diameter to the maximal diameter in 0.1 µm steps for each channel.Then we took the mean value of all these efficiencies and attributed them to each channel such that we get one efficiency for each channel.For the default channel configuration as well as for the channels based on the density distribution method, we did the efficiency calculation for each channel separately, using the according geometric mean values.
For Stokes numbers smaller than the validity range of the correcting formulas (aspiration, transmission and inertial deposition efficiency in the contraction), we applied the proposed formulas as they yielded efficiencies close to 1.This would be an appropriate description as we assume that the particles are small enough to follow the same trajectory as gas molecules.
The used formulas are valid for constant gas velocities (Brockmann, 2011).To conform with these assumptions as closely as possible, we calculated the efficiencies for 1-min intervals, with approximately constant wind velocity.As we basically only have anisoaxial sampling, we only used formulas for the anisoaxial regime.
Unfortunately, the proposed equation for the calm flow regime (Eq.A4) is not valid for the second part of the CLACE 2010 period, when the FM-100 was installed with its inlet facing downwards (zenith angle φ = 115 • ).Though, Grinshpun et al. (1993) only excluded angles larger than 90 • because it was not common to use an inlet facing downwards.However, V ts U cos φ correctly describes the sedimentation even if the zenith angle is larger than 90 • .We therefore apply this formula also for the time the FM-100 faced downwards.With the same argumentation, we extend the formula for sedimentation losses for the downward sampling (Eq.A13).If η tot could not be calculated for all droplet sizes (e.g.due to too high Stokes numbers), we excluded this size distribution from further analysis as it could not be corrected.

The effect of the Mie correction to the channel widths of the FM-100
It is remarkable that the Mie channels were rather wide and overlapped especially in the range where we expect most of the droplets (3 to 20 µm; see Bruijnzeel et al., 2005).But, the default procedure of deducing the channel thresholds (as it is done by the manufacturer) did not result in substantially different mean points, indicating that the LWC geo would not differ a lot from LWC dft .However, a proper error estimation of the LWC FM for the sizing uncertainty arising due to the non-monotonic Mie scattering curve can be deduced from the Mie channels.Consequently, our suggestion is to use the Mie channel approach if one is interested in the LWC including maximal error assumptions and not only in the N.
The effect of the Mie channel configuration on two typical droplet size distributions for maritime and continental low stratus clouds described by a log normal distribution (n log ) is shown in Fig. 6a and c.We used with N t,log = 288 cm −3 , σ log = 0.38 and D n,log = 7.7 µm for continental and N t,log = 74 cm −3 , σ log = 0.38 and D n,log = 13.1 µm for maritime droplet size distributions (according to Miles et al., 2000).
For this purpose we modeled the sampling behavior of the FM-100 by first translating the droplet size (D) into a scattering signal using the Mie band.If the Mie band of (D) fell into more than one channel, n log (D) was distributed proportional to the coverage of the Mie band in comparison to the channel height over the involved channels.The received distribution was what the FM-100 would measure and was then translated into a droplet size distribution by attributing the default diameter (D dft ) or the Mie diameter (D geo ) to the channel.The droplet size distribution for the default channels (n dft ) was shifted towards larger droplets for the continental size distribution (Fig. 6a) while for the maritime distribution the shape was in rather good agreement except for some spikes between 10 and 15 µm which are similar to those that have been recently discussed as an artifact from Mie scattering (Baumgardner et al., 2010).This simulation supports the assumption that spikes like these are indeed an artifact resulting from Mie scattering.The distribution based on the Mie channels (n geo ) is plotted with horizontal error bars indicating the width of the new channels (Fig. 6a and c).As these channels were wider than the default ones, the droplet size distribution was flatter.However, it is obvious that this is not an appropriate approach if one is interested in droplet size distributions as the Mie channels overlap.For this aim it is more useful to use the method presented in Sect.3.1.2,which is shown in Fig. 6b and d n * (D) (droplet number concentration with a resolution of 0.02 µm, Eq. 6) and n PDF,1µm (n PDF,aµm refers to channels with bin size D = a µm).However, the original curve n log was adequately represented, if a bin size of 2 µm (n PDF,2µm ) was used for the re-binning.For larger bin sizes used for the re-binning -4 µm (n PDF,4µm ) and 8 µm (n PDF,8µm ) -the shape of n log could no longer be adequately represented.
Based on this theoretical exercise, we conclude that using the probability density function method with a bin size of 2 µm is the best compromise if one is interested in droplet size distributions.The effect of this new approach on the measured LWC FM will be presented and discussed in Sect.4.3.

Particle loss mechanisms in the FM-100
Figure 7 shows the efficiencies for the different particle loss mechanisms calculated for the FM-100 under standard atmospheric conditions (T = 0 • C, P = 1013 hPa) for horizontal sampling using the formulas introduced in Appendix A. The η asp and η trm were close to one for droplets smaller than ≈ 20 µm independent of the wind speed regime.In the calm air regime (Fig. 7c; U 0 < 0.5 m s −1 ), η asp was independent of wind speed (U 0 ) and sampling angle θ s .However, η asp,calm decreased below 0.5 for droplets larger than 38 µm.In both, the moving air regime (Fig. 7a) and the slow moving air regime (Fig. 7b) η asp decreased with increasing θ s and increasing droplet diameter.Additionally, the transition from Eqs. (A1) to (A3) was obvious at 60 • sampling angle.This step showed a rather unphysical behavior from R v = 0.11 to 0.8 as particles of the same size with sampling angles larger than 60 • would reach the inlet with a higher probability than those with angles below 60 • .Both equations were deduced from experiments at discrete sampling angles (θ s = 0 • , 30 • , 45 • , 60 • and 90 • ).Additionally, Eq. (A3) was originally only suggested for sub-kinetical sampling (1.25 ≤ R v ≤ 6.25; 0.003 ≤ Stk ≤ 0.2, Hangal and Willeke, 1990a) while Eq.(A1) fitted the measured data with 0.25 ≤ R v ≤ 2; 0.01 ≤ Stk ≤ 6 (Durham and Lundgren, 1980;Hangal and Willeke, 1990a) except for θ s = 90 • .However, Eq. (A3) has been used recently for a much wider R v range (von der Weiden et al., 2009;Brockmann, 2011).Nevertheless, we are interested in a reasonable physical description for the loss corrections for the FM-100 and we therefore decided to use Eq.(A1) for 0 ≤ θ s < 90 • as an additional option for particle loss corrections as this could also be deduced as the valid range based on the comparison to measurements (Durham and Lundgren, 1980;Hangal and Willeke, 1990a).By doing so, we also avoid that η asp could not be calculated due to Stokes limitations as Eq.(A1) has a broader validity range than Eq.(A3).
For the η trm one panel for super-kinetical sampling (Fig. 7d) and one for sub-kinetical sampling (Fig. 7e) is shown as those two regimes differ in terms of loss mechanisms due to the formation of the vena contracta in the super-kinetical regime.In the sub-kinetical regime, η trm decreased quickly for droplets larger than around 10 µm and angles larger than 30 • .For larger R v this transition decreased to smaller sampling angles and smaller droplet diameters.In the super-kinetical regime (R v < 1), the formation of the vena contracta decreased η trm for smaller angles in a way that η trm was nearly independent of the sampling angle.In recent publications (von der Weiden et al., 2009;Brockmann, 2011), Eq. (A9) was stated to only be valid for R v >0.25 (corresponding to U 0 = 1.1 m s −1 ), although there were no such limitations in the original publication (Hangal and Willeke, 1990b).As wind speeds are often very low in fogs (especially in radiation fogs; Fuzzi et al., 1985) this would mean that particle losses could not be calculated for this range and could not be used for further analysis.There are, however, two options available as an approximation to solve this issue: (1) we set η trm = 1 for R v < 0.25 and consider the calculated η tot as an upper limit, or (2) we use Eq.(A9) also for R v < 0.25.A careful analysis of Eq. (A9) for R v < 0.25 for the FM-100 revealed that η trm got closer to one for decreasing R v and that therefore possibility (2) should be considered the more appropriate one.Nevertheless, we included both versions of η trm for our analysis of the CLACE 2010 data and will refer to the two options with TR1 to case (1) and TR to case (2).
The dominating contribution to the η tsp was η cont , while η grav and η turb for the contraction part as well as for the wind tunnel did not decrease below 0.95 (Fig. 7f).However, the product of all five loss mechanisms η tsp , already decreased below 0.9 for droplets around 14 µm, emphasizing that particle losses within the FM-100 should not be neglected even if the FM-100 is placed on a turning table.
The resulting η tot with the implementation of η trm for the whole super-kinetical regime and η asp (0-90 • ) = η asp (0-60 • ) (later on referred to as ASP09TR) for the three different R v regimes treated above are shown in Fig. 8a to c. Independent of the wind regime, η tot > 0.9 for droplets smaller than 10 µm.Interestingly, for droplets larger than 10 µm η tot decreased fastest with droplet size for the slow moving regime.So the common idea that sampling in calm air does not need any corrections for particle losses might be correct for aerosols, but for droplets, corrections appear to be essential.In the moving air regime η tot decreased with sampling angle.While for the slow motion regime the sampling angle played a minor role in comparison to the droplet size, in the moving regime, η tot rapidly decreased with increasing sampling angle.The counter-intuitive fact, that η tot for R v > 1 was higher  for larger droplets for sampling angles below ≈ 30 • than for R v < 1, could be explained in the way that η asp increases above 1 in the sub-kinetical regime, which increased η tot .Nevertheless, η tot was never above one for the regime we correct.
The contributions of the different loss mechanisms to the overall losses (L asp = 1−η asp 1−η tot , L trm = 1−η trm 1−η tot , and L tsp = 1−η tsp 1−η tot ; Fig. 8d to l) depend on R v , sampling angle and droplet diameter.For R v > 1 and sampling angles below ≈ 30 • , the losses were dominated by particle losses within the FM-100 as L trp was 1 (Fig. 8j to l).For R v > 1 and sampling angles above 30 • and droplet diameters > 20 µm losses were dominated by transmission losses L trm , with a small contribution of aspiration losses L asp .In the slow moving regime, the contributions of the different mechanisms were comparable.However, in the calm regime for droplets 15 µm, most losses happen due to aspiration.
To summarize, based on the theoretical framework of the description of particle loss mechanisms, it is important to consider particle losses when it comes to droplet size measurements with the FM-100.Losses of 40 % for droplets ≈ 20 µm should be expected for calm air (U 0 < 0.5 m s −1 ).The losses decrease with increasing wind speeds for sampling angles 30 • and increase for sampling angles 30 • .
In the sub-kinetical regime, the sampling angle is the critical parameter when it comes to particle losses.We therefore assume that it is more appropriate to evaluate the quality of the collected data with the presented approach, then to directly exclude data collected under larger sampling angles as we could show that even droplets collected at small sampling angles can be subject to major particle losses due to losses in the FM-100 as well as due to non-isokinetical sampling.
In the next section these loss calculations will be used to correct measured data from the CLACE 2010 campaign.We evaluated the particle losses for the four different categories summarized in Table 3.

Implementation of the Mie corrections and the particle losses for the CLACE 2010 campaign
The effect of the different corrections for particle losses and re-sizing as discussed in the previous sections on the CLACE 2010 data will be described in this section.
In order to evaluate our procedure of error attribution due to Mie scattering as well as due to particle losses, we apply our corrections to measured cloud droplet spectra from CLACE 2010.In contrast to Lance et al. (2010, who only used data with LWC > 100 mg m −3 ), we decided to choose a rather weak cloud criterion.The presence of a cloud was defined if the one minute mean values fulfilled the following criterion: LWC PVM > 5 mg m −3 and N FM > 10 cm −3 .We are aware of the risk of including very thin and hence inhomogeneous clouds by using this criterion, which might cause problems for comparing the LWC results especially at low values.We also tried to use a stricter cloud criterion in terms of higher thresholds, but found a strong selection bias in such comparisons and hence decided to keep the threshold as low as possible.Due to the mounting position of the FM-100, the inlet often was completely closed by frozen cloud droplets as the cold and humid updraft blew into the inlet of the FM-100.We therefore excluded periods with temperatures below 0 • C from data evaluation in order to exclude potential measurement artifacts that might arise due to freezing.
The cloud criterion was fulfilled for 106 h of the CLACE 2010 campaign (data collection period 56 days).During 71 h of the cloudy period (which was 66 % of the cloud time), the FM-100 was positioned horizontally.An overview of the LWC and the N during cloud sampling as well as the wind conditions around the FM-100 inlet are shown in Fig. 9.We chose geometric mean regressions as a tool to compare the LWC and N as we assume that all methods used to deduce LWC and N were error-prone.Based on the geometric mean regression, the FM-100 measured a smaller LWC than the PVM-100 (Fig. 9a).A comparison of the LWC PVM with the CWC (R 2 = 0.59, with slope m = 0.93 and intercept t = 0 not shown) revealed a good agreement between the two alternative approaches to measure the LWC.Hence, the PVM-100 can be considered an appropriate reference to validate our corrections for the FM-100 measurements.The sampling angle of the FM-100 was large during most of the time, such that only 4 % of the cloudy data were within the sampling angle criteria (below 30 • ) used by Westbeld et al. (2009).This is remarkable, as the inlet faced the expected mean wind direction during the first part of the campaign.Nevertheless, the median horizontal sampling angle during the first part was 38 • , indicating that the mean wind direction as measured by MeteoSwiss was not representative for the wind field at the FM-100 mounting position.The high vertical sampling angle (median 42 • relative to the FM-100), which resulted from strong updrafts, contributed additionally leading to the high sampling angles (Fig. 9d).Based on the sampling angles and the analysis presented in Sect.4.2, we expect that significant particle losses during sampling could explain the difference between LWC FM and LWC PVM , although the wind speed was not too high (Fig. 9d).However, from the comparison of N cr to N FM , we would not necessarily expect large particle losses (see Fig. 9b).Therefore, we will first present the effect of resizing in order to investigate whether improper sizing could explain the lower LWC FM before continuing with the effect of particle losses.

Corrections for droplet sizing and its effect on LWC FM
The difference between D geo and D dft was minor (Sect.4.1), so the regression lines for LWC geo and LWC dft were similar (Figs.9a and 10b).However, the spread of the LWC FM based on D geo was large if we consider LWC min (Fig. 10a) as a minimal estimate and LWC max as an upper estimate (Fig. 10c) of the LWC FM .Nevertheless, the linear regression line of LWC PVM versus LWC max was still clearly different from unity, meaning that even within the range of maximal error assumption (LWC FM ∈ [LWC min , LWC max ]), the difference between LWC PVM and LWC FM could not be explained by incorrect sizing.
A similar conclusion can be drawn from the comparison of the LWC based on probability density functions with different bin sizes for re-binning: the slope and intercept were in the same range as for LWC dft and LWC geo ; the same was true for the squared Pearson correlation coefficient R 2 (see Table 4).The LWC FM was still in the appropriate range, if the bin width > 2 µm was used, although the size distribution was no longer appropriately represented (Sect.4.1).So, independent of how we derived the droplet size distributions from our measured signal, the LWC FM did not rise to a level suggested by LWC PVM .
Interestingly, the correlation between LWC FM and LWC PVM is higher for horizontal sampling in comparison to the downward sampling period (see Table 4).As the sampled cloud time for horizontal sampling was nearly twice as long as for downward sampling, we do not consider this as an error that can be related to counting statistics.We rather take this as an additional indicator of particle losses for downward sampling conditions as the gravitational losses are supposed to be higher.After particle loss corrections this difference should vanish.Consequently, for the CLACE 2010 data, particle losses during sampling could be considered as the main reason for the under-sampling of the FM-100, although this was not expected based on droplet number concentrations.
As a general conclusion, the influence of the presented sizing correction methods is negligible, if the LWC is the only quantity of interest.However, if an error estimation of LWC FM is an object of the study, then LWC geo with the maximal error assumption by LWC FM ∈ [LWC min , LWC max ] should be used; if one is interested in size distributions, LWC PDF,2µm should be used.

Changes of LWC FM due to particle loss corrections
Table 4 summarizes the results of the different particle loss corrections.For the STANDARD correction the correlation slightly increased as a result of the decreasing fraction of cloud data that could be corrected (around 42 % of cloud data).Reasons why the correction could not be applied were either that the sampling angle > 90 • (11 % of the cloud data), R v was smaller than 0.25 (42 % of cloud data) or droplets with Stokes numbers larger than the Stokes limitations were abundant (5 % of the cloud data).For horizontal sampling the numbers were similar, while for downward sampling only around 20 % of the cloud data could be corrected as most of the data fell into the R v < 0.25 regime.However, the corrections for the remaining downward sampling data were such that LWC geo as well as LWC PDF,aµm were similar to LWC PVM .Although this is a promising result, it needs to be treated with care, as first, the correlation was small (R 2 ≈ 0.2), second, the LWC was always below 700 mg m −3 and third, the counting statistics was small.Besides the fact that we could only correct around 40 % of the CLACE 2010 data with this correction, the agreement between LWC geo and LWC PVM as well as between LWC PDF,aµm and LWC PVM improved, but still differed from one.  3 -for all data) on the LWC for LWC min , LWC geo , LWC max and LWC PDF,2µm for CLACE 2010 (blue circle: U 0 < 0.5 m s −1 ; green crosses: 0.5 < R v < 0.8 and θ s > 60 • ; gray dots: rest of the data fulfilling the cloud criterion).The solid red line represents a geometric mean regression with m: slope, t: intercept and R 2 : squared correlation coefficient.
By replacing η trm (R v < 0.25) = 1 (TR1 in Table 4) or continuing η trm for R v < 0.25 (TR in Table 4, as well as Fig. 11) a correction for nearly 85 % of the collected data was possible.Both approaches TR and TR1 did remarkably decrease the slope, however, they also decreased R 2 .As the slopes for TR were steeper than for TR1, we would suggest to use TR for the transmission regime.Moreover, this would also avoid any sharp steps for η trm when decreasing R v below 0.25.However, data with 0.5 > R v > 0.8 and θ s > 60 • (green crosses in Fig. 11, which was the regime where η asp shows an unphysical behavior) still had a higher slope (m = 1.55 for LWC geo and m = 1.52 for LWC PDF,2µm , not shown).Applying the ASP09TR correction moved those points closer to the one to one line and changed the slopes to around 1.1 for LWC geo as well as LWC PDF,aµm , and R 2 were comparable to the uncorrected data.For the horizontal sampling, slopes and intercepts were similar while the R 2 was even around 0.5.For the downward sampling, slopes were similar but intercepts were higher and R 2 lower, which would mean that the applied corrections did not have the same effect as for horizontal sampling.
We could think of different explanations for that: first, as the correlation for downward sampling was already worse for uncorrected sampling and still persisted the corrections for particle losses; it could be that the FM-100 was more protected by the building due to its tilting and therefore the cloud sampling was less representative than for the first period.Second, for the same reason, it could be that the wind field as measured by the ultrasonic anemometer was less representative for the wind field around the FM-100 inlet.Consequently, the corrections would not be as successful for the downward sampling as for the horizontal sampling.Therefore, it is difficult to evaluate whether the corrections for particle losses were appropriate for the downward sampling or whether the data themselves were worse for the downward sampling.Further studies with the PVM-100, the FM-100 and the ultrasonic anemometer mounted in close vicinity would be needed to further evaluate the performance of the particle loss corrections.
Although the effect of the particle losses on the LWC were considerable, the corrections did not change the relation between N cr and N eff FM (total droplet number concentration deduced from the FM-100 with D geo and corrections for particle loss) in a way that it was measurable by means of geometric mean regressions or R 2 (see Fig. 12).Larger droplets were mainly affected by particle loss calculations, from two SMPS systems and corrected for particle losses as described in Sect.2.2.4 versus cloud droplet number concentration measured by the FM-100 corrected for particle losses using ASP09TR -see Table 3 -for all data (N eff FM ).
as they were too heavy to follow the gas stream lines.Obviously, these particles play a minor role for N FM , which would mean that the ambient amount of larger droplets during CLACE 2010 was small.Nevertheless, these larger droplets determine the LWC, which is why the LWC FM was very sensitive to particle loss corrections.To summarize, if the FM-100 is used to study LWC rather than N, we strongly recommend making particle loss calculations.

Recommendation for future deployments of the FM-100
Based on the analysis presented here we have the following recommendations for future installations of the FM-100: 1.A careful analysis of the sampling system revealed that there is a considerable error in the LWC FM arising from the measurement principle.A possibility of reducing the errors from Mie scattering is to choose the 40 thresholds in such a way that they correspond better to the Mie curve, similar to what was done by Gonser et al. (2011).This is already a common procedure for other optical particle counters (e.g.Pinnick et al., 1981;Dye and Baumgardner, 1984) but has only been used by Gonser et al. (2011) when measuring with the FM-100.Additionally, the signal should be redistributed using probability density functions as proposed here.However, one needs to know the instrumental response of the FM-100 in detail as they differ between the individual instruments (e.g.range of detected scattering angles or laser wavelength).We therefore recommend to use a Mie band deduced from a set of scattering angles rather than a single Mie curve.Moreover, this needs to be done before the installation of the FM-100, as the channel thresholds can no longer be changed afterwards.
2. Additionally, not all droplets of the ambient air reach the sampling device due to aspiration and transmission losses.Moreover, a considerable amount of particles gets lost within the instrument before reaching the sampling region.While isoaxial sampling can be more or less achieved by mounting the FM-100 on a turnable platform, isokinetical sampling cannot be achieved with a pump running at constant speed.We therefore recommend doing loss calculations for the droplet measurements even if the instrument can be turned into the wind direction.In order to perform such calculations, use of an ultrasonic anemometer close by the FM-100 is crucial as well as a reference for the LWC such as a PVM-100.

Conclusions
In this work, the accuracy of the commercially available fog monitor FM-100 was investigated by focusing on the effect of Mie scattering on droplet sizing and on particle losses occurring during the operation.The conclusions based on the analysis of both uncertainties individually as well as the CLACE 2010 data set are the following: 1. Concerning the sizing procedure, the default (manufacturer's) channel selection is sufficient for the determination of the total droplet number concentration (N FM ) or the total liquid water content (LWC FM ).For a maximal error estimate of the LWC, the choice would be LWC geo as an appropriate estimate of the LWC and LWC min and LWC max as the maximal error assumption.Moreover, we showed that a redistribution of the measured scattering signal using a stochastic approach (based on probability density functions) leads to a more appropriate reproduction of the ambient droplet size distributions than conventional methods.
2. Depending on sampling angles and wind speeds, particle losses due to sampling losses and losses within the FM-100 can be as high as 100 %.Consequently, particle loss corrections (in the ASP09TR version, see Table 3 for details) for the FM-100 are needed if the focus of the study is the LWC FM or fluxes calculated based on the LWC FM .
Future studies should also explore whether a passive openpath droplet size spectrometer, e.g. as used on aircrafts, would yield better results even at the low wind speeds typically found near the ground surface under foggy conditions.-Turbulent inertial deposition η turb Depending on the size of the particle there are two different regimes of how particles are "thrown" to the tube wall by eddies: the turbulent diffusion-eddy impaction and the particle inertia-moderated regime (Brockmann, 2011).For the first one, particle deposition increases with particle size as their inertia gets larger.For the second regime, the particles are so large, that their trajectory does no longer perfectly follow that of a gas molecule that does not suffer from inertial effects, so particle losses increase slightly with size.There are different corrections suggested in the literature.Here, we use a correction based on Liu and Agarwal (1974) who introduced the dimensionless turbulent velocity V + and the dimensionless particle relaxation time τ + in order to describe the transition between the two regimes: where V t is the deposition velocity for turbulent inertial deposition, with τ + = 0.0395 Stk Re 1/8 , (A15) V t = V + TAS 5.03 Re 1/8 .(A16) For the moderate particle inertia regime (τ + ≥ 12.9), we use a constant V + = 0.1, and for the turbulent diffusion eddy (τ + ≤ 12.9) the turbulent velocity is estimated as V + = 0.0006 τ 2 + .
For the contraction part, there is only one formula available: Inertial loss in a contraction η cont In the contraction part droplets are accelerated due to the decreasing diameter of the transport tubing.Larger particles could eventually not follow the changes in the trajectories resulting in wall impaction due to inertia.Muyshondt et al. (1996) experimentally derived a formula for the inertial losses in the contraction part of a transport tubing: 3.14 exp (−0.0185 θ cont ) 1.24 , (A17) where A o is the cross sectional area of the wind tunnel, A i cross sectional area of the inlet, and θ cont is the contraction half angle of the contraction part.The formula is valid for 0.001 ≤ Stk (1 − A o /A i ) ≤ 100, and 12 • ≤ θ cont ≤ 90 • .Unfortunately, the θ cont of the contraction part of the FM-100 is only 6 • .As the losses get smaller with smaller θ cont within the validity range, we still use this formula in order to get an upper estimate for the losses, and hence we expect the true losses to be a bit smaller than this estimate.
The contraction part is longer than the second part with constant diameter.We therefore assume that we cannot ignore the inertial losses due to turbulence (η turb,cont ) as well as the gravitational losses (η grav,cont ).We therefore determine those efficiencies iteratively using the Eqs.( A13

Fig. 2 .
Fig.2.Schematic view of the theory of operation of the FM-100 (modified from Droplet Measurement Technologies, 2011).Cloud droplets (blue dots) are pulled through the wind tunnel at constant speed (True Air Speed = TAS) and pass the laser beam.The scattered light (red) from the particle is directed through the optical system and then detected by the qualifier and sizer.The inner and outer opening angle depend on the individual instrument and the position where exactly the droplet passed the laser beam.

Fig. 3 .
Fig. 3. Mie curves for a laser wavelength of λ = 658 nm as well as the default channels from the manufacturer (pink) and the Mie channels (green).The inset shows for channel 5 how the minimum diameter D min and maximum diameter D max are deduced from the intersections of the Mie curves with b low (D low ) and b up (D up ).Additionally, the geometric mean diameter D geo and the diameter of the default channels are depicted (D dft ).
Fig. 4. (a) to (c) Pulse amplitude b versus diameter (shown in the range of D min to D max and b low and b up ) for the channels 3, 4, and 5.(d) to (f) Normalized probability density function PDFN i for the same channels as in (a) to (c).(h) Discrete droplet size distribution n * with a resolution of 0.02 µm if the PDFN approach is used with the PDFN i functions from (d) to (f) and the number size distribution from (g). (i) Discrete droplet size distribution n * -gray area, same as in (h) -and the re-binned size distribution n PDF,1µm with the bin size of D = 1 µm (red bars).

Fig. 5 .
Fig.5.Illustration of the different particle loss mechanisms -(a) to (g) -as described in Sect.3.2 for the FM-100 (the small photograph shows the FM-100 at Jungfraujoch).Values for the FM-100 geometry are given in Table1.Detailed description of the formulas of the particle loss mechanisms are given in Appendix A.

Fig. 6 .
Fig. 6.Modeled sampling behavior of the FM-100 as described in Sect.4.3.1 for an assumed typical continental (left panels) and maritime (right panels) cloud droplet size distribution n log (D) (gray dashed lines).(a) and (c) Size distribution measured with default channels (n dft (D), magenta line) and the Mie channels (n geo (D), green line) including maximal and minimal errors for each channel (see Sect. 3.1.1).(b) and (d) Effect of the re-sizing on the apparent size distribution: the discrete droplet number distribution n * (D) with a resolution of 0.02 µm (gray area) and four different re-binned size distributions n PDF,aµm with bin size D = a µm (a = 1, 2, 4 and 8, see Sect.3.1.2for details).

Fig. 7 .
Fig. 7. for the different particle loss mechanisms for the FM-100 calculated under standard atmospheric conditions (p = 1013 mbar, T = 0 • C) using the equations presented in Appendix A for sampling angles θ s ∈ [0 • , 90 • ].For gray colors the efficiency is 1, decreasing from 0.99 (red) to 0 (blue), shaded area indicates efficiency >1.05.White indicates that the efficiencies could not be calculated, as the input variables were not inside the range of validity.For each velocity range of η asp , one representative panel (values in brackets) is shown: (a) moving air (U 0 = 5.24 m s −1 which corresponds to a velocity ratio R v =U 0 /U =1.2),(b) slow moving air (U 0 = 1.7 m s −1 which is equal to R v = 0.4) and (c) calm air (U 0 = 0.43 m s −1 which corresponds to a velocity ratio R v of 0.1).For η trm one panel for sub-kinetical sampling (d) and one for super-kinetical sampling (e) is shown.The positioning of the panels (a) to (e) versus the R v -axis on the left represents the range of the different velocity ranges for η asp and η trm .The different mechanisms contributing (η cont , η grav,cont , η turb,cont , η grav and η turb ) to transport efficiency η tsp are shown individually in (f) and cumulative in (g).
Fig. 8. (a) to (c) Total inlet efficiencies as a function of sampling angle θ s versus droplet diameter D for three different representative velocities (R v = 1.2, 0.4 and 0.09) of each velocity range.The individual percentaged contributions of aspiration losses (d) to (f), transmission losses (g) to (i) and transport losses (j) to (l) are shown as percentaged values (see black and white color bar).

Fig. 11 .
Fig. 11.Effect of particle losses (using TR corrections -see Table3-for all data) on the LWC for LWC min , LWC geo , LWC max and LWC PDF,2µm for CLACE 2010 (blue circle: U 0 < 0.5 m s −1 ; green crosses: 0.5 < R v < 0.8 and θ s > 60 • ; gray dots: rest of the data fulfilling the cloud criterion).The solid red line represents a geometric mean regression with m: slope, t: intercept and R 2 : squared correlation coefficient.

Fig. 12 .
Fig.12.Number concentrations of cloud residuals (N cr ) deduced from two SMPS systems and corrected for particle losses as described in Sect.2.2.4 versus cloud droplet number concentration measured by the FM-100 corrected for particle losses using ASP09TR -see Table3-for all data (N eff FM ).

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Sedimentation η grav Particles deposit due to gravitational forces on the lower wall of the FM-100 wind tunnel.There are different correction formulas available, depending on the flow conditions and the tube orientation.As the flow in the wind tunnel of the FM-100 is turbulent (Reynolds number, Re ≈ 23 000 for CLACE 2010, Re ≈ 21 000 at sea level pressure and 25 • C), we use the formulas presented bySchwendiman et al. (1975):η grav (D) = exp − 4 V ts L w cos θ TAS d o π , (A13)where L w is the length of the wind tunnel (till the laser region), d o is the diameter of the wind tunnel, True Air Speed TAS = 13.15 m s −1 , which is the mean value of the flow velocity in the wind tunnel measured by the pitot tube, and θ angle of inlet inclination (= 0 • for horizontal flow).This equation is valid for V ts sin θ TAS 1.

Table 1 .
Technical specifications of the FM-100 taken from Droplet Measurement Technologies (2011).
a Depending on data retrieval software.Technical maximum observed during our field deployment is ≈ 12.5 Hz with old instruments and ≈ 14.5 Hz with newer ones.b Depending on external pump rate.The sampling flow rate corresponds to the traveling velocity of the droplets.c Light collection angles differ for different instruments.

Table 2 .
Channel range of the default (ranging from D dft,min to D dft,max with a geometric mean diameter D dft ) and the new Mie channels (ranging from D min to D max with a geometric mean diameter D geo ).Values are given in units of µm.

Table 4 .
Slope, intercept and R 2 for geometric mean regressions between LWC PVM and LWC geo as well as LWC PDF,aµm for non-corrected data as well as for the different correction categories presented in Table3.Brackets indicate whether all cloud data from CLACE 2010 (all) or only data during horizontal sampling (hori) or downward sampling (down) were used. )-(A16). www.atmos-meas-tech.net/5/2237/2012/