Uncertainty in counting ice nucleating particles with continuous 1 diffusion flow chambers 2

This study investigates the measurement of ice nucleating particle (INP) concentration and sizing of crystals using continuous flow diffusion chambers (CFDCs). CFDCs have been deployed for decades to measure the formation of INPs under controlled humidity and temperature conditions in laboratory studies and by ambient aerosol populations. These measurements have, in turn, been used to construct parameterizations for use in models by relating the formation of ice crystals to state variables such as temperature, humidity, and aerosol particle properties such as composition and number. We show here that assumptions of ideal instrument behavior are not supported by measurements made with a commercially available CFDC, the SPectrometer for Ice Nucleation (SPIN), and the instrument on which it is based, the Zurich Ice Nucleation Chamber (ZINC). Non-ideal instrument behavior, which is likely inherent to varying degrees in all CFDCs, is caused by exposure of particles to different humidities and/or temperatures than predicated from theory. This can result in a systematic, and variable, underestimation of reported INP concentrations. We use a machine learning approach to show that non-ideality is most likely due to small scale flow features where the aerosols are combined with sheath flows and to minimize the uncertainty associated with measured INP concentrations. We suggest that detailed measurement, on an instrument-by-instrument basis, be performed to characterize this uncertainty.


Introduction
Aerosol particles affect the climate system via their ability to interact with radiation and act as the sites upon which water condenses to form liquid and ice clouds (Pruppacher and Klett, 1997;Seinfeld and Pandis, 2006;Boucher et al., 2013).Those that facilitate ice crystal formation above the temperature or below the humidity of homogeneous freezing are called ice nucleating particles (INPs) and these affect the formation and persistence of mixed-phase and cirrus clouds (Forster et al., 2007).The interactions between INPs and cold clouds are a measurement challenge because such clouds occur either high in the atmosphere or near the poles and are difficult to access (Rossow and Schiffer, 1999).Continuous flow diffusion chambers (CFDCs) have provided a means to understand ice cloud formation by measuring INP concentrations in the field.By exposing an ambient aerosol population to controlled humidity and temperature conditions, the ability of natural aerosols to activate as INPs can be quantified (DeMott et al., 2003a;DeMott et al., 2003b;Chou et al., 2011;Boose et al., 2016).
Measurements of INP concentration using CFDCs have been used to construct model parameterizations that relate the formation of ice crystals to temperature and aerosol particle number and size (DeMott et al., 2010;Tobo et al, 2013;DeMott et al., 2015).Using such parameterizations, global aerosol transport models attempt to link aerosol emissions to their potential to impact ice cloud formation and thus climate (Vergara-Temprado et al., 2016).The use of CFDC data for parameterization of ice formation in such models highlights the need for accurate and unbiased measurements.
CFDC instruments are able to determine INP concentration by drawing in aerosol particles and controlling the temperature and relative humidity to which they are exposed (Rogers, 1988; differences in geometry and flows, typically particles are drawn through an inlet and contained between two sheath flows (Figure 1).These three flows pass between two ice-coated walls that are held at different, sub-0º C, temperatures.Water vapor and heat diffuse from the warm wall to the cold wall, such that approximately linear gradients of both quantities exist across the width of the chamber.Because the saturation vapor pressure exhibits a nonlinear temperature dependence, the air within the chamber is supersaturated with respect to ice.The variation in heat and vapor diffusion results in a maximum in supersaturation near the center of the chamber (Rogers, 1988).
Particles constrained to a narrow central lamina by the sheath flows should, in theory, be exposed to only the maximum saturation with a small uncertainty in temperature and humidity.
The fractional width of the lamina is typically taken to be the ratio of the incoming aerosol flow rate to the total (sample + sheaths) flow rate through the chamber (Rogers, 1988).
A sufficiently large temperature gradient between the walls can cause lamina conditions to not only exceed ice but also liquid water saturation (Rogers, 1988;Stetzer et al., 2008;Garimella et al., 2016).Droplet formation is important since many CFDCs measure only the size of objects exiting the chamber with an Optical Particle Sizer (OPS, Rogers, 1988;Demott et al., 2015).The presence of droplets can therefore be misinterpreted as a higher abundance of ice crystals.The impact of droplet formation is minimized by the utilization of an "evaporation region" in most modern CFDCs.These regions are isothermal and ice-coated sections at the bottom of the chamber where small droplets are evaporated by subsaturated conditions with respect to liquid water.Nonetheless, a CFDC run at a sufficiently large temperature gradient between the walls can create droplets large enough to survive evaporation sections.This sets a condition known as "droplet breakthrough" that is specific to each CFDC's geometry and flow characteristics (Rogers, 1988;Stetzer et al., 2008;Garimella et al., 2016).2015) with a quantitative analysis of the source and effect of spreading and discussion of the impact on CFDC data.For this work we use the Zurich Ice Nucleation Chamber (ZINC, Stetzer et al., 2008) and the commercial version, the SPectrometer for Ice Nucleation (SPIN, Garimella et al., 2016).The automation of these instruments, in particular the large amount of "housekeeping" data autonomously recorded to characterize SPIN instrument behavior, makes these chambers suitable for exploring this effect.
We apply a machine learning algorithm for analysis in order to process the large amount of data and generate statistical inferences to constrain the spreading effect.We suggest the spreading effect can be best visualized as a deviation from laminar flow and non-isokinetic injection as the particles are drawn into the chamber.We conclude that the non-ideal conditions are likely universal but also dependent on the geometry and flow characteristics of each CFDC chamber.

Particle timing tests
The ZINC and SPIN CFDCs have been described in detail previously (Stetzer et al., 2008;Garimella et al., 2016).To measure the degree of particle spreading outside the lamina a precise particle pulse was introduced into the chambers.In the case of SPIN this was a 1 second pulse while for ZINC a 10 second pulse was used.In both cases a valve at the chamber inlet was used to control the pulse.Under ideal conditions this should correspond to an equivalent particle pulse at the chamber outlet.Non-idealities have been shown to lead to particle spreading across the width of the chamber as they traverse its length by DeMott et al. (2015).For this work the arrival of particles was measured at the chamber outlet with a Condensation Particle Counter (Brechtel, Inc.CPC Model 1720 for SPIN, and TSI CPC 3772/3787 for ZINC).A wider particle pulse (in time) measured at the outlet indicates more spreading of the particles across the width of the chamber, since the fastest particles travel closer to the center of the chamber under a laminar flow assumption.This is shown in Figure 2 for ZINC experiments at a total flow rate of 10 lpm and chamber conditions of -40º C and 102% relative humidity (RH, Panel A) and 110% RH with respect to water (Panel B). 10 second pulses were produced with 200 nm ammonium nitrate (Sigma Aldrich) particles which were wet-generated using an atomizer and size selected with a differential mobility analyzer (TSI DMA 3082).CPC measurement at the input (CPC in ) verifies production of a 10-second pulse while the output particles (CPC out ) continue for 20 -30 seconds.
The SPIN data exhibit the same behavior.SPIN particle distributions were measured for 30 1-second aerosol pulses at constant conditions of 20° C and ~10 lpm flow.100 nm diameter ammonium sulfate particles wet-generated and dried with a Brechtel Manufacturing, Inc. (BMI) 9203 Aerosol Generator and mobility diameter selected with a Brechtel, Inc. Differential Mobility Analyzer Model 2100 were used.Combining the arrival pulse with the shape of the velocity profile the corresponding distribution of particles across the width of the chamber can be determined (Figure 3).
A further ~250 pulse measurements using ambient aerosol particles were conducted using the SPIN setup at Storm Peak Laboratory (Steamboat Springs, Colorado, 3220 m M.S.L.; 40.455ºN, -106.744ºW) to capture the spreading effect variability in an environment where INP field measurement campaign occur (DeMott et al., 2003a).These tests were across a range of chamber thermodynamic conditions (lamina humidities between ice and water saturation at temperatures -15 to -40º C).

Machine learning prediction
A random forest regression (RFR) (Breiman, 2001) was used to predict the fraction of particles that remained in the aerosol lamina (hereafter " !"# ").In this application RFR is similar to a multiple linear regression except that it grows a forest of bootstrap aggregated (or "bagged") decision trees to fit the data instead of using a linear model.Bootstrap aggregation avoids overfitting the data, provides uncertainty quantification for each prediction using the outof-bag (oob) prediction error, ranks the variables by their importance by comparing oob prediction errors, and does not assume linear relationships between variables (Breiman, 2001).
First, the complete set of housekeeping variables recorded for SPIN is input to the RFR, for which they are termed "features".This housekeeping data set is normally recorded to verify instrument operation and no a priori assumptions are made as to which variables are the most important predictor of  !"# ; the RFR indicates the most import predictors by comparison to the experimental pulse results.As an example, ambient temperature might not be expected to be an important factor in the spreading effect but it was not removed from the data set; that decision was left to the RFR.Feature importance was observed to fall exponentially and those within the first two e-folding lengths of importance were maintained in a reduced RFR model.The reduced RFR subset included 65 variables including wall temperature, flows, and thermodynamic variables predominantly in the middle-top of the SPIN chamber (Garimella et al., 2016); this is the region of the chamber where aerosol is encased within the sheath flows.The top ten most important features are listed in Table 1.

Results and Discussion
Figure 4 shows the results from the 30 particle timing tests at 20° C and ~10 lpm flow conditions.The fraction of particles that remained in the aerosol lamina varied despite constant flow, aerosol properties, and temperature.Figure 5 shows the results from 267 ambient particle pulse experiments in the aforementioned temperature and saturation range.In Figure 5,  !"# is plotted against the reported lamina temperature and ice saturation ratio ( !"# ), the actively controlled variables in CFDC chambers.Data are not highly correlated to either.The mean and standard deviation of  !"# are 0.25 ± 0.14 and, depending on the specific conditions, the distribution exhibits values that vary between 0.03 and 0.73 (i.e., between 3 and 73% of particles were within the lamina).
The reduced RFR described in Section 2.2 can be used to predict  !"# (mean values and standard deviations) based on the SPIN variables shown to be most important.Figure 6 shows the performance of this approach, which has an oob mean squared prediction error of 0.008 whereas simply selecting the mean value for  !"# from the distribution in Figure 5 results in a mean squared error for predicting  !"# of ∼0.02; the RFR approach reduces the uncertainty by ∼60%.showed to be incorrect. = 3 corresponds to a constant 33% of particles existing within the Further evidence to support the spreading effect is provided by the size of the ice crystals measured at the output of a CFDC.Theoretically, a monodisperse population of an aerosol composition that only nucleates ice homogeneously should exhibit freezing at the same time and location within a CFDC chamber.This should translate to a monodisperse ice crystal size distribution at the chamber output; the size of the crystals should be a function of the chamber RH and temperature and equivalent to the amount of vapor-deposited water under these conditions.The result of the extended time it takes for particles to exit the chamber due to spreading would be (1) larger crystals due to extended time in a supersaturated region and (2) a broadening of the ice crystals size distribution due to residence time and supersaturation variability to which the particles are exposed.Experiments run with the ZINC chamber confirm a non-monodisperse ice crystal size distribution (Figure 7).Aerosol particles were assumed to nucleate ice immediately upon entering the chamber since the -40° C lamina temperature was below that required for homogeneous ice nucleation and four cases are considered.The combination of velocity profile and residence time from the pulse experiments (Figure 2) were used to determine the location of the particles in the lamina and therefore the time they were exposed to variable supersaturation and the subsequent size to which they would grow.The baseline crystal size was when all particles remained within the predicated lamina (i.e., within the dash lines in Figure 1) and is monodisperse at ~4 micrometers diameter (orange histogram).When minor spreading in time with respect to that of that predicted when particles remained within the lamina was allowed, at the level of +/-1 second, the ice crystal distribution broadened (3-4 micrometers diameter; magenta histogram).The extended time that ice crystals were observed to remain in ZINC experiments (Figure 2) caused a further broadening in ice crystal size distribution (3-7 micrometers diameter; blue histogram).The measured ice crystal size distribution (yellow histogram) shows particles predominantly from 2-7 micrometers and is most consistent with the calculations made for ice crystal growth that include the spreading effect.
Note that ice smaller than 3 micrometers diameter may be due to crystals that are undersized by passing through the edge of the ZINC OPS (Stetzer et al., 2008).
The effect of particle spreading outside the lamina on CFDC reports of INP concentration measurements can be visualized using the data collected here.Figure 8 shows idealized activation curves (i.e., nucleation of ice or droplets) at various  !"# values.Note that  !"# and  can be thought of interchangeably where 33% and 3 are, respectively, equivalent.The aerosol population is assumed to be "perfect" immersion mode INP that form ice crystals immediately upon exposure at water saturation ( !"# =1); this could be viewed as a laboratory test of effective immersion INPs.In the case where the CFDC is assumed to operate ideally, all particles are constrained within the lamina ( !"# = 100%) and all nucleation occurs at  !"# =1 (solid line).
The other three curves in Figure 8 correspond to increasingly less ideal behavior (i.e., increasingly fewer particles in the lamina), corresponding to  !"# falling from 33 to 10%.The deviation from the ideal case can be viewed as a higher than saturation condition at the centerline required so the particle farthest outside the lamina experiences this value.These can also be interpreted as cases where  is fixed but increases from 3, the value suggested by DeMott et al. (2015), to 10, the worst case found in this work.INP, whereas the rest are cloud condensation nuclei (CCN) that activate at exactly  !"# = 1.The evaporation section on the bottom of the heuristic chamber is equivalent to that of SPIN so that droplets evaporate until breakthrough at  !"# > 1.07 (Garimella et al., 2016).In the ideal case all particles are constrained within the lamina and 10% of particles nucleate ice at a CFDC saturation of  !"# = 1 (panel a, solid black line).The remaining 90% of particles break through as droplets at  !"# > 1.07 (panel a, solid blue line).The other three curves correspond to the increasingly less ideal behavior presented in Figure 8, corresponding to  !"# falling from 33 to 10%.In these cases an increasingly higher maximum saturation is required so that the particles farthest from the centerline experience  !"# = 1 (ice nucleation) and 1.07 (droplet breakthrough).The resulting activation curves if droplets and ice crystals are indistinguishable (i.e., a composite of the black and blue traces in panel a), historically the case for CFDC detectors (Rodgers, 1988), is shown in panel b.The shape of the idealized activation curve in Figure 9b resembles that of experimental CFDC activation curves (DeMott et al., 2015) due to the dependence of activated fraction on  !"# because of the particle spreading effect.

Conclusions
The results presented here indicate that neither the reported thermodynamic conditions nor results from a single timing test capture the full variability of  !"# in the SPIN CFDC.Following on the results of DeMott et al. (2015), the findings in this study indicate that  !"# is not unity in real CFDCs.We show that it is also variable in ZINC and SPIN.We believe this is likely universal to all CFDC instruments although the degree of uncertainty and magnitude of the effect are probably a function of instrument geometry, flow and thermodynamic conditions.The nonuniform time particles spend in a CFDC has complex results on ice nucleation and crystal growth, including larger and broader size distributions than predicted by theory.
A machine learning approach used housekeeping data to show that the most likely reason for the lack of ideality is small scale flow features near the area of sheathing the aerosol sample flow; the RFR deemed variables including wall temperature, flows, and thermodynamic variables predominantly in the middle to top section of the SPIN chamber (i.e., at the injection point) as most important.Moreover, the RFR approach was able to better predict  !"# , and therefore the conditions experienced by the aerosols in the chamber than standard CFDC flow theory with an overall reduction in uncertainty by ∼60%.
Finally, we show the particle spreading effect explains why CFDC chambers are often operated at non-physical  !"# values to measure immersion mode INP and why the reported numbers are strongly dependent on  !"# .Theoretically, immersion mode nucleation should occur at  !"# = 1, yet reports with CFDCs often show increased concentrations up to, and often well beyond, 1.05.By contrast, CCN instruments routinely activate essentially all particles into droplets at 1.01 -1.02.
We suggest laboratory work determining the extent of spreading variability be conducted for all CFDC chambers to minimize this bias and its variability.We suggest this work would (1) explore how experimental and chamber design influence the spreading effect, drawing comparisons to computational fluid dynamics simulations to complement the RFR statistical modeling and (2) which operational considerations (such as flow rates, inlet pressure drop, etc.) maximize probability of isokinetic injection of particles into the chamber.when exposed to water saturation (S liq =1).In the ideal case, where all particles are constrained within the lamina ( !"# 100%; all particles exist within the dash-dot lines in Figure 2), all nucleation occurs at a CFDC saturation of S liq =1 (bold solid line).The other three curves correspond to increasingly less ideal behavior (i.e., increasingly fewer particles in the lamina and existing farther from the centerline), corresponding to  !"# falling from 33 to 10%.In these cases an increasingly higher maximum CFDC saturation is required so that the particles farthest from the centerline experience S liq =1. 10 Figure 9. Fraction of particles that activate as a function of saturation with respect to liquid water.Unlike Figure 6, where all particles are assumed to be perfect immersion INPs which activate as ice crystals when exposed to water saturation (S liq =1), only 10% of particles are assumed to be perfect immersion INPs.In the ideal case where all particles are constrained within the lamina ( !"# 100%; all particles exist within the dash-dot lines in Figure 2), 10% of particles nucleate ice at a CFDC saturation of S liq =1 (panel a, bold red line).The remaining 90% of particles are assumed to be perfect CCN that activate at  !"# = 1.Droplets only survive the evaporation region of the chamber at  !"# > 1.07 (corresponding to the SPIN "droplet breakthrough" point; bold blue line, see text and Garimella et al. (2016) for details).The other three curves correspond to the increasingly less ideal behavior presented in Figure 6, with  !"# falling from 33 to 10%.In these cases an increasingly higher maximum CFDC saturation is required so that the particles farthest from the centerline experience S liq =1 and 1.
Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-1180,2017   Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.Instruments rarely follow theoretical predictions.In the case of CFDCs, this is often due to non-ideal flow conditions and deviations from isothermality.DeMott et al. (2015) discussed the effect of aerosol "spreading" outside the lamina, and the resulting low bias in the number of INP measured.Here, we extend the work of DeMott et al. ( Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-1180,2017   Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.
DeMott et al. (2015) noted the non-ideality of the Colorado State University CFDC chamber.They expanded upon the work ofTobo et al. (2013) by proposing the addition of a "calibration factor" () = 3 by which the measured INP number could be multiplied to provide a corrected value.By definition,Tobo et al. (2013) (and all previous studies) used  = 1; this corresponds to an assumption that all particles in a CFDC exist within the lamina, whichDeMott et al. (2015) Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-1180,2017   Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.lamina regardless of flow or thermodynamic state.The distribution found here corresponds to a variable correction factor in the range of  = 2.6 to 9.5, depending on the experiment, with a mean of 4. We note the  = 3 value reported by DeMott et al. (2015) is for a different CFDC but falls within the range measured here.Our work does not, however, support a fixed  value, at least for SPIN.

Figure 9
Figure 9 expands on Figure 8 by considering a case more applicable to measurement of an ambient aerosol population.In this case only 10% of the particles are perfect immersion mode Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-1180,2017   Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.

Figure 1 :
Figure 1: Schematic representation of an idealized CFDC.A particle-laden flow is passed between two ice-coated walls that are held at different temperatures below 0ºC.This results in water vapor and heat diffusing from the warm to the cold wall.Supersaturation, with a maximum near the centerline, results from the non-linear relationship of water vapor saturation with respect to temperature.Sheath flows along each wall are meant to isolate particles to a central lamina at or near the supersaturation maximum, which also theoretically restricts the temperature and superstation to which they are exposed.

Figure 2 .
Figure 2. Particle concentration as a function of time for particle pulse experiments using ZINC.The blue traces are the counts measured at the entrance of the chamber (CPC in ) while the red traces are the concentrations at the output (CPC out ).Both experiments were conducted at -40° C with Panel A at 102% RH and Panel B at 110% RH, both with respect to liquid water.Particles in the red trace occurring after the vertical dashed line are outside the initial pulse duration and are inferred to have moved out of the lamina.The ratio of particles within the pulse time at the outlet versus the total particles were 77.7 and 76.2% for Panels A and B, respectively.

Figure 3 .
Figure 3. Measured particle distribution across the chamber in the SPIN CFDC (Top; see text for details) corresponding to the velocity profile and  !"# as a function of temperature across the chamber (Bottom).The dash-dot lines show the location of particles if they were constrained to the theoretical aerosol lamina.Note that while the peak particle concentration correctly occurs within the lamina, some particles have migrated into the sheath and are therefore exposed to a supersaturation significantly lower than the maximum.

Figure 4 .
Figure 4. Measured  !"# as a function of total flow.In the ideal case, where all particles are constrained with the dash-dot lines in Figure 2, data points should form a horizontal line at 1.0.The histogram on the left is a distribution of  !"# with the corresponding kernel density estimate shown in red.

Figure 5 .
Figure 5. Measured  !"# as a function of  !"# in the aerosol lamina.Temperature for each data point is noted by the color bar.The histogram on the left is the distribution of  !"# from the measurements with the corresponding kernel density estimate shown in red.

Figure 6 .
Figure 6.Random forest regression prediction versus measured  !"# using the 65 SPIN variables determined by the algorithm to be most important (see text for details).Data points are the mean value predicted and error bars correspond to the standard deviation of the predictions by the random forest.A one-to-one line is shown in red.

Figure 7 .
Figure 7. Probability histogram of ice crystals diameter.Both experiments were conducted at -40° C with Panel A at 102% RH and Panel B at 110% RH, both with respect to liquid water.In the predicated case all particles are assumed to remain within the lamina, nucleate ice and grow to the same final size (orange).The crystal size distribution becomes broader if particles are

Figure 8 .
Figure 8. Fraction of particles that activate as a function of saturation with respect to liquid water.All particles are assumed to be perfect immersion INPs which activate as ice crystals .Phys.Discuss., doi:10.5194/acp-2016-1180,2017   Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.
07.The resulting activation curves if droplets and ice crystals are indistinguishable (i.e., a composite of the black and blue traces in panel a) is shown in panel b. .Phys.Discuss., doi:10.5194/acp-2016-1180,2017 Manuscript under review for journal Atmos.Chem.Phys.Published: 31 January 2017 c Author(s) 2017.CC-BY 3.0 License.