The NMASS is comprised of five parallel CPCs operating at an internal pressure of 120 hPa (Fig. 1). Each CPC detects particles above a different minimum size, determined by the maximum vapour supersaturation encountered by the particles. Operated in parallel, the CPCs provide continuous concentrations of particles in five different cumulative size classes between 3 and 60 nm. Knowing the response function of each CPC, numerical inversion techniques can then be applied to recover a size distribution from the continuous concentrations while taking into account the non-ideal response function of each channel.

Sample air enters the NMASS instrument through a pressure-reducing orifice (Sect. 3.4). Sample pressure is maintained at using a pressure controller upstream of a pump. Total flow through all five CPC modules is maintained at a constant value by adjusting a bypass flow using a solenoid control valve. With pressure and flow kept constant, the supersaturation in each CPC is determined by the absolute temperature of the saturator and by the difference in temperature between the saturator and the condenser. The five CPCs are set to different minimum detection sizes by varying this temperature difference while the saturator temperature of each unit is held constant. The sizing limits are constrained by diffusion losses within the instrument and practical limits to the degree of thermal control required for nucleating large particles at relatively low supersaturations.

The design of this instrument owes much to previous efforts to study and improve the performance of CPCs. In particular Saros et al. (1996), Wiedensohler et al. (1994), and Mcdermott et al. (1991) have demonstrated that the supersaturation within a CPC can be effectively manipulated to control its detection efficiency as a function of particle diameter (see McMurry, 2000, for a history of CPC development). The differences in detection efficiencies among different, individual CPCs have been used to determine the concentrations of particles over one or two size ranges, particularly to identify the presence of an ultrafine (< 10 nm) mode (e.g. Clarke and Kapustin, 2002, Schröder et al., 2002, Heintzenberg et al., 1999). These studies have not attempted to recover continuous size distributions from the discrete CPC measurements. Gallar et al. (2006) demonstrated that a size distribution could be recovered by inverting CPC concentrations measured by stepping the supersaturation of a single CPC over a large number of settings. CPC batteries have been examined by Kulmala et al. (2007) from the standpoint of using the composition-dependent sizing of different working fluids to understand the chemical composition of atmospheric aerosols, but not as a tool for measuring aerosol size distributions.

The NMASS instrument operates the five embedded CPCs using a single integrated data acquisition and control system, flow and temperature regulation systems and power supplies, and an external pump and pressure controller. The physical layout of the instrument is constrained by space and weight limitations for the operation on stratospheric aircraft (it was designed for use on the NASA ER-2 high-altitude research aircraft), the dissipation of heat, the need to limit particle losses due to diffusion, minimization of electronic noise, and accessibility to components for maintenance and repair. Because the instrument was originally designed for autonomous operation in wing-mounted aircraft pods, there is no integral display or user interface. The instrument has a mass of 35 kg in flight-ready configuration and requires an external 8 kg pump. Dimensions are approximately 720 mm long by 360 mm wide by 390 mm high. The instrument consumes < 400 W of power, including pumps, and operates from 28 VDC power (18–36 VDC range), which is usually abundant on research aircraft. The two NMASS units used on ATom and described in this paper show no substantive differences but will be referred to throughout the paper as NMASS 1 and NMASS 2 (NM1 and NM2 in figures), to differentiate between them.

The Wilson et al. (1983) CPC designed for the NASA ER-2 and WB-57 high-altitude research aircraft provided the concept for confining the aerosol to the centre streamline in the condenser and established a condenser geometry that functioned at pressures from 400 to 40 hPa. These features were incorporated in the NMASS CPCs which have been operated at pressures from 60 to 120 hPa depending on the altitude range of the particular aircraft.

In the NMASS, air enters a single inlet through a pressure-reducing orifice and is then carried to each of the CPCs (Fig. 1). The flow entering each CPC is split into two branches (Fig. 2). The first branch passes through a filter (Model DIF-BK40, Headline Filters Ltd., Aylesford, UK) to remove particles, and then through a saturator controlled at 39 ∘C where vapour from a perfluorinated organic compound (perfluorotributylamine, Fluorinert FC-43, 3M Specialty Chemicals, St. Paul, MN, USA) diffuses into the airstream to reach the saturation vapour pressure. The ratio of saturator to sample flow is constant in flight because total CPC flow and pressure are held constant. The vapour-laden saturator flow is carried to a vertical, cylindrical extension of the saturator, where the aerosol flow is introduced from a capillary coaxially into the centre streamline. After a short vertical section in which the Fluorinert vapour diffuses radially into the central aerosol flow, the combined flows pass into a cylindrical condenser maintained at a temperature below the saturator temperature. The rapid temperature drop causes the vapour to become supersaturated and nucleate into droplets onto the particles in the aerosol flow. The droplets grow by condensation and are sensed by an optical detector. The count rate of droplets can be converted into a particle concentration by dividing through the volumetric flow rate of the aerosol, which is determined from the measured pressure drop in the capillary. Key dimensions of the NMASS are given in the Supplement, Sect. S1.

The most commonly used working fluid for CPCs is n-butanol. In the NMASS, Fluorinert FC-43 is used instead of n-butanol for three primary reasons: (1) it offers good thermodynamic characteristics, including a vapour pressure of 4.5 hPa at 39 ∘C and low mass diffusivity; (2) it is not flammable, toxic or odorous (although it has a high global warming potential, GWP > 5000); and (3) it is an extremely inert compound that is not likely to interact chemically with atmospheric particles, minimizing sizing biases that can occur with n-butanol (e.g. Weber et al., 1993; Hanson et al., 2002). One positive aspect of Fluorinert's thermodynamic performance is that it requires less precise thermal control than do other commonly used CPC working fluids. Since the NMASS relies on differencing concentrations from the CPCs to get a size distribution, a stable diameter response of each CPC is important and requires precise thermal control. In Fig. 3, we compare the temperature dependence of the Kelvin diameter D*, or critical diameter, that refers to the smallest particle size onto which a given working fluid will condense at a given supersaturation (determined, for steady flow and pressure, by the temperature difference between the saturator and condenser), for n-butanol, diethylene glycol, and Fluorinert. For a given D* and temperature T, the slope dD*/dT is smaller for Fluorinert than for the common CPC working fluids n-butanol or diethylene glycol. The choice of Fluorinert thus reduces sizing variations caused by uncontrolled fluctuations in temperature. Details of these calculations are given in the Supplement, Sect. S2.

The supersaturation reached in the condenser of each CPC of the NMASS is a function of the heat and mass transfer within the condenser, which depends on pressure and flow rate as well as temperature. The dependence of the maximum supersaturation on pressure is complex and difficult to model (Stolzenburg and McMurry, 1991), especially since not all needed thermodynamic properties of Fluorinert such as mass diffusivity in air are known. Since the response of each CPC varies with ambient pressure, allowing the instrument pressure to vary with altitude on aircraft campaigns would require a large number of calibrations for the different pressure conditions, and parameterizations to characterize how the instrument response varies with pressure. To simplify calibration and avoid the related uncertainties with this parameterization, the CPCs within the NMASS are maintained at a constant internal pressure.

As the internal pressure of the NMASS must be below ambient pressure at all times, the choice of this pressure depends on the minimum anticipated ambient pressure. Diffusional and inertial particle losses are enhanced at low pressure, so it is desirable to use the highest practical instrument pressure. The NMASS was originally designed for operation on stratospheric research aircraft such as NASA's ER-2 and WB-57F; when operated in the stratosphere an internal pressure of 60 hPa is used. For lower altitude measurements, aboard tropospheric aircraft such as the NASA-DC8 and NOAA's WP-3D, an internal pressure of 100 or 120 hPa has been used. Internal pressure is maintained by sampling through a thin-plate orifice at the inlet to the instrument and controlling the downstream pressure using a pressure controller and external pump. The response of each CPC unit depends on the flow rate as well as the pressure, so the volumetric flow rate through the CPCs must be kept constant. As mass flow through the orifice changes with ambient pressure, this requires an active flow control system. As the aircraft ascends, flow through the orifice becomes insufficient for the CPCs, so a larger orifice must be switched into its place. The NMASS is thus operated with two different sized orifices, 500 and 750 µm, in the troposphere and with yet a third orifice of 1200 µm in the stratosphere. The desired orifice is selected using a Swagelok SS-44F6 ball valve machined with a second channel perpendicular to the original channel. An orifice is brazed into the exit of each of the channels. This is illustrated in Fig. S1 in the Supplement. Rather than operating as an on/off valve, after this modification when the valve is turned a different orifice is selected. During ATom, the orifice switch occurs at 450 hPa on ascent and 400 hPa on descent (providing some hysteresis to prevent rapid switching in the event the aircraft is flying level near the switching pressure). A valve actuator (M-series, Hanbay Inc., Pointe-Claire, Québec, Canada) is used to drive the orifice valve. We minimize particle losses through the pressure reducing inlet with a design based on that of Lee et al. (1993). A Nafion drier upstream of the NMASS instrument maintains RH to < 20 %, eliminating the possibility of condensation in the pressure reducer.

Total flow through the NMASS instrument is controlled automatically by adjusting a proportional control valve (Model 248A, MKS Instruments Inc., Andover, Massachusetts, USA) that regulates flow through a bypass line, as shown in Fig. 1. This flow circuit maintains a nearly constant volumetric flow through the CPCs even as changes in upstream pressure alter the volumetric flow downstream of the orifice. The flow through each CPC is determined by the pressure drop across the filter in the saturator (see Fig. 1) and the proportional control valve. The pressure drop across each capillary is continuously measured during operation, as shown in Fig. 1. Calibrations were done to relate these pressure drops to a volumetric flow, and it is these flows that are then used to determine the concentration in each channel from the number of particles counted.

Determining a size distribution by differencing parallel instruments requires precise control of the instrument response. At relatively low values of supersaturation, small changes in temperature difference between the saturator and condenser can produce large excursions in supersaturation, and thus d50 (see Fig. 3). The absolute temperature of each saturator is monitored by two high-precision thermistors per channel and maintained by resistive heaters. The power to the heaters is controlled by a custom proportional feedback control circuit. The temperatures of the condensers are maintained by thermoelectric (Peltier-type) coolers and governed by circuits that control the difference in temperature between the saturator and the condenser.

The counting efficiency of each NMASS channel as a function of diameter can be varied by changing the temperature difference between the saturator and condenser, but also varies with internal pressure. We chose to operate the NMASS at ∼ 120 hPa for the ATom mission. Condenser temperature settings were chosen to space the five channels of each NMASS approximately evenly within logarithmic space between 3 and 60 nm. The channels of the two instruments were offset from each other, to provide 10 distinct diameter cut-points, but also allow for nearly complete coverage of the nucleation and Aitken modes should one instrument experience problems in flight.

The Fluorinert droplets nucleated and grown in the condensers are detected with 5 simple optical particle counters which use near-IR laser diodes as the light source and a forward scattering geometry. The optics blocks and laser diode electronics are modified versions of the Model 3760/3010 detector (TSI Inc., St. Paul, MN, USA). The scattered light is detected with a photodiode. Custom electronics correct for shifting of the baseline voltage from the photodiode circuit as concentration increases. Analog pulses are converted to TTL-level signals within a shielded enclosure, then routed to 32 bit counter and timer circuits. Total counts in each channel are accumulated over a time period determined by software (typically 1 s). The fraction of time in each second in which particles are occupying the laser beam and the system cannot process another particle (the dead time) is measured using five additional 32 bit counters and timers. Corrections are made for dead time by dividing the number of counts by the fraction of measurement time for which the detector electronics are not busy processing. This correction allows ambient concentrations up to 3×105 cm-3 of air per channel to be accurately measured. Data acquisition and storage are controlled by a PC/104-bus computer.

Laboratory studies were used to determine the counting efficiencies of each NMASS channel as a function of particle diameter. Aerosols were produced with three different methods: (1) limonene ozonolysis, (2) atomization of ammonium sulfate, and (3) atomization of di-2-ethylhexyl (dioctyl) sebacate. These methods produce particles of widely differing composition that can help identify any composition-dependent sizing effects. The dependence of the counting efficiency with size was studied by placing a Boltzmann steady-state charge distribution on the generated particles with a Po-210 neutralizer and passing them through a nano-DMA to select particles of a single electrical mobility (Fig. 4). The fraction of doubly charged particles is small for particles with diameters < 100 nm. No neutralizer was included after the nano-DMA, so the particles being detected by the NMASS and CPC were negatively charged. The applicability of this calibration to atmospheric particles, which are mostly neutral, may be affected by the use of charged particles for the calibration. Stolzenburg and McMurry (1991) showed that positively and negatively charged particles have very similar activation diameters in a butanol CPC, while Winkler et al. (2008) and Kuang et al. (2012) found butanol, diethylene-glycol, and n-propanol CPCs to have higher sensitivity to charged particles than neutral particles only at small sizes (diameters less than 4 nm). Therefore, we assume that the effective difference between the performance of the NMASS CPC for charged and neutral particles will be small, and mostly limited to the smallest particle diameters (Iida et al., 2009). The effect of composition on counting efficiency is evaluated by comparing response curves from a single channel for the three different particle compositions.

We used a nano-DMA column (Model 3085, TSI Inc., St. Paul, MN, USA) in a custom-built DMA system with non-recirculating sheath flow. By varying the sheath flow between 3 and 16 L min-1, and adding dilution flow between 0 and 3.2 L min-1, we were able to size select particles from 2 to 80 nm whilst keeping the ratio of aerosol flow to sheath flow in the column at 1 : 10. To select particles with diameters > 100 nm, a longer custom-built DMA column was used in a DMA system with recirculating sheath flow. Dilution flow was again used to keep the ratio of aerosol to sheath flow at 1 : 10. We calculated the uncertainty on the diameter of particles selected by the DMA by propagating uncertainties in voltage, pressure, flow and DMA dimensions (see Sect. S4) using a root-mean-squared method. The overall diameter uncertainty was dominated by the width of the distribution selected by the DMA and so the full-width-half-maximum of this is reported as the total uncertainty on the particle diameter. We did not account for diffusional broadening of the DMA transfer function.

Two n-butanol-based nano-CPCs (a Model 3776 and Model 3025A, TSI Inc., St. Paul, MN, USA) were used as reference CPCs. Each of these instruments has a size-dependent response function, which was taken into account in the analysis. For the 3025A CPC, we used the Stolzenburg and McMurry (1991) calibration, taking the Kangasluoma et al. (2014) calibration with limonene ozonolysis products into account in the uncertainties. For the 3776 CPC, we used the Hermann et al. (2007) calibration with silver particles, taking into account calibrations with sodium chloride from the same paper and calibrations with sucrose and silver from Mordas et al. (2008) in the uncertainties. These calibrations and uncertainties were applied to all diameters < 10 nm for 3025A and < 7 nm for the 3776. At larger sizes the reference CPCs count particles with ∼ 100 % efficiency. To avoid the influence of differential diffusion losses between the reference TSI 3025A CPC and the NMASSs, the lengths of the sampling lines going to the CPC and the NMASS were made proportional to the flow rate passing through them.

The efficiency of each NMASS CPC is taken as the ratio of the standard temperature and pressure (STP, taken as 273.16 K and 1013 hPa) concentration measured in the NMASS to that measured in the reference CPC. The concentration of the NMASS and reference CPCs is calculated as the number of pulses counted by the instrument per unit of time divided by the flow rate, corrected for dead time. This concentration is corrected for pressure and temperature to get the STP concentration. The uncertainty in the NMASS downstream pressure at 120 hPa is ±0.5 hPa, and the CPC internal pressure uncertainty is ±2 hPa. The flow calibrations of the NMASS CPCs have an uncertainty of ±7 %, while the reference CPC flow uncertainties are ±10 %. The uncertainty on the count rate is √N, where N is the number of counts in the averaged interval (1 s time intervals are used for this calibration), for both NMASSs and CPCs. The temperature correction is small enough for uncertainties on it to be neglected. The total uncertainty on the NMASS efficiency is then the sum of the flow, pressure and counting uncertainties in quadrature.

The counting efficiency for each channel as a function of diameter for particles produced from limonene ozonolysis for the settings used during ATom are shown in Fig. 5. Fits to the response curves are included to guide the eye. Condenser temperatures and diameters at which each channel detects 10, 50, and 90 % of the particles are given in Table 1. For particles > 150 nm, the counting efficiency begins to drop off with increasing particle size due to impaction losses in the pressure reducer. We characterized these losses using size selected ammonium sulfate particles (Fig. 6). Ammonium sulfate was used for this calibration since it was not possible to generate enough limonene ozonolysis particles of large enough diameter, and, as discussed in Sect. 3.3 the NMASS seems to be insensitive to particle composition. The loss of these particles is likely to be dependent upon pressure upstream of the orifice (Lee et al., 1993). As the NMASS instrument is always paired with an optical particle counter to explicitly measure the accumulation mode, these impaction losses have no practical effect on the final size distribution produced by combining the instruments (Brock et al., 2018).

The repeatability of each CPC's response function is limited by temperature, pressure and flow control. The variation in 50 % detection efficiency diameter with respect to temperature difference between saturator and condenser is shown in Fig. 3. The saturator temperature was held constant at 34.8 ∘C, while the condenser temperature was varied between 26.0 and 27.9  ∘C.

The gradient of the Kelvin curve is a determining factor in the NMASS detection efficiency stability. If the curve is too steep, any small thermal instability will cause a large variation in d50. It can be seen in Fig.3 that the theoretical Kelvin curve for Fluorinert FC-43 becomes very steep at around 60 nm; therefore, we avoid setting any d50 above 60 nm in the interest of stability. The flow, pressure and temperature stability achieved in the NMASS are discussed in Sects. 3.4 and 3.5. Sizing is less accurate and precise the lower the supersaturation achieved in the CPC (corresponding to larger particles), as is seen in Fig. 5.

For a given temperature difference between saturator and condenser, the measured d50 in Fig. 3 is larger than the theoretical Kelvin diameter (Baron and Willeke, 2001). The Kelvin diameter is the minimum diameter at which it is possible for particles to nucleate, while d50 is the diameter at which 50 % of particles are actually detected in the instrument. The discrepancy between the theoretical Kelvin diameter and d50 in Fig. 3 is likely because the NMASS saturator does not reach the maximum theoretical supersaturation. Because we lack information on the mass and thermal diffusivities of FC-43, we cannot simulate the coupled heat and mass transfer within the condenser to explore this difference. However, as long as the degree of saturation is constant (which it is expected to be as pressure, flow and temperature are constant), the d50 of each NMASS channel should also be constant.

Sensitivity of the NMASS to the composition of the aerosol sample was tested by calibrating with ammonium sulfate and dioctyl sebacate particles generated using an atomizer, and comparing this to the calibration with limonene ozonolysis particles. These three compositions were chosen because they can be produced using a flow tube reactor or an atomizer, and represent a range of different particle compositions similar to those found in the atmosphere. Limonene ozonolysis products represent particles nucleated and grown with low volatility organic compounds, dioctyl sebacate particles are liquid organic droplets, and ammonium sulfate is representative of aged atmospheric sulfate particles fully neutralized by ammonia. Calibrations with these different compositions show no statistically significant variation between counting efficiency curves (Fig. 7). Note that sensitivity to composition was only done for particles > 20 nm in diameter, as it was not possible to produce smaller atomized particles of ammonium sulfate and dioctyl sebacate.

At the highest diameter settings (lowest condenser to saturator temperature difference), the supersaturation is at its lowest and thus more sensitive to any fluctuations in flow and temperature. In each of the NMASS instruments the highest diameter channel exhibits small fluctuations in cut-off diameter, most likely due to non-uniformities in supersaturation through the condenser block and being on the steepest part of the Kelvin curve here (see Fig. 3). NMASS 2 channel 5 shows the largest drift in d50, as illustrated in Fig. 8, which shows calibrations from three different days for this channel. The value of d50 varies from 36 to 39 nm, a shift of 8 %. Other channels exhibit stability within 5 %. The effect of these fluctuations in sizing performance on the accuracy of the size distributions recovered from the NMASS measurements is evaluated using Monte Carlo simulations as discussed in Sect. 4.2.

Each of the NMASS channels, i, records a single concentration value Xi, Xi=∫0∞N(Dp)Ki(Dp)dDp, where N(Dp) is the particle size distribution function, and Ki(Dp) the response function of channel i to a particle of size Dp. The inverse problem is to solve for N(Dp) given Ki(Dp) known within experimentally determined uncertainty, and Xi measured with known uncertainty. We use channels from both NMASSs in a single inversion and the calibrations ensure no large systematic differences between the two instruments. We use a version of the smoothed Twomey algorithm (Markowski, 1987) to generate a 20-bin per decade finite difference representation of N(Dp). Because the equation set is ill-posed, an infinity of possible N(Dp) will produce a given set of Xi (e.g. Wolfenbarger and Seinfeld, 1990). The algorithm uses a nonlinear technique to choose one smooth, non-negative solution that minimizes the discrepancy between the predicted and actual instrument response. Two adjustable parameters, a convergence criterion and a smoothing parameter, are required for this inversion procedure. The values of these parameters are determined using laboratory experiments with known aerosol size distributions and then fixed for most applications. We use binomial smoothing with two smoothing passes and a convergence criterion of 0.1 % (Marchand and Marmet, 1983). For the ATom project, the inversion was calculated over a size range from 2.7 to 300 nm, constrained by the concentration of particles with Dp>63 nm measured by an ultra-high sensitivity aerosol size spectrometer (UHSAS), and combined with the UHSAS and other instruments as described in Brock et al. (2018). The concentration data from all three instruments (NMASS 1, NMASS 2, and the UHSAS) are combined prior to inversion. Systematic uncertainties in concentrations between channels of each instrument are ∼ 5 %, are dominated by flow measurement uncertainties and counting statistics, and are evaluated in Sect. 4.2. The pressure variation in the impaction losses in the NMASS (Fig. 6) is not considered in the inversion because the UHSAS data constrain the large end of the inversion, and because the final size distribution is produced by combining the inverted NMASS data with the explicitly measured UHSAS size distribution at Dp=67 nm.

Because of the nonlinear inversion, it is not possible to directly calculate how uncertainties propagate from concentration and sizing errors through to the final size distribution. Instead, we use a Monte Carlo technique to calculate the range in variation of the number, surface area, and volume concentrations for several representative size distributions characteristic of the ATom project. To perform this analysis, eight size distributions that represent a range of those encountered during the ATom flights were simulated using a three-mode lognormal distribution (Table 2). These model distributions were then used to calculate the expected instrument response; that is, the concentrations that would have been measured by each channel of the NMASS were calculated from the known response functions. These concentrations were then each independently and randomly adjusted by a value falling within the concentration uncertainty as represented by one standard deviation of a Gaussian distribution. Further, the response functions of each channel were similarly independently and randomly adjusted in diameter space using the observed variation in each channel's response during calibration (Table 1). The “perturbed” concentration measurements and response functions were then inverted to recover N(Dp) using the Twomey–Markowski algorithm. The steps of random perturbation and inversion were repeated 1000 times for each representative size distribution. The inverted size distribution was compared to the “true” model size distribution for each iteration (Supplement, Fig. S2). The relative standard deviation σy for integrated number, surface, and volume, and for the peak diameter of the size distribution, was calculated as follows: σY=∑i=1NYi-Ymean2N-1Ytrue1/2, where i is the Monte Carlo iteration up to a maximum of N=1000, Y is the parameter of interest, Ymean the mean Y from all of the inverted size distributions, and Ytrue the true value of Y from the model input size distribution. Similarly, the mean relative bias By was calculated as follows: BY=Ymean-YtrueYtrue.

Values of these statistics for the eight test size distributions are given in Table 2. The mean magnitudes of BY for the integrated number, surface area, and volume were < 20 % for seven of the eight size distributions. The seventh size distribution (Case no. 4), which featured a very low number concentration (23 cm-3) with a modal diameter of 4 nm, near the bottom of the NMASS detection range, had a bias of +39 % for volume. The σY values, representing variability in the number, surface, and volume from the replicates of the inverted size distributions, were < 18 % except for the same size distribution, which had σY values of 24, 40, and 91 % for number, surface area, and volume, respectively. Note that the biases and variability of the solution for Case no. 8, which features a very small nucleation number mode (2.5 nm) but a very high number concentration (15 000 cm-3, representing a more typical case of very recent new particle formation) does not exhibit the variability and biases of Case no. 4. Thus, for most size distributions encountered in ATom, the uncertainties in integrated number, surface area, and volume generally can be considered to be ±20 %. However, uncertainties may be larger in cases where concentrations are low and modal diameters are at the extremes of the NMASS response.

Note that, for particles with diameters lying between the response curves of the first channels of each NMASS instrument (i.e. between ∼ 2.5 and 6 nm; Fig. 5), the inversion is essentially unconstrained. A concentration difference between these two channels could be attributed to large concentrations of ∼ 2.5 nm particles detected with low efficiency, or a smaller concentration of ∼ 5 nm particles detected with high efficiency. The number of particles assigned to this size range by the inversion is largely determined by the smoothing parameter, which averages adjacent inverted size bins to produce a smoothly varying size distribution. This ambiguity is evident in the consistently overpredicted concentrations for Dp<6 nm seen in the inverted size distributions (Fig. S2). Thus, the NMASS is not well suited for investigating the detailed dynamics of new particle formation and growth. An instrument with much greater size resolution, such as a nano-scanning mobility particle sizer (nano-SMPS), making repeated measurements of the time-varying evolution of the particle size distribution is needed for such studies. Such measurements of course are not possible on the rapidly moving ATom DC-8 airborne platform, which instead seeks to map the variation of particle characteristics in geophysical and thermodynamic space and use this information to evaluate the plausibility of various new particle formation mechanisms.

The system of two NMASSs was compared with an SMPS, the standard technique for ground-based measurements of nucleation-mode particle size distributions. Aerosols were generated by atomizing ammonium sulfate and dried with a silica gel diffusion drier before entering a custom-built DMA with recirculating sheath flow. The DMA was used to select a narrow size range of particles, and then the sample flow was split between the two NMASSs and an SMPS as shown in Fig. 9. The SMPS is made up of a TSI 3085 nano-DMA column and a TSI 3022A CPC. A short section of tube with an inner diameter of 1.59 mm is used after the first DMA to generate turbulence and ensure the sample flow is well mixed before it is split between the instruments. As the internal pump of the CPC is unable to keep stable flow at 0.3 L min-1, given the pressure drop in this mixing tube, an additional external pump is used, with a valve to set the CPC flow to 0.3 L min-1.

The first DMA was used to select particles of a given size, which were then sent to the NMASS and SMPS. The SMPS scanned for 10 min between 4 and 200 nm, and the average NMASS concentrations were calculated over this time. Concentrations from the SMPS and NMASS were inverted using the Twomey–Markowski method described in Sect. 4.1. DMA performance and the suitability of this method for inverting the SMPS data are discussed in the Supplement.

Comparisons of inverted size distributions from the SMPS and NMASS instruments are shown in Fig. 10, with a 20 nm peak selected by the DMA in the upper panel, and 32 nm in the lower panel. For the 20 nm peak, the SMPS peak appears at 19.9 nm and the NMASS peak at 21.2 nm, indicating a 6 % discrepancy. The largest uncertainties on the SMPS sizing come from the voltage and the time lag correction, which at 20 nm gives a total sizing uncertainty of ±2.4 nm. The peak of the SMPS and NMASS therefore agree within this uncertainty. The NMASS peak is broader than that of the SMPS because of the intrinsic resolution of only 10 size bins between 3 and 60 nm for the NMASS compared to the high resolution of the SMPS. Smoothing within the NMASS inversion algorithm further broadens the measured size distributions. Such smoothing is appropriate for atmospheric sampling, where geometric standard deviations > 1.4 are typical. The integrated total number concentration is 1364 cm-3 from the NMASS and 1213 from the SMPS, a discrepancy of 11 %. For the 32 nm peak, the larger uncertainties in NMASS 2 channel 5 (d50=40 nm), become apparent. The standard NMASS calibration places the peak of the distribution at 33.7 nm and the SMPS places it at 32.9 nm. SMPS uncertainties in diameter at 32 are ±2.4 nm, so this agrees within calculated uncertainty.

The effect of variation in sizing of NMASS 2 channel 5 is examined by recalculating the inversion with the range of calibrations from multiple days (Fig. 11). The resulting differences in the inverted size distribution move the peak between 33.7 and 37.8 nm. We expect this additional diameter uncertainty of about 12 % to show up between 27 and 60 nm, where the measurement from NMASS 2 channel 5 plays a determining role in the particle sizing.

The stability of the temperatures, flows, and pressures within the NMASSs is critical to maintaining constant instrument response during flight. In Fig. 11, we show key parameters for instrument stability: the CPC temperature difference, total CPC flow and instrument pressure. The greatest temperature instability is in NMASS 2 channel 5, where the temperature difference fluctuates by 0.46 ∘C. NMASS 2 channel 2 fluctuates by 0.2 ∘C; all other channels fluctuate by less than 0.2 ∘C. When the orifices changes at 400 hPa on ascent and 450 hPa on descent, both instrument pressure and CPC flow are perturbed. This perturbation lasts for a maximum of 20 s, and data taken during the perturbation are removed prior to analysis.

The pressure control system with two orifices, described in Sect. 2.4, maintains a total volume flow rate of 122–144 cm3 s-1 for NMASS 2 and generally between 123 and 131 cm3 s-1 for NMASS 1 over the ambient pressure range of 225–1100 hPa experienced in ATom flights. On this deployment, the bypass valve in NMASS 1 was too small, so at ambient pressures above 960 hPa, too much flow passed through the CPCs. Data from these times are either discarded, or the uncertainties on the inverted size distributions increased to reflect the additional uncertainty in counting efficiency introduced by excess flow. The downstream pressures occasionally experience fluctuations between 116 and 122 hPa with fast changes in ambient pressure, but discounting these episodes, remains between 119.5 and 120.5 hPa.

For operation on ATom, the sample flow is passed through a large diameter Nafion^™ dryer before entering the NMASSs. This reduced the relative humidity to below 20 %. This ensures that particles measured in the NMASS are classified consistently by dry diameter, and avoids potential problems of particle losses associated with water vapour condensation during flow expansion in the orifice or effects of water vapour on the performance of the CPC working fluid.

Example data from the NMASS measuring during ATom in February 2017 are shown in Fig. 12. Concentrations of the 10 NMASS channels, along with the total concentration of particles with diameter between 63 and 1000 nm measured by an ultra-high sensitivity aerosol spectrometer (Kupc et al., 2018) and the inverted size distribution are shown in Fig. 12a. From about 01:41 to 01:46 the large difference between the concentrations in channels 1 and 2 indicates recent or active new particle formation, since particles between 3 and 7 nm have a relatively short lifetime in the atmosphere and so must have been formed recently. Channels 1 and 2 vary independently of channels 3, 4, and 5 between 01:41 and 01:45, indicating two distinct modes of particles present. As concentrations in channels 1 and 2 become very similar after 01:48 and concentrations in channels 1–4 become very similar after 01:58, this indicates that most particles are now larger than 7 nm, and then larger than 28 nm.

Average size distributions for 1 min of data each are shown in Fig. 12b–d. These illustrate recent new particle formation (panel b), more aged recently formed particles (panel c) and older Aitken mode particles (panel d).