Intercomparison study of six HTDMAs: results and general recommendations for HTDMA operation

We report on an inter-comparison of six different hygroscopicity tandem differential mobility analysers (HTDMAs). These HTDMAs are used worldwide in laboratories and in field campaigns to measure the water uptake of aerosol particles and were never intercompared. After an investigation of the different design of the instruments with their advantages and inconveniencies, the methods for calibration, validation and analysis are presented. Measurements of nebulised ammonium sulphate as well as of secondary organic aerosol generated from a smog chamber were performed. Agreement and discrepancies between the instrument and to the theory are discussed, and final recommendations for a standard instrument are given, as a benchmark for laboratory or field experiments to ensure a high quality of HTDMA data.


Introduction
Atmospheric aerosols are typically hygroscopic and absorb significant amounts of water at high relative humidity (RH). Hygroscopic growth with increasing RH influences the light scattering by particles, their potential to act as cloud condensation nuclei, and their chemical reactivity. The RH dependence of light scattering is one of the parameters needed to estimate the direct climate forcing by aerosol particles. Thus, the dry particle size distribution and their size-dependent hygroscopic growth factors must be known to model the humidity dependence of the light scattering of an aerosol. Efforts are currently undertaken to include the effects of hygroscopic growth of aerosol particles in global climate models (GCM) in order to better predict the scattering properties and size distribution of aerosols under varying humidity conditions (Randall et al., 2007). The two most widely used techniques enabling measurement of the change in the amount of water absorbed in an aerosols particle for varying RH are the single particle levitation technique using an electrodynamic balance (EDB; Tang and Munkelwitz, 1993) and the hygroscopicity tandem differential mobility analyser (HTDMA; Liu et al., 1978;Swietlicki et al., 2008) technique. The EDB technique, which measures the properties of individual super-micrometer particles, is suitable for laboratory measurements. The HTDMA technique, which probes the hygroscopicity of all particles of a well-defined dry diameter at once, is suitable for field and laboratory measurements. HTDMA instruments cover the sub-micrometer diameter range, which contains the majority of the atmospheric aerosol particles.
All HTDMAs existing worldwide are custom built instruments and very few intercomparison studies between different instruments have been reported. This gap has been filled with this study as part of the EC project EUSAAR (European Supersites for Atmospheric Aerosol Research; http://www.eusaar.net/). Two intercomparison workshops have been conducted involving in total six different HTDMAs from five research groups with the aim to harmonise the design and the quality assurance protocols of HTDMAs.
This was done in order to ensure comparability of field measurements taken by different research groups. The overall objective of EUSAAR is the integration for air quality and climate studies of measurements of atmospheric aerosol properties performed in a distributed network of 20 high quality European ground-based stations.
The goals of these two instrument intercomparison workshops were threefold: first, careful calibration of the instruments and validation of performance and accuracy by measurement of different pure aerosols with well-known behaviour;second, identification of the reason for discrepancies between the measurements from different instruments;third, instrument comparison using a complex organic aerosol with unknown properties.
Secondary organic aerosol (SOA) generated in a smog chamber was chosen for that purpose. SOA is of particular interest because more than 50% of organic aerosol is formed via oxidation and subsequent condensation of gaseous compounds (Kanakidou et al., 2005). Characterisation of the hygroscopic properties of such SOA is a topic of current research.
In conclusion to this study, recommendations for HTDMA operation within EUSAAR are presented. The instruments shown in this study have been upgraded accordingly in order to ensure quality and comparability of field measurements performed by the different instruments at the EUSAAR supersites.
2 Experimental section 2.1 HTDMA operation principle During operation of an HTDMA, a quasi-monodisperse size cut of particles with dry diameter D 0 at RH  15% is selected from a polydisperse aerosol using a differential mobility analyser (DMA). Upon exiting the first DMA (DMA1) the aerosol is conditioned in a controlled humid environment before being passed into the second DMA (DMA2), which is held at a well defined RH. DMA2 is used to detect the resulting equilibrium particle diameter D(RH), which is normally larger than D 0 due to water absorption. The hygroscopic diameter growth factor (GF) is defined as the measured mobility diameter ratio: The sizing of the particle size distribution after humidification can be done in two alternative ways. Either by ramping the voltage (diameter) set point at DMA2 in discrete steps (commonly referred to as differential mobility particles sizer, DMPS) or by scanning the diameter range with a continuous exponential voltage ramp (commonly referred to as scanning mobility particle sizer, SMPS), while recording the particle number concentration with a concentration particle counter (CPC). The former method is slightly slower, whereas the latter method may result in a smearing of the measurement signal, if too short scan times are used . The total time for a single scan is of the order of 5 minutes, thus optimising the trade-off between maximising counting statistics and minimising the influence of variations of the aerosol concentration at the HTDMA inlet, which distort the recorded growth factor distribution. The measurement frequency can be increased considerably by constraining the scanned diameter range to a physically reasonable growth factor range for the aerosol being sampled and the RH set point.  Figure 1 shows the corresponding schematics illustrating the different humidification systems, inputs and process variables for RH regulation and the temperature stabilised regions. These are key factors that influence the accuracy and reproducibility of the measurements.

Sheath air flow systems
All HTDMAs were designed with re-circulating sheath/excess air systems in the DMAs.
This has the advantage of maintaining a more similar gas phase composition in the sheath air compared to the sample and facilitates easier sheath air RH control. Vacuum pumps are commonly used to generate recirculating sheath/excess air flows and have proven to be a robust method (Biskos et al., 2006;Johnson, 2008;Weingartner et al., 2002).
HTDMA2 through HTDMA6 applied the closed loop/vacuum pump set-up using a critical orifice or mass flow controller to control the sheath/excess air flow rate (see Table   1). Important considerations when choosing a pump are leak tightness, stability of the flow rate and an inert head space. The pistons in vacuum pumps generally operate at a frequency low enough to cause periodic flow oscillations. Rapid flow rate oscillations caused by the pump diaphragm can be dampened using a series of flow through volumes (Johnson et al., 2005) at the exit of the pump or by flow restrictions imposing a slight overpressure (Fletcher et al., 2007;Weingartner et al., 2002). In some setups, the overpressure tubes must be kept at a slightly higher temperature to avoid water condensation. Prior to the DMA temperature, equilibration can be achieved by directing the sheath air through an in-line heat exchanger. Exposure of the aerosol to higher temperatures inside a pump may also alter its chemical properties through changes in the gas phase / aerosol partitioning. HTDMA1 worked also with a closed loop sheath/excess air set-up, whereas PID-controlled blowers instead of vacuum pumps were used to generate the air flow. Despite the fact that precise regulation of the blower power and leak tightness are critical , this set-up has the advantage that the recalculating air stream is hardly heated nor compressed.

Temperature stability
Growth factor measurements in a HTDMA at a well defined RH are only possible if temperature gradients in DMA2 are  0.1 K because a temperature change of ± 0.1 K results in an RH change of ± 0.6% at an RH of 90%. The first HTDMA systems used passive temperature control methods (McMurry and Stolzenburg, 1989) ideally keeping their systems in air-conditioned rooms or insulating them from their surroundings (Virkkula et al., 1999), before active temperature control was introduced (Brechtel et al., 2000, Prenni et al. 2001. Present HTDMA instruments use water baths (Cubison et al., 2005;Hennig et al., 2005;Weingartner et al., 2002), temperature controlled cabinets (Cocker III et al., 2001;Duplissy et al., 2008;Prenni et al., 2001;Villani et al., 2008) or passive, insulated regions (Johnson, 2008;Virkkula et al., 1999). HTDMA 1 & 6 of this study had at least DMA2 operated in a temperature controlled cabinets; HTDMA 3 & 4 had at least DMA2 submersed in a water bath; the DMA2s of HTDMA 2 & 5 were placed in a thermally isolated environment (see Figure 1 and Table 1).

Humidifier design and RH regulation
A requirement of aerosol humidifiers is that the aerosol particles are humidified in a controlled and stable manner. The humidification system must generate water vapour, transfer the water vapour into the aerosol sample and/or sheath air flows and regulate the resulting RH. Exclusive humidification of the aerosol sample flow is only possible for HTDMAs using a closed-loop sheath air set-up for DMA2, where the RH of the sheath air will follow the RH of the incoming sample flow with a certain delay. Additional humidification of the sheath air flow is required for HTDMAs with an open sheath/excess air set-up and it can also be applied to significantly shorten the response time to RH set point changes for HTDMAs using a closed-loop set-up.
The generation of water vapour can be achieved by passing air over a surface of liquid water, possibly separated by a membrane such as Goretex™ or Nafion™, by bubbling air directly through water, or by using a water vapour saturated vermiculite. From the vapour source, the transfer of the water vapour into the sample or sheath flow is normally done with a laminar flow humidity exchanger or through a membrane such as Goretex™ or Nafion™. A source of dry air is applied by most instruments for RH regulation or for active drying of the sample flow. Connecting a vacuum pump to a Nafion™ dryer is a technique to generate dry air, which does not need regular maintenance nor any regeneration. Alternatively, Nafion™ dryers are used, which with a dry purge air flow or diffusion (silica gel) dryers require a secondary source of dry air or regeneration of absorbent regeneration, respectively.
Regulation of the humidity has been achieved by mixing humid and dry air in variable proportions (Biskos et al., 2006;Cubison et al., 2005;Johnson, 2008;McMurry and Stolzenburg, 1989;Weingartner et al., 2002), by temperature control of the liquid water, which acts as the vapour source (Virkkula et al., 1999), or by a combination of these two methods (Cruz and Pandis, 2000). HTDMA1, 2, 3 and 4 can perform a scanning of the RH in DMA2 automatically, while HTDMA5 and 6 require manual operation for RH set point changes. The latter makes it more difficult to achieve sufficient RH resolution in the hydration curve needed e.g. for a precise characterization of the deliquescence transition (see Section 3.2). The humidification set-up of the instruments involved in this intercomparison workshop are summarised in Table 1 (see also Figure 1).

Residence time of the aerosol at high RH
A sufficient residence time for growth factor equilibration at an RH virtually equal to the RH in DMA2 is required such that no significant growth occurs during sizing in DMA2.
Various papers have discussed whether organic/inorganic aerosol mixtures show mass transfer limitations of water uptake (contrary to pure inorganic salts which equilibrate within timescales of <1 s). Kerminen et al. (1997) considered the gas-phase transfer to particles before cloud activation, and calculated equilibration times <1 s. However, Chuang et al. (2003) found during a field study in Mexico City that 0-2% of the particles exhibited growth times larger than 2-3 s, which was explained by a low mass accommodation coefficient. Sjogren et al. (2007) and Chan and Chan (2005) Gysel et al. (2007) and Mikhailov et al. (2004) demonstrated that this artefact occurs for ammonium nitrate particles and it can be expected that also other compounds (e.g. semivolatile organics) may show this effect.
Evaporation artefacts, which will most likely lead to an underestimation of the GF, can be minimised by shortening the residence time or by decreasing the temperature. Clearly further studies are needed to identify the optimum residence time. Residence times of the different HTDMA instruments used in this study are given in Table 1.
In addition to the residence time effects, Biskos et al. (2006) observed that significant differences between the RH of sample and sheath flow ( 3% RH), can lead to erroneous results for inorganic salts. Therefore it is recommended to keep the RH difference between aerosol sample flow and sheath air flows as small as possible, ideally ±2%.
This is impossible in systems which do not control the humidity in the sample flow, but only in the DMA2 sheath flow such as HTDMA5. This system has only an uncontrolled

Measurement of the relevant RH
The relevant RH which determines the equilibrium GF measured by the HTDMA is when the GF is at equilibrium at the beginning of DMA2 and assuming no RH change within the classification region of DMA2. Measurement of the RH is normally the major source of uncertainty in HTDMA GF measurements. Previous studies have reported GF data with an RH uncertainty of up to ±4% RH (Prenni et al., 2007). HTDMA2) or by cooling the sample flow after humidification (e.g. HTDMA1).
Furthermore, the risk of condensation increases and possible consequences are high voltage arcs in DMA2 potentially damaging the instrument.

Aerosol generation
The HTDMA inter-comparison was done with inorganic salts with known hygroscopic growth and with secondary organic aerosols produced by photochemical oxidation of gaseous precursors. The latter was used as a proxy for ambient secondary organic aerosol.

Nebulisation of inorganic salts
Artificial aerosol particles were generated by nebulisation of a ~0.05 g/l salt solution ((NH 4 ) 2 SO 4 , purity >99.5%, Fluka; NaCl, >99.5%, Merck; NaNO 3 , >99%, Merck) in MilliQ water. The atomizer (TSI type 3076) was operated with clean air from a pure air generator (AADCO 737-series 15 A). The solution droplets were dried in a custom-built diffusion dryer with a residence time of ~60 s prior distribution to all HTDMAs. All HTDMAs were supplied with aerosols from the same nebuliser in order to exclude potential discrepancies between instruments caused by differences in the samples.

Secondary aerosol formation in a smog chamber
Photo-oxidation experiments were carried out in a 27-m 3 Teflon chamber (Paulsen et al., 2005) at 20°C and 50% RH and with 10 (±2) ppb of NO 2 . -pinene (Aldrich, 98%) was evaporated in a heated glass sampling bulb and flushed into the humidified chamber with pure air to generate a mixing ratio of 20 (±2) ppb. Rather low, atmospherically relevant precursor concentrations were chosen because it had been shown that high precursor concentrations reduce the hygroscopicity of photo-oxidized SOA due to gas-to-particle partitioning effects of the aerosol . Four xenon arc lamps (4 kW each) were used to simulate the solar light spectrum and initiate the photochemical reaction. Before turning on the lights the mixture was allowed to equilibrate within the chamber for approximately 30 minutes. Nucleation of SOA particles was observed one hour after the lights were switched on, followed by condensational growth to a final diameter after 8 hours of photo-oxidation. The particle number size distribution was measured using a TSI 3936 long column SMPS. The dry diameter selected by the HTDMAs was chosen to follow the current modal size of the SOA particle distribution, in order to make sure that the dominant fraction (at least 80%) of selected particles carried a single charge.
3 Calibration, validation and data analysis

Calibration
The particle sizing by the DMAs as well as the RH measurement can be checked and calibrated independently. Sizing is crucially dependent on correct flow rates and high voltage (HV) applied to the DMA. Therefore, all flows in the system, the analogue output for controlling the HV supply as well as the HV amplification factor must be calibrated.
The performance of the DMAs can be tested with certified particles of known size such as polystyrene latex (PSL) spheres, though this is difficult for diameter <100 nm. Stable sizing by DMA1 and DMA2 in addition to exact knowledge of possible small sizing offsets is a prerequisite for accurate HTDMA measurements. Both can be tested by a dry offset calibration measurement using a non-volatile aerosol, where the humidification is simply switched off. Eventually DMA2 will stabilize at the same RH as DMA1 and hence the true GF of particles passing the HTDMA will be unity. The corresponding measured GF reveals the offset of the two DMAs. Correction of this offset in all measurement data is done by using the actual measured D 0 as a reference diameter for the calculated growth factors according to Gysel et al. (2008). The temporal variability of the actual measured D 0 indicates the sizing stability of the HTDMA. Additionally, the final RH in DMA2 shows whether the RH in DMA1 is sufficiently low. also a saturation test. The measured dew points can periodically be checked by feeding air saturated with water vapour into the dew point sensors at a well defined temperature (the same temperature as in the DMA2) and by measuring the resulting dew point and DMA2 temperature Weingartner et al., 2002). This allows an internal calibration of the dew point sensors by adjusting the measured dew point temperatures to the measured DMA2 temperature. Care has to be taken that no water is lost by condensation in the transfer lines.

Validation of HTDMA accuracy
Periodic validation of accuracy and performance of a HTDMA should be tested with measurements of pure test substances with known hygroscopic properties such as ammonium sulphate.
The equilibrium size of inorganic aerosol particles in humid air often shows a hysteresis depending on their RH history (Seinfeld and Pandis, 2006). A crystalline particle exposed to increasing RH does not significantly change its size until the deliquescence relative humidity (DRH) is reached and a solution droplet is formed. At RH>DRH the particle is always present as a solution droplet. Once in the liquid phase, the particle can exist in a meta-stable equilibrium state as a supersaturated solution droplet at a RH<DRH.
Recrystallisation occurs at the efflorescence relative humidity (ERH) which is given by the supersaturation at which crystallization takes place. Hysteresis effects are very distinct for some inorganic salts such as sodium chloride or ammonium sulphate. Due to insoluble impurities, the crystallisation can occur at higher RH than the ERH. The DRH, ERH, and RH history of an atmospheric particle determines whether it is present as a solid or a liquid particle (Colberg et al., 2003;Wang et al., 2008), which is an important factor for many atmospheric impacts.

Standard data analysis
A first step of the data analysis is the determination of the actual measured D 0 as opposed to the nominal D 0 in order to account for small sizing offsets between the two DMAs as discussed in Section 3.1. The next step involves the inversion of the raw data with an appropriate algorithm (Swietlicki et al., 2008). We applied the TDMA inversion approach (TDMAinv) developed by Gysel et al. (2008). This algorithm uses a full TDMA kernel function and approximates the inverted growth factor probability density function (GF-PDF) as a piecewise linear function. The inversion routines are largely automated and the Often the singly charged particles dominate (>80%) and the HTDMA data analysis is straight forward and not biased by the multiply charged particles. Sometimes the number fraction of multiply charged particles is significant at certain diameter ranges -e.g. at D 0 150 nm in Fig. 2a or at D 0 60 nm in Fig 2b. In such cases the HTDMA signal is a superposition of contributions from different dry sizes, and hence an accurate retrieval of the growth information is impossible. Therefore HTDMA measurements must always be accompanied by number size distribution measurements and subsequent removal of those HTDMA data points, where the number fraction of singly charged particles dropped below a critical limit (~80%). This applies for field measurements but is also important for measurements of laboratory generated particles: Nebulised aerosol particles are often relatively large (modal dry diameter >100nm) and the HTDMA measurement of D<100nm can be significantly biased by multiply charged particles.
Accurate data analysis is also possible if multiply charged particles dominate after size selection with a number fraction of more than ~80% of doubly (or triply) charged particles. In such cases the HTDMA kernel function for two (or three) charges must be used for the inversion of the raw measurement distribution functions .
Alternatively the raw data can first be analysed as if all particles were singly charged, followed by correction of the obtained growth factors with a size and GF dependent offset as shown in Fig. 2c. The technique of setting the DMA1 to a voltage, where predominantly doubly (or triply) charged particles were selected, has been used in a recent smog chamber study to extend the measurement range of HTDMA to larger diameters (D 0 =250-575 nm) .

Results and discussion
Here we first present several experiments conducted with pure ammonium sulphate which aim to validate the accuracy and performance of HTDMA1 through 6 against theory. A second series of experiments with SOA provides an inter-comparison of the HTDMAs with a complex organic sample, where the actual behaviour is not known. This is followed by a discussion of discrepancies found between the measured GFs and theory as well as between the instruments.

Sizing stability
Dry ammonium sulphate particles were used to validate the stability of the diameter measurement. For this purpose the humidification of the HTDMA was switched off and the difference of the measured GF from unity revealed the sizing offset of the two DMAs (see above). The temporal variability of the actual measured D 0 indicates the sizing stability of the HTDMA. All instruments of this study were fairly stable with a temporal variability of D 0 of less than ±1% (see Table 1).

RH stability under constant laboratory temperature conditions
Here we show that the ability of a HTDMA to maintain constant RH is primarily determined by its humidification control and feedback system and how the critical parts are shielded against external temperature variations. All HTDMAs were able to hold the variability of the RH measured in DMA2 within the uncertainty imposed by the accuracy of this measurement ( The temperature of DMA2 is held constant in HTDMA4 and 6, while a considerable part of the sheath flow loop of DMA2 is exposed to ambient temperature. A drop or increase of laboratory temperature leads to a lower or higher RH in the external parts of the sheath flow loop, respectively, and all water absorbing parts such as filters then act as a source or sink of water vapour. This effect drives the RH in DMA2 off its target value, unless the counteracting regulation capacity of the humidification system is strong enough. Distinctly lower laboratory temperatures compared to DMA2 can also lead to condensation in the external parts of the sheath flow loop, in which case an effective RH control is impossible. Similar effects are responsible for the RH drift of HTDMA5 where the humidifier is held at constant temperature but not the DMA2. These two effects are the cause of the RH drop seen in Figure 3 at time zero. The GF bias values in Figure 3 show that the sharp temperature drop also causes large systematic measurement errors of up to 50% in HTDMA5 and 6, i.e. the particles where sometimes not deliquesced despite a measured RH clearly above 80%. HTDMA6 showed up to 3 growth modes indicating rapid RH fluctuations or strong inhomogeneity within the flow. HTDMA3 was running a humidogram during the temperature drop and therefore no conclusion can be drawn for its ability to keep a constant RH within varying laboratory temperature. However, even at a low RH (10%) an increase of GF bias was observed (from 0 to 5%) during the first 2 hours of the temperature drop. A consequence of the occurrence of GF bias larger than a few percent is that all measurements conducted under conditions with varying laboratory temperature exceeding a critical gradient must be treated as invalid.
Concluding, it is best to have the whole HTDMA system including sheath air loops in temperature controlled boxes/baths. A reduction of the water absorption capacity in the external parts of the sheath flow loop helps increasing the robustness of the RH control for those systems that are not completely temperature controlled.

Humidograms of pure ammonium sulphate
Pure ammonium sulphate was chosen as a test substance because it is a major component of the atmospheric aerosol and its thermodynamic behaviour is well characterised. In addition, ammonium sulphate particles are not volatile and exhibit an approximately spherical structure which renders a shape correction unnecessary. Theoretical diameter growth factors were obtained from the Aerosol Diameter Dependent Equilibrium Model (ADDEM; Topping et al., 2005). Measurements of ammonium sulphate particles with dry diameter D 0 =100 nm were performed at the beginning of the inter-comparison period and at regular intervals (about every 1 week) thereafter. This included complete growth curves as shown in Figure 4, whereas only data points with an RH gradient during a scan of RH<1% are considered.
Both hydration and dehydration curves of ammonium sulphate were recorded in this study, lasting between 40 minutes to 10 hours for a complete RH cycle depending on the instrument (see Table 1). The duration of an RH ramp is limited by the response time to RH set point changes in some instruments. Other instruments have very short response times, though a certain RH gradient should not be exceeded in order to assure equilibration of the RH in DMA2 and to keep RH changes during the scan of a single growth spectrum low. In addition to that, some instruments provided automated RH ramping and therefore better RH resolution in the hydration curve, desirable for a precise characterisation of the deliquescence transition (see Table 1).
The measurements of the six HTDMAs were reproducible and the GFs at 85% RH agreed with theory within ±2.1% for all HTDMAs except HTDMA5 which exhibited errors of up to ±5.6% (see also Table 2 for a summary of the validation results). It is interesting to note that at the deliquescence transition all HTDMAs, except HTDMA1, measured GFs in between the solid crystal (1.00) and the completely dissolved solution droplet (1.48).
As this phase transition is expected to be very fast (on the order of a few milliseconds) for sub-micron ammonium sulphate particles, all points should lay either on the upper or lower branch of the growth curve (Biskos et al., 2006). Impurities in the aerosol can be excluded because no such intermediate GFs were measured by HTDMA1, which sampled from the same nebuliser. It has to be emphasized that none of these "intermediate" points are the result of averaging two separated growth modes from solid and hydrated particles.
Bimodal growth distributions can occur when the RH in DMA2 crosses the DRH during a scan. Two phenomena could explain the measurement of intermediate GFs. First, aerosol and sheath air RH are not the same and they equilibrate within the DMA2 or second, the sheath air in the 2 nd DMA experiences a temperature gradient while passing through it, which results in a RH gradient. In both cases, the aerosol will deliquesce during passage through DMA2, thus resulting in an apparent size of the particle in between the solid and deliquesced state. Biskos et al. (2006) showed that intermediate points are measured at RH close to the DRH when the RH difference between aerosol and sheath air flow is larger than 3% RH close to DRH, which is the most probable explanation for the intermediate GFs measured by HTDMA5 and potentially also for HTDMA6 with two independent humidification systems. In HTDMA2 it is ensured that both aerosol and sheath air have the same RH and there this artefact is most probably caused by temperature gradients in the DMA2 which lacks a good temperature control. The heat exchangers for the sheath flow might be insufficient in HTDMA4 where DMA2 is submersed in a water bath. Additionally, particular care is needed for HTDMA4 to avoid large differences between the RH in the aerosol sample and the one in the sheath air. The existence of temperature gradients within the sheath air of DMA2 leads to inaccurate measurements of the DRH as shown in Table 2.
Summarising, all HTDMAs (except HTDMA5) find a good agreement between measured and theoretically predicted growth factors (difference < 2.1%). The DRH point is also measured within RH<±3% uncertainty of the literature value DRH=79.9%, indicating a fairly accurate RH calibration. The higher deviation of HTDMA5 is explained with the large differences between the RH in the aerosol sample (50%) and the one in the sheath air (85%).

Inter-comparison with SOA
The hygroscopic growth behaviour of SOA has been investigated in several previous studies. Some of these studies appear to agree with each other, some do not. However, a direct comparison of such results is rarely possible because the hygroscopic properties of SOA particles depend on precursor concentration, photochemical reaction time, etc.  and because the measurements are done at different RH in different studies. The performance of HTDMAs for SOA can therefore only be assessed by simultaneous measurements.
SOA produced by photo-oxidation of α-pinene was investigated during the two workshops. HTDMA1, the only instrument participating at both workshops, measured slightly different GFs (Figures 5 and 6). However, the bag of the chamber had been replaced with a new one just a few days before the experiments of the second workshop.
Most probably some semi-volatile material evaporating from the bag surface partitioned into the SOA, thus potentially explaining the observed difference.
The general sampling strategy employed was to measure just one dry size for several hours and then switch to a larger dry size. By selecting the largest dry size at which there were sufficient statistics it was possible to measure that size for a longer time without the influence of multiply charged particles (as the mode of the size distribution grew). By not cycling through a series of different dry sizes one could not see clearly if there was any difference between them at a specific time in the experiment. It should also be noted that below 100nm the Kelvin effect becomes increasingly important i.e. particles of identical composition will take on less water if they are smaller. All HTDMAs measured an increase of the GF with photo-chemical reaction time for a given dry size. It is not clear how the hygroscopicity of particles of different dry sizes compares. As the aerosol particles of a given size in the chamber are created by a combination of homogeneous nucleation, condensation and coagulation it is difficult to predict a general trend in the hygroscopicity of particles with different size at a given time. In contrast to the good agreement between the HTDMAs found for the inorganic salts, significant differences between the HTDMAs were observed for SOA. Possible reasons for part of the discrepancies will be discussed in the following. Results from the second workshop are presented in Figure 6. The upper panel shows results as analysed by each group with their own analysis procedures, while the lower panel shows the same data, re-analysed and corrected according to the recommendations provided in this paper (see Sect. 5): The GF values for HTDMA4 in the top panel of Figure 6 are too low because the RH in DMA1 was high (approx 33% instead of <15%). SOA experiences a GF of ~1.025 at RH=33% (measured with HTDMA1, while performing a humidogram Duplissy et al., 2008) and therefore the GF at 90% is underestimated by 2.5%. This bias was corrected in the data shown in the bottom panel of Figure 6. The effects of a too high RH in DMA1 would not be detected with validation experiments using e.g. pure (NH 4 ) 2 SO 4 , as they remain crystalline at RH<80%. As a consequence the RH in DMA1 has to be monitored continuously in order to ensure RH<15%. This artefact is caused by a too coarse growth factor resolution of the employed DMPS software, resulting in a high GF uncertainty. All points with insufficient sizing resolution were removed during the reanalysis (bottom panel of Figure 6).
HTDMA5 also changed the selected dry diameter during the course of the experiment (D 0 =50 and 75 nm) and shows lower GF when larger particles are selected. A possible explanation for this discrepancy is an insufficient equilibration time. As shown in Figure   1, HTDMA5 only prehumidifies the aerosol at 50% RH (8 seconds) before being fully humidified to the target RH within the DMA2, thus providing no residence time at all at high RH prior to sizing inside the 2 nd DMA. The measured growth factors are low because the SOA particles are not fully in equilibrium with the high RH during their presence in DMA2. Again, an insufficient residence time at high RH prior to sizing in DMA2 can influence the measured hygroscopic growth (Chan and Chan, 2005;Sjogren et al., 2007). Results shown for HTDMA5 in Figure 6 indicate that larger particles are more affected by this effect. It is therefore suggested to expose the aerosol sample to the nominal RH during at least 10s before measuring the GF. Analogously, it is also suggested to allow the particle to dry for at least 10s before the selection of the dry size by the DMA1.
After careful reanalysis of all raw data, good agreement between the GFs measured by the different HTDMAs was found within the first 4 hours of the experiment when D 0  50 nm.
However, discrepancies remained for particles with D 0 = 75 nm selected after 6 hours of photochemical reaction. HTDMA5, 6, 4 and 1 measured GF values of 1.09, 1.13, 1.15 and 1.2 respectively with a residence time of 0, 2, 8 and 15 seconds, respectively. This trend is in line with the hypothesis of kinetic limitations, though these discrepancies could be also due to temperature. The HTMDAs operate at different temperature, which could lead to a different partitioning of the SOA. At higher temperature, the more volatile compounds can evaporate from the particle phase to the gas phase. The remaining particle will have therefore a different chemical composition and thus could have different hygroscopic properties (Asa-Awuku et al., 2008;Meyer et al., 2008).

Discussion of discrepancies found for SOA
Even though the growth factor of SOA derived from photo-oxidation of -pinene is roughly known, discrepancies between measurements made by different HTDMAs remain open due to the limited number of direct inter-comparisons. A first hypothesis for the cause of these complex discrepancies is that the HTDMAs affect the gas-particle equilibrium of semi-volatile compounds of the SOA in a different manner by the way they dry or wet the aerosol. A second hypothesis is that the temperature at which the hygroscopicity is measured has an influence on the partitioning between gas and aerosol phase components, again leading to changes in the observed GF. A third hypothesis is that the residence time of the aerosol inside the instrument also could play a role, due to e.g. slow reversibility of oligomer formation, which could result in a slow increase of the equilibrium GF with increasing time at high RH.

Recommendations for operating HTDMAs
Based on the results of these workshops, recommendations for building a new generation of HTDMAs for field operation at the EUSAAR supersites, as well as standardised calibration, quality assurance and data analysis procedures are provided in the following: • The analogue output for controlling the HV supply as well as the HV amplification factor must be calibrated. • All flows rates must be calibrated.
• Temperature and dew point measurement must be calibrated.
• Capacitive RH sensors must be calibrated.

Instrument validation (see Sect. 4.1 and 3.3)
• Certified PSL spheres can be used to verify the sizing of the DMAs • The validation of accurate sizing and RH measurement should be done by recording a full hydration curve of ammonium sulphate including the deliquescence transition. • The correct size dependence of the GF of ammonium sulphate across the range of selected dry diameters should at least be verified for the nominal RH of the field measurements.

Instrument operation
• Small sizing offsets between DMA1 and DMA2 must be determined for all dry sizes with regular dry scans. We suggest to do this on a weekly basis. • The measurement quality can be improved by constraining the scanned diameter range to a physically reasonable growth factor range. • We suggest to conduct ambient measurements at RH=90% (where most ambient salts are deliquesced) and at a selection of the following particle dry diameters: 35, 50, 75, 110, 165 and/or 265 nm. This aims at providing comparable data sets from different sites.

Recommendation for data analysis
• An SMPS (or an alternative instrument giving the size distribution of the measured aerosol) must run beside the HTDMA and all measurements with a contribution of less than 80% singly charged particles must be removed. (See Sect. 3.3) • Small sizing offsets between DMA1 and DMA2 must be accounted for in the data analysis. (See Section 3.3) • An appropriate TDMA inversion algorithms such as TDMAinv or TDMAfit must be applied. (see Section 3.3) • All measured GFs should be corrected to the nominal RH if the measured RH was within ±2% of the target RH. All data outside the RH tolerance should be ignored. (See Sect. 1.4) 1) The measured DRH of ammonium sulphate is 79.9% RH for large particles (Tang and Munkelwitz, 1993).
2) The theoretical GF (for Do = 100nm) are taken Topping et al. (2005).     The bottom panel shows the results after a reanalysis using the procedure recommended in this paper.