2.1 Instruments

Determining the saturation vapor pressure over ice requires measurements from three water instruments, an optical particle counter, and temperature and pressure sensors (Fig. 1). Each of these measurements is described in the following sections, along with the instruments taking them, typical accuracies and precisions, and limitations. Instrumental uncertainties are used to generate bounds on the retrieved saturation vapor pressures.

Figure 1Layout of the instruments used in this analysis during the IsoCloud campaigns at the AIDA chamber. ChiWIS and SP-APicT, both open-path tunable diode laser absorption spectroscopy (TDLAS) instruments, provided water vapor measurements. APeT, an extractive TDLAS instrument with a heated inlet, provided total water (ice + vapor) measurements, and Welas provided ice particle concentrations. The difference between total water and water vapor measurements was used to calculate ice mass in the chamber. Gas temperature is taken as the average of thermocouples 1 through 4. Thermocouple 5 is excluded from the analysis due to the presence of a region of warm air at the top of the chamber. The whole chamber is within a thermally controlled housing that sets the base temperature of an experiment. The pumps draw gas out of the chamber in a pseudo-adiabatic expansion.

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Our primary source of information is ChiWIS, a mid-infrared tunable diode laser instrument operated in open-path mode using one of AIDA's White cell mirror systems. See Lamb et al. (2017) and Sarkozy et al. (2020) for instrument details. The instrument has a typical precision of 22 ppbv in H₂O in analyzed IsoCloud experiments for 1 Hz measurements at 299.2 hPa and 204.2 K, corresponding to relative precisions of 5 % and 0.02 % at 0.45 and 100 ppmv, respectively. Measured quantities are retrieved by fitting spectra calculated from line parameters in the HITRAN database (Gordon et al., 2017) to raw spectra, rather than by empirical calibration. Fitting is done using ICOSfit, a non-linear, least-squares fitting algorithm. Uncertainties in the spectroscopic parameters for the (413–524) line at 3789.63481 cm⁻¹ in the ν₁ band from which H₂O measurements are derived contribute an additional ±2.5 %–3 % systematic uncertainty. The uncertainty due to pressure broadening values varies slightly with temperature across the experimental range, but for simplicity we apply the maximal value of ± 3 % to all experiments. Errors in the linearization of the wavelength scale contribute another 0.2 % of systematic uncertainty to all experiments. Day- and experiment-specific systematic uncertainties due to the fit routine and in the path length contribute another ±1.1 %. See Sect. 3.5 for a complete discussion of uncertainty.

The SP-APicT (single-pass AIDA PCI in cloud TDL; Skrotzki, 2012) water vapor instrument is used to provide water vapor measurements in the case of thick ice clouds, which form in some IsoCloud experiments above 210 K (13 of 28 experiments). During warmer experiments that form very dense ice clouds, ChiWIS simultaneously experiences signal attenuation of up to 95 % and backscattering of light off the cloud into the detector, producing artifacts that affect retrieved concentrations. During these intervals, we rely on the SP-APicT instrument to provide water vapor measurements because that instrument's single-pass optical arrangement is much less sensitive to backscatter. At temperatures above 205 K, SP-APicT reports mixing ratios during ice-free periods about 1.5 % lower than ChiWIS. For consistency across all experiments, we arbitrarily scale up the substituted SP-APicT measurements by that factor (details can be found in Lamb et al., 2017). The resulting composite water vapor record uses ChiWIS measurements for 15 of 28 experiments, and scaled SP-APicT measurements for the remaining 13 experiments.

Total water measurements are provided by APeT (AIDA PCI extractive TDL), an extractive, tunable diode laser instrument (Ebert et al., 2008). In previous comparisons of AIDA instruments (Skrotzki, 2012), APeT measurements were found to be delayed by 17 s with respect to open-path in situ TDLAS ones. As is standard practice, we take the chamber ice content to be the difference between total water and vapor-phase measurements. To take advantage of the high precision ChiWIS affords at temperatures below 205 K, we use the composite water vapor record described above to calculate ice mass. However, APeT total water measurements also require harmonization with ChiWIS. APeT and SP-APicT derive their measured concentrations from the same H₂O spectral feature, and both instruments report values 1.5% below ChiWIS during ice free periods. We therefore scale up the APeT measurements by 1.5 % as well. After applying this time-invariant scaling factor, if there is still an offset between the water vapor record and APeT total water prior to the expansion (when there should be no ice cloud in the chamber), that offset is subtracted from the whole experiment. These offsets are most significant below 200 K where they are typically between +0.05 and +0.25 ppmv. Potential causes could include parasitic water absorption inside the instrument or outgassing from ice in the inlet of APeT (e.g., Buchholz and Ebert, 2014). See Supplement for details of instrument comparisons, and Table S3 for instrument offsets prior to pumping.

Ice particle concentrations are measured by the Welas 1 instrument. Ice particle number concentration is used to estimate the average radius of particles in the chamber and the average, per-particle growth rate. One component of this instrument's uncertainty comes from counting errors, which follow Poisson statistics and are proportional to $\mathrm{1}/\sqrt{n}$. However, experiments included in this analysis have high ice particle densities and small counting errors. We therefore neglect the counting errors in this analysis. The conversion of this instrument's count rate into a number concentration has a 10 % uncertainty. In experiments where particles are very small, the Welas 1 instrument likely undercounts them since its efficiency drops sharply for particles below 0.7 µm in diameter (Wagner and Möhler, 2013). We address the steps taken to characterize this undercounting in the following sections.

We assume a single chamber temperature at each point in time, and construct a value from the average of four thermocouples suspended at different heights in the chamber. The fifth thermocouple is not included in the analysis to avoid the introduction of bias from a known warm region at the top of the chamber. These measurements have an apparent precision of 0.3 K during pumpdowns and 0.15 K during static conditions between pumpdowns (Möhler et al., 2003). A mixing fan at the bottom of the chamber is always operational and enhances the uniformity of the chamber, with a mixing time constant of about 1 min. Figure 1 shows the positions of the instruments used during IsoCloud in the AIDA chamber, as well as the locations of the thermocouples.

2.2 Experiments

IsoCloud expansion experiments were designed to nucleate, grow, and maintain cold cirrus clouds with the goal of testing for the presence of anomalous supersaturation under conditions similar to the coldest parts of the atmosphere. To be a suitable test for anomalous supersaturation, an expansion experiment must satisfy two basic criteria. First, its duration must be significantly longer than the vapor relaxation times associated with cirrus growth. Relaxation times depend on experimental conditions, and are longer in the cases where particle number densities are small and diffusion limitation is strong. Second, cirrus cloud growth must continue for long enough to allow for the retrieval of the saturation vapor pressure over ice. In practice, this means that the chamber's ice-covered walls must serve as a source of vapor from which the cirrus cloud can continue to grow throughout the experiment. The remainder of this section describes a typical expansion experiment, addresses the consequences of running experiments in the presence of wall ice, and discusses the criteria for exclusion from analysis.

In a typical IsoCloud experiment, ice clouds are formed by pumping on a chamber filled with water vapor near saturation. Adiabatic expansion causes rapid cooling, which in turn leads to nucleation of ice. Air is kept close to saturation before pumping by preparing the walls with a thin coating of ice. In practice, chamber water vapor pressures are 80 %–90 % of MK saturation before the expansions, which suggests that the wall ice is 0.5–2 K colder than the chamber air. Pumping and adiabatic expansion cool the chamber air below the wall temperature, and given the presence of ice nucleating particles, the now-supersaturated chamber air will nucleate an ice cloud. Ice growth then draws the chamber vapor pressure below the saturation vapor pressure at wall temperature, and the walls become an additional source of water for the growing cirrus cloud. The transfer of mass from the walls is often large enough that chamber total water is greater at the end of pumping than at the beginning, despite loss to the pumps. Once the pumps cease, the chamber warms and the cirrus cloud dissipates and part of its mass is transferred through the vapor back to the walls. The total amount of cooling in an experiment varies from 5 to 9 K, depending on pump speed, and occurs primarily during the first ∼100 s of pumping when the chamber air behaves nearly adiabatically. Subsequently, heat flux from the walls becomes large enough to balance the adiabatic cooling. Cooling rates during the early stages of pumpdowns are equivalent to effective atmospheric updraft speeds of several meters per second, much faster than those typically associated with cold cirrus in the natural atmosphere.

Of the 48 IsoCloud experiments in March of 2013, six were reference expansions, and four others lacked measurements of one of the physical quantities required for analysis. Of the remaining 38 experiments, this analysis uses 28 and excludes 10. We include all experiments conducted with standard protocol in which the ice cloud can be reasonably expected to approach saturation. Five experiments are excluded for overly long relaxation times, and five for non-standard protocol. See Tables S3 and S4 for characteristics of included and excluded experiments, respectively. We estimate vapor relaxation times for each point in each experiment using the expression of Korolev and Mazin (2003), which takes into account cooling rate (effective updraft speed), ice particle number, and particle size to estimate the timescale for achieving a dynamical equilibrium value (see Sect. S2.3 for expression). For each experiment, we determine τ_min, the minimum relaxation time at any point during the experiment, and t_exp, the time interval over which the calculated relaxation time is within a factor of two of τ_min. We consider that an experiment should reasonably approach dynamical equilibrium if $t_{\exp }/{\mathit{\tau }}_{\min }>\mathrm{4}$.

The five non-standard experiments excluded are Experiment 1, which had an abnormally short pumping time, and Experiments 40–43, where the chamber was prepared with dry walls. Pumping in Experiment 1 lasted only 250 s, vs. 400–750 s in all other experiments; we would expect more inhomogeneities in the resulting ice cloud. Experiments with dry walls pose a problem for our analysis because the lack of an ice source means that these experiments do not involve extended periods of ice growth near saturation.

Figure 2Examples of experiments in which vapor is controlled by cirrus uptake (a–c) and wall flux (d–f). Experiment 16 (a-c) is a heterogeneous nucleation experiment onto ATD, and Experiment 30 (d–f) is a homogeneous nucleation experiment with SA aerosol. The top panels of each plot show the pressure (green) and temperature (red) evolution. The action of the chamber pumps results in a pseudo-adiabatic expansion that cools the chamber gas rapidly at first, then more slowly until the cooling is balanced by heat flux from the chamber walls. The chamber gas warms as soon as the pumps have stopped. The middle panels show Murphy–Koop (MK) saturation (red dashed line), measured saturation (black), ice particle number (light blue), and the cloud's ice water content (dark blue). Ice nucleation starts at the peak in saturation, and is followed by a sharp increase in particle number and rapid cloud growth. Saturation relaxes back to a constant value, where it stays until the pumps turn off. In the cirrus-dominated experiment, that value is the saturation vapor pressure over ice. In the wall flux-dominated experiment, that value of about 6 % supersaturation is what is required to drive enough ice growth to balance the wall outgassing. When the pumps stop, the vapor pressure returns to the wall-controlled value in the cirrus-controlled experiment, but in the wall flux-controlled experiment the decay rate is limited by wall uptake. The bottom panels show total water (green) and water vapor (black). The small data gap in Experiment 30 at around 1100 s is due to realignment of the chamber's White cell mirrors.

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The 28 experiments used in this analysis still show a range of characteristics, and can be grouped into two broad categories. In “cirrus-dominated” experiments (see Fig. 2, left, for example), the wall flux is comparable to ice uptake driven simply by the change in saturation vapor pressure on cooling. In these experiments water vapor concentrations draw down quickly to saturation. In the colder experiments, however, wall flux is generally far more substantial. In these “wall-dominated” experiments (Fig. 2, right), peak total water rises to many times greater than initial water vapor, water vapor remains supersaturated during the growth phase of the experiment, and then becomes subsaturated during evaporation. This deviation complicates analysis and requires a growth model to determine saturation vapor pressure. For consistency, we treat all experiments the same, and extract saturation vapor pressure using the same method.

The two examples shown in Fig. 2 illustrate the key features of each type of experiment. In the cirrus-dominated experiment (Fig. 2, left), the onset of nucleation produces rapid ice growth and a corresponding drawdown of vapor pressure to a value close to saturation. The ice cloud then grows slowly for the remainder of the expansion experiment, with water provided by the ice-covered chamber walls. In this particular case, a heterogeneous nucleation experiment with abundant ice nucleating particles, ice nucleation occurs at a relatively low supersaturation, and the ice particle number reaches ∼400 cm⁻³ before decreasing nearly in proportion to the action of the pump. After the pumping stops, the ice cloud decays over a roughly 200 s period, and the chamber vapor pressure returns to the wall-controlled value.

In the wall-dominated experiment (Fig. 2, right), significant supersaturation with respect to MK persists throughout the experiment. In this particular case, initial supersaturation is quite high since the chamber was prepared with only sulfuric acid droplets to study homogeneous nucleation. The onset of nucleation again produces a drawdown of supersaturation, but only to a value of about 6 %, which remains fairly constant for the duration of pumping. This is the value required to drive the strong continuing ice growth that balances the wall flux. Once the expansion stops, the chamber air warms, the walls become a water sink rather than a source, and chamber vapor pressure drops to RHice∼95 %, the value required to drive enough evaporation to balance wall uptake. After the ice cloud has nearly dissipated, the chamber vapor pressure again returns to the wall-controlled value.

These chamber dynamics mean that saturation vapor pressure in IsoCloud experiments cannot be determined simply by measuring the water vapor content in the chamber after an ice cloud has developed. The colder the experiment, the more wall dominated it typically becomes, so that experiments show steadily increasing long-term supersaturations with respect to Murphy–Koop saturation (MK) as temperature decreases, rising by approximately 5 % over the temperature range 225–185 K (Fig. 3). This rise should not be interpreted as the result of a temperature-dependent saturation vapor pressure, but instead as a temperature-dependent balance between wall flux and diffusional ice growth. The wall flux contribution is relatively larger for colder experiments because saturation vapor pressure falls sharply with reduced temperature and the diffusional ice growth rate drops with vapor concentration. The result is that the colder the temperature, the larger the supersaturation over ice required to produce steady-state relative humidity. For this reason we use an ice growth model to retrieve saturation vapor pressure by modeling vapor pressure evolution during each experiment. The model, fitting procedure, and uncertainty analysis are described in Sect. 3.

Figure 3Average measured saturation of the 28 IsoCloud experiments after relaxation back to a near-constant value. Supersaturations plotted are the average value of the final 200 s of pumping. Experiments are colored by aerosol/IN type: Arizona test dust (ATD, black), liquid sulfuric acid droplets (SA, red), secondary organic aerosol (SOA, green), and experiments containing both ATD and SA (blue). Warm, cirrus-dominated experiments (T≥195 K) typically show vapor pressures close to MK, with saturations from 0.98 to 1.00. Cold, wall-dominated experiments (below ∼195 K) show saturations that rise with decreasing temperature. Higher supersaturation is necessary for the cirrus growth rate to match the mass flux off the chamber walls. This effect means that an ice growth model is necessary to extract the saturation vapor pressure. Water vapor retrievals during the pumping interval in Experiment 33 are quite subsaturated with respect to MK.

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3.1 Ice growth model

The model is obtained by rearranging an expression for the diffusional growth rate over ice (Pruppacher and Klett, 1997) to calculate the far-field water vapor pressure:

Measured and derived quantities here are $\dot{m}$, the per-particle growth rate (change in total ice mass/time/particle number); $\stackrel{\mathrm{‾}}{r}$, the average particle radius; T_∞, the gas temperature in the chamber; and we identify the far-field vapor pressure e as the measured vapor pressure. Parameters are M_w, the molar mass of water; L_i, the latent heat of sublimation; $D_{\mathrm{v}}^{*}$, the diffusivity of water in air with kinetic corrections; α, the accommodation coefficient; and $k_{\mathrm{a}}^{*}$, the thermal accommodation coefficient, which is taken here to be unity (Fung and Tang, 1988). The average radius of the ice particles, $\stackrel{\mathrm{‾}}{r}$, is calculated from the total ice water mass and particle number counts described previously, and a temperature-dependent ice density. The bulk density of ice varies by about 1 % between −10 and −100 ^∘C; the values used in this work are from a quadratic fit to data from Eisenberg et al. (2005), which are based on the X-ray diffraction measurements of La Placa and Post (1960). We assume the particles are spherical, which is a reasonable approximation for small, micrometer-sized particles. The diffusivity of water vapor in air, $D_{\mathrm{v}}^{*}$, is also temperature dependent, and is evaluated using the functional form of Pruppacher and Klett (1997), which includes kinetic corrections (Okuyama and Zung, 1967; Fitzgerald, 1972). Note that one limitation of this method is that it can yield only a bulk value, and is not sensitive to situations in which a small subset of ice crystals are metastable.

3.2 Confounding issues and corrections

We apply sensitivity tests or corrections to three issues that might confound analysis: loss of ice crystals by pumping, uncertainty in the accommodation coefficient, and undercounting of particles. The issues are sufficiently unproblematic that they are not included in the formal uncertainty analysis of Sect. 3.5.

The pseudo-adiabatic expansion procedure during experiments results in a loss of ice mass as air is removed from the chamber. This loss must be accounted for in order to accurately estimate ice mass change by sublimation/deposition to/from the vapor. The pumps remove a constant volume of gas from the chamber in each time interval, and we assume that they act in the same manner upon the small ice particles found in our experiments. With this assumption, we correct the ice growth rate by subtracting the assumed pumping losses from the derivative of the cirrus ice mass.

The accommodation coefficient α in Eq. (1) is not well constrained, with significant variation in the literature. α can be thought of as the probability that a molecule of water vapor that strikes the surface of an ice particle is incorporated into the ice matrix, and can be sensitive to experimental conditions. For similar chamber experiments, studies have shown that the accommodation coefficient can be treated as a constant during an experiment (Lamb et al., 2020) with values close to 1 (Skrotzki et al., 2013; Lamb et al., 2020). We test the sensitivity of our vapor pressure model to uncertainty in the accommodation coefficient by running the model with different values of α, and find that the derived results for saturation vapor pressure are quite insensitive to the exact values of α in the range of 0.2 to 1 (Fig. S8 in the Supplement). We therefore use a value of 1 throughout this work, but note that if the true α value is below 0.2, then this assumption will result in an overestimate of the saturation vapor pressure.

Undercounting of particles may occur because the Welas 1 optical particle counter has a size cutoff for small particles of 0.7 µm in diameter. In these experiments, we never see evidence of very large particles, but very small particles are common at the beginnings and ends of experiments, immediately after nucleation or towards the end of sublimation, respectively. For some experiments at the coldest temperatures, where initial water vapor and final ice mass are small, we also expect undercounts throughout the experiment. Mean particle size in these experiments is strongly temperature dependent, ranging from ∼1 µm at 189 K to ∼5 µm at 235 K. Failure to account for undercounting would lead to an overly large average radius, and could produce a low bias in retrieved saturation vapor pressures.

We deal with the undercounts in two ways: we exclude all time periods in which the calculated average radius is less than 0.85 µm, and we conduct sensitivity tests on the resulting analyses. In several of the colder experiments, however, the mean calculated radius remains below 1 µm throughout the experiments. In these marginal cases assuming a log-normal distribution produces estimated undercounts of up to 50 % throughout the experiment (see Supplement for details of this calculation). We therefore conduct sensitivity analyses on all experiments of uncertainty due to potential undercounting by increasing ice particle counts by factors of 1.5, 2, and 5 (Fig. S9). Undercounting can result in underestimation of saturation vapor pressure, but most IsoCloud experiments show a sensitivity of less than ±0.5 % in retrieved saturation vapor pressure, even in the unrealistic case of undercounting by a factor of 5. Maximum sensitivity to undercounting occurs in the three homogeneous nucleation experiments, where particle sizes are smallest, but still remains under +2.5 % even in the most extreme case tested.

3.3 Ability to diagnose saturation vapor pressure

Before fitting our experimental data, we conduct a preliminary proof-of-concept exercise to evaluate whether the vapor pressure model is indeed sensitive to assumptions about saturation vapor pressure. We calculate evolution of the chamber vapor pressure during selected representative experiments under three different assumptions of saturation vapor pressure values: MK saturation, and MK multiplied by factors of 1.1 and 0.9. Comparing these calculations to the observed values, we see that even small changes in the assumed saturation vapor pressure result in significant deviations from the measured chamber water vapor in both cirrus-dominated and wall-dominated experiments (Fig. 4). Results suggest that experiments are sufficiently sensitive to resolve differences in saturation vapor pressure of a few percent. This test establishes that observations of chamber vapor pressure during ice growth can in fact constrain the saturation vapor pressure in all the IsoCloud experiments.

Figure 4Model output for experiments used in the previous example: the cirrus-dominated Experiment 16 (a) and wall-dominated Experiment 30 (b). Each output is calculated using observed quantities under three different assumptions about the “true” saturation vapor pressure of cirrus. The red line assumes the true value is 10 % lower than the MK saturation vapor pressure, the blue line assumes it is 10 % higher, and the green line assumes MK is the true saturation vapor pressure. Calculated saturations are smoothed by 30 points (∼30 s). Measured saturations are unsmoothed. Experiments are very sensitive to the assumed vapor pressure, although wall-controlled experiments are noisier overall since they are typically at lower temperatures. Experiment 16 shows spikes in measured water which are due to real sampling of different air masses during the turbulent period when the pumps are on and the cirrus cloud is growing. Experiment 30 shows oscillations in the model output due to in-mixing of warmer air from the top of the chamber. This type of temperature fluctuation is not captured by the model.

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3.4 Fitting procedure and region choice

The model is fit to the observed chamber vapor pressure using least-squares optimization. We use MPFIT (Markwardt, 2009), a Levenberg–Marquardt least-squares minimization routine written in IDL, based on the MINPACK algorithm (Moré, 1978). This routine attempts to minimize the difference between the model and observation by varying the scaling factor x in Eq. (1), which multiplies the Murphy–Koop parametrization of the saturation vapor pressure over ice. The fit routine yields a single value of x for each experiment, which is multiplied by MK saturation to best fit the observations.

The fit region for each experiment is selected using three criteria. (1) The fit region must start after the maximum ice particle number count has been attained. In most experiments, the maximum particle count is achieved within about 50 s of the peak in saturation associated with the onset of nucleation. During the preceding brief period of rapid ice growth, significant particle undercounts are likely. (2) We exclude all time periods when the Welas 1 instrument reports fewer than 12 ice particles per cm³. This criterion typically excludes the late portions of experiments when the ice cloud has almost completely decayed. (3) We exclude all the time periods in which the average particle radius is less than 0.85 µm, as described in Sect. 3.2, again because particle undercounts are likely. This criterion becomes relevant for cold experiments, in which vapor pressures are low and particles grow slowly and remain small (in IsoCloud experiments at temperatures below 195 K, average particle radius remains under 1.5 µm at all times). These criteria result in an average fit region length of ∼700 s. The shortest fit region is 259 s (Experiment 9) and the longest fit region is 1647 s (Experiment 21). Colder experiments tend to have longer fit regions, since in these experiments the ice cloud can linger for tens of minutes after pumping has ceased.

3.5 Uncertainty analysis

We calculate error bars for each experiment that reflect uncertainties from several sources: intrinsic measurement precision for water vapor and other key observables, uncertainty due to experimental artifacts (e.g., chamber inhomogeneities that affect model fits), and systematic offsets (e.g., line strength errors that produce multiplicative errors in derived vapor pressures). We group the first two categories, measurement precision and chamber artifacts, under the term “instrumental uncertainty”.

Instrumental uncertainty for each experiment is calculated using the Monte Carlo method: for each experiment, we generate 2000 parameter sets in which each physical parameter used in the calculation is randomly drawn from its estimated distribution, and then we run the fit routine on each set. See Table S1 for the list of parameters varied and their assumed distributions. AIDA chamber temperature uncertainty of 0.3 K is included in this table as a random variable, although the temporal correlation of temperature errors is not well known. Resulting error bars may therefore be slightly underestimated. The resulting distribution of saturation vapor pressure values is nearly normal in each experiment, and we take its standard deviation to be the component of the error bar associated with instrumental uncertainty. Sarkozy et al. (2020) estimate that mechanical vibrations and chamber inhomogeneities result in optical path length fluctuations of about 0.1 %. Due to the rapid timescales of these fluctuations, their associated uncertainty is added directly into the instrumental uncertainty budget.

The primary source of systematic offsets is uncertainty in the spectroscopic parameters used to retrieve water vapor concentrations from the observed spectral features. All spectroscopic parameters are taken from the HITRAN 2016 database (Gordon et al., 2017), which provides uncertainty estimates for several parameters used in this analysis, namely line strength (S), air-broadened half-width (γ_air), and the temperature-dependence coefficient (n_air) of γ_air. Line strength errors arise in two ways: through raw uncertainty of the measured line strength at the reference temperature of 296 K, and through uncertainty in the measured experimental gas temperature that propagates to uncertainty in the calculated temperature-dependent line strength. The ChiWIS instrument uses the H₂O line at 3789.63481 cm⁻¹, which has a stated 1σ uncertainties in S, γ_air, and n_air of ±1 %, ±1 %, and ±10 %, respectively, in HITRAN 2016. Uncertainty in S propagates directly into a ±1% systematic uncertainty in retrieved concentrations. The uncertainties in γ_air and n_air correspond to uncertainties in concentration retrieval of 0.5 % and 1.5 %, respectively, in the typical temperature and pressure range of the IsoCloud experiments. AIDA chamber temperature uncertainty is assumed to be randomly distributed, and contributes an additional line strength uncertainty of 0.1 % (note that typical temperature declines of 5–9 K during expansion experiments are automatically incorporated in the retrievals). Systematic errors due to uncertainty in spectroscopic parameters are added directly to the calculated error bars, and in all but the coldest experiments are the dominant source of uncertainty. A final contribution to systematic uncertainty comes from uncertainty in the length of the ChiWIS free space etalon, which propagates directly into the wavelength scale and contributes an estimated 0.2 % to all experiments.

Several other factors produce uncertainties on timescales of days or shorter and are treated here as contributing to the instrumental uncertainty budget. Uncertainty in White cell optical path length due to mechanical vibrations and chamber inhomogeneities occurs at rapid timescales and is estimated at 0.1 % (Sarkozy et al., 2020). Thermal expansion and contraction of the whole chamber over the experimental temperature range produces uncertainty of 0.1 % in the White cell path length and is day specific, since the chamber is run at a constant base temperature on each experimental day. Finally, the fit routine itself involves intrinsic uncertainty that is also likely day specific, since fits for each experimental day are typically done as a group and share typical temperature and water vapor concentrations. Sensitivity tests suggest that the choice of fit parameters (baseline, fit region, etc.) over a reasonable set of values may alter retrieved concentrations by about 1 %.

Because the final output of the analysis is the relationship of saturation vapor pressure to temperature x(T), we must consider a final source of uncertainty, that each experiment produces a single value for x but spans several degrees of cooling. We therefore construct horizontal error bars to acknowledge the spread in T, assigning them the standard deviation of chamber temperatures during the experimental fit period. These error bars are typically smaller in warmer experiments, since fit regions in that regime lie almost completely within the time interval when the wall heat flux balances the adiabatic cooling. Horizontal error bars are larger in colder experiments since the ice cloud often persists for some time after the pumps turn off and the chamber begins to warm back to its base temperature.