No anomalous supersaturation in ultracold cirrus laboratory experiments

High-altitude cirrus clouds are climatically important: their formation freeze-dries air ascending to the stratosphere to its final value, and their radiative impact is disproportionately large. However, their formation and growth are not fully understood, and multiple in situ aircraft campaigns have observed frequent and persistent apparent water vapor supersaturations of 5 %–25 % in ultracold cirrus (T<205 K), even in the presence of ice particles. A variety of explanations for these observations have been put forth, including that ultracold cirrus are dominated by metastable ice whose vapor pressure exceeds that of hexagonal ice. The 2013 IsoCloud campaign at the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) cloud and aerosol chamber allowed explicit testing of cirrus formation dynamics at these low temperatures. A series of 28 experiments allows robust estimation of the saturation vapor pressure over ice for temperatures between 189 and 235 K, with a variety of ice nucleating particles. Experiments are rapid enough (∼10 min) to allow detection of any metastable ice that may form, as the timescale for annealing to hexagonal ice is hours or longer over the whole experimental temperature range. We show that in all experiments, saturation vapor pressures are fully consistent with expected values for hexagonal ice and inconsistent with the highest values postulated for metastable ice, with no temperature-dependent deviations from expected saturation vapor pressure. If metastable ice forms in ultracold cirrus clouds, it appears to have a vapor pressure indistinguishable from that of hexagonal ice to within about 4.5 %.

A Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice

It is necessary to calculate the saturation vapor pressure of water and of ice for some purposes in many disciplines. A number of formulas are available for this calculation. These formulas either are tedious or are not very accurate. In this study, a new formula has been developed by integrating the Clausius–Clapeyron equation. This new formula is simple and easy to remember. In comparison with the International Association for the Properties of Water and Steam reference dataset, the mean relative errors from this new formula are only 0.001% and 0.006% for the saturation vapor pressure of water and of ice, respectively, within a wide range of temperatures from −100° to 100°C. In addition, this new formula yields a mean relative error of 0.0005% within the commonly occurring temperature range (10°–40°C). Therefore, this new formula has significant advantages over the improved Magnus formula and can be used to calculate the saturation vapor pressure of water and of ice in a wide variety of disciplines.

The vapor pressure over nano-crystalline ice

The crystallization of amorphous solid water (ASW) is known to form nano-crystalline ice. The influence of the nanoscale crystallite size on physical properties like the vapor pressure is relevant for processes in which the crystallization of amorphous ices occurs, e.g., in interstellar ices or cold ice cloud formation in planetary atmospheres, but up to now is not well understood. Here, we present laboratory measurements on the saturation vapor pressure over ice crystallized from ASW between 135 and 190 K. Below 160 K, where the crystallization of ASW is known to form nano-crystalline ice, we obtain a saturation vapor pressure that is 100 to 200 % higher compared to stable hexagonal ice. This elevated vapor pressure is in striking contrast to the vapor pressure of stacking disordered ice which is expected to be the prevailing ice polymorph at these temperatures with a vapor pressure at most 18 % higher than that of hexagonal ice. This apparent discrepancy can be reconciled by assuming that nanoscale crystallites form in the crystallization process of ASW. The high curvature of the nano-crystallites results in a vapor pressure increase that can be described by the Kelvin equation. Our measurements are consistent with the assumption that ASW is the first solid form of ice deposited from the vapor phase at temperatures up to 160 K. Nano-crystalline ice with a mean diameter between 7 and 19 nm forms thereafter by crystallization within the ASW matrix. The estimated crystal sizes are in agreement with reported crystal size measurements and remain stable for hours below 160 K. Thus, this ice polymorph may be regarded as an independent phase for many atmospheric processes below 160 K and we parameterize its vapor pressure using a constant Gibbs free energy difference of (982 ± 182) J mol−1 relative to hexagonal ice.

The vapor pressure over nano-crystalline ice

Crystallization of amorphous solid water (ASW) is known to form nano-crystalline ice. The influence of the nanoscale crystallite size on physical properties like the vapor pressure is relevant for processes where crystallization of amorphous ices occurs e.g. in interstellar ices or cold ice cloud formation in planetary atmospheres, but up to now not well understood. Here, we present laboratory measurements on the saturation vapor pressure over nano-crystalline ice between 135 K and 190 K. Below 160 K, where nano-crystalline ice is known to be metastable for extended periods, we obtain a saturation vapor pressure that is 100 % to 200 % higher compared to stable hexagonal ice. This elevated vapor pressure is in striking contrast to the vapor pressure of stacking disordered ice which is expected to be the prevailing ice polymorph at these temperatures with a vapor pressure at most 18 % higher than that of hexagonal ice. This apparent discrepancy can be reconciled by assuming that nanoscale crystallites with mean diameter between 7 nm and 19 nm form in the crystallization process of ASW. The high curvature of these nano-crystallites results in a vapor pressure increase which can be described by the Kelvin equation. Our measurements show, that at temperatures up to 160 K, ASW is the first solid form of ice deposited from the vapor phase and that nano-crystalline ice forms thereafter by crystallization within the ASW matrix. The size of the nano-crystallites remains stable for hours below 160 K and thus nano-crystalline ice may be regarded as an independent phase for many atmospheric processes below 160 K. We parameterize the vapor pressure of nano-crystalline ice using a constant Gibbs free energy difference of (982 ± 182) J mol−1 relative to hexagonal ice.