• Description: Rosemount Aerospace Model 0871ND4-FT Series 3 Ice Output Detector
• Manufacturer: Rosemount Aerospace Inc.
• Serial Number: 0871ND4-FT-0015

Figure by Greg Sova (greg.sova@und.edu)

From Mazin et al. (2001) paper "Thermodynamics of Icing Cylinder for Measurements of Liquid Water Content in Supercooled Clouds", should be possible to calibrate the RICE solely from signal change in sublimation periods instead of comparing to another liquid water detector.

The constant k is then multiplied by the negative change in frequency over time to get a supercooled liquid water content. Work on this stalled out when some values in the above equation were unable to be found or parameterized.

In private communication with Dr. Greg McFarquhar in April 2021, it was recommended to have a “comparison to adiabatic values when possible”. Work on this was deemed low priority for the time, but could provide value.

Original thesis idea was to use calibrated RICE values to determine the synoptic distribution of SLWC in Atlantic Snowstorms. When the calibration itself became involved enough to become its own thesis, this idea was shelved, but could provide scientific value in the future.

Dr. David Delene did some wind tunnel tests of the CDP, King Probe, and RICE Probe in May 2021, could be some valuable work comparing wind tunnel data to in-situ data.

Could be worth comparing the RICE SLWC values to the WISPER CWC values found during IMPACTS.

The Ludlam limit is the critical water content above which the freezing fraction of supercooled water is less than one. In other words, below the Ludlam limit, all of the supercooled water that comes in contact with the probe. Therefore, it is important to know when the RICE is sampling in conditions under the Ludlam limit, as those conditions are when the RICE is completely sampling environmental SLWC. Otherwise, some supercooled water could be shed from the probe prior to freezing, leading to a low bias.

The Ludlam limit has many factors, although air temperature is believed to be the most important. True air speed also has an influence as well as air pressure. The Ludlam limit has multiple derivations, although for airborne research, the derivations are challenging, which is why direct calculation of the Ludlam limit was avoided for this model of the RICE so far. However, it would be quite valuable for a direct understanding of the Ludlam limit to ensure high quality SLWC data. For now, the limit is addressed in the form of a temperature filter, not considering RICE SLWC values at air temperatures warmer than -3 degrees C. However, this number may not be appropriate at some true air speeds and pressures.

Some helpful resources and equations:

• Ludlam (1951). "The heat economy of a rimed cylinder".

The original Ludlam paper provides the following equation:

where m_c is the critical water content.

• Fraser et al. (1953). "Thermodynamic Limitations of Ice Accretion Instruments".

Fraser et al. gives the following equation for the critical water content:

Beware of the units, as thermal conductivity is measured in the archaic unit of CHU*sec^-1*ft^-3*deg C^-1, among other units.

• Bain and Gayet (1982). "Aircraft Measurements of Icing in Supercooled and Water Droplet/Ice Crystal Clouds".

Bain and Gayet give the following for the critical liquid water content:

with valuable parameterizations for the viscosity of air, latent heat of freezing, and convective heat transfer coefficient.

• Mazin et al. (2001). "Thermodynamics of Icing Cylinder for Measurements of Liquid Water Content in Supercooled Clouds".

Mazin et al. provides a calculation for the Ludlam limit:

along with a calculation for the heat transfer coefficient. Additionally, private communications with Dr. Alexei Korolev regarding this paper showed that the parameterization for the kinematic viscosity for this study was the following:

ν=(1000/P)(0.134+0.00085T_c)(1e-4)

• Mazin (1957). "The Physical Principles (Bases) of Aircraft Icing (Gidrometeoizdat)"

In Mazin et al. (2001), some of the unknowns are not well explained. They can apparently be derived from this work, the original work is in Russian, this is a machine-translated edition from 1979 from the Foreign Technology Division at WP-AFB, OH. Be warned, the document is very dry, 284 pages long, and the translation is imperfect.

Before giving up on direct Ludlam limit calculation, I wrote “is φ₀ from Mazin et al (2001) equal to p from page 47/284 of Mazin (1957)?”, so that might be a good starting point.