Ice growth diagram

Table of Contents

• Introduction
• Basic ice diagrams
  • Relative humidity with respect to water
  • Relative humidity with respect to ice
  • Vapor density excess
  • Relative humidity with respect to water (textbook version)
• Converting between ice supersaturation and vapor density excess
• Repository description
  • Root
  • Helper functions
  • Growth diagram profiles
  • Demo
• Growth diagram profiles
• Sources and credit

Introduction

Complete set of MATLAB code to plot the ice growth form diagram from Hueholt et al. (2022) "Revisiting Diagrams of Ice Growth Environments" Bulletin of the American Meteorological Society. Tested and confirmed operational on MATLAB 2020a+. The ice growth diagram can be cast into three moisture variables: relative humidity with respect to water, relative humidity with respect to ice, and vapor density excess over ice saturation. There are "textbook" and "applied" versions of each ice diagram. The "textbook" versions are designed to be the most aesthetically-pleasing. "Applied" versions are higher-contrast, allowing for data to be easily overlayed.
The version of record for this code corresponding to the paper can be found at the archive hosted on Open Science Foundation. To quickly replicate the figures from the paper, see the script makeFigures in the Demo subdirectory.

Figures 1, B1, B2, B3 from Hueholt et al. (2022) are reproduced on this repository under Fair Use for educational purposes. These figures are © Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this Work, please contact [email protected]. Any use of material in this Work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC § 108) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. All AMS journals and monograph publications are registered with the Copyright Clearance Center (https://www.copyright.com). Additional details are provided in the AMS Copyright Policy statement, available on the AMS website (https://www.ametsoc.org/PUBSCopyrightPolicy).

Basic ice diagrams

The following examples show how to make the three applied diagrams and the textbook diagram cast in terms of relative humidity with respect to water.

Ice growth diagram: relative humidity with respect to water

This is our preferred version of the diagram (Figure B1 from Hueholt et al. 2022). Relative humidity with respect to water is easier to understand and better represents the phase space of ice processes in the atmosphere than other moisture variables.

Minimal code to replicate

1. iceGrowthDiagramWater The code will automatically set inputs, including the necessary basic hd structure.

Full code to replicate

1. [hd] = makeGrowthDiagramStruct(1,1)
2. iceGrowthDiagramWater(hd,0,1,'southoutside',[55 105],[-70 0],0,1)

Ice growth diagram: relative humidity with respect to ice

For comparison to previous work, especially Bailey and Hallett (2009). This appears as Figure B2 in Hueholt et al. 2022.

Minimal code to replicate

1. iceGrowthDiagram The code will automatically set inputs, including the necessary basic hd structure.

Full code to replicate

1. [hd] = makeGrowthDiagramStruct(1,1)
2. iceGrowthDiagram(hd,1,0,1,'southoutside',[0 0.6],[-70 0],0,1)

Ice growth diagram: vapor density excess

For comparison to previous work, especially Kobayashi (1961), Furukawa and Wettlaufer (2007), or Libbrecht (2017). This appears as Figure B3 in Hueholt et al. 2022.

Minimal code to replicate

1. iceGrowthDiagramVaporExc The code will automatically set inputs, including the necessary basic hd structure.

Full code to replicate

1. [hd] = makeGrowthDiagramStruct(1,1)
2. iceGrowthDiagramVaporExc(hd,1,0,1,'southoutside',[0 0.351],[-70 0],0,1)

Ice growth diagram: relative humidity with respect to water (textbook edition)

This appears as Figure 1 in Hueholt et al. 2022. This code can also be used to generate analogous images in terms of relative humidity with respect to ice or vapor density excess.

Code to replicate

1. iceGrowthDiagramTextbook
2. The code will prompt the user for a phase. Input 'water' to obtain the diagram shown here.
3. The user will be prompted Y/N whether or not to save a PNG image. Enter Y to save, N to continue without saving.

Converting between ice supersaturation and vapor density excess

Two common units of supersaturation are ice supersaturation (percent or decimal) or vapor density excess beyond ice saturation (g/m^3). Converting between the two units is possible, but not intuitive. Use iceSupersatToVaporExc to convert between these units.

Example

Given an ice supersaturation of 3.8% at -8 deg Celsius, what is the vapor density excess at the same temperature?

1. [vde] = iceSupersatToVaporExc(0.038,-8)
   This returns vde = 0.0962. Thus a vapor density excess of 0.096 g/m^3 corresponds to an ice supersaturation of 3.8% at -8 deg Celsius!

To convert from ice supersaturation to relative humidity with respect to water use iceSupersatToRHw. For the reverse process from RHw to RHi, see rhwToRhi. To calculate vapor density excess from relative humidity with respect to water directly, use rhwToVaporExc.

Repository description

root

makeGrowthDiagramStruct: Creates a structure with the information needed to plot a growth diagram. Values are derived from Bailey and Hallett (2004) and Bailey and Hallett (2009).
iceGrowthDiagramWater: Plots the ice growth diagram in terms of relative humidity with respect to water. Input options allow for control of diagram aesthetics, e.g. isohumes, ventilation, legend, etc.
iceGrowthDiagram: Plots the ice growth diagram in terms of relative humidity with respect to ice. Input options allow for control of diagram aesthetics, e.g. isohumes, ventilation, legend, etc.
iceGrowthDiagramVaporExc: Plots the ice growth diagram in terms of vapor density excess over ice saturation. Input options allow for control of diagram aesthetics, e.g. isohumes, ventilation, legend, etc.

Helper functions subdirectory

rhwToRhi: Converts relative humidity with respect to water to relative humidity with respect to ice.
iceSupersatToRHw: Converts an ice supersaturation in percent to a relative humidity with respect to water, also in percent.
iceSupersatToVaporExc: Converts an ice supersaturation in decimal to a vapor density excess in g/m^3.
rhwToVaporExc: Converts a relative humidity with respect to water to vapor density excess in g/m^3.
eswLine: Outputs arrays useful to draw isohumes with respect to water on the diagram.
updraftSupersat: Uses the Twomey equation to calculate supersaturation in an updraft but only at a certain range of thermodynamic conditions well above freezing. Implemented as a curiosity.
ylimitsForIceDiagram: Generates labels and tick marks for the ICAO atmospheric height approximation axis on the ice diagram.

Growth diagram profiles subdirectory

growthDiagramProfile: Plots ice growth profiles for input radiosonde data. See the IGRA v2 repository for information on radiosonde data.
stationLookupIGRAv2: Looks up station names for titles of ice growth profiles.
IGRA v2 Station List.mat: List of radiosonde launch site station names.
utqiagvik_sample.mat: Sample data to make ice growth profiles.

Demo subdirectory

*.mat files: Radiosonde data files used for in-progress paper "Revisiting diagrams of ice growth environments."
makeFigures: Script used to make images for in-progress paper "Revisiting diagrams of ice growth environments."
Image files in this directory are used in the Github readme.

Growth diagram profiles

The function growthDiagramProfile can be used to plot data from radiosondes on the ice growth diagram. This shows what areas of the crystal growth space are accessible along a profile. A sample data structure from the Utqiagvik launch site is included in the "Growth diagram profiles" subdirectory. An example image is below.

Code to replicate

1. Open the sample Utqiagvik data in MATLAB: utqiagvik_sample = load('Demo/utq_djf1718.mat')
2. Make sure stationLookupIGRAv2 and IGRA v2 Station List.m are in the working directory. These are necessary to produce the title of the growth diagram profile.
3. growthDiagramProfile(utqiagvik_sample.utq_djf1718,1:121,1,'water',0,0)
4. The command window will prompt for a date. Type DJF 2017-2018.
5. The command window will prompt for a location. Type Utqiagvik, AK.

Code to import a general Integrated Global Radiosonde Archive (IGRA) v2 soundings data file can be found in the IGRA v2 repository.

Sources and Credit

This package was developed as part of Hueholt et al. (2022) "Revisiting Diagrams of Ice Growth Environments" in review at Bulletin of the American Meteorological Society. See this paper for details about the science behind the diagrams.

Bailey, M.P., & Hallett, J. (2004): Growth Rates and Habits of Ice Crystals between -20°C and -70°C. Journal of the Atmospheric Sciences, 61(5), 514-544. doi.org/10.1175/1520-0469(2004)061%3C0514:GRAHOI%3E2.0.CO;2
Bailey, M.P., & Hallett, J. (2009): A comprehensive habit diagram for atmospheric ice crystals: Confirmation from the laboratory, AIRS II, and other field studies. Journal of the Atmospheric Sciences, 66(9), 2888-2899. doi:10.1175/2009JAS2883.1
Furukawa, Y., and J. S. Wettlaufer, 2007: Snow and ice crystals. Physics Today, 60 (12), 70–71,485doi:10.1063/1.2825081, URL https://physicstoday.scitation.org/doi/10.1063/1.2825081.
Kobayashi, T., 1961: The growth of snow crystals at low supersaturations. Philosophical Magazine, 5326 (71), 1363–1370, doi:10.1080/14786436108241231, URL http://www.tandfonline.com/doi/533abs/10.1080/14786436108241231.
Libbrecht, K. G., 2017: Physical Dynamics of Ice Crystal Growth. Annu. Rev. Mater. Res., 57147 (1), 271–295, doi:10.1146/annurev-matsci-070616-124135, URL https://doi.org/10.1146/572annurev-matsci-070616-124135, publisher: Annual Reviews.

All code and documentation written by Daniel Hueholt, in collaboration with Dr. Sandra Yuter and Dr. Matthew Miller at North Carolina State University.

This work was supported by the National Science Foundation (AGS-1347491 and AGS-1905736), the National Aeronautics and Space Administration (80NSSC19K0354), and the North Carolina State University Honors Program (Hueholt).

Radiosonde data is from the Integrated Global Radiosonde Archive, version 2.