An estimate of the optical significance of trigonal ice particles

An estimate of the optical significance of trigonal ice particles
Institute for Climate and Atmospheric Science (ICAS) An estimate of the optical significance of trigonal ice particles Steven Dobbie Institute for Climate and Atmospheric Science University of Leeds Ben Murray, Chris Salzmann, Ryan Neely

Institute for Climate and Atmospheric Science

Photo credit: Wilson Bentley Digital Archives of the Jericho Historical Society (snowflakebentley.com)

Trigonal ice crystals sampled manually using cold slides and a micropscope Summit, Greenland at -28 oC On Oct 14, 2012

Heymsfield (1986) report that about 50% of the 5-50 µm crystals sampled in this cloud were trigonal plates with the majority of the others being columns (of unknown symmetry). Trigonal ice crystals sampled in the tropical tropopause layer. Formivar replica ice crystal in sampled from an aircraft at km in Dec 1973 where the temperature was -84 to -83C.

Bentley and Humphreys, 1962 Libbrecht, 2006, 2008

Yamashita (1973) in the laboratory found that trigonal ice crystals tended to be small (roughly <40 μm on the basal face), so it may be possible that the large number of poorly resolved smaller ice crystals reported by Lawson et al. (2008) were trigonal Trigonal ice crystals sampled in the tropical tropopause layer. Formivar replica ice crystal in sampled from an aircraft at km in Dec 1973 where the temperature was -84 to -83C.

Scalene crystals Institute for Climate and Atmospheric Science
“These crystals have six faces, but the faces are not equal in length. They therefore do not poses hexagonal symmetry and crystals which have six sides of varying length with 60o between faces are referred to as scalene hexagons.”

“Ice I comes in two crystalline forms: cubic ice (ice Ic) and hexagonal ice (ice Ih). Both of these forms of ice are made up of identical layers of puckered hexagonal rings of oxygen atoms which are connected via hydrogen bonds, but the stacking of these layers distinguishes the two phases. “

“Hence, the presence of stacking disorder in crystals provides a crystallographic explanation for the presence of trigonal crystals in the atmosphere.”

Photos from: Chris Westbrook Q. J. R. Meteorol. Soc. 137: 538–543, January 2011 B

Optics needed to assess radiative forcing Radiative transfer uses the extinction, single scattering albedo and asymmetry factor weighted by the size distributions of particles present and these specify the radiative transfer through layers of such particles. Solve with a two, four etc stream approximation.

Optics needed to assess radiative forcing

Optics needed to assess radiative forcing 1. Extinction How much radiation interacts with the particle through both absorption and scattering

Optics needed to assess radiative forcing 2. Single Scattering Abedo What proportion of radiation is scattering compared to scattering + absorption (ext)

Optics needed to assess radiative forcing 2. Asymmetry parameter, g A measure of the angular distribution of the scattered light. g is the forward projection of scattering – the backward projection of scattering.

ADT or ADA approximation (van de Hulst, 1957, 1981) m l P 𝜓=𝑘𝑙(𝑚−1)

ADA Approximation Extinction cross section (optical theorem) 𝜎 𝑒𝑥𝑡 = 4𝜋 𝑘 2 Re{𝑆 0 } Following Chylek and Klett, J. Opt Soc. Am. A. (1991) 𝑆(0)= 𝑘 2 2𝜋 (1− 𝑒 −𝑖𝜓 ) 𝑑𝑃 Phase shift 𝜓=𝑘𝑙 𝑚−1 |m-1|<<1

Comparison to Mie

ADT or ADA approximation – Hexagonal Crystal m l P 𝜓=𝑘𝑙(𝑚−1)

ADT or ADA approximation – Trigonal Crystal m l P 𝜓=𝑘𝑙(𝑚−1)

ADT or ADA approximation – Scalene Crystal l m P 𝜓=𝑘𝑙(𝑚−1)

ADT or ADA approximation – Scalene Crystal 1 dP 2 P/2 3 m 𝑆(0)= 𝑘 2 2𝜋 (1− 𝑒 −𝑖𝜓 ) 𝑑𝑃 𝜓=𝑘𝑙(𝑚−1)

ADT or ADA approximation – Scalene Crystal C C 1 dh C/2 2 (2C)cos(30) 3 m 𝑆(0)= 𝑘 2 2𝜋 (1− 𝑒 −𝑖𝜓 ) 𝑑𝐿𝑑ℎ 𝜓=𝑘𝑙(𝑚−1)

ADT or ADA approximation – Scalene Crystal C C 1 h C/2 l=2 3 h 𝑆(0)= 𝑘 2 𝐿 2𝜋 0 𝑐/2 (1− 𝑒 −𝑖𝑘2 3 ℎ(𝑚−1) ) 𝑑ℎ 𝜓=𝑘𝑙(𝑚−1) 𝑚= 𝑚 𝑟 − 𝑖𝑚 𝑖

𝑆(0)= 𝑘 2 𝐿 2𝜋 0 𝑐/2 (1− 𝑒 −𝑖𝑘2 3 ℎ(𝑚−1) ) 𝑑ℎ
Institute for Climate and Atmospheric Science 𝑆(0)= 𝑘 2 𝐿 2𝜋 0 𝑐/2 (1− 𝑒 −𝑖𝑘2 3 ℎ(𝑚−1) ) 𝑑ℎ 𝑚= 𝑚 𝑟 − 𝑖𝑚 𝑖

𝜎 𝑒𝑥𝑡 = 4𝜋 𝑘 2 Re{𝑆 0 } 𝜎 𝑒𝑥𝑡 =2𝐿 𝐶 2 − αγ+ηβ α 𝑏 2 + α α 𝑏 2
Institute for Climate and Atmospheric Science 𝜎 𝑒𝑥𝑡 = 4𝜋 𝑘 2 Re{𝑆 0 } 𝜎 𝑒𝑥𝑡 =2𝐿 𝐶 2 − αγ+ηβ α 𝑏 α α 𝑏 2 Where: γ= 𝑒 α𝑐 2 cos⁡( β𝑐 2 ) α=−𝑘 𝑚 𝑖 2 3 η= 𝑒 α𝑐 2 sin⁡( β𝑐 2 ) β=−𝑘 (𝑚 𝑟 −1)2 3 α 𝑏 2 = α 2 + β 2

ADT or ADA approximation – Scalene Crystal 1 dP 2 P/2 3 m 𝑆(0)= 𝑘 2 2𝜋 (1− 𝑒 −𝑖𝜓 ) 𝑑𝑃 Calculate regions 1-3 and add and double.

- Thank you -

Summary Institute for Climate and Atmospheric Science
Trigonal and scalene are prevalent in the atmosphere. Many extreme shapes to consider. Accurate and fast techniques needed to process the shapes. Understanding of conditions/histories that lead to these shapes.

Summary Institute for Climate and Atmospheric Science
Trigonal ice absorbs less than hexagonal or scalene shapes. Single scattering albedo consistently lower. More shapes need to be calculated and effects evaluated in radiative transfer calculations.

- Thank you -

What is up there? Froyd et al 2010:
Institute for Climate and Atmospheric Science What is up there? Froyd et al 2010:

AIDA Chamber, Karlsruhe Aqueous citric acid, Raffinose/M5AS, Levoglucosan, HMMA it has similar functionality to oxygenated organic compounds known to exist in atmospheric aerosols; its glass forming properties are similar to a range of other atmospherically relevant aqueous organic solutions and aqueous organic-sulphate mixtures; and Representative of products found in the atmosphere.

IN indirect effect

Radiative properties

Sun dogs – 22 Deg horizontally aligned plates Halo 22 deg due to this

Optics of triangular ice crystals
Institute for Climate and Atmospheric Science Optics of triangular ice crystals “They suggested that the initial ice to crystallise when water freezes is always stacking disordered ice , but the disorder can anneal out at warmer temperatures to leave pristine ice Ih “

Institute for Climate and Atmospheric Science Optics of triangular ice crystals “Malkin et al. (2012) suggested calling this ice stacking disordered ice (ice Isd) in order to distinguish it from the well-ordered forms of ice I (ice Ic and Ih). “ “Hence, the presence of stacking disorder in crystals provides a crystallographic explanation for the presence of trigonal crystals in the atmosphere.”

Institute for Climate and Atmospheric Science Optics of triangular ice crystals “Malkin et al. (2012) demonstrated that ~1 µm water droplets which froze homogeneously around -40oC crystallised to ice Isd which was fully disordered (50% of the layers were cubic and 50% were hexagonal and these were randomly arranged. Later Malkin et al. (submitted) have shown that introduction of heterogeneous ice nuclei to micron sized water droplet also leads to ice which contains substantial stacking disorder. “

An estimate of the optical significance of trigonal ice particles

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An estimate of the optical significance of trigonal ice particles

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