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

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Institute for Climate and Atmospheric Science Photo credit: Wilson Bentley Digital Archives of the Jericho Historical Society (snowflakebentley.com)

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

Institute for Climate and Atmospheric Science 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 16.2-16.7 km in Dec 1973 where the temperature was -84 to -83C.

Institute for Climate and Atmospheric Science Bentley and Humphreys, 1962 Libbrecht, 2006, 2008

Institute for Climate and Atmospheric Science 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 16.2-16.7 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.”

Scalene crystals Institute for Climate and Atmospheric Science “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. “

Scalene crystals Institute for Climate and Atmospheric Science “Hence, the presence of stacking disorder in crystals provides a crystallographic explanation for the presence of trigonal crystals in the atmosphere.”

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Institute for Climate and Atmospheric Science

Institute for Climate and Atmospheric Science

Institute for Climate and Atmospheric Science

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Institute for Climate and Atmospheric Science Photos from: Chris Westbrook Q. J. R. Meteorol. Soc. 137: 538–543, January 2011 B

Scalene crystals Institute for Climate and Atmospheric Science Photos from: Chris Westbrook Q. J. R. Meteorol. Soc. 137: 538–543, January 2011 B

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Institute for Climate and Atmospheric Science 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.

Institute for Climate and Atmospheric Science Optics needed to assess radiative forcing

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

Institute for Climate and Atmospheric Science Optics needed to assess radiative forcing 2. Single Scattering Abedo What proportion of radiation is scattering compared to scattering + absorption (ext)

Institute for Climate and Atmospheric Science 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.

Institute for Climate and Atmospheric Science ADT or ADA approximation (van de Hulst, 1957, 1981) m l P 𝜓=𝑘𝑙(𝑚−1)

Institute for Climate and Atmospheric Science 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

Institute for Climate and Atmospheric Science Comparison to Mie

Institute for Climate and Atmospheric Science ADT or ADA approximation – Hexagonal Crystal m l P 𝜓=𝑘𝑙(𝑚−1)

Institute for Climate and Atmospheric Science ADT or ADA approximation – Trigonal Crystal m l P 𝜓=𝑘𝑙(𝑚−1)

Institute for Climate and Atmospheric Science ADT or ADA approximation – Scalene Crystal l m P 𝜓=𝑘𝑙(𝑚−1)

Institute for Climate and Atmospheric Science 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)

Institute for Climate and Atmospheric Science 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)

Institute for Climate and Atmospheric Science 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 2 + 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

Institute for Climate and Atmospheric Science 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.

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Institute for Climate and Atmospheric Science

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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.

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

Institute for Climate and Atmospheric Science 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.

Institute for Climate and Atmospheric Science IN indirect effect

Institute for Climate and Atmospheric Science Radiative properties

Institute for Climate and Atmospheric Science 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 “ 

Optics of triangular ice crystals 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.”

Optics of triangular ice crystals 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. “