ESCI 340 Physical Meteorologoy Cloud Physics Lesson 5 Growth of Ice Crystals

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1 ESCI 340 Physicl Meteorologoy Cloud Physics Lesson 5 Growth of Ice Crystls References: A Short Course in Cloud Physics (3 rd ed.), Rogers nd Yu Microphysics of Clouds nd Precipittion ( nd ed.), Pruppcher nd Klett Ken Libbrecht s Field Guide to Snowflkes, Ken Libbrecht Reding: Rogers nd Yu, Chpter 9 PURPOSE 1) Describe the unique structure of the wter molecule nd how it reltes to the physicl properties of liquid wter nd ice. ) Understnd the formtion nd growth of ice crystls. 3) Describe the Bergeron (cold-cloud) process for precipittion formtion. STRUCTURE OF WATER Wter molecules re bent t n ngle of Wter molecules hve dipole, due to the different electron ffinities of hydrogen nd oxygen. The oxygen side of the molecule is negtively chrged, while the hydrogen side is positively chrged. Becuse of this structure, the intermoleculr (Vn Der Wls) forces re importnt, nd leds to the interesting behvior of wter compred to other substnces. The density of wter does not monotoniclly increse s temperture decreses. Insted, it reches mximum t bout 4 C (see digrm below).

2 The solid phse of wter is ctully less dense thn the liquid phse, unlike most other substnces (the specific volume of ice t 0 C is 1.09 cm 3 g 1.) Ice crystls hve different shpes, or hbits, depending on the conditions of temperture nd super-sturtion under which they form. The most common shpes re hexgonl pltes, hexgonl columns, nd dendrites. FORMATION OF ICE CRYSTALS Ice crystls cn form either by the freezing of super-cooled wter droplets, or vi deposition. Just s condenstion requires nucleus to provide surfce for the embryonic wter droplet to form round, so to does deposition. Ice crystls must form round some nuclei ο The exception is perhps cirrus clouds, which form t tempertures cold enough tht homogeneous nucletion of ice crystls my occur. The nuclei for deposition re clled ice nuclei. Ice nuclei re rre. Only one out of 10 million erosols is n effective ice nuclei. Little is known bout ice nuclei, but it ppers tht the primry ice nuclei in the tmosphere is the minerl kolinite, which is found in mny soils. Certin bcteri my lso be ice nuclei. Becuse ice nuclei re so rre, it is common to find clouds consisting of supercooled liquid wter droplets t tempertures s cold s 15 C, nd super-cooled liquid clouds hve even been found t tempertures s low s 40 C.

3 ο These super-cooled wter droplet will freeze instntly upon impct with objects, nd re primry concern when ircrft fly through such clouds since they form ice on the wings, propellers, nd engine intkes. ο The smller the drop, the more likely it is to be super-cooled t very low tempertures. Once n ice crystl forms it cn grow by diffusion, ccretion, or ggregtion. DIFFUSIONAL GROWTH OF ICE CRYSTALS Diffusionl growth of ice crystls is more rpid thn tht of liquid wter droplets becuse the sturtion vpor pressure over ice is less thn tht over wter. The diffusionl growth eqution for ice crystls is very similr to tht for wter droplets, nd is dm = 4π CD ( ρ ρr ). (1) dt where ρ R is the sturtion bsolute humidity t the surfce of the crystl, nd C is shpe fctor tht depends on the shpe of the crystl. ο This eqution is relly the sme s tht for wter droplets, becuse for sphere, C = R where R is the rdius of the sphere. The pproximte shpe fctors for vrious shpes re Shpe plte R /π prolte spheroid (used for ice needles) oblte spheroid C + b [( + b b) ] ln + rcsin 1 b 1 b where nd b re the semi-mjor nd semi-minor xes. 3

4 As with wter droplets, n eqution for the blnce of ltent het of sublimtion dded to the crystl, nd tht diffused wy from the crystl, must lso be used when discussing diffusionl growth. This eqution is ρ ρr K =. () T T L D R where L s is the ltent het of sublimtion. A form of the Clusius-Clpyron eqution is used to determine the sturtion vpor pressure over ice t the surfce of the crystl. The three equtions cn then be solved for the growth rte. The mximum growth rte occurs in the temperture rnge of 10 C to 15 C, so it is t these tempertures tht ice crystls grow fstest by diffusion. Unlike for wter droplets, diffusionl growth of ice crystls is fst enough to explin how precipittion consisting of single crystls (snow grins) cn form. When these melt, they become drizzle. For lrger precipittion to form, the ice crystls must grow by either ccretion (colliding with super-cooled wter droplets) to form grupel, or ggregtion (colliding with other ice crystls) to form snowflkes (which my then melt to become rin). The process of precipittion formtion in cold clouds by ice crystl diffusionl growth t the expense of liquid wter droplets is known s the Bergeron process. s BRANCHING VERSUS FACETING Ice crystls grow through the competing processes of brnching nd fceting. Fceting refers to the tendency for the wter molecules to form flt or crystlline surfces s they collect on the crystl. ο Fceting drives the fct tht ice crystls re hexgonl forms. Brnching refers to the tendency for the wter molecules to diffuse preferentilly to jutting or irregulr fetures the poke out from the surfce. ο Brnching drives the formtion of tendrils nd rms on ice crystls. When crystls first form they re smll, with noticeble, regulr fcets. As the crystl grows the tips grow preferentilly due to brnching. ο So, insted of hving flt fcets, they become concve. 4

5 As the crystl grows bigger, the point begin growing into brnches. The humidity in the environment of the snowflke chnges throughout its lifetime. This cn led to side brnching: ο In high super-sturtion environments the brnches will grow rpidly nd the tips will be more rounded. ο With lower super-sturtion the growth is slower, which fvors the formtion of fcets on the tip of the brnch. ο The edges of these fcets cn further grow into sidebrnces. COLLISION-COALESCENCE VERSUS THE BERGERON PROCESS In wrm clouds (those whose tops re not pprecibly colder thn freezing), the collision-colescence process is the only process tht cn explin the initition nd growth of precipittion. In cold clouds, either or both processes my be t work to explin initition of precipittion. The reltive importnce of either process depends on the type of cloud. In generl: ο The Bergeron process is likely more importnt in strtiform clouds, wheres collision-colescence is more importnt in convective clouds. In strtiform clouds, ice crystls from the very cold upper levels fll into the cold lower levels where they grow rpidly. As they fll further, they continue to grow by ccretion nd ggregtion. So, the precipittion is initited in the upper levels, but grows in the lower levels. 5