5. Ice crystal and aggregate properties (Pruppacher and Klett 1997 Secs. 2.2.1 and 2.2.2 plus various journal articles) According to the AMS Glossary of Meteorology, • Ice Crystal = “Any one of a number of macroscopic, crystalline forms in which ice appears, including hexagonal columns, hexagonal platelets, dendritic crystals, ice needles and combinations of these forms” • Snow = “Precipitation composed of white or translucent ice crystals, chiefly in complex branch hexagonal form and often agglomerated into snowflakes” • Snow Crystal = “Any of several types of ice crystal found in snow” – “A snow crystal is a single crystal, in contrast to a snowflake, which is usually an aggregate of many single snow crystals.” • Aggregation = “2. The process of clumping together of snow crystals following collision as they fall to form snowflakes” • Snowflake = “Colloquially an ice crystal, or more commonly an aggregation of many crystals that falls from a cloud” • In this class – Snow crystal = single ice crystal – Snowflake = aggregation of ice crystals = ice aggregate 1 • Ice particles grow by diffusion of water vapor = deposition • Called ice crystals or snow crystals • Snow crystals can grow by collision with other snow crystals = aggregation • Aggregates of snow crystals = snowflakes • Snow crystals (snowflakes) can also grow by collection of supercooled drops that freeze = riming • • • Eventually become graupel when crystal habit is lost Based on observations, supercooled (liquid water) clouds are common occurrence, especially if cloud top temperature is > -10°C With decreasing temperature, likelihood of ice increases such that at -20°C only about 10% of clouds consist entirely of supercooled drops (i.e., 90% have ice) (see below from PK97) Pruppacher and Klett (1997) (PK97) 2 5.1 Ice crystal shape (habit) • • Casual observations suggest that snow crystals appear in a large variety of shapes (or habits) – more later But detailed crystallographic studies reveal that snow crystals have one common basic shape – six-fold symmetric (hexagonal) prism with two basal planes (of type 0001) and six prism planes (of type 1010) (see top) – Other crystal faces are more rare (metastable), grow quickly and usually form edges (bottom) Basal face (plane) = c-axis growth Prism face (plane) = aaxis growth Pruppacher and Klett (1997) • Laboratory experiments reveal that ice crystal habit [or the rate of propagation of the basal faces (growth along c-axis) relative to that of prism faces (i.e., growth along a-axis)]varies in a characteristic manner with • Temperature and • Supersaturation 3 • At large vapor density excess (or supersaturation) with respect to ice, the snow crystal shape changes with decreasing temperature from a plate to a needle, to a column, to a sector plate, to a dendrite, back to a sector plate and finally back to a column Variation of ice crystal habit with temperature and supersaturation (top) or vapor density excess (bottom) – Cyclic plate-column-plate-column change in habit is due to a cyclic change of the preferential growth direction along the a-axis and caxis – Transition temperatures at -4°C, 9°C, -22°C – First two transitions are sharp; last at -22°C diffuse change (several °) • • At very low vapor density excess, the crystal shape changes between short column and a thick plate near -9°C, -22°C Close to or at ice saturation, ice crystal shape ceases to vary with temperature and assumes equilibrium shape, which is a thick hexagonal plate with a height-to-diameter ratio of 0.8 Pruppacher and Klett (1997) 4 • Although temperature is principal factor, humidity conditions in the environment also control important growth features of snow – – E.g., prior page, near -15°C, snow crystal habit varies with increasing vapor density excess from thick plate to thin plate to sector plate and finally to dendrite E.g., near -5°C, habit varies with increasing vapor density excess from short solid column, to hollow column to a needle with pronounced growth in c-axis direction • “Magono-Lee” diagram (right) summarizes observations of snow crystal habits • • “Magono-Lee Diagram” from observations of natural snow crystals Observations show similar temperature and humidity control of ice habit More recent observations tend to confirm • Good agreement between observations and lab studies • Comprehensive “MagonoLee classification” of natural ice habits next page Pruppacher and Klett (1997) 5 Magono-Lee Classification of Natural Snow Crystals (for reference) 6 Example of more recent ice crystal habit observations from the SPEC CPI SPEC Cloud Particle Imager (CPI) Source: http://www.specinc.com/cloud-particle-imager 7 Example CPI observations from deep tropical stratiform precipitation during TRMM Field Campaigns (FCs) Many of us study convection. What do ice crystals look like in stratiform regions associated with convection? Numerous vapor-grown crystals observed intermediate (400-600 µm) and large (> 800 µm) size range, including columns, capped columns, hexagonal plates and branched crystals. Initial formation of columns (-20°C to -25°C) (at echo top above CPI) and then capped columns as particles fell through planarcrystal growth regime (-12°C to -18°C) Aggregates with some minimal riming in larger sizes observed around melting level. Deposition dominates aggregation/riming in weak stratiform updrafts Heymsfield et al. (2002) 8 Example CPI observations from deep tropical stratiform precipitation during TRMM Field Campaigns (FCs) Many of us study convection. What do ice crystals look like on periphery of convection? In contrast to last example, particles in this example were rimed in intermediate and large sizes with aggregates evident Inferred updrafts above a few meters/sec were assessed, indicating deep updrafts, which led to extensive riming and complex crystal shapes often associated with freezing of cloud droplets at low temperatures Heymsfield et al. (2002) 9 Last one. What do ice crystals look like in deep anvil generated by nearby deep and extensive convection? Complex rimed crystals and aggregates of rimed crystals No supercooled liquid water measured in anvil so riming must have been acquired in convection and then advected to anvil Complex shapes fairly common for convective anvil… Heymsfield et al. (2002) 10 • For more specific and quantitative information on snow crystal shape, it is usually sufficient to characterize the relative size in two dimensions – The crystal diameter (d) and the crystal thickness (h) in the case of plate-like crystals – The crystal length (L) and the crystal width (d) for columnar type crystals • From observations, the length of columnar and the diameter of plate crystals (i.e., major dimension) range between 20 µm and 2 mm. – Maximum dimensions reach several mm • • Similarly, the thickness of plate-like crystals range from 10 to 60 µm, the width of warm temperature columns from 10 to 200 µm, and width of needles range from 10 to 150 µm (minor dimension) For simplicity in radar scatter models, often assume that ice crystals can be modeled as oblate or prolate spheroids with major and minor dimensions. – Only appropriate for lower frequency precipitation radar (S-band to X-band) and not necessarily higher frequency cloud radar (like W-band) • Observations further show that thickness and diameter of plate-like crystals and length and width of columnar crystals are characteristically related to each other – Power-law relationships between major and minor dimensions for each crystal type – if d↑, then h↑ for plates; If L↑, then d↑ for columns – See next page for details • Shape for aggregates (snowflakes) difficult to parameterize. As shown in images, bulk shape can vary from near spherical (major:minor ≈ 1) to highly asymmetric (very small minor:major << 1) – Bulk density is very low too so perhaps shape is not as important (i.e., effective sphere) 11 Dimensional relationships for snow crystals: Shape P1a = hexagonal plate P1b = sector plate P1c-r = simple ‘daisytype’ dendrite P1c-s = dendrite with sector branches C1g = thick solid plate C1e = solid column C1f = hollow column Pruppacher and Klett (1997) P1e,P1f,P2c,P2g,P3c,P4b = Dendrite (various) N1a = elementary needle N1e = Long solid column C1c, C1d = solid bullet 12 5.2 Snow crystal and snowflake size distributions • Similar to MP48, Gunn and Marshall (1958) proposed an exponential size distribution for aggregates of snow crystals based on observations (right) N (D ) = N 0 exp( − ΛD ), [1a ] where Λ = 25.5R −0.48 cm −1 , N 0 = 3.8 × 103 R −0.87m −3mm −1 , [1b] and D is the equivalent diameter of the water drop to which the ice crystal aggregate melts (i.e., equivalent melted drop diameter) and R is the rate of precipitation in mm h-1 of liquid water – Variety of snow and snowflake types, including aggregates of plate, columns and dendrites – Note typo error in units of Λ in Pruppacher and Klett (1997) • Sekhon and Srivastava (1970) found similar form as [1a] in snow except different equations for Λ, N0 in [1b] – – • Λ = 22.9 R-0.45 cm-1 N0 = 2.50 × 103 R-0.94 mm-1 m-3 SS70 also derive several useful relationships for snow – – – Median volume diameter: D0 = 0.14R0.45 (cm) Liquid water content W = 0.250R0.86 (g m-3) Reflectivity: Z= 1780R2.21 (mm6 m-3) Gunn and Marshall (1958) 13 • • Using a very large in-situ aircraft database from TRMM FC’s, Heymsfield et al. (2002) parameterized ice particle size distributions (PSDs) in deep tropical cirrus and stratiform precipitating clouds Heymsfield et al. (2002) found that ice PSD’s were well represented by gamma distributions of the form Exponential (exp) Gamma N (D ) = N 0 D µ exp(− λD ) [2] – • Also explored exponential distribution by forcing µ = 0 in [2] The slope parameter (λ) of both gamma and exponential distribution varied systematically with temperature during spirals (right) – – – – What is the trend of size (D0) with height? Values of exp (N0, λ) similar to past studies mid-latitude frontal and cirrus clouds Temperature is not only controlling factor but is a primary one Considerable variability of PSD during spirals manifested in rapid changes in N0 while µ and λ tended to be more stable Heymsfield et al. (2002) 14 5.3 Snow crystal and snowflake density • Most ice crystals, and all aggregates of ice crystals, have a bulk density less than that of solid ice (0.916 g cm-3) – – – Small amounts of air in capillary spaces of single crystals (e.g. hollow columns) tendency of single snow crystals to grow in skeletal fashion (e.g., dendrites) obvious air gaps when multiple snow crystals aggregate For most snow crystal types, increasing size implies decreasing bulk ice density Pruppacher and Klett (1997) From Heymsfield (1972) 15 Integrated bulk density and size/aspect ratio information for various snow crystal types For plates and dendrites For columns, needles, and bullets ρ = a1D c [3a ] ρ = a1Lc [4a ] h = a2 D f d = a2 L f [3b] ρ: bulk ice density (g cm-3) D: crystal diameter (cm) (major dimension) h: crystal thickness (cm) (minor dimension) [ 4b ] Coefficients in table below (Matrosov et al. 1996) ρ: bulk ice density (g cm-3) D: crystal length (cm) (major dimension) d: crystal thickness (cm) (minor dimension) Matrosov et al. (1996) from various sources in caption. 16 • Bulk density of snow aggregate (ρ, g cm-3) as function of aggregate diameter (D, cm) (or major dimension) was provided by Passarelli and Srivastava (1979) based on Magono and Nakamura (1965) data ρ = 0.015D −0.6 [ g cm −3 ] [5] • Illingworth (1994), Matrosov et al. (1996) and Ryzhkov et al. (1998) recommend relationship for bulk density of snow aggregates (ρ, g cm-3) in terms of the ice particle major dimension S (mm) (note units!) if ( S < 0.097 mm ) then ρ = 0.916 g cm −3 else ρ = 0.07 S −1.1 g cm −3 endif [ 6] Aggregate bulk ice density (g cm-3) 1 0.9 0.8 0.7 aggregate density Illingworth (1994) 0.6 aggregate density Passarelli and Srivastava (1979) 0.5 0.4 0.3 0.2 0.1 0 0.01 0.1 1 10 Aggregate Major Dimension (cm) • Equations [5] and [6] are in OK agreement for major dimension > 1 mm. Likely large variability in bulk ice density of aggregates under differing conditions 17 5.4 Snow crystal and snowflake orientation and refractive index • K ρ M= Ki ρi Mi + Ka ρa Refractive index of bulk ice, m=n+ik Ma [7 ] m2 − 1 [8] K= 2 m +2 • • • 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.003 0.0025 0.002 0.0015 n 0.001 k 0.0005 0 0 0.2 0.4 0.6 0.8 1 Imaginary component of refractive index (k) • In radar studies, usually assume major dimension of ice crystal or aggregate is in the horizontal unless there is a strong electric field, in which case ice particle is aligned with electric field, which is usually assumed strongest in vertical (Weinheimer and Few 1987) For dry ice particles (i.e., not in wet growth or melting), the refractive index is calculated with Debye theory using the bulk density of ice from earlier section. Recall… Use Debye mixing theory, Debye (1929), for ice and air mixtures (e.g., Battan 1973) Real component of refractive index (n) • Ice density (ρi, g cm-3) Where M:mass, ρ: density, m: refractive index; subscript i=ice (solid) and a=air (no subscript=mixture or bulk ice density) Can simplify [7] by noting that ma in [8] is ≈ 1 so Ka ≈ 0 and M ≈ Mi ∴→ K/ρ is constant. Hence, K for mixture is K K = i ρ [9] ρi Combine [4] and [5] to solve for refractive index of mixture (m) m2 = 2χ + 1 where 1− χ K χ = i ρ [10] ρi 18
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