Preface |
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xiii | |
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1 | (18) |
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1.1 Cloud and precipitation physics and parameterization perspective |
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1 | (1) |
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1.2 Types of microphysical parameterization models |
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2 | (2) |
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1.3 Warm-rain parameterizations |
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4 | (1) |
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1.4 Cold-rain and ice-phase parameterizations |
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5 | (2) |
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1.5 Hydrometeor characteristics overview |
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7 | (10) |
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17 | (2) |
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2 Foundations of microphysical parameterizations |
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19 | (40) |
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19 | (1) |
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19 | (2) |
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21 | (2) |
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2.4 Spectral density functions |
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23 | (4) |
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27 | (15) |
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2.6 Log-normal distribution |
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42 | (9) |
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2.7 Microphysical prognostic equations |
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51 | (6) |
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2.8 Bin microphysical parameterization spectra and moments |
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57 | (2) |
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3 Cloud-droplet and cloud-ice crystal nucleation |
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59 | (19) |
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59 | (2) |
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3.2 Heterogeneous nucleation of liquid-water droplets for bulk model parameterizations |
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61 | (7) |
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3.3 Heterogeneous liquid-water drop nucleation for bin model parameterizations |
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68 | (2) |
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3.4 Homogeneous ice-crystal nucleation parameterizations |
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70 | (2) |
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3.5 Heterogeneous ice-crystal nucleation parameterizations |
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72 | (6) |
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78 | (23) |
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78 | (3) |
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4.2 Liquid bulk saturation adjustments schemes |
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81 | (5) |
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4.3 Ice and mixed-phase bulk saturation adjustments schemes |
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86 | (5) |
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4.4 A saturation adjustment used in bin microphysical parameterizations |
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91 | (2) |
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4.5 Bulk model parameterization of condensation from a bin model with explicit condensation |
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93 | (4) |
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4.6 The saturation ratio prognostic equation |
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97 | (4) |
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5 Vapor diffusion growth of liquid-water drops |
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101 | (38) |
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101 | (1) |
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5.2 Mass flux of water vapor during diffusional growth of liquid-water drops |
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102 | (4) |
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5.3 Heat flux during vapor diffusional growth of liquid water |
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106 | (3) |
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5.4 Plane, pure, liquid-water surfaces |
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109 | (7) |
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116 | (2) |
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5.6 Curvature effects on vapor diffusion and Kelvin's law |
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118 | (2) |
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5.7 Solute effects on vapor diffusion and Raoult's law |
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120 | (1) |
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5.8 Combined curvature and solute effects and the Kohler curves |
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121 | (1) |
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122 | (2) |
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5.10 Higher-order approximations to the mass tendency equation |
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124 | (5) |
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129 | (5) |
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5.12 Bin model methods to vapor-diffusion mass gain and loss |
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134 | (4) |
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138 | (1) |
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6 Vapor diffusion growth of ice-water crystals and particles |
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139 | (13) |
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139 | (1) |
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6.2 Mass flux of water vapor during diffusional growth of ice water |
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140 | (1) |
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6.3 Heat flux during vapor diffusional growth of ice water |
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141 | (1) |
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6.4 Plane, pure, ice-water surfaces |
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141 | (1) |
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6.5 Ventilation effects for larger ice spheres |
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142 | (1) |
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143 | (5) |
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6.7 Effect of shape on ice-particle growth |
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148 | (4) |
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152 | (79) |
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152 | (1) |
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7.2 Various forms of the collection equation |
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153 | (2) |
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7.3 Analysis of continuous, quasi-stochastic, and pure-stochastic growth models |
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155 | (9) |
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164 | (1) |
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7.5 Geometric sweep-out area and gravitational sweep-out volume per unit time |
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165 | (1) |
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7.6 Approximate polynomials to the gravitational collection kernel |
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165 | (1) |
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7.7 The continuous collection growth equation as a two-body problem |
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166 | (2) |
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7.8 The basic form of an approximate stochastic collection equation |
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168 | (1) |
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7.9 Quasi-stochastic growth interpreted by Berry and Reinhardt |
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169 | (4) |
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7.10 Continuous collection growth equation parameterizations |
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173 | (4) |
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7.11 Gamma distributions for the general collection equations |
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177 | (6) |
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7.12 Log-normal general collection equations |
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183 | (5) |
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7.13 Approximations for terminal-velocity differences |
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188 | (3) |
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7.14 Long's kernel for rain collection cloud |
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191 | (3) |
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7.15 Analytical solution to the collection equation |
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194 | (1) |
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7.16 Long's kernel self-collection for rain and cloud |
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195 | (1) |
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7.17 Analytical self-collection solution for hydrometeors |
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196 | (1) |
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7.18 Reflectivity change for the gamma distribution owing to collection |
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197 | (1) |
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7.19 Numerical solutions to the quasi-stochastic collection equation |
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198 | (24) |
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7.20 Collection, collision, and coalescence efficiencies |
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222 | (9) |
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231 | (22) |
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231 | (1) |
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8.2 Collision breakup of drops |
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232 | (2) |
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8.3 Parameterization of drop breakup |
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234 | (19) |
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9 Autoconversions and conversions |
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253 | (40) |
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253 | (2) |
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9.2 Autoconversion schemes for cloud droplets to drizzle and raindrops |
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255 | (9) |
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9.3 Self-collection of drizzle drops and conversion of drizzle into raindrops |
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264 | (1) |
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9.4 Conversion of ice crystals into snow crystals and snow aggregates |
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264 | (3) |
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9.5 Conversion of ice crystals and snow aggregates into graupel by riming |
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267 | (3) |
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9.6 Conversion of graupel and frozen drops into small hail |
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270 | (1) |
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9.7 Conversion of three graupel species and frozen drops amongst each other owing to changes in density by collection of liquid particles |
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271 | (1) |
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9.8 Heat budgets used to determine conversions |
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272 | (6) |
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9.9 Probabilistic (immersion) freezing |
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278 | (5) |
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283 | (1) |
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9.11 Two-and three-body conversions |
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283 | (6) |
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9.12 Graupel density parameterizations and density prediction |
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289 | (1) |
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9.13 Density changes in graupel and frozen drops collecting cloud water |
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290 | (1) |
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9.14 Density changes in graupel and frozen drops collecting drizzle or rain water |
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290 | (1) |
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9.15 More recent approaches to conversion of ice |
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291 | (2) |
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293 | (19) |
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293 | (4) |
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10.2 Wet and spongy hail growth |
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297 | (1) |
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10.3 Heat-budget equation |
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298 | (3) |
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10.4 Temperature equations for hailstones |
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301 | (1) |
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10.5 Temperature equation for hailstones with heat storage |
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302 | (2) |
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10.6 Schumann-Ludlam limit for wet growth |
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304 | (2) |
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10.7 Collection efficiency of water drops for hail |
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306 | (1) |
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10.8 Hail microphysical recycling and low-density riming |
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307 | (5) |
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312 | (24) |
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312 | (1) |
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11.2 Snowflakes and snow aggregates |
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313 | (1) |
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11.3 Graupels and hailstones |
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313 | (2) |
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11.4 Melting of graupel and hail |
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315 | (11) |
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11.5 Soaking and liquid water on ice surfaces |
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326 | (2) |
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11.6 Shedding drops from melting hail or hail in wet growth |
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328 | (2) |
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11.7 Parameterization of shedding by hail particles of 9-19 mm |
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330 | (3) |
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11.8 Sensitivity tests with a hail melting model |
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333 | (3) |
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12 Microphysical parameterization problems and solutions |
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336 | (10) |
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12.1 Autoconversion of cloud to drizzle or rain development |
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336 | (2) |
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12.2 Gravitational sedimentation |
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338 | (2) |
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12.3 Collection and conversions |
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340 | (3) |
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343 | (1) |
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344 | (1) |
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12.6 Conversion of graupel and fro/en drops to hail |
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344 | (1) |
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12.7 Shape parameter diagnosis from precipitation equations |
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345 | (1) |
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13 Model dynamics and finite differences |
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346 | (21) |
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13.1 One-and-a-half-dimensional cloud model |
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346 | (2) |
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13.2 Two-dimensional dynamical models |
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348 | (7) |
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13.3 Three-dimensional dynamical model |
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355 | (12) |
Appendix |
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367 | (4) |
References |
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371 | (14) |
Index |
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385 | |