DRY GROWTH Latent heat is released due to freezing of water; this heat that is liberated warms the surface of the stone. At low to moderate LWC’s, this heat can be effectively dissipated to the surrounding air. Hence the stone remains below 0°C, and its surface is dry. This type of growth results in opaque ice since the rime contains quite a bit of air. WET GROWTH At larger riming rates (higher LWC’s and/or larger hail stones) latent heat release will warm the stone to 0°C, hence preventing most of the liquid water from being frozen. In this case the surface of the stone becomes an ice-water mesh, promoting the term ‘spongy ice’. Even higher LWC’s promote a complete liquid surface, called wet growth. Clear ice develops as this liquid layer freezes. This liquid surface may be partially shed in the wake of the hailstone. The shed water produces drops that may then rapidly freeze and become new hail embryo sources.

Simplified models for hailstone growth rates For dry growth: the accreted water freezes instantly. Heat is released at a fast-enough rate, that although the hail particle warms, it does not exceed 0 ˚C. The standard continuous-collection equation can be applied (same as used for graupel growth by accretion of supercooled droplets): Here, r and m refer to the growing hailstone, V(r) is its fall velocity (or rather, the net rate of falling, if the strength of the updraft needs to be considered), Wl is the liquid water content (the supercooled water), and Ec is the collection efficiency. Since freezing is instantaneous, in dry growth, we can just apply this equation to figure out the rate of change of mass of the hailstone. For wet growth, however, this equation has to be combined with a heat balance…

assume all excess water (that cannot be frozen) is shed For wet growth: assume all excess water (that cannot be frozen) is shed Then the growth rate is determined by the rate at which collected water can be frozen (and thus retained) Have to dissipate latent heat to the environment: balance between latent heating and dissipation determines the growth rate Assumptions: Ignore heat storage in the hailstone (probably not a great assumption) Ignore collection of any other species except supercooled cloud drops Then the energy equation becomes: Latent heat released by wet growth process Sensible heat transferred between hailstone and collected water Latent heat transferred as vapor condenses or evaporates from hailstone 0 (s.s) Diffusion of heat between hailstone and its environment (conduction away from hailstone)

To find the “critical water content”, the conditions where dry growth switches over to wet growth: set This is an “effective” liquid water content (since it includes the collection efficiency) As evaporation and conduction become more effective at dissipating the heat due to freezing (numerator increases), the critical liquid water content increases As the hailstone increases in size, the critical liquid water content decreases (collection of water increases with area and fallspeed)

Field-dependent Mechanism: charges on particles migrate to align with field

Over certain ranges, power laws apply: As a liquid drop grows (via on going collection of smaller drops), the surface tension that keeps small drops spherical becomes less able to contain the growing mass of liquid. The larger fallspeed increases the dynamic pressure, which flattens the lower side, making the drop look more like a hamburger bun than a ball, as suggested by the right-most panel in Fig. 9.4. As the cross-sectional area for a given volume increases, the drag eventually becomes so large that its increase with drop size almost matches the increase in weight with size. The fallspeed thus exhibits a very weak dependence on size toward the large end of continuum regime III. Over certain ranges, power laws apply: vp a Dpn

What is the definition of moist static energy, and what is the utility of this concept?

The First Law Revisited The gravitational potential for unit mass is called the geopotential Φ It is the work (units: J kg-1 or m2 s-2) that must be done against gravity to raise a mass of 1 kg from sea level to a height z (or pressure p) The First Law can be written And we recall that Combining, For an adiabatic process, dq = 0, so (h+Φ) is conserved => we call this the “dry static energy” and we can manipulate it to get equation for θ Note that the equation is in energy units (energy per unit mass)

The Dry Static Energy If we want to consider nonadiabatic processes (which are important in the atmosphere), then the rate of diabatic heating or cooling of a parcel ( )can be related to the rate of change of the dry static energy: where has units of energy per unit mass, per unit time: watts per kg The heating rate represents the combined effect of: Absorption of solar radiation (shortwave) Absorption and emission of terrestrial radiation (longwave) Release of the latent heat of condensation of water vapor Exchange of heat with surroundings due to mixing by random molecular motion (conduction) Exchange of heat with surroundings due to mixing by organized fluid motions (convection) Rate of heating due to conduction + convection Net radiative heating rate Rate of latent heat release

Latent heat term Relate to the time rate of change of water vapor mixing ratio in the parcel Divide this rate of change into two components: Then Denote the exchange term as Exchanges of water vapor with surroundings, due to conduction + convection Phase changes The time rate of change of the quantity in parentheses on the LHS is due to the sum of net radiative heating, rate of heating by conduction / convection, and rate of heating due to vapor exchange with surroundings

Moist Static Energy If, as shown on previous slide, we allow for the possibility of condensation or evaporation, we can define another energy quantity, the moist static energy, that is conserved as long as the latent heating is the only diabatic process (i.e., if entrainment or radiative heating or cooling are occurring, moist static energy is not conserved), and assuming hydrostatic equilibrium applies: Applied to atmosphere as a whole, over a long enough time period: the storage of energy is not systematically increasing or decreasing  we assume there is a balance between energy sources and sinks So over the longer term mean, dh/dt =0 which means How is this useful? E.g., apply energy budget at TOA and surface h