Diabatic heating

A second issue is the transport of trace gases in the stratosphere. How do the polar vortices form How readily are air parcels exchanged between the vortex and midlatitudes and between altitudes at different latitudes and seasons What are the diabatic heating and cooling rates at different times... 

Figure 3.3. Net radiative heating rate associated with (1) absorption of ultraviolet radiation by molecular oxygen in the upper mesosphere and thermosphere, and by ozone in the stratosphere and mesosphere, and (2) emission of infrared radiation by atmospheric CO2, O3, and H2O. Values given in K/day and positive in the summer hemisphere (net diabatic heating) and negative (net diabatic cooling) in the winter hemisphere. Prom London (1980).

A more practical approach is simply to derive the net mean circulation directly from the diabatic heating rate, q, as suggested by Dunkerton (1978). From the thermodynamic equation (3.60) in which it is assumed that d /dt and (v/a)(dO/dheat fluxes are negligibly small, one can deduce that... 

Note that the eddy heat flux does not appear in the transformed thermodynamic equation (3.65). From these equations, vd and wb may be derived directly from a knowledge of the diabatic heating rate. We... 

The parametrization of cumulus cloud rainfall utilizes some form of one-dimensional cloud model. These are called cumulus cloud parametrization schemes. Then-complexity ranges from instantaneous readjustments of the temperature and moisture profile to the moist adiabatic lapse rates when the relative humidity exceeds saturation, to representations of a set of one-dimensional cumulus clouds with a spectra of radii. These parametrizations typically focus on deep cumulus clouds, which produce the majority of rainfall and diabatic heating associated with the phase changes of water. Cumulus cloud parametrizations remain one of the major uncertainties in mesoscale models since they usually have a number of tunable coefficients, which are used to obtain the best agreement with observations. Also, since mesoscale-model resolution is close to the scale of thunderstorms, care must be taken so that the cumulus parametrization and the resolved moist thermodynamics in the model do not double count this component of the and Sq.. 

These developments follow theoretical advances built on vorticity theorems which are based on the conservation of both potential vorticity and potential temperature (i.e., entropy) on timescales for which friction, small-scale mixing, and diabatic heating can be ignored. IPV is a valuable atmospheric tracer which therefore shows the origin and predicted motion of atmospheric parcels indeed, it is the only such dynamical (as opposed to chemical) tracer. Since heating/cooling and friction act to alter the IPV, it is clear that careful representation of these plysical processes (i.e., parameterization ) in models and theories is crucial. 

When phase changes occur within the atmosphere, latent heat and the heat capacity of the condensate must also be included in Eq. (9.2.9). The heating per unit volume, Q, is called the diabatic heating and usually results from a combination of solar energy absorption and infrared radiative transfer. Heating due to frictional dissipation of the flow is generally negligible, and is omitted in Eq. (9.2.9). 

Because the time scale of the anticipated atmospheric motion associated with the temperature fluctuations is only one day, the thermal wind approximation caimot be used. However, diurnal variations in the pressure and wind fields can be estimated from the observed temperature field using classical tidal theory. The basic concept of the formulation is sketched here a detailed treatment can be found in Chapman Lindzen (1970). The theory is based on a linearization of the primative equations. A motionless atmospheric reference state is assumed with temperature profile To z) and a corresponding geopotential surface 4>o(z). It is further assumed that the diabatic heating and all other quantities vary as exp[i(j < — cot)] where s is a longitudinal wavenumber and co is 2 7r/(solar day) or integer multiples thereof. The amplitudes of the time-varying, dependent variables are taken to be sufficiently small so that only terms of first order need be retained. With these assumptions. 

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