Heat
Lagrangian systems: An air parcel is studied as it moves and changes in the atmosphere.
Sensible Heat: Heat that can be sensed by humans. It is that portion of total heat associated with a temperature change. Sometimes it called enthalpy (heat function). Sensible heat per unit mass is given by:
Cp is the specific heat at constant pressure of the material, the amount of energy necessary to change the temperature of one unit mass of material by 1o (usually oC or oK).
Latent Heat: Heat absorbed or released per unit mass by a system during a change of phase. Temperature does not measure the entire internal energy of a substance, only the translational kinetic energy part. Phase changes occur with no change in temperature.
Gas Water Ice
Process Gains Energy Loses Energy Evaporation Water mol. Environment (vaporizaton) Melting Water mol. Environment Sublimation Water mol. Environment Condensation Environment Water molecule Freezing Environment Water molecule (fusion) Deposition Environment Water molecule
Specific Heat: (heat capacity) Amount of heat energy required to change the temperature of one unit mass (usually kg or gram) of a substance by 1o (usually oC or oK). For water the specific heat is not constant. Specific heat for water varies from 4177.5 to 4216.89 J/kg oC. Also, it varies for ice and steam.
Lagrangian Heat Budget - Part 1
Using the hydrostatic equation: then, Substituting gives: Rearranging gives: and, eq. 3-5
Lapse Rate
In the dry adiabatic process: and,
which gives: or: Dry adiabatic lapse rate, Note: temperature decreases as parcel ascends and increases as parcel descends.
In terms of pressure. Written in derivative form: Substituting from General Gas Law Equation. Integrating from P1 and T1 to P2 and T2
Integrating from P1 and T1 to P2 and T2
Since,
Potential Temperature
Lapse rate in height units is: This can be written as: If we let T2 be defined as the Potential Temperature, Q, (the temperature the parcel would have if we moved it vertically to a particular height), then: and, Note: The solved problem, pg. 47, the parcel is descending from a height of 500 m to a height of 0 meters, ground level or sea level. Dz = 500 m
Lapse rate in pressure units: If we let T2 be the potential temperature, Q, then: Typically, in pressure units, the air parcel is moved to 1000 hPa (100 kPa).
Remember: Virtual temperature is given by the equation:
For cloudy skies: (liquid droplets and/or ice crystals) where, rs = saturation mixing ratio, rL = mixing ratio of liquid water.
Thermodynamic Diagrams
Eulerian Heat Budget
The change in temperature with time can be written in kinematic form as changes due to fluxes moving air and due to internal changes as: where, represents flux gradients of heat into or out of the volume (i.e., there is convergence into or divergence from the volume).(Dx, Dy, Dz are lengths of sides of the volume
Each of the change in flux terms is due in part to advection, conduction, turbulence and radiation.
Turbulence: A state of fluid flow in which the instantaneous velocities exhibit irregular and apparently random fluctuations.
Advection
Conduction and Surface Fluxes
Effective Surface Turbulent Heat Flux
During calm days with strong radiational heating, there is more thermals occurring, greater vertical mixing. Then, a better equation for the Effective Surface Turbulent Heat Flux is: or: where, qML = potential temp. at height of 500 m bH = convective transport coefficient = 5 x 10-4 aH = mixed-layer transport = 0.0063 wB=Buoyancy velocity scale
Wind Chill
Even in calm winds there should be a wind chill value due to the movement of the person.
Heat Index
There are several equations used to calculate the Heat Index.
Problems
Email: alcorn@ariel.met.tamu.edu
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