In the tugging on the temperature profile (by net radiant heating / cooling resulting from radiative disequilibrium at single wavelengths) by the absorption (and emission) by different bands, the larger - scale aspects of the temperature profile will tend to be shaped more by the bands with moderate amounts of absorption, while finer - scale variations will be more influenced by bands with larger optical thicknesses
per unit distance (where there can be significant emission and absorption by a thinner layer).
A sharp change in lapse rate will (absent sharp changes in optical thickness
per unit distance, which occurs at TOA and at the surface even in wavelength bands dominated by well - mixed gases) tend to differ from radiative equilibrium — the inflection point may correspond to a maximum deviation from radiative equilibrium if the radiative equilibrium profile has some intermediate lapse rate in that vicinity.
Including emission along a path (Schwarzchild's equation), a flux will approach saturation as the optical thickness becomes large over scales where the temperature variation is small; at smaller optical thicknesses, the temperature distribution may vary and larger temperature variations make the nonlinearity of the Planck function important, but over short distances, the temperature variation can be approximated as linear and the associated Planck function values can be approximated as linearly proportional to distance for small temperature changes, so the flux will approach an asymptotic value as a hyperbolic function (the difference between the flux and the saturation value of the flux will be proportional to 1 / optical thickness
per unit distance (assuming isotropic optical properties (or even somewhat anisotropic properties), it will have that proportionality for all directions and thus for the whole flux across an area).
Not exact matches
Rock to Liquid Jet aircraft today typically burn kerosene, an energy - dense hydrocarbon fuel that delivers as much as 48 megajoules
per kilogram (20,700 British thermal
units per pound), allowing for long -
distance travel.
Our analysis infers areas where there's more genetic difference than you'd expect
per unit of geographic
distance, and other areas where there's less.
When impending wheel lockup is detected, the computer signals the hydraulic control
unit to apply and release (automatically «pumping») the brakes several times
per second with split - second timing, providing a level of braking efficiency that even professional race car drivers can not duplicate and resulting in shorter stopping
distances and greater braking and steering control
The efficiency of a vehicle, for instance, is typically measured in miles
per gallon, or the
distance traveled
per unit of energy.
Crawfords Croft (2 Self catering
units, sleeps 2 adults and 2 children
per unit) is ideally situated, within walking
distance from the sea, river, Stilbaai harbour, as well as Skilpiesbaai Nature Reserve, which boas...
Crawfords Croft (2 Self catering
units, sleeps 2 adults and 2 children
per unit) is ideally situated, within walking
distance from the sea, river, Stilbaai harbour, as well as Skilpiesbaai Nature Reserve, which boasts scenic walking routes through the milkwood forest and access to the Skilpiesbaai beach, featuring the tidal fish traps (Viswywers) of early mankind to the area.
Re 392 Chris Dudley — I don't understand what you mean by R ^ 2T ^ 4 — and there should be something about how optical depth is proportional to R, and also, if you're going a significant
distance toward the center of such an object, there is the issue of spherical geometry; if the optical thickness is large enough across small changes in radius, then you don't need to account for the spherical geometry in the calculation of the flux
per unit area as a function of the temperature profile and optical thickness; however, the flux
per unit area outward will drop as an inverse square, except of course within the layers that are being heated through a different process (SW heating for a planet, radioactivity, latent and sensible heat loss associated with a cooling interior, gravitational potential energy conversion to enthalpy via compression (adiabatic warming) and settling of denser material under gravity (the later both leads to compression via increased pressure via increased gravity within the interior, and also is a source of kinetic energy which can be converted to heat)...
Aside from variations in line strength and line broadenning with height, their is the important point that, relative to the mass path of CO2 (
distances measured in terms of kg
per unit area), temperature variations at those heights occur over small scales.
You have to look at the absorption crosssection
per molecule of CO2 and count up the number of CO2 molecules
per unit area that would be in the path of a photon travelling a certain
distance in the atmosphere you can understand how such a low concentration of CO2 can have such a large effect.
Given the dimensions involved (surface to TOA times the speed of light = a few (or possibly tens of) milliseconds) this delay as the energy flows through the system multiple times at nearly the speed of light does not emulate the effects of a thermal insulator which actually slows the velocity (rate of forward progress,
distance travelled
per unit time, etc.).
«Inverse - square law The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy
per unit of area perpendicular to the source) is inversely proportional to the square of the
distance from the source; so an object (of the same size) twice as far away, receives only one - quarter the energy (in the same time period).»
That should be a quantity proportional to the kinetic energy
per unit vertical
distance at that altitude.
Pressure is force
per unit area and work, which has
units of energy is defined as force times
distance.