Lapse Rate, Stability, Scale Height and Geopotential Height

 

 

Lapse Rate

Adiabatic lapse rate is the rate of change of temperature of an air parcel as it moves upwards through the atmosphere in a way that there is no considerable exchange of heat with the surrounding air. The change is temperature is due to the fact that as the parcel moves up through the atmosphere, the atmospheric pressure decreases, causing the air parcel to expand. Since this expansion is adiabatic (no heat enters or leaves the system all temperature changes are internal), the work required for expansion is taken from the internal energy of the parcel, causing it to cool down. When the air is dry (little moisture content), the adiabatic lapse rate is about 9.8oC/km.

Dry and Wet Adiabatic Lapse rates:

Adiabatic lapse rates are usually differentiated as dry or wet (moist).

Dry Adiabatic Lapse Rate (DALR): is the rate of fall in temperature with altitude for a parcel of dry air (air with little relative humidity) rising under adiabatic conditions. In such an air parcel, condensation during uplift is low, and thus latent heat of condensation released is low (less heat added from inside). As a result, the fall in temperature with height is quite significant. The dry adiabatic lapse rate for the Earths atmosphere equals 8C/km. Dry Adiabatic Lapse rate is mainly associated with stable atmospheric conditions.

Wet Adiabatic Lapse Rate (WALR): When an air parcel that is saturated with water vapour rises, some of the vapour will condense and release latent heat. This process causes the parcel to cool more slowly than it would if it were not saturated. The moist adiabatic lapse rate varies considerably according to the variability of water vapour content the greater the amount of vapour, the smaller the adiabatic lapse rate. On average the WALR is taken as 4C/km. Wet Adiabatic Lapse rate is mainly associated with unstable conditions. As the air parcel rises and cools, it eventually loses moisture through condensation and its lapse rate increases and approaches the dry adiabatic value.

Average Adiabatic Lapse Rate (ALR) for the entire atmosphere is taken to be 6C/km. It is understandable that the lapse rate varies with place ant time.

 

Stability

The difference between the normal lapse rate in the atmosphere and the dry and moist adiabatic lapse rates determines the vertical stability of the atmosphere. For this reason, the lapse rate is of prime importance to meteorologists in forecasting certain types of cloud formations, the incidence of thunderstorms, and the intensity of atmospheric turbulence.

When there is little moisture in the air parcel, condensation of water vapour is low, so latent of condensation released will be low, and the rising parcel of air cools quickly, becomes dense and stops rising. There will be no cloud formation and hence no rain or thunderstorms. This simply means that the atmospheric condition is stable.

Conversely, when there is considerable moisture in the air parcel, condensation of water vapour will be reasonably high, resulting in a release of enough amount of latent heat to drive a violent thunderstorm. So the weather will be associated with instability.

Scale Height

Scale height is a general way to describe how a value fades away and it is commonly used to describe the atmosphere of a planet. It is the vertical distance over which the density and pressure fall by a factor of 1/e (approximately 2.72, the base of natural logarithms). The scale height of the Earth's atmosphere is about 8 km - the height of Everest - so that the pressure at the top of Everest is about 1/e=1/2.7~35% of the pressure at sea level. With these same assumptions of T, m, g all constant, the air density will also vary with altitude with the same scale height as the pressure.

Geopotential Height

Geopotential height is the height of a given pressure. Geopotential height is a vertical coordinate referenced to Earth's mean sea level an adjustment to geometric height (elevation above mean sea level) using the variation of gravity with latitude and elevation. One usually speaks of the geopotential height of a certain pressure level, which corresponds to the geopotential height at which that pressure occurs. Geopotential height can thus be considered a "gravity-adjusted height".

Geopotential height approximates the actual height of a pressure surface above mean sea-level. Therefore, a geopotential height observation represents the height of the pressure surface on which the observation was taken. A line drawn on a weather map connecting points of equal height (in meters) is called a height contour. That means, at every point along a given contour, the values of geopotential height are the same.

Notes & Handouts

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