LAPSE RATES, STABILITY AND INSTABILITY (Meteorology Notes)


LAPSE RATES, STABILITY AND INSTABILITY (METEOROLOGY NOTES)

Before consideration can be given to the formation of clouds and their characteristics, including flying conditions, attention must be paid to the upper air temperature structure and the terminology used to describe it.

Firstly, the term temperature lapse rate. A temperature lapse rate is the rate of decrease of temperature per unit increase of height and in aviation in the India is expressed in °C  per 1000 ft.  Different circumstances of static, ascending and descending air produce different lapse rates, which are known by the following names.

(a)     Environmental lapse rate (ELR)

Upper air temperatures are observed regularly through the troposphere into the stratosphere and may variously be referred to as the observed, environmental or ambient upper air temperatures. These environment temperatures vary with place and time as well as with altitude.

Environmental lapse rate is the observed rate of decrease of temperature with increase of height at a particular place and time

 

4000ft 10°C 10°C
3000 ft 11°C 11°C
2000 ft 12°C 12°C
1000 ft 14°C 14°C
Surface 16°C 15°C

Observed upper air temperatures

With the observed environment temperatures given in Table above, from the surface to 2000 ft the environmental lapse rate (ELR) is 2° C per 1000 ft while from 2000 ft to 4000 ft the ELR is 1°C per 1000 ft.  In fact where temperatures are decreasing with increase of height, the ELR is positive.

However, the observed upper air temperatures may be as shown in Table below. Where, as in first Table, the environmental temperatures remain unchanged with increase of height, the ELR is 0°C per 1000 ft and the layer from 1000 ft to 3000 ft would be called in isothermal layer.  If as in second Table, the environmental temperatures increase with increase of height (i.e. the usual temperature structure is inverted) the ELR is negative and the layer from 1000 ft to 3000 ft would be called an inversion layer or just ‘ an inversion’.  If the temperature inversion starts at the surface, it is usual to refer to the condition as a surface inversion.

15°C 4000 ft

09°C

15°C 3000 ft

11°C

15°C

2000 ft

09°C

15°C 1000 ft

08°C

15°C Surface

10°C

 

Dry adiabatic lapse rate (DALR)

This term is used in relation to vertically moving unsaturated air. The term adiabatic means that no heat is lost or gained from the system during a particular process.  Take the case of piston moving in a simple cylinder.  If the piston is moved so that it compresses the gas, work is done on the gas.  The energy required  for compression  passes to the gas leading to an increase of its internal energy, raising its temperature  ( of. bicycle hand pump, diesel engine, etc..)

Explanation of DALR

Piston Movement

 

 

 

 

 

 

 

Piston Moving In a Simple Cylinder To Compress

 

 

Cooling by expansion of a gas, as in some domestic refrigerators, is the reverse process.  In the atmosphere, because air is a poor conductor of heat, any rising bubble of air (called a ‘parcel’ by met men) can be considered ‘ thermally insulated’ from its environment as it expands and cools with no loss or gain of heat to or from its environment, i.e adiabatically.  So long as the vertically moving air remains unsaturated it changes its temperature at a predictable constant rate.

A formal definition would be: –

Dry adiabatic lapse (DALR) is the rate of cooling with ascent or warming with descent of unsaturated air displaced vertically in which the temperature changes due entirely to dynamical processes and their is no exchange of heat with the environment.  Expressed in terms of height, the DALR value is 3 ° C /1000 ft   (1°C per 100 m).

 

Lapse Rate

DALR

 

 

 

 

 

 

 

 

 

 

 

Saturated Adiabatic Lapse Rate (SALR)

In rising saturated air, condensation occurs and releases latent heat.  This heat partly offsets the expansional cooling so that the saturated adiabatic lapse rate value is less than that of the DALR.  The SALR has a variable value although an average at mean sea level in temperate latitudes its value is approximately 2 °C per 1000 ft (0.6 °C per 100m).

At high temperatures the SALR has a low value and at low temperature its value is greater, approaching the DALR value, and equalling it for all practical purposes at – 40 °C.  Thus the SALR value increases with altitude and also usually with latitude.  Remember that the SALR value is derived from the simple sum:

Per 1000 ft :

Cooling adiabatically due to expansion                   3 ° C

Warming due to latent heat of condensation           x° C

Resultant SALR value per 1000 feet                       3 – x °C

 

This may be shown graphically (fig below) for a given amount of cooling (‘t’ deg)

Saturated Adiabatic Lapse Rate

SALR

 

 

 

 

 

 

 

SALR

 

(a)      At high temperatures, large difference in saturation value, much condensation and latent heat released, hence a low SALR value.

(b)     At low temperatures, small difference in saturation values, little condensation and latent heat released, hence a high SALR value.

 

Typical Values of the SALR at mean sea level are:-

0°C 15° C 30° C

Cooling

3 3

3

Warming

0.5 1.5

22

Net Cooling = SALR (per 1000′) 2.5 1.5

1

Typical Values of SALR at MSL

Meteorology Notes

Values of SALR

 

 

 

 

 

 

 

 

 

 

 

Although the DALR applies to both ascending and descending unsaturated air (i.e. is reversible), the SALR strictly should only be applied to ascending saturated air. This is because in rising air excess water vapour will condense out and latent heat will be released, it cannot be assumed that the same amount of latent heat will be taken up to evaporate all the condensation instantaneously to maintain saturation of descending air.  The SALR may be defined as:

“Saturated adiabatic lapse rate (SALR) is the rate of cooling with ascent of saturated air in which the expansional cooling is partly offset by the latent heat of condensation, and there is no exchange of heat with the environment.  It has a variable value but in temperate latitudes at mean sea level, its value is approximately 1.5°C per 1000ft”.

By comparing the temperatures of rising parcels of air with the environmental temperatures of the air which surrounds them at their new upper levels, the stability (or instability) of the atmosphere at a particular place and time may be assessed.  As is true in other applications, a state of stability means that when an object is displaced, it will tend to return to its original position when the displacing force is removed.  In an unstable state, the displaced object will continue to become more displaced even though the original displacing force is removed.  In the case of atmospheric (in)stability, the object is the mass of air which produce different flying conditions.

Atmospheric Stability

If a body at rest is given a small displacement by applying an external force after a short time and then the force is removed, one of three things can happen: –

  • The body may return to its original position (stable equilibrium).

(b)     The body may remain at the point where the external force was removed (neutral equilibrium).

(c)      The body may continue to be displaced even when the external force is removed (unstable equilibrium).  In such a case, even a small displacement will grow and the original state breaks down, sometimes violently.

The stability of the atmosphere is considered in terms of the vertical displacement of parcels of air. The following definitions apply: –

(a)      A layer of air is said to be stable if a parcel of air with it, given a small initial push upwards, sinks back to the original level.

(b)     It is said to be neutral if a parcel of air, given a small initial push, remains at the level at which the force pushing it upwards is removed.

(c)      It is said to be unstable if the parcel of air continues to be displaced upwards on its own even when the initial force pushing it upwards is removed.

Principle of Buoyancy

It is well known principle of physics that in a fluid, a parcel having higher density sinks to a level where its density is equal to the surrounding fluid, while a parcel having lower density rises to a level where it density is equal to the surroundings. This is known as buoyancy and is responsible for convective motions in the atmosphere.  From the fundamental gas equation, it is known that at a given pressure, the density of a gas is inversely proportional to its temperature.  The principle of buoyancy may, therefore, be stated in terms of temperature as follows: –

(a)     A parcel of air, whose temperature is higher than the surroundings, rises upto a level where the temperature equalises.

(b)     A parcel of air, whose temperature is lower than the surroundings, sinks to a level where the temperature equalises.

In rising, the parcel of air cools at the adiabatic lapse rate (DALR or SALR as the case may be). By comparing the actual lapse rate with the adiabatic lapse rate, it is thus possible to determine whether the parcel of air will continue to rise or sink at any stage.

1

2 3 4 5 6

ELR 4°C

ELR 2°C ELR 1°C SALR 1.5°C DALR 3°C

18

24 25.5 21 21

3000′

22

26 28 27 24

2000′

26

28 29 28.5 27

1000′

30 30 30 30 30

Surface

Case I

Absolute Stability

Case II

Conditional Stability

Case III

Absolute Instability

ELR>DALR>SALR

DALR>ELR>SALR

DALR>  SALR>ELR

Comparison of ELR, SALR and DALR (Meteorology Notes)

Stability and Lapse rates

To examine the state of atmosphere on particular day one should examine whether the parcel whether dry or saturated will rise vertically or not. It is evident from foregoing discussion that dry parcels will follow DALR (Column 5 in the table above) and cool at a rate 3°C/1000′ during ascent.  Similarly saturated parcels will follow SALR and cool at a rate 1.5°C/1000′ in Indian region.

(a)      Case I.        ELR is 4°C/1000′ as shown in column I hence ELR>DALR>SALR which means whether the parcel is dry (column 5) or saturated (column 4) the environment temperature at any level is lesser than that of parcel.  In such a case parcel will rise unconditionally and it is a case of Absolute Instability.

(b)     Case II.       ELR is 1°C i.e. as in the column 3.  Hence ELR>SALR>DALR.  It follows from above analogy that in such a case parcel will be colder than environment at all levels irrespective of the fact whether they are dry or saturated.  Such saturation is known as Absolute Stability.

(c)      Case III.      ELR is 2°C i.e. as in the column 2.  Hence SALR>ELR>DALR.   Now if you examine column 2 & 4, you will notice that parcel of saturated will rise since temperature in column are higher than in column 2, but a comparison of column 2 and 5 will show that dry parcels will not rise since the temperature in column 5 are lesser than that in column 2 at all levels.  This situation is known as Conditional Instability where the condition is that parcels will rise and atmosphere will be unstable if parcels are saturated, whereas if the parcels remain dry atmosphere will be stable.

Latent Instability

Consider a layer of air in which the lapse rate itself varies, being stable in the lower levels but unstable aloft. Such a layer is said to have latent instability in the sense that instability is, so to say, hidden aloft and can be reached only if a sample of air is lifted upto some considerable height.

Potential (or convective ) instability)      

Finally, the term’s potential (or convective) stability and instability may be met. Whereas all of the cases considered so far have concerned parcels of air rising through the environment, potential (in) stability relates to what would happen if the whole environment were lifted bodily.  The simplest case to visualise is of a whole airstream moving from, say over the ocean or a low-lying plain rising up to a new location over a plateau.  Although both terms potential (in) stability and convective (in) stability may be found in meteorological literature, the prefix of potential may be prefigured because of its connotations of position. The case for ‘convective’ is that the (in) stability arised from the rearrangement of heat due to the bodily movement of the air.

That state of the atmosphere in which there is a high relative humidity at low levels and a low relative humidity at upper levels, such that if a lower layer of air is lifted bodily, the ELR value through the layer will gradually increase to attain finally an unstable value (fig below)

Meteorology Notes

Potential or Convective Instability

 

 

 

 

 

 

 

 

Potential (or convective) stability

 

 

 

That state of the atmosphere in which there is a low relative humidity at low levels and a high relative humidity at upper levels, such that if a layer of air is lifted bodily the ELR value through the layer will gradually decrease to attain finally a stable value (fig below)

When considering the possibility of development of instability and its associated flying conditions of turbulence, etc., due allowance must be made for the modification of the environment curve by any or all of the following: –

(i)      Diurnal variation of temperature of the underlying surface.

(ii)     Inflow of upper air of different temperatures at different  level.

(iii)    Movement of the whole airstream into an area of different surface temperatures.

  • Mixing within the airmass.
  • Bodily lifting of the whole mass of air and also of the increased humidity that will prevail in an airstream that has acted as a watershed.

 

Meteorology Notes

Potential Stability

 

 

 

 

 

 

 

 

 

 

 

 

 

Conclusion. (Meteorology Notes)

The above properties are summarised and illustrated below:

  • Dry air is stable if ELR is < DALR.
  • Dry air is unstable if ELR is > DALR.
  • Saturated air is stable if ELR is < SALR
  • Saturated air is unstable when ELR is > SALR.
  • Air, whether dry or saturated, is stable when ELR < SALR. This is known as absolute stability.
  • Air, whether dry or saturated, is unstable when ELR > DALR. This is known as absolute instability.
  • Air, in which the SALR<ELR<DALR has conditional stability i.e. it is stable so long as the air is dry but is unstable when the air becomes saturated.

It follows from the above that a layer wherein the lapse rate is zero (isothermal) of negative (inversion), has absolute stability.  On the other hand a layer in which as superadiabatic lapse rate (lapse rate greater than DALR exists), has absolute instability.

 

QUESTIONS (Meteorology Notes)

  1. A radio-sonde measures the upper air temperatures on a cloudless day when plotted on a temperature- height graph, these temperatures would give:
  • the path curve
  • the environment curve
  • the dry adiabatic curve

 

  1. A temperature inversion indicates a state of the atmosphere which is:-
  • absolutely stable
  • absolutely unstable
  • Conditional unstable

 

  1. An isothermal layer is a state of the atmosphere which is :
  • absolutely stable
  • absolutely unstable
  • Conditional unstable

 

  1. An ELR value between those of the SALR and DALR indicates:
  • absolutely stable
  • absolutely unstable
  • Conditional unstable

 

  1. On a clear night inland, the stability of the lowest layers of the atmosphere:
  • will decrease
  • will not change
  • will increase

 

  1. Air moving from the J & K to Bihar will:
  • become more stable
  • become more unstable
  • not experience any change in its stability

 

  1. The DALR value is :
  • 5 C deg/1000 ft
  • 98 C deg/1000 ft
  • 00 C deg/ 1000 ft

 

  1. For potential instability, the relative humidity must:
  • decrease with increase of altitude
  • remain constant with increase of altitude
  • increase with increase of altitude

 

  1. The instability of an airmass moving SE from Rajasthan to Orissa will normally:-
  • decrease
  • remain unchanged
  • increase

 

  1. It is true to say that:
  • At surface levels, greatest instability normally occurs in mid-morning when clouds are forming fastest.
  • The lapse rate through a layer of cloud is less than the SALR if the conditions are unstable.
  • Generally the ELR can never greatly exceed the DALR value in unsaturated air, nor greatly exceed the SALR value in saturated air.

 

  1. It is true to say that : –
  • At surface level, greatest instability normally occur in mid-morning when clouds are forming fastest.
  • The lapse rate through a layer of cloud is less than the SALR if the conditions are unstable.
  • Generally the ELR can never greatly exceed the DALR value in unsaturated air, nor greatly exceed the SALR value in saturated air.

 

 

 

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