Determination of temperature profiles

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I I

r

5 ^{I I}

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: : ~

: :

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I I J I I

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I I I I I

, ,"-

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')

...

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. - - /

I <!. C I I I

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__ ~ - relatl\edenSity

, , c: ^{r' '}

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I I 1~ ^{I I}

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i

30 ^{l i L} - - - -, - - - -,

1.2 1.1

0.9 0.8

20L-_----'_ _---"-_ _---l..-_----4--L._ _---L.- _ _

0.7 1.3

25

Relative dersity values

Figure 6.4: The relative density of the atmosphere above Durban as obtained from the LI DAR data of October 4 2001.

of the planetary waves in the atmosphere. The uncertainty in the realtive density profile is also shown in fig.(6.4). The uncertainty increases with altitude because of the increase in the sky background noise with altitude.

The uncertainty of the relative density profile is obtained from

~(}LIDAR

(!LIDAR

~S(z)

S(z) - K( z)

^(6.13)

species and that the atmosphere is in hydrost atic equilibrium with pressure, density and temperature related through the ideal gas law. It is assumed that atmospheric turbulence does not affect the mean air density, which is indeed the case when consideringthe temporal and spatial resolutions of the LIDAR data.

The possibility of finding the temperaturein this way was demonstrated for the first time using mechanically modulated searchlight s by Elt ermann (1953, 1954). The temperature profile for 10 October 1952 is shown in fig.(6.5) (Elterman 1953). This clearly shows that the temperature of the atmosphere initially decreaseswith altitudeup to the tropopause (~ 17 km) and there after the temperature increases with height in the stratosphere followed by the stratopause _(~ 55 km) and then the temperature decreases with height in the mesosphere. Preliminary studies using laser pulses as monochromatic light were obtained by Kent and Wright (1970).

The const ant mixingratio of themajoratmosph ericconstituents(N2,02 ,et c) and the negligible value of the H20 mixing ratiojustify the choice ofa con- stant value Wm for the air mean molecular weight. This has been proved adequat eto altitudes of up to80 km. Above thisalt it ude, dissociation of O2 must be taken into account .

In an ideal gas,theair pressurePr(z) ,densityg(z) andtemperature M(z) are rela ted by

() Un :g(z) . M(z) Pr Z

= _--::""':'-'"--_":""':"

Wm (6.14)

65,.----.----.---.----..:::::---,---.---.---,

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I I I I

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_ _ _ 1_ _ _ _ I _ _ _ 2 _ _ _ 1_ _ _ _I _ _ _ _I _ _ _ ~ _

I I 1 I

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I I l I , I I

320

200 220 240 260 280 300

Tenperarue(K)

10L..-_--'-_---'-_--"'---'---_-'-_---''--_--'--_----'---'

180

Figure 6.5: Temperature distribution from searchlight data (Elterman 1953).

and hydrostatic equilibr ium implies that

dpr(Z)

=

-e(z) .g(z) . dz (6.15)

where U_R is the universal gas constant which has value 8.31 J mol-1K-1 and g(z)is the acceleration due to gravity at alt it ude z. We assume that 9 remains constant throughout the alt it ude range of observation and is equal

The combinati on ofequations (6.14) and (6.15) leads to

dpr(Z) = d(Log Pr(Z))

= _ Wm'

g(z)dz

Pr( Z) U

R ·

M(z) (6 .1 6)

Ifthe acceleration due to gravity and the temperature are assumed to be constant in the ithlayer, the pressure at the bottom and top of the layer are related by

(6.17)

Hence the temperature in each layer may be expressed in terms of the log pressure difference between top and bottom as

(6.18)

whereM(Zi) is the temperature in thei^{t h} layer, assumed constant throughout the layer.

The density profile is measured up to the ^nth layer. The pressure at the top of this layer is fitted with the pressure of the CIRA - 1986 model Prm(Zn

+

~) for the corresponding month and latitude. The top and bottom pressure of the i^{t h} layer are then given by

(6.19)

(6.20)

thenumerator is the sameas equation (6.20). Therefore theexpression 1+X Pr(Zi- - )6z

can be written as

i z.

Pr(Zi

+

2 )

Using equat ion (6.18) , the expression for the temperature can be written in terms of X as

The statistical st andar d error of the temperature is

(6.21)

with

8M(Zi) 8Log

11 + XI

M(Zi) - Log

11 + XI

8X

(1

+

X) .Log(1

+

X)

6 z 2

8pr(Zi

+

2 ) Pr(Zi

+

2 )6z

(6.22)

(6.23)

(6.24)

where Prm is the pressure at the top of the ^nth layer and is fitted with the pressure of the CIRA - 19S6 model for the corresponding month and latitude.

Hauchecorne et al. (19S0) have shown that the contribution of the ex- trapolated pressure at the ^nth layer on the local pressure below decreases rapidly with altitude due to the exponential decrease of pressure with alti- tude, and its influence on the temperature determination is marginal. Then the term X represents a ratio of experimental density values from which ab- solute temperature can be deduced even though the density measurements are only relative.

The atmospheric transmission at the wavelength used for the new LIDAR (532 nm) is affected by Mie scattering, Rayleigh scattering and absorption by ozone. The attenuation of the LIDAR return due to aerosols, clouds, haze, and fogis difficult to estimate. In the temperature retrieval programme we only consider molecular scattering and absorption by ozone. A listing of the source code is given in Appendix B. Fig.(6.6) shows the LIDAR temperature profile for October 4 2001 obtained using the algorithm as outlined above.

The broken line shown in red is the CIRA-19S6 model. Again as with the relative density profile, the wave-like structures which appear above 40 km on the temperature profile are due to vertical propagation of planetary waves.

The atmospheric transmission at altitudes between 30 and 100 km is greater than 0.995 (Cole et al. 1965). The attenuation is therefore very low and may be determined by an atmospheric model. The resulting error is very small and much less important than other sources such as statistical fluctuations of the signal at high altitude.

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- OPA86 - - UDARuncertainty

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l I " " I 1 I I

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1 ,I I I I I

300 280

260 240

220 200

2OL-_----"-~"__L____'__ _- ' - -_ _'____ _____"__ _____'___---.J

180

'Ierrperanre (K)

Figure 6.6: L1DAR temperature profile obtained from the density profile for October 4 2001.