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Produced by the NASA Center for Aerospace Information (CASI)
SYSTEMATIC N84-18046

(NASA-CR- i'7537i) 1?FFECTS OF

ERRORS OH THE MIXING RATIOS OF TRACE GASES

OBTAINED FROM OCCULATICN SPECTRA ;Jet

ncla Propulsion Lab.) 35,P HC A03/MF A0 1 U s

CSC1^ 20F G3/74 0ncla

Effects of Systematic Errors on the Mixing Ratios of

Trace Gases Obtained from Occultation Spectra *

FEB 1

ggG

ld ^^

W. A. Shaffer and J. H. Shaw

Department of Physics

Tl ..r Ohio State University

Columbus, OH 43210

and

C. B. Farmer

Jet Propulsion Laboratory

Pasadena, CA 91103 '

* Thie work was supported in part by NASA Grant NSG-7469.
a

Abstract

The influence of systematic errors in the parameters of the models describing

the geometry and the atmosphere on the profiles of trace gases retrieved from simulated

soles occultation spectra, collected at satellite altitudes, is investigated. It is concluded

that, because of smearing effects and other uncertainties, it may be preferable to

calibrate the spectra internally by measuring absorption lines of as atmospheric gas such

as CO 2 whose vertical distribution can be assumed rather than to rely on externally

supplied information.
r

ORIGINAL PAGE IV

OF POOR QUALITY

Introduction

It is expected that high-resolution, infrared, solar, occultation spectra covering

wide spectral regions wlll soon be collected from satellite altitudes. 1 These spectra will

add significantly to our knowledge of atmospheric properties, including the latitudinal and

9

vertical distributions of many trace gases. However, the quantitative analysis of these

spectra requires a knowledge of the geometry of the experiment and of the

characteristics of the atmosphere along the ray paths. Although this information can be

obtained from external sources, features in the collected spectra, including, for example,

those of gases such as CO2 , whose vertical nihning-ratio profiles are well known, can be

2

used to calibrate the spectra internally.

In this paper the influence of systematic errors in the path geometry and the

atmospheric characteristics on the derived mixing-ratio profiles of trace gases is

estimated with the simulation methods used previously. 2 It is assumed that the data

consist of the equivalent widths of weak lines. The relative meri . of internal and

external calibration of spectra obtained from satellite altitudes are compared and it is

concluded that, in many cases, it may be preferable to calibrate the spectra internally by

measuring limes of a gas such as CO2 whose vertical and latitudinal distribution is

4 2

reasonably constant. Farmer et al. have previously found that calibrations, based on

C©2 lines, of solar spectra obtained from balloon altitudes also reduced systematic errors

associated with the atmospheric models and observational geometry.

1

_1

,R

-A,
(2)

ORIGINAL PAGE 1,9

OF -POOR QUALITY

Systematic Errors Associated with the External Calibration Method.

The equivalent width of a weak atmospheric line can be written as

W (zi) _ S3 Pi d i 61 i3 . El)

j

where S_ is the line intensity, p_ is the mixing-ratio of the absorbing gas, d _ is the air

density, and blij is the path length in the jth atmospheric layer traversed by the ith ray

which reaches the instrument at an angle z with respect to the local zenith. Some of the

quantities affecting these equivalent widths are summarized in Table 1. In general, if the

line intensity depends on parameters s , the mixing ratio on parameters t , the density on

9 P

parameters x , and the incremental path on parameters y , then the change in equivalent

q r

width caused by changes In these parameters

dW(zi) S j pith a1 i3 s

3

1 E

d

3

as I Ds + i E = At

g P 3 n c8tP P

^ Sl r Ayr

q ii Jr

It is convenient to assume, initially, that the line intensity is known accurately

and is independent of temperature. In this case the amount of absorber a(z 

i ) 

along the

incoming rays

aa(zi) = W(ziVS , (3)

and

Aa(z i) = 

3 

pi d j S1 a i

^

3 ^ ^ At p + 1 q ^ A. + --L- ' sal . r i3y Ayr (4)

P i q ii

where we have assumed that the set of x variables is independent of the set of y

q r

variables and the set of t variables iJ the union of the x and y sets.

q q r

The effects of errors in d and 61 i on the values of pi retrieved from a set of

a(zi) values have been studied by creating a set of measurements a(z i) with an appropriate

. ie

2
4

ORIGINAL PAGE E5

OF POOR QUALITY

set of values for the parameters x , and y . Mixing ratio profiles were retrieved

q r

successively from these data using incorrect values for each of the parameters x or y -

q r

If, for example, the Incorrect value x + Clad was used then, since the correct set of

absorber amount values were analyzed, A a{zi} = 0, and Eq. (4) becomes

Ax + I Ax = 0.

j P3

 axi

1 dj ax,

1

This can be written as

9 + ^ = 0-

j P d 3

If the local mixing-ratio values are independent then

9 + = 0,

P d

similarly (5)

=, + = 0 .

P

5,6 The program described by Snider and Goldman was used to calculate the

absorber amounts along the paths of 125 rags, with nearly equally-spaced tangent heights

between 0 and 50 km, to a satellite 500 km above the surface and at 45 4 latitude. The

absorber was assumed to have a constant mixing-ratio In all tbree dimensions and to be in

an atmosphere with the temperature and density profile of the MS. Standard

7 AtmosVnere. A wavelength of 5 urn, was assumed.

For these conditions the distance along a. rsy, such as that shown in Fig. I, from

the tangent point to the satellite is about 2500 km and the distance to a point 50 km

above the tangent point is about 800 Ian. Variations in the effective radius of the earth or

in the atmospheric temperature, density, and m# ng-ratio profiles along these paths have

3
% 16

ORIGINAL PAGE 19

OF POOR QUALITY

not been modelled, nor have the effects of the finite FOV of the instbmaaent and satellite

8

motion during the period of data collection. Kantor has shown the variability of the

density of the atmosphere between 20 and 60 km above the surface from the equator to

65° over periods of up to 72 hours and distances of up to 370 km, is typically several

percent. The finite angular FOV causes a spread of the beam at the tangent point of

about 2.5 kmlmzad. Satellite motion may cause the tangent heights of the rays to change

at rates as high as 3 km/sec. Thus the vertical resolution of typical measurements made

with a FOV of 1 mrad and for observation times of about one second is limited to a few

kilometers. These effects also set upper limits to the accuracy of the information which

can be derived from the spectra.

Layer Thickness

The paths of rays through the atmosphere and the total air mass traversed were

calculated by dividing the atmosphere into layers with the same vertical thickness. The

dependence of these calculated air masses on layer thickness is shown. in Fig. 2. for,

thicknesses of from 25 m to 20 km and rays with tangent heights of 2.6, 12, and 48 km.

The calculations are made by assuming there is a constant vertical temperature gradient

in each layer. For the two lowest rays, this is a good appro ,.dnation for all layer

thicl.messes. The larger variations in the calculated air mass traversed by the ray with a

tangent height of 48 km are attributed to the rapid changes in the temperature gradient

of the Standard Atmosphere near 50 km. Ian the 'rest of this work a layer thickness of 0.25

km was used. This sulk. caused Lmegularities seem in some of the, figures near the

tropopause level,.

r^

t

t

1

L" ^a

4
{q^1 9 ®

ORIGINAL n AGE 9^

Of p0i3R QUALITY

Atmospheric Refraction

•s;

The atmospheric dispersion from the visible to beyond 20 urn is small and, to a

very good approximation, rays of all wavelengths can be assumed to travel the same

paths. However, if refraction is not considered, the calculated air masses traversed by

rays with tangent heights between 0 and 90 km have the errors shown in Fig. S. H the

mixing ratio profile is retrieved by neglecting refraction, the calculated path segments

61 required in Eqs. l and 5 are incorrect and errors in the retrieved mixing- -ratio profiles `<^

1

are produced, as shown in Fig. 4. The irregularity, near. 10 km is due to the rapid change in l

the atmospheric temperature gradient at the tropopause.

Reference Pressure Errors " :3

The atmospheric pressure and density profiles were obtained from the vertical

s ^h^

temperature profile and the sea level pressure P . If the correct temperature profile is

!C]V

w_

used, the pressure and density at any other level and the air mass traversed by a ray with

a fixed tangent height are proportional to P Thus

Ad/d - AP /P ,

0

(6) r}^

0 0

and hence from Eq. (5)

AP/p = -AP /P (7)

0 0 !

The fractional errors in the retrieved mixing-ratio, Ap/p, shown in Pig. 5, and i

obtained for the case where the ray path geometry, is known accurately but AP /P is

o 0

equal to t5%, are not Lndependcnt df height, as expected from Eq. (7), because the change

in the air density causes the refraction effects to be modelled incorrectly. :.

-5,

5
r Lof

ORIGINAL PAee 

gj

OF P06R QUAL1

Incorrect reference level pressures may be used because of uncertainties in the

large-scale, global variations in atmospheric pressure, density, and temperature. In

addition, smaller-scale variations in these quantities of several percent may occur over

8

regions much smaller than those traversed by the rays. These variations are difficult to

model in the spectral analyses described here and they may limit the accuracy of the

retrieved mbting-ratio profiles. Since pressure and height are related, the use of an

incorrect reference pressure at a known altitude is equivalent to choosing an incorrect

altitude for the reference pressure. These relations can be estimated for an isothermal

atmosphere in which the pressure and density are given by

P(h) = P exp (-h/H), (8)

0

and d(h) = d exp (-h/H), (9)

0

where the scale height of the atmosphere

H = RT/Mg, (10)

is approximately 7 km below 50 km in the Standard Atmosphere.

Since

Ah/H = AP /P (11)

0 0

a five percent error in P is equivalent to an error of 0.4 ken in the tangent heights of all

0

the rays.

Errors in Atmospheric Temperature

The dependence of atmospheric density on temperature can be approximated by

considering an isothermal atmosphere with a fixed reference pressure P . Erom Eqs. (8)

0

and (10)

6

--- - -
r

AP = M9hPAT/RT2

OF PO

^ ^ OR QUALITY (12)

and, for a perfect gas,

d = MP/RT.

2

Thus Ad = MAP/PT - MP®T/RT , (13)

and dd/d : (h - H)®T/HT. (14)

As the temperature of the entire atmosphere is chased the density remains

constant near h = H but it increases at a rate of about 2.5%/K near 50 km. From Eq. (4)

the dependence of the errors in the retrieved miming-ratio profiles on these density

changes is also described by Eq. (14).

The fractional changes in the atmospheric density caused by changing the

temperatures at all levels in the standard atmosphere by ±5%K and the corresponding

fractional errors in the retrieved mixing-aatios in Fig. 6 are similar to those predicted by

Eq. (14). Larger errors in the mixing-ratio may occur if the line Intensities depend on

temperature. It is planted to discuss these effects elsewhere since they may be used to

obtain Improved estimates of the temperature profile If the midng-ratio of the absorbing

gas is known.

The differences in the tangent heights of rays which pass through the same air

masses in isothermal atmospheres at different temperatures are obtained from Eqs. (9)

and (14)

Ah = (H - h)AT/T . (15)

These differences increase to about 0 .4 km near 50 km for a one percent change

in the temperature of the entire atmosphere. in addition to mixing -ratio errors caused by
ORIGINAL RRGE 1,j

OF 130OR QUALITY

the use of incorrect vertical temperature profiles unmodelled horizontal temperature

variations may also affect the accuracy of the retrieved mbdng-ratio profiles.

Satellite Heights

It is seen from Fig. 1 that a change Aa, In the satellite height causes a change:

Aa cosh = Aa in the tangent heights of all the rays. From Eq. (9) Ad/d + AMR = 0.

Thus, for an isothermal atmosphere, the rate of change of density with height, and hence

of the air mass traversed with the tangent height of a ray, is about 14%/km. The errors in

the retrieved mixing- ratios caused by errors of #i km in the satellite height, shown in

Fig. 7, are approximately 14% and the vertical dependence is very similar to that caused

by errors in P . To reduce the errors to less than 1% the satellite height must be known i

o i

to better than 100 m. a

Latitude Error

The effective radius of the earth and the acceleration. due to gravity are both

latitude dependent and the air masses traversed by rays reaching an observer at fixed

Incoming angles vary with latitude. A series of calculations has shown that, for an. f' A

observer at 50 km, the air masses traversed by the rays varied by less Than X4% from the

value at 45°, as the latitude was varied from 0° to 90 0, and the changes were essentially

the same for all rags with tangent heights between 0 aiid 50 km. Thus, since the latitude

is always well deterroinedr these chaiiges should not be a significant source of error..

8

.1 Al

-777 777
ORIGINAL PAGE iS

OF POOR QUALITY

Incoming Angle Errors

Atmosphere paths are calculated from the angle z shown in Fig. 1, between the

local zenith and the arriving rays. This angle can by measured directly or it can be

calculated from the known position of the instrument and the time of observation,

provided atmospheric refraction is included.

An error Az in this angle causes an error Bb ^: LAz in the tangent height, where

L is the satellite-to-tangent height distance. For a satellite at 500 km, L1b/Az is

approximately 2.4 km/mr or 40 km/1°. This corresponds to a rate of change in the

atmopheric density, at the tangent height of about 60095/1". The changes in the retrieved

Ong--ratio caused by systematic errors in z of 0.01° and corresponding errors in b of

1

0.4 km are shown in Fig. 8. As expected, they are nearly independent of height and

average about 6%.

When the angle z is calculated from the parameters of the satellite orbit, errors

may arise from incorrect estimates of the satellite height, the position in its orbit, the

plane of the orbit, or the time of observation. For the tiro--dimensional geometry in Fig. 1

Z = 90 + 0, (lb)

AZ = DO .

cos® _ (R + b)/(R + a) , (17)

Ab = LAz ,

and -sinOAe = --(R + b)Aa/(R + a)2 + (a - b)AR/(R + a)2 + Ab/(R + a).

For a satellite with a = 500 km, R = 6400 km, and b << a, errors of 0.5 km in

a, of 6 km in R, or of 0.01° in 0 or z cause 7% errors at all heights in the derived

9
MIGINAL PA(;E d,S OF POOR QUALITY

rnixin.g--ratio profile. The same error is caused if the position. of the satellite in its orbit

is uncertain by 1.2 km or if there is a timing error of 0.16 sec. Since all of these errors

affect the derived mbdng-ratio profiles in the same manner as errors in the reference

pressure, additional information must be supplied if the origins of suspected errors are to

be identified.

Satellite Motion

For the Uvo-dimensional geometry in Fig. 1 and for a satellite in a circular orbit

at 500 km the tangent height of a ray changes at a rate of about 3.8 km/sec, in the

absence of refraction. The distortion of these paths due to changes in the atmospheric

density gradient and to refraction have been discussed by Oarriott 9 and Russell. 10

The corresponding irate of change of air mass, in an Isothermal atmosphere,

obtained from Eq. 9 is about 40%/sec. These rates of change of air mass as functions of

the change in apparent zenith angle were also calculated for an atmosphere with a

temperature gradient of 1 R/km and for the U. S. Standard Atmosphere with refraction

effects included. The results are shown in Fig. 9. In both cases the mean rate is about

4095/sec. However the rate varies significantly with the tangent heights of the rays

because it is affected both by refraction anti. by the atmospheric temperature gradient

near the tangent height. Since the mean air mass traversed by the sets of rays reaching

an instrument is obtained by weighting over the FOV these results shove that the weighting

is a function of the temperature profile and changes in the temperature gradient must be

considered when the mbeing-ratio profile is obtained from actual data.

- t

:iII i1

Ito

:) !1

10
r a '

ORIGINAL. PAGE 19

Summary

®F. Pp©R QUALITY

The amount of an absorbing gas along the atmospheric paths traversed by solar

rays can be obtained from the equivalent widths of weak absorption lines in solar spectra

provided the models used to describe the geometry of the experiment and the structure of

the atmosphere are la.-own. The effects of systematic errors in these parameters on the

retrieved mixing-ratio profiles of the absorber have been estimated. With the exception

of the c:fects of atmospheric refraction and errors in the temperature profile these errors

produce nearly identical effects on the retrieved profiles. These effects are equivalent to

an error in the tangent heights of the rays producing the set of spectra which is

Independent of the height of the ray. The magnitudes of these effects agree with those

estimated by making simplifying assumptions about the experiment design.

The existence of these errors can be detected by comparing the mixing-•ratio of

a gas whose vertical distribution in the atmosphere is known with that obtained by

analyses of the equivalent widths of its lines in the spectra. However, because of the

similarities of these effects it is not possible to determine, from these profile differences,

either the number of parameters in Table 2 which are in error or the magnitudes of these

errors unless additional information, is supplied or different types of measurements are

made. No discussion of the influence of several smearing effects present in the spectra

on the derived n ix€rtg-ratios has been given although it has been pointed out that these

can substantially reduce the vertical resolution. 11 Incorrectly modelled smearing.

effects may lead to systematic errors substantially larger than those in Table 2. In the

remainder of this discussion the method of internal calibration is discussed. Although

11

jl
-.,c-,..^_^..^,^-,.n-. ^,..__.-rM.s.^-.;-.--r=T:—;erg.^s^-:^.-^^_sre--...-^.elr:...-_...^^=.-r^^..-,•....,-....-,.-.^...-.-.^a.^....^.-.^r,.^i.,.^-,s^+^—... __.

I{

1

1 R

ORIGINAL PACE gq

OF POOR QUALITY

itself subject to systematic errors these are expected to be smaLi. This method does avoid

many of the errors due to the incorrect,modelling of smearing effects as well as many of

the systematic errors discussed above.

Internal Calibration of Occultation Spectra

When the information about the atmospheric paths is obtained from external

sources several e-*ors affect the retrieved profiles in nearly identical ways. This occurs,

in part, be ause the spectral information concerning the atmosphere, carried by a ray

with a fixed tangent height and which originates outside the atmosphere, and is collected

outside the atmosphere, is not influenced by the positions of either the source or the

detector along the ray and hence by the particular sets of parameters which describe

these positions. It has also been noted that the duality of the spectra is degraded by the

11 finite FOV of the instrument, satellite motion, atmospheric refraction, and temperature

i 12

- and density - profile variations along the atmospheric path and that it is unlikely that

all of these effects can be satisfactorily modelled in the analysis.

Internal calibration removes many of these uncertainties but also introduces new

ones. In this method, information about the atmospheric gs zh is obtained from absorption

Imes is the spectra. Lines of CO 2 are often measured because its vertical and latitudinal

mixing-ratio is nearly constant and the parameters of many CO Rues are accurately

known. We consider, initially, the information obtained by measuring the equivalent width

of a single creak CO2 lime, with a tetaperature-independent line intensity, is a single

spectrum. This allows one aspect of the path, such as the total amount of CO , to y

12
ORIGINAL RAGE 10

OF POOR QUALITY rs

be obtained. The additional information obtained by measuring the equivalent widths of

several lines in different regions of the curve of growth, by measuring lines whose

I

intensities are teumpsrature dependent, or by measuring the shapes of lines is considered

later.

If W0 and WI are the equivalent widths, in a single spectrum, of weak lines of

CO2 and a trace gas, respectively, and if the corresponding Line intensities S 0 and S are

temperature independent, then, from $q. (3), the amount of CO 2 along the path

a0 = O/S0 , (18)

and the amount of the other absorber

a - fit' IS (19)

1 1 1

If the CO2 nAiting-ratio p0 is constant with height and along the path traversed

then the total aft mass traversed

A = ©IS0p0 , (20)

and the mean mixing-ratio of the absorber along the ray path, relative to that of CO2

p1 = a1/A . (21)

These simple results are obtained because the incremental equivalent widths are additive.

In this approach both equivalent widths have been averaged in some (unknown) manner

over the FOV of the Instrument and they are weighted by the other factors discussed

above which affect the quality of the data. If the spectra are obtained by a Fourier

Transform Spectrometer information concerning both of the Lines W0 and WI is collected

simultaneously. Provided the lines are both weak and neither of the m xing—Yatios change

rapidly over the FOV both of their equivalent widths are siabjected to the same weighting

processes which are then automatically ratio.ed out of the final results. Thus the values

13
ORIGINAL PAGE 1*9

OF POOR QUALITY

for the total air mass traversed and the mean mixing-ratio of the unknown absorber given

by Eqs. (19) and (21) do not contain the implicit uncertainties associated with the

uncorrectable smearing effects of the external calibration methods.

Additional measurements or assumptions are still. required to obtain the

3

distribution of the unknown absorber with height. In the previous paper this distribution

was obtained from the measured equivalent widths WI and the known geometry and the

atmospheric structure. Thus the mixing-ratios could be determined either as a function

of altitude or of pressure.

In the internal calibration method the geometry is inferred by comparing the 0

measurements with another set obtained from Eq. (20) and by assuming the atmospheric

temperature, density, and CO 2 profiles are known. The unknown mixing-ratio is then

3

obtained as described previously. These atmospheric paths will differ from the actual

paths if these assumed profiles are incorrect. Thus errors in the mixing-ratio profile of

the unknown absorber will occur which will depend on the nature of the systematic error

and the method used to describe the profile. For example, an error of QPo (e.g. of one

percent) in the reference pressure Po does not affect the estimates of the total air mass

traversed since air masses are derived from Eq. (20). However, from Eq. (11) it can cause

a corresponding error Bh (-0.1 km) in the tangent heights of all rags and hence the entire

mixing--ratio is displaced vertically by Ah.

The effects of other types of errors can be estimated in a similar fashion and

they are listed in Table S. With the exception of errors in the temperature profile these

effects are independent of the tangent heights of the rays. If the values in Table 3 are

14
I

ORIGINAL PACE IS

OF POOR QUALITY1

added in quadrature the total uncertainty is less than I I=. This is less than the vertical

resolution due to the smearing effects already discussed. It is also smaller than the

vertical ;asolution of the trace gas profiles expected to be obtained from mid-infrared,

occultation spectra obtained with state of the art Fourier transform spectrometers at

balloon or satellite altitudes. If reasonable assumptions are made concerning the rate of

data collection and the SNR this resolution Is typically several kilometers. Thus internal

cilibration.13 appropriate for these measurements.

The internal calibration method does require the CO2 Hue intensiti,es and its

mixing-ratio. Although the spectrun of CO 2 has been extensively investigated the wide

range of intensities required to obtain accurate equivalent width information may require

additional quantitative laboratory measurements of CO 2 spectra. A careful evaluation of

4

the global and temporal variations in the atmospheric CO2

 raixing-ratio is also needed.

1S Mauersberger and Finstead have summarized some of the information on atmospheric

CO2 and have described some higher-than-expected CO2 mfg-ratios obtained above

25 km at aright.

Some additional types of information which may improve the accuracy of the

results is discussed below.

Relative Times of Data Collection

The rate of change dzI/dt of the zenith angles of the incoming rays and the

corresponding rate of change db/dt of the tangent height of rays reaching a satellite are

nearly constant in a given occultation. Thus the scatter in the equivalent tangent heights

3

15
ORIGINAL PME. i9

OF POOR QUALITY

b with time allows the consistency of the data to be estimated. Nearly constant

systematic shifts between all of the values obtained by internal calibration of the spectra

and those calculated from the orbital parameters may be due, for example, to timing

errors. Differences at low tangent heights below 10 kn may be caused by improperly

corrected refraction effect and uncertainties in the CO2 mixing-ratio or departures from

LTE may produce differences between the observed and calculated curves for tangent

heights above 70-80 km. However, good agreement can usually be expected for rays with

tangent heights between about 20 and 50 km and these data can be used to improve the

calibration of spectra which do not contain CO 2 lines suitable for calibration.

Measurements of Several Lines

The bands and lines of C 0 2 have a wide range of intensities. Thus by measuring

the equivalent widths of a number of lines in each spectrum the consistency of the

measurements can be estimated and those lines which are too weak to be measured

accurately or which lie outside the linear region, can be rejected. The effective SNR is

also improved by measuring a number of lines.

Because of the very large variation in the air masses traversed by rays with

tangent heights from 0 to above 50 km it is necessary to measure CO2 lines with a

corresponding range of temperature-independent intensities in order to maintain high

precision. In general, this will require measurements of CO2 lines, with small lower state

energies, in bands with different intensities.

" k

i

n. .

i

I

16

j.
f, ,1

ORIGINAL PAGE 1-9

OF POOR QUALITY

Lines Not in the Linear Region

It has so far been assumed that the equivalent widths of the CO calibration

2

lines can be obtained from Eq. (1), which can be written as

W (ai ) AWij .

i

If the CO2 lines are not in the linear region of the curve of growth the

incremental widths AW i depend on the local atmospheric temperature and density and

they are no longer additive. The weighting of such lutes over the POV and other smearing

effects is different from that for weaker CO2 lines or weak lines of trace gases.

In these cases one of the principal advantages of the internal calibration method,

the ability to assume that the smearing effects are the same for all lines, is lost. It is

therefore important to choose CO2 calibration lines which are in or close to the linear

region of the curve of growth.

Measurements of Temperature Dependent Lines

Because the atmosphere is not isothermal the weighting of the equivalent widths

of the lines over the POV depends on the temperature dependence of the lines in addition

to other effects previously consiftred. Since the stron4est lines of most trice gases are

not strongly temperature dependent CO a lines with a similar temperature dependence

should be chosen for calibration. Discussions of the atmospheric information contained in

temperature dependent CO 2 lines are given elsewhere. 14,15

Curve Pitting

Spectral curve-fitting is a powerful method of a acting information

17
ORIGINAL PAQE t

^q

OF POOR QUALITY

if the models describing the spectrumare accurate. l6,17 Parkll has shown that the

effects of satellite motion during data collection and also other effects distort the

occultation interferogarams and consequently the spectra derived from them and that

these smearing effects on the line shapes are difficnIt, to model accurately. These

3 methods are not explored in this paper. Shaffer and Shaver have shown that more

Information or the vertical distribution of gases can be obtained by collecting as may 1

spectra as possible during an occultation than by inferring the distribution from the

profiles of the lines in a single spectrum. One of the principal effects of measuring

equivalent widths is to smooth the noise in the data analymed.

Conclusions

Internal calibration of satellite occultation spectra from measurements of the

equivalent widths of weak, temperature -independent C Oa Hues may be preferable to

calibration based on error--prone external Information, It is expected that Internal

calibration should allow the paean tangent heights of the rays to estimated to about I km •

and the mixing ratios of trace gases to about five percent.

These imcertalaties increase if the intensities of the lines used for calibration. #

are temperature dependent md if toe li;aes are dot An the linear region gf the curve of

i growth 'because the weighting of the absorber over the POV and other smearIng effects

depend on the Brae parameters.

However, because of the large numbers and the wide range of intensities of COO

limes appearing in the solar spectrum tb—o accuutacy of the internal calibration method can

be maintained over wide height intervals.

r

I$

r
Table 1. Quantities Affecting the Equivalent

Widths of Weak Lines in Solar Spectra

Variable Parameter

Line Intensity Athos. temperature

height

Athos. density sea level pressure

Athos. temperature

profile

observer altitude

geometrical path atmos. refraction

latitude

ang..e of arrival of ray

0

19
Table 2. Sources of Error and Their Effects

Oig1t INAL PAGE 15

on Retrieved Mining Ratio Profiles Oj: POOR QUALITY

Quantity in Error

Mixing Ratio

Dependence on

Error,

Height

Change Required for

1% Error in Mixing Ratio

Refraction only important below 25 km

Reference Pressure independent of height AP = 10 mb

Temperature Profile increases with height

Satellite Height independent of height Oh = 80 m

Latitude It

Radius of Earth " " " 1 km'(at 45°)

Angle of Incoming Rays " " " 0,002°

Time of obs. " " " 0.03 secs •

Position in orbit " "

11 0.25 km
a

ORIGINAL 

I 

PAGE

OF POOR QUALITY

Table 3. Dependence of the Errors in the Tangent Heights of Rays

Made by Using Internal Calibration Methods on

Systematic Errors in the Assumed Parameters Values

Parameter

Systematic

Fractional

Errors (%)

Corresponding Change in

Tangent Height of Rays

Sea level pressure 0.1 km

Temp Profile I (3K) <0.5 km

CO2 mixing ratio 1 0.1 km

Line intensity 1 0.1 kin

Equivalent width 0.1 km

sF

1 f i

21
^i

Figtue Captions

ORIGINAL PAGE EEO

OF POOR QUALITY

Fig. 1 Occultation Geometry. For a mean earth radius A - 6360 1cm and a satellite

0

height a = 500 Itm the distance L is about 2500 km, the angle 9 is about 21 0 and

the zenith angle z is about 1110.

Fig. 2 The dependence of the air muss traversed by rags with 'tangent heights of

approximately 3, 12, and 48 km an the thickness of the atmospheric lagers used

t ^

in the calculation. The fractional change in air mass with respect to that

calculated for 25 m thick layers is shown.

Fig. 3 The dependence of the fractional air amass error along the rays, due to the

neglect of atmospheric refraction, on the tangent. height of the rays for the

case of an observer at 500 Ian.

Fig. 4 The height dependence of the fractional errors in the mixing-ratio profile

caused by the neg.:act of atmospheric refraction in the retrieval.

Fig. 5 The height dependence of the fractional errors tat the mixing ratio profile

caused by five percent errors in sea level pressure.

Fig. b The height dependence of the fractional errors in the retrieved mixing-ratio

profile caused by assuming ±5 K changes at all heights in the U. S. Standard

Atmosphere temperature profile.

II

F4 7 The height dependence of the fractional errors in the retrieved mixing-ratio

profile caused by errors of ±1 km in the satellite height. t

Fig. 8 The height dependence of the fractional errors in the retrieved mixing-ratio

profile caused by errors of 0.01 0 im the ausles of the incoming rays. a

22

71

4
t ^^

I

-1 Fig. 9 Fractional rate of change of air mass {sec ) for an observer at 500 km

a) U.S. Standard Atmosphere b) atmosphere with a temperature gradient of

1 Rlkm. The tangent heights of the rays decrease from 90 to 0 km.

.^I

.. r
References oRIGINAL PAGE 19

OP pooR QUAI.UTY

1. C. B. Farmer, NASA Upper Atmosphere Research Program, Summaries (1982).

2. C. B. Farmer, D. F. paper, B. D. Robbins, R. A. Toth, and C. Muller, J. Geophys.

Res §5,1621 (1980).

S. W. A. Shaffer, Ph.D. dins. Ohio State Univ. (1983), W A. Shaffer and J. H. Shag,

Appl. Opt. 22, 2977 (1983).

4. "The Stratosphere 1981 Theory and Measurements", W MO Global Ozone Research

and Monitoring Project Report No. 11 (1982).

5. D. B. Snider, J. Atmos. Sci. 33, 2178 (1975).

6. D. B. Snider and A. Goldman, BRL Report 1790, Aberdeen Proving Ground, Md.

21005 (1975).

7. U. S. Standard Atmosphere 1976, U. S. Govt. Print Office, Washington, D. C. (1976),

8. A. J. Kantor, "Variability of Atmospheric Density in the Middle Atmosphere,"

APGL-TR-83-0079, AFGL, Hanscom APB Mass 01731 (1983).

9. O. K. Garxiott, JOSA 69, 1064 (1972).

10. J. M. Russell, Ul:, Pure and Appl. Geophys. 118, 616 (1980).

11. J. H. Park, Appl. Opt. 21, 1356 (1982).

12. D. A. Roewe, J. C. Gille, and P. L. Bailey, Appl.. Opt. 21., $775 (1982).

13. K. Muersbexger and R. Finstead, Geophys. Res. Lett. 7, 873 (1980).

14. R. A. Toth, Appl. Opt. 16, 2661 (1977).

15. C. P. Rinsland, A. Goldman, F. J. Murcray, D. G. Murcray, M. A. H. Smith,

R. K. Seals, Jr., J. C. Lassen and P. L. Rinsland, JQSRT 30, 237 (1983).

16. Y. S. Chang, J. H. Shaver, J. G. Calvert, and W. M. Uselman, JQSRT 19, 599 (1978).

17. E. Niple and J. H. Shaw, Appl. Spectros. 33, 569 (1979).

24
11

• de

IN

ORIGINAL, PAGE 1,9

OF POOR QUALITY
ORIGINAL PAGE IS

OF POdR QUALITY

O

C

0

LLJ

0Ile - 

2

-4

IL TUC. 103 104

Layer Thickness (Meters)

7
40

ar

20

0L-

-20 -5

-d

-15 -!0

% Error in Air Mass

ti

091011VAL PAGE â^

OF POOR QUAL17'4' 1`

60

80
ORIGINAL PAGE TV

OF POOR QUALITY

50

25

d

0L0 25 50

% Error in Mixing Ratio Profile
i

d

ORIGINAL PA®C

Opr POOR QUALITY

APO= 5% ®P437-5%

50

25

B

C

^Ai

. r. ^i

10 0

°err Error in Fixing Ratio Profile

10

4

.41

"3i

..,

,.
ORIGINAL PAGE 99

OF POOR QUALITY

5G

AT= 5K AT=-5K

25

a

0

-io

a
0

%Erro r in Mixing Ratio Profile

o t-

-20

FiS.

ri

i

2

25

3

t

ORIGINAL PAGE 19

OF POOR QUALITY

QAp=- I KM AAO= I KM

,a

u

!}t.,j

50

Y!'
ORIGINAL PAGE 19

OF POOR QUALITY

AZo - 0.01 °

5t

AZO= 0.01 °

25

a ,e

,

i a^a

0 L.

-10

. .. 4

. i

'0 0 5 10

% Error in Mixing Ratio Pi°ofi le

H

- is
ORIGINAL PA(;E 1,1

'OF POOR QUALM

^. 0.6

7

UUi!1

N

[JS a

0.5

d

a

m

a

U 0.4

wa

as

v

w

a

c

00.3

U

O

110° III* 112°

Apparent Zenith Angle (Degrees)

b

d