The Umkehr method for retrieving the gross features of the vertical ozone distribution requires measurements of the ratio of zenith-sky radiances at two wavelengths in the near-UV region while the solar zenith angle (SZA) changes from 60 to 90 degrees. A Brewer spectrophotometer was used for taking such measurements extending the SZA range down to 96 degrees. Analyzed data from the Spring of 1991 imply that observations at twilight are of great significance in improving ozone retrievals in the upper stratosphere. Judged by the variance reduction for Umkehr layers 9 to 12 (25-30 percent for layer 11) and the increase in separation and amplitude of the averaging kernels for the relevant layers, the ozone retrievals in the upper stratosphere are shown to be in better agreement with climatological means

Gioulgkidis, Konstantinos

Lowe, Robert P.

Mcelroy, C. Tom

English

NASA Technical Reports Server

N95- 11092
INCLUSION OF THE SECOND UMKEHR IN THE CONVENTIONAL UMKEHR RETRIEVAL ANALYSIS
AS A MEANS OF IMPROVING OZONE RETRIEVALS IN THE UPPER STRATOSPHERE
Konstant£nos G£oulgkid£s and Robert P. Lowe
Department of Physics, The University of Western Ontario
London, Ontario Canada N6A 3K7
C. Tom McEZroy
Atmospheric Environment Service
4905 Dufferin Street
Downsview, Ontario, Canada M3H ST4
ABSTRACT
The Umkehr method for retrieving the gross
features of the vertical ozone distribution requires
measurements of the ratio of zenith-sky radiances at
two wavelengths in the near-UV region while the solar
zenith angle (SZA) changes from 60 to 90 degrees. A
Brewer spectrophotometer was used for taking such
measurements extending the SZA range down to 96
degrees.
Analyzed data from the Spring of 199I imply that
observations at twilight are of great significance in
improving ozcne retrievals in the upper stratosphere.
Judged by the variance reduction for Umkehr layers 9
to 12 (25-307, for layer ll) and the increase in
separation and amplitude of the averaging kernels for
the relevant layers, the ozone retrievals in the upper
stratosphere are shown to be in better agreement with
climatological means.
t. BACKGROUND TO THE PROBLEM
The physical process of scattering, whether in
diffuse transmission or in diffuse reflection, has
long been investigated as a method of inferring the
profile of ozone and those of other minor atmospheric
constituents. The Umkehr Effect, first noticed by
G6tz, is a classical example of diffuse transmission
where the vertical ozone distribution is deduced from
measurements of the ratio of radiances measured at two
wavelengths in the near-UV while the SZA varies near
twilight.
G_tz et al., (1934) discussed a method for
calculating the gross features of the ozone profile
and even attempted to report on possible profile
distortion errors caused by the neglect of secondary
scattering and aerosols.
A more accurate method for deriving ozone profiles
from Umkehr measurements was given by Diitsch (1959);
he linearized the problem in hand using a series
expansion, correcting for second order terms with an
iterative procedure.
In the last twenty years, profile inversion has
undergone very rapid development. DeLuisi (1979)
studied the possibility of shortening the time
required for an Umkehr observation by incorporating
more wavelength pairs in the measurement procedure and
demonstrated that there is a 'trade-off' between the
number of wavelength pairs and SZAs used, leading to
almost the same information content about the ozone
profile. More recent developments were based on a
better set of standard profiles and their
climatological covariance.
It has long been noticed that the Conventional
Umkehr (CU), where the 60 to 90 ° range of SZA is used,
delivers less ozone than normal for the area of the
ozone maximum and the uppermost layers, and more ozone
for the lowermost layers. Part of the error was found
to be caused by atmospheric aerosols [DeLuisi et al.,
1979]; it was evident that only stratospheric aerosols
can cause significant profile distortions, especially
for layers 7, 8 and 9 where the technique is most
effective.
In this paper we present a method for improving
ozone retrievals in the upper stratosphere by
incorporating observations before sunrise or after
sunset in the CU retrieval analysis; we will call that
the Extended Umkehr (EU). The results for the random
errors in the retrievals are also presented along with
the averaging kernels and compared to the results of
the CU analysis.
2. METHODOLOGY
A series of measurements of light scattered from
the clear zenith-sky with SZA contains information
about the vertical profile of an absorber, assuming
that the absorber concentration remains constant
during the observation period. If we were to look at
the contribution to the total intensity received at
the ground from light scattered at a thin layer
centered at altitude z, then for monochromatic
radiation we would be given
I = I s [M] (1)
Z,BC Z c g
where I is the radiation reaching altitude z, s is
Z C
the scattering cross-section and [M] z is the air
density at altitude z. (1} is highly non-linear for it
depends on the atmospheric density profile and the
amount of radiation reaching a particular altitude.
Therefore, for each SZA the singly scattered radiation
comes from a fairly well-defined layer, the effective
scattering layer which moves higher up as the SZA
increases. This scanning effect provides information
790
https://ntrs.nasa.gov/search.jsp?R=19950004679 2020-06-16T11:30:06+00:00Z
about the vertical ozone distribution.
A retrieval problem can in general be stated as
follows: given a set of experimental observations in
which the unknown parameter (or set of parameters) is
related to in a complicated way, find the optimum
solution. In our case we have an independent virtual
measurement x with covariance S and a direct
0 x
measurement y with error covariance S ; then the
y
optimum solution (x) is the one which maximizes the
conditional probability P(xly,x0). By means of Bayes
theorem and under the assumption of independent
Gaussian statistics [Martin, pp9-21, 1971], we obtain
[ BF(x)IT S-' (y-F(x:)) (2)
x0 x ax Y
In the case of Umkehr analysis for ozone profiles, the
forward calculation is not linear as already been
discussed; linearizing then about a state x (a
n
guessed value of the solution) yields
F(x) = F(x ) + K (x-x) + 0 (_'¢-x)z (3)
n n n n
BF I
where K - [
n c9x I X n'
Finally substituting (3) to (2), we obtain
and g = S x - SxKrn [ KnSxKn r + S ]-I K S (5)
y n x
where x has been replaced by x to show the
n+l
iterative nature of the solution [Rodgers, 1976].
Equations (4) and (5) comprise the non-linear
optimal estimation algorithm and in this form were
used as the inverse model in this paper. When such an
iterative method is used it is imperative to have a
criterion for convergence. Throughout this analysis
the process is stopped when the root-mean-square
deviation of the solution vector from one iteration to
the next is less than 17.. A quality check was also
used based on a xZ-test, namely in determining the
confidence interval to within which the retrieved
profile successfully reproduces the measurements.
3. APPLICATION OF THE METHOD TO OZONE PROFILES
Umkehr measurements were taken at London, Ontario
using a Brewer spectrophotometer (#020), in the spring
and summer of 1991.
Linear interpolation is used to derive the
first-guess profile, using measured total ozone as
predictor, from a set of eight standard ozone profiles
[NOAA Tech. Memo., 1980].
A series of standard SZAs is used in the inversion
algorithm (65, 70, "]4, "]7, 80, 83, 85, 86.5, 88 - 95)
such that the Umkehr curve is represented well. The
assumed error in the total ozone measurement is 1
matm-cm.
Total ozone measurements revealed that ozone was
stable on day 108 under good observing conditions.
Total SOz measurements with the same instrument showed
small amounts, less than ~1-2 matm-cm; therefore, no
serious SOz interference to Umkehr measurements is
expected for that day [WM0, Report #18, p145, 19881.
Also polarization measurements performed with the same
instrument showed no significant aerosol loading, thus
avoiding any ozone profile distortions as their
effects were not included in the forward calculation.
The elements of the measurement vector y are
[ l(O'_'t) ] + C (6)
N(O) = logto l(O'_'z) o
where O is the SZA, I(O,_,) is the zenith-sky radiance
at wavelength _,, and C is the extraterrestrial
0
constant which combines solar spectrum and
instrumental response. This unknown constant is
removed by subtracting the N(60 °) from each of the
other N-values; this process also removes any solar
variability with t>3.5 hours, the time required for a
complete Umkehr observation.
The elements of the profile vector x are ln(x ),l
where x is the ozone amount in Umkehr layer i.
I
Figure 1 shows the retrieved ozone profile and
figure 2 the agreement between the measured Umkehr
curve and that reconstructed from the retrieved
profile. The f_ting is good up to 93 ° of SZA whereas
at 94 and 95 quite off, as indicated by the fitting
residuals. It is known that during twilight the
optical path increases dramatically with SZA and that
most of the radiation attenuation occurs near the
tangent point; therefore, any subvisible clouds near
the horizon or even increased multiple scattering
effects due to local aerosols might have affected the
measurements. The quality check performed, indicates
that for day 108 the retrieved ozone profile
reproduces the measurements to within the 807.
confidence interval.
Although any ozone changes in the upper
stratosphere, due to rapid altering of the ozone
photochemistry during twilight, are of concern to the
inverse method, the a priori covariance matrix used
allows for a 207. variability at the relevant layers
(9-13); with the exception of layer 9, most of the
information for these layers comes out of the a priori
than the measurements.
4. ERROR ANALYSIS
An advantage of the Rodgers retrieval method is
that it provides an estimate of the uncertainties in
the retrieved profiles due to (a) measurement noise,
(b) uncertain model parameters and inverse model bias,
and (c) the inherent finite vertical resolution of the
observing system. The observing system characteri-
zation can be carried out by studying the Transfer
Function
T(x,b,x a) = I[ F(x,b) * c , I_, x ] = x (71
y a
^
where l() is the inverse model, b the best estimate of
model parameters b, c the measurement error and x
y a
the best estimate of the true state x. Linearizing
about x and, I_ and x a yields
791
z_
C_
L_J
>-
<_
n_
I
it
13
12
11
1C
9
8
7
6
5
4
3
2
1
LONDON, DAY 108/1991
SUNRISE
L i
i i i i i i
0.00 0.02 0.04 0.06 0.08 0.10
0 3 COLUMN PER LAYER
(ofm-cm)
Figure 1
Retrieved height profile of ozone on day 108, 1991;
the plots give the ozone reduced column [atm-cm) per
Umkehr layer along with the total errors in the
retrieval. The solid line corresponds to the first
guess ozone profile. The total first guess (F.G.O a)
and retrieved amounts (RETR.) are also noted.
DAY 108, 1991; SUNRISE
0.0
o
I.--
.<
a:: -0.2
l,
o
o
o--0.4
o
J
C)
w
N --0.6
_J
<
rv"
o -O.8
Z
o OBSERVED
........
I I I I I I I
RMS FIT : 0.685
0.02
__ 0.00
_r-O.02
n,-
I I I I
65 70 75 80 85 90 95
SOLAR ZENITH ANGLE (DEG.)
Figure 2
Reconstructed Umkehr curve based on the retrieved
ozone profile on day o108, 1991. All the curves have
been normalized to 60 , as discussed in the text. The
fitting residuals are also shown in the bottom plots
and the RMS fit number noted.
_-x= (T(_ 6,xa)-xl+(A-l)(x-x)+D._j K c +D e +n (x -x) (8)
• y b b y y a a
for the total error in the retrieval.
Therefore, the overall error comprises:
Random errors (A - I)()( - x) + D _: and
y y
Systematic errors (T()_ 6,xa)-x)+D K c +D (x -x)
• y b b a a
[Rodgers, 1990]
The error analysis presented in this paper was
carried out only for the random errors in the
retrievals. The measurement process can be thought of
as a mapping from profile space to measurement space.
In this process, certain portions of the profile space
cannot be measured (those corresponding to high
frequency components or fine scale information about
the profile) and this leads to an error called the
null-space error, with covariance
S = (A - I) S (A - I)T (9)
N x
Figure 3 shows the null-space error covariance for
both the CU and the EU. The patterns presented (rows
of matrix S ) tend to have larger values at the top
N
and bottom of the plot where there is little
information about the true profile in the
measurements. Note that inclusion of measurements
before sunrise in the CU analysis reduced the
amplitude of the errors for the uppermost layers 10 to
12, implying a greater information content of the EU.
Another useful diagnostic to look at is the
averaging kernel of the retrieval
A = D K (10)
y x
which describes the retrieved profile as a weighted
average of the true profile. The rows of A are peaked
functions with FWHM characterizing the resolution of
the observing system; their shape is an indication of
anomalous retrievals (double peaks) [Rod_ers, 1990].
The averaging kernels for the retrievals
undertaken in this paper are shown in figure 4. As
seen, inclusion of the second Umkehr increased the
amplitude and separation of the averaging kernels for
the uppermost layers compared with the CU analysis. In
doing so the retrieval becomes more meaningful for
layers 6 to 9 where the technique is mostly sensitive.
In figure 5, we present results for the CU, the EU
and the first guess profile errors along with the
variance reduction as a fraction of the first guess
error variance (upper abscissa scale applies) for day
108; the EU reduced the variance by ~35Z for layer 11,
~177. for layer 10, ~llZ for layer 12 and only slightly
for layers 5, 7 and 9 compared to the CU.
5. CONCLUSIONS
As was found before, the CU technique does not
appear to provide any useful information below about
19 km but showed some potential in monitoring
long-term changes in the upper stratospheric ozone;
the same holds for the short Umkehr (SU} [DeLuisi et
al., 1985].
792
DAY 108 199
!
13
12
11
10
,., 9
>--
< 8
" 7
a: 6
"1-
'" 5 )
3
<
L , , ,
-0.04-0.020.00 0.02 0.04 0.06
NULL-SPACE COVARIANCE
KEY : EXTENDED UMKEHR
CONVENTIONAL UMKEHR (layers 10-12)
Figure 3
The rows of the null-space error covariance matrix of
the EU retrievals are plotted along with similar
patterns based on the CU analysis (layers 10-12,
only). Note the reduction in null-space variance for
the uppermost layers.
-J 7
5
3
FRACTIONAL VARIANCE REDUCTION
0.0 0.2 0.4 0.6 0.8 1.0 1.2
t _ _ 0 Fir_I Guess Error
_11 _ Solution Error
12 _L__ , 0 Vorlonce reduction
_ 10
D 5
2
I
00 0,02 03 0,0:; 06 07
STANDARD ERROR (fractional)
Figure 5
Results for the CU, EU and the first guess profile
errors on day 108, 1991. The variance reduction is
also plotted as a fraction of the first guess error
variance where the upper abscissa scale applies. The
solid line is based on the CU analysis. Note the
variance reduction of the EU compared to the CU
analysis.
DAY 108, 199 ; SUNRISE
0 1 2 3 4 5 6
-- AVERAGING KERNELS EXTENDED UMKI:'HR
AVERAGING KERNELS CONVENTIONAL UMKEHR
The new EU which we have introduced for retrieving
height profiles of ozone from Umkehr measurements, is
potentially useful for correcting ozone retrievals in
layers 7 to 12 by improving the information content of
the technique and therefore contributing to a better
understanding of the upper stratosphere global ozone
trends in the future.
More refinement may be needed with respect to
including the effects of multiple scatteringo which
become important at SZA greater than 93 , and
exploringothe possibility of reducing the range of SZA
to 80-95 by incorporating more wavelength pairs in
the inversion procedure. One last comment is in order.
The studies of Dave et al., 1979 and DeLuisi, 1979
made clear that Umkehr retrievals for the upper layers
7-9 are significantly affected by stratospheric
aerosols and so corrections should always be applied
for these scattering effects, especially after major
volcanic eruptions.
ACKNOWLEDGMENTS
We are most grateful to J.J. Bellefleur of AES,
Canada for his attention in helping with instrument
Figure 4
Averaging kernels for the ozone retrieval on day
i08, 1991. Each kernel has been misplaced by 0.5
for clarity. The corresponding averaging kernels
for the CU analysis (-*-) are also shown for"
layers 6 to 12.
related problems. The financial support of lhe
Canadian Network for Space Research and of" the
Atmospheric Environment Service has been greatly
appreciated.
REFERENCES
Dave, J.V., J.J. DeLuisi and C.L. Mateer, WMO Special
Environ. Rep. No 14, 1979.
DeLuisi, J.J., Appl. Opt., 18, 3190, 1979.
DeLuisi, J.J., J. Geophys. Res,, 84, 1766, 1979.
DeLuisi, J.J., C.L Mateer and P.K. Bhartia, Atmosph.
Ozone (ed. by Zerefos, C.S., A. Chazi), 1985.
Diitsch, H.U., Arch. Met. Geoph. BtokI., A.Bd. ll, 1959.
G6tz, F.W.P, A.R. Meetham, and G.M.B. Dobson, Proc.
Roy. Soc. Lond., A145, 416, 1934.
Martin, B.R., Statistics for Physicists, Academic
Press, Inc. London, 1971.
Mateer, C.L., J.J. Dekuisi, and C.C. Porco, NOAA Tcch.
Memo. ERL ARL-86, 1980.
Rodgers, C.D., Rev. Geophys. and Space Phys., 14, 609,
1976.
Rodgers, C.D,, J. Geophys. Res., 95, 5587, 1990.
WMO, Global Ozone Research and Monitoring
Project-Report No 18, 1988.
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Inclusion of the second Umkehr in the conventional Umkehr retrieval analysis as a means of improving ozone retrievals in the upper stratosphere

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