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Calhoun: The NPS Institutional Archive
Theses and Dissertations Thesis Collection
1971
Calculation of levels of relative contribution of the
carbon-dioxide channel radiance from TIROS VII in
the case of a large-scale stratospheric warming in
January 1964.
Giaque, Larry Lee.
http://hdl.handle.net/10945/15595
CALCULATION OF LEVELS OF
RELATIVE CONTRIBUTION OF THE
CARBON -DIOXIDE CHANNEL RADIANCE
FROM TIROS VII IN THE CASE OF A
LARGE SCALE STRATOSPHERIC
mumc ARY IQfi,
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LARRV LEE GIAUQUE
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UnitedNavai Postgra
tatesuate School
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^SCHOOL
MONTEREY, CALIF. 9394U
T.H E k "i JL k
CALCULATION OF LEVELS OF RELATIVE CONTRIBUTIONOF THE CARBON- DIOXIDE CHANNEL RADIANCE FROM
TIROS VII IN THE CASE OF A LARGE-SCALESTRATOSPHERIC WARMING IN JANUARY 1964
by
Larry Lee Giauque
Thesis Advisor: F. L. Martin
September 1971
Approved box public Mdlzait; dlbViibuutLon uiilLniutzd.
Calculation of Levels of Relative Contribution of theCarbon-dioxide Channel Radiance from TIROS VII in the Case of
a Large-scale Stratospheric Warming in January 1964
by
Larry Lee GiauqueLieutenant Commander, United States Navy
B.A. , University of Colorado, 1961
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN METEOROLOGY
• LV>iJi
NAVAL POSTGRADUATE SCHOOLSeptember 1971
ABSTRACT
A case study of a winter stratospheric warming in the western
hemisphere in January 1964 between 60 and 40 north latitudes was
conducted. Utilizing TIROS VII radiance data and analyzed height
fields, a stepwise regression equation was determined to specify lowerI
stratospheric layer temperatures. These temperatures were used with
standard atmospheric temperatures to construct a sounding for use in a
radiance computer program. Finally, this computed radiance was com-
pared to regression values to determine if prediction and study of
stratospheric warmings are valid and useful.
TABLE OF CONTENTS
I. INTRODUCTION 9
II. DATA PROCESSING 12
III. STATISTICAL PROCEDURES AND INTERPRETATIONS . c 14
A. DEFINITION OF DATA SETS 14
B. TEST OF AN INDEPENDENT DATA SAMPLE 16
C. STATISTICAL INFERENCES OF THE TEST 18
D. CONSTRUCTION OF WARM AND COLD MODEL STRATOSPHERES ... 21
IV. A NUMERICAL RADIATIVE COMPUTATION 26
V. CONCLUSIONS 37
APPENDIX - Computer Program . . c . . . .38
LIST OF REFERENCES 59
INITIAL DISTRIBUTION LIST '^
FORM DD 1473 61
LIST OF TABLES
I. Substratifications of sample data 14
II. Stepwise order of entry of variablesin the regression equation 4, including F
upon-entry at step k, the test statisticCritical F, , and multiple correlation co-efficient R, at each step 16
III. Comparison of explained variance betweenthe dependent sample and independent sample .... 17
IV. Means and standard deviations of 15-jj.
temperatures and predictor thicknessesfor samples S (15) and S (15) 20
W K.
V. Layer mean statistics for the warm andcold cases S
TT (15) and 3^(15) 21W K.
VI. Comparison of 10 mb temperatures of thewarm and cold models to those of thestandard atmosphere 22
VII. Comparison of I5-jj temperature compuccJfrom the sample mean and the modelatmosphere radiance calculations 30
LIST OF FIGURES
1, Warm and cold model atmospheres 23
2. Proposed model warm atmosphericsounding 28
3. Proposed model cold atmosphericsounding 29
4. Carbon-dioxide channel radiancecontributions for equal incrementsof In p (warm model atmosphere) 32
5. Carbon-dioxide channel radiancecontributions for equal incrementsof In p (cold model atmosphere) 33
6. Warm case equal area weighting curvecorresponding to Figure 4 34
7. Cold case equal area weighting curvecorresponding to Figure 5 35
TABLE OF SYMBOLS AND ABBREVIATIONS
A. Regression coefficients
B(X,T) Planck intensity function at wave length X and
temperature T
Carbon dioxide
Degrees Celsius
F-ratio upon entry at step k
Acceleration of gravity
Greenwich Mean Time
Outgoing monochromatic radiance
Degrees Kelvin
Kilometer
Meter
Millibars
Detected radiance
Atmospheric pressure
Specific constituent mixing ratio
Multiple regression coefficient
Dry air gas constant
Warm hemisphere sample of 10 January 1964
Cold hemisphere sample of 10 January 1964
Warm hemisphere sample of 15 January 1964
Cold hemisphere sample of 15 January 1964
T Temperature
X. Regression predictors
Y Regression predictand
co2
c
Fk
g
GMT
hK
km
m
mb
N
P
q
R
Rd
sw(io)
sK(io)
V 15)
SK(15)
Y Regression predictand test values
t Weighting function as a function of In p
h Height above mean sea level
T(h) Transmittance of the atmosphere to the outgoing15-(J. band of C0
? , between the levels Z = h andZ = 00
§ Filter function centered at wavelength X,
spanning the increment AX
X Wavelength
-4|j Microns, identical to 10 cms
AZ Thickness of atmospheric layer
1-CC The significance of the predictor addedexpressed as a probability
ACKNOWLEDGEMENTS
The author wishes to express his appreciation to his advisor,
Professor F. L. Martin, for his suggestions, advice, guidance and
support in this research.
Appreciation is also expressed to the W. R. Church Computer
Facility of the Naval Postgraduate School.
8
I. INTRODUCTION
The launch of the TIROS VII meteorological satellite on 19 June 1963
led to the remote sensing of stratospheric temperatures on a quasi-
global scale. The orbits of TIROS VII were almost circular and had an
average height of 635 km. The plane of the satellite orbit was inclined
to the equitorial plane at an angle 58 , which resulted in scan-coverage
between 60 north and 60 south latitudes. TIROS VII was equipped with
a five-channel scanning radiometer, one of which measured the filtered
thermal radiation of CO in the half-power wavelength range 14.8 to
15.5(a [Staff members, 1964]. The C09
in the stratosphere should emit
at the same temperature as the air (of which it is a part), thus the
observed intensities can be interpreted in terms of a weighted-mean,
equivalent black-body cempcraLure in the stratosphere. Radiation
transfer theory leads to the radiance from the 15-(j band [Warnecke,
1967] as
x2
p=0.1
r r <H(X, In p)N15
=J J
$(X) d(ln P)~ B(X » T(ln p)) d (ln p) dX (1)
X1
p=1000
In (1), the 15 -|j band is assumed opaque to the surface radiation. If
the weighting function ty (In p) is defined as
x2r dT(X,ln p)
% (In p) =J
$(\) B(X,T(ln p)) ^ (ln p)d\ (2)
the integral (1) reduces to
p=1000.
N15
=J
[l|» (In p)] d (In p) (3)
p=0.1
Thus the contribution of each layer to the radiance, N, sensed by the
radiometer can be determined as a function of pressure. Radiative
transfer theory applied to model atmospheres by Nordberg et al. [1965]
indicates that maximum radiation, \[f (In p), in the 15-|d range is
emitted by the low stratosphere. The maximum weighting contribution at
small nadir angles originates at about 25 km but the 15-(j. temperature
corresponds to different heights from time to time because the tempera-
ture structure in the stratosphere changes with time [Belmont et al.,
1968]. Radiance should also then be statistically related to the mean
temperature or thickness between various pressure levels in the stratos-
phere. The latter conjecture was the originating hypothesis of this
investigation.
Several studies have appeared in the literature which strongly
support a relationship with 15-|j temperatures at pressure levels in
the stratosphere. Belmont et al. [1968], Nordberg et al. [1965],
Warnecke [1967] and Teweles [1966] indicated that 15-[j temperatures
depict some of the large scale horizontal wave activity in the thermal
fields of the lower stratosphere. In addition, Kennedy [1966], has
compiled an atlas of ten-day mean isotherm charts recorded by the
15-|j channel of TIROS VII for the period June 1963 through July 1964.
These charts were presented by Kennedy as indicative of the spatial
temperature distribution of the lower stratosphere during the total
period of analysis of TIROS VII. Between 60 north and 60 south
10
latitudes these charts depict, for example, the proper seasonal
distribution of stratospheric isotherms at about 25 km.
Dense cloud bands will cause a decrease in the 15-p temperature
and will raise the peak elevation of its radiance weighting function.
Although data presented in the Kennedy Atlas were not corrected for
cloud contamination, nevertheless, the reduction to ten-day mean 15-|j
temperatures was considered by Kennedy to have eliminated the cloud
contamination effect. This atlas served as a source for grid point
15-p. temperature data for the case studies investigated in this
dissertation.
Since the 15 -p. temperatures are weighted over an indefinite thick-
ness range in the stratosphere, Belmont et al. [1968] has raised the
question, "which pressure level in the stratosphere does the 15-[a
temperature best represent?" Moreover, Shen et al. r 1968] have shown
the usefulness of 15-(J temperature fields in detecting stratospheric
warming events in the Southern Hemisphere polar winter. This paper
seeks tc relate statistically the various layer-contributions to the
15-|j temperature in the case of a winter stratospheric warming in the
polar latitudes of the Western Hemisphere. This case was centered
time-wise on 15 January 1964.
11
II. DATA PROCESSING
The 15—Jj temperatures were extracted from the Kennedy Atlas [1966]
of stratospheric mean 15-|j isotherms, using charts 42 (10 January 1964)
and 43 (15 January 1964). Grid points values for 60 , 50 , and 40
north and every 5 of longitude around the globe were carefully inter-
polated to the nearest whole degree Kelvin. These 216 grid points
were further divided into two hemispheres : that between 70 west and
110 east longitude corresponding to the "cold" sample since it
approximated the sector of the winter cold vortex. The "warm" hemisphere
between 110 east and 70 west longitude (the "Western" Hemisphere) con-
tained the warm stratospheric anticyclone. There were 108 grid points
located in each sample.
Thickness values at each o£ the 216 grid points were noted and tor
both dates of interest were determined from the Northern Hemisphere
analyses of 10, 30, 50, 100 and 300 mb contour charts. These charts
were found in the January 1964 series of map analyses of the Institute
of Meteorology and Geophysics of the Free University of Berlin [1964],
Contour values from each pressure level and at each grid point were
differenced to determine four thicknesses in the stratosphere and upper
troposphere:
10 - 30 mb thickness, denoted X, (i, j)
30 - 50 mb thickness, denoted X~(i,j)
50 - 100 mb thickness, denoted X„(i,j)
100 - 300 mb thickness, denoted X, (i,j)
Finally, the dependent variable is the 15-(j temperature and is denoted
hereafter as Y(i,j).
12
The statistical model is then to be expressed in the multiple-
regression form
Y = A + A..X- + A_X_ + A_X_ + A.X. (4)oil 22 33 44
where the coefficients A , A.. , A^, A« and A, are to be determined by
the least squares techniques. All of the variables for input into
equation (4) were encoded onto punched cards in a format consistent
with the requirements of the stepwise regression program, BMD02R
[Dixon, 1966], This program is available in the Library of the W. R.
Church Computer Center of the Naval Postgraduate School.
13
III. STATISTICAL PROCEDURES AND INTERPRETATIONS
A. DEFINITION OF DATA SETS
As noted previously, it was necessary to stratify the data for the
two map-times into cold and warm stratospheric "hemispheres". According
to the stratospheric contour and temperature analyses of the Free
University of Berlin, the warming anticyclone had reached its peak
intensity in the Western Hemisphere on 15 January 1964, with a well-
defined cold hemisphere adjacent. The stratospheric warming was still
in a developing stage on 10 January 1964. This led to the four sub-
stratifications of sample data, which for simplicity will be denoted in
Table I.
TABLE I
Substratifications of Sample Data
Date Warm Cold
10 January STT (10) S HO)
15 January ST7 (15) S (15)
Actually the last two, S (15) and S (15) were used to generate the
multiple regression equations of type applicable to the warm and cold
hemispheres, respectively. These equations were then to be tested for
diagnostic significance by applying them to the independent samples
S (10) and S (10). Each of the four stratifications had 108 data samplew K.
sets.
The BMD02R regression analysis not only generates a multiple
regression equation similar to (4) but also performs a step-wise
14
screening in the process: it first determines that independent variable
X. which explains the highest percentage variance of Y. Then at step
two, it determines the X. in the remaining predictor set that explains
the largest percentage of the residual variance unexplained by the
first variable, and so forth, for steps three and four.
The BMD02R program also computes for each step the F-statistic
upon-entry of the kth variable selected, where F, is expressible at
step k as [Dixon, 1966]
F. (l,n-k-l) = (fo cum. expl.var. , step k) - ($ cum, expl. var. , step k-1)
(Jjo unexplained variance at step k)
In the present problem, two tests were to be made using X, , X , X_ and
X. with a total sample size of n=108 in the warm and cold cases STT (15)4 W
and S (15), respectively. Based upon the magnitude of F, of (5), Table
II indicates tlie order of entry of the predictors selected and the
corresponding F, -statistic with which they entered.
For each predictor tested, its significance at step k may be
cassessed by comparison of its F, value with a Critical F
Tdefined
after Miller [1962] as
Fk
= Fa/P-k+l
a,n-k-l), a = 0.05 (6)
in order that the over all regression be assured of significance at the
1-CC confidence level. The set of Critical F. values to be used fork
comparison are adjoined to Table II.
The four-predictor regression equations having the form of (4) are
as follows:
S (15), Y=112.213 - .04842X1+ .03686X
2+ .18648X + .07498X
4(7)
15
TABLE II
Stepwise order of entry of variables in
the regression equation (4), including F,
upon-entry at step k, the test statisticCritical F , and multiple correlation co-
efficient R, at each step
Sample--Warm, Sw(15), n=108 Sample-•Cold, S„(15), n=108
Criti-cal
Values
<StepNo.
Vari-ableenter-
Fk
Mult.Corr.
Coeff.
Vari-ableenter-
Mult.Corr.
k Coeff.ing ing
k=l X3
179.13 .7926 X3
14.81 .4252 6.51
2 Xl
54.20 .8688 Xl
8.42 .4905 6.00
3 X4
39.20 .9066 X4
4.21 .5083 5.19
4 X2
4.36 .9106 X2
1.72 .5201 3.96
S_,(15), Y=171.927 + .04872Xn+ .06728X_ + .10750X_ - .07642X. (8)
K i 2. 5 h
Table II shows that all thickness predictors entered at a confidence
level of 95 percent for each entry in equation (7). On the other hand,
for the cold case, the order of entry was identical to that of S (15)w
but the levels of significance for X, and X9were subcritical. How-
ever, in the cold case, the standard error of estimate continued to
decrease from step three to step four, so the full four predictor
equation (8) was retained for testing against the independent sample
S (10). A more complete justification for retaining the full set ofJs.
predictors can be found at the end of III-C.
B. TEST ON AN INDEPENDENT DATA SAMPLE
In order to test the validity of equations (7) and (8) developed
from S (15) and S (15) , the coefficients from these samples wereW Js.
16
combined through the matrix multiplication (9) to form the
estimator-predictand of the independent data
Y - (A , A^, A , A~, A.) (9)
using the sets S (10) and S (10). The regression between (Y,Y) forW K
the independent sample gave the results listed in Table III as com-
pared to the dependent case.
TABLE III
Comparison of explained variance betweenthe dependent sample and independent sample
Dependent Sample
"/? Exp 1
«
Variance
Independent Sample
£Expl.
R(Yj Y) Fn(1,106)
Variance 1
W
K
82.92
27.05
47.11 .6864
76.61 .8753
94.426
347.266
There was a sizeable shrinkage in explained variance in the warm
case when applying the regression from the SI7 (15) case to the inde-
pendent data set. However, in this case the F-test still indicated
confidence well over the 95 percent level of belief in spite of the
shrinkage. The result of the regression for the cold case showed a
significant improvement in the explained variance of T in the
independent sample, an unexpected result which will be discussed
below.
17
C. STATISTICAL INFERENCES OF THE TEST
The stratospheric warming which seemed to reach its maximum
magnitude over the entire "warm" hemisphere on 15 January, had also
spread to some extent into the "cold" hemisphere. The fact that the
warming process had encompassed the entire warm sector and a part of
the cold sector may explain the wide range of explained variance
between the two sectors on 15 January including the rather low
explained variance in S (15).K.
A statistical reason for the observed shrinkage in explained
variance in passing from the dependent equation (7) to the inde-
pendent sample of 10 January may be ascribed to the incomplete
development of the full warm hemisphere as of this date, so that the
sample of 10 January actually consisted of a mixture of warm and cold
data points. In other words, the warm hemisphere of 10 January seems
not to have been as clearly stratified as a warm hemisphere as that
of 15 January.
The phenomenon of an increased percentage explained variance in
passing from equation (8) to the independent cold sample of 10
January was subject to a similar conjecture. The relatively small
multiple regression coefficient resulting from S (15) seemed toK
indicate that a stratospheric warming effect had also begun to
spread into the "cold" hemisphere, and in consequence only 27.05
percent of the variance of Y was explained by the specification
equation (8). On the other hand, the much larger percentage of the
variance explained by (8) applied to S (10) seems to indicate that
the cold stratification for the 10 January case was more uniform
than the dependent case chosen for 15 January.
18
In retrospect, a more flexible sampling procedure which might
have improved the results should have involved more care in deline-
ating the stratifications of the areas of warm and cold stratospheres,
respectively. For example, it now seems reasonable to limit the
warm area sample to those stratospheric grid points having anti-
cyclonic contour curvature and not necessarily assigning an entire
hemisphere to the sample. Similar considerations, with regard to
cyclonic curvature might well have afforded a better criterion for
the cold stratification in both the dependent and independent cases.
It was now possible to offer a more complete statistical reason
for retaining all four predictors in the right side of equation (8).
Even though the dependent cold sample from which equation (8) was
derived seems to have been not uniformly stratified, the use of the
resulting predictand was well verified (R(Y,Y) = .8753) on the more
stable stratified cold hemisphere of 10 January.
It was also noteworthy that a choice of S (10) as the dependentK
cold sample gave the same order of entry for variables as indicated
in Table II, with all individual predictors significant at well above
the 95 percent confidence limit.
With Y based upon equation (8), the ensuing regression between
Y and Y for 10 January was
Y = -95.3142 + 1.4298Y, R(Y,Y) = .8753 (10)
so that by equation (10) all predictors would have had the same
coefficient matrix apart from the constant multiplier, 1.4298.
Thus equations (7) and (8) are adopted as the representative
regression equations for the warm and cold stratospheric samples,
respectively.
19
Since the regression equations just listed must be satisfied
by the sample means, it is useful to list the mean properties of
these two atmospheric samples S IT (15) and S Tr (15). Table IV is aW K
compilation of the means and standard deviations of all variables
which appear in equations (7) and (8) for 15 January 1964.
TABLE IV
Means and standard deviations of 15-|a
temperatures and predictor thicknessesfor samples S TT (15) and Sv (15)
Sw (15) S
K (15)
Vrbl. Mean Std. Dev. Mean Std. Dev.
T15
226. 16K 3.68923 217. 96K 4.79275
h 7298.1 gpm 327.7286 6796.5 gpm 268.4886
h 3356 .
1
126.8544 3149.4 100.4864
h 4520.6 165.8544 4221.9 162.5060
X4
7017.0 125.0733 6998.1 138.5645
Y 226. 16K 217. 96K
The standard deviation of X.. (the 10 to 30 mb thickness) was
considerably larger than the other levels; however, it is a layer
subject to more radiosonde error than those below it. Also inter-
polation of contour height to grid points was more subjective at
10 mb due to stronger gradients than existed at lower levels in the
stratosphere.
Because of the equivalence of thickness to mean temperature of
an isobaric layer through the integrated form of the hydrostatic
equation
20
Rrf
p1 -
AZ = — In — T (11)g P 2
it is possible to ascribe a mean temperature to each of the four
isobaric layers of thicknesses hitherto denoted X.. , X , X_ and X, .
These mean temperatures corresponding to the mean thicknesses already
listed in Table IV are given in Table V for the warm and cold stratos-
pheres respectively, along with other relevant statistics used in the
specification of the 15-|j, temperature. The statistic R(Y,X.) is the
simple correlation between T1
,. and the ith layer- thickness.
TABLE V
Layer mean statistics for the warmand cold cases S
T7 (15) and S H5)
"arm Case Cold Case
7~ Mid- ~R(Y,x7) Layer R(Y,X.) LayerLayer . x J 1 J
point mean mean(nib)
press. temp. temp.
xr 10 - 30 17.32 mb .195 226. 96K
X2
: 30 - 50 38.73 .663 224.40
X3
: 50 - 100 70.71 .793 222.82
X, : 100 - 300 173.20 .656 218.22
.750 211. 36K
.281 210.56
.161 208.09
-.340 217.63
D. CONSTRUCTION OF WARM AND COLD MODEL STRATOSPHERES
From the mean temperatures listed in Table V, stratospheric model
temperature-pressure distributions were constructed for the warm and
cold cases in Figure 1: A-B-C-D showing the lower stratosphere tempera-
tures in the warm case and A'-B'-C'-D' showing the lower stratosphere
temperatures in the cold case at 17.3, 38.7, 70.7 and 173.2 mb
21
respectively. The lowest points D and D' lie within a half degree
Celsius of one another, at the 173.2 mb level.
Since no mean temperatures were available from this study below
173.2 mb, the cold and warm cases were adjoined to the Cold and Warm
Supplemental Standard Atmospheres [Dubin et al., 1966] at latitude
60 north in January. The cold and warm January standard profiles
below 300 mb were vitually identical and for the purpose of the
modeling done here were taken as the unique curve E-F-G in Figure 1.
This led to a minor inconsistency in the mean temperatures to be
expected in the layer 100-300 mb in the cold and warm cases,
respectively.
The expected temperature at 10 mb for the warm and cold models were
obtained by extrapolating the lines B - A and B 1 - A 1 in Figure 1 to
the 10 mb level. This techniaue led to the results listed in Table VI:
TABLE VI
Comparison of 10 mb temperatures of the warm and coldmodels to those of the January Supplemental StandardAtmosphere (60 north)
Warm Cold
10 mb, model -43.65C -61.15C
Jan. 60N Supp. -43.75C -73.50C
It is clear that the lower stratospheric temperatures from the warm
sample are in good agreement with the January warm standard, while the
cold sample was not as clearly definitive of the cold standard for the
reasons already cited in III-C.
The remainder of the model above the 10 mb level was fitted in both
models by extending linearly the T-ln p profile from 10 mb upward to
22
X
£ 10
30
50
100
300
1000 mb «-
210 220 230 240Temperature
Fig. 1. Warm and cold model atmospheres
250 260
23
the listed stratopeaks of the Warm and Cold Supplemental Standards
[Dubin et al., 1966]. These peaks occur over the range:
p = 0.7 to 0.423 mb where T = -5C
p = 0.44 to 0.26 mb where T = -17C
Above the top of these levels, the listed lapse rate above the
stratopeak was used to extend the T-ln p models to the level p=0.1
mb, which is commonly taken as the top of the atmosphere in
radiative-transfer theory.
The simple correlation coefficients listed in Table V give some
indication of the layers contributing most heavily to the specification
of T-.C-. The results in the warm case (Table V) indicate a maximum
influence or weight from the layer 50-100 mb centered at 18.1 km
(70 mb). However, there is considerable additional influence from
the 30-50 mb and 100-300 mb layers (at 26.4 and 12.2 km, respectively).
Note that the influence from the layers X~, X„ and X, as indicated by
R(Y,X.) seem significant,, This will be discussed further in IV.
On the other hand, the cold model atmosphere has the maximum
influence detectable from this study in view of the high correlation
coefficient R(Y,X ), (Table V), attributable to the layer 10-30 mb and
this influence decreases systematically below this level. The signifi-
cant negative correlation in the lowest level (100-300 mb) is appar-
ently due to the low warm tropopause which is synoptically expected
with a cold stratospheric vortex situation. The overlying deep cold
layer (100-10 mb) apparently acts as an effective absorber, and
relatively low-emittance re-radiator of the CO radiation started in
the high troposphere. In other words, this negative correlation in
the lowest layer is apparently related to the relatively steep lapse
24
rate between the lowest part of the stratosphere and the warm
tropospheric layer immediately below.
25
IV. A NUMERICAL RADIATIVE COMPUTATION
A brief discussion of the upwelling radiance from an arbitrary
planetary atmosphere having a temperature distribution T = T(p) and
constituent distributions q. = q.(p), i=l, .»., 3, is given. V. Kunde
[1967] prepared a detailed theoretical study of a number of planetary
atmospheres detailing the necessary theoretical computations for the
upwelling radiances sensed by various medium resolution infrared radio-
meters. Kunde 1
s theory [Kunde, 1967] made use of spherically hori-
zontal symmetry of all sounding properties in the atmosphere, and
computed the transmitted radiative contributions from each level p to
p+dp. Thus he made use of the generalized formula for outgoing radiance
dl, = B, [A,T(ln p)] ,,?T
, d(ln p) (12)
in the case of a satellite sensor having optical filter response
§, = 1.0. In equation (12), the transmittance T is the constituentA
product-transmissivity at pressure p, and T must be a decreasing
function of pressure. The Curtis-Godson approximation is used for
correcting the vertical absorber mass distribution, and for deducing
the resultant pressure-effect upon line broadening.
When CO is the main emitter and the earth's 15-|a band the main
source of outgoing radiation, the surface may be considered black in
the terrestrial spectrum (reflectivity zero). The problem was further
simplified by assumed constancy of the mixing ratio of CO at
q = 0.477 gm/kg. The details of the vertical variation of water
vapor and ozone mixing ratios, which are highly variable for each gas,
were supplied in the form of a sounding distribution of each. These
26
gases are distributed relative to height or, equivalently to the
pressure p = p(h,T).
Based on the results of III-D, two model vertical profiles T(p)
were determined from Figure 1 with sufficient vertical resolution
(about thirty significant levels) to cover the entire range of pressure
from p = 1013.5 mb to p = 0.1 mb, for both the warm and cold cases in
Figures 2 and 3.
The vertical distributions of water vapor and ozone enter the com-
putation of N, ,. only in a very secondary manner since there is only
slight overlap between the water vapor rotational band wings and the
14.0-16.3|J. response function placed upon the sensors of the 15-\1
channel of TIROS VII. The sensor response function $(X.) associated
with the jth subinterval, £\. ., of the 15—jj. channel are listed in the
TIROS VII Radiation Data Catalog and Users' Manual [Staff. 1965].
The water vapor and ozone mixing ratio distributions with height
actually used were listed for Maniwaki, Quebec (46N, 76W) based upon
the real time radiosonde observations taken on 29 September 1958 at
1200 GMT. The Maniwaki surface values (at 996.0 mb) of mixing ratio
were considered identical to those at 1013.5 mb of the present models
atmospheric base level.
The integral i|/(ln p) of equation (2) represents the contribution
2to the total filtered radiance at a point in space in watts /m /ster of
depth and includes the Planck-Kirchhof f transmittance attributed to a
small pressure increment dp, as essentially specified by the radiosonde
(including the constituent mixing ratios).
The Kunde radiative transfer theory [Kunde, 1967] was applied to
both of the model atmospheres as input, and with the model-invariant
27
10
CL,
30
50
100
300
1000 mb220 230 240 250
Temperature K.
260
Fig. 2. Proposed model warm atmospheric sounding
28
.1
a,10
30
50
100
300
1000 mb210 220 230 240
Temperature K.
250 260
Fig. 3. Proposed model cold atmospheric sounding
29
mixing ratio distributions of q n (p) and q_ (p). The Kunde computerH2° °3
program is listed in the Appendix. The program was designed to give the
total filtered N and the corresponding T, - computed by five-point
interpolation from the laboratory calibration of N vs ^-.c- In this
theoretical program no instrument degradation need be considered.
Finally the first important output of the program gives N and the
effective T.. _ for the model atmospheres. It also gives a pressure-
height weighting function essentially equivalent to ijj(ln p) = dN/d(ln p)
appropriate to the contribution to N for equal increments of In p.
The results of the model -atmosphere radiance computation after Kunde
[1967] applied to the warm and cold models (and the implied soundings,
Figures 2 and 3) led to the following results for calculated N and the
resultant 15-|a temperatures.
TABLE VII
Comparison of 15-(j temperature computedfrom the sample-mean and the modelatmosphere radiance calculations
2 —N (watts /m /ster) T [Kunde] T = Y
S I7 (15) 3.048 228. 9K 226. 2Kw
SK(15) 2.460 218. IK 217. 9K
In Table VII the corresponding values are in columns 3 and 4, whereas
the contrast between the model atmospheres is to be seen by comparing
row 2 against row 3. It is to be noted that the warm case emits a
greater N than the cold sample, and that the model atmospheres adopted
reproduce the respective sample mean T1
,. temperatures effectively.
30
Another important output of the Kunde program is the percentage of
total N associated with increments of In p between p = 0.1 and
p = 1013.5 mb. This output was listed in the Kunde program by kilo-
meter intervals and at equivalent pressure levels for the warm and cold
model atmospheres and the results summed to give the weight functions
ill (In p) in the form of block-diagrams on a In p scale (Figures 4 and
5). These block diagrams were subsequently smoothed preserving equal
areas of \|f (In p) from block-to-block and the results appear as Figures
6 and 7.
It is now useful to reconsider the simple correlation coefficients
between T.. ,. (and therefore N) , and the layer thicknesses given in Table
V. For the cold atmosphere, the negative correlation attributable to
the layer 100-300 mb has been explained by the compensating cool
shielding layer C'B 1 which occurs even when a temperature rise occurs
at or near 300 mb. However, the correlation coefficient of 0.750
between the 10-30 mb thickness and the total radiance was due to
sampling variations in temperature of B'A' about the mean profile T(p)
of Figure 1, with a warmer than average upper layer able to contribute
more radiance to space than if the layer were sampled as relatively
cold. This result verifies the positive correlation R(T 1C.,X, ) = 0.750
found for the cold case.
A similar argument was applied to the warm case where the lapse rate
from the upper troposphere to the stratopeak was continuously of an
inversion nature. Any layer sampled in S (15), if warmer than the mean,w
tends to have greater emittance to space, whereas it will have smaller
emittance when cooler than normal accounting for the positive correlations
in Table V. This effect is especially prominent near the level of
31
1.25
2.5
5.0
10
20
(X40
80
160
320
640
lOOOmb .1 .2 .3 .4 .5 .6 .7 .8 .9
ty(In p) watts /m /ster
Fig. 4. Carbon-dioxide channel radiance contributions for
equal increments of In p (warm model atmosphere)
32
.6
1.25
2.5
5.0
a.
10
20
40
80
160
320
640
lOOOmb • JL * -< • O • t • J IT ^7 .8 .9
\Jj(In p) watts /m /ster
Fig. 5. Carbon-dioxide channel radiance contributions for
equal increments of In p (cold model atmosphere)
33
.6
1.25
2.5
5.0
ex
10
20
40
80
160
320
640
1000 mb1 .2 .3 .4 .5 .6 .7 .8 .9
2ty
(In p) watts/m /ster
Fig. 6. Warm case equal area weighting curve correspondingto Fig. 4
34
(X
«-.J
.6
1.25
2.5
5.0
10
20
40
80
160
320
640
1000 mb .7 .8 .9
\|f (In p) watts/m /ster
Fig. 7. Cold case equal area weighting curve correspondingto Fig. 5
35
maximum weighting functionty
(In p), which occurs in the range
50-100 mb.
36
V. CONCLUSIONS
The results of this study of a northern hemisphere stratospheric
warming indicate that a polar-orbiting satellite with a 15-^ sensor
can be used as a tool to study stratospheric warming processes. The
layers of the lower stratosphere which are initially affected can be
identified by comparison of regression values to normal soundings for
that of the anticyclonic area or the vortex area. Although this study
was concerned only with one stratospheric warming, the correlation
coefficients are large enough to seem significant. This was especially
true in the S (15) sample which was particularly well stratified withw
respect to the warmingo
A daily synoptic analysis of the C0_ channel radiance information
from a polar-orbiting satellite should provide initial indications u£
when a stratospheric warming is beginning. The development of such a
warming may easily be followed as it progresses around the glode.
Future operational study in this area by use of smaller sectors, using
successive-day swath continuity might allow enough data-definition to
follow such a warming as it develops in the vertical and could become
a tool for the study of stratospheric warmings.
37
APPENDIX
KUNDE RADIANCE PROGRAM FOR 15 -(J BAND OF C02
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LIST OF REFERENCES
Belmont, A. D. , G. W. Nicholas and W. C. Shen, 1968: Comparison of15-(j TIROS VII Data with Radiosonde Temperatures. Journal ofApplied Meteorology , 7_, 284-289.
Dixon, W. J., (Ed.), 1966: Biomedical Computer Programs , HealthSciences Computing Facility, University of California at LosAngeles, 585 pp.
Dubin, M. , Sissenwine, N. and Teweles, S., 1966: U. S. StandardAtmosphere Suppliments, 1966 , National Science Services Admin-istration, National Aeronautics and Space Administration andUnited States Air Force, 289 pp.
Kennedy, J. S. , 1966: An Atlas of Stratospheric Mean Isotherms DerivedFrom TIROS VII Observations , 85 pp.
Kunde, V. G. , 1967: Theoretical Computations of the Outgoing InfraredRadiance from a Planetary Atmosphere , 117 pp.
Meteorological Analyses , Institute for Meteorology and Geophysics of theFree University of Berlin, January-March 1964.
n.iiler, k.. C», i^oz: ^tanistiical ircvIj.ct!i.on by L/iscriruznanL Analysxs,Meteor. Monogr ., 4, No. 25, Boston, Mass., Amer. Meteor. Soc,53 pp.
Nordberg, W. , 1966: Satellite Radiation Measurements in SpectralRegions. Satellite Data in Meteorological Research , NationalCenter for Atmospheric Research, NCAR-TN-11, Boulder, Colo.,199-213.
Shen, W. C, G. W. Nichols and A. D. Belmont, 1968: Antartic Stratos-pheric Warming During 1963 Revealed by 15-u. TIROS VII Data e
Journal of Applied Meteorology, 7_, 268-283.
Teweles, S., 1966: Radiometer data in the 15-u band. Satellite Datain Meteorological Research , National Center for AtmosphericResearch, NCAR-TN-11, Boulder, Colo., 251-257.
Staff Members. 1965: TIROS VII Radiation Data Catalog and Users'Manual . National Space Science Data Center, Greenbelt, Md.,
269 pp.
Warnecke, G,, 1967: The Remote Sensing of Stratospheric Temperaturesand Some Results From the Nimbus II Satellite Experiment , GoddardSpace Flight Center, Greenbelt, Md., 24 pp.
59
INITIAL DISTRIBUTION LIST
No. Copies
1. Lieutenant Commander Larry L. Giauque 2
Fleet Weather CentralBox 2 COMNAVMARIANASFPO San Francisco, 96630
2. Professor Frank L. Martin 6
Department of MeteorologyNaval Postgraduate SchoolMonterey, California 93940
3. Department of Meteorology 3
Naval Postgraduate SchoolMonterey, California 93940
4. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
5. Defense Documentation Center 2:
Cameron StationAlexandria, Virginia 22314
60
Security Classification
DOCUMENT CONTROL DATA -R&D'Security c las si lie alion of title, body ol abstract and indexing annotation must be entered when the overall report is classified)
1 originating activity (Corporate author)
Naval Postgraduate School
Monterey, California 93940
2*. REPORT SECURITY CLASSIFICATION
Unclassified2b. GROUP
3 REPOR T TITLE
Calculation of Levels of Relative Contribution of the Carbon-dioxideChannel Radiance from TIROS VII in the Case of a Large-scaleStratospheric Warming in January 1964
4 DESCRIPTIVE NOTES (Type of report and. in c lus ive dates)
Master's Thesis; September 19715 tj THORISI (First name, middle initial, last name)
Larry Lee Giauque
6 REPOR T D A TE
September 1971
7a. TOTAL NO. OF PAGES
62
76. NO. OF RE FS
12ea. CONTRACT OR GRANT NO.
6. PROJEC T NO
9a. ORIGINATOR'S REPORT NUMBER(S)
96. OTHER REPORT NO(S) (Any other numbers that may be assignedthis report)
10 DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited.
II. SUPPLEMENTARY NOTES 12. SPONSO RING MILI TAR Y ACTIVITY
Naval Postgraduate SchoolMonterey, California 93940
13. ABSTRACT
A case study of a winter stratospheric warming in the westernhemisphere in January 1964 between 60° and 40 north latitudes wasconducted. Utilizing TIROS VII radiance data and analyzed heightfields, a stepwise regression equation was determined to specify lowerstratospheric layer temperatures. These temperatures were used withstandard atmospheric temperatures to construct a sounding for use in
a radiance computer program. Finally, this computed radiance wascompared to regression values to determine if prediction and study ofstratospheric warmings are valid and useful.
DD, NOV 68 I "T / >*J
S/N 0101 -807-681 1
PAGE I )
61Security Classification
A-31408
Security Classification
key wo R OSLINK A
ROLELINK C
ROLE
Stratospheric Warming
Channel Radiance
Stratospheric layer temperatures
TIROS VII radiance data
DD ,
F
„r.,1473 (
S/N 0101-607-6321
BACK62
Security Classification A - 140a
. IUDERY
ThesisG35c.l
.131315iauque
Calculation of lev-els of relative con-tribution of the car-bon-dioxide channelradiance f rom : TEROS -'
VII in the case. Ofa if
large-scale stfitt&rtYspheric warm^rttf^^YJanuary 1964? l TJDERY
Thes
G35c.l
131315Giaque
Calculation fo lev-els of relative con-tribution of the car-bon-dioxide channelradiance from TIROSVII in the case of a
large-scale strato-spheric warming in
January 1964.
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