AN ABSTRACT OF THE THESIS OF
Andrew S. Kowaiski for the degree of Master of Science in Atmospheric Sciences
presented on February 9, 1993.
Title: Satellite Infrared Measurement of Sea Surface Temperature: Empirically Eval-
uating the Thin Approximation
Abstract Approved:
Redacted for privacy
.
James A. Coakley, Jr.
Satellite technology represents the only technique for measuring sea surface
temperatures (SSTs) on a global scale. SSTs are important as boundary conditions for
climate and atmospheric boundary layer models which attempt to describe phenomena
of all scales, ranging from local forecasts to predictions of global warming.
Historical use of infrared satellite measurements for SST determination has been
based on a theory which assumes that the atmosphere is 'thin', i.e., that atmospheric
absorption of infrared radiation emitted from the sea surface has very little effect on
the radiant intensity that is measured by satellites. However, a variety of independent
radiative transfer models point to the possibility that the so-called 'thin approximation'
is violated for humid atmospheres such as those found in the tropics, leading to errors
in the retrieved SST that would be unacceptable to those who make use of such
products. Furthermore, such tropical regions represent a significant portion of the
globe, where coupled ocean-atmosphere disturbances can have global effects (e.g., the
tropical Pacific El Nifio-Southern Oscillation events).
This study evaluates the thin approximation empirically, by combining radiative
transfer theory and satellite data from the Eastern Atlantic ocean region studied during
the Atlantic Statocumulus Transition Experiment (ASTEX). Six months of satellite data
from May, June, and July of 1983 and 1984 are analyzed. To the degree that the data
may be considered representative of globally valid relationships between measured
variables, it is shown that the thin approximation is not appropriate for the tropics.
This suggests that new methods are necessary for retrieving SSTs from the more
humid regions of the globe.
Satellite Infrared Measurement of Sea Surface Temperature:
Empirically Evaluating the Thin Approximation
by
Andrew S. Kowaiski
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Completed February 9, 1993
Commencement June 1993
APPROVED:
Redacted for privacy
l4ofessor of Atmospheric Science in4i arge of major
Redacted for privacy
Dean of ollege of Oceanic and
Redacted for privacy
Dean of Graduite School
Date thesis is presented January 30, 1993
Typed by Andrew S. Kowaiski
ic Sciences
ACKNOWLEDGMENTS
I want to thank everyone who offered me any encouragement and hope for
completion of this effort over the last few years. Specifically, however:
Thanks to Dr. Jim Coakley for all of his guidance, support, and tolerance of
my occasionally pessimistic attitude. I'm continually amazed by his ability to analyze
familiar scientific problems from entirely new perspectives.
Thanks to Dr. Steve Esbensen for pointing me in the direction of the 'final
stretch', and for help with description of water vapor fields.
Thanks to David V. Judge, David Simas, and Dean \rickers for helping me to
achieve some efficiency with those lousy tools we
call
computers.
Thanks to Cole, Fu-Lung, and Fred for reviewing my presentations, and for
being friends when I needed them.
Thanks to Mom and Dad for all of the asked-for advice, and for supporting just
about every decision I've ever made.
Thanks to the late Dr. Alan Watts for reminding me that it is all but a game.
This work was supported by the Office of Naval Research.
Part of this work included the analysis of AVHRR observations at the Scientific
Computing Division of the National Center for Atmospheric Research which was made
possible by a grant from the National Science Foundation ATM-8912669.
Table of Contents
Chapter 1
Satellite Infrared Measurement of Sea Surface
Temperature: Empirically Evaluating the Thin
Section 1
Section 2
Section 3
Section 4
Section 5
Section 6
..........................
............................
Radiative Transfer Theory ...................
SST Theory ............................
The Thin Approximation ...................
Approximation
1
Introduction
1
3
5
10
........ 12
Empirical Analysis of the Thin Approximation ......
Model Analysis of the Thin Approximation
18
..... 19
1
Spatially Uniform Sea Surface Temperature
2
Empirical Determination of Gamma
3
Empirical Evaluation of the Homogeneity
4
......................... 33
Larger Scale Gamma-Derived SST Fields ....... 38
Variability in Gamma .................... 51
........... 25
Assumption
5
Section 7
View Angle as an Independent Variable
......... 56
............ 62
Bibliography ........................................ 66
Section 8
Conclusion and Recommendations
List of Figures
Figure 1
Ref lectivities for Water as a Function of Angle for
AVHRR Channels
Figure 2
........................ 6
Effect of Negating Water Vapor Above Indicated
Altitude - Channel 4
Figure 3
..................... 8
Effect of Negating Water Vapor Above Indicated
Altitude - Channel 5
..................... 9
Figure 4
Gamma versus Pathlength for 3 Model Atmospheres
Figure 5
Gamma Plot Displaying Skillful Regression
Figure 6
Figure 7
21
Gamma Plot Displaying High Skill in Meaningless
........................... 23
Incongruous Gamma Plot with High Skill and
Uniformity
Figure 9
............................ 25
Frequency Distributions for Gamma Using Different
Skill Thresholds
........................ 26
................. 28
Figure 10
Gamma Versus View Angle
Figure 11
Distribution of Total Water Vapor for July, 1988 (cm)
Figure 12
Figure 13
16
.......
Gamma Plot Displaying Clustering Problem ...... 22
Regression
Figure 8
.
.
30
...................
View Angle Versus Latitude ................. 32
Gamma Versus Latitude
31
Figure 14
Retrieved SST Field for Incongruous Gamma Plot
.
.
Figure 15
Retrieved SST Field for 'Cooperative' Gamma Plot
.
.
Figure 16
Retrieved SST Field for 'Cooperative' Gamma Plot
.
.
34
35
36
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Retrieved SST Field for 'Cooperative' Gamma Plot
Figure 25
Retrieved SST Field for July 1983
44
46
................... 51
......... 52
Model recreation of a Gamma Plot for the Arctic
................... 53
Model Gamma Plot, Middle-Latitude climatology, SST
............................. 54
Model Gamma Plot, Middle-Latitude climatology,
Reversed SST Gradient
Figure 33
43
Model recreation of a Gamma Plot for the
Gradient
Figure 32
42
Model recreation of a Gamma Plot for the Tropical
climatology atmosphere
Figure 31
41
............................... 49
Middle-Latitude climatology atmosphere
Figure 30
40
Applied Channel 4 Temperature Correction for May of
climatology atmosphere
Figure 29
39
.............
Retrieved SST Field for July 1984 ............. 47
1983
Figure 28
37
..................... 45
July SST Climatology
Figure 27
.
.....................
Retrieved SST Field for May 1983 .............
Retrieved SST Field for May 1984 .............
June SST Climatology ....................
Retrieved SST Field for June 1983 ............
Retrieved SST Field for June 1984 ............
May SST Climatology
Figure 24
Figure 26
.
................... 55
Frequency Histogram of View Angles, First Geographic
Position
.............................. 57
Figure 34
Frequency Histogram of View Ang'es, Second
Geographic Position
Figure 35
Frequency Histogram of View Angles, Third
Geographic Position
Figure 36
...................... 58
Frequency Histogram of View Angles, Fifth Geographic
Position
Figure 38
...................... 57
Frequency Histogram of View Angles, Fourth
Geographic Position
Figure 37
...................... 57
.............................. 58
Frequency Histogram of View Angles, Sixth Geographic
Position .............................. 58
Figure 39
Frequency Histogram of View Angles, Seventh
Geographic Position
Figure 40
...................... 59
Frequency Histogram of View Angles, Ninth
Geographic Position
Figure 42
59
Frequency Histogram of View Angles, Eighth
Geographic Position
Figure 41
......................
...................... 59
Frequency Histogram of View Angles, Tenth
Geographic Position
...................... 60
Satellite Infrared Measurement of Sea Surface Temperature:
Empirically Evaluating the Thin Approximation
Section 1:
Introduction
One of the more important parameters for describing the interaction of the
atmosphere and ocean is the sea surface temperature (SST). This quantity appears
in model formulations that determine the fluxes of vapor and latent and sensible
heat from the surface into the atmosphere (e.g., Albrecht et. aL, 1979; Betts and
Ridgeway, 1988). Climate modeling also relies heavily on accurate knowledge of
SST (e.g, Ramanathan and Collins, 1991) as an important entity in any theoretical
climate system. Thus, for increased understanding of climate and maiine boundary
layer processes, dependable measurements of SST are of paramount importance.
Satellite-derived SSTs are not restricted by the same spatial sampling limita-
tions which apply to shipboard measurements and which make such measurements
inappropriate for global scale modeling. Theoretical accuracies for infrared, satellite
measurement of SST (e.g., McClain et. al., 1985) rival those reported from available
shipboard measurements, and intercomparison has shown that these claimed accuracies
are not overstated (Bernstein and Chelton, 1985). Also, while ships can measure the
bulk thermometric temperature of the ocean from depths of nearly a meter, satellites
measure the skin temperature which regulates the fluxes of latent and sensible heat
across the surface (Schluessel el. al., 1990), and which can be significantly different
from the 'bulk' value under certain circumstances. For these reasons, satellite measurement has been increasingly recognized as the appropriate means of determining
large scale SST.
2
The greatest uncertainty in the determination of SST from satellite infrared
measurements is the presence of water in the atmosphere. Other uncertainties include
the effects of aerosols, which can become globally significant following volcanic
eruptions and are believed to be important for certain regions, and trace gases which
absorb at the relevant wavelengths. In liquid or solid form, intervening atmospheric
water (i.e., a cloud) generally acts as a strong absorber and makes it impossible to
accurately determine the SST using infrared measurements from space. Fortunately,
algorithms exist to identify cloud-free pixels in infrared imagery data (e.g., Coakley
and Bretherton, 1982). For cloud-free pixels, the infrared signal that is seen by
satellites is determined only by the surface temperature and emissivity (usually the
surface is presumed to be a black body, which is a very good approximation for the
wavelengths treated here; this assumption will be analyzed later) and the temperature
and absorptivity of the intervening atmosphere. The advanced very high resolution
radiometer (AVHRR) which flies on the TIROS-N series of NOAA satellites has
been adapted to the 'atmospheric window' region of the infrared spectrum, where
atmospheric absorption is at a minimum. In this window region, atmospheric effects
are dominated by water vapor, but also affected somewhat by carbon dioxide, ozone,
and methane.
3
Section 2:
Radiative Transfer Theory
Traditional theory in radiative transfer (adapted from Liou, 1980) assumes that
linear processes of absorption, scattering, and emission act to modify monochromatic
radiation propagating through a medium. For infrared radiation in the atmospheric
window, the effect of scattering may be neglected for cloud-free situations such as
those in which it is attempted to measure the SST. Kirchhoff's law dictates that
emissivity and absorptivity of the medium be identical. This implies that propagation
of monochromatic radiation through the atmosphere is governed by Schwarzschild's
equation:
dIA(s)
dTA(S1, s)
where
IA+BA(T(s))
(1)
is radiant intensity for wavelength .X, r is the optical depth over a pathlength
from point s to si (over which the fractional absorption and fractional emission are
exactly equal), and BA is the Planck function evaluated at a temperature T along
the path. The negative signs arise through the definition of optical depth which is
taken to decrease with s increasing toward si (i.e., drA(s1, s)
kApds, where
k,,
is the absorption/emission coefficient and p represents absorber density, which may
have a functional dependence on pathlength). When equation (1) is multiplied by the
integrating factor e(31,$) and integrated from s=0 to s=sl over the transmissivity,
the result is
sl
J
si
fdiA(s)
e_(81MdrA(sl, s)
drA(s1,$)
0
= f 1AeT(313)drA(s1, s)+
0
si
IBA(T(s))e_T(813)drA(s1,
0
(2)
4
where the term on the left and the first term on the right represent a perfect differential,
since
d{IA(s)e_T81}
dI(s)
drA(s1,$)
drA(sl,$)
using the product rule of differentiating.
e_TA(shIs)
- IA(s)e13)
Noting then that
TA(s1, sl)
(3)
= 0, the
integration simplifies to yield the well-known solution to Schwarzschild's equation:
sl
IA(sl) = IA(0)e
TA(31,O)
f
BA(T(s))e"drA(s1, s)
0
which is readily adaptable for satellite applications (sl
oo).
(4)
5
Section 3:
SST Theory
The relationship between transmissivity,
eTA
and optical depth
=
(5)
= dtA
allows the solution to Schwarzschild's equation to be written as
I(s1)
IA(0)tA(81,O) +
fB(T(s))dt(s1s)
(6)
Considering that the satellite sees I (s 1 - oo) the work of Deschamps and Phulpin
(1980)
is followed by defining the radiance deficit introduced by atmospheric inter-
vention as LIA
BA(TO) - I(s1), where
T0
is the SST (throughout this paper,
T0
will be used to represent the true SST, while any predicted value of the SST will be
represented by T3).
An assumption has been made here that the surface is a black body (emissivity of
unity). Simple calculations using the optical constants of water reported by Downing
and Williams
(1975)
for reflectivity of the ocean surface at wavelengths corresponding
to those used in 'window' wavelengths show that this assumption is valid for view
angles utilized by the AVHRR. AVHRR Channels
centered at
3.7, 10.8,
3, 4,
and
5
represent narrow bands
and 12.0 m, respectively. Note that for water pathlengths in
excess of approximately 1mm, transmissivity is negligible in the infrared (Robinson,
1985)
and therefore reflectivity and absorptivity (equal to emissivity) must sum to
unity.
As can be seen in Figure 1 (dashed lines included for reference), only for viewing
angles in excess of sixty degrees (the extreme limbs of the scan for the AVHRR) does
6
LOG REFLECTMTiES FOR AVH RR CHANNELS
0.5
1.0
>
0
-j
-
Lii
0
0
2.0
2.5
3.OL
0
20
40
60
ANGLE tN DEGREES
80
100
Figure 1 Reflectivities for Water as a Function of Angle for AVHRR Channels
the emissivity differ from unity (as represented on this graph by non-zero reflectivity)
by more than three percent for any of the wavelengths, and for viewing angles below
forty-five degrees (fifty degrees for channels 4 and 5), the emissivity is unity to within
one percent or better.
For small temperature deviations, the derivative of the Planck function with
respect to temperature can be approximated such that
(7)
()To
where /TA is defined as the brightness temperature deficit due to the radiance deficit
LXI), caused by the intervening atmosphere [the brightness temperature,
such that
BA(T,) = IA(s1)
and the resulting deficit as LT
To
is defined
T)]. Typical
7
deficits (measured and modeled) are on the order of five percent or less for both
temperature and radiance, and the Planck function is sufficiently linear when evaluated
at climatological temperatures that (7) results in negligible error in treating the finite
difference ratio as a derivative. This allows the integral equation for radiance deficit to
be rewritten in terms of a temperature deficit. Using the definition of radiance deficit,
and substituting for the radiance seen by the satellite using (6), (7) becomes
sl
B,(To)
B( To)tA(sl, 0)
f B,(T(3))dtA(S1, 0)
aB
(8)
(-a)m
Employing again the fact that t,(s1, sl) = 1 (for optical depth = 0), and therefore
B(To) = B(To)t,(s1, sl), to take the surface term inside the integral, leaving
sl
f (B(To)
- BA(T(s)))dt(sl, s)
(9)
()T
Finally, a first order expansion of the Planck function about the SST gives
BA(TO)
B(T(s))
()TO(To T(s))
(10)
which is valid for atmospheric temperatures which are not drastically different from the
surface temperature (i.e., relatively near the surface, where the significant absorption
by water vapor is).
Figures 2 and 3 show for AVHRR channels 4 & 5, at nadir views, that the
brightness temperature deficits are not significantly affected by changes (restricted to
realistic values) in the water vapor profile above .-.s6km for all profiles. In fact, it can
be seen that the regions with significant moisture content are found, not surprisingly,
where the atmospheric temperature is nearly as warm as the surface, and thus the
8
NADIR BRIGHTNESS TEMPERATURE DEFICITS
'[I]
8
0
0
w
6
I-
0
uJ
c
I
0
2
5
10
15
20
AL11TUDE ABOVE WHICH WATER NEGATED (KM)
Figure 2 Effect of Negating Water Vapor Above Indicated Altitude - Channel 4
temperature condition imposed upon (10) is met. These figures were generated by
using a band-type model for atmospheric transmission, and comparing the effects of
negating all water vapor above the indicated altitudes. The band model used in this
study utilizes the standard Goody Random Model with line strengths reported by Kyle
(1975) and treats absorption by the water vapor continuum using extinction coefficients
determined by Roberts et. al. (1976).
The Planck-expansion substitution of (10) allows the partial derivative to be
taken out of the integral, simplifying the entire expression to
= J(To
T(s))dtA(s1,$)
(11)
9
NADIR BRIGHTNESS TEMPERATURE DEFICITS
i1i
8
0
0
i.i
0
6
I-
0
w
04
IC)
I
0
TITUDE
2
ARCTIC
5
10
15
20
ALTITUDE ABOVE WHICH WATER NEGATED (KM)
Figure 3 Effect of Negating Water Vapor Above Indicated Altitude - Channel 5
where the brightness temperature deficit is a function of only the surface temperature
and atmospheric temperature profile, and the transmissivity as a function of height
through the atmosphere.
10
Section 4:
The Thin Approximation
The traditional approach to simplifying (11) has been to assume that the atmos-
phere is 'thin' in the window region; i.e., that transmission is near unity for the full
depth of the atmosphere. This assumption allows (5) to be simplified to give
dtA(sl,$) = tAdT(s1,$)
di-(s1,$) = kAdU(sl,$)
(12)
where U is absorber amount integrated over the path. Note that, for the case of
continuum absorption, a pressure weighted absorber amount is defined as U(sl, .$) =
sl
f p,eds,
where Pu is the density of the absorbing gas, in this case, water vapor, and e is
the vapor pressure. The definition of U chosen here is dependent on the satellite zenith
angle, 0, since
ds = dz/(cos0),
and 0 may be considered constant in all of the above
integral equations. Subsequently the approximation allows (11) to be rewritten as
kA
J(T(s)
- To)dU(sl, s)
(13)
which shows that the brightness temperature deficit is a function of the absorption
coefficient (wavelength dependent) and a universal function (i.e., independent of
wavelength within the window region) of temperature and absorber amount.
For two wavelengths which are affected by the same absorber, this simplification
allows determination of T0 using two such equations, where the two unknowns are T0
and the integral term in (13), whose numerical value is not of immediate importance
to the SST problem. The two brightness temperatures, T, are measured by the
satellite instrument.
temperatures.
This method is in effect a linear combination of brightness
In practice, regression is used to determine the coefficients which
11
multiply the brightness temperattires in linear combination (McClain, 1983) resulting
in an equation of the form
ao +
aT
(14)
where T is the SST retrieved by the algorithm and i represents the channel number.
The coefficients (a's) are determined by regressing measured ship and/or buoy SSTs
(thus neglecting skin/bulk differences in SST) with (14) using coincident measurements
of the (T's) from satellites. These coefficients are termed Multichannel Sea Surface
Temperature (MCSST) coefficients, and were, until recently, utilized by the NOAA
National Environmental Satellite, Data, and Information Service (NESDIS) to generate
and distribute global SST fields.
12
Section 5:
Model Analysis of the Thin Approximation
The decision to resort to regression was originally motivated by the questionable
validity of the two assumptions pointed out by Deschamps and Phulpin (1980): 1) that
the thin approximation holds; and 2) that the absorption coefficient, kA is independent
of temperature and thus may be taken outside of the integral over the height of the
atmosphere, as is done to obtain (13). Analysis of each of these assumptions is possible
from any number of data sets, but Prabhakara et. al. (1974) gave perhaps the best
evidence for direct comparison of the importance of these two assumptions.
Prabhakara et. al. (1974) showed that the effect of two differing mean absorberweighted temperatures representing a broad range of climatic conditions give rise to
little difference in transmissivity as a function of absorbing water vapor amount. Plots
of transmissivity versus water vapor path, however, make it clear that for precipitable
water contents in excess of a few centimeters, the thin approximation breaks down for
wavelengths corresponding to AVHRR channels at 11 and 12 m. These investigators
modelled water vapor transmission as the product of e- type (dependent on vapor
pressure), p-type (dependent on
total
pressure), and I-type (from water vapor lines)
transmissivities.
Stephens (1990) showed that the climatological distribution of precipitable water
exceeds this threshold nearly everywhere in the tropics, and when the effect of
increased air mass due to non-nadir viewing angles is taken into effect, one finds
that the thin approximation may hold only for midlatitude/low-view-angle and other
combinations which further minimize the water vapor path. The thin approximation
evidently deserves closer attention.
13
Further evidence exists in previous literature that the thin approximation is
inappropriate for some atmospheric profiles. McMillin (1975) presented the results
of radiative transfer calculations using a subset of the atmospheric profiles (SST,
temperature and humidity soundings) given by Wark et. aL (1962). Table 1 has been
adapted from the tabulation of radiance values reported by McMillin (1975). Using
the transmissivities reported by the model, optical depths may be determined using (5),
and 'approximate transmissivities' calculated using the thin approximation (12), which
may be expressed as t, = 1
T),
when known boundsry conditions are applied. Table
1 shows the transmissivity errors introduced by making the thin approximation for this
data set. In this table as defined by McMillin, the atmosphere number corresponds
to the profile from the set defined by Wark, Qtot is the total amount of precipitable
water vapor, and airmass denotes the secant of the viewing angle. The column headed
't (approx)' lists the approximate transmissivities. Here, the atmospheres have been
ordered in terms of increasing humidity, so as to show the importance of water vapor
amount for the error in making the thin approximation. For brevity, some of the cases
displayed by McMillin have been omitted, since they represent near duplication of
the presented data.
Liewellyn-Jones et. al. (1984) used a line-by-line model to calculate atmospheric absorption, and reported transmissivities consistent with those from the above
mentioned models. Likewise, here, a band-type model has been used to examine
the relative importance of each of the two terms on the right-hand side of (4), and
has shown that the integral term makes a significant contribution, overwhelming the
surface term in the case of tropical profiles, even for nadir viewing angles. This too
suggests an error in maldng the thin approximation
14
Table 1 Transmissivity Errors Resulting from the Thin Approximation
Atmc.phuc
Qtoc (cm)
Ainnug
18
0.134
1.0
17
0.258
2.0
1.0
8
0.404
_____________
2.0
1.0
2.0
20
0.559
1.0
15
0.687
2.0
1.0
2.0
13
0.956
1.0
19
1.083
4
1.187
2.0
1.0
2.0
1.0
2.0
1.275
1.0
2.0
6
1.546
11
1.745
3
2.500
1.0
2.0
1.0
2.0
1.0
2.0
60
2.725
2
2.882
1.0
57
3.244
2.0
1.0
2.0
30
3.655
10
3.864
71
4.024
68
4.224
2.0
1.0
2.0
59
4.312
1.0
58
4.628
56
5.072
1.0
2.0
1.0
2.0
1.0
2.0
1.0
2.0
__j.0
__.0
69
5.169
55
5.486
1.0
2.0
1.0
2.0
1.0
2.0
(model)
0.99521
0.99074
0.98746
0.97690
0.97161
0.94784
0.95881
0.92559
O.93300
0.87901
0.90195
0.82509
0.86492
0.76128
0.85989
0.75437
0.83925
0.71975
0.83017
0.70514
0.74156
0.56913
0.70939
0.53012
0.57846
0.35195
0.65087
0.44647
0.58649
0.36115
0.46243
0.22970
0.45003
0.21727
0.43771
0.20482
0.47248
0.24045
0.35623
0.13636
0.35921
0.14013
0.29444
0.09455
0.28201
0.08694
0.28851
0.09705
t (appmx)
% cnor
0.9952
0.9907
0.9874
0.00
0.00
09166
0.03
0.9712
0.9464
0.9579
0.9227
0.9306
0.8710
0.8968
0.8077
0.8549
0.7272
0.04
0.8491
0.7181
0.8248
0.6712
0.8139
0.6506
0.7010
0.4364
0.6567
0.3654
0.4526
-0.0443
0.5706
0.1936
0.4664
-0.0185
0.2287
-0.4710
0.2016
-0.5266
0.1738
-03856
0.2502
-0.4253
-0.0322
-0.9925
-0.0239
-0.9652
-0.2227
-1.3587
-0.2658
-1.4426
-0.2430
-13996
0.01
0.15
0.09
0.31
0.25
0.91
0.57
2.10
1.16
4.47
1.26
4.80
1.73
6.75
1.96
7.73
5.47
23.33
7.43
31.08
21.76
11238
12.34
56.64
20.48
105.11
50.53
306.04
55.21
342.37
60.29
385.91
47.04
276.86
109.03
827.82
106.64
788.75
175.62
1537.00
194.25
1759.31
184.24
1642.22
Still other studies have suggested the need for MCSST-like coefficients particular
to specific regions (which would provide more, local information about the water vapor
content of the atmosphere), and viewing angle dependencies in the regression models
utilized (e.g., Minnett, 1990). Indeed, the MCSSTs distributed by NOAA NESDIS as
of April 1992 (Duda, personal communication) include relatively strong dependencies
in zenith angle, but are meant for global use. The equation for NOAA 11 daytime
retrievals is written as
T8 =
l.02015T4 + 2.320(T4
1'5) + O.489(secO - 1)(T4 - T5) - 278.6
(15)
15
The apparent problem with such an approach (relying heavily on regression), is that
the dependence on satellite zenith angle is physically incorrect. Accounting for a
dependence on zenith angle in linear models should not be necessary in very dry
regions. In the tropics, however, it may be quite important, even for modest, nonnadir viewing angles.
Examples of the disparity between dry and moist regions are seen in Table 1.
Wark's eighteenth atmosphere would be well-approximated by the thin limit, even for
a doubled pathlength. In such conditions, zenith angle effects on pathlength could well
be neglected. On the other hand, atmospheres with more than 4.0 cm of precipitable
water will be poorly represented by the thin limit (e.g., number 71), even at nadir
viewing angles. Further, in the intermediate range of a few cm of precipitable water
(e.g., number 57), the thin limit seems adequate for nadir views, but gives poor results
on the limbs of the scan.
Walton (1988) argued for a nonlinear approach to the problem, citing inadequacies in the theory of MCSSTs, based upon the thin approximation. He used the
radiative transfer model of Weinreb and Hill (1980), to show that the parameter -y,
which McMillin and Crosby (1984) had shown to be constant when the thin limit holds,
was actually dependent on water vapor amount (this -y is used to linearly relate the SST
to radiative quantities measured from satellite, akin to an MCSST relationship, and
will
be defined and examined in more detail later). Here, this conclusion is supported
by plotting -y (determined using the band-type model to calculate transmissivities) as a
function of the secant of the viewing angle through three climatological atmospheres,
in Figure 4. Note that the secant of the viewing angle is a multiplicative factor on the
pathlength. The result is similar to Walton's findings. As can be seen in the figure,
y
16
8
7
)IE
6
=
)IE
*
,
A
TROPICAL
MIDLATITUDE
ARCTIC
4
3
A
0
A
0
A
0
A
0
A
0
A
p
0
A
A
21-
1.0
1.2
1.4
1.6
SECANT OF VIEW ANGLE
1.8
2.0
Figure 4 Gamma versus Pathlength for 3 Model Atmospheres
is most sensitive to view angle in the tropics, where the water vapor content is high.
Walton then provided a graphical, nonlinear method of retrieving SST, but made
use of a disguised version of the thin approximation in the 'Physical Justification and
Derivation' for the method. Using the results of Prabhakara et. al. (1974), he
assumed that transmission was linear in absorber amount, which, as previously noted,
is equivalent to making the thin approximation, and is only valid for low water vapor
paths.
Specifically, Walton (1988) began with an equation of the form
T=T5+(T3)(li)
(16)
17
where the symbols have been converted from Walton's notation to be consistent with
the preceding developments; this is Walton's equation number (A2). Here, T is a
weighted mean atmospheric temperature. The next equation (A3) is
T,
=2's
/c,U(T3).
This succession of equations implies t = 1
(17)
kAU, which is a reiteration of (12).
18
Section 6: Empirical Analysis of the Thin Approximation
The previously mentioned theory of McMillin and Crosby (1984) makes use
of the approximate equality of sea-surface temperatures and effective radiating atmo-
spheric temperatures. From (11), it can be seen that the magnitude of the difference
between these two quantities can, as an alternative to the thin approximation, explain
the observed magnitudes of brightness temperature deficits.
The Planck function for one channel is expanded in terms of the Planck function
for another channel within the window region to arrive at a predictive equation for
surface emittance of the form
B4(T) = 14(81) + 7(14(81)
I(s))
(18)
In this equation, I is the radiance found when applying the channel 4 Planck function
to the channel 5 brightness temperature, and 'y is the ratio defined by
= (1
t4(si3O))/(14(si3O)
t5(si3O))
(19)
When the thin limit holds (in relatively dry atmospheres), this y is a constant equal
to k4/(k4
k5), which is found using (12) in integrated form, i.e., t,
1
kAU. As
an alternative, McMillin and Crosby (1984) show that if temperature is expanded in
terms of the Planck function, again using two channels, then the following is obtained
to predict SST
T3=T4-i-7(T4T5)
(20)
which if7 is constant) is identical in form to (14), the MCSST equation, with MCSST
coefficients ao = 0, a = (1 + 'y), and a5 = 'y. The ao term is generally included
19
in the MCSST regression to account for skin/bulk SST differences and possible lack
of calibration accuracy in the instrument.
As mentioned before, however,
has been found to have a dependence on total
water vapor path, when model calculations are used to evaluate (19). A method will
now be introduced for attempting to evaluate
using satellite data, rather than relying
on the accuracy of models to support or detract from McMillin's claim for constant
.
1 Spatially Uniform Sea Surface Temperature
For a small region of the ocean, it is assumed that the SST is spatially uniform
and statistically stationary over some small scales. The time scale is determined by
the rate of the satellite as it passes over and scans the scene. The spatial scale must
be small enough to permit the uniform SST condition to hold, and yet large enough
to permit significant variations in the satellite view angle. In this case, as the satellite
passes over the region, variations in water vapor path will be due only to variations in
view angle and to variations in absolute humidity in the clear-sky portions of the scan,
assuming that all cloud contamination (including that of the sub-pixel scale) has been
removed. Equation (18) can then be applied to the measured radiances for the small
region, where
T8
is constant if unknown, and a plot of 14(sl)
versus 14(31)
I(s1)
will thus yield a straight line with a slope of 7. Extrapolation of this straight line
(on such a plot) to the point where
14(81)
I(s1) = 0 would theoretically result
in 14(s1) equalling the surface emitted radiance, via (16), from which the SST may
be directly determined.
This method has been applied to 50 by 50 (latitude x longitude) regions of the
larger Atlantic Stratocumulus Transition Experiment (ASTEX) region in the Eastern
Atlantic Ocean. The initial data set consists of NOAA 11 and NOAA 12 daytime
overpasses (nighttime cloud masking proved to be an intractable problem) collected
and graciously provided by Dr. Phil Durkee's group from the Naval Postgraduate
School, during ASTEX in June of 1992. This set occupies the region from 28° North
to 44° North and 13° West to 33° West. A second set of NOAA 7 overpasses from
May, June, and July of 1983 and 1984 have been
included
in the analysis to provide
some data for tropical regions (made available by the Data Services and Support group
at NCAR); this second set occupies the region from 5° North to 45° North and 10°
West to 40° West.
In this analysis, as in any satellite infrared SST analysis, it is imperative that
cloud contamination be identified and removed from the data. For this reason, the
'Spatial Coherence' method of Coakley and Bretherton (1982) has been employed. The
current version of this method reports cloud-free radiances for (64km)2 'subframes'
(16 x 16 scan line x scan spot pixel arrays for the 4km GAC data). These cloud-free
radiances are the average of pixels which are determined to be associated with the
warmest spatially homogeneous layer in the scan (the 'cloud-free foot' of a spatial
coherence 'arch': these terms are defined in Coakley and Bretherton, 1982). The
pursuant analysis will thus be based on 'subframe statistics' rather than raw radiance
data.
Figure 5 shows a plot of subframe statistics { 14 (s 1) versus 14(s 1) - I (si) }
in a 5° by 5° region from the Eastern Atlantic. The southwest and northeast corners
of the region are denoted at the top of the graph, as will be the case for all of the
subsequent 'Gamma plots'. These data were from a NOAA 7 overpass on May 14,
1984. In this particular case, the points define a straight line, modeled here with a
21
99.5%
as
significance level on the hindcast sample skill which is denoted on the plot
0.901.
The skill is the square of the sample correlation coefficient, and represents
variance explained by the regression model. The negative of the slope of the regression
line is also indicated, here, as 4.82 (this would be the estimate of 'y for this plot). Such
plots have been created, each with regression analysis and estimate of the skill, for a
subset of the 50 by
50
regions in the larger analysis scene over the ASTEX experiment.
In order to be included in the analysis, a
50
by 50 region must have at least twenty
subframes which have cloud-free statistics (typically, there are about 40 to 50 total
subframes in an analysis region). All of the plots are not necessarily as 'cooperative'
as the one shown in Figure 5, however. It was assumed that the 'uncooperative' cases
represented scenes for which the assumption of a uniform SST was violated.
For 5by 5Box with SW corner 25.N,35.W
101
SKILL = 0.90 1
SLOPE = 4.823
100
99
-
98
-
E
E
3
E
'-a
.-
97
96
-
95
1.6
A
I
I
1.8
2.0
I4
Figure
5
2.2
2.4
2.6
I (mW m's('cm)
Gamma Plot Displaying Skillful Regression
2.8
22
It became obvious that some objective method of identifying the uncooperative
cases was needed. Figure 6 shows data from June 2, 1984. In this case, the skill of
the regression was significant at the 99.5% level, but it is obvious from inspection
that the regression is tainted by the fact that the data are from two distinct groups,
with very different SSTs. Initially, cases such as this one were eliminated by simply
boosting the cutoff value for the skill/correlation coefficient, but this proved to be an
inadequate method of objectively eliminating regressions that were presumed to be
affected by SST gradients.
For 5by 5Box with SW corner 15.N,3O.W
1i
II
SKILL = 0.760
SLOPE =
3.386
102 -
-o
E
-
100
98
0.6
0.8
1.0
I4
I
1.2
1.4
1.6
(mW m'srcm)
Figure 6 Gamma Plot Displaying Clustering Problem
As can be seen in figure 7, which includes data from both sides of the Northwest
African coast from an overpass on July 3, 1984, a skill cutoff is not sufficient for
23
eliminating meaningless regressions of data from obviously different climates. In this
plot, the tight grouping of the oceanic data points (lower-right cluster) couples with
but a single high-leverage point from the African continent (with corresponding large
radiant
intensity
in Channel 4) to yield a regression line that describes 95% of the
variance in the data (i.e., a correlation coefficient of greater than 0.97). The gradient
in surface temperature defines the slope of the regression line. While this is not
indicative of a meaningful linear relationship between the 14(s1) and 14(31)
- I(s1)
variables, it is representative of among the strongest correlations that could be found
in Gamma plots by utilizing regression. As an extreme case, this demonstrates the
effect of non-uniform SST on the technique of retrieving 'y. Obviously, a method of
eliminating regressions due to clustering from SST gradients is needed.
1 6C
1 4C
F
E
.t°
12C
E
E
1 OC
80
3.0
2.5
2.0
I4
1.5
I
1.0
0,5
0.0
(mW m'sr'cm)
Figure 7 Gamma Plot Displaying High Skill in Meaningless Regression
24
To eliminate this clustering problem, another statistical test was applied to all
of the plots. Bendat and Piersol (1966) described a Chi-Square Goodness-of-Fit test
that can be applied to determine whether the frequency distribution of a sample data
set is consistent with a theoretical frequency distribution (e.g., a normal distribution,
a uniform distribution, etc.) over the domain of the variables. Here, in order to
avoid the problem of statistically different groups, cases where there was at least 90%
confidence that the data from
either
variable (14(s1) OR 14(s1) - I(s1)) were not
uniformly distributed over the domains of the variables have been excluded. This
is a conservative selection criteria, allowing retention of only those regressions for
which the data were well distributed along the regression line. The test was
applied
by dividing the domain of the variable into four bins, and comparing the resultant
frequency distribution with a uniform distribution using the Chi-Square criteria with
three degrees of freedom.
In the end, a low correlation coefficient threshold of 0.6 (i.e., where the
regression line describes 36% of the variance in the Gamma plot) was applied
to eliminate the least skillful regressions, mostly for the sake of computational
conservation.
Further analysis will be presented later with selection of a better
threshold in mind, keeping several values of skill cutoff in order to test sensitivity
of the results to the threshold. Nevertheless, regardless of the choice of the skill
cutoff, the Gamma plots remaining after application of this cutoff and the Goodness-
of-Fit for uniformity test are still found to contain cases that do not agree with the
theory and assumptions applied here.
Figure 8 shows an example of such an incongruous Gamma plot, created from
an overpass on June 13 of 1983. Since the absorption due to water vapor in channel
25
10
E
'p
I-
'In
F:
E9
92
0.4
LJ.'P
(mW mrcm)
Figure 8 Incongruous Gamma Plot with High Skill and Uniformity
5 is greater than the absorption in channel 4, figure 8 and all those like it which
result in positive slopes must be interpreted as resulting from some form of gradient
in the SST field. This claim can be proven by considering the null hypothesis that
SST is everywhere constant in the plot. Under such conditions, only a decrease in
water vapor could lead to an increase in 14(sl). But, as water vapor decreases, the
channel 5 brightness temperature should increase faster than the channel 4 brightness
temperature (stronger absorption in channel 5). Thus,
14(sl)
I(s1) must decrease.
Hence, this null hypothesis is rejected.
2 Empirical Determination of Gamma
The initial data set including overpasses from NOAA 11 and 12 in June of
26
1992 proved to have too few suitable estimates of -y. Due to differences in instrument
spectral filter functions, data from different instruments were kept separate. For both
the NOAA 11 and 12 overpasses in June of 1992, only seven of the Gamma plots
met the two criteria of Chi-Square uniformity and at least 36% variance explained by
the Gamma linear model.
The NOAA 7 data set from May, June, and July of 1983 and 1984 is spatially and
temporally more extensive than the 1992 data set. The following analysis includes this
NOAA 7 data, and the number of Gamma plots meeting the two criteria are shown
as a function of higher skill thresholds.
jofcovnmos- 53
SKILLCUT= 0.65
1:
-2
0
2
4
0
ofGomrnoi
SKILLCUT = 0.75
I
0.0:-
Av .
0.I
p
Sty.
I
04'
-2
0
2
1.80
S
10
34
3.61
0ev. -
rL.r,:
4
4
5
II
y or liammos -
= 0.85
Avg. = 3.74
Std. Dev. = 1.68
()
I
0
2
4
Figure 9 Frequency Distributions for Gamma Using Different Skill Thresholds
Figure 9 shows three frequency distributions for 'y, each with a different skill
27
threshold for selecting Gamma plots. The average and standard deviation of the 's
that passed the uniformity and skill cut-offs are also shown, as is the number of Gamma
plots that survived the indicated threshold. In every case of skill threshold, Gamma
plots with positive slopes (implying negative y's) are not included in the distribution,
since these plots are obviously indicative of a breakdown in the SST uniformity criteria.
It seems from this figure that the skill threshold is not too important, as long as it
is chosen sufficiently high to eliminate the completely unskillful regressions from the
analysis, and that a choice of -y = 3.7 ± 1.7 is probably adequate in defining a mean
and a range for the empirically-determined
y.
It is quite reassuring to note that this
range is in accord with what the models predict (see figure 4), for low to middle
latitudes such as those in the ASTEX analysis region.
One disappointing (and surprising) result that fell out of the analysis was the
need for more data, considering the large analysis region and time frame. For example,
if the skill threshold for 'good' Gamma plots is placed at 065 (the first cut-off from
figure 9), there are still only fifty-three plots which satisfy the cloud-free, uniformity,
and skill conditions. In other words, the sea surface as seen from satellites is not very
often sufficiently uniform for the technique to work. The number of Gamma plots
included in the analysis decreases as the skill threshold for selection is increased.
Despite the lack of a large pool of Gamma plots that might be necessary to
analyze dependencies in such factors as view angle and latitude, it may still be useful
to look at these relationships. Figure 10 shows, for the three values of skill threshold,
the empirical relationship between 'y and satellite zenith angle (roughly equal to the
viewing angle from nadir the small difference is due to the curvature of the earth,
and is not very large for the orbital altitudes and scanning limits of the AVFIRR
28
instrument). For each level of skill cutoff, the linear trend is included using a dashed
line, and the slopes are indicated for comparison.
ciuuu -
SLOPE = -0.01
I.
H
I
0
20
40
00
ULLCUI - U.I
I
SLOPE = -0.00
-
---
2
0
20
WN
-
40
00
40
II
S$QU.CLJT - 0.05
SLOPE = O.O7
:-
2
C.'
0
-----h- -------A
20
tWM4G
Figure 10 Gamma Versus View Angle
Here, it is seen that the selection of skill cutoff does affect conclusions about the
possible relationship between 'y and viewing angle (effectively, pathlength) for this set
of data. Unfortunately, it is only at the highest level of skill that the anticipated increase
in Gamma with viewing angle is found, and here there are very few observations. This
highlights the need for a large data set when applying this empirical technique, since
the highest skill values may be needed but are relatively infrequent.
Note that, based on the model calculations, the sensitivity of y to view angle
is not expected to be global. On the contrary, it should have almost no dependence
29
on pathlength for atmospheres that are very dry, i.e., nearer the poles (these are the
atmospheres that would satisfy the thin approximation of constant 'y); while in regions
of very high water vapor, the dependence should be more pronounced. Due to the
lack of a large set of 7's and view angles, the trend for y to increase with increasing
pathlength is not statistically significant. It is suggestive, however, and consistent
with what the models have predicted.
The relationship between
and geographic position is even less tenable for the
selected region and data. In general, throughout the globe, one would expect to find an
increase in the total water vapor loading as the equator is approached. For the eastern
North Atlantic in the summer, however, the water vapor distribution is governed more
by the global-scale circulation pattern which brings subsiding, dry air from the North
and West, with a low-level return flow through the South-Easterly trade winds.
Figure 11 shows the distribution of water vapor for July of 1988 for the entire
globe. This figure was generated by Esbensen et. al. (1993) using water vapor fields
from Wentz (1989), inferred from the Special Scanning Microwave/Imager (SSM/I).
According to Esbensen (personal communication, 1992), the broad, dry regions to the
west of major continents at subtropical latitudes, where gradients of water vapor are
not directed toward the poles, are a consistent feature of the global scale water vapor
distribution for the summer months. Much of the ASTEX region is engulfed in just
such a thy subsidence area.
Due to this dependence on large-scale circulation, gradients of total water vapor
with latitude are not nearly what might be expected from zonally-averaged temperature
profiles via the Clausius-Clapeyron equation (Rogers and Yau, 1989). Thus, the model
prediction for
based on tropical climatology is not applicable to the tropical portions
30
SSM/I Columnar Water Vapor Analysis
90N
ON
30N
0
30S
'Os
'Os
0
GOE
flOE
180
120W
SOW
0
Figure 11 Distribution of Total Water Vapor for July, 1988 (cm)
of the ASTEX region, and the plot of
versus latitude (figure 12), which is generated
empirically from the Gamma plots, does not agree with the model results depicted
in figure 4.
It is somewhat disturbing to find that y increases with increasing latitude. If
the gradient of water vapor is not significant with latitude across the region (as figure
11 would predict), then one would expect to find virtually no dependence of y with
latitude. Thus the trend apparent in figure 12 would seem to detract from the previous
31
- u.o
SLOPE = 0.10
A
I
4
A
-
___4---1
A
2:
A
0
20
40
10
SLOPE = 0.08
A
8
A
A
___-;1i
0
20
40
LLCUI
I
I
80
V.5
SLOPE = 0.12
A
____--A
-
__A-A
A
Figure 12 Gamma Versus Latitude
conclusions about 'y versus viewing angle. However, should a non-physical correlation
exist between the view angle and the latitude (due to coincidence perhaps, or possibly
complex factors including any number of related possibilities such as cloud detection
or perceived SST uniformity as determined by the Goodness-of-Fit test), then figure 12
would lose meaning. Figure 13 shows just such a correlation. Evidently the number of
Gamma plots included in the analysis is probably not adequate for drawing conclusions
about the dependence of y with latitude for this region. However, regardless of
this result, pathlength increases with view angle, with a secant dependence, and this
dependence dominates latitudinal effects on pathlength for the ASTEX region.
40
2O-a
Figure 13 View Angle Versus Latitude
40
SLOPE
O.5o
33
3 Empirical Evaluation of the Homogeneity Assumption
With -y determined from the distribution in figure 9 (i' = 3.7), attention can then
be returned to some selected cases of Gamma plots with very high skill values, to
evaluate the assumption that positive slopes (negative -y) imply a large SST gradient.
Since it would be unwieldy to examine all of the Gamma plots (incongruous or
otherwise), the analysis is limited to those with skill in excess of 0.9, that is, where at
least 90% of the variance in the Gamma plot was explained by the linear regression.
For the six months of analyzed data, only four Gamma plots resulted in such high
values of skill (representing excellent agreement between the linear model and the
data), including both of the Gamma plots shown in figures 5 and 8, as well as two
other Gamma plots, each of which displayed negative slopes (positive y) in agreement
with the criteria for uniform SST.
Figures 14 through 17 show the retrieved SST field images for these high skill
cases, derived from equation (18) using -y = 3.7 in every case. The latitude and
longitude ranges covered by the field are indicated on the plots. Blackened areas are
indicative of regions where the Spatial Coherence Algorithm was unable to detect a
cloud-free foot; whiter regions denote warmer SSTs, and darker denote colder SSTs.
Retrieved SSTs are written into the images for clarity, especially in the homogeneous
cases where the plotted gradients are too weak to be seen by inspection of the image.
The first case (figure 14) is for the same data that created the incongruous
Gamma Plot in figure 8, and a strong gradient in the SST field is evident. The
gradient has a strong meridional component (orthogonal to the scan), which suggests
that the effect of the selected versus retrieved -y (from figure 8, 'y
6.7) is not
LAT
35
34
33
32
31
30
LON
-15
-14
-13
-12
-11
-10
Figure 14 Retrieved SST Field for Incongruous Gamma Plot
entirely responsible for the retrieved SST gradient. Figure 15 shows the SST field for
the selected cooperative Gamma plot from figure 5. It is quite obvious that, relative to
the gradients present in figure 14, the SST field is uniform for this 5° by 5° region.
Finally, the remaining two cases where the skill exceeded 0.9 are presented.
Representing an overpass on June 1, 1984 is the SST field for a Gamma plot which
yielded a slope of 3.83 is figure 16. Figure 17 is from an overpass on June 14, 1983
where the slope of the Gamma plot was 1.41. Both of these remaining 'cooperative'
cases (Gamma plots not shown) have y's which fall within the range identified from
figure 9, and have quite uniform SST fields relative to the strong gradients shown in
figure 14.
35
LAT
30
22.8
22.8
22.5
22.5
23.3
23.0
22.5
22.6
29
23.2
22.9
22.6
23.1
23.0
22.8
23.4
23.0
22.7
23.4
23.2
22.8
23.2
23.2
23.0
28
27
26
23.6
23.3
23.7
23.0
23.3
23.3
23.2
23.5
25
LON -35
-34
-33
-32
-31
-30
Figure 15 Retrieved SST Field for 'Cooperative' Gamma Plot
36
LAT
30
29
28
27
26
25
LON -30
-29
-28
-27
-26
-25
Figure 16 Retrieved SST Field for 'Cooperative' Gamma Plot
37
LAT
10
LON -40
-39
-38
-37
-36
-35
Figure 17 Retrieved SST Field for 'Cooperative' Gamma Plot
38
4 Larger Scale Gamma-Derived SST Fields
As a further check on the Gamma method of deriving SST, the large scale SST
field for the ASTEX region is compared with the climatology of Esbensen and Kushnir
(1981, hereafter referred to as E-K) for the same region. The E-K climatology is
composed of in situ observations.
On the following page, figure 18 shows the E-K climatological SST contours
for the month of May. Following it are figures 19 and 20 which show the SST
fields for May of 1983 and 1984 which was retrieved using the Gamma method with
y determined above to be 3.7. Likewise, figures 21-23 display the comparison for
the month of June, and figures 24-26 show the case for July. All of the plots have
contouring intervals of 1°C.
39
Esbenun Xushnir Climatology
SEA SURFACE TEMPERATURE
MAY
GL: 21.553
SST
NH: 21 .553
SH: IE1O
NIH: 12.52
MAX: 28.1
5 OI
4 5I
4 Ot
3 5N
3 ON
2 5N
2 ON
1 5N
iON
Fl I
4 lW
CON= 14
30W
15
16
17
18
19
20
21
20W
22
23
24
25
26
27
28
Figure 18 May SST Climatology
lOW
40
SST(°C) for may83
50
LAT
16
30
F20
20
10
01-
40
-25
I
25
Figure 19 Retrieved SST Field for May 1983
LON1°
41
SST(° C) for may84
50
LAT
40
19
30
18
---- 22
-21 23
20
2
10
27
0
40
25
Figure 20 Retrieved SST Field for May 1984
LON1°
42
Esbensen Kushnir Climatology
SEA SURFACE TEMPERATURE
JUN
SST
GL: 22.546
NH: 22.546
514: 1E1O
MIN: 13.97
MAX: 27.67
5 ON
4 5N
40N
3 SN
3 ON
2514
2 ON
1 5N
iON
5N
40W
CON= 14
30W
15
16
17
18
19
20
21
20W
22
23
24
25
26
27
Figure 21 June SST Climatology
lOW
43
SST(UC) for june83
50
-
LAT
-1516
19
18-
30L
n
20
10 H
------ 28
0.
40
-25
Figure 22 Retrieved SST Field for June 1983
LON1°
44
SST(UC) for june84
50
LAT
-18
-2040
/9
30
20
10
27
iI
40
25
Figure 23 Retrieved SST Field for June 1984
LON1°
45
Esbensen Kushnir Climatology
SEA SURFACE TEUPERATURE
JUL
SST
CL: 23.538
NH: 23.538
SH: 1E1O
MIN: 16.74
MAX: 27.56
5 ON
4 5N
4 ON
3 5N
3 ON
2 5N
2 ON
1 5N
1 ON
5N
40W
CON= 17
30W
18
19
20
21
22
23
24
20W
25
26
27
Figure 24 July SST Climatology
lOW
46
SST(°C) for july83
50
LAT
40
20
30
20
10
7.-
.-.-.-.--- j).,
-40
25
Figure 25 Retrieved SST Field for July 1983
LON1°
47
SST(°C) for julv84
50
LAT
40
30
I::
19
JEEII'7
20
20
21
23
2
10
-29
0
40
25
Figure 26 Retrieved SST Field for July 1984
LO N
10
48
The key point from these figures (18-26) is that SST retrievals using the
empirically-determined -y agree quite well with the E-K climatology in terms of
absolute values of SST and also in terms of the relative features (gradients), with
the notable exception of the region off the Western coast of Africa. It is believed that
this exception may be explained in terms of contamination by Saharan dust. May et al.
(1992) studied the effects of desert silicates in the lower and middle troposphere for
precisely this region during the summer of 1990. They found a typical situation with
a dust optical depth maximum just off the African coast, decreasing westward (due to
advection by the prevailing easterlies) in the subtropical Atlantic. These investigators
found that dust contamination- led to cold biases in satellite-derived SSTs of greater
than 1°C for both the MCSST and cross-product (CPSST, Walton, 1988) retrieval
algorithms. Apparently, the Gamma method suffers from a contamination bias of the
same source and magnitude.
49
Channel 4 deficit (°C) for may83
50
LAT
30
10 L:-
6 -_
or
40
25
LO N
Figure 27 Applied Channel 4 Temperature Correction for May of 1983
To demonstrate that the corrections applied to measured brightness temperatures
are non-trivial, one example is shown of a contour of the correction field. Figure
27 shows the retrieved channel 4 brightness temperature deficit (LTA, channel 4)
for the entire ASTEX region, averaged over the month of May, 1983. Since this
deficit is generally a function of water vapor path, it is not surprising that the
majority of the contour plot is similar to the water vapor contour shown in figure
11. Again, disagreement is found off the Western coast of Africa, due presumably
10
50
to dust contamination.
51
5 Variability in Gamma
Finally, focus is returned to the band-type radiative transfer model to explore
possible explanations for the variability that was found in the empirically-derived -y.
The satellite viewing geometry is recreated in the model. The method is tested first
for the 'ideal' case. No SST gradient is applied, and pathlength changes are due solely
to viewing angle. The result is unanticipated.
-r - -
- -
IWF)IL.J1
iMil
r-. - -
I WIII
Retreved7=6.130
125
110
Dashed line represents 7line retrieved by the method
1051 Solid liges represçnt true 7-line reloionships fpr individ
0
2
4
( (mW m1srcm)
Figure 28 Model recreation of a Gamma Plot for the Tropical climatology atmosphere
In figure 28, calculated radiances from each viewing angle from a typical
procession of subframes are plotted and connected to the surface emittance (and
corresponding value of 14(81)
I(s1) = 0) with a line of slope
-y.
Variations in
-y are due to the different pathlengths and hence water vapor amounts. When the
52
individual points are regressed as a straight line, the slope of that line is not very
close to any of the values of y. Worse, the value of surface emittance that would be
retrieved using the method exceeds the true surface emittance greatly, resulting in an
SST error of more than 5°C.
The problem with the method appears to be that, in the moist tropical climatology, -y varies with water vapor nearly as much as does the 14(31)
1(s1) variable.
m,u
7 = 3.570
Midlatitude Profile
98
:
S..
S..
H
'S
97
j96
:
95
E
*
94
93
Dashed line represents 7line retrieved by the method
92
0.0
pild )ine
represent frue,7ljne ielaionhip for, indjv
0.5
ll
1.0
1.5
2.0
(mW m's('cm)
Figure 29 Model recreation of a Gamma Plot for the
Middle-Latitude climatology atmosphere
In drier atmospheres, this problem is less pronounced. The error in retrieved
SST for the Middle-Latitude climatology atmosphere (shown in figure 29) is less than
1°C. For the Arctic case (figure 30), the SST error is negligible.
53
Arctic Profile
48.70
Retrieved 7 = 4.230
48.60
48.50
...
E
-Q
48.40
E
E
48.30
48.20
48.10
0.00
Dashed line represents 7line retrieved by the method
oli liges repfesnt ,tru 7-lige rIa1iionhips fpr idiyidaI
0.02
0.04
I4
0.06
I
0.08
0.10
0.12
(mW msr1rn)
Figure 30 Model recreation of a Gamma Plot for the Arctic climatology atmosphere
In terms of water vapor profiles, the ASTEX region falls somewhere between
the tropics and middle latitudes. This is evident from geography, but is supported
as well by measured values of 14(81) - I(s1) in comparison with the model results.
Thus, it is likely that the estimate of 'y from figure 9 is too high due to variations
in 'y with viewing angle, and the retrieved SST fields are likely too warm. From the
comparisons with the E-K climatology, it seems that the warm bias in SST is probably
more similar to the middle latitude case (#.il°C) than to the tropical case ("-5°C).
With the note that y is quite sensitive to changes in viewing angle, the model
is then used to test the sensitivity of the method to gradients in SST. The middle
latitude atmosphere is used. As in the above plots, five successive viewing angles
are included which span approximately four degrees of longitude across the satellite
54
swath. The viewing angles are 17.72°(defined as near-nadir), 27.83°, 32.94°, 38.19°
and 43.54°(near-limb). The applied SST gradient is linear in distance. The gradient is
chosen to be in the same direction as the scan, to maximize the effect of the gradient
on the retrieved value of y.
Midlotitude Profile
93.6
5.100
Retrieved
93.4
93.2
E
L)
I-
r' 93.0
E
E
-
92.8
92.4L.
1.30
1.35
1.40
I4
I
1.45
1.50
1.55
(mW mrcm)
Figure 31 Model Gamma Plot, Middle-Latitude climatology, SST Gradient
Figure 31 shows the effect of an SST which increases by a total of 0.1°C from
near-nadir to near-limb. Here, the retrieved value of y would be overestimated by
about one half, relative to the zero-gradient case. The SST error would be more
than 2°C. For the plot in figure 32, the gradient is reversed (warmest at near-nadir).
Relative to the zero-gradient case, the value of
would be underestimated by about
one third, and the retrieved SST would be cold by roughly 1°C.
55
93.60
I
Midlatitude Profile
I II,II1IJIIIIlII.1J.II1lI..I
Retrieved y = 2.290
93.50
93.40
E
93.30
E
E
93.20
93.10
93.00
1.30
,I,
1.35
..
I
1.40
I4
1.45
1
1.50
1.55
1.60
(mW mrlcm)
Figure 32 Model Gamma Plot, Middle-Latitude climatology, Reversed SST Gradient
Compared to the gradients observed in figures 18-26, it seems that the gradients
required to cause the observed variability in the retrieved y are not very large at all.
However, the gradients applied in the model were perpendicular to the sub-satellite
path (i.e., the gradient were in the direction of the scan, roughly east to west), which is
not typical of large-scale SST fields. Note the bias toward overestimating SST. Since
the satellite scans in both directions, over six months worth of data, it is reasonable to
assume equal frequencies of positive and negative gradients with regard to scan angle.
Again, 'y would tend to be overestimated by the method.
56
Section 7:
View Angle as an Independent Variable
Obviously, view angle is a very important variable for the method employed
here. The preceding statistical analysis treats view angle as an
independent
variable.
Thus, it seems wise to verify that this variable is not systematically dependent on the
geometry of the orbital relationship between the satellite and geographic location. In
other words, if there is a systematic relationship between view angle and geographic
position, then certain regions of the ocean with persistent SST gradients might yield
incongruous gamma plots, making the method inappropriate for such regions. Figure
13 suggests that just such a relationship may exist between view angle and latitude.
The figure, however, shows only a small sampling of view angles and geographic
positions, as restricted by the criteria imposed by the method.
To ascertain that view angle is not systematically dependent on geographic
position for the 1983/84 ASTEX data set, all of the cloud-free observations for
individual sub&ames have been gathered into a single data file, recording the view
angle, latitude, and longitude. Over 300,000 subframes had cloud-free radiances.
A random sampling of ten positions (defined as 1° by 1° latitude x longitude
regions) has been selected, for which the frequency histogram of view angles has been
computed. The results are presented in figures 33-42.
57
k4.....,.... 4...
1.0
Afll lc.w
I
0.8
r
0.S
0.4
0.2
I
-40
-40
_____________
-20
0
20
40
00
Figure 33 Frequency Histogram of View Angles, First Geographic Position.
I
F
-40
-40
-20
0
M41.
20
40
00
Figure 34 Frequency Histogram of View Angles, Second Geographic Position.
,
Figure 35 Frequency Histogram of View Angles, Third Geographic Position.
58
I
-40
-40
-20
0
20
40
40
Figure 36 Frequency Histogram of View Angles, Fourth Geographic Position.
I
I
I
-40
-
Figure 37 Frequency Histogram of View Angles, Fifth Geographic Position.
I
E
I
I
Figure 38 Frequency Histogram of View Angles, Sixth Geographic Position.
59
I
E
I
.-. _.,_
Figure 39 Frequency Histogram of View Angles, Seventh Geographic Position.
I
I
I
Figure 40 Frequency Histogram of View Angles, Eighth Geographic Position.
I
I
I
-40
-20
0
20
40
SO
Figure 41 Frequency Histogram of View Angles, Ninth Geographic Position.
I
I
-
-40
20
0
Ms
Figure 42 Frequency Histogram of View Angles, Tenth Geographic Position.
61
From figures 33-42, it seems that, when there are more than a few cloud-free
observations for a particular location, the distribution of view angles from which the
location is observed is not systematically exactly predictable. Neither however, is
it obvious that there is no bias toward certain view angles for particular geographic
locations. The number of observations is not sufficient to make statistical conclusions
about the lack of such a bias. Certainly, as figures 33 and 42 attest, some locations
are rarely identified as having cloud-free pixels over the observed months. However,
this is particular to either the location (frequently cloudy during the season of the
observations) or the cloud retrieval algorithm, and is not indicative of a systematic
dependence in the view angle variable on geographic location. Note that the locations
for the two sparsely populated histograms are nearly adjacent.
For the purpose of this analysis, it does not seem inappropriate to treat view
angle as an independent variable.
62
Section 8: Conclusion and Recommendations
Many radiative transfer models have shown that the "thin approximation" made
in the derivation of linear regression models for SST retrievals is invalid for moist
atmospheres such as those found in the tropics. Walton (1988) did this by showing a
dependence of 'y on water vapor amount McMillin and Crosby (1984) defined 'y and
showed that it is constant when the thin approximation holds. This model result has
been reproduced here by using satellite zenith angles to modify the total water vapor
path (y depending on zenith angle, especially in the tropics). Further, the dependence
of y on zenith angle has been shown here using just satellite data and the condition
of a uniform SST over small regions.
For the relatively few 5° by 50 latitude-longitude regions where there were
sufficient cloud-free observations over a uniform SST field, the empirically-derived
value of y
3.7 ± 1.7 for the ASTEX region is in agreement with model predictions
for similar latitudes/total water vapor paths. Also, since variations in the secant of
the viewing angle dominate the variations in total water vapor paths, a dependence
of y on total water vapor path has been found that agrees qualitatively with what the
models have predicted. This dependence is only evident when the most restrictive
regression skill cutoff has been applied in rejecting non-uniform SST fields.
Unfortunately, despite the accumulation of six months of data from the NOAA 7
polar orbiter over a region spanning 40° of latitude and 30° of longitude, the number of
cases where a value of y could be determined was small (figure 9). The samples of 'y
were too small to constitute a statistical data set from which zenith angle, geographical,
or seasonal dependence could be confidently determined. Also, the 1992 data set for
63
NOAA 11 and 12 was nearly useless in terms of such an analysis, due to the few cases
which met the prescribed criteria. Nevertheless, the trends in the data for the highest
skill cases suggest that the models' results are supported by the satellite observations.
An evident drawback of the method applied here is that no
in situ
observations
were used to confirm assumptions that were inferred from satellite measurements about
the underlying SST fields; i.e., was the SST field truly uniform when the method
objectively determined it to be so? The attempt to show the dependence of
on water
vapor path using satellite data only was motivated by the problems associated with
satellite/ship 'match-ups' of SST, including skin/bulk temperature differences, and
the problem of defining 'coincident' measurements. This approach brought about the
necessity for assuming that the SST field was sufficiently uniform to apply the method
described above, and the lack of
significant
statistical conclusions is apparently due
to the relative scarcity of such uniform SST fields. The use of in
situ
observations in
conjunction with the method would alleviate the restrictions placed on the data by the
uniform SST criterion, and likely make statistical analysis more meaningful.
Within the limitations of the data analyzed, the assumption of uniformity
has been shown self-consistent, considering gradients in the retrieved SST field
for the accepted cases (figures 15-17) versus that found in data rejected due to
presumed nonuniformity (figure 14). The monthly mean SST fields retrieved using the
empirically-derived 7 compare favorably to the in-situ climatology, except in the same
region where other satellite infrared SST methods also fall due to dust contamination
(the dust problem is a separate one, relative to the at-hand issue of correcting for
water vapor).
The sensitivity of y to changes in water vapor path exceeded expectations,
however. Application of the method to radiative transfer model-simulated radiances
yielded the result that -y would tend to be overestimated, particularly in the most moist
atmospheric conditions. The sensitivity of the method to gradients in SST was also
explored. It was found that even relatively slight SST gradients could cause significant
errors in the estimation of -y, with a bias toward overestimation. Both of these effects
on the value of 'y retrieved by the method could be eliminated by the use of in situ data.
Simple linear and non-linear methods of regression to predict brightness temperature deficits based on differences in brightness temperatures from different wavelengths may be valuable in terms of operational efficiency and root mean square error
for sampled regions. However, these regression relationships are representative only
of the regions in which buoy or ship data have been collected for model 'truth', and
the most humid regions of the globe (e.g., western tropical Pacific) may not fit these
models very well at all.
Future attempts to 'match-up' satellite observations with surface-based SST
measurements should consider direct application of equation (18), from which
may
be determined. This y is more physically meaningful than regression coefficients, and
appears to be functionally related to the
total
water vapor burden of the atmospheric
path through which the sensor measurements are attenuated. In particular, attention
should be focused on moist atmospheres where variations of water vapor path with
view angle are most pronounced, and where the thin approximation is apparently not
valid.
Without dedication to the use of in situ observations to confirm and calibrate
65
space-borne methods, the geophysical sciences will not be best served by satellite
technology.
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