Infrared sensing of sea surface temperature from space

Infrared sensing of sea surface temperature from space

REMOTE SENSING OF ENVIRONMENT 10:101-114(1980) 101 Infrared Sensing of Sea Surface Temperature from Space MIRIAM SIDRAN Department of Natural Scie...

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REMOTE SENSING OF ENVIRONMENT

10:101-114(1980)

101

Infrared Sensing of Sea Surface Temperature from Space

MIRIAM SIDRAN Department of Natural Sciences, The Bernard M. Baruch College of the City University of New York, 17 Lexington Avenue, New York, New York 10010

Error sources in infrared remote sensing of sea surface temperature are discussed, e.g., impedect transmittance models, uncertain or unknown atmospheric pressure-temperature-humidity vertical profiles, temperature discontinuities at the air-sea interface, temperature differences between surface and bulk water, and neglect of surface emissivity and reflectance. Some of these are analyzed using a simplified version of the transmittance function of Prabhakara et al. (1974). The rms error in conventional sea surface temperature retrievals, in which computers are used to integrate the equation of radiative transfer over many atmospheric layers, has thus far been reduced to about +_ 1 K (Maul, 1980). This error is for o p ~ n u m conditions, and seems irreducible. Unless the accuracy can be improved, it seems impractical to spend so much effort on lengthy computer retrievals. Prabhakara et al. (1974) have devised a much simpler retrieval method using three infrared bands, which yields an rms error of -+ 1.1 K. A very simple method yielding _+ L0 K with two infrared bands is described here.

Introduction

A prime task of meteorological satellites is to map the sea surface temperature T~. Such satellites now routinely gather multiband infrared data from which Ts may be determined within about 1 K, under optimum conditions with current procedures. This accuracy is acceptible for some applications, but only marginally useful for others. It is also difficult to achieve. The chief absorber of radiation in the atmospheric window between wavelengths X = 8 # m and 14 /~m is water vapor. The atmospheric transmittance is the fraction of the spectral radiance emitted by the sea which reaches the satellite after partial absorption by the atmosphere. To retrieve T~ from the signal /sat received in one spectral band by the satellite sensor, T must be found as a function of the amount of water vapor in the atmosphere. Various transmittance ©Elsevier North Holland Inc., 1980 52 Vanderbflt Ave., New York, NY 10017

functions have been used by different investigators, e.g., Anding and Kauth (1970) and Selby et al. (1976). Maul et al. (1978) used the ~ function of Davis and Viesee (1964) to quantify Ts gradients across current boundaries. This function does not include effects of temperature on water vapor absorption. In the work presented here, a temperature-dependent function is used: it is a simplified version of one due to Prabhakara et al. (PDK) (1974). Transmittances obtained with this function agree with those of Maul et al. (1978) within the standard deviation of their results. To retrieve Ts, the surface spectral radiance eBs is computed from the received signal Isat as described below. Here, e is the surface emissivity, and B~ is the spectral radiance of a black body at temperature T~. The received portion I ~ of eB~ is TeB,. Atmospheric water vapor not only absorbs part of eBb, but further contaminates Isat by contributing its own 0034-4257/80/000101 + 14501.75

102

MIRIAM SIDRAN

thermal radiation, i.e. I ~ and /ref in Eq. (1). Thus, Isa t is the sum of three terms. I=t = I~a + I~r + Iref,

I~a='ren,.

(1)

Here, I ~ is the received portion of the upward spectral radiance of the atmosphere after emission and absorption by its successive layers. The downward atmospheric spectral radiance, reflected upward at the sea surface, and attenuated in its path to the sensor, contributes the small term I ~ . Equation (1) is a simple form of the well-known equation of radiative transfer which is discussed below. Ideally, ~, la~, and Iref are found from the measured vertical profile of pressure, temperature, and relative humidity (PTRH). Since Isa t is known, Eq. (1) may be solved for Bs, from which Ts may be found by inverting the Planck function (Lowan and Blanch, 1940). In this report, the magnitudes of the terms in Eq. (1) are evaluated, and their contributions to the error in T~ retrieval assessed. Calculations involving the PTRH profile are costly and complicated. It is therefore convenient to simplify Eq. (1) by assuming that the sea radiates as a black body, i.e., that e = 1 throughout the 8-14 gm window, so that the reflectance ( l - e ) = 0 , and the term Iref vanishes. Most T, retrieval programs use this assumption. In this work, the consequences of the assumption are analyzed. Actually, e~0.99 in the window, and varies slightly with wavelength. Usually the PTRH profile and total moisture content are unknown. In that case, two or more infrared bands may be used to self-correct for water vapor effects, but the results are less accurate

than with a known profile, and the calculation is longer and more complex. Thus, one should seek a more suitable method. One simple retrieval scheme suggested by PDK (1974) requires no knowledge of the PTRH profile, or of the total water content of the atmosphere. PDK used data for eight cloud-free locations viewed by the Nimbus-4 satellite in three infrared bands. Their method, which is described here, gave the sea surface temperature T~ for each location with an rms error of -_+1.1 K. This paper presents an even simpler retrieval scheme which gives comparable accuracy with two infrared bands.

The Transmittance Function

In the 8-14-gm window, atmospheric scattering is negligible, so that attenuation is due primarily to water vapor absorption (McClatchey et al., 1972). The transmittance of a uniform gas in a given spectral band is actually the product of three quantities, %, zp, and Zl. Here, % and zp refer to the water vapor continuum, and zl refers to the water vapor lines. PDK (1974) tabulated values of these quantities for three infrared bands. for various values of temperature T and precipitable water vapor w; from these they found the products ~. We have used these data extensively. Their three bands, called channels 1-3, were centered at 803, 859, 923.5 cm-1. The corresponding bandwidths were 56, 56, and 73 cm-I. Continuum absorption, i.e., absorption in the wings of strong water vapor lines which peak far outside the window, is associated with collision broadening of the distant lines. Molecular line shapes are imperfectly understood in the con-

INFRARED SENSING O F SEA SURFACE T E M P E R A T U R E

tinuum region. Therefore, the coefficients for continuum absorption used in these transmittance quantities are only approximate. Additional measurements are needed to specify their temperature and spectral variations more precisely. However, since transmittance functions are needed for remote sensing, these coefficients are used despite their inadequacies. The quantity % refers to the component of continuum absorption produced by water-water collisions. PDK found the % values for each spectral band by means of Eq. (9,).

1-e=exp(-ekew),

103

vapor amount in g cm -~ of atmospheric path. The coefficients k¢ were measured by Burch (1970) for a temperature T = 296 K. These were found by Bignell (1970) to decrease 2% per 1 K rise in absorber temperature, i.e.,

k.(T)=k~(B96)[1-O.O2(T-296) ]. (3) The water vapor partial pressure e is proportional to w, i.e., e=sw, with s constant. Thus, %(T) = exp[ -b(T)w2],

in which b(T)=ske(T ). Values of the coefficients b, computed from the PDK (1974) table are listed in Table 1. Selby et al. (1976) used an equivalent form of %, with different notation and

(2)

in which e is the water vapor partial pressure in bars, and w is the water

TABLE I Comparison of transmittance values computed from Eq. (6) with those of PDK (1974). Pressure = 1030 rob. CrL~rm~ 1, T = 300 K a=0.1924 b = 0.04074

CrmNNEL 2, T = 3 0 0 K a =0.1038 b = 0.03036

CrmNNEL 3, T = 3 0 0 K a =0.0560 b = 0.02424

W

T

T

T

T

T

T

g cm - s

Eq. (6)

PDK

Eq. (6)

PDK

Eq. (6)

PDK

0.5 1.O 2.0 3.0 4.0 6.0 8.0

0.879 0.792 0.622 0.458 0.314 0.118 0.032

0.875 0.790 0.622 0.459 0.314 0.117 0.932

0.931 0.874 0.748 0.608 0.468 0.233 0.092

0.933 0.874 0.749 0.608 0.468 0.2.33 0.091

0.960 0.923 0.829 0.712 0.585 0.343 0.167

0.962 0.924 0.828 0.713 0.585 0.343 0.167

CrL~C~L i, T = 280 K a •0.1557 b = 0.05845

(4)

CrL~7~_~ 2, T = 2 8 0 K a =0.0800 b = 0.04356

Crt~'Nm~ 3, T = 280 K a =0.0436 b = 0.03479

W

T

T

T

T

T

T

g cm - 2

Eq. (6)

PDK

Eq. (6)

PDK

Eq. (6)

PDK

0.5 1.0 2.0 3.0 4.0 6.0 8.0

0.895 0.807 0.615 0.422 0.260 0.071 0.012

0.893 0.805 0.615 0.423 0.261 0.070 0.012

0.945 0.884 0.738 0.569 0.403 0.157 0.044

0.946 0.886 0.738 0.568 0.492 0.156 0.044

0.965 0.925 0.811 0.666 0.510 0.245 0.090

0.968 0.927 0.812 0.665 0.510 0.244 0.089

104

MIRIAM SIDB.AN

units. Their equation for the temperature variation of the coefficients ke, found empirically by Roberts et al. (1976), is based on more recent measurements than Eq. (3), but yields similar k e values. The quantity ¢p is associated with that component of the continuum absorption produced by collisions of H 2 0 with other molecules. Hence it depends on total pressure P; i.e.,

%=exp(-kpwP),

To find the vertical transmittance of the atmosphere, the gas is assumed to consist of N layers, each with a small moisture content w, and r is computed from Eq. (6) for each layer. The transmittance r, of the nth layer depends on w,, and on the coefficients a , and b, evaluated for the average P and T values in the layer. The total transmittance of the atmosphere is the product of the N values of %.

(5) N

in which k v for each spectral band is a function of T. Both PDK (1974) and Selby et al. (1976) used ¢p functions equivalent to Eq. (5). The quantity ¢t is associated with absorption by lines which peak within the window; thus Tt varies strongly with wavelength. In computing the ¢1 values, PDK (1974) performed a line-by-line integration using a statistical band model to find mean intensities, halfwidths, and spacing of spectral lines in each channel. PDK's form of ¢1 is relatively complex. In these investigations, it was empirically found that the products Cpzt of the PDK (1974) tabular values may be represented by the single expression exp(-aw°'7), in which a=a(e,T). Some values of the coefficients a are presented in Table 1; other values are found by interpolation. The total transmittance is given by Eq. (6).

r=%~'pzl=exp(-aw°'7--bw2).

(6)

This applies to laboratory conditions, and to relatively short atmospheric paths for which the gas is nearly uniform. Equation (6) accurately reproduces the PDK r values, as shown by the data in Table 1.

' / ' = 1"I "/'n='1"I~'2'/'3 . . . "TN. n=l

(7)

Details of the calculation for a thousandlayered atmosphere are described by Maul and Sidran (1973). Transmittance of a Model Atmosphere

The transmittance of the 15 ° North Annual U.S. Standard Atmosphere (1972) was computed from its PTRH profile by means of Eqs. (6) and (7). Surface values of PTRH were P--1013.25 mb, T= 299.65 K, and RH--75%. The total precipitable water vapor w = 4 g cm -~ in the vertical column. This atmosphere was selected because (a) its PTRH profile exhibits minimal seasonal fluctuation, which permits a rough comparison to be made among results obtained in this region by different investigators, (b) it has few discontinuities in vertical structure, which simplifies programming, and (c) the meridian of 15 ° north latitude transects an area of interest in weather formation. To find z for other w values, all relative humidity values in the standard atmosphere profile were multiplied by w/4. Since the temperature of a gas

INFRARED SENSING O F SEA SURFACE TEMPERATURE i

i

i

105 I

I

0.8 5

Li.I

o0.6 Z

I..mO.4 Z

re,

t..0.2

I

I

I

I

I

I

2

5

4

5

w ( g - e r a -z ) FIGURE 1. Transmittance ¢ computed for the adjusted model atmospheres, as a function of total precipitable water vapor w.

varies adiabatically with moisture content (Hess, 1959), the T profile was also adjusted. For example, at the air-sea interface, the air temperature would vary between 302.5 K for dry air and 298.9 K for w = 5 g cm -2. Values of • for the PDK channels 1 - 3 were found using these modified PTRH profiles; they are plotted in Fig. 1. Comparison

of

Transmittance Results Transmittance results found by different investigators are model-dependent (Maul and Sidran, 1972). However, Eqs. (6) and (7) give r values which are roughly equivalent to those found with some other r models. Selby et al. (1976) computed the transmittance of the 15°N standard (unmodified) atmosphere using a temperature-dependent r fimction whose form resembles that of PDK (1974). From their graph, we estimate their transmittances

to be 0.23, 0.42 and 0.52 in three infrared bands with the same central wavelengths as channels 1-3. These results are not exactly comparable with ours because the bandwidths were only 25 c m -1. Earlier computer programs used by these authors yielded slightly higher or lower z values than these. The authors state that their present computer program (LOWTm~ IV) tends to overestimate r for atmospheric paths with high moisture content; this would apply to the standard 15°N atmosphere for which w = 4 g cm -2. In Fig. 1, our z values for this atmosphere are 0.15, 0.37 and 0.58 for channels 1-3. The channel 2 transmittances of Fig. 1 were compared with values of r found by Maul et al. (1978) for a channel 25-cm-1 wide, centered at 862 cm -x. These authors used the Davis and Viesee (1964) function to find transmittanees of ten c l o u d - f r e e atmospheres from their monthly mean PTRH profiles. The range of surface temperatures was 16 K; how-

106

MIRIAM SIDRAN

TMILE 2 Comparison of channel 2 transmittance values computed for the adjusted model atmospheres with those computed from Eq. (8) of Maul et al. (1978) w (g cm -e)

T, (X)

r Eq. (6)"

Eq. (8)

0.5 1.0 2.0 3.0 4.0 5.0

302.1 301.8 301.1 300.3 299.6 298.9

0.794 0.688 0.544 0.445 0.370 0.312

0.835 0.739 0.575 0.449 0.361 0.311

"Integrated over the layers of the atmosphere by ir~ans of Eq. (7).

ever the r function does not include a temperature dependence. They found a simple relationship for T versus w by means of a least squares fit of the data,

• =d+fw+gw 2.

(S)

In Eq. (8), d=0.941, f = -0.021, and g-0.019. In Table 2, transmittances obtained from Eq. (8) are listed with our channel 2 results from Fig. 1. The two sets agree within ± 7%. The agreement is much closer for the large w values common in the tropics. Three of the atmospheres used by Maul et al. (1978) were at low latitudes, i.e. between 13°N and 18°N; standard deviations for these were between 4 and 9%, i.e. lower than for the other atmospheres. The two v sets agree within these limits. Calculation of Emissivity Equation (1) includes sea surface emissivity e. Emissivities of smooth and rough water surfaces were computed using the equations of Parker and Abbott (1964). Input data were complex indices of refraction tabulated by Hale and Querry (1973). Slope distributions for rough water surfaces as a function of wind speed were

those of Cox and Munk (1954). The emissivities were found to be independent of surface roughness up to wind speeds of 14 m sec-1. Although the small term Iref in Eq. (1) was found to change slightly with surface roughness, this effect only changed the retrieved surface temperature Ts by less than 0.04 K. Therefore, in the ensuing discussion, the sea is assumed to be a fiat radiator and reflector.

The Equation of Radiative Transfer In Eq. (1), I ~

is the integral of

Ba(Ta)d1"', between the limits z'=~ at the air-sea interface and z ' = 1 at the top of the troposphere, i.e., 1

fJz Bo(To)d

P o

(The upper atmosphere is neglected, since it contains no significant amount of water vapor.) B~ is the upward spectral radiance, computed from the Planck function, of an infinitesimally thin air layer with temperature Ta. A constant B, may be found such that

I~=~IB,,d~"=Ba(1-~-);

(9)

/~a is the weighted mean upward spectral radiance of the troposphere. The solution of Eq. (9) is described by Maul and Sidran (1973). The downward spectral radiance reaching the sea surface is the integral of B,(Tr)d1"" between the limits z " = ~ at the top of the troposphere, and ~" = 1 at the bottom. B, is the downward spectral radiance of an infinitesimally thin air layer with temperature Tr. A fraction ( l - e ) is reflected upward, and a smaller fraction z ( 1 - e) is received by the sensor.

INFRARED SENSING O F SEA SURFACE T E M P E R A T U R E

Thus the received spectral radiance Iref= Z(1 - e ) ~ l B ~ ( r ~ ) d ~ "" due to reflection. A constant /~ may be found such that

flg,

"

= ~ ( 1 - e ) ( 1 - ~)/~;

(10)

D

B, is the weighted mean downward spectral radiance of the troposphere. The equation of radiative transfer (1) now takes the form

I~t=reB,+&(1-r ) +r/~(1- r)(1-e).

(11)

Selby et al. (1978) have graphically described the procedure for finding the last two terms in Eq. (11) for a three-layered atmosphere. With the black-body assumption e = 1, Eq. (11) is reduced to its more familiar form (e.g., Craig, 1965). Solving Eq. (11) for B~ yields

Bs= Isat-Ba(1 -'r) - z/~(1-r)(1-e)

,

(19.)

from which T, may be found by inverting the Planck function. Spectral Radiances and Temperatures in Remote Sensing The spectral radiance terms in Eqs. (1) and (9)-(11) were evaluated for vertical viewing of the sea surface through the adjusted model atmospheres. At the surface, air and water temperatures were

107

assumed the same. The radiance terms are plotted in Fig. 2(a-c) as functions of w. Sea surface emissivities, given in Fig. 2, were used to generate the solid curves; the dashed curves are for the black-body assumption e = 1. Although numerical values of the spectral radiances may be model dependent, the conclusions are independent of the model. Figure 2 shows that I~a decreases and I ~ increases with increasing w. For large w values, the air contributes more than the sea to the signals received in the more absorbent channels, 1 and 2. This tends to cause large errors in retrieved T~ as explained below. The temperatures T~ and Tsa t a r e plotted in Fig. 3(a-c) as functions of w; each Tsat corresponds to the total spectral radiance/sat received by the sensor. Also plotted are the temperature depressions A T d, defined by

Ts=T t+aTd.

(13)

When the correction term A T a is large, its contribution to the error in Ts is proportionately large; this occurs for large w in the longer wavelength channels, 1 and 2, as shown by Fig. 3. The black-body approximation e= 1, represented by the dashed curves of Figs. 2 and 3, underestimates the correction term A T d in Eq. (13), and therefore also the retrieved temperature Ts. The error has two components: setting Iref=0 in Eqs. (11) and (12) contributes a small positive error to AT, t, while setting I ~ = zBs contributes a larger negative error. The net error, 0T~, is negative; it is the difference between the dashed and solid curves of A T a. Its absolute value, [0T, I, is also plotted in Fig. 3(a-c). As w increases, the error 0T~ goes from - 1 . 4 K

108

MIBIAM SIDBAN

'_

%-

....

Bs

EBs

4

Iso!

~ 2L Z

V

CHANNEL I

'~ I

)" = 12,0- i2.9/.tm

I sea f'f)

I

I

I

2

:3

I

1

4

5

I

I

W ( g - c m -2 )

(a) I

f

I

'E:¢ 5 TI

4- ~\

"

" ~

"~\ 3" ~ ~ ~.

$ ¢r _J o:

I$ot

CHANNEL 2 v = 8 3 1 - 8 8 7 cm-I X = I I . 5 - 12.0/zm loir

2~

lsea

,

------E=I

I

I

i

2

I

3

i

4

I

,5

w ( g - c m -2 )

FIGURE 2. Spectral radiance terms in the radiative ~ Eqs. (1) and (11), computed for the adjusted model atmospheres, as a function of total precipitable water vapor w. Dashed curves are for e-- 1. I ~ is too small to be shown on this scale. (a) Channel 1. Co) Channel 2. (e) Channel 3.

INFRARED SENSING O F SEA SURFACE T E M P E R A T U R E I

•E

5

I

~-=.~-__-

109

I

I

I

B,

. . . . . . . . . . .

~,~.

~

Isa t

4

;3

CHANNEL 3 960 cm-I X= 10.4- 11,3 /zm

hl 0

v = 887-

z 2 n.-

E

~

/

~

Isea

/

Iair

------E--I - E = 0.993

i

I

2

I

I

3 4 w ( g - c m -2 )

5

(e) FIGURE 2.

I

I

Continued

I

!

I

20

302 18

30O \\

"

~

T$

16

298 ,v. 0

296 294

\,

14-~

1 1 / "~

292

12

a.

CHANNEL I

~ ~ .

---~--

I

~ ~ = 0 . 9 8 2

290

o

288

I0 8

1> .-I ~

6

~

4

286 284

-..

I~T~I I

Tsot

~

2

3

4

5

w ( g - c m -2 )

(a) FIGURE 3. Temperatures Ts and Trot computed for the ad|nsted model atmospheres, as a function of total precipitable water vapor w. Temperature depressions A Td from Eq. (13) versus w. Temperature errors 1OT,[ due to the black body approximation versus w. Dashed curves are for the black-body a p p r o ~ n a t i o n • ffi 1. (a) Channel 1. (b) Channel 2. (c) Channel 3.

ll0

MIRIAM SIDRAN

' ~ . .

'

'

'

'

20

'

502

300 ~ ' ~

18

" . ~

Ts

t6 ,4

ATd

i0 o

298 ; 296 I-~ 294 -o 292 -

_ CHANNEL 2 ---,-'1

290 288

-

/

o. ~ ~ /

~

-

~

Tso t

f l

286 . / j r /

"

I~T,I I

2

3

4

5

w ( g - c m -2 )

Co) i

i

i

I

I

20 302 18

3OO

"~-.

Ts

16 14 - ~

o

~

cO

12

294 292 290

I0

CHANNEL 3 ------E=I E = 0.993

8

288

ZXTd

o

--1 a.

I> -I ="

6 4

286

I~T,I

284

I

2

3

4

5

W ( g - c m -2 )

(c) FIGURE 3. Con~n,~_~

to zero in channel 1, from - 0 . 6 K to - 0 . 1 K in channel 2, and from - 0 . 5 K to - 0 . 2 K in channel 3. Thus the error is largest for the driest atmosphere, and for the channel with the smallest e, i.e., channel 1.

Maul (1980) has quantified the error due to neglecting reflection in the spectral band 25-cm-1 wide, centered at 862 cm-1. W e interpret his results as representing the combined error from both the above sources. In that case, his error

I N F R A R E D SENSING O F SEA S U R F A C E T E M P E R A T U R E

range of - 0 . 7 K to - 0 . 2 K is similar to our range for channel 2, although a different ~ function was used in obtaining them. For w > 1 g cm -2, 10T I is small relative to other errors cited below; for large w it is negligible. Thus in most cases of interest, the assumption e = 1 is useful in retrieving T~. These results can be extrapolated for other viewing angles 0. With increasing 0 > 3 0 °, e decreases sharply, while w increases with increasing path length. The increase in 10LI due to e is more than compensated by its decrease due to w. Thus for large angles, 0T~ is very small, except for extremely dry atmospheres.

111

further; no error estimate is available for this source. Instrument noise is small, amounting to -4-0.1 to ___0.2 K, depending on the sensor temperature (Smith et al., 1971). The Geostationary Operational Environmental Satellite (GOES), digitizes the transmitted Tsat values in steps of 0.5 K. The uncertainty in retrieved T, is therefore 0.5 K / ¢ for this satellite (Maul et al., 1978). For example the uncertainty in Ts for the standard (unmodified) 15°N atmosphere due to this digital Ts would be 1.4 K in channel 2. Considering all error sources, Maul (1980) concludes that T, may be retrieved with an rms error of about ± 1 K, using the best conventional techniques.

Sources of Error

Simple Retrieval Schemes Several important error sources were discussed above. Errors due to large w values, unknown P T R H profiles, and inexact ~"functions may be compensated by using model atmospheres, multiband measurements, and ground truth data from selected sites. Maul (1979; 1980) has performed a more inclusive error analysis than that described herein. There are several sources of error which cannot be compensated by improved P T R H profiles or ¢ models, or by more exact computer programs. Such errors may be estimated. For example, the sea surface radiates at a temperature T~, while ships sample the underlying water temperature Tw as ground truth; T w - T ~ is usually between + 1.5 and - 0 . 5 K. Maul (1980) estimates the rms error from this source to be ___0.4 to ___0.5 K. Another significant error source is the temperature discontinuity at the air-sea interface, which commonly amounts to ± 1 K to ± 2 K, but may range even

PDK (1974) reported a simple scheme for retrieving the sea surface temperature T, from the temperatures T~t observed in channels 1 - 3 by the Nimbus-4 interferometer. The temperature data, listed in Table 3, were for eight cloud-free locations with u n k n o w n P T R H profiles, for which surface temperatures were known from ship measurements. They assumed that the variation of A T a in Eq. (13) is nearly linear with w, i.e., A T d = k ( X ) w . However, k(X) is also a function of w, so that curves of A T a and Tat in Figs. 3 are not linear with w. Nevertheless, PDK chose a constant value k(X) for each band, such that the graph of Tsat(X) versus k(X) was nearly a straight line, whose temperature intercept gave the surface temperature Ts. T h e k ( h ) values for channels 1-3, chosen by a leastsquares fit, were 0.191, 0.131 and 0.104 c m 2 / g m . The rms error in Ts was + 1.1 K.

112

MIRIAM SIDRAN TABLE 3 Ship and satellite data for eight cloud-free locations used in retrieval of sea surface temperatures by the short method of PDK (1974). These data were also used in Eqs. (14)-(17) to retrieve sea surface temperatures. Tship values are sea surface temperatures measured directly from ships. Tsat (1), Tsar(2), and T,at(3) are temperatures corresponding to /sat values observed in channels 1 - 3, respectively, by the Nimbus-4 meteorological satellite.

r=t(1)

T=,(2)

r,,~(3)

(°N)

(°W)

(K)

(K)

(K)

(K)

41.0 36.6 44.6 39.4 15.1 19.7 11.0 35.6

62.5 60.9 37.1 69.1 144.7 82.6 53.5 33.8

272.9 284.5 280.9 286.9 292.7 291.2 287.8 281.2

275.2 286.9 283.1 290.6 294.9 294.2 291.7 283.8

276.8 287.9 284.0 291.8 296.1 295.6 293.4 285.0

281.0 290.5 287.0 296.2 301.2 301.5 300.5 291.0

LATITUDE

LONGITUDE

These Nimbus data were fed into our computer program which integrated Eqs. (9) and (10) over many atmospheric layers, using the z function of Eq. (6), and retrieved Ts with an rms error of _ 1.7 K. We then devised Eq. (14) which retrieves T, from the same data with an rms error of _ 1.3 K.

Ts--2Tsat(Z)- Tsat(1),

_ 1.0 K with the Nimbus temperature data from channels 2 and 3.

Ts=4.7Tsat(3)-3.7Tsat(2 ).

This accuracy is only slightly improved by using Nimbus data from all three channels, as in Eq. (17)

7: = 3.976T

1.2 Tsat(1 ).

(16)

(14)

in which T~t(3 ) and T~t(1 ) are the effective temperatures observed in channels 3 and 1, respectively. Equation (15), a modification of Eq. (14), reduces the rms error to + 1.0 K.

Ts=2.2Zsat(3 ) -

T~p

(15)

Equation (15) achieves a better result than our lengthy computer program, and matches the best obtained by conventional methods. It eliminates the need to integrate the equation of radiative transfer over numerous atmospheric layers using uncertain ~ functions. Although it applies only to data for these channels, in principle such a relationship could be found for any pair of infrared bands. For example, Eq. (16) yields an rms error of

,(3)- 2.329

- 0.6495T~t(1).

(17)

Here, the coefficients of the effective temperatures Ts~t were optimized by a least squares technique. The rms error is ___0.9 K. Summary and Conclusions A simplified version of the transmittance model of PDK (1974) was used to find transmittances of model atmospheres in channels 1-3. Results were compared with those found by Selby et al. (1976) and by Maul et al. (1978). The results depend on the transmittance model used (Maul and Sidran, 1972). Molecular line shapes in the continuum

INFRARED SENSING OF SEA SURFACE TEMPERATURE

113

region are not completely understood. use of m infrared bands increases the More laboratory m e a s u r e m e n t s are computation m-fold. needed to define the thermal and specUsually, Eqs. (9) and (10) are intral variations of the absorption coeffi- tegrated over many atmospheric layers, cients more exactly. Transmittances each of small moisture content, by means found by Maul et al. were within 7% of of high-speed computers to retrieve Ts. our values, while those of Selby et al. Such a retrieval with the Nimbus-4 data differed by larger percentages. of Table 3 yielded an rms error of ___1.7 The transmittances were used to com- K. PDK (1974) have suggested a simple pute spectral radiances and equivalent alternative, and we have devised an even temperahtres in channels 1 - 3 for various simpler one. Using Nimbus-4 data in Eq. vertical P T R H profiles. A l t h o u g h (15) or Eq. (16), the rms error in retrieved numerical results are model dependent, Ts is _ 1.0 K, which matches the best conclusions are i n d e p e n d e n t of the results obtained thus far by conventional model. Errors in remote sensing of T~ due methods. Such a m e t h o d could be found to imperfect • models and P T R H profiles for any two infrared bands. It could proincrease with atmospheric absorption, vide a viable alternative to the more being largest for long wavelength chan- complex procedures until and unless they nels and for large values of w. Errors due become more accurate, which is unlikely. to the assumption that the sea is a blackbody radiator increase with decreasing values of w and e; such errors are significant for longer wavelengths and for very References dry atmospheres. However in most cases Anding D. and Kauth, R. (1970), Estimation of interest, the black-body assumption, of sea surface temperature from space. Rewhich greatly simplifies the computation, mote Sens. Environ. 1:217-220. contributes little error to the result. Bigneil, K. J. (1970), The water vapor inOther significant errors are due to unfrared continuum. Quart. ]. Roy. Meteor certain values of temperature discontinuSoc. 96: 390-403. ities at the air-sea interface, and difBurch, D. E. (1970), Investigation of the abferences between surface and bulk water sorption of infrared radiation of atmotemperatures. With k n o w n P T R H prospheric gases. Publ. U-4784, Philco-Ford files, the overall retrieval error may be Corp., Aeronutronic Division, Newport reduced to ___1 K (Maul, 1980) by judiBeach, CA: p. 27. cious use of ground truth data for selected Cox, C. and Munk, W. (1954), Measurements sites. of the roughness of the sea surface from If P T R H profiles are completely unphotographs of the sun's glitter. ]. Opt. known, multiband measurements can be Soc. Am. 44: 838-850. used to correct for water vapor absorp- Craig, R. A. (1965), The Upper Atmosphere: tion, by means of suitable model P T R H Meteorology and Physics. Academic Press, profiles and selected ground truth temNew York, p. 282. perature data, b u t the accuracy is lower Davis, P. and Viesee, W. (1964), A model for than with known P T R H profiles. Without computing infrared transmission through ground truth data, the error may be as atmospheric water vapor and carbon dihigh as _ 3 K or _ 4 K (Maul, 1980).Also, oxide. ]. Geophys. Res. 69: 3785-3794.

114

Hale, G. M. and Querry, M. R. (1973), Optical constants of water in the 200-nm to 200-/xm wavelength region. Appl. Opt. 12: 555-563. Hess, S. L. (1959), Introduction to Theoretical Meteorology. Holt, Rinehart and Winston, New York, pp. 43-44. Lowan, A. N. and Blanch, G. (1940), Tables of Planck's radiation and photon functions. 1. Opt. Soc. Am. 30: 70-81. Maul, G. A. (1980), Sea surface temperature determination using infrared techniques, NOAA Technical Memorandum NMFSSEFC-9, Proceedings of Coastal Zone Color Workshop. U.S. Dept. of Commerce, Natl. Marine Fisheries Service, Miami, FL, pp. 39-40. Maul, G. A. (1979), Regional-scale sea surface temperature determination from the Geostationary Environmental Operational Satellite. Sixth Ocean Thermal Energy Conversion Conference, Conf-790631/1, U.S. Department of Energy, Washington, D.C. June 19-22. pp. 2C-2/1-2C-2/6. Maul, G. A., DeWitt, P. W., Yanaway, A., and Baig, S. R. (1978), Geostationary satellite observations of Gulf Stream meanders: infrared measurements and time series analysis. ]. Geophys. Res. 83: 6123-6135. Maul, G. A. and Sidran, M. (1973), Atmospheric effects on ocean surface temperature sensing from the NOAA satellite scanning radiometer. ]. Geophys. Res. 78:1909 1916. Maul, G. A. and Sidran, M. (1972), Comment on "Estimation of sea surface temperature from space" by D. Anding and R. Kauth. Remote Sens. Environ. 2: 165-169. McClatchey, R. A., Fenn, R. W., Selby, J. E. A., Volz, F. E., and Garing, J. S. (1972), -

MIRIAM SIDRAN

Optical Properties of the Atmosphere, Third Ed., Environmental Research Papers No. 411. Air Force Cambridge Research Labs., Hanscom Field, Bedford, MA, p. 24. Parker, W. J. and Abbott, G. L. (1964), Theoretical and experimental studies of the total emittance of metals. Symposium on Thermal Radiation of Solids. NASA SP-55, pp. 11-28. Prabhakara, C., Dalu, G., and Kunde, V. G. (1974), Estimation of sea surface temperature from remote sensing in the 11- to 13-/tm window region. ]. Geophys. Res. 79: 5039-5044. Roberts, R. E., Selby, J. E. A., and Biberman, L. M. (1976), Infrared continuum absorption by atmospheric water vapor in the 8-12 /tm window. Appl. Opt. 14: 20852090. Selby, J. E. A., Kneizys, F. X., Chetwynd, J. H., Jr. and McClatchey, R. A., (1978), Atmospheric transmittance/radiance: computer code LOWTRAN4. Air Force Geophys. Lab., Opt. Phys. Div. Proj. 7670, Hanscom AFB, MA, p. 10. Selby, J. E. A., Shettle, E. P., and McClatchey, R. A. (1976), Atmospheric transmittance from 0.25 to 28.5 #m: Supplement LOWTaAS3B. AFGL-TR-76-0258, environmental research papers No. 587. Air Force Geophys. Lab., Opt. Phys. Div. Proj. 7670. Hanscom AFB, MA, pp. 12-16. Smith, W. L., Abel, P. G., and Wool/, H. M., (1971), The high resolution infrared radiation sounder experiment. Nimbus-4 Users Guide, Section 3, p. 40. U.S. Standard Atmosphere (1972), Supt. of Documents, U.S. Government Printing Office, Washington, D.C. Received 19 September 1977; Revised 13 March 1980