simultaneous measurements of skin sea surface temperature and sea surface emissivity from a single...

Simultaneous measurements of skin sea surfacetemperature and sea surface emissivityfrom a single thermal imagery

Kyu Yoshimori, Sumio Tamba, and Ryuzo Yokoyama

A novel method, to our knowledge, to measure simultaneously the thermal emissivity and skin temper-ature of a sea surface has been developed. The proposed method uses an infrared image that includesa sea surface and a reference object located near the surface. By combining this image with skyradiation temperature, we retrieve both skin sea surface temperature and sea surface emissivity from thesingle infrared image. Because the method requires no knowledge of thermal radiative properties ofactual sea surfaces, it can be used even for a contaminated sea surface whose emissivity is hard todetermine theoretically, e.g., oil slicks or slicks produced by biological wastes. Experimental resultsdemonstrate that the estimated emissivity agrees with the theoretical prediction and, also, the recoveredtemperature distribution of skin sea surface has no appreciable high-temperature area that is due toreflection of the reference object. The method allows the acquisition of match-up data of radiometric seasurface temperatures that precisely correspond to the satellite observable data. © 2002 Optical Societyof America

OCIS code: 010.4450.

1. Introduction

The global temperature distributions of oceans thatare observed from satellite platforms are widely un-derstood as one of the basic indices for Earth’s envi-ronments. In the current status, the achievedaccuracy of satellite-derived sea surface temperature�SST� is of the order of 0.3–0.6 K,1 but this situationhas remained almost unchanged for more than adozen years. Various disturbances involved in sat-ellite observations need to be corrected to improvethat accuracy. The atmospheric effects are, ofcourse, the largest disturbances in satellite-derivedSST, but there are other substantial disturbancesincluding sea surface emissivity and bulk-skin tem-perature differences.

The satellite-derived SST is currently estimated bysome empirical relationships between observed

K. Yoshimori �[email protected]� and R. Yokoyama arewith the Department of Computer and Information Science, Fac-ulty of Engineering, Iwate University, Ueda 4-3-5, Morioka, Iwate020-8551, Japan. S. Tamba is with the Center for Computer andCommunications, Hirosaki University, Bunnkyo-cho 3, Hirosaki,Aomori 036-8561, Japan.

Received 24 September 2001; revised manuscript received 11April 2002.

0003-6935�02�244937-08$15.00�0© 2002 Optical Society of America

brightness temperatures and sea truth SST. Theusual sea truth SST that is obtained by traditionaltechniques is called bulk SST. It represents the wa-ter temperature at approximately 1 m below the seasurface and then does not generally coincide withskin SST, which satellite sensors are sensitive to onlyin terms of radiometric measurements.2,3 We expectone reason that prevents improvement in that accu-racy is a lack of a standard technique to obtain seatruth data that precisely corresponds to the satelliteobservable data, that is, the skin SST.

This paper develops a technique to obtain both skinSST and sea surface emissivity from a position neara sea surface, namely, from a vessel. The proposedmethod uses an infrared image that includes a seasurface and a special object as a reference object. Bycombining this image with sky radiation tempera-ture, we retrieve both skin SST and sea surfaceemissivity from the single infrared image. Our ex-perimental results demonstrate that the estimatedemissivity agrees with the theoretical prediction,and, also, the recovered temperature distribution ofthe skin sea surface has no appreciable high-temperature area that is due to reflection of thatspecial object.

In Section 2 we present the principle of our method.In Section 3 we show a field experiment, which wasconducted as a part of the Mutsu Bay sea surface

20 August 2002 � Vol. 41, No. 24 � APPLIED OPTICS 4937

temperature validation experiment (MUBEX).4 Wesummarize a relevant part of the experiment andillustrate the main instruments used for that study.In Section 4 we present a specific analysis of infraredimagery of sea surfaces. Finally, in Section 5 weshow the measured results of sea surface emissivityand a recovered image of the skin SST distribution,and in Section 6 we give a summary.

2. Principle of Method

The present method to measure skin SST and seasurface emissivity is based on a standard techniquein radiometric temperature measurement. It iswell known that, in general, radiation that ema-nates from an element of a sea surface contains twocomponents: �1� the radiation that is emitted bythe element of the sea surface and �2� the radiationof a background, usually sky, that is reflected on thesame element of the sea surface.5,6 Let us nowconsider a situation in which a floating object, suchas a spherical fish float, is observed on a calm seasurface. Figure 1�a� shows the spherical float thatwe use in the present study. In this case, there isa sea surface area near the object that contains thereflection of radiation emitted by this object. If weknow the brightness temperatures of the object andsky, we may determine both sea surface emissivityand skin SST by comparing the radiance in that seasurface area �area A in Fig. 1�b�� with the radiancein another sea surface �area B� that includes skyreflection. In this paper we call the object to beused for this purpose the reference object. Let thebrightness temperature of the sea surface in area Abe Tro, and let the brightness temperature in area Bbe Trs, then each radiance in area A or area B isgiven by

B��Tro� � ��B��T� � �1 � �� B��To��,ro

� �1 � ��,ro� B��Ta�, (1)

B��Trs� � ��B��T� � �1 � �� B��Ts��,rs

� �1 � ��,rs� B��Ta�. (2)

Here � is the wavelength of the observed thermalradiation, To and Ts are, respectively, the brightnesstemperatures of the reference object and the sky, �� isthe �spectral� emissivity of the sea surface, ��,ro or ��,rsis the �spectral� transmittance along the optical pathfrom the infrared detector to area A or B, Ta is theatmospheric temperature, and T is the skin SST,which is assumed to be the same in both A and Bareas. In Eqs. �1� and �2� the atmospheric conditionsare assumed to be uniform. The function B��T� rep-resents the spectral radiance of a blackbody withtemperature T. This function is given by the Plancklaw,

B��T� �c

4�

c1

�5

1exp�c2��T� � 1

, (3)

where c1 4.992579 10�24 J � m and c2 1.438833 10�2 m � K are the first and second radi-

ation constants and c 2.997925 108 m�s is thespeed of light. We solve Eqs. �1� and �2� for �� toobtain

�� 1 � �B��Tro��,ro � B��Trs��,rs

� �1��,ro � 1��,rs� B��Ta��B��To� � B��Ts��.

(4)

This equation gives a general expression for the seasurface emissivity obtained by the present method.We now consider a rather special condition that issuited for our experimental situation. If the two op-tical paths from the detector to areas A and B are sosimilar that the atmospheric emission terms in the

Fig. 1. �a� Spherical fish float as a reference object. The sea statethat appears in the photograph is different from that at the time ofthe experiment. �b� An infrared image of the reference objectobtained by our field experiment. Area A contains the reflectionof the object, and area B reflects sky radiation.

4938 APPLIED OPTICS � Vol. 41, No. 24 � 20 August 2002

right-hand side of Eq. �4� cancel out, this equationreduces to

�� 1 �1��

B��Tro� � B��Trs�

B��To� � B��Ts�, (5)

where we set �� ,ro ��,rs. In addition, if theoptical path is of the order of several meters, one mayverify that �� in Eq. �5� is, to a good approximation,regarded to be unity.7 We then obtain the followingequation for ��, expressed in terms of the observableradiances:

�� 1 �B��Tro� � B��Trs�

B��To� � B��Ts�. (6)

Under this condition, B��T� in Eqs. �1� and �2� isexpressed by

B��T� � �B��To��B��Trs� � B��Ts��

� B��Ts��B��Tro� � B��To��

��B��Trs� � B��Ts�� B��Tro� � B��To�� .

(7)

The radiance B��T� in Eq. �7� can be inverted to giveT by a usual technique of radiometric temperaturemeasurement, even if an actual infrared detector hasnonlinear properties and a finite bandwidth. On thebasis of formulas �6� and �7�, we determine the seasurface emissivity and skin SST from a single infra-red image that includes the reference object.

Note that, although the brightness temperature ofthe reference object may be determined from the seasurface image, the brightness temperature of the skyis usually required as additional information, unlessthe infrared image includes the reflected part of thesky.8,9 We also note that, so far as the multiple re-flections between the reference object and the seasurface are small enough to be neglected, what weneed to know are the brightness temperatures of thereference object and sky. Knowledge of the thermalemissivity of the reference object is not required forthe present method.

3. Field Experiment

In this section we describe our field experiment thatwas performed during the period of the MUBEX cam-paign. This campaign was held as a Japan–UnitedKingdom joint research project. The main goal ofthe campaign was to validate the accuracy ofsatellite-derived SST and to investigate the physicalbehaviors of heat exchange proceeding at an air–seainterface. Plans and details of the experiment havebeen reported in part by Yokoyama et al.4 and byParkes et al.10

Our experiment was conducted on 27 July 1997 atMutsu Bay in Aomori Prefecture located in the north-ern part of Japan. The latitude and longitude ofMutsu Bay are 40° 50� N–41° 20� N and 140° 30�E–141° 20� E, and its topographical map is shown inFig. 2. To perform off-shore experiments, we used a

research vessel, the Daini Misago, which suppliedthe instruments used for the study. The main in-struments included a thermal infrared camera �TIC�and a thermal infrared radiometer �THI�. The set-tings of these instruments and other supplementaryapparatuses are illustrated in Fig. 3. The TIC is athermal imaging system that is of the two-axis mirrorscanning type with a mercury cadmium telluride de-tector cooled by a built-in cooler. The spectral rangeof the TIC was from 8 to 12 �m. This imaging sys-tem was mounted on the top of a ladder pole placed atthe bow of the vessel. The direction of the TIC wasinclined toward the moving direction of the vesselfrom the nadir to the sea surface. The inclinationangle, denoted �0 and used in the mathematical de-scription for the experimental situation given in Ap-pendix A, was 23°. The total height, h, of the TICfrom the average sea surface was 5 m. The field ofview was �max 30° for the horizontal direction �H�and �max 28.5° for the vertical direction �V�, andthe number of pixels were pmax 255 �H� and lmax

Fig. 2. Topographical map of Mutsu Bay.

Fig. 3. Setup of the MUBEX experimental apparatus. The TICand the THI are mounted on the top of a ladder pole placed at thebow of the research vessel. The direction of the TIC is inclined 23°toward the moving direction of the vessel from the nadir of the seasurface, and the direction of the THI is inclined with the sameangle toward the moving direction of the vessel from the zenith.


239 �V�. The angular resolution for one pixel wasthen 0.118° �H� 0.119° �V�. The period � for scan-ning one frame was 1 s. The actual size of the seasurface image was approximately 2.5 m 2.5 m.During the experiment, the THI measured the radio-metric temperature of the sky every second. Thespectral range of the THI was from 8 to 12 �m, andthe spot size was 150 mrad. This radiometer wasmounted on the top of the same ladder pole, and thedirection of the THI was inclined with the same angle�0 toward the moving direction of the vessel from thezenith.

On the day of the experiment, the weather condi-tion was fine and cloud free. The wind condition wasmoderate with almost constant wind velocity around1 m�s. Then the sea state was calm so that the seasurface could be regarded as a plane. The wind ve-locity and the wind direction were continuously mea-sured by an anemometer and then converted intoagainst-land values. Figure 4 shows the drift ofwind conditions over the observation period, with theaverage brightness temperature and its standard de-viation calculated over each infrared image of the seasurface �255 239 pixels�. We see that the experi-mental conditions were stable. The experimentaltime was midnight, around 2:21 a.m. There was nosunlight, but reflection of skylight always existed be-cause of the finite reflectance of sea surfaces in infra-red regions.

We took seven infrared images of the sea surfacethat included the spherical float. The period for thisobservation was approximately 7 s. Figures 5 show

six infrared images to be analyzed �marked by circlesin Fig. 4�. One of these images is already shown inFig. 1�b�, with a different gray-scale map to showclearly the temperature distribution of the sea sur-face. In Fig. 1�b� area A contains the reflection of thereference object, the spherical float, and area B re-flects sky radiation. A relatively high-temperaturestream, i.e., wake, is seen downward from the refer-ence object. It indicates a turbulence caused by alocal water current around the reference object. Al-though this fact is not ideal for our purpose becausearea A and area B were in the region of a wake, andthen the skin temperatures in both areas may differ,we use these images to demonstrate the presentmethod. One reason for choosing such infraredimages arises from the operational plan for theMUBEX observation. For another experimentalpurpose, the research vessel towed a thermisterchain to measure the longitudinal temperature dis-tribution of subsurface bulk water, and, owing to thesystem requirement for stability, the vessel usuallyneeded to run against the local current with around1-kn speed while measurements were made. Thenthe images had to be taken from the downstream sideof the object. Another reason for choosing the im-ages is that these images are indeed the origin of theidea of the present method. In Figs. 5 the positionsof the reference object are different image by imagebecause these images were taken from a slowly run-ning vessel. This positional difference results in thedifferent viewing angles of the measured sea surfaceemissivity.

4. Image Analysis

We have applied the present method to the six infra-red images obtained by the TIC. To apply themethod to those infrared images, we must divide thesea surface into areas A and B. It is then essentialto verify whether a certain pixel of the sea surfaceinvolves the object reflection or the sky reflection.For this purpose, we developed �see Appendix A� amathematical description that specifies the relation-ship between an infrared image obtained by the TICand the actual experimental space. This analysisincludes a ray-tracing technique to determine the re-flected points on the reference object and the corre-sponding sea surface points that reflect them. Onthe basis of the locations of these points and therelationship between the infrared image and the ac-tual experimental space, the brightness tempera-tures To of the object, Tro in area A, and Trs in area Bare determined from each infrared image.

Figure 6 shows an example of the correspondenceof the points on the sea surface and reflected pointson the reference object. The marked pixels on thesea surface are localized in the highest-temperatureregion near the object. This location specifies areaA. In other words, if the reflected point is not foundon the object, i.e., b in Eq. �A12� becomes a complexnumber, the sea surface belongs to area B. The re-flected points on the object are localized in the imme-diate vicinity of the edge of the sphere because the

Fig. 4. Stability of wind conditions and skin SST during the pe-riod of measurements. The average brightness temperature �T�and its standard deviation �T are calculated over each infraredimage of the sea surface �255 239 pixels�. Six circles indicateinfrared images used for the measurement of sea surface emissiv-ity �shown in Fig. 5�.


line of sight from the TIC to the object is almost per-pendicular to the sea surface. Under this condition,the shadowing effects caused by the spherical objectare negligible, except on the sea surface nearest to theobject. In addition, the temperature distribution thatappeared on the upper side of the sphere is not seenfrom area A. It does not affect the measurement.

The brightness temperature Tro is determined asan average temperature in area A, whereas thebrightness temperature Trs is computed as an aver-age temperature in the wake area whose tempera-ture is regarded to be uniform. Similarly, thebrightness temperature To of the object is determinedas an average temperature of the reflected points.The order of the brightness temperature of the objectis comparable with the atmospheric temperature andis found to be To � 20 °C. The sky brightness tem-perature measured by the THI is of the order of Ts ��18 °C. Then, by making use of Eqs. �6� and �7�, werecover the sea surface emissivity and skin SST dis-tribution over each infrared image.

5. Results and Discussion

The measured sea surface emissivity is shown in Fig.7. The viewing angle of the emissivity varies from

18° to 32°. Each angle corresponds to a differentlocation of the reference object, i.e., the position ofarea A on each infrared image. The emissivity of asea surface, computed with a known refractive indexof seawater,11 is also shown, for comparison. Thisemissivity ��; T�, observed by a finite-band detector,for a given viewing angle � to the sea surface havingthe temperature T is expressed as a weighted aver-age of the spectral emissivity �� given by Fresnel’sformula, i.e.,

��; T� �� N�B��T��d�

� N�B��T�d�

, (8)

where B��T� is the Planck function defined by Eq. �3�and N� denotes the spectral sensitivity of the detec-tor. Equation �8� gives the observed emissivity for aplane sea surface valid under most experimental sit-uations. In a usual case in which the bandwidth ofthe detector is limited within the atmospheric infra-red window, the dependence of this emissivity onthe skin SST is negligible. If the wave effects are

Fig. 5. Six infrared images to be analyzed. Each measurement time is shown under each image. The positions of the reference objectare different image by image because these images are obtained from a slowly running vessel. Each position corresponds to a differentlocation of area A and has a different viewing angle of sea surface emissivity.


dominant, however, Eq. �8� needs to be averagedover a possible surface inclination �facet� of seasurface.5,6,12–14 Because the sea surface is almostplanar in our experiment, we omit the wave effectsand adopt the emissivity given by Eq. �8� as a theo-retical prediction. The measured values of emissiv-ity are, on the average, 0.002 �or 0.2%� larger than thetheoretical values. The main cause of this error isthought to be the temperature difference betweenarea A and area B. This temperature difference isestimated from the standard deviation of tempera-ture in area B as 0.05 °C.

A comparison of recovered skin SST image andoriginal brightness temperature image is shown in

Fig. 8. The average temperature difference betweenthe two images is 0.3 °C, which is introduced by anonunity of sea surface emissivity. We see that thehighest-temperature region that is to reflection of thereference object is almost removed in the recoveredtemperature distribution of skin sea surface.

6. Concluding Remarks

A method to obtain simultaneously the thermal emis-sivity and the skin sea surface temperature has beendeveloped. The proposed method has been demon-strated experimentally, and the results are promis-ing.

Because this method requires no knowledge ofthermal radiative properties of actual sea surfaces,we expect that it can be used even for a contaminatedsea surface whose emissivity is hard to determinetheoretically. For example, oil slicks or slicks pro-duced by biological wastes are frequently observed inpractice. Use of the method allows the acquisition ofmatch-up data of radiometric SSTs that precisely cor-respond to the satellite observable data.

We will conclude this paper with some suggestionsfor an improved experiment based on the presentmethod. First, to avoid the wake and to maintainmore precisely the basic assumption that the temper-atures in area A and B be the same, a properly de-signed experiment should take data on the upstreamof the object. Otherwise, the reference object shouldbe suspended so that it is separate from the sea sur-face. This may greatly improve the accuracy of themeasured emissivity. Second, for the reference ob-ject, it is desirable to use an available blackbody or anobject whose directional properties of emissivity is wellcharacterized because directions from the object to thedetector and to the sea surface are different. Third,

Fig. 6. Correspondence of the points on the sea surface in area Aand reflection points on the reference object.

Fig. 7. Measured emissivity of the sea surface from the six infra-red images. Each small and bold error bar indicates the accuracyspecified by the noise-equivalent temperature resolution, 0.075 °C,of the TIC. Each large error bar shows the variation caused bythat of the SST in each B area, which contains approximately 34 to81 pixels. The dotted curve shows the emissivity of a plane sea-water surface, for comparison.

Fig. 8. Comparison of a part of sea surface images near the ref-erence object: �a� original brightness temperature image and �b�skin SST image recovered by the present method.


when the method is applied to a wavy surface ex-panded under an inhomogeneous cloud distribution,the radiance distribution of the sky needs to be ac-quired to compensate for the wave effects.7,8 A mea-surement time much longer than the correlation timeof the sea surface slope is also required so that bothfluctuations of emissivity and reflected sky directioncaused by different inclinations of the sea surface aresufficiently averaged. Finally, as an extended style ofthe present method, it may be useful to use two refer-ence objects with different temperatures, instead ofusing sky as one of the two. This eliminates the in-ference of the cloud condition on the measured results.

Appendix A: Mathematical Description for a DynamicExperimental Situation

For the image analysis presented in Section 4, wedeveloped a mathematical description that specifiesthe correspondence of a certain pixel of a TIC imagewith an actual observed position on the sea surface.This mathematical description includes a ray-tracingtechnique to determine the reflected points on thereference object and the corresponding sea surfacepoints that reflect them.

As shown in Fig. 9, we take the Cartesian coordi-nate system whose x and y axes coincide with a calmsea surface and whose z axis is parallel to its outwardnormal n �0, 0, 1�. We assume, at time t 0, thelocation of the TIC is at the position H �0, 0, h�.The vessel moves in the direction of increasing y, witha constant velocity V. Thus the position of the TICat t � 0 is written as H�t� H � Vt, where V �0,V, 0�. While the vessel is moved, the TIC scans pixelby pixel in the x direction while scanning line by linetoward the direction of decreasing y �see Fig. 9�. Inthis case, the unit viewing vector s �sx, sy, sz�, whichcorresponds to an observed point P �x, y, 0� on thesea surface, is given by

s �P � H�t�

�P � H�t��, (A1)

where � � denotes the absolute value of the three-dimensional vector. This s vector is also expressedin terms of the scanning angles as

s � �sin �� p�, cos �� p�sin ��l �, �cos �� p�cos ��l ��,(A2)

where ��p� or ��l � is the horizontal or vertical scan-ning angle of the pth pixel on the lth line, �p, l �, of theTIC image and is expressed in terms of the parame-ters shown in Section 4, as

�� p� ��max

pmax�p �

pmax

2 � , (A3)

��l � ��max

lmax�lmax

2� l� � �0. (A4)

By comparing each component of Eq. �A1� with thoseof Eq. �A2�, we obtain

sin �� p� �x

�P � H�t��, (A5a)

cos �� p�sin ��l � �y � Vt

�P � H�t��, (A5b)

cos �� p�cos ��l � �h

�P � H�t��. (A5c)

We divide Eqs. �A5a� and �A5b� by Eq. �A5c� to elim-inate �P � H�t�� in these equations. Then we obtainthe relationship between the x and the y componentsof the sea surface point P observed at time t and thecorresponding pixel �p, l � of the infrared image:

x � htan �� p�

cos ��l �, (A6a)

y � h tan ��l � � Vt. (A6b)

Because the scanning period for one image is �, thetime t in which point P is observed is well approxi-mated by l��lmax. Then Eq. �A6b� reduces to

y � h tan ��l � �l

lmaxV�. (A7)

Formulas �A6a� and �A7� represent the relationshipbetween a certain pixel of the TIC image of the seasurface and the actual position on the observed seasurface when the vessel moves with a constant veloc-ity and the TIC scans one frame with a finite dura-tion.

Next, we determine the reflected point on the ref-erence object. This is necessary to verify whether acertain sea surface contains the object reflection orthe sky reflection. We assume the reference object isa sphere with radius r, centered at u �ux, uy, uz�.Let the pixel for this center of the sphere be �pu, lu�,and let the depth of the sphere below sea surface bed. Then the z component of the center is uz r � d.Because the relative height of the TIC from the center

Fig. 9. Coordinate system in the dynamic experimental situation.


of the sphere is h � �r � d�, ux and uy may be ex-pressed in terms of the pixel parameters �pu, lu�, as inthe same formulas as in Eqs. �A6a� and �A7�, with hreplaced by h � �r � d�:

ux � �h � �r � d��tan �� pu�

cos ��lu�, (A8a)

uy � �h � �r � d��tan ��lu� �lu

lmaxV�. (A8b)

For a plane sea surface, the ray along with the view-ing vector s is reflected to the specular direction onthe surface, and so the reflected ray vector, o, is re-lated to s as

o � s � 2�n � s�n, (A9)

where n is the unit normal to the surface. We nowdetermine the reflected point X �X, Y, Z� on thereference object; i.e., a ray that is emanated from thatpoint is reflected on the surface at P and then prop-agates into the TIC that is located along the oppositedirection to s. Because X lies on the straight line ofextending the reflected ray vector o, it is expressed as

X � P � bo, (A10)

where b is a parameter. At the same time, X lies onthe sphere of radius r; centered at u, it must satisfy

�X � u� � r. (A11)

From Eqs. �A10� and �A11�, we determine the lengthb from point P to the points at which the ray inter-sects with the sphere. The reflected point X is thenearest intersection to P, and b is expressed by

b � ��P � u� � o� � ��P � u� � o�2

� �P � u�2 � r2 1�2. (A12)

Finally, we seek the corresponding pixel �pX, lX� ofthis reflected point X. Because the x and y compo-nents of X are related to the scanning angles, ��pX�and ��lX�, as in the same manner as in Eqs. �A6a� and�A7�, with h replaced by h � Z, we readily have

X � �h � Z�tan �� pX�

cos ��lX�, (A13a)

Y � �h � Z�tan ��lX� �lX

lmaxV�. (A13b)

Equation �A13b� can easily be inverted numericallyto obtain lX. By substituting this lX into Eq. �A13a�,we can invert this equation numerically to obtain pX.Note that the parameters involved in the above for-mulas, such as the position of the reference object u,the radius r, and the depth d, can be determined fromeach TIC image, by making use of the present math-

ematical description of the dynamic experimentalsystem.

This paper has been reported in part in the IEEEInternational Geoscience and Remote Sensing Sym-posium, Sydney, Australia, 9–13 July 2001. TheMutsu Bay Experiment is supported by the grantsfrom National Space Development Agency of Japan;Japanese Scientific Promotion Society; The Royal So-ciety, UK; National Environmental Research Coun-cil, UK; and Daiwa Anglo-Japanese Foundation.

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simultaneous measurements of skin sea surface temperature and sea surface emissivity from a single...

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