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Effect of atmospheric radiance errors inradiometric sea-surface skin temperature measurements

Craig James Donlon and Timothy John Nightingale

Errors in measurements of sea-surface skin temperature ~SSST! caused by inappropriate measurementsof sky radiance are discussed; both model simulations and in situ data obtained in the Atlantic Ocean areused. These errors are typically caused by incorrect radiometer view geometry ~pointing!, temporalmismatches between the sea surface and atmospheric views, and the effect of wind on the sea surface.For clear-sky, overcast, or high-humidity atmospheric conditions, SSST is relatively insensitive ~,0.1 K!to sky-pointing errors of 610° and to temporal mismatches between the sea and sky views. In mixed-cloud conditions, SSST errors greater than 60.25 K are possible as a result either of poor radiometerpointing or of a temporal mismatch between the sea and sky views. Sea-surface emissivity also changeswith sea view pointing angle. Sea view pointing errors should remain below 5° for SSST errors of ,0.1K. We conclude that the clear-sky requirement of satellite infrared SSST observations means thatsky-pointing errors are small when one is obtaining in situ SSST validation data at zenith angles of ,40°.At zenith angles greater than this, large errors are possible in high-wind-speed conditions. We recom-mend that high-resolution inclinometer measurements always be used, together with regular alternatingsea and sky views, and that the temporal mismatch between sea and sky views be as small as possible.These results have important implications for the development of operational autonomous instrumentsfor determining SSST for the long-term validation of satellite SSST. © 2000 Optical Society of America

OCIS codes: 010.4450, 010.1290, 260.3060, 120.5630, 120.0280, 120.6780.

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1. Introduction

Sea-surface skin temperature ~SSST! may be signif-icantly different from the subsurface bulk sea-surfacetemperature because of a characteristically strongtemperature gradient in the oceanic viscous sub-layer.1 The mean difference between the SSST andthe subsurface bulk sea-surface temperature is ap-proximately 20.25 K.1 The value of the SSST isrequired operationally not only for the accurate val-idation of satellite-derived SSST data products butfor investigating and parameterizing heat, moisture,and gas exchange2 between the atmospheric and oce-anic reservoirs. The SSST is commonly derivedfrom in situ measurements of infrared emission. Weconsider how the accuracies of SSST measurements

C. J. Donlon ~craig.donlon@jrc.it! is with the Marine Environ-ment Unit, Space Applications Institute, Joint Research Centre ofthe European Community, I-21020 Ispra, Italy. T. J. Nightingale~t.j.nightingale@rl.ac.uk! is with the Rutherford Appleton Labora-ory, Chilton, Didcot, Oxon OX11 OQX, England.

Received 4 May 1999; revised manuscript received 17 November999.0003-6935y00y152387-06$15.00y0© 2000 Optical Society of America

taken with an in situ radiometer are determined byinstrument geometry, alignment, and observingstrategy.

Over a flat sea surface, the upwelling spectral ra-diance R~u, l!up at angle u from nadir and wavelengthl is made from two components:

R~u, l!up 5 e~u, l!B~SSST, l!

1 @1 2 e~u, l!#R~u, l!down, (1)

where B~SSST, l! is the blackbody spectral radianceat the SSST, R~u, l!down is the downwelling spectralsky radiance at angle u from zenith, and e~u, l! is the

resnel emissivity of seawater. In practice, an ob-erving instrument has a finite spectral and spatialesponse, and Eq. ~1! is often approximated as

R# ~u#!up 5 e#~u#!B# ~SSST! 1 @1 2 e#~u#!#R# ~u#!down, (2)

where R# ~u#!up and R# ~u#!down are upwelling and down-welling radiances, respectively, at the sea surface atmean nadir and zenith angles u# and B# ~T! is thePlanck function at temperature T, each integratedover the instrumental filter function and field of view.Both R# ~u#!up and R# ~u#!down can be observed directly; so,neglecting attenuation along a short atmospheric

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path length, we can express B~SSST! entirely interms of measured or calculated quantities:

B# ~SSST! 5R# ~u#!up 2 @1 2 e#~u#0!#R# ~u#!down

e#~u#0!, (3)

here u#0 represents the nominal orientation of thefields of view that we used to calculate emissivity.The SSST can then be obtained with the inverse ofthe function B# ~T!.

In regions of high atmospheric transmission, thedownwelling sky radiance R# ~u#!down is determinedargely by the atmospheric water content and by themount, species, and height of clouds. The first-amed property changes relatively slowly with posi-ion and time, but the others can be highly variable.n general, the radiant temperature of a clear sky isooler than that of an overcast sky, and high cloudases will appear cooler than low cloud bases, regard-ess of cloud species. Overcast skies and conditionsf high humidity are characterized by a fairly uni-orm downwelling sky radiance in all directions.lear skies are characterized by radiant tempera-

ures that increase with zenith angle. Under bro-en cloud, the sky radiance can exhibit considerablepatial and temporal variability.It follows that an incorrect selection of the sky view

enith or azimuth direction, significant mismatchesn time between sea-surface and sky view measure-

ents, modification of the sea–sky view geometrywing to misalignment or platform movement, or thenfluence of surface roughness could result in a mea-urement of R# ~u#!down that does not adequately repre-

sent the reflected radiance contribution to R# ~u#!up.Our aim in this paper is to consider how well Eq. ~3!epresents the true SSST and, in particular, how theccuracy of the retrieved SSST is affected by ournderstanding and choice of R# ~u#!down and e#~u#!.A stirred-water bath radiometer calibration has

een proposed to account explicitly for all aspects ofea-surface behavior,4 but there are considerable

problems with this technique, including differencesbetween the surface roughness of the sea surface andthe water bath, temperature gradients within thewater bath,5 and the difficulty of deploying such asystem.6 As a result, we focus on the errors associatedwith a radiometer that makes direct measurementsof the downwelling sky radiance.

2. In situ Measurements

During the Atlantic Meridional Transect-7 ~AMT-7!xperiment ~September–October 1998!, a scan-ing infrared sea-surface temperature radiometerSISTeR! was deployed on the forward mast of. R. S. James Clark Ross, viewing the sea surface at0° from nadir. The SISTeR instrument is an accu-ate self-calibrating radiometer with a 13° ~full cone!eld of view that relies on two internal radianceources maintained at different temperatures to cal-brate each measurement sequence. All SISTeRata were collected with a narrow-band ~,1-mm! fil-er centered at 10.8 mm. e# was derived from the

388 APPLIED OPTICS y Vol. 39, No. 15 y 20 May 2000

resnel emissivity of pure water, corrected for sea-water effects,8 and weighted with the combined SIS-TeR spectral window and detector functions for a seaview angle of 40°. We note that some improvementsmight be achieved if the instrument were pointedcloser to nadir because of the slightly higher value fore#~u#! and its lower variability with viewing angle.However, in the case of ship deployments it is oftendifficult to achieve such a configuration because theradiometer needs to view the undisturbed sea surfaceforward of the ship’s bow wave. We also note that,close to nadir, direct reflections from any platformsuperstructure may require additional consideration.

Upwelling radiances R# ~u#!up were obtained with theSISTeR instrument from the sea surface at 40° fromnadir, followed by an ensemble of downwelling skyradiances R# ~u#!down in the same azimuth direction, at10° increments from just above the horizon to verti-cally upward. A measurement sequence was com-pleted every 84 s.

We specifically use data obtained in calm-sea con-ditions to eliminate errors associated with ship move-ments: We use the scanning ability of ourinstrument to provide sky radiance data that can beused to simulate the effect of ship movement. Inthis way, errors that are due to the incorrect choice ofsky radiance angle can be discussed in terms of de-ployment geometry, ship movements, and temporalmismatches between sea and sky views.

3. Pointing Errors

We investigate errors in measurement of SSSTcaused by pointing errors ~PE’s! for clear-sky, over-cast, and broken-cloud conditions with in situ radi-ometer data from the AMT-7 experiment. With Eq.~3! we calculate a nominally correct SSST, SSSTtrue,by using the 40° sky view and also SSST’s by usingeach of the incorrect sky radiance angles, SSSTPE.We define the SSST errors that are due to pointingerrors, dSSSTPE, as

dSSSTPE 5 SSSTPE 2 SSSTtrue. (4)

Figure 1~a! presents sky brightness temperature ~BT!bservations for sky views at zenith angles from 80°o 0° ~80° points 10° above the horizon and 0° verti-ally upward! on day 287 of 1998. The atmosphereas free from clouds for the majority of the time,lthough small isolated cumulus and altocumulusere sometimes present. Our observations show a

moothly varying BT, decreasing from 260 K at 80°just above the horizon! to 215 K at 0° ~pointing ver-ically! as the atmospheric path length decreasesith decreasing sky view angle. An isolated cumu-

us is seen at day 287.54 ~just after midday local time!n only the 0°–50° sky view data. By late afternoontmospheric activity has increased and sky BT be-omes increasingly variable as more cumulus andltocumulus clouds invade the sky.Figure 1~b! presents dSSSTPE @Eq. ~4!# for each of

he sky views discussed above. Immediately appar-nt is the fact that, under clear-sky conditions,

dpf

dSSSTPE is relatively insensitive to PE: The radi-ometer PE must be greater than 20° before dSSSTPEexceeds 0.1 K. Conversely, once a partially cloudyatmosphere is encountered, dSSSTPE becomes ex-tremely sensitive to PE ~e.g., after day 287.63!.

Figure 1~c! presents sky BT observations for zenithangles from 0° to 80° obtained on day 286. The ob-served atmospheric state was characterized by amixed sky composed of cumulus, altocumulus, and

Fig. 1. ~a! Sky brightness temperatures obtained from a SISTeRuring the AMT-7 experiment for day 287 of 1998. 80° indicates aointing sky view. ~b! SSST error owing to incorrect pointing of tor day 286 of 1998. In each panel, the 40° data denote the corre

stratocumulus clouds at different levels. Consider-able variability is evident in this figure, and at 286.65a large bank of stratocumulus dominated the sky,which is seen as a convergence of all sky view BT’s toa relatively warm value of 285 K. The correspond-ing dSSSTPE is shown in Fig. 1~d! and demonstratesthe insensitivity of dSSSTPE to PE under a com-pletely overcast sky ~at day 286.605! but highlightsthe magnitude and variability of dSSSTPE in mixed-

ometer mounted upon the foremast of R. R. S. James Clark Rossiew pointing at 10° above the horizon, and 0° indicates a verticallySTeR radiometer sky view. ~c!, ~d! As in ~a! and ~b!, respectively,y radiance and SSST for the AMT-7 deployment geometry.

radisky v

he SIct sk

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cloud conditions. Even small ~,10°! PE’s may resultin significant ~.0.1-K! SSST errors.

For an instrument such as SISTeR, which viewsthe sea and the sky in the same azimuth direction,the sensitivity of retrieved SSST to roll under a clearsky is double that which is due to sky-pointing erroralone, as the nadir sea view angle decreases withincreasing zenith sky view angle. However, anyother choice of azimuth direction for the sky view islikely to compromise severely SSST retrievals undermixed skies.

4. Emissive Errors

The emissivity of the sea is also dependent on theangle of incidence of the sea view at the sea surfaceand provides a further mechanism by which the in-clination of the observing platform can affect the re-trieved SSST. We can estimate the emissive effectof roll and list on retrieved SSST by differentiatingB# ~SSST! with respect to e#~u#!. From Eqs. ~2! and ~3!,nd dropping dependencies for clarity, we can derive

]B#

]e#5 ~1ye#0!

]R# up

]e#, (5)

]R# up

]e#5 ~B# 2 R# down!, (6)

dSSSTemissive 5 Du#]B#

]e#

de#

du#Y dB#

dT

5 Du#~1ye#0!~B# 2 R# down!de#

du#Y dB#

dT, (7)

here Du# is the amplitude of the list or roll. Takings an example the SISTeR instrument described inection 2, we adopt its 10.8-mm filter and 13° field ofiew. At the baseline 40° zenith angle sea and skyiews used for the measurements described in Sec-ion 3, de#ydu# is approximately 3.1 3 1024 deg21.

The largest errors will occur under clear skies.From day 287.56 to day 287.59 @Fig. 1~a!#, the mean

SST is 291.8 K and the mean sky brightness tem-erature is 210.3 K, giving a SSST error of Du# 3 17

mKydeg. Under cloudy skies the sensitivity to rollis small. From day 286.6049 to day 286.6057 @Fig.

~c!#, the mean SSST is 292.3 K and the mean skyrightness temperature is 285.4 K, giving a SSSTrror of Du# 3 2 mKydeg. We conclude that, underlear skies, the orientation of the radiometer muste known to better then 5° for the magnitude ofSSSTemissive to remain below 0.1 K.

5. Surface Roughness Errors

A real sea surface has a roughness determined by thesurface winds.9 This roughness affects both the ef-fective emissivity of the sea surface and the region ofthe sky that is seen in reflection.10–13 At observingangles below approximately 60° from nadir the effec-tive emissivity of a wind-roughened surface tends todecrease with increasing wind speed. Watts et al.10

showed that this effect is not so severe as originally

390 APPLIED OPTICS y Vol. 39, No. 15 y 20 May 2000

described by Masuda et al.,11 as a compensating in-crease in secondary reflections of surface radiancetends to enhance the effective surface emissivity.The sky reflection lobe also becomes progressivelybroader with increasing wind speed, and the meanlobe zenith angle moves nearer the horizon. Partic-ularly under clear skies, the latter effect also tends tocompensate for the drop in effective emissivity withincreasing wind speed as the sky becomes progres-sively warmer with increasing zenith angle. We as-sess the effect of surface roughness on the accuracy ofSSST’s retrieved with Eq. ~3! through an extension ofthe model of Watts et al.

We again adopt the SISTeR instrument describedin Section 2. Examples of clear- and overcast-skyradiance fields ~Fig. 2~a!# were generated from time-averaged sky radiances from day 287.56 to day287.59 @Fig. 1~a!# and from day 286.6049 to day286.6057 @Fig. 1~c!#, respectively. The mean SSST’sof Section 4 were retained. Synthesized upwelling

Fig. 2. ~a! Averaged overcast and clear-sky radiance profiles fromays 286 and 287. ~b! Estimated SSST errors under overcast and

clear skies that are due to wind-induced sea-surface roughness ata 40° zenith viewing angle. ~c! Estimated SSST errors over awind-roughened sea surface that are due to an encroaching cloudedge at a 40° zenith viewing angle.

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and downwelling radiances for the SISTeR field ofview and viewing geometry were calculated with themodel of Watts et al. for a range of wind speeds.Wind-affected sea-surface skin radiances were thenretrieved with Eq. ~3! and converted to temperaturesSSSTwind. Wind-induced errors dSSSTwind were es-timated from the differences between SSSTwind andSSSTtrue:

dSSSTwind 5 SSSTwind 2 SSSTtrue. (8)

Under overcast skies @Fig. 2~b!# the amplitude ofSSSTwind is consistently very small ~,3 mK!, as the

sky temperature is relatively constant and close tothe SSST. The error under a clear sky @Fig. 2~c!#eaches its maximum amplitude ~;30 mK! at a windpeed near 10 ms21. At this point the decreasing

emissive radiance from the sea surface begins to levelout, and the total upwelling radiance is insteaddriven by steadily increasing reflected sky radiancecontributions.

To assess the effect of cloud in the field of view, werepeat the previous test with composite sky radianceprofiles, made from step changes between the clear-and the overcast-sky radiance profiles of Fig. 2~c! atincreasing zenith angles. These changes may be in-terpreted as an expanding circular cloud directlyoverhead in a clear sky. As the cloud begins to im-pinge upon the reflection lobe, the direct measure-ment of the sky starts to underrepresent the truereflected radiance and the retrieved SSST errordSSSTwind increases, reaching its maximum just ashe cloud front touches the edge of the upward-ooking field of view. Similarly, just as the cloudully crosses the instrument’s upward-looking field ofiew, the reverse is true and the error reaches itsaximum negative extent.At low wind speeds the reflectance lobe is narrow,

o the maximum SSST error is moderate in ampli-ude ~,50 mK! and restricted in extent to the regionf sky immediately surrounding the instrument’spward-looking field of view. With increasing windpeeds the single direct sky measurement becomesncreasingly more unrepresentative of the broaden-ng reflection lobe, and the retrieved SSSTwind be-omes sensitive to cloud in increasingly large regionsf the sky. The maximum error amplitude reaches.2 K at 10 ms21 but increases relatively little withurther increases in wind speed. Although evenore severe tests of cloud effect are conceivable, this

rror magnitude will be broadly representative of theorst case in difficult observing conditions, for in-

tance, when a large low cloud passes overhead.For other zenith viewing angles below 40° the

vercast-sky wind error remains small and the max-mum clear-sky error amplitude generally decreasesith falling view angle. With increasing view an-les, however, both of these error amplitudes riseubstantially. At 60° and 15 ms21 the overcast- and

clear-sky errors are 50 mK and 0.5 K, respectively.The maximum cloud-front error amplitudes remainbroadly similar at all zenith viewing angles up to 60°.

6. Discussion and Conclusions

We have used observations and model simulations toinvestigate SSST measurement errors caused by in-appropriate sky radiance measurements that resultfrom incorrect radiometer deployment, ship move-ments, and long time intervals between sea and skyviews. For clear-sky conditions, SSST errors thatare due to ship movement or to an inappropriateradiometer deployment geometry are only moder-ately sensitive to PE’s. For overcast conditions andhigh-humidity conditions ~such as in the tropics, notshown here!, SSST errors caused by to PE’s will be ata minimum because the difference between the radi-ant temperatures of the sea surface and the sky willbe relatively small. Further, all these atmosphericsituations are characterized by slow and smoothlyvarying sky radiances, so temporal errors associatedwith nonsimultaneous sea and sky measurementsare also small. We conclude that, when in situ SSSTs used to validate satellite SSST measurements atenith angles below 40°, the effect of PE is smallecause of the clear-sky requirement for satelliteSST observations. However, if accurate in situ

SSST’s are required irrespective of the surface rough-ness conditions or atmospheric state ~e.g., for gasxchange experiments!, all PE’s should be less than5°, and temporal PE’s should be minimized if SSST

rrors of 0.1 K are not to be exceeded. In extremeases, the magnitude of errors for mixed sky condi-ions may approach the mean difference between theSST and the subsurface bulk sea-surface tempera-ure of 20.25 K, particularly at higher wind speeds,here some degradation of the SSST measurement is

nevitable.A pragmatic approach to alleviating the majority of

rrors associated with ship movements or changingloud cover is to average SSST data in time. How-ver, this assumes that cloud cover has a randompatial distribution, which, in general, is not the case.arine atmosphere clouds tend to form in particular

atterns ~e.g., Benard cells or cloud streets!, so, de-ending on the particular sampling characteristics ofradiometer, it is possible for sky views to become

liased to clear sky ~or cloudy sky! when sea views areaken in cloudy conditions. A similar aliasing prob-em is also possible for ship pitch and roll movements.ndividual radiometer deployments should be care-ully planned to keep sky-pointing errors below 50°.table deployment platforms should be chosen, andegular sky view observations should be obtainedlose in time to the sea view data. This is particu-arly important when we consider that the majority ofperational in situ radiometer systems are unable toeasure simultaneously both the oceanic and the

tmospheric radiances. We recommended limitinghe radiometer zenith angle to 15°–40° so emissiveffects associated with wind and ship movement wille limited as much as possible.Inclinometers should be used to provide a detailed

ecord of platform movements simultaneously withll radiometer measurements, and a range of sky

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Meterological Organisation Global Atmospheric Radiation

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view data should be obtained. This is particularlyimportant for conditions of broken cloud and whensignificant platform movement is expected. Addi-tional measurements should include those of wavesize and direction and the surface wind speed.These data can then be used to ensure that the mostappropriate emissivities and sea and sky radiancedata are used in the derivation of SSST.

Thanks are due to Phil Watts for the provision ofhis emissivity model. The authors also thank JerryBurgen and the ship’s company of R. R. S. James

lark Ross. We acknowledge the support of theritish Antarctic Survey Ice and Climate Divisionnd the Natural Environment Research CouncilNERC! of the United Kingdom. C. Donlon was sup-orted in part under NASA research grant NAGW-110, and T. Nightingale was funded by a NERCrant for the postlaunch support of the second Alongrack Scanning Radiometer ~ATSR-2!.

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