Understanding radiative transfer in the midwave infrared, a precursor to full spectrum atmospheric compensation

Transcription

1 Undertanding radiative tranfer in the idwave infrared, a precuror to full pectru atopheric copenation Michael K. Griffin *, Hiao-hua K. Burke, John P. Kereke MI incoln aboratory, 244 Wood Street, exington, MA, USA ABSRAC he copenation for atopheric effect in the VNIR/SWIR ha reached a ature tage of developent with any algorith available for application (AREM, FAASH, ACORN, etc.). Copenation of WIR data i the focu of a nuber of proiing algorith. A gap in developent exit in the MWIR where little or no atopheric copenation work ha been done yet an increaed interet in MWIR application i eerging. o obtain atopheric copenation over the full pectru (viible through WIR), a better undertanding of the radiative effect in the MWIR i needed. he MWIR i characterized by a unique cobination of reduced olar irradiance and low theral eiion (for typical eitting urface), both providing relatively equal contribution to the daytie MWIR radiance. In the MWIR and WIR, the copenation proble can be viewed a two interdependent procee: copenation for the effect of the atophere and the uncoupling of the urface teperature and eiivity. he forer require calculation of the atopheric tranittance due to gae, aerool, and thin cloud and the path radiance directed toward the enor (both olar cattered and theral eiion in the MWIR). A fraework for a cobined MWIR/WIR copenation approach i preented where both cattering and aborption by atopheric particle and gae are conidered. Keyword: MWIR, WIR, hyperpectral, atopheric copenation, radiative tranfer. INRODUCION Hyperpectral iaging enor have been ued to aid in the detection and identification of divere urface eleent, topographical, and geological feature, abient dut and aerool, oke fro fire, a well a upended gaeou effluent. Hyperpectral data are not iune to the effect of the intervening atophere. he ter atopheric copenation refer to the reoval of unwanted atopheric coponent of the eaured radiance o that an etiate of the urface leaving radiance or reflectance can be obtained. For hyperpectral data analyi in the reflected olar pectral regie, the general objective of atopheric copenation algorith i to reove olar illuination and atopheric effect (predoinantly aerool cattering and water vapor aborption) fro the eaured pectral data o that an accurate etiate of the urface reflectance can be obtained. In the theral eiive region of the pectru, the objective i two-fold: ) reove atopheric coponent of the enor-eaured radiance to obtain a ground-leaving radiance, and 2) eparate the teperature and eiivity coponent fro the retrieved radiance, the priary product being an etiate of the urface pectral eiivity. Difficultie can arie when atopheric condition are treing (e.g., high oiture, heavy aerool/particulate loading, partial cloud cover, low un angle). he effect are further enhanced when the eaured ignal i low (over low reflectance or cold urface or for pectral region of low olar or theral radiance). In the MWIR (3 6 µ), the reflected olar radiance i quite all copared to that in the VNIR and the theral eiive radiance for noral urface and atopheric condition i alo at a iniu. hee factor provide a unique challenge to thoe who attept to derive inforation fro MWIR data. he following ection will highlight the typical pectral and radioetric ignature to be found in the MWIR for different cenario. he equation governing the tranfer of radiation in thi regie will alo be exained. * griffin@ll.it.edu; Voice: ; FAX: Algorith and echnologie for Multipectral, Hyperpectral, and Ultrapectral Iagery X, edited by Sylvia S. Shen, Paul E. ewi, Proceeding of SPIE Vol (SPIE, Bellingha, WA, 2004) X/04/$5 doi: 0.7/

2 2. MWIR SPECRA CHARACERISICS o etiate the underlying urface-leaving radiance fro a reote airborne or paceborne platfor, the effect of the intervening atophere ut be conidered. ypically, at MWIR wavelength, the radiative flux i ipacted by the aborption by well-ixed gae uch a Ozone (O 3 ), Oxygen (O 2 ), Nitrogen (N 2 ), Methane (CH 4 ), Nitrou Oxide (N 2 O), Nitrogen Dioxide (NO 2 ) and Carbon Dioxide (CO 2 ), and the aborption by water vapor. Mixed gae can be odeled accurately and play an iportant role in the retrieval of pecific propertie of the earth-atophere yte 2. Figure provide exaple of the atopheric aborption (defined a tranittance) over the pectral region fro 2.5 to 7 µ for two atopheric condition: ) clear and dry and 2) hazy and huid. he curve were produced with Modtran 3 over a full (00 k) nadir atopheric path. hee cae produce value for atopheric aborption that repreent the extree bound for a noinal atophere. It i clear that the MWIR pectral band i doinated by trongly aborbing gae. One oderately traniive window region exit between 3 and 4 icron with iniu aborption near 3.8 µ for dry atophere and 3.9 µ for oit atophere. A econd traniive region exit between 4.6 and 5.4 µ with iniu aborption value near 4.6 µ. In contrat with the VNIR/SWIR pectral band, which exhibit nuerou atopheric window, the MWIR ha liited pectral region for retrieving urface inforation. he aborption curve in Fig. can be divided into contribution fro individual gae and aerool. Fro Fig. 2 it can be een that nuerou gae have aborption feature in the MWIR; the aborption curve for ten gae including water vapor are plotted. Water vapor i the ajor aborber in the MWIR and provide the bulk of the total atopheric aborption hown in Fig.. Since the aount of water vapor in the atophere varie greatly both patially and teporally, it effect on traniion in the MWIR can alo vary. Plotted in Fig. 2 i the water vapor aborption for the dry cae hown in Fig., which repreent an etiate of the iniu aborption to be expected. wo ajor H 2 O aborption band are found in the MWIR: a trong band near 2.7 µ and the ajor water vapor coplex of line near 6.7 µ. he latter band pan over 3 µ fro 5 to 8 µ and repreent a priary region of the pectru for obtaining inforation ued to retrieve layered atopheric water vapor aount. It can be een that the water vapor aborption overwhel weaker aborption by other gae, even for relatively dry atophere Aborption Hazy Wet Atophere Clear Dry Atophere Wavelength (µ) Figure. Plot of the atopheric aborption acro the MWIR pectral region for two atopheric condition: hazy/wet and clear/ dry. Proc. of SPIE Vol

3 Aborption H2O CO2 N2 O2 CH4 N2O HNO3 O3 NO2 CO Wavelength (µ) Figure 2. Plot of the noinal abient atopheric aborption for 0 olecular pecie that exhibit aborption feature in the MWIR. Carbon dioxide aborb trongly between 4. and 4.4 µ and alo near 2.8 µ. he 2.7 µ H2O aborption otly eclipe the latter CO 2 band. CO 2 alo exhibit a oderate aborption line at 4.85 and 5.2 µ; the effect of both are diinihed by water vapor. Aborption by CO 2 at 4.25 µ i trong enough to provide the opportunity to etiate atopheric teperature in the Stratophere uing retrieval algorith. Adjacent to thi CO 2 band i a trong N 2 O aborption band centered at 4.5 µ. Weaker band are alo found at 2.9, 3.9 and 4.05 µ, but only the 3.9 µ band fall within the MWIR window. Molecular nitrogen alo diplay a broad area of oderate aborption at 4.3 µ, the effect being to broaden the CO 2 aborption region to 3.9 µ. A oderate CH 4 aborption band i located near 3.3 µ on the edge of the water vapor band and extending into the MWIR window. Minor O 3 aborption i preent at 4.75 µ; CO diplay inor aborption fro 4.5 to 4.9 µ. Other gae, uch a O 2, NO 2 and HNO 3 a well a CH 4 and O 3 diplay aborption fro 5.5 to 7 µ, but the effect are copletely encopaed by the expanive water vapor band. Scattering by olecule i negligible at thee wavelength 4, and cattering and aborption by noral atopheric aerool produce traniion loe between 2 and 5 percent depending on the aerool type and viibility. In contrat to the MWIR, traniion loe due to aerool in the VNIR/SWIR are typically two to three tie that aount. ypical aborption lo baed on Modtran 3 aerool odeling i liited to 4 percent with iniu aborption occurring for aritie aerool and axiu aborption found in urban aerool that tend to contain ignificant aount of carbon. Figure 3 diplay plot of the cattering and aborption acro the MWIR for the two extree aerool condition ued in the calculation for the Fig. curve. he cattering fro aerool i found to vary lowly and continuouly with wavelength with a light decreae in traniion lo toward longer wavelength in the MWIR. Model have been developed baed upon the ize and near-pherical hape of aerool to etiate the effect of cattering on the traniion of olar and theral energy in the atophere Surface Eiivity wo paraeter define the effect of the urface in (4), the urface teperature and eiivity. In (4), repreent the urface kin or radiative teperature, which can differ draatically fro the ore coonly ued urface air 350 Proc. of SPIE Vol. 5425

4 .00 raniion Clear Ab Clear Scat Hazy Ab Hazy Scat Ato WV Wavelength (µ) Figure 3. Aerool traniion curve due to aborption and cattering are plotted for the MWIR pectral region for two different condition. Atopheric water vapor traniion i alo hown for coparion (right axi correpond to the water vapor value). teperature. he urface eiivity ε which i aued here to be - ρ, the urface reflectance, i generally characterized by value above 0.85 in the MWIR and WIR 6. Figure 4 provide exaple of the urface eiivity for four urface type: aphalt, concrete, conifer tree, and gra. Value in the MWIR window range fro for anade urface uch a concrete and aphalt to 0.99 for natural urface feature uch a gra and tree. he value ugget that only a all percentage of the downwelling olar or theral ignal will be reflected and retranitted up to the enor. 3. MWIR RADIOMERIC CHARACERISICS In the VNIR, cattering of the un energy by the earth-atophere yte doinate the radiative tranfer; therally eitted radiance i negligible for alot all condition (fire can be an exception 7 ). he oppoite i true for the WIR, where the theral eiion fro the earth and atophere doinate. he MWIR pectral region i unique in that it i not ituated near the peak of a ource of eiion in the teperature regie of interet and the olar contribution i greatly reduced. Solar radiation ha no coponent in the tranfer of radiation in the WIR, however, the aborption of olar radiation by the earth and the atophere will alter the teperature and the reultant re-eiion in the WIR. Between the two pectral region where contribution fro both ource are iportant, the radiative tranfer i ore coplex with both cattering and aborption effect needing conideration. In Figure 5, exaple of the total radiance for the two cae ued in Fig. are given. OA radiance were coputed uing Modtran with a contant (0.05) urface reflectance. A radiance iniu i een near 2.7 µ where water vapor aborption and low olar radiance cobine to iniize the reflected radiance. he difference in the two curve i all through the MWIR window region, beyond which water vapor aborption produce an increaing eparation in the total radiance curve. he abolute radiance i typically below W/ 2 -r-µ through the MWIR window with increaingly higher value ( 4 W/ 2 -r-µ) beyond the CO 2 aborption band. Proc. of SPIE Vol

5 Figure 4. Graph of the urface eiivity in the MWIR for four urface aterial are hown. he vertical line denote the noinal bound for the MWIR atopheric window region Dry and Clear Wet and Hazy otal Radiance (W/2-r-µ) Wavelength (µ) Figure 5. Curve depicting the MWIR radiance that reache the OA fro a urface of contant (0.05) reflectance and two et of atopheric condition, ) dry and clear, and 2) wet and hazy. 352 Proc. of SPIE Vol. 5425

6 Figure 6 provide a plot of the individual coponent of the radiative tranfer: urface eitted theral radiance, urface reflected downwelling olar and theral radiance, theral path radiance, and reflected path olar radiance. he agnitude of each coponent i hown a a fraction of the total radiance received at the OA. he left plot repreent value for dry and clear atopheric condition and the plot on the right for a wet and hazy cene. he agnitude of both the olar and theral path radiance i a direct reult of the aount of atopheric aborption and cattering, priarily fro water vapor and aerool, repectively. Both radiance coponent increae with increaing huidity and aerool turbidity. he urface coponent (reflected infrared and olar and theral eitted) are alo affected, but in a different anner. he traniion of the urface eitted radiance i attenuated ore for a urkier path, a i the downwelling radiance reflected by the urface back toward the enor. For the MWIR window region ( µ), the OA radiance i doinated by the urface coponent, which ake up fro 80-95% of the total radiance depending on the atopheric condition. he reaining 5 20% i due to the path theral eiion with a all aount fro cattered olar radiation. Beyond the CO2 aborption band, the contribution to the OA radiance fro urface-reflected olar or theral radiation i very all even for very dry condition (le than 2% at 5 µ). 4. MWIR RANSFER he tranfer of radiation in the MWIR ut include both olar reflected and theral eitted coponent. Separate equation can be written for each radiance ource. For clear-ky condition, auing a plane-parallel atophere and a abertian urface, the upwelling radiance at the enor (or OA) S due to cattered olar radiation can be expreed by 8, where S = S + S i the cattered path radiance at the enor and ( ε ) S S( ε ) t, () S i the total (diffue and direct) olar radiance that reache the urface, ε i the urface eiivity, t i the atopheric tranittance for the urface to enor path and S i the pherical albedo. A dependence on wavelength i aued for each paraeter. he two ter on the right-hand ide of () are the cattered path radiance and the urface reflected radiance. he adjacency effect ter ha not been included here, which i equivalent to auing that the target and urrounding background eiivitie are the ae. he direct coponent of the downwelling olar radiance at the urface i given by the forula, Dry and Clear Condition Wet and Hazy Condition Figure 6. Plot of the five radiance coponent for the two et of atopheric condition are hown. he plot depict the fraction of the total radiance for each coponent diplayed in a tacked plot. Proc. of SPIE Vol

7 S,dir = µ F 0 t d. (2) Here F 0 i the olar radiance at the OA, µ 0 i the coine of the olar zenith angle, d i the earth-un ditance ratio and t 0 i the traniion fro the OA to the urface along the un to urface path. he diffue coponent of the downwelling olar radiance i due to ultiple cattering by atopheric olecule and particulate and can be coputed by ultiple cattering code uch a DISOR n-trea 9, which i packaged with Modtran. For therally eitted and aborbed radiation, uing the ae auption a before, the upwelling radiance at the enor (or OA) under clear-ky condition can be expreed by 0, ( ) = ε B t + + ( ε ) S( ε ) t. (3) In (3), i the theral path radiance at the enor and i the downwelling theral radiance at the urface, B i the Planck function, and i the urface kin teperature. A before all paraeter have a dependence on wavelength. he three ter on the right-hand ide of (3) repreent the urface eitted theral radiation, the path radiance, and the reflected downwelling theral radiance coponent of the total eaured radiance at the enor, repectively. Equation () and (3) can be cobined to provide the total radiance received at the enor (or OA), = ( + S ) + t B( ) + ( ε ) ε. (4) S + S ( ) ε he firt ter on the right i the total path radiance fro both cattered olar and theral eitted coponent. he econd ter i the radiance fro the urface either fro theral eiion or fro reflection of downwelling olar or theral radiation. he total at-enor radiance for the MWIR can be divided into three coponent, the path radiance, the urface eitted, and urface reflected downwelling radiance. 5. AMOSPHERIC COMPENSAION In the VNIR/SWIR pectral region where reflected olar radiance i the priary ource of radiant energy, the priary product of atopheric copenation odel i to recover the pectral urface reflectance. For pectral region doinated by infrared radiative tranfer, the priary product of atopheric copenation odel i till the urface reflectance (or ore coonly the urface eiivity), however, the coplex relationhip between urface eiivity and teperature require an extra tep to the atopheric copenation proce. he firt tep retrieve the urfaceleaving radiance by copenating for atopheric effect in a anner iilar to that ued in the VNIR/SWIR. he urface-leaving radiance can be defined a fc = ε B( ). he econd tep require the eparation of the teperature and eiivity coponent of fc uing one of any technique appropriate to the type of enor aking the eaureent. Fro Figure 6, it i apparent that oe ter in (4) contribute ore to the overall at-enor radiance than other. he path-reflected olar radiance and the urface-reflected downwelling theral radiance together provide between and 4 percent of the radiance received at the enor in the MWIR window. Below 3 µ, the path reflected olar radiance appear to provide a ignificant contribution, but due to the very all ource radiance thi contribution i eentially negligible. Neglecting thee two ter for now, we can iplify (4) lightly, + t fc t + ( ε ) S S( ε ), (5) 354 Proc. of SPIE Vol. 5425

8 For thi pectral region, there are now three ter that cobine to approxiate the cloud-free at-enor radiance: the path theral (5-8%), the urface eitted (56-65%) and the reflected downwelling olar radiance (22-30%), with relative contribution to the MWIR window at-enor radiance hown in parenthei. Beyond the 4.25 µ CO 2 band, the olar coponent diinihe o the third ter in (5) can be neglected, + t, λ > 4.5µ. (6) fc Equation (5) and (6) contain two theral radiance ter plu a olar reflectance ter fro which the urface leaving radiance can be obtained, fc = t ( ε ) S S( ε ), (7) where the econd ter on the right i needed for proceing at wavelength le than 4.5 µ. One proble with (7) i iediately apparent: both fc and the reflected olar ter are function of ε. One ethod to circuvent thi i to aue a contant value for the eiivity in the reflected olar ter. For high eiivitie (ε > 0.9), and noinal value for the pherical albedo (S ~ 0.), the olar reflected ter can be approxiated by ( ε ) S. herefore, a typical eiivity variation in the MWIR window of 5-0% would reult in an error in the agnitude of the reflected olar ter of a iilar aount (5-0%). Conidering the agnitude of S which i typically all ( W/ 2 -r-µ), the effect of thi auption would be on the order of 0.0 W/ 2 -r-µ. he etiated total radiance in the MWIR window range fro 0.5 to 0.60 W/ 2 -r-µ, o the error in aking thi auption would be in the range of 2-5%. A further iplification to (7) with thee auption would reult in ( B[ ] S ) = t * t S fc = ε. (8) he quantity * fc repreent the total urface leaving radiance (a cobination of the theral eitted and reflected downwelling olar radiance). he unknown in (8) are the upwelling theral radiance at the enor, the downwelling olar radiance at the urface, and the atopheric traniion. Spectral value for thee variable can be etiated fro radiative tranfer odel calculation uing cene appropriate odel input to obtain an etiate of the total urface leaving radiance in the MWIR. Equation (8) can be expanded to include coponent that were previouly neglected (downwelling theral radiance and the reflected path olar radiance) to iniize error incurred by their excluion. echnique that ight be ued to olve (8) would all require a ufficient knowledge or etiate of the atopheric condition. Etiating the profile of teperature and huidity i an iportant tep to accurately deterining the tranittance between the enor and the urface uing a radiative tranfer odel uch a Modtran. With a goal of fat and efficient atopheric copenation, a forward odeling approach uing large ulti-dienional look-up-table created fro a erie of Modtran run could be ued to provide etiate of the required paraeter. hee table hould include enitivitie due to atopheric water vapor and aerool (the priary variable atopheric contituent). Specific condition uch a very dark pixel (ε ~ ) in the MWIR window could provide inforation on the theral coponent of (8). While thi i a valid and ueful tep in proceing WIR eaureent, the pectral variability of the urface eiivity being greater in the MWIR than in the WIR ake the application ore difficult. 6. SUMMARY he pectral and radioetric characteritic of the radiative tranfer proce in the MWIR have been exained. he effect of ixed gae are nuerou in the MWIR, although uch of the pectral region i doinated by water vapor and carbon dioxide aborption. Aerool were found to till have an influence in the MWIR and hould be included in any radiative tranfer calculation. Surface eiivity varie le than in the VNIR/SWIR, with typical value at or above Proc. of SPIE Vol

9 0.85. Cobining radiative tranfer equation for both the olar reflective and the theral eiive regie, and neglecting ter that provided inial contribution to the overall at-enor radiance, the expected at-enor radiance could be etiated. Fro thi a iplified equation for the urface-leaving radiance including both olar and theral coponent wa derived. iited availability of MWIR data precluded application of the technique at thi tie. ACKNOWEDGMENS he author acknowledge upport for thi work by Mr. Ernie Reith and Mr. Wayne Hallada of the National Geopatial- Intelligence Agency. hi work wa ponored by the Departent of Defene under Contract F C Opinion, interpretation, concluion and recoendation are thoe of the author and not necearily endored by the United State Governent. REFERENCES. Griffin, M.K. and H.K. Burke, Copenation of Hyperpectral Data for Atopheric Effect, incoln aboratory Journal, 4, 29-54, Malku, W., Rando orentz Band Model with Exponential-tailed S ine Intenity Ditribution Function, J. Opt. Soc. A., 57, , Berk, A,.S. Berntein, G.P. Anderon, P.K. Acharya, D.C. Roberton, J.H. Chetwynd, and S.M. Adler-Golden, MODRAN Cloud and Multiple Scattering Upgrade with Application to AVIRIS, Reote Sen. Environ., 65, , McCartney, E.J., Optic of the Atophere; Scattering by Molecule and Particle, John Wiley & Son, New York, NY, 408 pp. 5. Shettle, E.P., and R.W. Fenn, Model for the Aerool of the ower Atophere and the Effect of Huidity Variation on heir Optical Propertie, AFG R , Air Force Geophyic aboratory, Hanco AFB, MA, 94 pp, Becker, F., he Ipact of Spectral Eiivity on the Meaureent of and Surface eperature fro a Satellite, Int. J. Reote Sen.,, , Griffin, M.K., S.M. Hu, H.K. Burke, and J.W. Snow, Characterization and Delineation of Plue, Cloud and Fire in Hyperpectral Iage, SPIE 4049, , Verote, E.F., N. El Saleou, C.O. Jutice, Y.J. Kaufan, J.. Privette,. Reer, J.C. Roger and D. anre, Atopheric Correction of Viible to Middle-Infrared EOS-MODIS Data Over and Surface: Background, Operational Algorith and Validation, J. Geophy. Re., 02, 73-74, Stane, K., S.-C. ay, W. Wicobe and K. Jayaweera, Nuerically Stable Algorith For Dicrete-Ordinate- Method Radiative ranfer In Multiple Scattering and Eitting ayered Media, Appl. Opt., 27, , Gu, D., A.R. Gillepie, A.B. Kahle, and F.D. Palluconi, Autonoou Atopheric Copenation (AAC) of High Reolution Hyperpectral heral Infrared Reote-Sening Iagery, IEEE ran.on Geo. & Re. Sen., 38, , Caelle, V., E. Valor, C. Coll, and E. Rubio, heral Band Selection for the PRISM Intruent. Analyi of Eiivity-eperature Separation Algorith, J. Geophy. Re., 02, 45-64, Proc. of SPIE Vol. 5425