PILOT-81 VVA EXPERIMENT-Analysis of the Multi-Path Transmissometer-Radiometer Measurements

Transcription

1 PILOT-81 VVA EXPERIMENT-Analyss of the Mult-Path Transmssometer-Radometer Measurements R.A. Sutherland and J.E. Butterfeld ARL-TR-2953 Aprl 2003 Approved for publc release; dstrbuton unlmted.

2 NOTICES Dsclamers The fndngs n ths report are not to be construed as an offcal Department of the Army poston, unless so desgnated by other authorzed documents. Ctaton of manufacturers or trade names does not consttute an offcal endorsement or approval of the use thereof. DESTRUCTION NOTICE When ths document s no longer needed, destroy t by any method that wll prevent dsclosure of ts contents or reconstructon of the document.

3 Army Research Laboratory Whte Sands Mssle Range, NM ARL-TR-2953 Aprl 2003 PILOT-81 VVA EXPERIMENT-Analyss of the Mult-Path Transmssometer-Radometer Measurements R.A. Sutherland and J.E. Butterfeld Survvablty/Lethalty Analyss Drectorate, ARL Approved for publc release; dstrbuton unlmted.

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5 Contents Preface Acknowledgements v v Executve Summary 1 1. Introducton 3 2. Overvew of the Experment General Layout Descrpton of Trals Meteorologcal Measurements MPTR Feld Data Reducton Transmssometer Mode Fgure 4a Radometer Mode Examples of Feld-Processed Data Transmttance Data Radance data: Analytcal Methods Multple Scatterng Emssvty And Reflectvty Functons Beer s Law and Lnear Models Sem-emprcal Methods Transmssometer Analyss, Log-T Method Radometer Analyss, Log-R Method Example From Mult-tral Analyss (Near IR Band) 21

6 7. Results from IR Imagery (Md- and Far Infrared) Estmaton of Optcal Thckness Determnaton of Path Radance Summary and Dscusson Performance of Sem-emprcal Methods Performance of Log-R/T Correlaton Methods of Analyss Relatonshp to the Sky-to-Ground Rato Lmtatons of Lnear Models-Path Radance Lmtatons of Lnear Models-Transmttance Caveats and Comments Future Requrements References 33 Appendx A. MPTR Theory 35 Appendx B. Clear Ar Constants 39 Appendx C. Mult-Tral Summary 41 Appendx D. Mult-Pxel Data From Ir Imagery 45 Acronyms 48 Report Documentaton Page 49 v

7 Lst of Fgures Fgure 1. Sketch of feld set-up at the SLAD 100 ft tower ste...5 Fgure 2. Photographs of test ste and smoke generaton...7 Fgure 3. On ste meteorologcal measurements...9 Fgure 4. Examples of MPTR sgnals for (a) transmssometer modeand (b) radometer mode...10 Fgure 5. Example of mult-band MPTR feld data (tral 21608, graphte)...13 Fgure 6. Theoretcal calculatons of emssvty and reflectvty (1)...17 Fgure 7. Demonstraton of the Log T correlaton method appled to the MPTR transmssometer data...19 Fgure 8. Demonstraton of Log-R correlaton method appled to MPTR radometer data...20 Fgure 9. Example of mult-tral analyss for graphte, near IR...21 Fgure 10. Example of mult-tral analyss for brass, near IR...22 Fgure 11. Plots showng results from analyss of magery...25 Fgure 12. Example comparng lnear models wth theory...29 Fgure C1. Mult-tral summary, graphte-vsble...41 Fgure C2. Mult-tral summary, graphte md-r...42 Fgure C3. Mult-tral summary, brass-vsble...43 Fgure C4. Mult-tral summary, brass md-r...44 Fgure D1. Photograph of sngle data frame from IR mager...45 Fgure D2. Dual band mult-pxel tme scans of total radance for graphte...46 Fgure D3. Dual band mult-pxel tme scans of total radance for brass...47 Tables Table 1. Identfcaton of MPTR Bandpasses...6 Table 2. Tral data for 16 February Table 3. Summary of sem-emprcal parameters derved from measurements...27 Table B1. MPTR Clear Ar Normalzaton Constants...39 v

8 Preface In modelng the effects of nfrared (IR) screenng smokes on battlefeld operatons, one must account for the fact that the obscurant tself can be a strong source of IR radaton, often generatng sgnals comparable to, or even much greater than, those from potental targets. The degree to whch ths happens s dependent upon the aerosol optcal thckness, emssvty, and temperature as they affect absorpton, scatterng, and natural blackbody (thermal) emssons, whch for the condtons normally encountered n terrestral applcatons, are strongest at the IR wavelengths. The problem has been recognzed for some tme by the user communty and requrements for ncorporatng emssve effects nto the classcal wargame models such as CASTFOREM have been put forth by both the U.S. Army Tranng and Doctrne Command (TRADOC ) and the Natonal Ground Intellgence Center (NGIC). The problem was addressed by the U.S. Army Research Laboratory (ARL)/Survvablty Lethalty Analyses Drectorate (SLAD) staff n the md-1990s as part of a plot program from whch arose the creaton of a formal techncal program called SCIMITAR 1 whch eventually led to the development of the PILOT81 2 model for smulatng emssve sources and later to the executon of the feld experment of the same name descrbed heren. All work was performed n-house through varous SLAD tools, technques, and met (TTM)] programs supported wth 6.2 (development) fundng and n cooperaton wth SLAD system leaders supported wth 6.6 (analyss) fundng. The major purpose of the experment was to provde an accurate and relable database for the development and verfcaton of the PILOT81 model (and any others of smlar capablty). The man source of data was acqured wth the ARL/SLAD Multple-Path Transmssometer Radometer System, or MPTR, whch provded the measurements necessary to determne both the obscurant drect transmttance and the more llusve path emsson and radance requred for modelng emssve smokes. These ntal experments were lmted n scope to eght feld trals and two obscurant types released nto the atmosphere at temperatures slghtly above ambent and thus nclude effects of both thermal emsson and multple n-scatterng over four spectral bands from the vsble through far IR. 1 Anderson, L., Chenault, T., Churchman, J., Homack, R. and T. Smelker, 1999, SCIMITAR-Scene and Countermeasure Integraton for Munton Interacton wth Targets, U.S. Army Research Laboratory Techncal report, ARL-TR-1633, September Sutherland, R.A, 2002, Determnaton and use of IR band Emssvtes n a Multple Scatterng and Thermally Emttng Aerosol Medum, U.S. Army Research Laboratory Techncal Report, ARL-TR-2688, July v

9 Acknowledgements The followng U. S. Army Research Laboratory, Survvablty/Lethalty Analyses Drectorate personnel partcpated n the feld experment: Joe Churchman, Test Conductor; Lon Anderson, nfrared magery; Steve Lacy, meteorologcal data; Erc Boschert and Ron Hagy, Aerosol Generator. Charle Garret wrote the envronmental mpact statement and dd the search of exstng obscurants databases; and Felca Chamberlan supervsed the safety requrements. Charles Lopez, New Mexco Sate Unversty student, performed the data reducton on the dual band magery and helped wth the data. Mr. Pete Schugart, Tranng and Doctrne Command Analyss Center /Whte Sands Mssle Range and Mr. Frank Polesk, Natonal Ground Intellgence Center, were the orgnal catalysts drvng the requrements for emssve smokes modelng. v

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11 Executve Summary The PILOT81 Emssve Sources Verfcaton Experment produced one of the few databases avalable for quantfyng the radatve emssons of nfrared (IR) screenng smokes and the potental effects on mult-band sensor systems. The major source of data was the U.S. Army Research Laboratory (ARL), Survvablty/Lethalty Analyses Drectorate (SLAD) Mult-Path Transmssometer Radometer (MPTR) system whch provded near smultaneous and collnear measurements of both drect transmsson and total radance over three samplng paths (two transmsson and one total radance) and four spectral bands from the vsble through far IR. Other on-ste nstrumentaton ncluded a dual band IR mager meteorologcal van hgh volume aerosol generator The experments, per se, conssted of eght trals utlzng both brass and graphte flakes as the (arborne) emssve obscurant. Obscurants were released nto the atmosphere at four dstnct mass flow rates producng sem-contnuous aerosol clouds correspondng to a range of optcal depths from τ=0 to a maxmum of about τ=8. The formal objectve of the experment was to provde a database for developng and evaluatng obscuraton models used n IR scene smulatons such as SCIMITAR 1. The study also utlzed the newly nvented Log-R correlaton method to enable a drect expermental determnaton of the sky-to-ground parameter whch s a key nput for contemporary sensor performance models and a requrement for modelng such systems n tactcal wargames such as (CASTFOREM) 2. The experments also flled a sgnfcant vod n the Army s program of Smoke Weeks whch offers a wealth of nformaton on aerosol transmssvty but leaves a sgnfcant dearth of nformaton on aerosol emssvty (and reflectvty) whch are key to modelng emssve aerosol effects. The prmary models chosen as representatve of the current state-of-the-art n Army modelng applcatons are COMBIC 3 for determnng cloud transmttance and PILOT81 4 for determnng path emsson/radance. Overall the MPTR measurements produced convncng evdence for the valdty of the newly developed Log R method for analyzng path radance as well as the more usual Log T method for analyzng transmsson measurements. In general, the obscurant mass extncton coeffcents determned from the MPTR transmssometer measurements agreed wth COMBIC for all four spectral bands that were consdered. Also the results from the MPTR 1 Anderson, L., Chenault, T. Churchman, J., Homack, R. and T. Smelker, 1999, SCIMITAR-Scene and Countermeasure Integraton for Munton Interacton wth Targets, U.S. Army Research Laboratory Techncal report, ARL-TR-1633, September Mackey, D.C., Dxon, D.S., Jensen, K.G., Loncarch, and J.T. Swam, 1992, CASTFOREM (Combned Arms and Support Task Force Evaluaton Model). Update: Methodologes, Department of the Army Techncal Documentaton, TRAC-WSMR-TD Wetmore, A. and S.D. Ayres, COMBIC-Combned Obscuraton Model for Battlefeld Induced Contamnants, US Army Research Laboratory Techncal Report, ARL-TR-1831, August Sutherland R.A., 2002, Determnaton and use of IR band Emssvtes n a Multple Scatterng and Thermally Emttng Aerosol Medum, U.S. Army Research Laboratory Techncal Report, ARL-TR-2688, July

12 radometer measurements were n good qualtatve agreement wth PILOT81 over all optcal depths consdered; however, the quanttatve performance was mproved by tweakng the results usng sem-emprcal emssvty and reflectvty functons n place of the more theoretcally rgorous multple scatterng solutons developed (strctly) for sothermal clouds of radal symmetry. The experments were lmted n scope to two emssve smoke types and obscurant temperatures of a few degrees above ambent. 2

13 1. Introducton Possbly the two most mportant radatve parameters needed to characterze the effects of arborne obscurants on the performance of modern IR systems s the drect beam transmttance and the ntegrated path radance. Together, these two parameters can be used to model the total radant sgnal avalable at the entrance aperture of the recever a gven optcal system as: I rec ( τ ) = I T ( τ ) + I S( ω, τ ) (1) tgt where τ s the obscurant optcal thckness, T (τ) s the drect transmttance, ω s the obscurant sngle scatterng albedo and the ndex refers to the partcular recever spectral bandpass of nterest (tab. 2). Defned as such, the frst term n eq 1 represents that fracton of the receved sgnal havng orgnated from some hard target of surface radance, I tgt, that reaches the recever essentally unmpeded by the ntervenng medum (.e., drect transmsson) and the second represents all other stray contrbutons from the aerosol cloud and/or the ambent surroundngs at all ponts along the propagaton path (.e., path radance). In eq 1, the (normalzed) path radance functon, S(ω ;τ), s generally comprsed of two parts accountng for both the reflectve and emssve propertes of the aerosol cloud as: path radance functon : bkg S( ω ; τ ) = a R( ω ; τ ) + b E( ω ; τ ) where the frst term accounts for all contrbutons due to n-scatter orgnatng from the ambent surroundngs, and the second accounts for all contrbutons orgnatng from thermal emssons nternal to the aerosol cloud. In wrtng the above expressons as such, ambent nputs were assumed to be sotropc and the obscurant temperature can be treated as unform. These approxmatons are made for convenence n establshng manageable gudelnes for the analyss of the feld data to follow and do not necessarly reflect any lmtatons on the scope of the study. A more complete descrpton of the underlyng theory and the physcal processes nvolved s gven n the PILOT81 documentaton (1). Wth ths beng the case, the parameters, a and b become the sole ambent drvers representng, respectvely, the atmospherc sources for nscatter and the aerosol (obscurant) sources for thermal emsson. For IR scenaros t s furthermore customary to express these parameters n terms of ther equvalent blackbody temperatures as: atmospherc drvers : a F (T ) σt F (T 4 ) σt. π * 4 * amb amb cld cld = ; b = 3 I bkg π I bkg. where T ext and T cld represent the equvalent blackbody temperature (absolute) of the ambent atmosphere and the aerosol cloud, respectvely, and the functons F * (T) represents the calculated fractonal blackbody rradance wthn the partcular spectral band of concern. It may be notced n eq 3 that the background radance, I bkg, as used here turns out to be a smple ) (2) (3) 3

14 normalzng factor that actually cancels out when used n eq 1. Later ths parameter wll be assocated wth clear ar radometer measurements n the analyss. In all of the above expressons and those to follow, the obscurant optcal thckness, or optcal depth, τ, s the ndependent varable representng the obscurant and s defned formally n terms of the path ntegrated aerosol concentraton and s related to the Beer s Law for drect transmttance as: transmttance : T ( τ ) = exp( τ ) optcal thckness; (4) τ = α L o C( r') dr' where C(r ) represents the aerosol mass concentraton at any pont, r, along the target-recever path of propagaton, and L s the total path length. The (band dependent) obscurant mass extncton coeffcent, α, accounts for both absorpton and out-scatterng along the path [.e., α=α abs + α sct ] and s related to the sngle scatterng albedo as [ω=α sct /(α abs +α sct )]. In applcatons, the path ntegral n eq 4 s sometmes referred to as the concentraton path length, or smply the CL Product and s a property of the aerosol mass propertes, ndependent of the recever bandpass. Reasonable estmates of the optcal propertes of a wde range of mltary obscurants can be found n the COMBIC documentaton (2). The man purpose of the analyss descrbed heren was to develop and test methods for determnng the relatonshps between the obscurant optcal thckness, the drect transmttance, and the normalzed path radance usng measurements obtaned from the SLAD or MPTR, system (3). As t happens, methods for determnng the obscurant drect transmttance have been developed and refned over the years n the course of the varous Smoke Weeks conducted by the U.S. Army and summarzed n detal elsewhere (4). However, methods for determnng the path radance are not as well understood and there s lttle quanttatve data avalable, especally for wavelengths n the IR where the effects of both multple scatterng and thermal emsson can be mportant. Despte ths dearth of nformaton, t s nevertheless mportant to realze that for emssve sources t s actually the (nterferng) path radance that can lmt system performance and not necessarly the drectly transmtted sgnal alone, a fact that has often been overlooked n the past but one that has agan been addressed n recent expermental studes (5). It s ths latter defcency that s most fully addressed n ths report. The ultmate applcaton for the analyss here s to mprove the representaton of emssve obscurant effects n scene smulatons models such as SCIMITAR (6), systems performance models such as TARGAC (7), and wargame smulatons such as CASTFOREM (8). In the remander of the report, sectons 2, 3, and 4 are used to descrbe the expermental set-up, develop the MPTR theory, and present examples of actual feld measurements. Secton 5 ncludes a bref descrpton of the use of the aerosol emssvty and reflectvty functons, both theoretcal and sem-emprcal, and the ratonale behnd the Log R/T correlaton methods for extractng the aerosol transmttance and path radance from the MPTR data. Sectons 7 and 8 4

15 present an overvew of the entrety of the mult-tral experments usng both the MPTR and the supportng IR magery. In the fnal secton we demonstrate utlty of the results n modelng emssve obscurant effects usng sem-emprcal methods, explan the relatonshp of the MPTR measurements to the sky-to-ground parameters used n the older models, and dscuss the lmtatons of the of other modelng approaches based on lnear approxmatons. There are four appendces; the frst three provdng detals of the MPTR measurements and the fourth gvng more detal on the use of conventonal IR magery. 2. Overvew of the Experment A unque and defnng feature of the experment was the smultaneous measurement of drect transmsson and total radance over multple paths and multple spectral bands through artfcally generated aerosol clouds of vared optcal thcknesses. Radatve measurements were performed wth both the MPTR system and a research grade dual band IR mager. The experments were conducted near the SLAD 100 ft tower ste at the Whte Sands Mssle Range, NM. The general expermental layout s shown n fgure 1. North Plume GS-1 Background GS-2 WIND Generator Recever Fgure 1. Sketch of feld set-up at the SLAD 100 ft tower ste. Key elements of the experment were; (a) three horzontal samplng lnes, two for transmsson, one for radance, (b) a varable rate aerosol generator for ether brass or graphte, (c) supportng meteorologcal measurements, (d) vsble band vdeo documentaton, and (e) supportng IR dual band magery. 5

16 2.1 General Layout In the fgure. 1, the central lne of sght (bold arrow) was drected outward along a headng of roughly 44 and was the man path over whch the MPTR total radance was measured aganst the dstant natural background. Smultaneous measurements of drect transmsson were performed along the two outer (dashed) paths termnatng at the locatons labeled GS-1 and GS-2 where the MPTR gude sources were located. The total dstance from the MPTR recever to the gude sources was about 525 m and the angle separatng the two transmssometer paths was approxmately 4. In all cases the lnes of sght were parallel to the (earth) surface and fxed at a heght of 2 m. All transmsson and radance measurements were synchronzed to wthn about 1/10 s and were carred out smultaneously over the four spectral bands dentfed n table 1. Table 1. Identfcaton of MPTR Bandpasses. Band 1: λ 1 = um, vsble Band 2: λ 2 =1.06 um, near nfrared Band 3: λ 3 =3-5 um, md nfrared Band 4: λ 4 =8-12 um, far nfrared The experments (eght trals total) were carred out n a sngle day over the course of about 90 mn under generally far weather condtons (see meteorologcal data later). The aerosol generator was located at a pont about half the dstance between the MPTR recever and the transmssometer gude sources and from 25 to 50 m upwnd of and generally perpendcular to the man path- the exact dstance and locaton dependng upon the wnd speed and drecton. 2.2 Descrpton of Trals There were eght full trals of roughly 6 mn duraton each and all conducted successvely n alternatng pars of ether graphte or brass powder usng the general scheme of table 2. Table 2. Tral data for 16 February Tral No Start End Type R(#/m) :45:59 12:55:56 Dust N/A :56:59 13:08:28 Graphte :09:45 13:23:12 Brass :24:14 13:34:17 Graphte :34:59 13:45:27 Brass :46:29 13:58:22 Graphte :59:15 14:09:27 Brass :09:59 14:20:27 Graphte :20:59 14:31:28 Brass 2.0 6

17 The frst column n table 2 dentfes the tral number by date (216) and set (01through 09), the next two columns dentfy the precse tme of day (Mountan Standard Tme (MST)) for the start and end of each tral, the fourth column dentfes the obscurant type, and the ffth column gves the generator mass emsson rate settng. As noted, the generator mass emsson rate for the frst par of trals was set at 10 lb per mnute (the maxmum used) and then adjusted ncrementally downward to a mnmum of 2 lb per mnute for the fnal set. The frst tral was a shakedown run usng locally generated dust and s not ncluded n the formal analyss. The man trals were conducted n rapd successon n an attempt to complete all of the experments durng nearly constant meteorologcal condtons (see meteorologcal data later). The general appearance of the obscurant clouds s demonstrated n the photographs of fgure 2 whch were taken wth a commercal vsble band dgtal camera. Fgure 2. Photographs of test ste and smoke generaton. The two upper photographs n fgure 2 were taken from near the top of the 100 ft tower lookng generally eastward and downward along the man samplng path and the lower two were taken from ground level near the base of the tower. In both cases the left photograph refers to brass and the rght refers to graphte. In the uppermost photographs, the aerosol generator and supply vehcle can be seen to the mmedate rght of the aerosol plume. Other objects are the bare drt 7

18 road, power poles, and a varety of other natural and manmade features n the background. In the lower photographs, the large object n the foreground s the blackbody source used for calbraton and the two brght lghts most apparent at the left and rght extremtes n the brass example are the MPTR gude sources at the locatons labeled GS-1 and GS-2 n fgure 1. The brass powder produced a vsbly brght, brownsh, cloud smlar n color to the appearance n bulk samples. Lkewse, the graphte powder produced a vsbly dark, nearly black, cloud wth occasonal patches of a lght gray most often seen near the cloud edges. In all cases the method of aerosol generaton produced reasonably well-defned, sem-contnuous plumes of about the sze and concentraton expected and wth the characterstc nternal chaotc structure characterstc of such clouds when generated n the real (turbulent) atmosphere. Overall the plumes were well behaved n that they were constraned to near the ground and mantaned a reasonably coherent large scale structure over the testng dstance. However, some cases of local vertcal loftng could be seen n the vsble band magery whch most often occurred for the graphte trals at ponts nearest the generator and was later evdenced n the transmssometer data. 2.3 Meteorologcal Measurements The weather durng the earler part of the week of the experments was characterzed by strong frontal actvty that caused excessvely hgh wnds the day pror to the experments; however, by the tme the trals were conducted the condtons had changed to generally far and cloud free wth lght to moderate wnds. Fgure 3 shows the on-ste measurements for the full durnal perod that were obtaned from a moble van located approxmately 100 m southwest of the man area. 8

19 Fgure 3. On ste meteorologcal measurements. Wth reference to the measurements shown n fgure 3, the wnds durng the mornng were lght and varable n both speed and drecton makng t more or less unsutable for testng because of the problems encountered n correctly placng the aerosol generator such as to ntersect the nstrumented lne. By the afternoon, however, the wnds had stablzed notceably and eventually settled n to a drecton consstently from the south (180º) n general agreement wth the forecast from the nearby range C staton. The tme perod durng whch the experments were conducted are ndcated by the vertcal hash marks n fgure 3. As noted, the experments were started near 1130 hrs (MST) shortly after the wnds had stablzed to a mean speed of about 3 m/s; however, they dd ncrease durng the course of the experment to a value of about 5 m/s by the end. Ths tmeframe was slghtly past local noon, thus the sun was near apex at about 30º south roughly along the same headng as the plume centerlne and perpendcular to the man samplng lne. Accordng to the radometer data, the solar (drect + dffuse) rradance that day was at a mdday maxmum of about 650 W/m 2 durng the begnnng of the experment and decreased to about 600 W/m 2 by the tme the trals were completed. Ar temperature was nomnally about 45 C at the begnnng and dropped to about 40 C by the end. 9

20 3. MPTR Feld Data Reducton The SLAD MPTR system as employed for ths test provdes a measure of the total radance aganst a natural background over a central lne of sght plus a measure of the drect radance from the gude sources over two adjonng lnes of sght as noted prevously n fgure 1. Pror to the analyss, the raw sgnals are subjected to a certan amount of calbraton, normalzaton, and manpulaton to compensate for clear ar atmospherc effects so that the reduced data s representatve solely of the aerosol cloud. In the fnal analyss, the data are used to yeld estmates of the relatve transmttance and normalzed path radance as defned n the ntroducton of secton 1. The methods for dong ths are descrbed n detal n appendx A. In ths secton the process s dscussed n somewhat abbrevated detal usng the examples of raw data plotted n fgure 4 as a reference. Fgure 4. Examples of MPTR sgnals for (a) transmssometer mode and (b) radometer mode. In fgure 4, the upper sketch refers to the transmssometer mode (tral 21608, graphte) and the lower sketch refers to the radometer mode (tral 21609, brass). As ndcated, a typcal tral takes about 5 7 mn (.e., 600+ s), whch ncludes tme for both data collecton durng the (smoke) event and tme before and after to allow for calbraton. The onset and duraton of these varous tme perods, annotated on the fgure, are usually clear from nspecton of the raw sgnals and are evdenced by a sudden changes n sgnal level; these tme perods wll not be overly elaborated on n ths secton. Both sets of data were taken n the vsble band and are dscussed more fully n the followng paragraphs. 10

21 3.1 Transmssometer Mode (Fgure 4a) In normal MPTR operaton all raw transmssometer sgnals are calbrated and scaled n the feld to gve real tme measures of what s called the relatve (aerosol) transmttance. The calbraton process nvolves takng measurements for some short tme perod before (and sometmes after) each tral. These data are then used to normalze the sgnal to the clear ar readngs. More detals are gven n appendx A but the procedure ultmately produces a tme dependent relatve transmttance, T (t), extracted from the raw data as follows: T ( t ) X ( t ) X X X mn = (5) where X (t) represents the raw (voltage) sgnal receved n one of the four optcal channels dentfed prevously n table 2 (.e., =1,4) and t s elapsed tme. The scalng parameters, X max and X mn, are obtaned from readngs taken n the tme perod just pror to the release of the obscurant. In the example of fgure 4a, the frst 20 s or so labeled start represent the ntal clear ar readng to determne X max, whch s followed mmedately by a nomnal s tme perod labeled shutter closed to determne a zero readng, X mn. The net effect of eq 5 s thus to produce a sgnal normalzed to the clear ar value such that the new clear ar reference s set to 100 percent. Note that ths normalzaton procedure also elmnates the need to know the actual value of the radance from the gude sources. After another short perod of clear ar readngs labeled shutter open, the obscurant s released and reaches the samplng lne a short tme later as evdenced by an mmedate decrease n the sgnal at the pont labeled obscurant on. (After some specfed elapsed tme (fve mn for these trals), the generator s turned off, and the sgnal slowly rses as the smoke clears as s evdent near the end of the trace n the regon marked off. Although the effects of generator fluctuatons cannot be entrely ruled out, the ntense and very rapd fluctuatons n the sgnal durng the tme that the obscurant s on s due, for the most part, to mechancal wnd turbulence as t affects aerosol concentraton and s often observed n experments of ths type when conducted durng daytme condtons. Calbrated and scaled as such the reduced sgnal now represents the aerosol transmttance from whch can be mmedately calculated the optcal depth and path ntegrated concentraton as a functon of tme usng the nverted form of Beer s Law, that s: max mn optcal thckness τ (t) = -Ln[T (t)] path concentraton : CL( t 1 ) = τ ( t ) α : (6) The ntal and less pronounced sgnal reducton just pror to the obscurant release s an artfact due to dust and other debrs created by the generator startup and s to be gnored n the analyss. 11

22 where t s to be noted that the CL product, beng a measure of the obscurant mass, s ndependent of the partcular bandpass selected and thus should yeld the same result for all four optcal channels. Note also that the CL product cannot be determned from the transmttance measurements alone unless there s an ndependent measurement of α, the band-dependent mass extncton coeffcent (assumed to be a constant for a gven spectral regon and ndependent of tme). In calculatng the CL product for later use, an average was computed based on all four spectral bands assumng a known value for the mean as determned from laboratory data. Ths data, for the record, were taken to be <α>= 1.0 (m 2 /gm) for brass and <α>=1.45 (m 2 /gm) for graphte. These and other assumptons concernng the obscurant optcal behavor are dscussed n later sectons. 3.2 Radometer Mode (Fgure 4b) The ntal steps n the radometer mode are very smlar to those of the transmssometer mode. However, n ths case there are no artfcal gude sources n the path so that the pre-event readngs n ths case correspond the clear ar readngs taken aganst the natural background. Thus the correspondng equaton for the radometer mode s dentcal n form to that of eq 5, that s: Y ( t ) Ymn R ( t ) = (7) Y Y where, n ths case Y (t) represents the tme-dependent radometer sgnal. The scalng parameters Y mn and Y max are obtaned n the same manner as before usng the pre-event opened and closed shutter readngs. In fgure4b, t s nterestng to note that n ths case the sgnal actually ncreases when the obscurant (brass) s ntroduced. Ths ndcates that the loss n sgnal due to extncton (.e., lower transmttance) s more that compensated by the gan n sgnal due to the path radance. However, n most other cases, the IR n partcular, the obscured sgnal s more lkely to decrease as wll be seen n later examples. Wth the raw data so calbrated the resultant sgnal now represents a measurement of the total receved radance (actually normalzed to the clear ar) dscussed n secton 1. The next task s to separate out the transmttance and path radance contrbutons usng the basc relatonshp of eq 1. There s a problem because measurements are not all collnear; however, any errors are mnmzed provded that the obscurant concentraton dstrbutons over the three samplng lnes are not nordnately dfferent. Thus, t s vald to calculate the path radance from the measured data by performng a pont by pont dfferencng at each tme nterval usng the smultaneous measurements from all three paths, gnorng for the moment the slght delay due to obscurant transport. That s, usng and rearrangng the tme-dependent normalzed verson of eq 1, for each tme sample, t, the result s: max path radance : mn S ( t ) = R ( t ) T ( t ) where the total radance, R (t), s obtaned from the radometer samplng path and the transmttance, T (t) s obtaned by averagng over the two transmssometer paths. At ths pont t s also necessary to assume that the tme lag for obscurant transport between the samplng lnes s small compared to the averagng tme whch s the same as assumng that the measurements are essentally tme synchronzed. The fact that these condtons are approxmately mantaned 12 (8)

23 was qualtatvely verfed from the magery data and more quanttatvely from the correlaton analyss dscussed n later sectons. 4. Examples of Feld-Processed Data Before proceedng to the actual analyss t s worthwhle to examne some general trends that become more or less mmedately apparent from casual nspecton of the feld-processed raw data. The example for graphte (tral 21608) shown n fgure 5 wll serve as a reference for dscusson. NOTES: (a) LOS-1relatve transmttance measurements performed over LOS-1 (b) LOS-0 total radance measurements performed over LOS-0 (c) LOS-2 relatve transmttance measurements performed over LOS-2 Fgure 5. Example of mult-band MPTR feld data (tral 21608, graphte). 13

24 In all cases (fg. 5), the ntroducton of the obscurant markng the begnnng of the event near the 60 s mark and the endng some 300 s later s mmedately evdent from the traces and need not be elaborated upon further. The four rows n each matrx correspond to the four spectral bands dentfed table 1. Note that the center column, (b) LOS-0, shows both the orgnal, nearly featureless, total sgnal plus a mathematcally enhanced verson that shows more detal n the fluctuatons. 4.1 Transmttance Data Perhaps the most dstnctve feature seen n the measured data s the fact that the transmttance traces for all four bands are nearly dentcal for each of the two transmssometer lnes of sght. Ths statement apples not only to the overall magntude of the sgnal but also to the detals of the fluctuatons. Ths observaton was later found to be true for all trals, both brass and graphte, and s not necessarly unexpected snce t s known from other sources that the mass extncton coeffcents for both obscurant types are nearly ndependent of wavelength (2). It s somewhat more nterestng to note that there s also a hgh degree of correlaton between the traces for the two (separated) transmssometer paths. Ths, too, s not entrely unexpected snce, n both cases, the measurements are based on the same cloud sampled over slghtly dfferent paths, but t does attest ndrectly to the consstency of the data n the sense that there appear to be no artfacts brought about by faulty samplng technques. It s also noteworthy that the transmttance along the path nearest the generator source (.e., upwnd, LOS-2 s slghtly hgher than that along the farther downwnd path (.e., LOS-1). Ths dfference was more evdent for graphte than for brass and was probably due to aerodynamc and thermal loftng of the cloud as a whole whch was also observed n the vdeo data. Another observaton of some nterest s the fact that the path nearest the source has some very hgh frequency components that appear to be damped farther downwnd whch may be ndcatve of the ncreased mxng generally predcted by dffuson theory. Overall the same general behavor descrbe here was also observed for brass (not shown) although t was consstently found that, for a gven tral par, the mean transmttance for graphte was lower than that for brass whch s consstent wth other fndngs on the relatve magntude of the mass extncton coeffcent for the two obscurant types dscussed earler. 4.2 Radance Data Lookng frst at the two shorter wavelength bands, perhaps the most mmedate and dstnctve feature of the (unenhanced) radance plots of fgure 5 s the fact that the measured total radance s almost unaffected by the ntroducton of the obscurant. Ths behavor was noted prevously and s an ndcaton of the near zero balance between the competng processes of sgnal attenuaton and path emsson whch actually resulted n a net ncrease n total radance for the case of brass that was noted earler (fg. 4b). For the graphte sample, however, the sgnal s reduced n both cases ndcatng that attenuaton s the more domnant mechansm although the dfference s small. The enhanced plots show that the net effect s about the same for the vsble and the near IR bands, even n the detals of the fluctuatons. At the longer wavelengths t appears that attenuaton becomes relatvely more sgnfcant as evdenced by the fact that both traces decrease when the obscurant s ntroduced, much more so for the far IR band than for the md-ir band. However, at ths pont t becomes clear that the far 14

25 IR sgnal has approached the lower threshold of the MPTR senstvty as evdenced by the consstent cappng out at low sgnal levels. Ths effect was even more evdent from the other trals and for ths reason the far IR data from the MPTR was not used n the analyss. However, the qualtatve aspects of the data were later verfed wth the thermal magery where t was observed that total radance n the far IR band was consstently lower that n the md IR band as dscussed n more detal n secton 8. Another nterestng feature seen from the radance plots s the near perfect correlaton n the fluctuatons between the vsble and near IR bands whch s most clearly shown n the enhanced plots. The same may be sad of the correlatons between the md- and far IR bands although the evdence s less convncng due to the problem wth the threshold. It s reasonably clear, however, that the correlatons between the longer and shorter bands are not nearly as strong. For brass (not shown), the cross-band correlatons n total radance were not nearly as strong as for the graphte example for any of the bands studed. The reasons for the specfc behavor are not totally clear but may be due to the fact that the domnant mechansms at the shorter wavelengths derve manly from ambent n-scatter whle those at the longer wavelengths derve manly from nternal thermal emsson. In a later secton the correlatons are analyzed analytcally usng all trals. 5. Analytcal Methods In ths secton the theoretcal framework s revewed and analytcal procedures brought to bear n the analyss of the expermental data. The underlyng assumptons are; (1) that the processed feld measurements do ndeed provde an accurate measure of mult-band transmttance and the correspondng (near) smultaneous mult-band path radance for each of the spectral bands consdered, (2) that the transmttance data can be tested n terms of the Beer s Law relatonshp, and (3) that the path radance results can be explaned usng sem-emprcal methods based on theoretcal calculatons of emssvty and reflectvty. There s, of course, the possblty that the data may contan new fndngs beyond the scope of exstng theory. It s thus left for the analyss to provde the means necessary to test the varous relatonshps predcted by exstng theory and to determne tests for valdatng new fndngs. For the drect transmttance measurements, the applcable method s the well known Log-T correlaton technque whch essentally tests the data aganst the Beer s Law relatonshp. For the path radance measurements, the methods are not so well-known and necesstated the nventon of an analogous new technque, whch we called the Log-R method that essentally exposes departures from deal lnear behavor. Sem-emprcal methods were then developed based on exact calculatons suppled by PILOT81 model whch was compared wth the measurements. 5.1 Multple Scatterng Emssvty and Reflectvty Functons The dffculty n applyng the expressons of secton 1 to the task at hand les n the fact that the emssvty and reflectvty functons are generally not known from measurements and are dffcult to calculate n real world applcatons. However, t s possble to generate exact 15

26 solutons that are rgorous for certan dealzed stuatons that mght be smlar to those of the real world that can be used as gudelnes for the analyss and ths s the phlosophy behnd the sem-analytcal approach taken here. For a homogeneous and sotropc cloud of radal symmetry, the emssvty and reflectvty functons can be computed exactly over any path through the cloud from ntegral expressons of the followng form (1): emssvty : E( ω, τ ) = τ o J ( ω; τ )e where J (ω;τ) s the so-named emssve source functon, generally obtaned from models such as PILOT81 (1), and τ s the optcal thckness as calculated over the total length of the targetrecever path. A smlar calculaton can be performed for the reflectvty functon; however, for an sothermal cloud, t s smpler to use the followng conservaton relatonshp: sothermal clouds : τ dτ E( ω; τ ) + R( ω; τ ) = 1 T( τ ) where the expresson on the rght sde s dentcal to the classcal defnton of absorptvty, (.e., A(τ)=1-T(τ)), although ths termnology s somethng of a msnomer snce the transmttance accounts for both absorpton and out-scatterng. Equaton 10 s vald for all spectral bands and all cloud geometres but, as noted, s strctly applcable only for the case of sothermal clouds and the condton of sotropc scatterng. Some plots of the emssvty and reflectvty functons for optcal depths up to τ=4 based upon source functons obtaned wth PILOT81 are shown n fgure 6. (9) (10) 16

27 Fgure 6. Theoretcal calculatons of emssvty and reflectvty (1). As s evdent from nspecton, the functons are well-behaved and predctable n the sense that all curves ncrease monotoncally wth ncreasng optcal depth, beng somewhat lnear n the begnnng and then levelng off as the optcal depth ncreases to the pont becomng more or less nsenstve to changes at the hgher values. Note the smlartes but also the reversal of the orderng of the curves for albedo n the two cases. The logarthmc plots are shown here for later reference and are useful n that they demonstrate a lnear tendency, especally for the emssvty case and smaller values of optcal depth and the extremes of albedo. 5.2 Beer s Law and Lnear Models Perhaps the smplest approxmaton that can be appled for the analyss s to assume the source functon, J (ω;τ), to be constant over the path of nterest. In ths case the ntegraton n eq 9 can be performed mmedately to yeld the followng smple Beer s Law form for the normalzed path radance. Beer's Law (path radance): S ( τ ) = [ 1 T ( τ )] 0 = [ 1 exp( α CL )] (11) 17

28 where the superscrpt o s used to denote zeroth order and the transmssvty s expanded n terms of the obscurant mass extncton coeffcent and CL Product. The Beer s Law s referred to as a lnear model, n part, because t s lnear wth respect to transmttance, but, of more mportance, s the fact that t s also lnear wth respect to the logarthm [Ln(1-S)], the sgnfcance of whch wll be made more clear later n ths secton. Despte the smplstc appearance and lmted range of valdty, the above expresson plays a central role n modelng and analyss. 5.3 Sem-emprcal Methods For thn optcal depths and for some other specal cases, the Beer s Law, or lnear form gven by eq 11 s suffcent for estmatng path radance; however, for the more general case nvolvng both thermal emsson and multple n-scatter the need for a more comprehensve approach s antcpated and, thus, defne a hgher order sem-emprcal ntutve approxmaton based on the general form of the plots of fgure 6 as follows: sem - emprcal : E( τ ) = β [ 1 exp( )]... emssvty R( τ ) = A( τ ) E( τ )... reflectvty τ A( τ ) = 1 exp( )... absorptvty τ 1 where the varous constants [β,τ 1,τ 2 ] are emprcally based, band dependent, scalng parameters to be derved from the analyss. In practce, t was found that these functons dd an accurate job n mantanng the overall qualtatve features of the rgorous solutons whle at the same tme offerng a more flexble bass for analyss. τ τ 2 (12) 5.4 Transmssometer Analyss, Log-T Method The Log-T correlaton technque s an often-used method for analyzng transmttance measurements and s based solely on the Beer s Law of extncton. Brefly, the approach s to frst defne a test metrc, Z (t) as follows: Ln T Correlaton Method : Z ( t ) = Ln[T ( t )] where T (t) represents the (tme dependent) measured transmttance as determned n the manner descrbed n secton 3. It s clear from nspecton that a pont by pont plot of Z (t) versus CL(t) should, f all assumptons are correct, yeld a straght lne ntersectng the orgn wth a slope equal to the value, α, the obscurant mass extncton coeffcent for the spectral band of nterest. Ths s the essence of the Log-T correlaton method and an example of how t works usng real measured data s demonstrated n fgure 7. (13) 18

29 Fgure 7. Demonstraton of the Log T correlaton method appled to the MPTR transmssometer data. In fgure 7, the upper plot labeled (a) s taken as the startng pont and shows the raw tme dependent transmttance measurements taken, for ths partcular example from Tral (graphte). The next step, llustrated n the plot labeled (b), s to compute the test varable, Z (t), usng the logarthmc expresson of eq 13 at each tme step. Next the test varable, Z (t) s plotted versus CL(t) n the plot labeled (c), whch s the essence of the Log-T correlaton method for whch the result here does ndeed ndcate a clear lnear relatonshp as expected. In ths case, the analyss yelds a slope slghtly greater than unty, ndcatng that the mass extncton coeffcent for ths partcular spectral band s somewhat smaller than the mean. The last plot labeled (d) s formed by nvertng eq 13 to recover the pont-by-pont transmttance plus the correspondng Beer s Law analytcal ft. The partcular results here are more or less representatve of all trals whch, when taken together, gve convncng evdence of the valdty of the theory and the varous underlyng assumptons, more of whch wll be dscussed n later sectons. 19

30 5.5 Radometer Analyss, Log-R Method The Log-R correlaton approach s smlar to the Log-T approach except that the underlyng framework s based on the Beer s Law expresson for attenuaton [.e., A(τ)=1-T(τ)] rather than extncton. The analogous test metrc n ths case becomes: Ln R Correlaton Method : Z ( t ) = Ln[ 1 S ( t )] (14) where S (t) s the normalzed path radance. The ratonale behnd ths partcular choce of test metrc les n the form of the zeroth order soluton of eq 11. That s, upon takng the approprate logarthm as suggested by eq 14 and followng through wth the Beer s Law expresson, a pontby-pont plot of the new metrc, Z (t), versus CL(t) should, f the assumptons are correct, yeld a straght lne nterceptng the orgn and, as before, wth slope equal to the value of the mass extncton coeffcent. Of course devatons from a straght lne then ndcate departures from the underlyng assumptons, the most lkely nvolvng ssues of thermal emsson, multple scatterng, and combnatons thereof not treated n the lnear approxmaton. An example of how the method works usng real measured data from tral (graphte) s shown n fgure 8. Fgure 8. Demonstraton of Log-R correlaton method appled to MPTR radometer data. 20

31 In ths case, the startng pont, labeled (a) n fgure 8, s represented by a plot of the total radance plus the correspondng transmttance (taken as the average over the two transmssometer paths). The next step s to subtract the drect transmttance from the total radance to obtan the normalzed path radance n accordance wth the dscusson leadng up to eq 8 n secton 4. The result from ths step s shown n the plot labeled (b) where the nterestng fact s noted the that the path radance n ths cases accounts for approxmately percent of the total radance. The next step s to take the approprate logarthm and form the correlaton wth optcal depth whch s shown n the plot labeled (c), and n nverted form n the plot labeled (d). Ths s the essence of the Log-R correlaton method whch does, ndeed, show evdence of an ntal lnear relatonshp (dashed lne) wth sgnfcant departures at hgher optcal depths as expected. The smooth curves n the fnal two plots represent analytcal representatons based on the sem-emprcal relatonshps descrbed n secton Example From Mult-tral Analyss (Near IR Band) In ths secton, the analyss methodologes are appled to the entrety of the eght trals makng up the experment (tab. 2) usng the near IR band as an example. Results for the other bands are presented n appendx C. The purpose n performng multple trals was to get a good database coverng a wde range of optcal depths, or mass loadngs, for both obscurant types. The entrety of the experment was done n as short a tme as possble so that the meteorologcal and atmospherc condtons dd not change apprecably. The results for the near IR band are summarzed n the plots of fgure 9 for all graphte trals and fgure 10 for all brass trals. Fgure 9. Example of mult-tral analyss for graphte, near IR. 21

32 Fgure 10. Example of mult-tral analyss for brass, near IR. In each of the fgures, the results are grouped nto a 4x4 matrx of plots wth the rows and columns defned as follows. The frst column n each set represents the measured transmttance plotted as a functon of tme along wth the correspondng optcal depth (x10) as determned from the Beer s Law relatonshp at each tme step. In both cases the plots represent the average over the two transmssometer paths. The second column represents the measured total radance along wth the calculated path radance as determned from eq 8. Both the transmttance and radance data refer to relatve values as determned by normalzng to the clear ar readngs as dscussed n secton 4. The remanng two columns represent the results of the Log-T analyss appled to the transmssometer data (thrd column) and the correspondng results of the Log R analyss appled to the radometer data (fourth column). In all cases the horzontal rows refer to each of the four generator settngs (mass emsson rate) as ndcated on the margn to the rght. Some nsght can be ganed mmedately from even a casual nspecton of the general trends n the varous plots. For example, t s clear from examnaton of the transmttance plots that the optcal thckness ncreases (and consequently the transmttance decreases) wth ncreasng mass loadng and the fact that, for the same mass loadng, the graphte optcal thckness s generally hgher than the correspondng value for brass (actually most notceable at the lower mass loadngs). There was some early concern that, at the hgher mass loadngs, the transmttance may be so low as to exceed the lower threshold of the MPTR system. Evdently ths s true for the extreme cases where the transmttance appears to bottom out and the optcal thckness appears to exceed the upper lmt near τ=12. Later t was establshed that ths lmt occurred for measurements performed at optcal depths exceedng τ=8 whch were subsequently gnored n the analyss. 22

33 Referrng now to the radance data (second column), t s apparent that the measured total radance s much less senstve to mass loadng than ether the optcal thckness or the transmttance. In fact, there s almost no change n the measured value of ether the path radance (lower trace) or the total radance (upper trace) n the lower three scans for ether sample. Another mportant qualtatve observaton s the fact that the total radance s relatvely nsenstve to the optcal depth fluctuatons, much unlke ether the path radance or transmttance. The reason for ths behavor s, of course, due to the nature of the competton between the drect and dffuse contrbutons alluded to n prevous sectons. It s also mmedately apparent from the second column that the path radance s ntally hgher for graphte (75 percent) than for brass (50 percent) and that both ncrease wth ncreasng mass loadng, quckly reachng a saturaton level most evdent n the extreme rates where the path radance makes up the near entrety of the total radance, a fact most apparent n the extreme for graphte. Turnng now to the Log-T analyss results (thrd column) t s clear that, despte the varatons and fluctuatons n the raw transmttance measurements, the results of the analyss show a much more ordered vew as manfested by the near straght lne relatonshps. The apparent nose n the data whch generally appears to ncrease wth ncreasng optcal thckness could be due to real world (turbulent-drven) fluctuatons but s more lkely due to expermental errors often observed n these type experments when the transmsson s very low. For both samples, the results strongly support the Beer s Law formulaton as evdenced by the near straght lnes n most cases although there s some ndcaton of a mass loadng effect manfested by a slght ncrease n slope wth ncreased obscurant rate for optcal depths approachng the MPTR lmt. Overall, however, the plots are well-behaved and tend to verfy the ntal assumptons concernng the expected obscurant behavor upon whch the experments were based. Turnng next to the Log-R analyss (fourth column), a cursory nspecton of the results confrms our earler fndngs supportng the lnear dependence at the lower optcal depths whch s apparent n both cases. However, the breakdown of the lnear regon s also mmedately apparent as evdenced by the flattenng out of the plots n the saturaton regon at the hgher optcal depths whch s most apparent n the graphte sample. Drect comparson between of the graphte and brass show a dfference n the path radance behavor, most evdent n the maxmum value attaned (~3 for graphte, ~ 4 for brass) and due presumably to the dfference n the obscurant optcal propertes, most lkely the sngle scatterng albedo. To summarze to ths pont, the results thus far tend to support the underlyng theory and, ths not necessarly unexpected, for the transmttance measurements whch have been the subject of past experments. The major new surprse les n the success of the Log-R method n presentng the results n the form of well- behaved correlaton plots whch show major promse as a new tool for quantfyng path radance. Although the conclusons, to ths pont, are based only on the MPTR near IR measurements, smlar results apply for the other bands and are presented ether n appendx C or n the secton to follow. 23

34 7. Results from IR Imagery (Md- and Far Infrared) The full set of measurements from the dual band IR mager was not avalable at the tme of ths report, but some prelmnary data were extracted from the frst two trals to more or less corroborate the MPTR results. In ths secton, an analyss smlar to that of secton 6 s descrbed usng a selected porton from each (tme-dependent) frame of the IR magery. The IR data were collected at a rate of 30 frames per second wth each frame consstng of a 320x240 pxel matrx for each of the two spectral bands (.e., md-and far IR) and are descrbed n more detal n appendx D. The analyss here apples to the average radance from a 10x10 pxel area located approxmately half way between the transmssometer gude sources whch s roughly the same area sampled by the MPRT (cf. fg. 1, appendx D). A major techncal advantage offered by the MPTR s the use of the transmssometer gude sources to determne the cloud transmttance and the subsequent optcal depth nether of whch are drectly attanable from conventonal magery taken alone. Thus the frst major task s to determne an accurate method for calculatng the (tme-dependent) optcal thckness for the path correspondng to the selected pxel area. Once ths s done, then the path radance can be calculated from the IR magery usng eq 8, and the analyss can proceed n the same manner as descrbed n secton Estmaton Of Optcal Thckness For the partcular stuaton here, a fortutous crcumstance exsts wheren the extncton coeffcent, and, hence, the transmttance s (nearly) the same for both the md- and far IR bands suggestng that a band dfferencng approach may be accurate and feasble for calculatng the optcal depth usng the emprcal relatonshps of secton 5. Stated brefly, the method s to teratvely adjust the optcal thckness at every tme step so as to smultaneously balance the fundamental relatonshp of eq 1 for the two spectral bands treated. That s: magery analyss : Y ( τ,t ) R ( t ) = Y ( τ,t ) R ( t ) (15) where, R 3 (t) and R 4 (t), refer respectvely to the measured md- and far IR total radance obtaned drectly from the magery and Y 3 (τ,t) and Y 4 (τ,t) refer to modeled values based on the emprcal parameters derved from the MPTR analyss. Equaton 15 s solved usng teratve methods to fnd the optmal optcal depth at each tme step whch s then assumed the same for both spectral regons. In practce, the method worked better than expected wth the bggest uncertantes beng n the nherently ll-condtoned saturaton regon occurrng at the hgher optcal depths. 24

35 7.2 Determnaton of Path Radance The results of the frame-by-frame extracton of the IR sgnal and the correspondng calculated optcal depth are shown n fgure 11. The plots produced the equvalent of a tme scan of total radance comparable, n prncple, to that obtaned wth MPTR radometer. In fgure 11, the plots on the left refer to graphte, and those on the rght refer to brass. Fgure 11. Plots showng results from analyss of magery. In fgure 11, the upper two plots show tme traces of the normalzed total radance for the two bands as obtaned n the manner descrbed n secton 6 plus the calculated optcal depth (shown x10) as determned from eq 15. The lower two plots represent the results of the correspondng Log-R analyss and the subsequent comparson wth the sem-emprcal expressons. Lookng frst at the upper traces n the radance plots, n all cases, the effect of the obscurant s not necessarly large, resultng at most n a reducton of the total radance by only 20 percent whch occurs for the far IR brass case. It s also evdent from the md-ir results that, upon the ntroducton of the obscurant, the total radance decreases slghtly for the graphte sample but ncreases slghtly for the brass sample. Both of these observatons are n qualtatve agreement wth the MPTR data although t does appear that the earler results showed a more marked effect 25

36 than those from the magery. An examnaton of other pxel areas n the md-ir magery confrmed the fact that the total radance n most cases s less affected by the graphte and, n some cases showng an actual ncrease when the obscurant s ntroduced (appendx D). Perhaps the most sgnfcant new fndng from the magery to ths pont s the fact that, for both obscurant types, the total radance for the far IR band s measurably lower than that for the md-ir band wth the effect beng more pronounced for the brass sample than for the graphte sample. Ths may be due, n part, to the slghtly smaller mass extncton coeffcent n the far IR band although ths alone cannot explan the magntude of the dfference. Another plausble explanaton may be based on dfferences n the obscurant albedos, although any conclusons at ths pont are rsky due to the nteractng envronmental and obscurant factors dentfed n the fundamental relatonshp of secton 1 whch are all present n the IR bands. Turnng now to the lower plots of fgure 11, the Log R method for the far IR agan resulted n well-behaved correlaton plots wth the same characterstc features observed from the MPTR analyss. The lnear theory n both cases appears to be vald only for optcal depths less than about 0.50 for graphte and only about 0.25 for brass whch s a much lower threshold than was observed for the md IR. There also appears to be more scatter n the graphte correlaton plots when compared wth brass and ths agan may be due to dfferences n the balance between emssve and reflectve processes for the dfferent obscurant types as predcted by theory. However, some cauton s needed n nterpretng the results as some artfacts were found n the magery due presumable to tme lags, and one adjustment on the order of a few seconds was requred for the graphte data. 8. Summary and Dscusson From the evdence presented, clearly the MPTR measurements, coupled wth the Log-R/T correlaton methods, provde a relable source of data for the expermental determnaton of both the aerosol transmttance and path emsson/radance. The same statement may be appled to the IR magery although the results at ths pont are not conclusve. In ths sense, the major object of the experment was accomplshed; however, a number of new fndngs surfaced n the course of the analyss whch are brefly summarzed n ths secton. In the fnal two paragraphs some of the more sgnfcant techncal caveats are revewed and some future requrements are dscussed. 8.1 Performance of Sem-emprcal Methods From a modelng pont of vew, perhaps the most sgnfcant fndng thus far s that the measured data can be represented by farly smple sem-emprcal expressons that are consstent wth the exstng theory underlyng the ARL COMBIC and PILOT81 methods. It s equally mportant that the analyss allows for the separaton of the purely obscurant effects from the purely ambent effects such that the results can be appled to arbtrary ambent condtons other than those of the experment, per se. Ths latter pont s convenently summarzed n quanttatve form n table 3 whch gves our best estmates of the sem-emprcally derved parameters dscussed n secton 6. The correspondng sem-emprcal mathematcal expressons are formed by recastng the equatons of secton 1 nto a slghtly more practcal form as follows: 26

37 transmttance : T ( t ) = exp[ α CL( t )] I I drect radance : dr total ( t ) = I src ( t ) = I T ( t ) total radance : dr ( t ) + { I amb R ( t ) + I cld E ( t ) (16) where CL(t) s the tme-dependent path ntegrated concentraton, or CL Product, whch we assume to be known or derved from the analyss. In ths expresson, the quanttes I amb and I cld take the place of the relatve parameters a and b n eq 2 and are assumed known or calculated from the ambent temperatures usng eq 4 or some equvalent measurement. Lkewse, the quantty, I src s assumed to be a known nput representng ether the target or background dependng upon the specfc applcaton. The remanng unknowns n eq 16 are the obscurant cloud reflectvty and emssvty functons whch, n general, can be estmated from frst prncples usng models such as PILOT81, provded that the mass extncton coeffcent and albedo are known, or, more accurately, from the sem-emprcal relatonshps of eq 12 and the parameters of table 2 f the obscurant under consderaton s one of those tested. Table 3. Summary of sem-emprcal parameters derved from measurements. a. graphte α τ 1 τ 2 β a b md r far r b. brass α τ 1 τ 2 β a b md r far r For completeness the frst two columns of table 3 lsts the best estmates of the obscurant mass extncton coeffcent and sngle scatterng albedo whch are based ether upon the Log R/T analyss or from other sources n the lterature. The next three columns are the best estmates of the parameters needed to calculate the emssvty and reflectvty functons usng the sememprcal relatonshps of eq 12. The fnal two columns gve the best estmates of the envronmental parameters (a and b ) that best descrbe the envronmental nputs approprate for the partcular atmospherc condtons experenced durng the experments and are related to the approprate clear ar readngs as dscussed n appendx B. 8.2 Performance of Log-R/T Correlaton Methods of Analyss In general, the Log-T correlaton method worked well n analyzng the MPTR transmssometer measurements. For the most part, all plots consstently produced reasonable lnear relatonshps for all mass loadngs and good estmates for the correspondng emprcally derved optcal constants (tab. 3) whch are n general good agreement wth theory (.e., COMBIC) and wth expermental fndngs from other studes. Lkewse, the analogous Log-R correlaton method 27

38 worked well n analyzng the MPTR radometer measurements. In partcular, the path radance results at the smaller optcal depths exhbtng the expected lnear behavor, and the results at the larger optcal depths exhbted large devatons due to hgher order effects that are generally consstent wth theory (.e., PILOT81). The exercse usng the dual band Delta R method for estmatng optcal depth (eq 15) from the IR magery offers a sgnfcant techncal mprovement over the lnear method and was surprsngly successful, but prelmnary. 8.3 Relatonshp to the Sky-to-Ground Rato One of the most mportant parameters used to model the effects of target-background contrast and the consequent effects on mltary systems s the so-named sky-to-ground parameter, whch s a key nput n tactcal wargame smulatons such as CASTFOREM and dscussed n detal n the older lterature (9). Although there have been numerous concept papers wrtten on the mportance of obscurant-nduced contrast effects, there s lttle drect data on quanttatve feld measurements comparable to the study here. As t turns out, the normalzed path radance as defned here can be used to determne other obscurant parameters such as the target-background contrast and contrast transmsson and s thus entrely equvalent to a sky-to-ground parameter measurement. Ths s shown by startng wth the usual defnton of target background: I( τ tgt ) I( τ bkg ) contrastc( τ ) = (17) I( τ ) whch can be evaluated mmedately by applyng eq 1 of the man text twce, once for the targetrecever path and once for the background-recever path accountng for the total radance n each case. That s: bkg Itgt( o )[T( τ tgt ) + S( τ tgt )] Ibkg( o )[T( τ bkg ) + S( τ bkg )] C( τ ) = (18) I ( o )[T( τ ) + S( τ )] bkg where, as n all cases throughout, T(τ) s the aerosol transmttance and S(τ) s the normalzed total path radance. It s usual n applcatons to assume that the two paths (target and background) are nearly concdent so that the followng approxmatons apply: bkg bkg T( τ S( τ tgt tgt ) T( τ ) S( τ bkg bkg ) = T( τ ) ) = S( τ ) (19) whch, upon followng through n eq 18, leads to a cancellaton of the path radance terms n the numerator and a subsequently less nvolved expresson. That s, after some rearrangng: Itgt( o ) Ibkg( o ) T( τ ) C( τ ) = [ ][ ] (20) I ( o ) T( τ ) + S( τ ) bkg where the frst term n square brackets s called the ntrnsc (or unobscured) target-background contrast, and the functon n the second set of brackets s called the contrast transmsson whch 28

39 s formally defned as the rato of the (obscured) contrast to the (unobscured) contrast. That s, defnng C(o) as the ntrnsc contrast and substtutng the exponental form for transmttance, results n: 1 C( τ ) = C( o ){ } 1 S( τ ) / T( τ ) (21) whch s dentcal to the usual expresson f S(τ) s dentfed wth the sky-to-ground parameter. It should be remarked that the orgn of the sky-to-ground rato termnology traces to the treatment of clear ar scenaros and a sem-nfnte plane layer atmosphere appled along a horzontal path n whch case the Beer s Law expressons are adequate. The extenson here, however, represents the more general case makng the assocatons wth the sky and the unqualfed usage of the Beer s Law somewhat msleadng to the unntated reader. 8.4 Lmtatons of Lnear Models-Path Radance The results of the Log-R correlaton analyss dscussed n the varous fgures of secton 5 clearly demonstrate the lmtatons of the lnear approxmatons n accurately modelng path radance, especally at the hgher optcal depths. The usage of such models to determne optcal thckness from radance measurements s also naccurate and msleadng, especally n the saturaton regon dentfed n fgure 11. However, a quck dsmssal of such models as a vald approxmaton s somewhat premature for reasons that wll be made apparent later n ths secton. To llustrate the results are re-examned usng the example of fgure 12 as a reference. Fgure 12. Example comparng lnear models wth theory. The plot on the left was produced usng the Log-R method as descrbed n secton 7 as appled to a typcal graphte tral usng the near IR measurements. As usual the path radance data plots are characterzed by an ntal lnear regon followed by a transton to the saturaton regon where the plots tend to a constant value as the cloud becomes optcally thck, much n the manner predcted by PILOT81 (fg. 6). The Crrus model represented by the upper straght lne n Fg. 12 s reported to be derved from sngle scatterng and s ncluded here at the request of the 29

40 SCIMITAR group (10). The lower straght lne represents a lmt that s referred to as the modfed lnear regon. The example here demonstrates the lmtatons of models based on the lnear approach although t s clear that the performance can be mproved sgnfcantly by adoptng the modfed emprcal method suggested n fgure 12. However, the real sgnfcance of ths example s that the lnear regon extends up to an optcal depth of about τ=3 whch s surprsngly larger than mght be expected. The case for brass n the vsble band (fg. 3, appendx C) s even more surprsng n that the lnear regon extends up to almost τ=8. On the other hand, for brass n the far IR (fg. 12) the lnear regon extends up to only about τ=0.50. In the followng paragraphs these fndngs are examned n lght of the more general theory underlyng the PILOT81 model. The fact that the plots are ntally lnear s not necessarly unexpected, and ths observaton mght be nterpreted (although not necessarly so) as an ndcaton of the predomnance of sngle scatterng. Although ths latter statement s true, t can be msleadng because there are a number of other stuatons where a lnear form s theoretcally predcted. To understand why ths unexpected lnear behavor mght be happenng consder that there are at least four other common stuatons wheren the theory predcts lnear behavor even n the multple scatterng and emsson regme. The frst obvous case s the stuaton where the source functon s essentally constant over the path of propagaton whch was already dscussed n connecton wth eq 12. Ths s the stuaton commonly modeled n clear ar scenaros for horzontal propagaton through plane parallel layers that hstorcally lead to the development of the sky-to-ground parameter. Another obvous stuaton s the case of temperature equlbrum whch occurs when the ambent nput radance s equal to the cloud blackbody radance (.e., when a =b ) n whch case, accordng to eq 10, the path radance expresson reduces to the lnear form. The thrd case occurs for the extreme of conservatve scatterng (.e., ω=1) whch s apparently the stuaton noted earler for brass. The fourth stuaton occurs for the extreme of total absorpton (.e., ω=0) n whch case all multple and sngle scatterng contrbutons are zero, and the lnear form s strctly applcable. It s nterestng that the results from the experments suggest that some of these condtons are not far from those that actually were experenced durng some of the feld trals. 8.5 Lmtatons of Lnear Models-Transmttance The results thus far are encouragng n the sense that the lnear model may often be a good approxmaton for modelng path radance from the known optcal thckness, even n cases where there s strong emsson and multple scatterng. On the other hand one must proceed wth more cauton when dealng wth the nverse applcaton to determne the optcal depth from radance measurements as s sometmes attempted wth feld magery. The reason for cauton s clear from casual nspecton of the saturaton regon n the Log-R plots wheren the path radance attans a constant value ndependent of any changes n the actual optcal thckness. Ths ll condtonng of the process can be demonstrated by examnng the error, τ, ntroduced n usng the lnear approxmaton, that s: τ τ Ln[ 1 S( ω; τ )] (22) 30

41 where, τ, represents the actual measured optcal depth and the second term represents the expected error, whch s mmedately recognzed as beng dentcal to the argument, Z(t), used n the Log-R method of eq 14. Thus the magntude of the error can be read drectly from fg. 12 as the dfference between the lnear model curve and the correspondng data ponts. Ths s demonstrated n fg. 12b whch demonstrates the error ntroduced by usng the lnear approxmaton to calculate transmttance solely from radance measurements. It s mmedately clear that the lnear method s adequate for small optcal depths but the error grows rapdly beyond the lnear threshold and ultmately exceeds two orders of magntude at the extreme, thus serously under-predctng sensor performance. Unfortunately, much of the data of record from the Smoke Weeks apply to the saturaton regon where the largest uncertantes occur. Ths stuaton was, of course, not unantcpated here and was motvaton for usng the MPTR system and for desgnng the experment to cover a wde range of lght to heavy mass loadngs. 8.6 Caveats and Comments The revew of results and the varous cross-checks suggest that the experment was successful n obtanng an accurate and relable database on the smultaneous measurements of path radance and optcal thckness for a wde range of obscurant mass loadngs. On the other hand, there are a number of caveats that need to be addressed, the frst s that the measurements were all obtaned over a sngle set of horzontal paths and over (near) constant ambent condtons and, thus, some cauton needs to exercsed n extendng to more unversal scenaros. However, the manner n whch the analyss was conducted to separately extract weather dependent and obscurant dependent parameters allows for scalng of the results over a wde range of ambent condtons as mpled n eq 16. Ths hypothess s based on good theoretcal grounds but has not necessarly been tested wth real data. The second caveat s that, n performng the analyss the mplct assumpton of sotropc scatterng was also made but ths assumpton also was not tested drectly. In practce, ths means that somewhat dfferent results mght be expected f dfferent vewng angles were used and ths would be especally mportant at the shorter wavelengths and thnner optcal depths where angular dependent solar n-scatterng s most sgnfcant. Such detals can be addressed wth modelng but are dffcult to verfy n the feld due to the nordnate dffculty n measurng all of the necessary nputs. These detals are quanttatvely mportant but probably do not alter most of the broader qualtatve nformaton derved from the experments. The thrd caveat nvolved scalng the results to hgher (or lower) values for the envronmental nputs (.e., eq 16). All nput radatve sources were mplctly assumed to be sotropc and for the obscurant cloud to be sothermal. Agan, these assumptons do not necessarly reflect on the capablty of the models but are more a matter of practcal concern n the dffculty n actually measurng all possble nputs accurately. However, based on the a posteror results, no drect evdence shows that a more accurate characterzaton of the ambent nputs would change any of the major conclusons. Fnally, the assumpton that the cloud s sothermal s probably not serous for the expermental stuaton here because the aerosol generaton process does not heat the cloud much beyond the ambent, and, thus, detals of the cloud temperature structure are of lessened sgnfcance. 31

42 8.7 Future Requrements Besdes the usual problem of tryng to quanttatvely extend the fndngs to arbtrary scenaros of the real world whch tself s unquantfable n a practcal sense, there are a number of more realzable goals for the mmedate future. The frst requrement s to valdate the thermal magery data usng some of the same technques and relatonshps as used here for the MPTR. Our experence (somewhat lmted) wth the IR magery (appendx D) suggests a new method for extendng the analyss to the spatal regme and technques that may elmnate the bas n estmatng the optcal thckness from magery. A more practcal requrement s to explot the fact that we have produced a method for obtanng a near drect measurement of the tradtonal skyto-ground parameter needed by the user communty. Other more esoterc requrements nvolve the analyss of the statstcal relatonshp between the drectly transmtted sgnal and the nterferng path radance sgnal. These two quanttes seem to correlate qute well n some applcatons and not so well n other applcatons and may explan some of the scatter n the correlaton plots. From a theoretcal standpont ths s a problem that needs to be addressed usng a stochastc modelng approach whch was more or less avoded n the analyss thus far. There are also practcal applcatons for developng ths type of analytcal approach for synthetc scene development for future systems analyss where the requrements on accurate statstcal renderngs are of ncreased sgnfcance. From a practcal vewpont, two mmedate follow-on experments are evdent. The frst s to repeat the experments durng nghttme so as to elmnate the effect of solar loadng and thus the measurements would lend more accurate nformaton on the aerosol emssvty. The second s to nclude a set of experments wth the obscurant heated to a temperature that may be several (or even several hundred) degrees hgher than the ambent temperature. Such strongly emssve condtons are expected to affect IR sensor performance, and the need for accurate modelng for ths case has been ponted out by the user communty. It was, n fact, ths latter defcency that lead to the development of the PILOT81 model and was a prme motvator n performng the analyss of the expermental data. 32

43 9. References 1 Sutherland, R.A., Determnaton and use of IR band Emssvtes n a Multple Scatterng and Thermally Emttng Aerosol Medum, ARL Techncal report, n revew. 2. Wetmore, A. and S.D. Ayres, COMBIC-Combned Obscuraton Model for Battlefeld Induced Contamnants, US Army Research Laboratory Techncal Report, ARL-TR-1831, August de Jong, A.H.,1984, Results of NL Transmsson and Emsson Measurements durng Smoke Week VB and VI, Proceedngs of Smoke Symposum VIII, Aprl, Hoock, D.W. and R.A. Sutherland, 1993, (Obscurant Countermeasures), Chapter 7 n the EO/IR Handbook, publshed by SPIE, Bellngham, WA. 5. Kuhlman, M.R., et. al., 1995, Evaluaton of Physcal Propertes of a Foregn Smoke FMTR , prepared for Natonal Ground Intellgence Center, August Anderson, L., Chenault, T., Churchman, J., Hornack, R. and T. Smelker, 1999, Scene and Countermeasure Integraton for Munton Interacton wth Targets, U.S. Army Research Laboratory Techncal report, ARL-TR-1633, September Gllespe, P.S.,1995, TARGAC Techncal Descrpton and User s Gude, U.S. Army Research Laboratory Techncal Report, ARL-TR-273-3, Aprl Mackey, D.C., Dxon, D.S., Jensen, K.G., Loncarch, and J.T. Swam,1992, CASTFOREM (Combned Arms and Support Task Force Evaluaton Model) Update: Methodologes, Department of the Army Techncal Documentaton, TRAC-WSMR-TD Seagraves, M.A. and J.M. Davs, 1989, Target Acquston Tactcal Decson Ad Software Techncal Documentaton, ASL-TR-0252, September Chenault, T., Equaton of the form P=J(1-e -t ), Crrus computer program, unpublshed. 11. Lopez, C. and R.A. Sutherland, 2002, Software Methods for Imagery Analyss, U.S. Army Research Laboratory Techncal Note, n preparaton, December

44

45 Appendx A. MPTR Theory In the basc transmssometer confguraton, the raw sgnal s generally assumed to be comprsed of the followng contrbutons, ncludng sgnal, nose, and nterference components of varous orgn: S dr ( λ ) = R sys ( s ){[( I + [ I + [ I + [ I + N src * ems * ems atm f src dr ( τ ( τ + I ( δω, τ ) + I aer atm } + N ) + I ) + I sys bkg )e * sct * sct ( τ ( τ ( τ aer bkg aer atm + τ f atm bkg ) ]... drect transmttance ( δω, τ )]... forward scatter )]... path radance, aerosol )]... path radance, atmosphere ( s )... nose, atmsophere & system (A1) In eq A1, the quantty labeled R sys (s), s the system response functon that converts the optcal sgnal (s) to a voltage sgnal (S dr ) and s usually assumed to be a lnear functon for sgnal levels n the regon of practcal nterest; although ths assumpton can break down at very hgh sgnal levels called the saturaton regon. In eq A1, the total path optcal thckness ncludes contrbutons from both the smoke aerosol, t aer, and the ntervenng atmosphere, τ atm, whch taken together make up the total path optcal thckness (τ=τ aer +τ atm ). Also, n eq A1, the frst term nsde the curly braces represents the totalty of any drectly transmtted radance and can nclude contrbutons from both the transmssometer source, I src, plus any spll over from the background, I bkg, wthn the recever feld of vew. The second term represents any contrbuton due to forward scatterng wthn the feld of vew, δω, of the transmtter-recever optcal path. Most transmssometer systems are desgned such that: I bkg ( λ ) << I ( λ ) (A2) where acknowledgment of the fact that both the background and source ntenstes are dependent upon the partcular bandpass ( ) under consderaton. Thus, from eq A2 t s clear that the background terms can be neglected n comparson wth the (very ntense) artfcal source terms, a condton that greatly smplfes the expresson for practcal applcatons. The thrd and fourth terms n eq A1 arse from ether thermal emsson, I * ems(τ), or n-scatter from the surroundngs, I * sct(τ), ether from the smoke aerosol, I * (τ aer ), or the ntervenng atmosphere, I * (τ atm ). In, the usual transmssometer confguraton, the source beam, I src, s optcally modulated wth a mechancal chopper at the transmtter aperture to create an alternatng current (ac) sgnal whch s synchronzed to the recever electroncs. The sgnal s then synchronously detected at the chopper frequency (usually around 1000 Hz) n such a way that any drect current (dc) component such as that due to a constant background s not sensed. Ths method of detecton wll elmnate most of the path radance term, thus for all practcal purposes the radance terms are not measured. Therefore for the modulated sgnal that the transmssometer system actually sees, eq A1was replaced wth the followng more smplfed form: 35 src

46 S mod ( λ ) = R sys ( s ){ I src [ e ( τ aer + τ atm ) + fdr( δω, τ )] + Natm } + N sys (A3) where the condton of eq A2was accounted for by gnorng the terms nvolvng I bkg and by usng the subscrpt mod to dstngush from the drect sgnal. For an deal nstrument, the forward scatterng term can be mnmzed by usng narrow beam recever optcs and collmated transmtter beams. For obscurants comprsed of partcles very much larger than the wavelength, the forward scatterng lobe s very narrow and very concentrated and can even domnate the sgnal; however, for the types obscurants used here, the effect s generally neglgble. The remanng nose terms n eq A1 represent both optcal and electronc nose orgnatng ether from the ntervenng atmospherc path, N atm or purely from the system hardware, N sys. In practce nether of these terms can be completely elmnated but can be accounted for, n the mean, such that:... < N... < N atm sys ( t ) >= 0 ( t ) >= 0 (A4) where the symbol <X(t)> s used to denote a (short term) average wth respect to tme. Thus the mean level of nose can be elmnated; however, fluctuatons about the mean are almost always present n the feld data. The basc radometer confguraton s smlar to the transmssometer confguraton except that the artfcal optcally chopped lght source s elmnated thus leavng only the natural background for the clear ar source. Also, the forward scatter component n ths case forms an authentc contrbuton to the path radance snce I bkg s from a natural ambent source and, along ths same lne of reasonng, the atmospherc-nduced nose contrbuton s a bona fde component of the atmospherc source functon. Thus n the radance mode, eq A3s replaced wth the followng expresson: S rad ( λ ) = R + I + I * ems * ems + N sys sys ( r ){ I ( τ ( τ aer atm ( r ) bkg e ) + I ) + I ( τ atm + τ atm ) * sct * sct ( τ ( τ aer atm ) } (A5) where, n ths case, R sys (r) s the system response functon for the radometer recever and N sys (r) s the correspondng radometrc system nose. In the followng paragraphs, the assumpton s that ether eq A3 or eq A5 represents the relatonshp between the receved optcal sgnal and the system output for the transmssometer and radometer modes respectvely. It wll turn out that the stuaton can be smplfed even further by normalzed the sgnals to ther clear ar readngs whch has the effect of elmnatng the system response functon, R sys, whch cancels out. It s necessary, however, that the response functon be lnear n order for ths to be vald. Thus, provded that all sources of error have been kept at a neglgble level, then the net result of the data processng procedure should yeld a measurement very nearly equal to the aerosol transmttance. That s, assumng S mn to be zero (on average) for the calbrated sgnal and 36

47 realzng that S max refers to the clear ar transmttance (mean=100%), we have from eq A5, for the deal case: Rsys( s )I src [ e Trel( λ,t ) = R ( s )I [ e sys e... e ( raer + τ atm ) τ atm src ( τ aer + τ atm ) = e ( τ atm ) τ aer + + f ( δω, τ f ( δω, τ, for δω 0 tot atm )]] ) (A6) whch mples that the relatve readng so normalzed s a good estmate of the aerosol transmttance provded that the forward scatterng contrbuton s neglgble; an assumpton that was later tested wth the a posteror data. Wth the data so calbrated and agan assumng the nose terms to be elmnated and notng that S max agan refers to the clear ar case, and proceedng n a manner smlar to that leadng to eq A6, the radometrc mode s: R I e + [ I ( τ aer + τ atm ) * bkg aer rel = τ atm Ibkge ( τ + I aer * atm ) + I ( τ whch, n ths case represents the rato of the total (drect + dffuse) radance to the pre-event clear ar total radance. In most feld tests, the atmospherc contrbuton s kept small by conductng the trals only under clear ar condtons n whch case, assumng a near horzontal path, we have: atm * atm ) ( τ atm )] (A7) J( τ atm ) = J ( 1 e τ atm... 0;... for τ o ) atm 0 (A8) where J o s a constant less than or equal to unty dependng upon the obscurant albedo and s referred to as the atmospherc optcal source functon. Insertng ths approxmaton for J(τ atm ) n the lmt and assumng [exp(-τ atm )~1], after some mnor rearrangement and cancellaton, the followng expresson analogous to the fnal form of eq A6: R rel = I bkg e... = T( τ τ aer are + I I bkg * aer ) + S ( τ * aer aer ( τ aer ) ) where the frst term on the rght s the drect transmttance whch can be ndependently calculated from the transmssometer mode measurement, and the second s an addtonal contrbuton brought about by the ncluson of the path radance and can be thought of as a normalzed, or relatve, path radance. That s: (A9) 37

48 S * gr I ( τ I * τ ) = aer aer (A10) ( whch s also referred to as the sky-to-ground rato dscussed n the man text. Thus the MPTR system provdes all of the nformaton needed to account for the two major obscuraton parameters used n sensor performance modelng. bkg ) 38

49 Appendx B. Clear Ar Constants In executng the experments, an effort was made to complete the entre set of trals as quckly as possble so as to avod any problems assocated wth varatons n the atmospherc condtons whch could nfluence the clear ar readngs. In ths secton, the values of the clear ar readngs obtaned along the three man samplng paths as measured near the begnnng of each tral are documented. The data n table B1 refer to a the orgnal 12-bt dgtal readngs, or counts, whch are assumed proportonal to the ncomng radant sgnal. Inspecton of the table values ndcates that the most sgnfcant varatons were n the vsble band readngs where dfferences were as hgh as 30 percent. On the other hand, the near IR readngs were the most consstent wth dfferences no hgher than 5 percent or so. The effect of the varatons here are, of course, strongly mtgated by the fact that ndependent calbratons were performed pror to each event, thus avodng any large error. Table B1. MPTR Clear Ar Normalzaton Constants. (a) Transmssometer Tral LOS-1 Vsble Near r md r Far r LOS-2 Vsble Near r md r Far r (b) Radometer Tral LOS-0 Vsble near r md r far r

50

51 Appendx C. Mult-Tral Summary Presented n ths secton, s the remander of the results from the mult-tral analyss dscussed brefly for the sngle set of near IR results for both graphte and brass presented n secton 6. Fgures C1 C4 present the remander of the results for vsble and md-ir bands n the same format as that used n fgures 9 and 10. Fgure C1. Mult-tral summary, graphte-vsble. 41

52 Fgure C2. Mult-tral summary, graphte md-r. 42

53 Fgure C3. Mult-tral summary, brass-vsble. 43

54 Fgure C4. Mult-tral summary, brass md-r. It s reasonably clear from examnaton of ether of the transmssometer correlaton plots that the experments yelded consstent and well-behaved results. Ths s partcularly clear from the thrd column representng the transmttance correlaton plots whch are, n all cases, produced hghly convncng evdence of lnear relatonshps as predcted by theory. There are, however, some ndcatons of an upward curvature trend n the plots beng most notceable at the hgher mass loadngs whch may be due to effects beyond the scope of the present study. It s also apparent that the scatter n the plots tends to ncrease wth ncreasng optcal depth whch s to be expected because of the smaller sgnals nvolved. The results from the path radance correlaton plots are also consstent and well-behaved n that all show a ntal lnear trend, consstent wth the Beer s Law of attenuaton, n the thn layer regon but wth sgnfcant departures at hgher optcal depths and eventually approachng the classcal lmt n the extreme at the hgher mass loadngs. A most nterestng excepton s shown for the case of brass n the vsble band whch exhbts the lnear trend throughout the full range of optcal thckness. 44

55 Appendx D. Mult-Pxel Data From Ir Imagery In the man text, the use of the dual band IR magery data was lmted to only a few pxels manly for the purpose of verfyng the MPTR results. However, we do have plans to extend the analyss nto the spatal regme usng the IR magery. Some of our prelmnary fndngs suggest that a pxel by pxel analyss of the tme scans such as those dscussed n secton 7 may offer advantages beyond those obtaned usng conventonal magng analyss tools. The method of samplng the IR magery s demonstrated n fgure D1 (11). Fgure D1. Photograph of sngle data frame from IR mager. The photograph of fgure D1 represents a sngle frame taken from the md-ir magery fle and represents a roughly 320x240 pxel area scanned at a rate of 30 frames per second. The task n ths secton was to sample the magery at each of the nne dscrete ponts labeled a through for each tme step and thus produce a tme trace of total radance smlar to those of fgures 9 and

56 The results for both the md- and far IR bands are shown n fgure D2 (graphte, tral 21608) and fgure D3 (brass, tral 21609). Fgure D2. Dual band mult-pxel tme scans of total radance for graphte. 46

57 Fgure D3. Dual band mult-pxel tme scans of total radance for brass. In each of the fgures, the two dstnct columns refer ether to the 3 5 um band or the 8 12 um band as noted. Note also that both the extreme upper and extreme lower scans n all cases correspond to paths termnated by the tranmssometer sources and are thus much more ntense than the others whch are termnated by the natural background, whatever t may be. Several thngs are mmedately apparent from even a causal nspecton of the plots. Frst, for the md-ir band, the net effect of the obscurant s not large especally for the case of brass whereupon the total radance, n most cases, actually ncreases when the obscurant s ntroduced as was observed earler. On the other hand the effect of the obscurant on the far IR band s much more pronounced and more so for the brass example where the traces actually bottom out at the lower threshold. Ths too was noted n the earler dscussons of Secton 9. Another nterestng feature of the plots s the hgh degree of correlaton between and among the varous scans whch s most evdent n fgures D2 and D3 from the plots along rows of a gven column where the traces appear to be almost dentcal except for a small tme lag that s almost mperceptble at the scale shown here. Ths hgh degree of correlaton s, of course, not entrely unexpected snce the scans represent the same cloud dstrbuton sampled smultaneously at dfferent locatons. A further study to quantfy the cross-band correlatons usng a varety of statstcal approaches s beng pursued elsewhere. 47