High Spectra Resoution Infrared Radiance Modeing Using Optima Spectra Samping (OSS) Method J.-L. Moncet and G. Uymin
Background Optima Spectra Samping (OSS) method is a fast and accurate monochromatic RT modeing technique appicabe to a ide range of remote-sensing patforms Originay deveoped to support instrument/sounding agorithm trades, vaidation studies Same method is appicabe across the spectrum (from microave to UV) Monochromatic radiative transfer makes it directy appicabe to mutipe scattering, non-positive ILS (interferometers) Physicay based approach makes the method robust and utimatey aeviates need for extensive fast mode vaidation Trade-off beteen accuracy and speed depends on specifics of probem at hand Computationay efficient cacuation of radiances and Jacobians makes OSS attractive for operationa environment Initia research-grade version of OSS mode: NPOESS CrIS, CMIS, ATMS EDR agorithms AMSU/MHS processing at AER NAST-I (W. Smith) Parae R&D effort (under Navy SBIR) ed to improved training and ne faster and more accurate RT mode Used for AIRS instrument 2
ESFT and k-distribution methods Correated-k assumption breaks don for singe absorber in the presence of ines of different strengths or nonreguary spaced ines No satisfactory treatment of gas mixture hen reative abundance of individua species changes ith atitude The exponentia sum fitting (ESFT) and k-distribution methods approximate band transmittances in homogenous atmospheres as, τ ( u) = i= k u Weights i can be interpreted in terms of the probabiity distribution of the absorption coefficient over the spectra interva i = g and k i is a representative k-vaue for the interva N i = e i k k i i p i ( k) Probems ith extending ESFT or k-distribution concept to inhomogeneous atmospheres ies in difficuty of ensuring physica consistency beteen the k- vaues in each ayers Extension of the k-distribution method to non-homogeneous atmospheres is based on observation that minima and maxima of absorption in different ayers coincide spectray Correated-k method verticay integrates RT equation in g-space Equivaent to assuming a correspondence beteen k s of same ranking in different ayers dk ( k < ) i k i [ k, ] i k i 3
OSS soution for inhomogeneous atmospheres Proper treatment of overapping absorbers requires accurate characterization of the mutivariate probabiity distribution of absorption coefficients for a ayers and moecues High dimensionaity of the probem makes it impractica to attempt to sove directy for the k s ithout use of appropriate constraints OSS soution: Reduce the probem to a one-dimensiona frequency search Impose the constraint that the k s correspond to actua vaues of absorption coefficient for a moecues and ayers at the seected frequencies 4
OSS parameters generation Parameter generation starts from a set of M uniformy spaced monochromatic transmittances (or radiances) Compute ith a ine-by-ine mode (currenty LBLRTM) Use a gobay representative ensembe (S) of atmospheres Search for the smaest subset of frequencies (nodes) and associated eights i i i =,.., N ( ν, ) for hich the rms error computed over the ensembe S is ess than a prescribed toerance for a eves L NM F HG N bg bg bg i s i= s s ε N p = τ p iτ ν p I KJ 2 O QP 2 5
OSS Search Procedure Procedure consists of starting ith number of nodes N= and searching for the spectra ocation ν that produces the smaest error among the M possibe ocations N is then incremented by one and search for ν N proceed in the same fashion Procedure stop hen prescribed error toerance for training set is reached For each tria combination, eights are obtained by inear regression Detais of search method are provided in companion poster 9- point fit 8- point fit 6
Radiance training For infrared remote sensing, fit is done in radiances (or brightness temperatures), hich naturay emphasizes eves near the peak of channe eighting function ε N L NM s = r s F HG Radiance training takes into account functions that vary soy across channe passband (Panck function, surface emissivity/refectivity, etc) N i= r i s i ν I KJ 2 O QP 2 Set of training scenes incudes appropriate variabiity Vieing ange Surface emissivity and refectivity Observer atitude Soar anges Stratification (in vieing ange, surface emissivity, etc) may be used to ensure uniform eve of accuracy (threshod rms) across the range of conditions 7
OSS vs. Frequency (or Radiance) Samping Method Comparison of number of points used by OSS and RSM provide some quantitative assessment of abiity of OSS approach to expoit spectra redundancies RSM treats radiance as random variabe and reies on fact that estimates of mean improves as number of sampes increases (no eighting) For a same eve of accuracy, reduction in number of sampes ith OSS, in 700-750 cm - region, is greater than 90% (in this exampe ine-by-ine cacuations are samped on 0-4 cm - grid, i.e. 5000 pts per bin) 62 pts ν=0.5 cm - 6 pts 0. pts ν=0.5 cm - 70 pts 8
OSS Radiative Transfer Mode () Radiative transfer is performed monochromaticay (one node at a time) from precomputed absorption coefficients for the fixed and variabes constituents N N A A B B e j b g s N s b sg N d i b g = = R Τ Τ B Θ + ε Τ B + ε Τ Τ Τ B Θ Panck function and surface emissivity are evauated at the precise node spectra ocation (as opposed to using effective vaues for the channe) Severa channes may share the same node: computed radiance is added (after appropriate eighting is appied) to partia resuts for the channes that use that node Number of variabe moecues varies from node to node Moecues currenty incuded are: H 2 O, CO 2,O 3, N 2 O, CO, CH 4 Grouping beteen fixed and variabe gases is decided at run time 9
Tota monochromatic optica depth for a ayer Nvar τ = τ + τ + τ fix Fixed gases optica depth P τ fix = k fix u dry = k fix u HG g KJ here k fix is the effective absorption coefficient for the fixed gases mixture Dry variabe gases τ m = kmum Water vapor sef-broadening effect handed by assuming that absorption coefficient depends ineary on specific humidity L NM Approximation does not hod in the near ing ( non-inear dependence of absorption of ine hafidth) OSS Radiative Transfer Mode (2) m= 2 τ k q F O QP = + k q u m I 0
OSS Radiative Transfer Mode (3) Absorption coefficients are stored in each ayer as a function of temperature Use quadratic interpoation in temperature 3-points Lagrange interpoation provides continuous st derivatives ( θ θ )( θ θ ) ( ) i i+ k( θ ) = ki ki+ ( θi θi)( θi θi+ ) ( θ θ )( θ θ ) ( ) k k k i i+ + i i+ + i+ ( θi θi )( θi θi+ ) Depend ony on ayer temperature; computed ony once prior to performing the RT cacuations
Impact of absorption coefficient errors Impact of errors in treatment of absorption coefficients on computed brightness temperatures is sma Maximum errors for AIRS reach 0.05 K (rms error < ~0.02K) Coud be reduced further in CO 2 bands and 2400-2500 cm - region (N 2 continuum) by extending temperature range of the tabes (and by reducing temperature step size - no impact on computationa efficiency) Not a high priority Exampe: AIRS instrument - nadir vieing 2
AIRS OSS mode Seection accuracy of 0.05K and 0. K in brightness temperature EIA: 0 to 60 º Random surface emissivity in range 0.9-. Variabe H 2 O and O 3 0.05K training 0.0K training 73-74% of nodes are common to at east to channes Average number of points per channe is 2. and.36 for 0.05K and 0.K training, respectivey 3
AIRS mode accuracy Vaidate: 52 diverse ECMWF profie set Errors are due to OSS samping and optica depth interpoation (no radiative transfer errors) Independent set: 52 ECMWF profies (see Saunders, 2003) Nadir vieing ange Surface emissivity =0.99 Same 0-eve RT scheme used for both LBLRTM and fast OSS mode 4
Anaytica Jacobians () With monochromatic RT, anaytica Jacobian computation is trivia For exampe, in the case of a non refective surface computation of Jacobians rt moecuar amounts reduces to here R D u m = D τ = BΤ Σ + u m Contribution to TOA radiances of upeing radiation incident at bottom of ayer is independent of X and is derived in the process of merging ayers successivey (from bottom up) for radiance computation Temperature Jacobians: R Θ = B Θ b g Τ Τ + D τ Θ 5
Anaytica Jacobians (2) Derivative rt amount for variabe moecues Dry variabe gases τ u m = k m ( θ ) Water vapor τ τ ( θ, q ) τ ( θ, q ) u ( θ, q ) = + u m dry k m u u + k m fix k u u fix ( θ, ) ( θ ) = k q + q u q Derivatives of optica depth rt to temperature ( θ, q ) ( ) k ( θ ) τ k θ, q = θ θ ( ) + m dry km θ u ( θ ) k θ (2 θ θ θ ) θ θ θ θ θ u + m fix θ u fix ( k k ) i i+ = i i+ ( i i)( i i+ ) (2 θ θ θ ) ( k k ) i i+ + i ( θi θi )( θi θi+ ) i+ Dry gas amounts derived from reative concentration ith respect to moist air (not mixing ratios) 6
AIRS Jacobians accuracy OSS Jacobians for temperature and ater vapor compared to LBLRTM finite difference resuts Differences generay ithin 5 % (profie average) ith 0.05 K mode, reaching 8% (ater vapor and ozone) for a fe profies Channe # 453 (793. cm - ) 7
Computationa Efficiency Number of operation/ayer for cear sky transmittance cacuations at a singe node: 3 mutipications per constituent (6 for ater vapor) (see Side 0 and ) exponentia OSS and existing transmittance parameterizations (e.g. OPTRAN, RTTOV or SARTA) shoud become simiar in terms of number of operations hen number of nodes approaches ~2.5 Average number of points per channe for AIRS mode is 2. and.36 ith 0.05K and 0.K threshod Adding Jacobians rt a state vector eements (atmosphere and surface) to radiance computation ony doubes execution time (in cear sky) 8
Future ork Tune training for non-ocaized ILS (e.g. eaky apodized interferometer functions or narroband imagers) for handing spectra variation of emissivity ithin band pass Tune training for couds (ith and /o scattering in daytime and nighttime) Improve handing of variabe vieing anges Trade improved schemes for treatment of ayer emission (e.g. inear-in-tau) against number of eves 9