Channel radiance calculations for MOPITT forward modeling and operational retrievals

Transcription

1 Channe radiance cacuations for MOPITT forward modeing and operationa retrievas G.L. Francis, D.P. Edwards, and J.C. Gie Atmospheric Chemistry Division Nationa Center for Atmospheric Research ABSTRACT The MOPITT (Measurement of Poution in the Troposphere) instrument, to be aunched on the Earth Observing System Terra patform, empoys gas-correation spectroscopy to measure profies of tropospheric carbon monoxide and the tota coumn of methane. The modeing of the instrument, and the associated radiative transfer, comprise the forward mode empoyed in the retrieva cacuations. The MOPITT forward mode has been impemented through a hierarchy of radiation codes whose saient features are reviewed here. Keywords: forward modeing, correation spectroscopy, MOPITT, carbon monoxide, methane 1. INTRODUCTION The MOPITT instrument, to be aunched on the EOS Terra patform, wi provide the first extended goba measurements of tropospheric carbon monoxide and methane. Profies of CO wi be determined at severa eves in the troposphere, as we as CO and CH 4 coumn abundances. The CO profie and tota coumn wi have an anticipated accuracy of 10 percent, with the CH 4 coumn determined to 1 percent. There is considerabe interest in extended goba measurements of CO and CH 4. CO exhibits seasona and regiona variations due to industria and agricutura processes, particuary biomass burning. It aso pays a roe in HO x chemistry, infuencing the distribution of the hydroxy radica OH, a major oxidizing component of the troposphere. Due to its fairy ong ifetime, CO can be used as an atmospheric tracer of three-dimensiona tropospheric motion. The vertica CO distribution can mirror chemica transport by deep convection, which contributes to tropospherestratosphere exchange through convective overshoots at the tropopause. The goba distributions The Nationa Center for Atmospheric Research is sponsored by the Nationa Science Foundation

2 of CO and CH 4 coumn abundance can provide verticay-averaged signatures of organized motion by tropospheric wave activity. Both CO and CH 4 chemicay infuence the tropospheric O 3 distribution. CH 4 is aso increasing in the atmosphere and the anthropogenic sources of this increase are not we identified. In the stratosphere, this increase is impicated in observed increases in water vapor through CH 4 oxidation. MOPITT empoys gas correation radiometers to extract a target gas signa and separate its contribution to the top-of-atmosphere (TOA) radiance from that due to contaminating species and the underying surface. Both pressure-moduated radiometers (PMR) and ength-moduated radiometers (LMR) are empoyed 1. In a gas correation radiometer, TOA radiance passes through a ce containing the same gas as the target gas being measured. For MOPITT the target gas is either CO or CH 4, depending on the channe. By reguary varying the ce ength (LMR) or the ce pressure (PMR) between two states, the optica depth of each correation ce is moduated at the positions of the spectra ines of the target gas. As a resut, two different signas are obtained in each channe, corresponding to each of the two ce states. The average (A) of these two signas yieds information about the surface and contaminating gases, whie the difference (D) of the two signas gives information about the target gases. Since radiative processes in the ine wings occur at ower atitudes, a set of appropriate PMR and LMR channes can sampe radiance originating at different atitudes, thereby providing profie information. Forward modeing of the sateite channe radiances must combine accuracy and precision whie providing for variations in target and contaminating gases, temperature, viewing geometry and surface properties. To achieve this, a set of radiation modes has been deveoped and appied to the cacuation of channe radiances for the MOPITT instrument. Within their range of appicabiity, each in turn is an effective too. In the foowing sections we briefy review the saient features of these modes and discuss their structure and appication. 2. THE MOPITT EQUATION OF TRANSFER The i-th channe radiance measured by MOPITT has the form S A,D i = I(ν)h A,D i (ν)w i (ν)dν (1) where S A,D i is the average or difference channe radiance, h A,D i (ν) is the correation ce A or D response, and w i (ν) isthei-th normaized channe bocker fiter. Assuming cear-sky conditions, no scattering and an underying Lambertian surface, the TOA monochromatic radiance I(ν) has the foowing form:

3 0 I(ν) = B(ν, T )dτ(ν, p, θ sat ) p s + ɛ(ν)b(ν, T s )τ(ν, p s,θ sat ) + (1 ɛ(ν)) F d(ν) π τ(ν, p s,θ sat ) + (1 ɛ(ν)) F (ν) π sec θ τ(ν, p s,θ )τ(ν, p s,θ sat ) (2) Here B(ν, T ) is the Panck function at temperature T, F d (ν) is the downward diffuse therma fux at the surface, F (ν) is the soar fux at TOA, ɛ(ν) is the surface emissivity and τ(ν, p, θ) is the monochromatic transmittance from pressure eve p to TOA at ange θ. T s and p s denote surface temperature and pressure, respectivey. Depending on the particuar channe, one or more of the terms appearing here are dominant. In the CO therma band ( cm 1 ) the TOA radiance is dominated by surface emission as we as atmospheric absorption and emission. These are the first two terms on the right hand side of Equation (2). In both the CO shortwave band ( cm 1 ) and the CH 4 shortwave band ( cm 1 ), the TOA radiance during the day is dominated by refected soar radiation, the fourth term. Downweing therma radiation refected by the surface is given by the third term, which makes a non-negigibe contribution in the CO therma band, especiay for ow surface temperatures. Together, the instrument response characteristics (Equation 1) and the equation of transfer (Equation 2) comprise the forward mode used by MOPITT. It provides the radiances seen by the instrument under the conditions of the measurement. 3. THE MOPITT FORWARD MODEL HIERARCHY 3.1 GENLN2: Line-by-ine cacuations Gas correation spectroscopy introduces a high resoution spectra fiter into the measurement process, having ine widths of order 0.1 cm 1. In addition, cacuations with spectra resoutions as fine as cm 1 are required to construct the databases which are key components of the higher-eve MOPITT radiation codes MOPABS and MOPFAS discussed beow. Line-by-ine (LBL) cacuations must therefore be performed to provide these fiters and databases. These are provided by the genera purpose radiance and transmittance mode GENLN2 2. GENLN2 incorporates Voigt ine shapes throughout, with fu treatment of ine wings, the effect of overapping spectra ines both within the same band and between bands, and continuum absorption. It uses the HITRAN96 database and performs optima atmospheric ayering as we as ray tracing in spherica geometry, and a two-stage spectra cacuation for regions cose to, and far from, ine center.

4 Athough too cumbersome for operationa use, TOA radiances provided by GENLN2 give benchmarks against which faster MOPITT codes can be assessed. GENLN2 LBL cacuations have previousy been appied to many other sateite instruments, and are currenty in use for the deveopment 3 of the HIRDLS 5 (High Resoution Dynamics Limb Sounder) instrument schedued for aunch aboard EOS-CHEM. 3.2 MOPABS: An optica-depth ookup tabe mode An intermediate step in the MOPITT radiation code hierarchy, MOPABS 4 computes channe radiances through a monochromatic absorption coefficient fitting scheme. This technique expicity mirrors much of the underying physics of the radiative transfer, permitting the cacuation to be readiy adapted for use by other instruments. In particuar, the MOPABS method is being appied to mode radiances for the MOPITT Airborne Test Radiometer (MATR) and the MODIS (Moderate Resoution Imaging Spectrometer) Airborne Simuator (MAS). Radiances from the atter are being used to deveop coud-cearing agorithms for use in MOPITT retrievas. The essence of the MOPABS agorithm can be summarized as foows. LBL cacuations are performed with GENLN2, giving monochromatic optica depths K g,ref (T ref ) for each gas g and each ayer in an appropriate reference atmosphere having specified temperature T ref and constituent coumn abundances A g,ref ( =1,n). A simiar cacuation is performed for the same atmosphere with ayer temperatures artificiay changed to T ref ± 50 K. A quadratic poynomia fit of the ogarithm of the optica depth against temperature is then made in each ayer over this temperature range, giving frequency-dependent quadratic coefficients {a,b,c }. To this point a quantities are pre-computed. Two steps are required to obtain monochromatic optica depths for a given test atmosphere at run-time. Denote the test atmosphere temperatures in ayer by T, and the corresponding ayer coumn abundances for gas g by A g ( =1,n). In the first step, the optica depth for gas g at temperature T in the presence of the reference constituents foows from the quadratic fit as K g,ref (T )=exp(a +b (T T ref )+c (T T ref ) 2 ). In the second step, the monochromatic optica depth in ayer of the test atmosphere for gas g is obtained by a rescaing: K g (T )= K g,ref A g (T ). A g,ref Knowing K g (T ) in each ayer, the monochromatic transmittance from eve p to TOA at zenith ange θ is obtained as foows: [ ] 1 τ(ν, p,θ)=exp K g (T )/sec θ. = g

5 Then the TOA radiances foow from Equation 2 and the channe radiances from Equation 1. This method has essentiay ine-by-ine accuracy and is consideraby faster. Channe radiance cacuations for a given test atmosphere can typicay be competed in a few minutes. Whie this is sti too sow for operationa retrievas, MOPABS is an important too for the deveopment of a truy fast forward mode. In addition, MOPABS has broad appications to other MOPITT work, as mentioned earier. 3.3 MOPFAS: The MOPITT operationa fast forward mode The MOPFAS 4 code currenty provides the fast forward mode cacuations used by MOPITT. It achieves faster performance than MOPABS by reformuating the cacuation so that time-consuming spectra integrations are avoided. To accompish this, Equations (1) and (2) are coectivey regarded as a statement about spectray integrated quantities, particuary spectray integrated transmittances, or products thereof. Specificay, we define the integrated, normaized channe transmittance from TOA to eve p at ange θ for the channe response function φ A,D i (ν) as T A,D i (p,θ) 1 Φ A,D τ(ν, p,θ) φ A,D i (ν)dν i ν i where Φ A,D i φ A,D i ν i (ν)dν. Each term in Equation (1) and (2) can then be written using T or products of T. For exampe, the signa component due to atmospheric emission takes the form S A,D i (AtmTh) = Φ A,D i 1 =L B i (T )[T A,D i (p 1,θ sat ) T A,D i (p,θ sat )]. (3) In Equation (3), T is the ayer-mean temperature, θ sat is the sateite zenith ange and we assume the spectra variation of the Panck function B i (T ) over the channe passband can be negected. Simiar expressions hod for the remaining three terms in Equation (2). It is usefu to define an effective absorption coefficient k g (θ) in each pressure ayer for each gas g, k g (θ) 1 [ T g ] A g (θ) n (p,θ) T g (p 1,θ) which determines T recursivey. In this way, the probem of computing channe radiances is reduced to determining k g (θ). (4)

6 The OPTRAN 7,8 regression scheme is appied to estabish a correspondence between k and atmospheric state profies, such that the former can be inferred accuratey and quicky given the atter. The regression maps a set of predictors, derived from the state profies, onto corresponding vaues of k. The predictors are functions of absorber amount, pressure, temperature and viewing geometry. The regression coefficients inking the predictors and k are pre-computed in the foowing way. Spectray integrated transmittances T A,D i (p,θ) are first computed by MOPABS for an ensembe of training atmospheres representative of a wide range of atmospheric states. The ensembe incudes highy pouted panetary boundary ayer measurements with high CO and CH 4 mixing ratios 9,as we as mode cacuations by the MOZART 6 chemica transport mode for a seasons and a variety of atitudes. These transmittances determine corresponding vaues of k, which are tabuated. The predictors for each training atmosphere are aso tabuated. The regression coefficients are computed through a east-squares fit over the ensembe after first mapping k and the predictors onto an absorber amount grid, from pressure eves in physica space. Since k depends most strongy on absorber amount, which is then aready accounted for, the regression is abe to focus argey on the weaker dependencies of k on pressure and temperature. This method improves the overa accuracy of the fit. The resuting j-th regression coefficient on absorber eve m, for gas g, is denoted C g jm. This competes the pre-cacuation of Cg jm. At run time, the predictors for a given test atmosphere are cacuated on each pressure eve, then transformed to absorber amount space where the regression coefficients are appied. For the test atmosphere, denote the j-th predictor on absorber eve m for gas g by Z g,test jm. Then the effective absorption coefficients for the test atmosphere are given by inear equations of the foowing form: k g,test m = C g m0 + J j=1 C g mj Zg,test jm. A transformation back to physica space yieds k test on pressure eves. Equation (4) then gives T A,D i (p,θ). The TOA radiances and MOPITT instrument signas foow from expressions ike Equation (3). MOPFAS yieds channe radiances in good accord with MOPABS cacuations. Over a representative ensembe of test atmospheres, MOPFAS and MOPABS have mean differences of 0.05 to 0.1 percent, with maximum differences of 0.4 to0.7 percent, depending on channe and band. In addition, a MOPFAS cacuation is about 10 5 times faster than GENLN2 LBL cacuations. The MOPFAS predictors are carefuy chosen to maximize their effectiveness for yieding accurate MOPITT channe radiances. This imits the agorithm s use in other contexts, so that MOPFAS performance improvements over MOPABS and LBL occur at the price of speciaization.

7 4. SUMMARY AND FUTURE WORK A hierarchy of radiation codes has been deveoped for the MOPITT program which together comprise a powerfu and accurate suite of toos to perform MOPITT forward modeing cacuations. These codes are undergoing incrementa refinement to improve their accuracy and performance. Variants of these codes wi aso provide a starting point for the deveopment of forward modeing toos for HIRDLS. An aternate version of MOPFAS is currenty being deveoped using the correated-k approach. Correated-k provides a means to reformuate spectra integrations in terms of integrations over smooth absorption coefficient probabiity distributions. The approximate correation between distributions at different eves permits pre-cacuation of the probabiity distributions for an appropriate atmospheric ensembe. MOPITT instrument fiters can be buit into this scheme. At run time an interpoation gives the probabiity distributions for a given test atmosphere, from which the integrated transmittances are constructed. The technique is physicay transparent, yieding an agorithm simiar to MOPABS. Further deveopment of this method wi be reported in a future pubication. ACKNOWLEDGMENTS The Nationa Center for Atmospheric Research is sponsored by the Nationa Science Foundation. REFERENCES 1. Drummond, J.R., Measurements of Poution in the Troposphere (MOPITT), in The use of EOS for Studies of Atmospheric Physics, edited by J. C. Gie and G. Visconti, pp , North Hoand, Amsterdam, Edwards, D.P., GENLN2: A genera ine-by-ine atmospheric transmittance and radiance mode. Version 3.0 description and users guide, Rep. NCAR/TN-367+ST, Nat. Cent. for Atmos. Res., Bouder, Coo., Edwards, David P., John C. Gie, Pau L. Baiey and John J. Barnett, Seection of sounding channes for the High Resoution Dynamics Limb Sounder, App. Opt., 34, , Edwards, D.P,. C. Havorson, and J.C.Gie, Radiative transfer modeing for the EOS-Terra MOPITT instrument, to appear in J. Geophys. Res., Gie, J.C. and J.J. Barnett, The high resoution dynamics imb sounder (HIRDLS). An instrument for the study of goba change, Rend. Sc. Int. Fis. Enrico Fermi CXV, , 1992.

8 6. Haugustaine, D.A., G.P.Brasseur, S.Waters, P.J.Rasch, J.-F. Muer, L. K. Emmons, and M.A.Carro, MOZART: A goba chemica transport mode for ozone and reated chemica tracers, Part 2. Mode resuts and evauation, to appear in J. Geophys. Res., McMiin, L.M., L.J.Crone, M.D. Godberg, and T.J. Keespies, Atmospheric transmittance of an absorbing gas. 4. OPTRAN: a computationay fast and accurate transmittance mode for absorbing gases with fixed and with variabe mixing ratios at variabe viewing anges, App. Opt. 34, , McMiin, L.M., L.J.Crone, and T.J. Keespies, Atmospheric transmittance of an absorbing gas. 5. Improvements to the OPTRAN approach, App. Opt. 34, , Pan, Liwen, John C. Gie, David P. Edwards, Pau L. Baiey, and Cive D. Rodgers, Retrieva of tropospheric carbon monoxide for the MOPITT experiment, J. Geophys. Res., 103, D24, , 1998.