Using MetOp-A AVHRR Clear-Sky Measurements to Cloud-Clear MetOp-A IASI Column Radiances

Transcription

1 1104 J O U R N L O F T M O S P H E R I C N D O C E N I C T E C H N O L O G Y VOLUME 28 Usg MetOp- VHRR Clear-Sky Measuremets to Cloud-Clear MetOp- ISI Colum Radaces ERIC S. MDDY, THOMS S. KING, ND HIBING SUN Dell, Ic., Farfax, Vrga WLTER W. WOLF, CHRISTOPHER D. BRNET, NDREW HEIDINGER, ZHOHUI CHENG, ND MITCHELL D. GOLDBERG NO/NESDIS/STR, Camp Sprgs, Marylad NTONI GMBCORT, CHEN ZHNG, ND KEXIN ZHNG Dell, Ic., Farfax, Vrga (Mauscrpt receved 26 November 2010, fal form 25 February 2011) BSTRCT Hgh spatal resoluto measuremets from the dvaced Very Hgh Resoluto Radometer (VHRR) o the Meteorologcal Operato (MetOp)- satellte that are collocated to the footprts from the Ifrared tmospherc Soudg Iterferometer (ISI) o the satellte are exploted to mprove ad qualty cotrol cloud-cleared radaces obtaed from the ISI. For a partal set of mostly ocea MetOp- orbts collected o 3 October 2010 for lattudes betwee 708S ad 758N, these cloud-cleared radaces ad clear-sky subpxel VHRR measuremets wth the ISI footprt agree to better tha 0.25-K root-mea-squared dfferece for VHRR wdow chaels wth almost zero bas. For the same dataset, surface sk temperatures retreved usg the combed VHRR, ISI, ad dvaced Mcrowave Soudg Ut (MSU) cloudclearg algorthm match well wth ECMWF model surface sk temperatures over ocea, yeldg total ucertates #1.2 K for scees wth up to 97% cloudess. 1. Itroducto Meteorologcal Operato (MetOp)-, the frst a seres of three plaed Europea Orgazato for the Explotato of Meteorologcal Satelltes (EUMETST) polar-orbtg satelltes, was successfully lauched October 2006 ad carres a wde array of strumets for measurg varous atmospherc, oceac, ad surface parameters. Icluded the strumet sute are several hertage strumets provded by the Natoal Oceac ad tmospherc dmstrato (NO), such as the dvaced Very Hgh Resoluto Radometer (VHRR) ad the dvaced Mcrowave Soudg Ut (MSU). I addto to these hertage strumets, MetOp- carres a ew geerato of advaced Correspodg author address: Erc S. Maddy, Dell, Ic., Farfax, V E-mal: erc.maddy@oaa.gov strumets, whch clude the Ifrared tmospherc Soudg Iterferometer (ISI). ISI s a cross-track-scag Mchelso terferometer that measures 8461 chaels at 0.25 cm 21 spacg betwee 645 ad 2760 cm 21 ( mm) a array of crcular footprts wth a adr spatal resoluto of roughly 50 km 3 50 km (wth a correspodg sgle footprt spatal resoluto at adr of roughly 12 km). Spectral measuremets from the ISI cota formato o the vertcal temperature profle, surface parameters (e.g., temperature, emssvty, reflectvty), clouds, ad the vertcal dstrbuto of tropospherc ad stratospherc trace gases such as H 2 O, CO, CH 4,CO 2, HNO 3, ad O 3 (Cayla 1993; Maddy et al. 2009). I addto, comparsos wth other hgh spectral resoluto spacebore souders, such as the tmospherc Ifrared Souder (IRS) flyg oboard the Natoal eroautcs ad Space dmstrato s (NS s) Earth Observg System (EOS) qua platform, have demostrated the excellet -orbt calbrato ad performace of ISI. DOI: /JTECH-D Ó 2011 merca Meteorologcal Socety

2 SEPTEMBER 2011 M DDY ET L Whle both IRS ad ISI have demostrated mprovemet to forecast models, the accurate treatmet of clouds has log bee a lmtg factor to maxmzg the utlty of IR souder data (Le Marshall et al. 2006; Collard ad McNally 2009). Ths s true because clouds have a cosderable effect o observed IR radaces, ad at 12-km spatal resoluto less tha 10% of ISI footprts are expected to be cloud free. Methods to hadle clouds are therefore requred to optmally utlze IR souder data umercal weather predcto (NWP) models ad for varous other operatoal ad research purposes. There are several approaches for hadlg the effect of clouds the IR, the most commo of whch clude the followg: avodg the clouds by screeg for clearsky footprts, drectly modelg the radatve effect of the clouds usg sophstcated radatve trasfer ad cloud mcrophyscal models, ad estmatg the clear-sky porto of a IR scee by usg a umber of adjacet ad varably cloudy footprts coupled wth a estmate of the clear-sky radace from a forecast model or collocated satellte strumet that s less lkely to be affected by clouds. The last approach, termed cloud clearg, s curretly used at NO/Natoal Evrometal Satellte, Data, ad Iformato Servce (NESDIS) for operatoal ISI processg ad s brefly descrbed the followg. NO curretly operatoally processes 100% of ISI data from calbrated ad apodzed level 1C (L1C) spectral measuremets to geophyscal level 2 (L2) products ad dstrbutes these products to the NO/ Comprehesve Large rray-data Stewardshp System (CLSS) (avalable ole at gov/saa/products/welcome). The curret algorthm used to produce the L2 products from ISI s largely based o the IRS scece team (ST) algorthm (uma et al. 2003), cludg the fast radatve trasfer algorthm (RT) (Strow et al. 2003) ad fast egevector regresso (Goldberg et al. 2003; Zhou et al. 2008), as well as cloud-clearg ad physcal retreval methodologes (Susskd et al. 2003), ad s descrbed the ISI L2 lgorthm Theoretcal Bass Documet (TBD). The curret NO operatoal cloud-clearg methodology uses the same fast egevector regresso methodology that s descrbed Goldberg et al. (2003) to provde temperature ad mosture geophyscal profles as well as surface parameters usg MetOp- cloudy-sky ISI spectral measuremets ad MSU mcrowave souder brghtess temperatures as puts. These regresso output parameters are the matched wth clmatologcal trace gas abudaces (e.g., O 3,N 2 O, etc.) ad used as puts to a RT (Strow et al. 2003) to produce a clearsky radace estmate. Ths clear-sky radace estmate s the used to extrapolate cloud-cleared radaces (CCs) from a spatal terpolato of multple cloudy frared footprts the ISI array of footprts collocated to the mcrowave footprt. The array of footprts s sometmes referred to as a feld of regard (FOR). s the surface-leavg radace the array of ISI footprts becomes obscured because of creasg cloudess, the regresso operator reles more heavly o the mcrowave measuremets to determe the atmospherc profles ad surface temperature. Ufortuately, broad vertcal weghtg fuctos ad possble sdelobe cotamato lmt the formato cotet of mcrowave souders such as MSU the lower atmosphere. I addto, because the clear-sky estmate s produced va a radatve trasfer model, accurate a pror assumptos about frared surface characterstcs, such as emssvty, are requred to compute accurate radaces. Therefore, scees wth low-alttude clouds where the surface-leavg radaces are costraed etrely by the mcrowave measuremets ca produce errat CCs that, tur, produce errat soudg products. Radaces computed from the corrupted products ca agree wth the measuremets wth the error budget, makg detecto ad removal of the errat scees mpractcal. These ad other lmtatos usg MSU for cloud clearg as appled to the IRS cloud-clearg algorthm were dscussed Baret et al. (2005) ad form part of the mpetus for the work descrbed ths paper. I ths paper we wll descrbe future upgrades to the operatoal cloud-clearg algorthm beg used for ISI processg wth NO/NESDIS. Specfcally, our ew cloud-clearg algorthm leverages off of the MetOp- VHRR Clouds from VHRR (CLVR-x) cloud mask (Hedger 2010; Thomas et al. 2004) to provde hgh-qualty, hgh spatal resoluto IR wdow clear-sky scee radace estmates requred for cloudclearg puts ad qualty assurace. For stace, Wag ad Cao (2008) showed that the mea dfferece betwee collocated VHRR ad ISI for VHRR chaels 4 ad 5 s geerally less tha 0.4 K, wth a stadard devato of 0.3 K. Therefore, the drect use of VHRR clear-sky measuremets decreases lmtatos of the curret algorthm to provde hgh-qualty clear-sky radace estmates throughout the atmospherc colum, ad especally ear the surface to a hgh degree of accuracy. I secto 2 we descrbe the ISI VHRR collocato procedures ad the VHRR cloud mask products. I secto 3 we fully descrbe our syergstc ISI VHRR cloud-clearg algorthm ad provde a aalyss of the performace of the ew algorthm secto 4.

3 1106 J O U R N L O F T M O S P H E R I C N D O C E N I C T E C H N O L O G Y VOLUME 28 FIG. 1. ISI spectrum for r Force Geophyscs Laboratory (FGL) U.S. Stadard Tropcal tmosphere, 1976 (black) ad overlad VHRR SRFs (red) for VHRR chaels 4 ad VHRR ISI collocato ad VHRR CLVR-x cloud maskg VHRR/3 s a sx-chael magg ad scag radometer that measures three solar chaels the vsble ear frared rego ad three thermal frared chaels. VHRR has a stataeous feld of vew of 1.3 mrad, correspodg to a 1.1-km footprt at adr. The crosstrack sca swath of the strumet exteds o ether sde of adr, provdg a swath that exteds beyod the ISI cross-track swath wdth of o ether sde of adr. Two-pot (deep space ad teral blackbody) calbrato of the thermal IR chaels s performed o a sca-le-by-sca-le bass, ad a prelauch olearty correcto has bee performed o the data (Sullva 1999). a. Collocato betwee VHRR ad ISI measuremets typcal ISI spectrum ad the spectral respose fuctos (SRFs) of VHRR Chaels 4 ad 5 are show Fg. 1. ISI s spectral rage fully overlaps VHRR logwave thermal frared chaels 4 ad 5, wth omal spectral cetrods of 10.8 ad 12 mm, respectvely. The complete spectral overlap betwee ISI ad VHRR the logwave IR wdow rego provdes a uque opportuty to characterze subpxel varablty wth the ISI footprts because these splt wdow thermal frared chaels are geerally used to derve sea surface temperature ad other surface propertes. Hgh spatal resoluto VHRR measuremets collocated wth the ISI spatal footprts therefore deally eable the detecto ad removal of the spectral fgerprt of clouds from ISI spectra. Collocato betwee ISI ad VHRR uses a algorthm developed for use wth IRS ad Moderate Resoluto Imagg Spectroradometer (MODIS) data o NS s qua satellte (Su et al. 2006) ad s a exteso of the algorthms descrbed L et al. (2005). Explaed brefly, ths algorthm fds the closest VHRR observato to the ceter of the ISI footprt ad performs a outward search to fd all of the VHRR pxels fallg wth the ISI footprt. weght, here termed the tegrated pot spread fucto (IPSF), s assged to each collocated VHRR pxel, whch depeds o the agular dfferece betwee the VHRR pxels ad the ceter pxel. For stace, weghts earest to the ceter of the ISI footprt are gve a value of 1, whle weghts o the edge of the ISI footprt are gve a weghtg of 0. b. CLVR-x cloud maskg The CLVR-x product (Thomas et al. 2004; Hedger 2010) provdes hgh spatal resoluto ( 1 km) cloud maskg oe of four categores, wth 0 correspodg to cofdetly clear, 1 correspodg to probably clear, 2 correspodg to probably cloudy, ad 3 correspodg to cloudy. I our processg we tegrate varous surface parameters usg the CLVR-x mask to determe allsky (mask 5 0, 1, 2, 3), cofdetly clear-sky (mask 5 0), ad cofdetly ad probably clear-sky (mask 5 0, 1) VHRR radaces as well as the average cloud-top temperature ad pressure ad the stadard devato of the cloud-top temperature from the CLVR-x product. For stace, for pxels determed to be cofdetly clear sky by the CLVR-x cloud mask, we calculate the clear VHRR radace VHRR spectral bad each ISI footprt R clr as follows: clr VHRR 5 å R clr l51 IPSF l R clr,l. (1) I Eq. (1), R clr,l s the radace of the cofdetly clearsky VHRR pxel l, clr VHRR s the umber of cofdetly clear-sky VHRR pxels collocated to the ISI footprt, ad IPSF l s the tegrated pot spread fucto for pxel l. We have also assumed that the IPSF has bee ormalzed to uty. Example collocatos for the sgle day of ISI ad VHRR data obtaed o 3 October 2010 are show Fg. 2. ISI measuremets R at waveumber (R ) are spectrally averaged oto the VHRR SRF for chael, SRF, usg R 5 å SRF, R, (2)

4 SEPTEMBER 2011 M DDY ET L TBLE 1. Bas, stadard devato (std dev) ad correlato coeffcet r betwee spatally covolved VHRR measuremets ad spectrally covolved ISI measuremets for VHRR chaels 4 ad 5 for both all-sky ad clear-sky cases. VHRR chael Bas (K) ll-sky cases Std dev (K) r Bas (K) Clear-sky cases Std dev (K) r FIG. 2. Collocatos of VHRR BTs ad ISI BTs for 3 Oct ISI data were spectrally covolved oto the VHRR chael 4 SRF, whle VHRR was spatally covolved oto the ISI footprts. Collocatos for all cases are show (black dots), whle collocato for cases determed by the CLVR-X cloud mask to be clear are also show (red). Results for VHRR chael 5 are smlar. ad plotted agast the spatally collocated ad averaged [usg Eq. (1)] all-sky ad cofdetly clear-sky VHRR measuremets. The umber of successful collocatos, that s, those correspodg to cases where both the ISI ad VHRR qualty assurace (Q) flags dcate hghest qualty, s The correlato betwee the all-sky VHRR measuremets ad ISI measuremets for ths set of cases s very hgh, gvg a value of for both chaels cosdered. summary of statstcs for the ISI VHRR collocatos for both all-sky ad clear-sky ( cases) are provded Table 1 for VHRR chaels 4 ad 5. Smlar to the fdgs dscussed Wag ad Cao (2008), the dffereces betwee VHRR ad ISI for our ouform ad clear-sky scees show temperaturead sca-depedet bases. These temperature-depedet bases suggest possble problems wth olearty VHRR calbrato (Wag ad Cao 2008). I what follows, we have performed a brghtess temperature depedet bas correcto to the VHRR measuremets R, R9 5 a 1 (1 1 b )R, (3) to make them better agree wth the ISI measuremets. The correcto coeffcets are lsted Table 2. We have also foud sca agle depedet bases betwee ISI ad VHRR that are symmetrc about adr ad are o the order of 0.2 K for both VHRR chaels 4 ad 5. t ths pot, we have ot attempted to correct these sca agle depedet dffereces because they are much smaller tha the sdelobe correctos requred to use the MSU. Wag ad Cao (2008) dscuss these sca agle depedet dffereces ad the possble causes for the sca agle depedece more detal. 3. revew of cloud-clearg methodology The two-spot, adjacet footprt cloud-clearg methodology assumes that the spectral radace two adjacet footprts, deoted R FOV j, dffer oly the product of the cloud fracto ad cloud emssvty N j j accordg to R FOV j 5 (1 2 N j j )Rclr 1 N j j Rcld, (4) where R FOV j s the measured radace footprt j, ad R clr ad R cld are the true clear-sky ad true cloudy-sky colum radaces, respectvely, for footprt j 5 1, 2. By defg a ew parameter h 5 N 1 1 /(N2 2 2 N1 1 ), ad assumg the cloud emssvtes are equal footprts 1 ad 2 (.e., ), we ca smultaeously solve both equatos for R clr to eable estmato of the cloudcleared radace R cc, gvg R cc 5 RFOV 1 1 h(r FOV 1 ). (5) Wth those substtutos, the problem of determg the cloud-cleared radace R cc the two adjacet footprts the reduces to the determato of the parameter h. The authors ote that R cc s ot guarateed to be exactly equal to the true clear-sky scee radace R clr from Eq. (4) because measuremets are susceptble to strumet ose ad there s a possblty that our TBLE 2. Slope ad offset coeffcets betwee VHRR ad ISI measuremets. VHRR chael a (K) b [K (K) 21 ]

5 1108 J O U R N L O F T M O S P H E R I C N D O C E N I C T E C H N O L O G Y VOLUME 28 assumpto that the two footprts dffer oly ther respectve cloud fractos s ot true (e.g., water vapor or surface varablty betwee the two adjacet footprts). Smth (1968), Chahe (1974), ad McMll ad Dea (1982) showed that a sgle chael or small subset of chaels ca remove the radatve effect of clouds from etre spectrum provded that a depedet estmate of the clear-sky radace for the two footprts R clr s gve. I our otato, the soluto for adjacet spot, sgle-chael cloud clearg s gve by solvg Eq. (5) for h, yeldg h 5 Rclr 2 R FOV 1 R FOV 1 2 R FOV. (6) 2 Chahe (1977) ad Chahe et al. (1977) showed that the formulato of the cloud-clearg equatos the h otato eables determato of clear-sky IR spectra affected by J 2 1 cloud formatos J footprts. Joer ad Rokke (2000) employed the h otato a varatoal cotext to cloud clear Televso ad Ifrared Observato Satellte (TIROS) Operatoal Vertcal Souder data wth J 5 3. Susskd et al. (2003) used the 3 3 3arrayofIRSpxelscollocatedtoaMSU footprt ad Chahe s h methodology to determe as may as 4hs to cloud clear IRS spectra. The IRS approach provdes the bass for the operatoal ISI MSU cloud-clearg algorthm curretly employed by NO/NESDIS, ad therefore shares may of the beefts ad lmtatos of the IRS algorthm. s descrbed secto 1, the coupled IRS MSU or ISI MSU algorthm reles heavly o the MSU measuremets to provde puts to a forward model, whch tur provdes the clear-sky estmate R clr. The IR forward model requres the complete atmospherc state, cludg temperature, mosture, ad trace gas profles as well as IR surface propertes, such as surface emssvty ad reflectvty order to compute R clr.msu measuremets are geerally oly sestve to temperature profles, surface temperature, ad mosture profles requrg oe to make assumptos regardg the IR surface propertes ad trace gas profles. Therefore, ay bases the MSU geophyscal profles, ether assumed surface parameters or trace gas profles, ad/or bases the forward model tself drectly affect the determato of h ad the error characterstcs of the ferred R cc. Clear-sky radace estmates from collocated hgh spatal resoluto mager measuremets (e.g., from MODIS) caalsobeusedtoremovetheeffectsofcloudsfromir souder measuremets. For stace, Smth et al. (2004) ad L et al. (2005) showed that the collocated IRS IR souder ad qua MODIS mager measuremets eable drect calculato of hgh-qualty cloud-cleared radaces wthout the use of a forward model to estmate R clr. Ther methods rely o the hgh spatal resoluto MODIS measuremets ad cloud mask to estmate clearsky measuremets MODIS IR spectral bads spatally collocated ad averaged oto the IRS footprts. The use of IR spectral bads coverg the spectral domas sampled by the IRS strumet eables drect comparso of the clear-sky MODIS measuremets to IRS, ad therefore does ot requre a pror assumptos about the geophyscal state (.e., surface propertes, trace gas cocetratos, ad/or water vapor abudaces) to eable calculato of clear-sky radaces. I a smlar fasho, the followg we utlze the spatally averaged ad collocated VHRR clear-sky radaces aggregated oto the ISI footprts ad deoted R clr to produce h ad R cc. We expad o the methodology descrbed L et al. (2005) by provdg a error aalyss of R cc wth respect to the composte put varables to the CC algorthm. Explct treatmet of the errors duced through cloud clearg leads to a mproved qualty cotrol scheme ad a more optmal selecto of footprts eablg a reducto the ose the cloud-clearg algorthm. I addto, our use of the h otato has the advatage that multple cloud formatos (e.g., type, heght, etc.) ca be cleared ad wll be the subject of a future publcato. a. descrpto of the VHRR/ISI cloud-clearg algorthm lthough there are varous methods to determe h gve R clr ad R FOV j, the method of least squares eables a smple soluto to our problem. The least squares problem for determg h from the clear-sky VHRR pxels ca be wrtte as the mmzato of the objectve fucto gve Eq. (7): J(h) 5 å N cha 1 s 2 fr clr 2 [R FOV 1 1 h(r FOV 1 )]g 2. (7) I Eq. (7), N cha correspods to the umber of VHRR chaels used, whch s 2, ad s 2 s the sum of the expected varace the VHRR clear-sky radace chael ad the expected varace the spectrally averaged ISI radace chael. For smplcty we assume that the s 2 5 1:0 radace ut squared; however, we have foud that modfyg these weghts does ot affect the qualty of the cloud-cleared radaces to a large degree. Takg the dervatve of Eq. (7) wth respect to h,

6 SEPTEMBER 2011 M DDY ET L J(h) h 5 å 2 [(R FOV 1 s 2 R clr )(R FOV 1 ) 1 h(r FOV 1 ) 2 ], (8) ad settg the result equal to zero eables mmzato of ths objectve fucto. Solvg the prevous equato for h yelds the least squares soluto for h ad s gve by h 5 å 1 s 2 (R clr 2 R FOV 1 )(R FOV 1 ) å 1 s 2 (R FOV 1 ) 2. (9) From Eq. (9), we ca see that the magtude of extrapolato parameter h learly depeds o the cotrast R clr 2 R FOV 1 ad olearly depeds o the cotrast betwee the adjacet footprts R FOV 1. I the ext secto we further develop the mathematcs that eable the characterzato of the respose of Eqs. (5) ad (9) to the cotrast betwee varous put varables to the algorthm ad to the ucertates the put varables themselves. b. Cloud-clearg error estmates The potetally large correctos (e.g., may tes of kelvs) that are requred by cloud clearg warrat quatfcato of the ucertates the cloud-clearg process. Calculatg the dfferetal of Eq. (5) as dr cc 5 (1 1 h)drfov 1 2 hdr FOV 2 5 (1 1 h)dr FOV 1 2 hdr FOV 2 1 Rcc h ~R FOV j dh 1 ( ~ R FOV 1 2 ~ R FOV 2 )dh, (10) where R ~ FOV j 5 R FOV j 1 dr FOV j, eables estmato of the bas the cloud-cleared radace dr cc. The bas s composed of two terms the frst arsg from fact that ose R cc s a lear combato of strumet ose R FOV 1 ad R FOV 2, ad deoted dr FOV 1 ad dr FOV 2 respectvely; ad the secod arsg from bases h. Geerally speakg, the magtude of dh, whch s a fucto of the ucertaty the composte varables used to determe h (e.g., R clr ad R FOV j ), ad the cotrast betwee the footprts used to derve h modulates the magtude of the spectral correlato of dr cc. We also ote that self-apodzato of the spectra resultg from strumet FOV geometry ad strumet mperfectos as well as user-selected apodzato of the terferogram (e.g., ether Gaussa or Blackma apodzato) to reduce sdelobes also troduces spectral correlato to the ISI radom ose. Because the frst two terms of Eq. (10) are learly proportoal to h, we ca therefore expect that the magtude of h tself wll also effect the magtude of the spectral correlato dr cc. I addto, because h depeds o the squared recprocal of the cotrast betwee footprts, dh wll be a strogly olear fucto of the cotrast betwee footprts, multpled by the ucertates the two footprts used for cloud clearg. O a case-by-case bass t s ot geerally possble to estmate the bas R cc ; however, calculatg the covarace of Eq. (10) ad takg the expectato of the result eables us to statstcally estmate some of the terms of the error covarace of R cc. It ca be show that the error covarace of the cloud-cleared radace S cc e takes the form S cc e 5 (1 1 h) 2 S FOV 1 e 1 h 2 S FOV 2 e 1 E[( R ~ FOV 1 2 R ~ FOV 2 ) 3 dhdh T ( R ~ FOV 1 2 R ~ FOV 2 ) T ] 1 cross-correlato terms, (11) where E() deotes the statstcal expectato. lthough small dffereces the calbrato betwee the ISI footprts exst (see Collard ad McNally 2009), statstcally, the expectato of ose the ISI footprts should be equal to the spectral error covarace of the ISI strumet, whch we deote as S e (.e., S FOV 1 e 5 S FOV 2 e 5 S e ). We ca therefore rewrte Eq. (11) as S cc e 5 [(11h) 2 1 h 2 ]S e 1 E[( R ~ FOV 1 2 R ~ FOV 2 )dhdh T 3 ( R ~ FOV 1 2 R ~ FOV 2 ) T ] 1 cross-correlato terms. (12) It s clear from Eq. (12) that the cloud-clearg process amplfes the spectral error covarace of the ISI measuremets S e by a factor of a(h) 2 5 (1 1 h) 2 1 h 2, (13) the square root of whch we wll term the amplfcato factor. From Eq. (13), we ca also see that as h / 0 (.e., the footprts are cloud free), the a(h) / 1. The error aalyss descrbed by Eqs. (11) ad (12) s complcated by the cross-correlato terms [e.g., dr FOV 1 dh T (R FOV 1 ) T ] that wll be dffcult to estmate. Noetheless, from these equatos t s clear that a well-desged cloud-clearg algorthm should mmze both the radom ose amplfcato ad the spectral error correlato troduced by the cloud-clearg process. Ths ca be accomplshed for each set of ISI footprts ad collocated VHRR clear-sky pxels aggregated oto the ISI footprt by selectg

7 1110 J O U R N L O F T M O S P H E R I C N D O C E N I C T E C H N O L O G Y VOLUME 28 FIG. 3. Schematc of the cloud-clearg algorthm llustratg that the radace each footprt R FOV j s assumed to be a lear combato of a clear-sky radace R clr ad cloudy-sky radace R cld wth the relatve weghtg descrbed by the cloud fracto N j each footprt j. The collocated VHRR measuremets for chael that are determed to be clear by the CLVR-x cloud mask for pxel l ad deoted R clr,l the fgure are averaged ad used as a estmate of the clear radace R clr. For clarty, these subpxel measuremet locatos are show for oly oe footprt ad the sze of the subpxel footprts s exaggerated. To compare apples to apples, the ISI spectral measuremets are also spectrally tegrated oto the VHRR badpasses. The cloudclearg algorthm cycles through varous combatos of the ISI footprts (e.g., f j 5 2, k 5 1g, fj 5 2, k 5 3g, f j 5 4, k 5 2g, etc.),estmatesh( j, k) usg Eq. (9), ad produces a cloud-cleared radace va Eq. (5) for each combato. The algorthm the selects the optmal combato of footprts;.e., the oes that mmze the fgure of mert fom( j, k) descrbed secto 3c. It s ot possble to tell from ths geeral example whch footprts would be used our algorthm; however, the algorthm would lkely ot choose footprts 1 ad 3 to perform cloud clearg because the cloud fracto these two footprts s very smlar (.e., N 3 N 1 ), ad hece h } 1/(R FOV 1 ) 2 /. () cases where the cotrast betwee footprts R FOV 1 s large order to mmze a(h) } h } 1/(R FOV 1 ) 2, ad also the spectral correlato as gve Eq. (10); ad () cases where the dstace from the ISI radace to the clear-sky estmate s small (.e., R FOV 1 R clr ), order to mmze a(h) } R clr 2 R FOV 1. descrpto of our cloud-clearg algorthm s gve the ext secto. c. Cloud-clearg algorthm mplemetato The use of VHRR eables characterzato of subpxel cloud varablty wth the ISI footprts ad, more mportatly, eables detecto of cloud-free or clear-sky footprts. s descrbed the secto 3b, cloud clearg amplfes the radom compoets of ose the ISI measuremets; therefore, our approach to hadle clouds s two proged. If VHRR determes that ay of the ISI footprts are clear sky, the we average those clear-sky footprts ad skp cloud clearg (ths s commoly referred to as hole hutg ); otherwse, we perform cloud clearg. The steps of our algorthm are preseted more detaled the followg ad a schematc of the algorthm s show Fg. 3: () ggregate the collocated clear-sky VHRR radace for each chael R clr oto the ISI footprts.

8 SEPTEMBER 2011 M DDY ET L FIG. 4. CLVR-X cloud mask for several partal MetOp- orbts o 3 Oct For ths dataset, 10% of the sgle FOV ISI footprts are clear, 2.5% of the ISI FORs are clear, ad 39% of the ISI FORs are completely overcast. If fewer tha 3% of all collocated VHRR pxels are masked clear by the CLVR-x mask, the reject the curret case. () If ay ISI footprt s determed by VHRR to be clear-sky, the R cc s set equal to the average ISI spectral radaces those clear-sky footprts. I ths case a(h) sequalto1/ clr,where clr s the umber of clear-sky ISI footprts p ffffffffffffff wth the ISI array. Proceed to step 9. () If o clear-sky ISI footprts are foud, the sort the j ISI footprts by 1/N cha å N cha R FOV j. (v) For each sorted cloudy ISI footprt ( j 5 1, 2,..., 4) select a eghborg footprt (k 5 2, 3, 4, j 6¼ k order matters), gvg a total of sx possbltes. We order the FOVs such that the warmest FOV always correspods to R FOV 1 order to mmze the ose amplfcato. (v) For each par ( j, k) calculateh( j, k) usgeq.(9). (v) Calculate R cc ( j, k) from Eq. (5). (v) Calculate x 2 ( j, k) 5 å 1/s 2 f[rclr 2 R cc (j, k)]g 2 ad a[h( j, k)]. (v) Defe a fgure of mert for each par of footprts ( j, k) wth qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fom( j, k) 5 [x 2 ( j, k)] 2 1 a[h( j, k)] 2. (x) Select the par of footprts (j9, k9)wthfom(j9, k9) 5 m fom( j, k). (x) pply qualty cotrol to the selected cloudcleared radace R cc ( j9, k9) by requrg that x 2 ( j9, k9) # 5.0 K ad a[h( j9, k9)] # 10. The qualty cotrol thresholds for x 2 ( j, k) ad a[h( j9, k9)] are very lberal ad were selected such that we maxmze the umber of cases that get through our cloud-clearg algorthm. 4. Performace of the cloud-clearg algorthm I ths secto we perform a aalyss of the results of the cloud-clearg algorthm by comparg the cloudcleared radaces R cc ( j9, k9) to the subpxel clear-sky VHRR measuremets R clr. To test the accuracy of the cloud-cleared radaces over a large rage of atmospherc codtos, we selected a subset of 66 ght graules from fve partal ISI orbts o 3 October For the aalyss that follows, the results have bee restrcted to lattudes betwee 708S ad758n. The authors ote that the polar orbt of MetOp- samples the poles more tha the mddle or low lattudes. restrcto to vestgate lattudes betwee 708Sad758N was made due to a lower avalablty of subpxel clear-sky estmates from VHRR at hgher lattudes ad a lower acceptace rate of the ISI L2 retrevals. Fgure 4 shows the VHRR CLVR-X cloud mask for the several partal MetOp- orbts that form our dataset. I creatg the fgure, we restrcted vewg agles from VHRR to be wth those vewed by ISI. It s worthwhle to ote that for ths dataset the CLVR-X cloud mask determed 10% of the sgle FOV ISI footprts to be clear sky, 2.5% of the array of ISI footprts to be clear sky, ad 39% of the array of ISI footprts to be completely covered wth clouds (.e., they are overcast). Fgure 5 llustrates the mprovemet yeld resultg from the use of a cloud-clearg algorthm ad also

9 1112 JOURNL OF TMOSPHERIC ND OCENIC TECHNOLOGY VOLUME 28 FIG. 5. (top left) Map of VHRR measuremets averaged oto the ISI footprts where the ay of ISI footprts comprsg the ISI FOR were determed to be clear sky. (top rght) Map of the cloud-cleared ISI measuremets spectrally averaged oto the VHRR SRF for VHRR chael 4. (bottom left) Map of the coldest ISI footprt (FOV) the ISI array. (bottom rght) Map of the dfferece betwee the ISI cloud-cleared radaces ad the clear estmate Rclr for VHRR chael 4. the performace of the algorthm. The top left pael of Fg. 5 shows the VHRR chael 4 brghtess temperature for ay ISI FOR where at least oe footprt was determed to be clear sky. The top rght pael shows the spectrally covolved cloud-cleared brghtess temperature for the equvalet VHRR chael 4 SRF where Rcc met the qualty cotrol thresholds descrbed secto 3c. The bottom rght pael llustrates the ablty of the cloud-clearg algorthm to ft the subpxel clear-sky VHRR measuremet VHRR chael 4 by showg clr the dfferece betwee Rcc ad R, where each are coverted to a brghtess temperature. The bottom left pael shows the coldest brghtess temperature the ISI FOR spectrally covolved for VHRR chael 4. pparet from the bottom rght pael, the cloudclearg hole-hutg algorthm fts the VHRR subpxel clear-sky scees extremely well. The probablty dstrbuto fucto ad cumulatve dstrbuto fucto for the dfferece betwee the subpxel clear-sky VHRR measuremets for VHRR chael 4 ad ISI cloudcleared radaces are also show Fg. 6. For ths dataset of partal orbts, the root-mea-squared dfferece clr (RMSD) ad bas betwee the Rcc ad R for VHRR chael 4 s ad K. Lkewse, the rootmea-squared dfferece ad bas betwee the Rcc ad for VHRR chael 5 s ad K. Rclr Oe area for possble mprovemet of the algorthm s for lad cases. Over lad the bottom rght pael shows larger departures especally over hgh surface terra, such as the U.S. ad Caada Rockes ad the des rage South merca. These larger dffereces over lad surfaces could be due to a umber of factors, cludg dffereces the subpxel VHRR footprt versus the ISI footprt aggregate surface emssvty, surface temperature, water vapor amout, or other geophyscal varablty ot properly accouted for by our

10 SEPTEMBER 2011 M DDY ET L FIG. 6. PDF (sold) ad CDF (dotted) of the dfferece betwee the ISI cloud-cleared radaces ad the clear estmate R clr for VHRR chael 4 ( cm 21 ) for the fve partal MetOp- orbts o 3 Oct FIG. 7. PDF (sold) ad CDF (dashed) of the amplfcato factor as calculated from Eq. (12). The PDF ad CDF whe the fgure of mert used the algorthm to decde footprts j9 ad k9 cossts of oly the x 2 term (red curves), ad the PDF ad CDF whe the fgure of mert cludes both x 2 ad a(h) (black curves) are show. algorthm. Nevertheless, f we oly cosder lad cases ths partal set of orbts we fd the RMSD ad bas for VHRR chael 4 s ad K ad the RMSD ad bas for VHRR chael 5 s ad K. I the prevous secto we developed equatos to descrbe the error characterstcs of R cc ad argued that a successful algorthm should mmze both the dfferece betwee the clear estmate ad cloud-cleared radace ad also the ose amplfcato resultg from cloud clearg. Fgure 7 compares the amplfcato factor a[h( j, k)] resultat from two systems that use dfferet fgures of mert (foms) to select optmal footprts for cloud clearg. The black curves Fg. 7 correspod to a system that uses a fom that mmzes the root-measquared agreemet betwee the subpxel clear-sky radaces observed by VHRR ad ISI cloud-cleared radaces x 2 ( j, k) ad the amplfcato factor a[h( j, k)], whle the red curves correspod to a system that uses a fom that mmzes oly the RMSD agreemet x 2 ( j, k). The data plotted ths fgure are for oly those cases that passed our qualty cotrol descrbed above. Whle the probablty dstrbuto fuctos (PDFs) ad cumulatve dstrbuto fuctos (CDFs) of a[h( j, k)] for each fom agree well for a[h( j, k)] # 1, for larger amplfcato factors we see that the black CDF curves (fom uses both quattes) approaches 1 much faster tha the red CDF curve. Ths meas that our algorthm wll lmt the radom ose amplfcato much better tha a algorthm that does ot cosder a[h( j, k)]. It s also worthwhle to ote that for ths esemble, roughly 48% of our ISI FORs clude at least oe clear-sky FOV; that s, a(h) # 1. Ths meas that over the scale of the ISI FOR, whch s 50 km, f 3% of the 1-km VHRR clear-sky pxels collocated to ISI footprts are foud to be cloud free (.e., the FOR s ot overcast), the 18% of the atmosphere s cloud free over a scale of 50 km, p ffffff 30% of the atmosphere s cloud free over a scale of 2 / km, 35% of the atmosphere s cloud free over a scale of 25 km (roughly half a ISI footprt), ad 48% of that the scee s cloud free over a scale of the ISI footprt sze, 12 km. Thus, 3% of the VHRR pxels collocated to a ISI footprt s sx 1-km VHRR pxels. Ths fdg s extremely mportat to ote the cotext of the developmet of future IR souders wth hgh spatal resoluto, ad also for cloud model parameterzatos ad studes of cloud spatal scalg; however, the use of dataset wth more days ad geographcal scees would be requred to provde robustess to these fdgs. ssurg good accuracy of R cc ( j9, k9) relatve to Rclr does ot guaratee good performace of the radaces themselves. Because ISI s a thermal souder, the ablty of our algorthm to remove the effect of clouds s drectly depedet o the thermal cotrast betwee clouds ad the surface-leavg radaces. We would therefore expect that the largest degree of dffculty for the algorthm would be for udetected low clouds. To test the qualty ad usefuless of R cc we also ru the NO operatoal ISI retrevals usg R cc as puts to produce estmates of the geophyscal state observed by ISI. To determe the qualty of our R cc for ear-surface propertes, we compared the ECMWF model output ocea sk temperature to retreved ocea surface sk temperature for two system cofguratos. The frst cofgurato used the

11 1114 J O U R N L O F T M O S P H E R I C N D O C E N I C T E C H N O L O G Y VOLUME 28 TBLE 3. Bas, stadard devato (std dev), correlato coeffcet r, ad % outlers betwee ECMWF model ocea surface sk temperatures ad retreved sk temperatures that utlzed ether VHRR, ISI, ad MSU cloud clearg or the IRSbased ISI plus MSU cloud clearg. We defe a outler as the % of cases fallg outsde j3 Kj about the mea dfferece. VHRR 1 ISI 1 MSU ISI 1 MSU Bas (K) Std dev (K) r % outlers FIG. 8. PDF of the dfferece betwee retreved ocea sk temperatures ad ECMWF aalyss modeled sk temperatures for the fve partal MetOp- orbts o 3 Oct The surface temperature retrevals where the cloud-clearg algorthm utlzed formato from VHRR, ISI, ad MSU (blue), ad surface temperature retrevals where the cloud-clearg algorthm utlzed formato from ISI ad MSU oly (red) are show. Qualty cotrol for each system was commo so that the same esemble was used each system cofgurato. curret operatoal IRS-based ISI plus MSU cloudclearg algorthm ad L2 processor descrbed secto 1, whle the secod cofgurato used the combed VHRR, ISI, ad MSU cloud-clearg algorthm descrbed ths paper. I the combed VHRR, ISI, ad MSU system cofgurato the L2 processor was told that the cloud-cleared radaces were clear wth omal ISI NEDN. s dscussed secto 3b, the process of cloud clearg amplfes the radom compoets of ISI spectral ose. We would therefore expect that the performace of the retreval algorthm that the VHRR, ISI, ad MSU cloud-cleared radaces would be suboptmal due to the fact that ose amplfcato s ot explctly hadled. The beefts of addg VHRR to the cloud-clearg algorthm are show Fg. 8. Here, the blue curves correspod to surface temperature retrevals from cloudcleared radaces that utlzed formato from VHRR, ISI, ad MSU, whle red curves correspod to surface temperature retrevals from cloud-cleared radaces that utlzed formato from ISI ad MSU oly. Qualty cotrol for the ISI retrevals s based o a seres of threshold tests for varous retreval covergece crtera ad coarse data qualty checks. To esure our comparso was far, we used a commo rejecto for each system so that the same esemble s cosdered each PDF (secto 3c). The percet of cases accepted by both systems was 42.7% ad statstcs are summarzed Table 3. Geerally speakg the system that utlzes VHRR to qualty cotrol ad produce cloud-cleared radaces shows a much smaller, f oexstet, cold tal the dffereces betwee retreved ocea surface sk temperatures ad ECMWF model ocea surface sk temperatures. Ths cold tal, whch s a tedecy for the retrevals to be colder tha the model, s a drect result of cloud cotamato the cloud-cleared radace. ddg VHRR to the cloud-clearg algorthm also tghtes the PDF toward a more Gaussa shape wth a smaller stadard devato, whch aga llustrates the hgh qualty ad low ose (correlated ad radom) of the cloudcleared radaces produced usg our approach. 5. Coclusos I ths paper we have developed a methodology that eables the determato of hgh-qualty cloud-cleared radaces from hgh spectral resoluto souders usg collocated hgh spatal resoluto mager measuremets. Buldg o the results of Smth et al. (2004) ad L et al. (2005) ad examg the propagato of errors through the cloud-clearg algorthm lead us to a mproved qualty cotrol scheme ad more optmal selecto of footprts (a combato cloud-clearg hole-hutg approach) that demads low-magtude ose amplfcato for the cloud-cleared radaces. I addto, by formulatg the problem the h otato, our approach has the advatage that multple cloud formatos ca be cleared from the spectra smultaeously, whch wll be the subject of a future publcato. Whe faced wth real data from MetOp-, the combato VHRR, ISI, ad MSU algorthm successfully removes the effects of clouds from the ISI radaces for 42% of cases attempted. Cosderg that 39% of cases were rejected because the array of ISI footprts was determed by the CLVR-x cloud mask to be completely covered wth clouds, a 42% yeld over the etre esemble correspods to a 70% 5 100[42/( )]% success rate for the cloud-clearg algorthm. I addto, after correctg for some

12 SEPTEMBER 2011 M DDY ET L calbrato dffereces betwee VHRR ad ISI, these cloud-cleared radaces agree wth subpxel clearsky VHRR radaces to better tha 0.2-K RMSD, wth almost o bas for ether surface sestve VHRR wdow chael. lthough the dataset used to test the algorthm was ot global extet, the dataset cluded a wde varety of atmospherc codtos, so t s expected that the algorthm performace should exted to global codtos. To guaratee the performace of the cloud-cleared radaces, we ra our cloud-cleared radaces through the operatoal L2 processor for ISI assumg that the radaces were clear. For the partal set of MetOp- orbts cosdered o 3 October 2010 betwee 708S ad 758N lattude, surface temperature retrevals ru usg the combed VHRR, ISI, ad MSU algorthm agree wth the ECMWF model surface sk temperatures to better tha 0.2 K the mea, wth a stadard devato of 1.2 K, ad demostrate the hgh accuracy ad precso of these cloud-cleared radaces for chaels spag the atmospherc colum ad cludg the surface. Relatve to the curret operatoal system, these statstcs represet a 2-K mprovemet the bas ad a 1-K mprovemet the radom compoet of error for the surface temperature retreval. s oted secto 4, we dd ot hadle the ose amplfcato of the cloud-cleared radaces for the VHRR, ISI, ad MSU algorthm, ad therefore we would expect that the algorthm performace s better tha that reported here. other terestg fdg that has mplcatos for the desg of future IR soudg strumets as well as the uderstadg of cloud sze ad spatal scalg follows from the spatal scalg of cloud-free pxels over the ISI array of footprts. We foud for ths esemble that the 61% of cases that at least 3% of the 1-km VHRR pxels collocated oto the ISI footprts were determed to be cloud free over the 50-km ISI array, all four footprts were cloud free 18% of the tme, three footprts were cloud free 25% of the tme, two footprts were cloud free 35% of the tme, ad at least oe of the 12-km footprts were cloud free 50% of the tme. Ths dcates that there s o smple progresso the probablty of fdg clear-sky pxels smaller FOVs ad also that there s a potetal to ru the ISI retrevals at a hgher spatal resoluto tha a 50-km MSU footprt. We atcpate that the ext release of the ISI operatoal retrevals wll corporate the VHRR data to the cloud-clearg algorthm. ckowledgmets. Ths work was supported by NO Offce of System Developmet (OSD) Product Systems Developmet ad Itegrato (PSDI) fudg. The authors wsh to thak ECMWF for the model data, EUMETST, ad Murty Dvakarla for dscussos related to ths work. The vews, opos, ad fdgs cotaed ths paper are those of the authors ad should ot be costrued as a offcal Natoal Oceac ad tmospherc dmstrato, Natoal eroautcs ad Space dmstrato, or U.S. Govermet posto, polcy, or decso. REFERENCES uma, H. H., ad Coauthors, 2003: IRS/MSU/HSB o the qua msso: Desg, scece objectves, data products ad processg systems. IEEE Tras. Geosc. Remote Ses., 41, Baret, C. D., M. Goldberg, T. Kg, N. Nall, W. Wolf, L. Zhou, ad J. We, 2005: lteratve cloud clearg methodologes for the tmospherc Ifrared Souder (IRS). tmospherc ad Evrometal Remote Sesg Data Processg ad Utlzato: Numercal tmospherc Predcto ad Evrometal Motorg, H.-L.. Huag et al., Eds., Iteratoal Socety for Optcal Egeerg (SPIE Proceedgs, Vol. 5890), do: / Cayla, F., 1993: ISI frared terferometer for operatos ad research. NTO SI Seres Tech. Rep. 9, 10 pp. Chahe, M. T., 1974: Remote soudg of cloudy atmospheres. I. The sgle cloud layer. J. tmos. Sc., 31, , 1977: Remote soudg of cloudy atmospheres. II. Multple cloud formatos. J. tmos. Sc., 34, , H. H. uma, ad F. W. Taylor, 1977: Remote soudg of cloudy atmospheres. III. Expermetal verfcatos. J. tmos. Sc., 34, Collard,. D., ad. P. McNally, 2009: The assmlato of Ifrared tmospherc Soudg Iterferometer radaces at ECMWF. Quart. J. Roy. Meteor. Soc., 135, Goldberg, M., L. Qu, Y. McMll, W. Wolf, L. Zhou, ad M. Dvakarla, 2003: IRS ear-real-tme products ad algorthms support of operatoal weather predcto. IEEE Tras. Geosc. Remote Ses., 41, Hedger,., 2010: CLVR-x Cloud Mask lgorthm Theoretcal Bass Documet (TBD). Uversty of Wscos Madso. [valable ole at clavrx_docs.html.] Joer, J., ad L. Rokke, 2000: Varatoal cloud-clearg wth TOVS data. Quart. J. Roy. Meteor. Soc., 126, Le Marshall, J., ad Coauthors, 2006: Improvg global aalyss ad forecastg wth IRS. Bull. mer. Meteor. Soc., 87, L, J., C.-Y. Lu, H.-L. Huag, T. J. Schmt, X. Wu, W. P. Mezel, ad J. J. Gurka, 2005: Optmal cloud-clearg for IRS radaces usg MODIS. IEEE Tras. Geosc. Remote Ses., 43, Maddy, E. S., C. D. Baret, ad. Gambacorta, 2009: computatoally effcet retreval algorthm for hyperspectral souders corporatg a pror formato. IEEE Geosc. Remote Ses. Lett., 6, McMll, L. M., ad C. Dea, 1982: Evaluato of a ew operatoal techque for producg clear radaces. J. ppl. Meteor., 21,

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