Guido Msiello nd Crmine Serio DIFA, Uniersity of Bsilict, Itly 1
Bsic methodologicl steps to retriee surfce emissiity Step 1: Represent emissiity with Fourier cosine truncted series to lower it dimensionlity below tht of the IASI spectrum. Step 2: Constrin the retriel with Lbortory mesurements Step 3: Blnce between Atmospheric nd Emissiity Constrints with 2-Dimensionl L-cure criterion 2
Bsic methodologicl steps to retriee surfce emissiity Step 2: Constrin the retriel with Lbortory mesurements Guido Msiello, Crmine Serio, nd Vincenzo Cuomo, "Eploiting Qurtz Spectrl Signture for the Detection of Cloud-Affected Stellite Infrred Obsertions oer Africn Desert Ares," Appl. Opt. 43, 2305-2315 2004 3
4 Bckground Retriel Methodology: the retriel problem is formulted within the contet of optiml estimtion 1 1 T T S K y S K y + ε 1 1 T T S F R S F R + ε o o o o F K F R y = = = = = How we modify the Physics to include surfce emissiity Linerize
5 How we modify the Physics to include surfce emissiity Use the logit trnsform to mp emissiity from the interl [0,1] to the rnge [-, + ] ε i y i = logit ε i = log i = 1,, N ch ; Nch = 1 ε i IASI chnnels which hs the inerse ep y i ε i = i = 1,, Nch i 1+ ep y i
6 To retriee for emissiity, the gien rdince Ri, with i the chnnel, is first linerized lso with respect to the function yi, tht is we consider in the inerse problem lso liner term of the type
Continue. Second, we deelop the function in truncted cosine series 7
Continue. nd Inserting the truncted cosine trnsform within the liner term 3, we get 8
9 The Fourier trnsform llows us to work in terms of spectrl resolution, ectly the wy we del with this concept. For se emissity, 60 Fourier Coefficients re enough
but, if we wnt to resole the Qurtz Resthrlen bnds in desert soil we need more thn 200 Fourier Coefficients 10
11 Bckground Retriel Methodology: the retriel problem is formulted within the contet of optiml estimtion 1 1 T T S K y S K y + ε 1 1 T T S F R S F R + ε o o o o F K F R y = = = = = From the size of bckground constrint we introduce informtion from lbortory mesurements Linerize
12 Lbortory emissiity is used for the bckground, men nd corince mtri ssumed to be digonl ASTER-Slisbury dt bse
The whole corince mtri for tmospheric prmeters nd emissiity is built up in block-digonl mtri 13 Atmosphere S γ 1S 0 Atm 0 = Emis γ 2S Emissiity γ 1 nd γ 2 cn be optimized to blnce between the two terms. Blncing is obtined with n originl nd fully nlyticl implementtion of 2-D L-cure criterion
14 Fully 2-D L-cure method, outline of the mthemtics inoled
Retriel eercise oer desert res 16 Shr Desert Arbin Desert Nmibi Desert Khlri Snn July 22, 2007, 6:45 Arbi 8:35 Other
Results: Nmibi desert 17 ε in LW lower thn in the SW. It mens fine grin of snds
Simultneously retrieed 18 with εσ: T s, T, H 2 O, O 3
Arbin desert 19 Corse piels Western
Shr desert 20
Klhri Snn 21
Conclusions 22 We he deeloped physicl inerse methodology to retriee the emissiity spectrum simultneously with Surfce Temperture nd Atmospheric prmeters: Temperture, wter pour nd ozone. The methodology relies minly on three bsic ides Deelop the emissiity spectrum in truncted Fourier cosine series Constrin the solution with Lbortory mesurements Blnce the optiml estimtion finl product with 2-Dimensionl L-cure criterion A test retriel eercise with IASI obsertions oer desert re shows tht the retrieed emissiity spectrum is cpble to cpture the fine detils of the surfce emission, een with non committl bckground corince mtri for emissiity The methodology will be soon pplied to derie mps t globl scle of the emissiity spectrum.
Set of prmeters retrieed 23 with φ-iasi Simultneously Emissiity spectrum Skin Temperture Temperture profile Wter pour profile Ozone profile Sequentilly, column mount CO CO 2 CH 4 N 2 O