3. SINGLE VS MULTI-POLARIZATION DESCRIPTORS

Transcription

1 . INGLE V MULI-OLAIZAION DECIO. olarsaton and urface catterng he man roblem for the quanttate estmaton of sol mosture and/or surface roughness from A data les n the searaton of ther nddual effects on the backscattered sgnal. olarmetry lays here an mortant role as t allows ether a drect searaton or a arametersaton of roughness and mosture effects wthn the scatterng roblem. he scatterng roblem of electromagnetc waes from randomly rough surfaces has been an actual research toc oer decades and s stll not satsfactorly soled due to the lack of an exact closed-form soluton. Howeer, for many ractcal alcaton, aroxmate solutons are suffcent. In the absence of any drect relatonsh between surface arameters and backscatterng sgnal models emrcal relatons hae been deeloed. In the feld of radar remote sensng the most common aroxmaton methods are based on the ealuaton of backscatterng amltudes consderng sngle or dual-channel A data. he choce of an arorate scatterng model s essental for the quanttate estmaton of the surface arameters. On the one hand t must contan enough hyscal structure whle on the other hand t should hae a rght balance between the amount of arameters needed for ther descrton and aalable obserables. As natural surfaces are comlex stochastc objects a ror nformaton and assumtons can be used to smlfy the nerson roblem. Hence, for some of the scatterng model n order to obtan an accurate estmate of sol mosture, nformaton about the surface roughness was requred or roughness has been consdered as a dsturbng effect and seeral condtons hae been deeloed n order to mnmse ts nfluence (Hajnsek,. Howeer, an ndeendent estmate of roughness condtons s not ossble by usng only a sngle olarsaton and sngle- frequency A system. Increasng the amount of oberables by usng a fully olarmetrc data set, the amount of surface arameters and ts estmaton quantty ncreases. Howeer, the man lmtaton of usng models based on olarmetrc backscatterng amltudes s ther nsuffcency to deal - at leas n a ractcal way - wth dffuse or secondary scatterng rocesses, deolarsaton effects caused by the surface roughness, and the resence of multlcate and / or addte nose comonents. A large class of natural surface scatterers, s charactersed by secondary and/or multle scatterng effects. Wth ncreasng surface roughness, relate to the waelength, the effect of multle scatterng becomes stronger, generatng an adequate scatterng comonent. Dhedral scatterng due to small correlaton lengths charactersed by >, and/or dffuse scatterng ( contrbuton affects the backscattered sgnal. Also, effects nduced by the resence of egetaton coer can not be accounted wth surface scatterng models. Both effects lead to a olaton of the requred condtons of most models and/or to based estmaton of the roughness and mosture arameters.

2 .. olarmetrc Coherence he frst way followed n order to extend the obseraton sace was by ncororatng olarmetrc hase nformaton n form of (second-order correlaton (coherence coeffcents between dfferent olarsatons. Indeed, correlaton coeffcents at dfferent olarsatons hae been reorted to be senste to surface arameters. he - correlaton coeffcent < > γ : ( < > < > has been ealuated wth resect to ts senstty to delectrc constant and/or rms heght condton of rough surfaces n (Borgeaud, 994. An ncreased correlaton to sol mosture condtons wthn a certan roughness range has been reorted. In contrary, (-(- correlaton coeffcent γ ( ( : < < ( ( > < has been found to correlate wth surface roughness, ndeendent on the surface mosture content and the local ncdence angle (Hajnsek,. Further nestgatons n (Matta, 997 demonstrated that the crcular olarsaton correlaton coeffcent < LL > γ LL : ( < > < > LL LL s wdely ndeendent on the delectrc roertes of rough surfaces and deends only on the surface roughness. Its ndeendence from the azmuth toograhc tlt has been reorted n (chuler. hus, γ LL can be used for robust quanttate surface roughness estmates. > > ( More recently the olarmetrc scatterng ansotroy obtaned from the egen-alues of the olarmetrc coherence matrx has been ealuated to be a senste estmate for the surface roughness (Cloude 999. hs s n accordance wth the obseratons about the crcular olarsaton correlaton coeffcent as the ansotroy A can be nterreted as a generalsed rotaton narant exresson of γ LL n case where the coherency matrx s dagonal. λ λ A : λ λ λ, λ Egenalues of [] (4 Both arameters, γ LL and A, are by defnton normalsed between and and hae n frst order - a drect lnear relatonsh to the surface roughness γll ks A for ks (5 he rce to be ayed for usng the rotaton narant ansotroy s ts ery nosy nature esecally at the low range of ts range.e. for smooth surfaces (Hajnsek. In ths case

3 the amltudes of the secondary scatterng mechansms, exressed by the second and thrd egenalues are ery small, down to -5 [db] or een less. As ths s close to the system nose floor, A s strongly affected by addte nose effects. Howeer, by addte flterng the nfluence can be reduced. Concernng the aluable surface roughness range, radar sensors oeratng at lower frequences (L-band allow the coerage of a suffcently wde range of natural surfaces, as t can be seen n ab. ks ks Band ID Waelength [cm] for rms heght.5 [cm] for rms heght 4 [cm] X C L ab.: he surface roughness range for natural surface calculated for dfferent waelength Based on these exermental obseratons a olarmetrc scatterng model usng as a startng ont the M (Bragg-Model an extended Bragg model (X-Bragg, has been deeloed, whch allows quanttate estmaton of roughness and delectrc constant oer a wde range of natural bare surfaces. X-Bragg assumes reflecton symmetrc surfaces, where the axs of symmetry s defned by the mean normal to the surface ector. It accounts for cross-olarsed as well as deolarsaton effects. he alcaton of the model to exermental data demonstrate a hgh nerson accuracy shows a good agreement between nerted alues and ground measurements (Hajnsek,. Howeer, the man lmtaton for surface arameters estmaton from olarmetrc A data s the resence of egetaton. hs combned wth the fact that most natural surfaces are temorarly or ermanently coered by egetaton restrcts sgnfcantly the mortance of radar remote sensng for a wde sectrum of geohyscal and enronmental alcatons. Howeer, the eoluton of radar technology and technques allows otmsm concernng the taton of ths lmtaton.. he Extended or X-Bragg model Based on these exermental obseratons, a new model for the nestgaton of surface arameters from olarmetrc A data s ntroduced n ths aer. he roosed model s a two comonent model ncludng a Bragg scatterng term and a roughness nduced rotaton symmetrc dsturbance. In order to decoule the real art of the delectrc constant ε from surface roughness s, the model s addressed n terms of the olarmetrc scatterng entroy (H, scatterng ansotroy (A and alha angle (α whch are dered from the egenalues and

4 egenectors of the olarmetrc coherency matrx (Cloude et al hs allows the mlementaton of a smle nerson algorthm for both surface roughness and sol mosture... econd Order catterng Descrton of urface catterers In order to descrbe correlaton roertes of natural scatterers, the olarmetrc coherency matrx whch contans the second order moments of the scatterng rocess s ntroduced. Its formaton s based on the ntroducton of a scatterng ector k r as the ectorsaton of the scatterng matrx [] usng the aul sn matrces bass set (Cloude et al. 996, Cloude et al.. [ ] k : VH [ ] he coherency matrx [] s formed by aeragng the outer roduct of [ ] : k k ( ( r k as ( ( ( ( 4 ( he dagonal elements of [] are gen by the real backscattered ower alues whle the offdagonal elements contan the comlex cross correlatons between the elements of k r. [] s by defnton hermtan oste sem-defnte, whch mles that t has real non-negate egenalues and orthogonal egenectors, and can always be dagonalsed by an untary smlarty transformaton of the form (Cloude et al. 997 λ [ ] [ U ][ Λ][ U ] where [ Λ λ, λ ( ] [ ] [ e, e e ] U, (6 (7 (8 [Λ] s a dagonal matrx wth elements the real non-negate egenalues, λ λ λ of [], and [U ] s the untary egenector matrx wth columns corresondng to the orthonormal egenectors e, e and. he dagonalsaton of the coherency matrx [] may be e nterreted as ts decomoston nto a non-coherent sum of three ndeendent scatterng contrbutons [ ] [ U ][ Λ][ U ] λ( e e λ ( e e λ ( e e (9 he contrbuton of each scatterng mechansm n terms of ower s gen by the arorate egenalue. he nformaton about whch knd of scatterng mechansm s obtaned s contaned n the corresondng egenectors. here are three mortant hyscal features arsng drectly from the dagonalsaton of the coherency matrx. he frst two are obtaned from the egenalues of [] whch - normalsed by the absolute scatterng magntudes - can be nterreted as scatterng robabltes (Cloude et al.

5 λ λ : λ λ λ λ j j ( Usng the robabltes two ratos for the descrton of an arbtrary rough surface can be defned: the olarmetrc scatterng entroy H and the scatterng ansotroy A, whch are defned as H log ( A ( Both arameters ary between and. he entroy can be nterreted as a measure of the randomness of the scatterng rocess. he ansotroy defnes the relaton between the second and the thrd egenalues, and s a measure for the dfference of the secondary scatterng mechansms. For smooth surfaces, H becomes zero mlyng a non-deolarsng scatterng rocess descrbed by a sngle scatterng matrx and ncreases wth surface roughness. Deolarsng surfaces are charactersed by non-zero entroy alues. A can be zero een for rough surfaces. For surfaces charactersed by ntermedate entroy alues, a hgh ansotroy ndcates the resence of only one strong secondary scatterng rocess, whle a low ansotroy ndcates the aearance of two equally strong scatterng rocesses. For azmuthaly symmetrc surfaces λ λ by defnton and A becomes (Cloude et al. 996, Cloude et al.. In ths sense, the ansotroy rodes comlementary nformaton to the entroy and facltates the nterretaton of the surface scatterer. he great adantage of these two arameters arses from the narance of the egenalue roblem under untary transformatons: he same surface leads to the same egenalues and consequently to the same entroy and ansotroy alues ndeendently on the bass used to measure the corresondng scatterng matrx. he thrd mortant arameter s obtaned from the egenectors of []. Each egenector e can be exressed n terms of fe angles as (Cloude et al. 997 e [ cos α ex ( φ sn α cos β ex ( φ sn α sn β ex ( φ ] he β angles can be nterreted as a rotaton of the corresondng egenector n the e lane erendcular to the scatterng lane, whle φ, φ and φ are accountng for the hase relatons between the elements of e. More mortant n the context of ths work s the mean scatterng angle α defned as α ( α α α (4 he alha angle α ndcates the tye of the mean scatterng rocess occurrng (Cloude et al Its nterretaton n terms of the surface scatterng roblem wll be gen n the followng sectons. eturnng now to the M, the corresondng scatterng ector k r s gen by

6 ( ( ex sn ex cos m m k s s φ α φ α (5 where m denotes the absolute scatterng amltude. he coherency matrx of a Bragg scatterer follows as [ ] ( ( ( ( m k k s r r (6 wo of the three off-dagonal elements dsaear as a consequence of zero cross-olarsaton, whle the thrd one deends only on the surface delectrc constant and the radar ncdence angle. he corresondng normalsed correlaton coeffcent s one ( ( ( ( : ( ( γ (7 as a consequence of the nablty of the M to descrbe deolarsaton effects. egardng now the nterretaton of the alha angle, from (5 follows that α smlar to the co-olarsed rato s / s ndeendent of roughness, and therefore, can be used for the estmaton of the delectrc constant f the local ncdence angle s known arccos α (8 As shown n Fgure, for a dry surface the alha angle α s small and ncreases wth ncreasng sol mosture. he hghest senstty occurs between and m [ol. %] and saturates wth further ncreasng of m. 5 degrees 6 degrees Fgure he relaton of the alha angle to the olumetrc sol mosture

7 ummarsng, the man lmtatons of the M are ts small surface roughness aldty range below. ks and the saturaton of ts senstty to sol mosture content aboe m [ol. %]. Its nablty to descrbe deolarsaton effects restrcts ts usefulness regardng the nterretaton and nerson of exermental data from natural surfaces. Howeer, the robustness of M nsde ts aldty range and ts releant hyscal background leaded to seeral nestgatons to use t as a aluable startng ont for an extended model. As mentoned n the reous secton, two man effects hae to be ntroduced n order to extend the Bragg scatterng model for a wder range of roughness condtons: non-zero crossolarsed backscatterng and deolarsaton. In fact, conentonal two- or multle-scale extensons ntroduce cross-olarsaton but fal to exress deolarsaton effects. An alternate way to ntroduce roughness dsturbance s to model the surface as a reflecton symmetrc deolarser by rotatng the Bragg coherency matrx [] about an angle ß n the lane erendcular to the scatterng lane (Lee et al. as [ ( β ] cos β sn β sn β cos β ( ( ( ( and erformng a confguratonal aeragng oer a gen dstrbuton (ß of ß: π [ ] [ β ] cos β sn β sn β cos β ( ( β dβ ( he wdth of the assumed dstrbuton corresonds to the amount of roughness dsturbance of the modelled surface. Assumng (ß to be a unform dstrbuton about zero wth wdth ß (see Fgure the coherency matrx for the rough surface becomes C C sn c( β [ ] C sn c( β C ( sn c( 4β β β ( β β ( π β C ( ( sn c 4β ( (9 (.5

8 ensor catterng lane Azmuthal Orented urface β urface k (β β Fgure chematc reresentaton of the unform dstrbuton of the sloe β β wth snc(x sn(x / x. he coeffcents C, C, and C descrbng the Bragg comonents of the surface, and are gen by C C ( ( C ( Equaton ( reresents the coherency matrx of an extended Bragg surface charactersed by cross-olarsed energy and at the same tme a olarmetrc coherence less than one γ ( ( : sn c( β ( sn c( 4β /. he wdth of the dstrbuton ß descrbes the roughness comonent and controls both, the leel of cross-olarsed ower and the ((- coherence. Fg. (.4 show the araton of ((- coherence (Fg. (.4 and normalsed cross-olarsed ower accordng to (. In the lmt of a smooth surface (.e. ß, the ((- coherence s one and the backscattered ower zero. In ths case, the coherency matrx obtans the form of the ure Bragg coherency matrx (see (6. Wth ncreasng roughness (.e. ncreasng ß, the ower ncreases, whle the ((- coherence decreases monotoncally from to zero. In ths hgh roughness lmt, the surface becomes azmuthally symmetrc. (4

9 Fgure Varaton of the coherence and the cross olarsed ower wth ncreasng β Furthermore, t s mortant to realse that, whle the ncrease of cross olarsed ower wth roughness deends on the delectrc constant of the surface (and the ncdence angle the decrease of the ((- coherence s ndeendent from both. On the other hand, accordng to (, the rato s ndeendent on the surface roughness and deends only on the delectrc constant of the surface and the ncdence angle as shown n Fgure 4. hus, the extended Bragg model s charactersed by an nherent searaton of roughness and mosture effects obtaned n form of ratos of the elements of the coherency matrx allowng an ndeendent estmaton of these arameters. (5 Fgure 4. he olarsaton rato as a functon of the β arameter.