Condition for Precise Measurement of Soil Surface Roughness

Transcription

1 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 2, MARCH [10] C. L. Watha, J. M. Norman, J. M. Wees, G. Campbe, and B. L. Bad, Simpe equation to approximate the bidirectiona refectance from vegetative canopies and bare soi surfaces, App. Opt., vo. 24, pp , [11] T. Nison and A. Kuusk, A refectance mode for the homogeneous pant canopy and its inversion, Remote Sens. Environ., vo. 27, pp , [12] X. Li and A. H. Straher, Geometric-optica bidirectiona refectance modeing of the discrete crown vegetation canopy: Effect of crown shape and mutua shadowing, IEEE Trans. Geosci. Remote Sensing, vo. 30, pp , [13] W. Wanner, X. Li, and A. H. Straher, On the derivation of kernes for kerne-driven modes of bidirectiona refectance, J. Geophys. Res., vo. 100, pp , [14] W. C. Snyder and Z. Wan, BRDF modes to predict spectra refectance and emissivity in the therma infrared, IEEE Trans. Geosci. Remote Sensing, vo. 36, pp , Jan [15] F. E. Nicodemus, Radiometry, vo. 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Environ., vo. 58, pp , Condition for Precise Measurement of Soi Surface Roughness Yisok Oh and Young Chu Kay Abstract Whereas it is we known that eectromagnetic scattering by a randomy rough surface is strongy infuenced by the surface-height correation function, it is not cear as to how ong a surface-height profie is needed and at what interva it shoud be samped to experimentay quantify the correation function of a rea surface. This paper presents the resuts of a Monte Caro simuation conducted to answer these questions. It was determined that, in order to measure the rms height and the correation ength with a precision of 610%, the surface segment shoud be at east 40 ong and 200 ong, respectivey, where is the mean (or true) vaue of the surface correation ength. Shorter segment engths can be used if mutipe segments are measured and then the estimated vaues are averaged. The second part of the study focused on the reationship between samping interva and measurement precision. It was found that, in order to estimate the surface roughness parameters with a precision of 65%, it is necessary that the surface be samped at a spacing no onger than 0.2 of the correation ength. I. INTRODUCTION Extraction of soi moisture and vegetation biomass information from imaging radar data has been a subject of intense interest for a ong time. However, the technique has not been very successfu, in part because of the compexity of natura soi surfaces, specificay, the difficuty in estimating the surface roughness and the inhomogeneity of the soi moisture. Furthermore, theoretica and numerica modes, whie we suited for idea rough surfaces, are not easy to impement for natura soi surfaces. An attempt has been made to retrieve soi moisture and surface roughness together from poarimetric radar scattering data through the use of an inversion agorithm [1]. Because the dynamic range of the backscattering coefficient associated with the surface roughness is comparabe to or arger than that associated with the soi moisture, the surface roughness shoud be estimated accuratey for retrieving the soi moisture with good accuracy. In this paper, the effect of surface roughness on radar scattering from soi surfaces is discussed and the resuts of a simuation study aimed at quantifying criteria for accurate estimation of surface roughness parameters are presented. According to experimenta observations [1], whereas the height distribution of natura soi surfaces is characterized by Gaussian density functions, the measured correation functions of the surface height profies more cosey resembe exponentia functions, as shown in Fig. 1. The measured correation function shown in Fig. 1 was obtained by averaging more than 300 normaized correation functions measured from natura soi surfaces. The anguar responses of the vv-poarized backscattering coefficients for the exponentia, Gaussian, and the measured correation functions were computed and are shown in Fig. 1 for a surface with s =0:01 m, =0:1m, and "r = (10; 2) at f =1:5GHz by using the sma perturbation method (SPM), where s is the rms height and is the correation ength. The arge difference in trend between the exponentia and Gaussian curves, particuary in the higher anguar range, shows the importance of the shape of the correation function on the backscattering coefficient. Manuscript received December 5, 1996; revised Juy 11, This work was supported by the Korean Agency of Defense Deveopment. The authors are with the Schoo of Eectronic and Eectrica Engineering, Hong-Ik University, Seou, Korea. Pubisher Item Identifier S (98) /98$ IEEE

2 692 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 2, MARCH 1998 Fig. 2. Surface profies generated for both a Gaussian and an exponentia correation function. and Ce(j) =s 2 exp 0 jjj1x (3) the corresponding weighting functions are given by WG(i) = 21x 1=2 p s exp 02 i1x 2 and We(i) = p 21x p sk0 i1x (4) Fig. 1. Roe of the surface correation function of the surface-height profie. comparison of the measured correation function with Gaussian and exponentia functions and the effect of the correation function on the backscattering coefficient. II. SIMULATION PROCEDURE In order to examine the surface characteristics of random surfaces, severa randomy rough surfaces are generated by using the technique given in [2], as foows: Z(k) = M j=0m W(j)X(j+k) (1) where Z(k) is the surface height distribution, X(i) is a Gaussian random deviate N (0; 1), and W (j) is the weighting function given by W (j) =F 01 F[C(j)] (2) where C(j) is the correation function and F [] denotes the Fourier transform operator. For a surface characterized by a Gaussian or an exponentia correation function, given respectivey by CG(j) =s 2 exp 0 j1x 2 where 1x is the samping distance and K0[] is the modified Besse function of the second kind. Using the above equations, randomy rough surfaces were generated. The profies shown in Fig. 2 are for surfaces with s = 0:032 unit and = 0:46 unit for Gaussian and exponentia correation functions, both with a Gaussian height distribution. III. SIMULATION RESULTS The simuation procedure described in the preceding section was used to generate four profies of different rms heights and correation engths. In each case, the profie was onger than 1000, where is the correation ength. These profies were then used to determine the foowing: a) reationships between the measurement precision associated with estimating the surface roughness parameters (rms height s and correation ength ) and the ength of the surface-height profie L (by using ony specific segment engths of the tota generated profie); b) improvement provided by averaging mutipe segments on the estimates of s and ; c) reationship between measurement precision and samping interva 1x. A. Dependence on Segment Length Fig. 3 shows the pots of two correation functions cacuated, as given in [3], for the same surface, but on the basis of segments of different engths. It is cear from the pots that the 2000-unitong segment produces an exponentia ooking correation function,

3 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 2, MARCH (c) Fig. 3. Effect of the profie segment ength on the correation functions, the corresponding roughness spectrums, and (c) the maximum errors of the roughness spectrums. Fig. 4. Effect of averaging mutipe segments on the correation functions and the maximum errors in the roughness spectrums.

4 694 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 2, MARCH 1998 Fig. 5. Rms height and correation ength computed from each profie segment. Fig. 6. Standard deviations of rms height and correation ength, as a function of profie segment ength. whereas the short segment (L = 50unit) produces an osciatory function and it is accurate ony for dispacements shorter than the correation ength (1.0 unit). The scattering coefficient is proportiona to the Fourier transform of the correation function, which is the roughness spectrum, in the SPM mode and the dominant term in the physica optics (PO) mode is aso proportiona to the roughness spectrum. Therefore, the roughness spectrums corresponding to the correation curves in Fig. 3 are computed and shown in Fig. 3. The osciatory behavior of the correation curve for a profie segment of ength L =50unit gives the maximum error of 3.7 db, comparing with the exponentia curve. In order to reduce a numerica and aiasing error, a Gaussian-type window was used and the averaged maximum error of ten segments in the roughness spectrum was computed for each segment ength, as shown in Fig. 3(c). Fig. 3(c) shows that the profie ength shoud be at east 200 ong to get a precision of 62 db in the roughness spectrum, where is the profie correation ength. Fig. 4 and show the improvement in measurement precision provided by averaging mutipe equa-ength segments of the same profie. Figs. 3(c) and 4 show that averaging five 50-ong segments is equivaent to a resut from a singe 100-ong segment, in the sense of maximum error in the roughness spectrum. For ong segments of the same profie, the rms height (standard deviation of surface height) and the correation ength (dispacement j1x, such that the normaized correation function C e (j)=s 2 = e 01 ) are computed [3], as shown in Fig. 5 and. The standard deviations of the rms height and the correation ength are 7.6% and 25.1% of the mean vaues, respectivey, as shown in Fig. 5 and. By repeating the process for many different profie segment engths of the same profie, the standard deviations s and, associated with the estimates of s and (as percentages of the true means s and ) are cacuated. The resuts are dispayed in Fig. 6 and, which show that s and decrease in an exponentia-ike manner with segment ength L. To determine s with s=s 0:1, it is sufficient to use a singe segment 40 in ength, but to estimate with = 0:1, the segment ength has to be at east 200 in ength. Averaging mutipe segments does not necessariy resut in the same correation function, even when the tota segment ength is the same. The shorter the segment ength, the shorter the estimated vaue

5 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 2, MARCH Fig. 7. Dependence on the profie segment ength L when cacuating averaged rms height and averaged correation ength. Fig. 8. Effect of the samping distance for correation ength and rms height s. of the rms height and the correation ength, as shown in Fig. 7 and. B. Samping Distance The precision associated with the measurements of the roughness parameters s and is aso dependent on the samping distance 1x. According to the resuts shown in Fig. 8, which dispays the estimated vaues of [in Fig. 8] and s [in Fig. 8], as a function of 1x (measured in units of ) for a segment 2000 unit in ength, 1x shoud be no more than 0:2 to keep the error in estimating to within 65% and no more than 0:5 for the same error bound when estimating s. IV. CONCLUSION Based on the simuation study invoving the generation of random surfaces, it is recommended that, in order to measure the rms height and the correation ength of a rough surface with a precision of about 610% of their mean vaues, the surface segment ength shoud be 40 and 200, respectivey. Shorter segments engths can be used if mutipe segments are measured and then the estimated vaues are averaged. And the samping distance 1x shoud be no more than 0:2 in ength, where is the true correation ength of the surface. ACKNOWLEDGMENT The authors wish to thank Dr. F. Uaby for his encouragement and his carefu proofreading of this paper. REFERENCES [1] Y. Oh, K. Sarabandi, and F. T. Uaby, An empirica mode and an inversion technique for radar scattering from bare soi surfaces, IEEE Trans. Geosci. Remote Sensing, vo. 30, pp , Mar [2] A. K. Fung and M. F. Chen, Numerica simuation of scattering from simpe and composite random surfaces, J. Opt. Soc. Amer. A, vo. 2, pp , Dec [3] F. T. Uaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Active and Passive, vo. II. Norwood, MA: Artech House, 1986, ch. 11.