1. On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara

2. Importance of Water Circle

3. Electromagnetic Spectrum

4. Why Synthetic Aperture Radar? Advantages: All weather free All day free High resolution Penetration  thickness information Very sensitive to Moisture Disadvantages: Expensive Large data volume More difficult in image analyses

5. Synthetic Aperture Radar (SAR)

6. Outline 1. Surface Backscattering On Modeling : Tradition Backscattering Models Integral Equation Model Dielectric and Roughness Properties 2.On Estimate Bare Surface Soil Moisture Current Inverse Techniques Examples from AIRSAR and SIR-C 3.On Estimate Vegetated Surface Soil Moisture Radar Decomposition Technique Proposed Technique Using Multi-Temporal Measurements and its demonstration

7. Small Perturbation Model pq = vv or hh is the fourier transform of the surface correlation function. Exponential Guass Validity Condition: ks < 0.3, kl < 3 & rms slope < 0.3

8. Physical Optical Model is nth power of fourier transform of the surface correlation function. Guass Exponential Validity Condition: 0.05λ λ, & m < 0.25

9. Geometric Optical Model Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7 rms slope - m Reflectivity

10. Dielectric Properties of Soil Solid Material - 4.7 Water - frequency & temperature Soil - frequency, moisture, temperature, and texture Im DC Clay 80% & Sand 20% Clay 20% & Sand 80%

11. Surface Roughness Measurement

12. Surface Roughness Properties Stationary Random Rough Surface Description: surface rms. Height correlation length correlation function 1/e Gauss Exponential

13. Surface Roughness Correlation Functions Surface Roughness Measurements at Washita Site power spectral density function Characteristics: Exponential function has higher frequency components Power spectrum  FT  surface profile or correlation function

14. Problems in Roughness Measurements

15. Simulation of Surface Roughness

16. Effect of Multi-scale Surface roughness on Backscattering

17. Validity Regions of Classical Surface Backscattering Models

18. Measured Co-Polarization Ratio by Scatterometer

19. Integral Equation Model (1) where k Z = k cos , k X = k sin , and pp = vv or hh, the symbol is the Fourier transform of the nth power of the surface correlation coefficient.

20. Integral Equation (2) where, are the Fresnel reflection coefficients for horizontal and vertical polarization.

21. Comparing IEM Model with SIR-C & AIRSAR Measurements

22. Summary on Surface Scattering Models Surface roughness parameters are described by the surface auto-correlation function, rms height, and correlation length Tradition surface scattering models (SP, PO, and GO) are outside of application range due to restrictions on surface roughness parameters Recently developed IEM model has much wider application range for surface roughness parameters Research is needed for better techniques to describe natural surface properties

23. Current Concept on Using Repeat-pass Measurements Basic Concept Two measurements => the relative change in dielectric properties The absolute dielectric properties <= one measurement is known

24. Problem of Repeat-pass Measurements Problems: Large dynamic range ks & kl => a different response of dielectric properties Roughness effects can not be eliminated Effect is greater VV than HH large incidence than small incidence Normalized Polarization functions - R/min(R) SP-VV SP-HH GO Relative moisture change in % 23°

25. Current Techniques Using Polarization Measurements Basic understanding on HH and VV difference: As dielectric constant, the difference As roughness (especially rms height), the difference As incidence angle, the difference Common idea of the current algorithms Inverse - two equations  two unknowns.

26. Current Algorithms for Bare Surface (1) Oh et al., 1992. Semi-empirical model  ground scatterometer measurements Using 3 polarizations  2 measurements

27. Current Algorithms for Bare Surface (2) Dubios et al., 1995 Semi-empirical model  ground scatterometer measurements Using 2 co-polarizations  2 measurements

28. Current Algorithms for Bare Surface (3) Shi et al., 1997. Semi-empirical model  IEM simulated most possible conditions Using 2 combined co-polarizations  2 measurements

29. Study Site Description 1992 Soil Moisture Experiment

30. 0 -12 -9 -3 -6 dB Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992) VV HH HV June 12 June 18 June 16 June 13 VV difference to first day June 15 June 10

31. Estimated Surface Soil Moisture Maps vegetation <4 % 8-12 12-16 4-8 28-32 32-36 20-24 16-20 24-28 > 36 % June 10 June 15 June 18 June 13 June 16 June 12

32. Estimated Surface Roughness Parameter vegetation < -24 dB -22--20 -20--18 -24--22 -12--10 -10--8 -16--14 -18--16 -14--12 > -8 dB June 12 June 10 June 13 June 15June 16 June 18

33. Estimated Surface Soil Moisture Maps Using SIR-C’s L-band in April, 1994 vegetation <4 % 8-12 12-16 4-8 28-32 32-36 20-24 16-20 24-28 > 36 % 121315 161718

34. Comparing Field Measurements Standard Error (RMSE)  3.4% in Soil Moisture estimation Standard Error (RMSE)  1.9 dB in roughness estimation

35. Basic Consideration (1) Common idea of the current algorithm Inverse - two equations  two unknowns. It can be re-ranged to one equation for one unknown. Disadvantages: Requires both formula all in good accuracy Error in the estimated one unknown  the other

36. Basic Consideration (1) - continue in (a) in (b) in (c) Different weight  sensitive to different surface parameter Independent direct estimation of soil moisture and RMS height (a) ks(b) Sr(c) Rh

37. Basic Consideration (2) IEM -- Power expansion and nonlinear relationships Higher order inverse formula  improve accuracy Example: estimate surface RMS height s s s’

38. Basic Consideration (3) Tradition Backscattering Models Inverse model for different roughness region  improve accuracy

39. Validation Using Michigan's Scatterometer Data  Correlation: m v - 0.75, rms height - 0.96  RMSE: m v - 4.1%, rms height - 0.34cm mvmv S RMSE for S Measured parameters Estimated incidence

40. Characteristics of Backscattering Model (4) First-order backscattering model Surface parameters – surface dielectric and roughness properties Vegetation parameters – dielectric properties, scatter number densities, shapes, size, size distribution, & orientation Fraction of vegetation cover Direct volume backscattering (1) Direct surface backscattering (4 & 3) Surface & volume interaction (2) Double pass extinction

41. Radar Target Decomposition Covariance (or correlation) matrix Decomposition based on eigenvalues and eigenvectors where, are the eigenvalues of the covariance matrix, k are the eigenvectors, and k’ means the adjoint (complex conjugate transposed ) of k.

42. Radar Target Decomposition Technique Total Power: single, double, multi Total Power: single, double, multi VV: single, double, multi VV: single, double, multi HH Correlation or covariance matrix -> Eigen values & vectors VV, HH, VH

43. Relationships in scattering components between decomposition and backscattering model 1.First component in decomposition (single scattering) – direct volume, surface & its passes vegetation 2.Second component (double-bounce scattering) – Surface & volume interaction terms 3.Third component – defuse or multi-scattering terms

44. Properties of Double Scattering Component under Time Series Measurements 1.Variation in Time Scale surface roughness vegetation growth surface soil moisture 2.In backscattering Model 3.Ratio of two measurements independent of vegetation properties depends only on the reflectivity ratio

45. Comparison with Field Measurements VV, HH, VH Two Corn Fields Dielectric Constant Date Normalized VV & HH cross product of double scattering components for any n < m Corresponding reflectivity ratio Correlation=0.93, RMSE=0.42 dB

46. Estimate Absolute Surface Reflectance A) B) C) A) B) C) estimation

47. Current Evaluations Validity range of the second component measurements –Effect of radar calibration and system noise –What type and vegetation condition? How to obtain vegetation and surface roughness information –What we can do with the first component measurements? What to do with sparse vegetated surface?

48. Summary Time series measurements with second decomposed components (double reflection) –A promising (direct and simple technique) to estimate the relative change in dielectric constant for certain type of the vegetated surfaces – A great possibility to derive soil moisture algorithm for the vegetated surface Advantages of this technique –Do not require any information on vegetation –Can be applied to partially covered vegetation surface