volume | PIER Journals

Abstract

We consider the Global Navigation Satellite System Reflectometry (GNSS-R) for land applications. A distinct feature of land is that the topography has multiple elevations. The rms of elevations is in meters causing random phases between different elevations, which affect the coherent wave that has definite phase and the Fresnel zone effects as shown previously by a Kirchhoff numerical simulator (KA simulator). In this paper, we develop a physical patch model that is computationally efficient. The entire area within the footprint is divided intopatches. Each patch is small enough to satisfy the plane wave incidence and is large enough to ignore mutual wave interactions between patches. The bistatic scattering cross section of each patch for the coherent and incoherent field is computed. The bistatic cross section of plane wave incidence is obtained from lookup tables (LUTs) of the numerical 3D solution of Maxwell equations (NMM3D). The SWC represents the summation of weighted coherent fields over patches. The SWICI represents the summation of weighted incoherent intensities over patches. The formula of the received power is the sum of powers from the SWC and SWICI (the SWC/SWICI formula). The weighting factor of each patch is based on thegeometry, spherical waves, and the considerations of field amplitudes and phase variations. We also present an alternative formula, the ``correlation'' formula, using the summation of power from each physicalarea and correlations of SWCs from areas. The SWC/SWICI formula and the ``correlation'' formula are shown analytically to be the same. Results are compared with the KA simulator and two common models (the coherent model and the incoherent model). Results of the patch modelare consistent with the KA simulator. For the simulation cases, the results fall between the coherent model and the incoherent model. The patch model is much more computationally efficient than the KA simulator and the results are more accurate. In examples of this paper, the patch model results are independent of patch size as long as the patch size smaller than 50 m and much larger than the wavelength of GNSS-R frequency.

1. Gu, W., H. Xu, and L. Tsang, "A numerical Kirchhoff simulator for GNSS land applications," Progress In Electromagnetics Research, Vol. 164, 119-133, 2019.
doi:10.2528/PIER18121803

2. Chew, C., R. Shah, C. Zu®ada, G. Hajj, D. Masters, and A. J. Mannucci, "Demonstrating soil moisture remote sensing with observations from the UK TechDemoSat-1 satellite mission," Geophysical Research Letters, Vol. 43, No. 7, 3317-3324, 2016.
doi:10.1002/2016GL068189

3. Kim, H. and V. Lakshmi, "Use of Cyclone Global Navigation Satellite System (CYGNSS) observations for estimation of soil moisture," Geophysical Research Letters, Vol. 45, No. 16, 8272-8282, 2018.
doi:10.1029/2018GL078923

4. Al-Khaldi, M., J. Johnson, A. O'Brien, F. Mattia, and A. Balenzano, "GNSS-R time-series soil moisture retrievals from vegetated surfaces," IGARSS 2018 | 2018 IEEE International Geoscience and Remote Sensing Symposium, 2035-2038, 2018.

5. Cardellach, E., F. Fabra, O. Nogues-Correig, S. Oliveras, S. Ribo, and A. Rius, "GNSS-R ground- based and airborne campaigns for ocean, land, ice and snow techniques: Application to the GOLD- RTR datasets," Radio Sci., Vol. 46, 2011.
doi:10.1002/2017GL074513

6. Li, W., E. Cardellach, F. Fabra, A. Rius, S. Ribo, and M. Martin-Neira, "First spaceborne phase altimetry over sea ice using TechDemoSat-1 GNSS-R signals," Geophys. Res. Lett., Vol. 44, 2017.
doi:10.1175/JTECH-D-16-0196.1

7. Clarizia, M. P. and C. S. Ruf, "Bayesian wind speed estimation conditioned on signi¯cant wave height for GNSS-R ocean observations," J. Atmos. Oceanic Technol., Vol. 34, 1193-1202, 2017.
doi:10.1109/JSTARS.2018.2825948

8. Ruf, C., S. Gleason, and D. S. McKague, "Assessment of CYGNSS wind speed retrieval uncertainty," IEEE J. Sel. Topics Appl. Earth Obs. Remote Sens., Vol. 12, No. 1, 87-97, Jan. 2019.
doi:10.1109/JSTARS.2017.2743172

9. Yueh, S., X. Xu, R. Shah, Y. Kim, J. L. Garrison, A. Komanduru, and K. Elder, "Remote sensing of snow water equivalent using coherent re°ection from satellite signals of opportunity: Theoretical modeling," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 10, No. 12, 5529-5540, 2017.

10. Tsang, L., J. Zhu, Y. Du, and R. Gao, "Electromagnetic scattering model for GNSS-R land applications including effects of multiple elevations in random rough surfaces," IEEE GNSS+R 2019, Benevento, Italy, May 20--22, 2019.
doi:10.1109/TGRS.2010.2040748

11. Huang, S., L. Tsang, E. G. Njoku, and K. S. Chen, "Backscattering coefficients, coherent reflectivities, and emissivities of randomly rough soil surfaces at L-band for SMAP applications based on numerical solutions of maxwell equations in three-dimensional simulations," IEEE Trans. Geoscience and Remote Sensing, Vol. 48, 2557-2568, 2010.
doi:10.1109/TGRS.2015.2451671

12. Liao, T.-H., L. Tsang, S. Huang, N. Niamsuwan, S. Jaruwatanadilok, S. B. Kim, et al. "Copolarized and cross-polarized backscattering from random rough soil surfaces from L-band to Ku-band using numerical solutions of Maxwell's equations with near-field precondition," IEEE Trans. Geoscience and Remote Sensing, Vol. 54, 651-662, 2016.
doi:10.1016/0021-9991(74)90089-8

13. DeSanto, J. A. and O. Shisha, "Numerical solution of a singular integral equation in random rough surface scattering theory," Journal of Computational Physics, Vol. 15, No. 2, 286-292, 1974.
doi:10.1109/TGRS.2016.2631126

14. Kim, S.-B., J. J. Van Zyl, J. T. Johnson, M. Moghaddam, L. Tsang, A. Colliander, et al. "Surface soil moisture retrieval using the L-band synthetic aperture radar onboard the soil moisture active-passive satellite and evaluation at core validation sites," IEEE Trans. Geoscience and Remote Sensing, Vol. 55, 1897-1914, 2017.

15. Gleason, S., Level 1B DDM calibration algorithm theoretical basis document, CYGNSS Project Document 148-0137, Rev 2, Aug. 20, 2018.
doi:10.1002/0471224278

16. Tsang, L. and J. Kong, Scattering of Electromagnetic Waves, Vol. 3: Advanced Topics, Wiley Interscience, 2001.
doi:10.1016/0034-4257(91)90057-D

17. Jackson, T. J. and T. J. Schmugge, "Vegetation effects on the microwave emission of soils," Remote Sensing of Environment, Vol. 36, No. 3, 203-212, 1991.
doi:10.1109/ACCESS.2017.2714620

18. Huang, H., L. Tsang, E.G. Njoku, A. Colliander, T.-H. Liao, and K.-H. Ding, "Propagation and scattering by a layer of randomly distributed dielectric cylinders using monte carlo simulations of 3D Maxwell equations with applications in microwave interactions with vegetation," IEEE Access, Vol. 5, 11985-12003, 2017.
doi:10.1109/JSTARS.2017.2703602

19. Tan, S., J. Zhu, L. Tsang, and S. V. Nghiem, "Microwave signatures of snow cover using numerical Maxwell equations based on discrete dipole approximation in bicontinuous media and half-space dyadic Green's function," IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., Vol. 10, No. 11, 4686-4702, Nov. 2017.

20. Tsang, L. and J. Kong, "Scattering of Electromagnetic Waves, Vol. 1: Theories and Applications," Wiley Interscience, 2001.

Dr. Jiyue Zhu

Professor Leung Tsang

Dr. Haokui Xu