volume | PIER Journals

Abstract

In this paper, we derived Analytical Kirchhoff Solutions (AKS) for bistatic scattering near the specular directions at P band and L band for applications in Signals of Opportunity (SoOp). The land surface profiles are divided into three scales: microwave roughness f₁, fine scale topography f₂, and coarse scale 30-meter DEM f₃. The microwave roughness and the fine scale topography are treated as random rough surfaces, while the coarse scale topography from DEM data are treated as deterministic planar patches. The salient features of the AKS model are (i) analytical expressions are obtained for both coherent waves and incoherent waves, (ii) Monte Carlo simulations are not required making the AKS computationally efficient, (iii) the analytical solutions are expressed in terms of the spectrum, so that the dividing line between microwave roughness and fine scale topography is not required, and the rough surface spectrum derived from lidar elevation measurements can be incorporated directly. The results of the three approaches, AKS, the Numerical Kirchhoff Approach (NKA) and the Fine Scale Partial Coherent Patch (FPCP) model, are indistinguishable for both the coherent waves and the incoherent waves. The agreements validate the AKS and FPCP approaches as NKA is a brute force accurate method based on Kirchhoff integral using 2 cm discretization and high-performance computers. Results show that the f₂ profiles of fine scale topography have significant effects. The results of three Kirchhoff approaches fall in-between the results of the two versions of Geometric Optics (GO) approximations to the Kirchhoff integral [1, 2]. The two GO versions are with and without attenuation due to microwave roughness. The GO with microwave attenuation is also known as the ``Improved Geometric Optics Model (IGOM)''. Numerical results of coherent waves and incoherent waves are illustrated for remote sensing of snow and soil moisture at P band and L band. For P band, the histograms of the phase are shown. Results of the coherent waves are dependent on the sizes of the area as well as topographical elevations and slopes. AKS results are used to illustrate the coherent waves at P band on area sizes up to 1.5 km using 30-meter DEM topography elevations and derived slopes at Sanford, Brazos Peak, and Lobato Tank, Colorado, USA. For L band, the AKS results of Cross-Track are in good agreement with CYGNSS data over San Luis Valley, USA. In comparing CPU, it takes merely 25 seconds on a single CPU core for AKS to compute for a 15 km by 15 km DDM pixel which has 250000 DEM 30-meter patches. The CPU for AKS is slightly more than the 20 seconds required for GO.

1. Al-Khaldi, M. M., J. T. Johnson, A. J. O'Brien, A. Balenzano, and F. Mattia, "Time-series retrieval of soil moisture using CYGNSS," IEEE Transactions on Geoscience and Remote Sensing, Vol. 57, No. 7, 4322-4331, 2019.
doi:10.1109/TGRS.2018.2890646 Google Scholar

2. Campbell, J. D., A. Melebari, and M. Moghaddam, "Modeling the effects of topography on delay-Doppler maps," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 13, 1740-1751, 2020.
doi:10.1109/JSTARS.2020.2981570 Google Scholar

3. Unwin, M., P. Jales, J. Tye, C. Gommenginger, G. Foti, and J. Rosello, "Spaceborne GNSS-reflectometry on TechDemoSat-1: Early mission operations and exploitation," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 9, No. 10, 4525-4539, 2016.
doi:10.1109/JSTARS.2016.2603846 Google Scholar

4. Ruf, C., A. Lyons, M. Unwin, J. Dickinson, R. Rose, D. Rose, and M. Vincent, "CYGNSS: Enabling the future of hurricane prediction [Remote Sensing Satellites," IEEE Geoscience and Remote Sensing Magazine, Vol. 1, No. 2, 52-67, 2013.
doi:10.1109/MGRS.2013.2260911 Google Scholar

5. Clarizia, M. P. and C. S. Ruf, "Wind speed retrieval algorithm for the cyclone global navigation satellite system (CYGNSS) mission," IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No. 8, 4419-4432, 2016.
doi:10.1109/TGRS.2016.2541343 Google Scholar

6. Li, W., E. Cardellach, F. Fabra, A. Rius, S. Ribó, and M. Martín-Neira, "First spaceborne phase altimetry over sea ice using TechDemoSat-1 GNSS-R signals," Geophysical Research Letters, Vol. 44, No. 16, 8369-8376, 2017.
doi:10.1002/2017GL074513 Google Scholar

7. Nghiem, S. V., C. Zuffada, R. Shah, C. Chew, S. T. Lowe, A. J. Mannucci, E. Cardellach, G. R. Brakenridge, G. Geller, and A. Rosenqvist, "Wetland monitoring with global navigation satellite system reflectometry: Wetland monitoring with GNSS-R," Earth and Space Science, Vol. 4, No. 1, 16-39, Hoboken, N.J., 2017.
doi:10.1002/2016EA000194 Google Scholar

8. 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 Google Scholar

9. Chew, C. C. and E. E. Small, "Soil moisture sensing using spaceborne GNSS reflections: Comparison of CYGNSS reflectivity to SMAP soil moisture," Geophysical Research Letters, Vol. 45, No. 9, 4049-4057, 2018.
doi:10.1029/2018GL077905 Google Scholar

10. Clarizia, M. P., N. Pierdicca, F. Costantini, and N. Floury, "Analysis of CYGNSS data for soil moisture retrieval," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 12, No. 7, 2227-2235, 2019.
doi:10.1109/JSTARS.2019.2895510 Google Scholar

11. Shah, R., X. Xu, S. Yueh, C. S. Chae, K. Elder, B. Starr, and Y. Kim, "Remote sensing of snow water equivalent using P-band coherent reflection," IEEE Geoscience and Remote Sensing Letters, Vol. 14, No. 3, 309-313, 2017.
doi:10.1109/LGRS.2016.2636664 Google Scholar

12. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves Advanced Topics, Wiley series in remote sensing, Wiley, 2001.
doi:10.1002/0471224278

13. Zavorotny, V. and A. Voronovich, "Scattering of GPS signals from the ocean with wind remote sensing application," IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 2, 951-964, 2000.
doi:10.1109/36.841977 Google Scholar

14. Thompson, D., T. Elfouhaily, and J. Garrison, "An improved geometrical optics model for bistatic GPS scattering from the ocean surface," IEEE Transactions on Geoscience and Remote Sensing, Vol. 43, No. 12, 2810-2821, Dec. 2005.
doi:10.1109/TGRS.2005.857895 Google Scholar

15. Campbell, J. D., et al. "Intercomparison of models for CYGNSS delay-Doppler maps at a validation site in the San Luis Valley of Colorado," IGARSS 2021, Brussels, Belgium, Jul. 11-16, 2021. Google Scholar

16. Carreno-Luengo, H., J. A. Crespo, R. Akbar, A. Bringer, A. Warnock, M. Morris, and C. Ruf, "The CYGNSS mission: On-going science team investigations," Remote Sensing, Vol. 13, No. 9, 1814, Basel, Switzerland, 2021.
doi:10.3390/rs13091814 Google Scholar

17. Bringer, A., J. Johnson, C. Toth, C. Ruf, and M. Moghaddam, "Studies of terrain surface roughness and its effects on GNSS-R systems using airborne LIDAR measurements," IGARSS 2021, Brussels, Belgium, Jul. 11-16, 2021. Google Scholar

18. Dente, L., L. Guerriero, D. Comite, and N. Pierdicca, "Space-borne GNSS-R signal over a complex topography: Modeling and validation," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 13, 1218-1233, 2020.
doi:10.1109/JSTARS.2020.2975187 Google Scholar

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

20. Zhu, J., L. Tsang, and H. Xu, "A physical patch model for GNSS-R land applications," Progress In Electromagnetics Research, Vol. 165, 93-105, 2019.
doi:10.2528/PIER19031003 Google Scholar

21. Xu, H., J. Zhu, L. Tsang, and S. B. Kim, "A fine scale partially coherent patch model including topographical effects for GNSS-R DDM simulations," Progress In Electromagnetics Research, Vol. 170, 97-128, 2021.
doi:10.2528/PIER20121201 Google Scholar

22. Yueh, S., R. Shah, X. Xu, K. Elder, and B. Starr, "Experimental demonstration of soil moisture remote sensing using P-band satellite signals of opportunity," IEEE Geoscience and Remote Sensing Letters, Vol. 17, No. 2, 207-211, 2020.
doi:10.1109/LGRS.2019.2918764 Google Scholar

23. Huang, S., L. Tsang, E. G. Njoku, and K. S. Chan, "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 Transactions on Geoscience and Remote Sensing, Vol. 48, No. 6, 2557-2568, 2010.
doi:10.1109/TGRS.2010.2040748 Google Scholar

24. Al-Khaldi, M. M., J. T. Johnson, S. Gleason, E. Loria, A. J. O'Brien, and Y. Yi, "An algorithm for detecting coherence in cyclone global navigation satellite system mission Level-1 delay-Doppler maps," IEEE Transactions on Geoscience and Remote Sensing, Vol. 59, No. 5, 4454-4463, 2021.
doi:10.1109/TGRS.2020.3009784 Google Scholar

25. Jia, Y., S. Jin, H. Chen, Q. Yan, P. Savi, Y. Jin, and Y. Yuan, "Temporal-spatial soil moisture estimation from CYGNSS using machine learning regression with a preclassification approach," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 14, 4879-4893, 2021.
doi:10.1109/JSTARS.2021.3076470 Google Scholar

26. Munoz-Martin, J. F., L. F. Capon, J. A. Ruiz-de-Azua, and A. Camps, "The flexible microwave Payload-2: A SDR-based GNSS-reflectometer and L-band radiometer for CubeSats," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 13, 1298-1311, 2020.
doi:10.1109/JSTARS.2020.2977959 Google Scholar

27. Perez-Portero, A., J. F. Munoz-Martin, H. Park, and A. Camps, "Airborne GNSS-R: A key enabling technology for environmental monitoring," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 1, 2021. Google Scholar

28. Yueh, S. H., R. Shah, X. Xu, B. Stiles, and X. Bosch-Lluis, "A satellite synthetic aperture radar concept using P-band signals of opportunity," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 14, 2796-2816, 2021.
doi:10.1109/JSTARS.2021.3059242 Google Scholar

Dr. Bowen Ren

Dr. Jiyue Zhu

Professor Leung Tsang

Dr. Haokui Xu