ABSTRACT The amount of water stored in snowpack is the single most important measurement for the management of water supply and flood control systems. The available water content in snow is called the snow water equivalent (SWE). The product of snow density and depth provides an estimate of SWE. In this paper, snow depth and density are estimated by a nonlinear least squares fitting algorithm. The inputs to this algorithm are global positioning system (GPS) signals and a simple GPS interferometric reflectometry (GPS-IR) model. The elevation angles of interest at the GPS receiving antenna are between 50 and 300. A snow-covered prairie grass field experiment shows potential for inferring snow water equivalent using GPS-IR. For this case study, the average inferred snow depth (17.9 cm) is within the in situ measurement range (17.6 cm ± 1.5 cm). However, the average inferred snow density (0.13 g.cm-3) overestimates the in situ measurements (0.08 g.cm-3 ± 0.02 g.cm-3). Consequently, the average inferred SWE (2.33 g.cm-2) also overestimates the in situ calculations (1.38 g.cm-2 ± 0.36 g.cm-2).
Cite this paper
M. Jacobson, "Snow Water Equivalent Estimation for a Snow-Covered Prairie Grass Field by GPS Interferometric Reflectometry," Positioning, Vol. 3 No. 3, 2012, pp. 31-41. doi: 10.4236/pos.2012.33005.
 G. L. Schaefer and R. F. Paetzold, “SNOTEL (Snowpack Telemetry) and SCAN (Soil Climate Analysis Network). Presented at Automated Weather Stations for Applications in Agriculture and Water Resources Management: Current Use and Future,” 2000.
 M. C. Serreze, M. P. Clark, R. L. Armstrong, D. A. Mc-Ginnis and R. S. Pulwarty, “Characteristics of the Western United States Snowpack from Snowpack Telemetry (SNOTEL) Data,” Water Resources Research, Vol. 35, No. 7, 1999, pp. 2145-2160.
 N. P. Molotch and R. C. Bales, “SNOTEL Representatives in the Rio Grande Headwaters on the Basis of Physiographics and Remotely Sensed Snow Cover Persistence,” Hydrological Processes, Vol. 20, No. 4, 2006, pp. 723-739. doi:10.1002/hyp.6128
 K. M. Larson, E. Gutmann, V. Zavorotny, J. Braun, M. Williams and F. Nievinski, “Can We Measure Snow Depth with GPS Receivers?” Geophysical Research Letters, Vol. 36, 2009, p. L17502.
 C. A. Campbell, B. G. McConkey, R. P. Zentner, F. Selles and F. B. Dyck, “Benefits of Wheat Stubble Strips for Conserving Snow in Southwestern Saskatchewan,” Journal of Soil and Water Conservation, Vol. 47, No. 1, 1992, pp. 112-115.
 H. N. Hayhoe, R. G. Pelletier and D. R. Coote, “Estimating Snowmelt Runoff Erosion Indices for Canada,” Journal of Soil and Water Conservation, Vol. 50, No. 2, 1995, pp. 174-179.
 B. G. McConkey, R. P. Zentner and W. Nicholaichuk, “Perennial Grass Windbreaks for Continuous Wheat Production on the Canadian Prairies,” Journal of Soil and Water Conservation, Vol. 45, No. 1,1990, pp. 482-485.
 H. Steppuhnand and J. Waddington, “Conserving Water and Increasing Alfalfa Production Using a Tall Wheat-grass Windbreak System,” Journal of Soil and Water Conservation, Vol. 51, No. 5, 1996, pp. 439-445.
 E. T. Engman, “The Use of Remote Sensing Data in Watershed Research,” Journal of Soil and Water Conservation, Vol. 50, No. 5, 1995, pp. 438-440.
 T. R. Perkins, T. C. Pagano and D. C. Garen, “Innovative Operational Seasonal Water Supply Forecasting Technologies,” Journal of Soil and Water Conservation, Vol. 64, No. 1, 2009, pp. 15A-17A.
 S. J. Bhuyan, L. J. Marzen, J. K. Koelliker, J. A. Harrington Jr. and P. L. Barnes, “Assessment of Runoff and Sediment Yield Using Remote Sensing, GIS, and AG-NPS,” Journal of Soil and Water Conservation, Vol. 57, No. 6, 2002, pp. 351-363.
 E. R. Hunt Jr., J. H. Everitt, J. C. Ritchie, M. S. Moran, D. T. Booth, G. L. Anderson, P. E. Clark and M. S. Seyfried, “Applications and Research Using Remote Sensing for Rangeland Management,” Photogrammetric Engineering & Remote Sensing, Vol. 69, No. 6, 2003, pp. 675-693.
 J. F. Galantowicz and A. W. England, “Radiobrightness Signatures of Energy Balance Processes: Melt/Freeze Cycles in Snow and Prairie Grass Covered Ground,” IEEE IGARSS, Pasadena, 8-12 August 1994, pp. 596-598.
 A. El-Rabbany, “Introduction to GPS the Global Positioning System,” Artech House, Norwood, 2006.
 S. G. Jin, G. P. Feng and S. Gleason, “Remote Sensing Using GNSS Signals: Current Status and Future Directions,” Advances in Space Research, Vol. 47, No. 10, 2011, pp. 1645-1653. doi:10.1016/j.asr.2011.01.036
 K. M. Larson and F. G. Nievinski, “GPS Snow Sensing: Results from the Earth Scope Plate Boundary Observatory,” GPS Solutions, 2012.
 E. Gutmann, K. M. Larson, M. Williams, F. G. Nievinski and V. Zavorotny, “Snow Measurement by GPS Interferometric Reflectometry: An Evaluation at Niwot Ridge, Colorado,” Hydrologic Processes, 2011.
 M. D. Jacobson, “Inferring Snow Water Equivalent for a Snow-Covered Ground Reflector Using GPS Multipath Signals,” Remote Sensing, Vol. 2, No. 10, 2010, pp. 2426-2441. doi:10.3390/rs2102426
 M. D. Jacobson, “Dielectric-Covered Ground Reflectors in GPS Multipath Reception—Theory and Measurement,” IEEE Xplore—Geoscience and Remote Sensing Letters, Vol. 5, No. 3, 2008, pp. 396-399.
 M. D. Jacobson, “Snow-Covered Lake Ice in GPS Multipath Reception—Theory and Measurement,” Advances in Space Research, Vol. 46, No. 2, 2010, pp. 221-227.
 K. M. Larson, J. Braun, E. E. Small, V. Zavorotny, E. Gutmann and A. Bilich, “GPS Multipath and Its Relation to Near-Surface Soil Moisture Content,” IEEE J-STARS, Vol. 3, 2010, pp. 91-99.
 E. E. Small, K. M. Larson and J. J. Braun, “Sensing Vegetation Growth with Reflected GPS Signals,” Geophysical Research Letters, Vol. 37, 2010, p. L12401.
 V. Zavorotny, K. M. Larson, J. Braun, E. E. Small, E. Gutmann and A. Bilich, “A Physical Model for GPS Multipath Caused by Land Reflections: Toward Bare Soil Moisture Retrievals,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 3, No. 1, 2010, pp. 100-110.
 S. Jin and A. Komjathy, “GNSS Reflectometry and Remote Sensing: New Objectives and Results,” Advances in Space Research, Vol. 46, No. 2, 2010, pp. 111-117.
 S. Gleason and D. Gebre-Egziabher, “GNSS Applications and Methods,” Artech House, Norwood, 2009.
 E. D. Kaplan and C. J. Hegarty, “Understanding GPS Principles and Applications,” Artech House, Norwood, 2006.
 S. T. Lowe, P. Kroger, G. Franklin, J. L. LaBerecque, J. Lerma, M. Lough, M. R. Marcin, R. J. Muellerschoen, D. Spitzmesser and L. E. Young, “A Delay/Doppler-Mapping Receiver System for GPS-Reflection Remote Sensing,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 40, No. 5, 2003, pp. 1150-1163. doi:10.1109/TGRS.2002.1010901
 M. S. Grant, S. T. Acton and S. J. Katzberg, “Terrain Moisture Classification Using GPS Surface-Reflected Signals,” IEEE Xplore—Geoscience and Remote Sensing Letters, Vol. 4, No. 1, 2007, pp. 41-45.
 K. M. Larson, E. E. Small, E. Gutmann, A. Bilich, J. Braun and V. U. Zavorotny, “Use of GPS Receivers as a Soil Moisture Network for Water Cycle Studies,” IEEE Xplore—Geoscience and Remote Sensing Letters, Vol. 35, 2008, p. L24405, doi:10.1029/2008GL036013
 D. Masters, V. U. Zavorotny, S. J.Katzberg and W. Emery, “GPS Signal Scattering from Land for Moisture Content Determination,” Proceedings of IEEE 2000 International Geoscience and Remote Sensing Symposium, Honolulu, 24-28 July 2000, pp. 3090-3092.
 A. Kavak, G. Xu and W. J. Vogel, “GPS Multipath Fade Measurements to Determine L-Band Ground Reflectivity Properties,” Proceedings of the 20th NASA Propagation Experimenters Meeting, Fairbanks, 4-6 June 1996, pp. 257-263.
 A. Kavak, W. J. Vogel and G. Xu, “Using GPS to Measure Ground Complex Permittivity,” Electronics Letters, Vol. 34, No. 3, 1998, pp. 254-255.
 S. J. Katzber, O. Torres, M. S. Grant and D. Masters, “Utilizing Calibrated GPS Reflected Signals to Estimate Soil Reflectivity and Dielectric Constant: Results from SMEX02,” Remote Sensing of Environment, Vol. 100, No. 1, 2006, pp. 17-28. doi:10.1016/j.rse.2005.09.015
 M. B. Rivas, J. A. Maslanik and P. Axelrad, “BistaticScattering of GPS Signals off Arctic Sea Ice,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 3, 2010, pp. 1548-1553.
 D. Cline, S. Yueh, B. Chapman, B. Stankov, A. Gasiewski, D. Masters, K. Elder, R. Kelly, T. H. Painter, S. Miller, S. Katzberg and L. Mahrt, “NASA Cold Land Processes Experiment (CLPX 2002/03): Airborne Remote Sensing,” Journal of Hydrometeorology, Vol. 10, 2009, pp. 338-346. doi:10.1175/2008JHM883.1
 A. Komjathy, J. A. Maslanik, V. U. Zavorotny, P. Axelrad and S. J. Katzberg, “Towards GPS Surface Reflection Remote Sensing of Sea Ice Conditions,” Proceedings of 6th International Conference on Remote Sensing for the Marine and Coastal Environment, Charleston, 1-3 May 2000, pp. 447-456.
 A. Komjathy, J. A. Maslanik, V. U. Zavorotny, P. Axelrad and S. J. Katzberg, “Sea Ice Remote Sensing Using Surface Reflected GPS Signals,” Proceedings of IEEE 2000 International Geoscience and Remote Sensing Symposium, Honolulu, 24-28 July 2000, pp. 2855-2857.
 S. Gleason, S. Lowe and V. Zavorotny, “Remote Sensing Using Bistatic GNSS Reflections in GNSS Applications and Methods,” Artech House, Norwood, 2009.
 S. Gleason, “Towards Sea Ice Remote Sensing with Space Detected GPS Signals: Demonstration of Technical Feasibility and Initial Consistency Check Using Low Resolution Sea Ice Information,” Remote Sensing, Vol. 2, No. 8, 2010, pp. 2017-2039. doi:10.3390/rs2082017
 F. Fabra, E. Cardellach, O. Nogués, S. Oliveras, S. Ribó, A. Rius and M. Belmonte-Rivas, “Sea Ice Remote Sensing with GNSS Reflections,” Instrumentation Viewpoint ISSN 1886-4864, 2009
 M. Wiehl, R. Legresy and R. Dietrich, “Potential of Reflected GNSS Signals for Ice Sheet Remote Sensing,” Progress in Electromagnetics Research, Vol. 40, 2003, pp. 177-205. doi:10.2528/PIER02102202
 D. Herceg, N. Krejic and Z. Luzanin, “Quasi-Newton’s Method with Correction,” Novi Sad Journal of Mathematics, Vol. 26, No. 1, 1996, pp. 115-127.
 W. L. Stutzman, “Polarization in Electromagnetic Systems,” Artech House, Norwood, 1993.
 P. Beckman and A. Spizzichino, “The Scattering of Electromagnetic Waves from Rough Surfaces,” Artech House, Norwood, 1987.
 R. B. Adler, L. J. Chu and R. M. Fano, “Electromagnetic Energy Transmission and Radiation,” Wiley, New York, 1960.
 M. E. Tiuri, A. H. Sihvola, E. G. Nyfors and M. T. Hallikaiken, “The Complex Dielectric Constant of Snow at Microwave Frequencies,” IEEE Journal of Oceanic Engineering, Vol. 9, No. 5, 1984, pp. 377-382.
 ASAE D293.2 JUN1989 (R2005), “Dielectric Properties of Grain and Seed,” American Society of Agricultural and Biological Engineers (ASABE) Standards, 2006, pp. 592-601.
 F. T. Ulaby and M. A. El-Rayes, “Microwave Dielectric Spectrum of Vegetation—Part II: Dual-Dispersion Model,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 25, No. 5, 1987, pp. 550-557.
 F. T. Ulaby, R. K. Moore and A. K. Fung, “Microwave Remote Sensing, Active and Passive, Volume II,” Artech House, Norwood, 1986.
 F. T. Ulaby, R. K. Moore and A. K. Fung, “Microwave Remote Sensing, Active and Passive, Volume III,” Artech House, Norwood, 1986.
 N. R. Peplinski, F. T. Ulaby and M. C. Dobson, “Dielectric Properties of Soils in the 0.3 -1.3-GHz Range,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 3, 1995, pp. 803-807. doi:10.1109/36.387598
 J. M. Martinez, “A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix Factorizations,” SIAM Journal on Numerical Analysis, Vol. 27, No. 4, 1990, pp. 1034-1049.
 V. L. Mironov, R. D. De Roo and I. V. Savin, “Temperature-Dependable Microwave Dielectric Model for an Arctic Soil,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 6, 2010, pp. 2544-2556,
 M. T. Hallikainen, F. T.Ulaby, M. C. Dobson, M. A. El-Rayes and L. K. Wu, “Microwave Dielectric Behavior of Wet Soil—Part I: Empirical Models and Experimental Observations,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 23, No. 1, 1985, pp. 25-34.
 M. C. Dobson, F. T. Ulaby, M. T. Hallikainen and M. A. El-Rayes, “Microwave Dielectric Behavior of Wet Soil— Part II: Dielectric Mixing Models,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 23, No. 1, 1985, pp. 35-46. doi:10.1109/TGRS.1985.289498