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### Jacobson_Mark_1041.pdf

1. 1. Estimating Snow Water Equivalent for aSnow-Covered Ground Reflector using GPS Multipath Signals Dr. Mark Jacobson Mathematics Department 1500 University Drive, Billings, MT 59101 mjacobson@msubillings.edu
2. 2. I. Introduction Proof-of-concept method for estimating snow water equivalent (SWE) at the GPS frequency of 1.5 GHz SWE is the single most important parameter for hydrological studies because it represents the amount of water potentially available for runoff SWE estimations are used for the management of water supply and flood control systems The U.S. D.O.A. operates and manages the Snowpack Telemetry (SNOTEL) system, 730 sites GPS signals could provide a new and economical technique for estimating SWE
3. 3. II. Theory
4. 4. Relative received power at the antenna is rh  rv  exp(i ) 2 4 (h  t ) sin P  1 where,  2 0h = height of antenna above conducting surface, m elevation angle, degreesi  1c  2.997925  108 m/s, the speed of light in a vacuumf  1.57542  109 Hz0  c / f  0.1902937 m, free-space wavelengtht = snow layer thickness, m   snow   s  i s"  s  1  2  d d  relative density of dry snow, g cm−3
5. 5. For a single-layer of snow above a conductingsurface with horizontal polarization, x = h andvertical polarization, x = v iZ x tan  1 sin rx  Zh  iZ x tan  1   cos 2  2 Zv    cos 2  t   cos 2   sin  0
6. 6. III. Measurements and Computation March 31, 2007 T = -1.7 C, t = 7.6 cm, h = 45.1 cm, no snow density data III. Measurements and Computation March 31, 2007 T = -1.7 C, t = 7.6 cm, h = 45.1 cm
7. 7. Equipment Setup for GPS Measurements
8. 8. In order to utilize a Quasi-Newton Algorithm (QNA)efficiently in finding estimates of snow depth and density, weapproximate the relative complex permittivity value of drysnow as snow    i    1  2 d s " s s    " s s = 1 2SE , snow = − , , snow n = 8,168 − 2 =1From 45 input pairs, the smallest SE produced the following: t = 6.8 cm  d  0.30  s  1.60
9. 9. IV. Conclusions Theoretical results and GPS measurements are in good agreement using a nonlinear QNA Estimating SWE may be possible using a nonlinear least squares technique “Inferring Snow Water Equivalent for a Snow-Covered Ground Reflector Using GPS Multipath Signals”, Remote Sensing, Vol. 2, 2426-2441, October 2010
10. 10. V. Future Work Try a QNA for a snow layer above frozen soil Collect more in situ measurements of snow depth, snow density, and frozen soil permittivity Try other nonlinear least-squares algorithms: Levenbeg-Marquardt and Conjugate Gradient Incorporate 2 or more snow layers in the theoretical model
11. 11. V. Future Work (continued) Incorporate the antenna pattern in the theoretical model Incorporate surface roughness of snow and frozen soil in the theoretical model Use a horizontally-mounted (zenith-pointing) GPS antenna Investigate this technique for GPS antennas housed on an aircraft or satellite
12. 12. Acknowledgment Montana State University Billings – Dr. Tasneem Khaleel, Dean CAS – Dr. Maggie McBride, Math Dept. – RACE Grant Ron and Jeanne Jacobson, my parents Wade Dotson, Trimble Navigation C. McFarland and T. McFarland, land owners Anonymous reviewers of paper