On the Edge: Multipath Measures Snow Depth

The September “Innovation” column in this magazine, 
“It’s Not All Bad: Understanding and Using GNSS 
Multipath,” by Andria Bilich and Kristine Larson, mentions the use of multipath in studying soil moisture, ocean altimetry and winds, and snow sensing. An 
experiment the authors conducted, designed to study soil moisture, yielded a surprise bonus: a new methodology for measuring snow depth via GPS multipath. It has important implications for weather and flood forecasting, and could also bring new insight to bear on GPS antenna design.

In the “Innovation” column, the authors wrote, “Motivated by our studies showing that multipath effects could clearly be seen in geodetic-quality data collected with multipath-suppressing antennas, we proposed that these same GPS data could be used to extract a multipath parameter that would correlate with changes in the reflectance of the ground surface. . . .

“We carried out an experiment designed to more rigorously demonstrate the link between GPS signal-to-noise ratio (SNR) and soil moisture. Specifically, we were interested in using GPS reflection parameters to determine the soil’s volumetric water content — the fraction of the total volume of soil occupied by water, an important input to climate and meteorological models. Traditional soil moisture sensors (water content reflectometers) were buried in the ground at multiple depths (2.5 and 7.5 centimeters) at a site just south of the University of Colorado.”

Here Comes the Storm. During the experiment, two late-season snowstorms swept over Boulder. Larson and colleagues discovered that changes in multipath clearly correlated with changes in the snow’s depth, as measured by hand and with ultrasonic sensors at the test site. While it has been long recognized that snow can affect a GPS signal, this demonstrates for the first time that a standard GPS receiver, antenna, and installation — deliberately designed to suppress multipath — can be used to measure snow depth.

On September 11, Geophysical Research Letters, published by the American Geophysical Union, featured an article titled “Can We Measure Snow Depth with GPS Receivers?” by Larson and Felipe Nievinski of the Department of Aerospace Engineering Sciences, University of Colorado; Ethan Gutmann and John Brown of the National Center for Atmospheric Research; Valery Zavorotny of the National Oceanic and Atmospheric Administration; and Mark W. Williams, from UC’s Department of Geography, all based in Boulder.

The authors adapted an algorithm used for modeling GPS multipath from bare soil to predict GPS SNR for snow, introducing a uniform planar layer of the snow on the top of soil. The algorithm treats both direct and surface-reflected waves at two opposite circular polarizations as plane waves that sum up coherently at the antenna. They write:

“The amplitude and the phase of the reflected wave is driven by a polarization-dependent, complex-value reflection coefficient at the upper interface of such a combined medium with a known vertical profile of the dielectric permittivity e. The reflection coefficient is calculated numerically using an iterative algorithm in which the medium is split into sub-layers with a constant e. For the soil part, we use a known soil profile model that depends on the soil type and moisture. For frozen soil, soil moisture (liquid water) is low, as for very dry soil. For the snow part, we take a constant profile with e, considering relatively dry and wet snow layer thicknesses.

“After calculating the complex amplitude of the reflected wave at each polarization, we multiply it by a corresponding complex antenna gain. The same procedure is applied to the complex amplitude of the direct wave. After that, the modulation pattern of the received power, or the SNR, as a function of the GPS satellite elevation angle is obtained by summing up coherently all the signals coming from the antenna output and taking the absolute value square of the sum.”

Figure 1(a) shows GPS SNR measurements for one satellite on the day immediately before and the day immediately after an overnight snowfall of 35 centimeters (roughly 10 inches). Figure  1(b) shows the corresponding model predictions for multipath. The two figure 
portions amply demonstrate that the multipath has a significantly lower frequency if snow is present as compared with bare soil. The authors further noted that the model amplitudes do not show as pronounced a dependence on satellite elevation angle as the observations, and state the necessity of further work on antenna gains in order to use model amplitude predictions.

Figure 1. (a) GPS SNR measurements for PRN 7 observed at Marshall GPS site on days 107 (red) and 108 (black) after direct signal component has been removed. Approximately 35 centimeters of snow had fallen by day 108. (b) Model predictions for GPS multipath from day 107 with no snow on the ground (red), and day 108 after 35 centimeters of new snow fall had accumulated (black) using an assumed density of 240 kg m-3 (figures reproduced by permission of American Geophysical Union).

How Deep the Snow. The authors propose that the hundreds of geodetic GPS receivers operating in snowy regions of the United States, originally installed for plate deformation studies, surveying, and weather monitoring, could also provide a cost-effective means to estimate snow depth.

Currently, a few conventional monitor points measure snow depth, but only at that point, and the data does not extrapolate well. Snow forms an important component of the climate system and a critical storage component in the hydrologic cycle. Accurate data of the amount of water stored in the snowpack is critical for water supply management and flood control systems. As more snow falls at higher elevations, varying greatly even within one valley or watershed, current remote-sensing snow monitors do not supply adequate data. Further, snow may be redistributed by wind, avalanches, and non-uniform melting, so that continuous data would be very helpful.

Using GPS multipath to map snow depth could improve watershed analyses and flood prediction — and, carried steps further, produce data to help better understand multipath, bringing innovation to future antenna designs.

FIGURE 2. Snow depth derived from GPS (red squares), the three ultrasonic snow depth sensors (blue lines), and field measurements (black diamonds). Bars on field observations are one standard deviation. GPS snow-depth estimates during the first storm (doy 85.5–86.5) are not shown (gray region) because the SNR data indicate that snow was on top of the antenna.

Kristine Larson was featured as one of the “50 GNSS Leaders to Watch” in the May 2009 issue of GPS World.

Manufacturer

For the experiment a Trimble NetRS receiver was used with a TRM29659.00 choke-ring antenna with SCIT radome, pointed at zenith.