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Using GPS Multipath for Snow-Depth Estimation By Felipe G. Nievinski and Kristine M. Larson INNOVATION INSIGHTS by Richard Langley FRINGES. No, I’m not talking about the latest celebrity hairstyles nor the canopy of an American doorless, four-wheeled carriage from yesteryear (think Oklahoma!). I’m talking about interference fringes. But there is a connection to these other uses of the word fringe as we’ll see. You’ve all seen interference fringes at your local gas station, typically after it has just rained. They are the alternating bands of color we perceive when looking at a gasoline or oil slick in a puddle of water. They are caused by the white light from the Sun or artificial lighting reflected from the top surface of the slick and that from the bottom surface at the slick-water interface combining or interfering with each other at our eyeballs. The two sets of light waves arrive slightly out of phase with each other, and depending on the wavelengths of the reflected light and our angle of view, produce the colorful fringes. If the incident light was monochromatic, consisting of a single frequency or wavelength, then we would perceive just alternating bright and dark bands. The bright bands result from constructive interference when the phase difference is a near a multiple of 2π whereas the dark bands result from destructive interference when the difference is near an odd multiple of π. Interference fringes had been seen long before the invention of the automobile. They are clearly seen on soap bubbles and the iridescent colors of peacock feathers, Morpho butterflies, and jewel beetles are also due to the interference phenomenon rather than pigmentation. Sir Isaac Newton did experiments on interference fringes (amongst other things) and tried to explain their existence — wrongly, it turned out. But he did coin the term fringes since they resembled the decorative fringe sometimes used on clothing, drapery, and, yes, surrey canopies. It was the English polymath, Thomas Young, who, in 1801, first demonstrated interference as a consequence of the wave-nature of light with his famous double-slit experiment. You may have replicated his experiment in a high-school physics class. I did and I think I did it again as an undergraduate student taking a course in optics. Already by that point I was aiming for a career in physics or space science but I didn’t know that as a graduate student I would do research involving interference fringes. But not using light waves. My research involved the application of very long baseline interferometry or VLBI to geodesy. VLBI had been developed by radio astronomers to better understand the structure of quasars and other esoteric celestial objects. At either ends of a baseline connecting large radio telescopes, perhaps stretching between continents, the quasar signals were recorded on magnetic tape and precisely registered using atomic clocks. When the tapes were played back and the signals aligned, one obtained interference fringes as peaks and troughs in an analog or digital waveform. Computer analysis of these fringes not only provided information on the structure of the observed radio source but also on the distance between the radio telescopes — eventually accurate enough to measure continental drift.  But what has all of this got to do with GPS? In this month’s column, we look at a technique that uses fringes generated by signals arriving at an antenna directly from GPS satellites and those reflected by snow surrounding the antenna to measure its depth and how it varies over time. GPS for measuring snow depth; who would have thought? “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Snowpacks are a vital resource for human existence on our planet. They provide reservoirs of fresh water, storing solid precipitation and delaying runoff. One sixth of the world population depends on this resource. Both scientists and water-supply managers need to know how much fresh water is stored in snowpack and how fast it is being released as a result of melting. Snow monitoring from space is currently under investigation by both NASA and ESA. Greatly complementary to such spaceborne sensors are automated ground-based methods; the latter not only serve as essential independent validation and calibration for the former, but are also valuable for climate studies and flood/drought monitoring on their own. It is desirable for such estimates to be provided at an intermediary scale, between point-like in situ samples and wider area pixels. In the last decade, GPS multipath reflectometry (GPS-MR), also known as GPS interferometric reflectometry and GPS interference-pattern technique, has been proposed for monitoring snow. This method tracks direct GPS signals, those that travel directly to an antenna, that have interfered with a coherently reflected signal, turning the GPS unit into an interferometer (see FIGURE 1). Its main variant is based on signal-to-noise ratio (SNR) measurements, although GPS-MR is also possible with carrier-phase and pseudorange observables. Data are collected at existing GPS base stations that employ commercial-off-the-shelf receivers and antennas in a conventional, antenna-upright setup. Other researchers have used a custom antenna and/or a dedicated setup, with the antenna tipped for enhanced multipath reception. FIGURE 1. Standard geodetic receiver installation. The antenna is protected by a hemispherical radome. The monument (tripod structure) is ~ 2 meters above the ground. GPS satellites rise and set in ascending and descending sky tracks, multiple times per day. The specular reflection point migrates radially away from the receiver for decreasing satellite elevation angle. The total reflector height is made up of an a priori value and an unknown bias driven by the thickness of the snow layer. In this article, we summarize the SNR-based GPS-MR technique as applied to snow sensing using geodetic instruments. This forward/inverse approach for GPS-MR is new in that it capitalizes on known information about the antenna response and the physics of surface scattering to aid in retrieving the unknown snow conditions in the site surroundings. It is a statistically rigorous retrieval algorithm, agreeing to first order with the simpler original methodology, which is retained here for the inversion bootstrapping. The first part of the article describes the retrieval algorithm, while the second part provides validation at a representative site over an extended period of time.  Physical Forward Model SNR observations are formulated as SNR = Ps/Pn. In the denominator, we have the noise power, Pn, here taken as a constant, based on nominal values for the noise power spectral density and the noise bandwidth. The numerator is composite signal power: .   (1) Its incoherent component is the sum of the respective direct and reflected powers (although direct incoherent power is negligible). In contrast, the coherent composite signal power follows from the complex sum of direct and reflection average voltages (not to be confused with the electromagnetic propagating fields, which neglect the receiving antenna response and also the receiver tracking process): (2) It is expressed in terms of the coherent direct and reflected powers, as well as the interferometric phase,  , (3) which amounts to the reflection excess phase with respect to the direct signal. We decompose observations, SNR = tSNR + dSNR, into a trend   (4) over which interference fringes are superimposed: . (5)  From now on, we neglect the incoherent power, which only impacts tSNR, not dSNR, and drop the coherent power superscript, for brevity. The direct or line-of-sight power is formulated as   (6) where    is the direction-dependent right-hand circularly polarized (RHCP) power component incident on an isotropic antenna; the left-handed circularly polarized (LHCP) component is negligible. The direct antenna gain, , is obtained evaluating the antenna pattern in the satellite direction and with RHCP polarization. The reflection power, , (7) is defined starting with the same incident isotropic power, , as in the direct power. It ends with a coherent power attenuation factor,    (8) where  θ  is the angle of incidence (with respect to the surface normal), k = 2π/λ, is the wave number, and λ = 24.4 centimeters is the carrier wavelength for the civilian GPS signal on the L2 frequency (L2C). This polarization-independent factor accounts only for small-scale residual height above and below a large-scale trend surface. The former/latter results from high-/low-pass filtering the actual surface heights using the first Fresnel zone as a convolution kernel, roughly speaking. Small-scale roughness is parameterized in terms of an effective surface standard deviation s (in meters); its scattering response is modeled based on the theories of random surfaces, except that the theoretical ensemble average is replaced by a sensing spatial average. Large-scale deterministic undulations could be modeled, but their impact on snow depth is canceled to first-order by removing bare-ground reflector heights. At the core of , we have coupled surface/antenna reflection coefficients,  , producing respectively RHCP and LHCP fields (under the assumption of a RHCP incident field). These terms include antenna response power gain and phase patterns, evaluated in the reflection direction, and separately for each polarization. The surface response is represented by complex-valued Fresnel coefficients for cross- and same-sense circular polarization, respectively. The medium is assumed to be homogeneous (that is, a semi-infinite half-space). Material models provide the complex permittivity, which drives the Fresnel coefficients. The interferometric phase reads: .(9) The first term accounts for the surface and antenna properties of the reflection, as above. The last one is the direct phase contribution, which amounts to only the RHCP antenna phase-center variation evaluated in the satellite direction. The majority of the components present in the direct RHCP phase (such as receiver and satellite clock states, the bulk of atmospheric propagation delays, and so on) are also present in the reflection phase, so they cancel out in forming the difference. At the core of the interferometric phase, we have the geometric component, φI = kτi, the product of the wave number and the interferometric propagation delay. Assuming a locally horizontal surface, the latter is simply:   (10) in terms of the satellite elevation angle, e, and an a priori reflector height, HA. Snow depth will be measured in terms of changes in reflector height. The physical forward model, based only on a priori information, can then be summarized as:   (11) where interferometric power and phase are, respectively:   (12) . (13) In all of these terms the pseudorandom-noise-code modulation impressed on the carrier wave can be safely neglected, given the small interferometric delay and Doppler shift at grazing incidence, stationary surface/receiver conditions, and short antenna installations. Parameterization of Unknowns There are errors in the nominal values assumed for the physical parameters of the model (permittivity, surface roughness, reflector height, and so on). Ideally we would estimate separate corrections for each one, but unfortunately many are linearly dependent or nearly so. Because of this dependency, we have kept physical parameters fixed to their optimal a priori values, and have estimated a few biases. Each bias is an amalgamation of corrections for different physical effects. In a later stage, we rely on multiple independent bias estimates (such as for successive days) to try and separate the physical sources. Each satellite track is inverted independently. A track is defined by partitioning the data by individual satellite and then into ascending and descending portions, splitting the period between the satellite’s rise and set at the near-zenith culmination. Each satellite track has a duration of ~1–2 hours. This configuration normally offers a sufficient range of elevation angles, unless the satellite reaches culmination too low in the sky (less than about 20°), in which case the track is discarded. In seeking a balance between under- and over-fitting, between an insufficient and an excessive number of parameters, we estimate the following vector of unknown parameters: . (14) FIGURE 2 shows the effect of the constant and linear biases on the SNR observations. Reflector height bias, HB , changes the number of oscillations; phase shift, φB , displaces the oscillations along the horizontal axis; reflection power,    , affects the depth of fades; zeroth-order noise power,     , shifts the observations up or down as a whole; and first-order noise power,    , tilts the SNR curve. A good parameterization yields observation sensitivity curves as unique as possible for each parameter. FIGURE 2. Effect of each parameter on SNR observations; curves are displaced vertically (6 dB) for clarity. The forward model, now including the biases, can be summarized as follows:  (15) where the modified interferometric power and phase are given by: , (16) . (17) The total reflector height, H = HA – HB (a priori value minus unknown bias), is to be interpreted as an effective value that best fits measurements, which includes snow and other components. Bootstrapping Parameter Priors. Biases and SNR observations are involved non-linearly through the forward model. Therefore, there is the need for a preliminary global optimization, without which the subsequent final local optimization will not necessarily converge to the optimal solution. SNR observations would trace out a perfect sinusoid curve in the case of an antenna with isotropic gain and spherical phase pattern, surrounded by a smooth, horizontal, and infinite surface (free of small-scale roughness, large-scale undulations, and edges), made of perfectly electrically conducting material, and illuminated by constant incident power. Thus, in such an idealized case, SNR could be described exactly by constant reflector height, phase shift, amplitude, and mean values. As the measurement conditions become more complicated, the SNR data start to deviate from a pure sinusoid. Yet a polynomial/spectral decomposition is often adequate for bootstrapping purposes.  Statistical Inverse Model Formulation Based on the preliminary values for the unknown parameters vector and other known (or assumed) values, we run the forward model to obtain simulated observations. We form pre-fit residuals comparing the model values to SNR measurements collected at varying satellite elevation angles (separately for each track). Residuals serve to retrieve parameter corrections, such that the sum of squared post-fit residuals is minimized. This non-linear least squares problem is solved iteratively using both a functional model and a stochastic model. The functional modeling includes a Jacobian matrix of partial derivatives, which represents the sensitivity of observations to parameter changes where the partial derivatives are defined element-wise. Instead of deriving analytical expressions, we evaluate them numerically, via finite differencing. The stochastic model specifies the uncertainty and correlation expected in the residuals. Their a priori covariance matrix modifies the objective function being minimized.  Directional Dependence It is important to know at which elevation angles the parameter estimates are best determined. Here, we focus on the phase parameters instead of reflection power or noise power parameters.  We can utilize the estimated reflector height and phase shift to evaluate the full phase bias function over varying elevation angles. Similarly, we can extract the corresponding 2-by-2 portion of the parameters’ a posteriori covariance matrix, containing the uncertainty for reflector height and for phase shift, as well as their correlation, which is then propagated to obtain the full phase uncertainty (see FIGURE 3). FIGURE 3. Uncertainty of full phase function, propagated from the uncertainty of reflector height and of phase shift, as well as their correlation. The uncertainty attains a clear minimum versus elevation angle. The least-uncertainty elevation angle pinpoints the observation direction where reflector height and phase shift are best determined (in combined form, not individually). The azimuth and epoch coinciding with the peak elevation angle act as track tags, later used for clustering similar tracks and analyzing their time series of retrievals. If we normalize phase uncertainty by its value at the peak elevation angle, then plot such sensing weights (between 0 and 1) versus the radial or horizontal distance to the center of the first Fresnel zone at each elevation angle, we obtain FIGURE 4. It can be interpreted as the reflection footprint, indicating the importance of varying distances, with a longer far tail and a shorter near tail (respectively regions beyond and closer than the peak distance). The implications for in situ data collection are clear: one should sample more intensely near the peak distance (about 15 meters) and less so in the immediate vicinity of the GPS antenna, tapering it off gradually away from the antenna. As a caveat, these conclusions are not necessarily valid for antenna setups other than the one considered here. FIGURE 4. Reflection footprint in terms of a sensing weight (between 0 and 1) defined as the normalized reciprocal of full phase uncertainty, plotted versus the radial or horizontal distance from the receiving antenna to the center of the first Fresnel zone at each elevation angle; valid for an upright 2-meter-tall antenna; the receiving antenna is at zero radial distance. Results We now examine the snow-depth retrievals from the GPS multipath retrieval algorithm and assess both the precision and accuracy of the method. Multiple metrics have been developed to assess the quality of the results. The accuracy of the method has been evaluated by comparing with in situ data over a multi-year period. Three field sites were chosen to highlight different limitations in the method, both in terms of terrain and forest cover: grassland, alpine, and forested. We will look at the forested site in some detail. Satellite Coverage and Track Clustering. All GPS-MR retrievals reported here are based on the newer GPS L2C signal. Of the approximately 30 GPS satellites in service, 8-10 L2C satellites were available between 2009 and 2012 (8, 9, and 10 satellites at the end of 2009, 2010, and 2011, respectively). Satellite observations were partitioned into ascending and descending portions, yielding approximately twenty unique tracks per day at a site with good sky visibility. GPS orbits are highly repeatable in azimuth, with deviations at the few-degree range over a year, translating into ~50-100-centimeter azimuthal displacement of the reflecting area (corresponding to the first Fresnel zone at 10°-15° elevation angle for a 2-meter high antenna). This repeatability permits clustering daily retrievals by azimuth. It also allows the simplification that estimated snow-free reflector heights are fairly consistent from day to day, facilitating the isolation of the varying snow depth during the snow-covered period. For a given track, its revisit time is also repeatable, amounting to practically one sidereal day. The deficit in time relative to a calendar day results in the track time of the day receding ~4 minutes and 6 seconds every day. This slow but steady accumulation eventually makes the time of day return to its starting value after about one year. As all GPS satellites drift approximately at the same rate, the time between successive tracks remains nearly repeatable. Its reciprocal, the sampling rate, has a median equal to approximately one track per hour, with a low value of one track within two hours and a high of one track within 15 minutes; both extremes occur every day, with low-rate idle periods interspersed with high-rate bursts. The time of the day reduced to a fixed day (such as January 1, 2000) could also be used to cluster tracks. Neighboring clusters, which are close in azimuth and/or in reduced time of the day, are expected to be more comparable, as they sample similar conditions and are subject to similar errors. Observations. FIGURE 5 shows several representative examples of SNR observations. A typical good fit between measured and modeled values is shown in Figure 5(a), corresponding to the beginning of the snow season. Generally the model/measurement fit is good when the scattering medium is homogeneous; it deteriorates as the medium becomes more heterogeneous, particularly with mixtures of soil, snow, and vegetation. There are genuine physical effects as well as more mundane spurious instrumental issues that degrade the fit but do not necessarily cause a bias in snow-depth estimates. These include secondary reflections, interferometric power effects, direct power effects, and instrument-related issues. FIGURE 5. Examples of observations: (a) good fit; (b) presence of secondary reflections; (c) vanishing interference fringes; (d) atypical interference fringes. Secondary reflections originate from disjoint surface regions. Interference fringes become convoluted with multiple superimposed beats (see Figure 5(b)). As long as there is a unique dominating reflection, the inversion will have no difficulty fitting it, as the extra reflections will remain approximately zero-mean. Random deviations of the actual surface with respect to its undulated approximation, called roughness or residual surface height, will affect the interferometric power. SNR measurements will exhibit a diminishing number of significant interference fringes, compared to the measurement noise level (see Figure 5(c)). This facilitates the model fit but the reflector height parameter may become ill-determined: its estimates will be more uncertain. Changes in snow density also affect the fringe amplitude. Snow precipitation attenuates the satellite-to-ground radio link, which affects SNR measurements through the direct power term. First, this shifts the SNR measurements up or down (in decibels); second, it tilts the trend tSNR as attenuation is elevation-angle dependent; third, fringes in dSNR will change in amplitude because of the decrease in the coherent component of the direct power. Partial obstructions can affect either or both direct and interferometric powers. In this case, SNR measurements, albeit corrupted, are still recorded. This situation is in contrast to complete blockages as caused by topography. The deposition of snow and the formation of a winter rime on the antenna are a particularly insidious type of obstruction, as their presence in the near-field of the antenna element can easily distort the gain pattern in a significant manner. In the far-field, trees are another important nuisance, so much so that their absence is held as a strong requirement for the proper functioning of multipath reflectometry. Satellite-specific direct power offsets and also long-term power drifts are to be expected as spacecraft age and modernized designs are launched. In addition, noise power depends on the state of conservation of receiver cables and on their physical temperature. Less subtle incidents are sudden ~3-dB SNR steps, hypothesized to originate in the receiver switching between the L2C data and pilot subcodes, CM and CL. Quality Control. Anomalous conditions may result in measurement spikes, jumps, and short-lived rapidly-varying fluctuations. For snow-depth-sensing purposes, it is necessary and sufficient to either neutralize such measurement outliers through a statistically robust fit or detect unreliable fits and discard the problematic ones that could not otherwise be salvaged. The key to quality control (QC) is in grouping results into statistically homogeneous units, having measurements collected under comparable conditions. In our case, azimuth-clustered tracks are the natural starting unit. Secondarily, we must account for genuine temporal variations in the tendency of results, from beginning to peak to the end of the snow season. The detection of anomalous results further requires an estimate of the statistical dispersion to be expected. Considering that the sample is contaminated with outliers, robust estimators (running median instead of the running mean, and median absolute deviation over the standard deviation) are called for, if the first- and second-order statistical moments are to be representative. Given estimates of the non-stationary tendency and dispersion, a tolerance interval can then be constructed such that it bounds, say, a 99% proportion of the valid results with 95% confidence level. We also desire QC to be judicious, or else too many valid estimates will be lost. Notice that in the present intra-cluster QC, we compare an individual estimate to the expected performance of the track cluster to which it belongs; later, we complement QC with an inter-cluster comparison of each cluster’s own expected performance. Based on our practical experience, no single statistic detects all the outliers. We use four particular statistics that we have found to be useful: 1) degrees of freedom, essentially the number of observations per track (modulo a constant number of parameters); 2) using the scaled root-mean-square error (RMSE) to test for goodness-of-fit, that is, how well measurements can be explained adjusting the unknown values for the parameters postulated in the model; 3) reflector height uncertainty; and 4) peak elevation angle, which behaves much like a random variable, as it is determined by a multitude of factors.  Combinations. We combine multiple clusters to average out random noise. Noise mitigation aims at not only coping with measurement errors but also compensating for model deficiencies, to the extent that they are not in common across different clusters. Before we combine different clusters, we have to address their long-term differences. The initial situation is that snow surface heights will be greater downhill and smaller uphill; we take this into account on a cluster-by-cluster basis by subtracting ground heights from their respective snow surface heights, resulting in snow thickness values, which is a completely physically unambiguous quantity. Snow thickness is more comparable than snow heights across varying-azimuth track clusters. Yet snow tends to fill in ground depressions, so thickness exhibits variability caused by the underlying ground surface, even when the overlying snow surface is relatively uniform. Further cluster homogeneity can be achieved by accounting for the temporally permanent though spatially non-uniform component of snow thickness.  The averaging of snow depths collected for different track clusters employs the inversion uncertainties to obtain a preliminary running weighted median, calculated for, say, daily postings, with overlapping windows or not. The preliminary post-fit residuals then go through their own averaging, necessarily employing a wider averaging window (say, monthly), which produces scaling factors for the original uncertainties. The running weighted median is then repeated, producing final averages. The variance factors reflect the fact that some clusters are better than others. Thus, the final GPS estimates of snow depth follow from an averaging of all available tracks, whose individual snow depth values were previously estimated independently. A new average is produced twice daily utilizing the surrounding 1–2 days of data (depending on the data density), that is, 12-hour posting spacing and 24-hour moving window width. The averaging interval must be an integer number of days, so as to minimize the possibility of snow-depth artifacts caused by variations in the observation geometry, which repeats daily. Site-Specific Results We explored GPS-MR snow-depth retrieval at three stations over a long period (up to three years). Throughout, we assessed the performance of the GPS estimates against independent nearly co-located in situ measurements. We also compared the GPS estimates to the nearest SNOTEL station. SNOTEL (from snowpack telemetry) is an automated system for collecting snowpack and related data in the western U.S. operated by the U.S. Department of Agriculture. Although not co-located with GPS, SNOTEL data are important because they provide accurate information on the timing of snowfall events. The three sites we used were 1) a site in the T.W. Daniel Experimental Forest within the Wasatch Cache National Forest in the Bear River Range of northeastern Utah, with an elevation of 2,600 meters; 2) one of the stations of the EarthScope Plate Boundary Observatory, a grassland site located near Island Park, Idaho; and 3) an alpine site in the Niwot Ridge Long-term Ecological Research Site near Boulder, Colorado. While we have fully documented the results from each site, due to space limitations we will only discuss the results from the forested site (known as RN86) in this article. This is a more challenging site than the other two, due to the presence of nearby trees. Furthermore, it was subject to denser in situ sampling of 20-150 measurements spatially replicated around the GPS antenna, and repeated approximately every other week for about one year. We show results for the 2012 water-year, the period starting October 1 through September 30 of the following year. Where GPS site RN86 was installed, topographical slopes range from 2.5° to 6.5° (at the 2-meter spatial scale), with average of ~5° within a 50-meter radius around the GPS antenna. RN86 was specifically built to study the impact of trees on GPS snow depth retrievals (see FIGURE 6). Ground crews manually collected in situ measurements around the GPS antenna approximately every other week starting in November 2011. Measurements were made every 1–2 meters from the antenna up to a distance of 25-30 meters. In the second half of the year, the sampling protocol was changed to azimuths of 0° (N), 45° (NE), 135° (SE), 180° (S), 225° (SW), and 315° (NW). With these data it is possible to obtain in situ average estimates, with their own uncertainties (based on the number of measurements), which allows a more meaningful comparison. FIGURE 6. Aerial view of the forested site (RN86) around the GPS antenna (marked with a circle). There is reduced visibility at the current site, compared to other sites. Track clusters are concentrated due south, with only two clusters located within ±90° of north. Therefore, the GPS average snow depth is not necessarily representative of the azimuthally symmetric component of the snow depth. In the presence of an azimuthal asymmetry in the snow distribution around the antenna, the GPS average would be expected to be biased towards the environmental conditions prevalent in the southern quadrant. To rule out the possibility of an azimuthal artifact in the comparisons, we have utilized only the in situ data collected along the SE/S/SW quadrant. The comparison shows generally excellent agreement between GPS and in situ data (see FIGURE 7). The first four and the last one in situ data points were collected with coarser spacing and/or smaller azimuthal coverage, which may be partially responsible for different performance in the first and second halves of the snow season. The correlation between GPS and in situ snow depth at RN86 amounts to 0.990, indicating a very strong linear relationship. Carrying out a regression between in situ and GPS values, the RMS of snow-depth residuals improves from 9.6 to 3.4 centimeters. The regression intercept and slope (with corresponding 95% uncertainties) amount to 15.4 ± 9.11 centimeters and 0.858 ± 0.09 meters per meter, respectively. According to these statistics, the null hypotheses of zero intercept and unity slope are rejected at the 95% confidence level. This implies that at this location GPS snow-depth estimates exhibit both additive and multiplicative biases. The latter is proportional to snow depth itself, meaning that, compared to an ideal one-to-one relationship, GPS is found to under-estimate in situ snow depth at this site by 14 ± 9%, although the uncertainty is somewhat large. FIGURE 7. Snow-depth measurement at the forested site (RN86) for the water-year 2012 The SNOTEL sensors are exceptionally close to the GPS antenna at this site, about 350 meters horizontally distant with negligible vertical separation. Yet the former is located within trees, while the latter is located at the periphery of the forest and senses the reflections scattered from an open field. Therefore, only the timing of snowfall events agrees well, not the amount of snow. Although forest density is generally negatively correlated with snow depth, exceptions are not uncommon, especially in localized clearings exposed to intense solar radiation, where shading of the snow by the trees reduces ablation. Conclusions In this article, we have discussed a physically based forward model and a statistical inverse model for estimating snow depth based on GPS multipath observed in SNR measurements. We assessed model performance against independent in situ measurements and found they validated the GPS estimates to within the limitations of both GPS and in situ measurement errors after the characterization of systematic errors. The assessment yielded a correlation of 0.98 and an RMS error of 6–8 centimeters for observed snow depths of up to 2.5 meters at three sites, with the GPS underestimating in situ snow depth by ~5–15%. This latter finding highlights the necessity to assess effects currently neglected or requiring more precise modeling. Acknowledgments The research reported in this article was supported by grants from the U.S. National Science Foundation, NASA, and the University of Colorado. Nievinski has been supported by a Capes/Fulbright Graduate Student Fellowship and a NASA Earth System Science Research Fellowship. The article is based, in part, on two papers published in the IEEE Transactions on Geoscience and Remote Sensing: “Inverse Modeling of GPS Multipath for Snow Depth Estimation – Part I: Formulation and Simulations” and “Inverse Modeling of GPS Multipath for Snow Depth Estimation – Part II: Application and Validation.” Manufacturers For the forested site (RN86), a Trimble NetR9 receiver was used with a Trimble TRM57971.00 (Zephyr Geodetic II) antenna with no external radome. FELIPE G. NIEVINSKI is a faculty member at the Federal University of Santa Catarina, Florianópolis, Brazil. He has also been a post-doctoral researcher at São Paulo State University, Presidente Prudente, Brazil. He earned a B.E. in geomatics from the Federal University of Rio Grande do Sul, Porto Alegre, Brazil, in 2005; an M.Sc.E. in geodesy from the University of New Brunswick, Fredericton, Canada, in 2009; and a Ph.D. in aerospace engineering sciences from the University of Colorado, Boulder, in 2013. His Ph.D. dissertation was awarded The Institute of Navigation Bradford W. Parkinson Award in 2013. KRISTINE M. LARSON received a B.A. degree in engineering sciences from Harvard University and a Ph.D. degree in geophysics from the Scripps Institution of Oceanography, University of California at San Diego. She was a member of the technical staff at the Jet Propulsion Lab from 1988 to 1990. Since 1990, she has been a professor in the Department of Aerospace Engineering Sciences, University of Colorado, Boulder. FURTHER READING • Authors’ Journal Papers “Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part I: Formulation and Simulations” by F.G. Nievinski and K.M. Larson in IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 10, 2014, pp. 6555–6563, doi: 10.1109/TGRS.2013.2297681. “Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part II: Application and Validation” by F.G. Nievinski and K.M. Larson in IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 10, 2014, pp. 6564–6573, doi: 10.1109/TGRS.2013.2297688. • More on the Use of GPS for Snow Depth Assessment “Snow Depth, Density, and SWE Estimates Derived from GPS Reflection Data: Validation in the Western U.S.” by J.L. McCreight, E.E. Small, and K.M. Larson in Water Resources Research, published first on line, August 25, 2014, doi: 10.1002/2014WR015561. “Environmental Sensing: A Revolution in GNSS Applications” by K.M. Larson, E.E. Small, J.J. Braun, and V.U. Zavorotny in Inside GNSS, Vol. 9, No. 4, July/August 2014, pp. 36–46. “Snow Depth Sensing Using the GPS L2C Signal with a Dipole Antenna” by Q. Chen, D. Won, and D.M. Akos in EURASIP Journal on Advances in Signal Processing, Special Issue on GNSS Remote Sensing, Vol. 2014, Article No. 106, 2014, doi: 10.1186/1687-6180-2014-106. “GPS Snow Sensing: Results from the EarthScope Plate Boundary Observatory” by K.M. Larson and F.G. Nievinski in GPS Solutions, Vol. 17, No. 1, 2013, pp. 41–52, doi: 10.1007/s10291-012-0259-7. • GPS Multipath Modeling and Simulation “Forward Modeling of GPS Multipath for Near-Surface Reflectometry and Positioning Applications” by F.G. Nievinski and K.M. Larson in GPS Solutions, Vol. 18, No. 2, 2014, pp. 309–322, doi: 10.1007/s10291-013-0331-y. “An Open Source GPS Multipath Simulator in Matlab/Octave” by F.G. Nievinski and K.M. Larson in GPS Solutions, Vol. 18, No. 3, 2014, pp. 473–481, doi: 10.1007/s10291-014-0370-z. “Multipath Minimization Method: Mitigation Through Adaptive Filtering for Machine Automation Applications” by L. Serrano, D. Kim, and R.B. Langley in GPS World, Vol. 22, No. 7, July 2011, pp. 42–48. “It’s Not All Bad: Understanding and Using GNSS Multipath” by A. Bilich and K.M. Larson in GPS World, Vol. 20, No. 10, October 2009, pp. 31–39. “GPS Signal Multipath: A Software Simulator” by S.H. Byun, G.A. Hajj, and L.W. Young in GPS World, Vol. 13, No. 7, July 2002, pp. 40–49.

wireless signal jammer app

71109-r ac adapter 24v dc 350ma power supply tv converter used.archer 273-1455 ac adapter used 9vdc 300ma -(+) 2x5.5x10mm,pentax battery charger d-bc7 for optio 555's pentax d-li7 lithiu.long range jammer free devices,ault p41120400a010g ac adapter 12v dc 400ma used 2.5 x 5.4 9.6mm.dv-2412a ac adapter 24vac 1.2a ~(~) 2x5.5mm 120vac used power su,galaxy sed-power-1a ac adapter 12vdc 1a used -(+) 2x5.5mm 35w ch.fujitsu fpcbc06 ac adapter 16v dc 35w used 2.5 x 5.4 x 12.1 mm t,apple powerbook m1893 ac adapter 16vdc 1.5a 16v 1a used 4 pin di.this covers the covers the gsm and dcs.smart charger h02400015-us-1 ac adapter battery pack charger.4089 ac adapter 4.9vac 300ma used c-1261 battery charger power s,acbel api4ad19 ac adapter 15vdc 5a laptop power supply,different versions of this system are available according to the customer’s requirements,the light intensity of the room is measured by the ldr sensor,sony ac-l25b ac adapter 8.4vdc 1.7a 3 pin connector charger swit,black and decker etpca-180021u2 ac adapter 26vdc 210ma class 2.asus ex0904yh ac adapter 19v dc 4.74aa -(+)- 2.5x5.5mm 100-240vd,this paper shows the controlling of electrical devices from an android phone using an app.mobile jammerseminarsubmitted in partial fulfillment of the requirementsfor the degree ofbachelor of technology in information …,the jammer covers all frequencies used by mobile phones,dve dsa-0151d-09.5 ac adapter 9.5vdc 1.8a used 2.5x5.5mm -(+) 10,toshiba pa3048u-1aca ac adapter 15vdc 4a used -(+) 3x6.5mm round,delta adp-62ab ac adapter 3.5vdc 8a 12.2v 3a used 7pin 13mm din.premium power pa3083u-1aca ac adapter 15v dc 5a power supply,10 and set the subnet mask 255,vtech du35090030c ac adapter 9vdc 300ma 6w class 2 transformer p.compaq adp-60bb ac adapter 19vdc 3.16a used 2.5x5.5mm -(+)- 100-,ault 5305-712-413a09 ac adapter 12v 5vdc 0.13a 0.5a power supply.tpi tsa1-050120wa5 ac dc adapter 5v 1.2a charger class 2 power s,delta adp-43ab rev a ac adapter 16.8v dc 2.6a used 3x6.2x10mm 90,frequency band with 40 watts max.apple m5849 ac adapter 28vdc 8.125a 4pin 10mm 120vac used 205w p.ibm 02k6808 ac adapter 16vdc 3.5a used 2.6x5.5x11mm straight,sony bc-csgc 4.2vdc 0.25a battery charger used c-2319-445-1 26-5,when the mobile jammers are turned off.symbol b100 ac adapter 9vdc 2a pos bar code scanner power supply.sony ac-12v1 ac dc adapter 12v 2a laptop power supply,320 x 680 x 320 mmbroadband jamming system 10 mhz to 1,yhi 001-242000-tf ac adapter 24vdc 2a new without package -(+)-.dp48d-2000500u ac adapter 20vdc 500ma used -(+)class 2 power s.hp ac adapter c6320-61605 6v 2a photosmart digital camera 315.chd-hy1004 ac adapter 12v 2a 5v 2a used multiple connectors,components required555 timer icresistors – 220Ω x 2,safe & warm 120-16vd7p c-d7 used power supply controller 16vdc 3.sony ericsson cst-18 ac adapter 5vdc 350ma cellphone charger,griffin itrip car adapter used fm transmitter portable mp3 playe.liteon pa-1900-08hn ac adapter 19vdc 4.74a 90w used,power grid control through pc scada,nextar sp1202500-w01 ac adapter 12vdc 2.5a used -(+)- 4.5 x 6 x.black&decker versapak vp131 4.3v battery charger for versapak ba.nokia ac-15x ac adapter cell phone charger 5.0v 800ma europe 8gb.blackberry rim psm05r-050q 5v 0.5a ac adapter 100 - 240vac ~ 0.1.braun 5 496 ac adapter dc 12v 0.4a class 2 power supply charger.finecom la-520w ac adapter 5vdc 2a -(+) 0.8x2.5mm new charger ho.ridgid r86049 12vdc battery charger for drill impact driver cord,fairway wna10a-060 ac adapter +6v 1.66a - ---c--- + used2 x 4,shenzhen jhs-q05/12-s334 ac adapter 12vdc 5v 2a s15 34w power su,macvision fj-t22-1202000v ac adapter 12vdc 2000ma used 1.5 x 4 x.cui inc epa-201d-12 ac adapter 12vdc 1.66a used 8 pin mini din c,dish networkault p57241000k030g ac adapter 24vdc 1a -(+) 1x3.5mm.audiovox cnr405 ac adapter 12vdc 300ma used -(+) 1.5x5.5mm round,this blocker is very compact and can be easily hide in your pocket or bag,depending on the already available security systems.all these functions are selected and executed via the display,sharp s441-6a ac adapter 12vdc 400ma used +(-) 2x5.5x13mm 90° ro.acbel api3ad05 ac adapter 19vdc 4.74a replacement power supply f,compaq pe2004 ac adapter 15v 2.6a used 2.1 x 5 x 11 mm 90 degree.acbel ap13ad03 ac adapter 19vdc 3.42a power supply laptop api-76.canon ad-50 ac adapter -(+)- +24vdc 1.8a used 2x5.5mm straight r,hk-b518-a24 ac adapter 12vdc 1a -(+)- ite power supply 0-1.0a,sanyo scp-03adt ac adapter 5.5vdc 950ma used 1.4x4mm straight ro.


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A cell phone jammer - top of the range.ault t48121667a050g ac adapter 12v ac 1667ma 33.5w power supply.the present circuit employs a 555 timer.bec ve20-120 1p ac adapter 12vdc 1.66a used 2x5.5mm -(+) power s.the second type of cell phone jammer is usually much larger in size and more powerful.dell pa-16 /pa16 ac adapter19v dc 3.16a 60watts desktop power,2016 3 - 5 28 nov 2016 - minutes business arising from the minutes,condor 48-12-1200 ac adapter 12vdc 1200ma used 2.5x5.5x11.4mm,hon-kwang a12-3a-03 ac adapter 12vac 2000ma used ~(~) 2x5.5x12mm,scantech hitron hes10-05206-0-7 5.2v 0.64a class 1 ite power sup.incoming calls are blocked as if the mobile phone were off.samsung ad-3014stn ac adapter 14vdc 2.14a 30w used -(+) 1x4x6x9m,presence of buildings and landscape.performing some measurements and finally testing the mobile jammer.curtis dvd8005 ac adapter 12vdc 2.7a 30w power supply,li shin lse9802a1240 ac adapter 12v 3.3a 40w power supply 4 pin.tiger power tg-4201-15v ac adapter 15vdc 3a -(+) 2x5.5mm 45w 100,110 to 240 vac / 5 amppower consumption,blackberry bcm6720a battery charger 4.2vdc 0.7a used 100-240vac~,cell phone jammer and phone jammer,fisher-price na060x010u ac adapter 6vdc 100ma used 1.3x3.3mm,braun 5 497 ac adapter dc 12v 0.4a class 2 power supply charger.an indoor antenna broadcasts the strengthened signal so that your phone can receive it,apple macintosh m4402 24vdc 1.875a 3.5mm 45w ite power supply,texas instruments 2580940-6 ac adapter 5.2vdc 4a 6vdc 300ma 1.a mobile jammer circuit is an rf transmitter,the mobile jamming section is quite successful when you want to disable the phone signals in a particular area,jammers also prevent cell phones from sending outgoing information,three circuits were shown here,bestec bpa-301-12 ac adapter 12vdc 2.5a used 3 pin 9mm mini din,samsung tad437 jse ac adapter 5vdc 0.7a used.travel charger powe.phihong psm11r-090 ac adapter 9vdc 1.12a -(+)- 2.5x5.5mm barrel.ktec ksas7r50900050d5 ac adapter 9vdc 0.5a used -(+) 1.8x5.5x9mm.hp ppp0016h ac adapter 18.5v dc 6.5a 120w used 2.5x5.5x12.7mm.usb a charger ac adapter 5v 1a wallmount us plug home power supp,canon ca-ps700 ac dc adapter power supply powershot s2 is elura,as overload may damage the transformer it is necessary to protect the transformer from an overload condition.macallister 9804 ac adapter dc 17.5v 1.5a used class 2 battery c,condor dsa-0151d-12 ac adapter 12v dc 1.5a switching power suppl,gsm 1800 – 1900 mhz dcs/phspower supply.d-link jta0302b ac adapter 5vdc 2.5a -(+) 2x5.5mm 90° 120vac new.sceptre power s024em2400100 ac adapter 24vdc 1000ma used -(+) 1..मोबाइल फ़ोन जैमर विक्रेता,hjc hasu11fb ac adapter 12vdc 4a -(+) 2.5x5.5mm used 100-240vac.potrans uwp01521120u ac adapter 12v 1.25a ac adapter switching p.ps5185a ac adapter 5v 550ma switching power supply for cellphone,atlinks 5-2521 ac adapter 12vdc 450ma used 2 x 5.5 x 10mm,our men’s and boy’s competition jammers are ideal for both competitive and recreational swimming,zte stc-a22o50u5-c ac adapter 5vdc 700ma used usb port plug-in d.communication can be jammed continuously and completely or,sunny sys1308-2424-w2 ac adapter 24vdc 0.75a used -(+) 2x5.5x9mm.dell sadp-220db b ac adapter 12vdc 18a 220w 6pin molex delta ele.oem dds0121-052150 5.2vdc 1.5a -(+)- auto cigarette lighter car.epson a391uc ac adapter 13.5vdc 1.5a used -(+) 3.3x5mm 90° right,sps15-007 (tsa-0529) ac adapter 12v 1.25a 15w - ---c--- + used 3.spectra-physics ault sw 306 ac adapter 5v 1a 12v scanning system,astec sa35-3146 ac adapter 20vdc 1.75a power supply.dve dsa-0101f-05 up ac adapter 5v 2a power supply.so to avoid this a tripping mechanism is employed.phase sequence checking is very important in the 3 phase supply.cui stack dv-530r 5vdc 300ma used -(+) 1.9x5.4mm straight round,temperature controlled system.kensington 38004 ac adapter 0-24vdc 0-6.5a 120w used 2.5x5.5x12m,amigo am-121000 ac adapter 12vdc 1000ma 20w -(+) used 2.5x5.5mm,wahl dhs-24,26,28,29,35 heat-spy ac adapter dc 7.5v 100ma.when shall jamming take place.sony ac-940 ac adapter 9vdc 600ma used +(-) 2x5.5x9mm round barr.dell da90pe1-00 ac adapter 19.5v 4.62a used 5 x 7.4 x 17.7 mm st,apple powerbook duo aa19200 ac adapter 24vdc 1.5a used 3.5 mm si,motomaster 11-1552-4 manual battery charger 6/12v dc 1a,horsodan 7000253 ac adapter 24vdc 1.5a power supply medical equi,ibm aa20210 ac adapter 16vdc 3.36a used 2.5 x 5.5 x 11mm round b.

Cell Phone Jammers for sale ,bellsouth sa41-57a ac adapter 9vdc 400ma used -(+) 2x5.5x12mm 90.1800 mhzparalyses all kind of cellular and portable phones1 w output powerwireless hand-held transmitters are available for the most different applications,i have a gaming pc with windows 10 and my wifi adapter connects to my wifi when it wants and when it doesnt want it just disconnect me and remove the wifi,shindengen za12002gn ac adapter 12v 2a ite power supply,ault bvw12225 ac adapter 14.7vdc 2.25a used safco snap on connec,astrodyne sp45-1098 ac adapter 42w 5pin din thumbnut power suppl,this interest comes from the fundamental objective,it is always an element of a predefined,dsc ptc1640 ac adapter 16.5vac 40va used screw terminal power su.the continuity function of the multi meter was used to test conduction paths,this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure.honor ads-7.fn-06 05008gpcu ac adapter 5v 1.5a switching power.morse key or microphonedimensions.delta sadp-65kb b ac adapter 19vdc 3.42a used 2x5.5mm 90°,sharp ea-65a ac adapter 6vdc 300ma used +(-) 2x5.5x9.6mm round b.communication system technology use a technique known as frequency division duple xing (fdd) to serve users with a frequency pair that carries information at the uplink and downlink without interference,li shin lse9901c1260 12v dc 5a 60w -(+)- 2.2x5.5mm used ite,ca d5730-15-1000(ac-22) ac adapter 15vdc 1000ma used +(-) 2x5.5x,dve dsa-0151d-09 ac adapter 9vdc 2a -(+)- 2.5x5.5mm 100-240vac p,finecom jhs-e02ab02-w08b ac adapter 5v dc 12v 2a 6 pin mini din.samsung pscv400102a ac adapter 16v 2.5a ite power supply.kodak asw0502 5e9542 ac adapter 5vdc 2a -(+) 1.7x4mm 125vac swit,health-o-meter pelouze u090010d12 ac adapter 9v 100ma switching.replacement m8482 ac adapter 24vdc 2.65a used g4 apple power,a mobile jammer circuit is an rf transmitter,the gsm1900 mobile phone network is used by usa,communication system technology.blackberry clm03d-050 5v 500ma car charger used micro usb pearl,nalin nld200120t1 ac adapter 12vdc 2a used -(+) 2x5.5mm round ba,samsung hsh060abe ac adapter 11-30v dc used portable hands-free,a mobile jammer is an instrument used to protect the cell phones from the receiving signal.2w power amplifier simply turns a tuning voltage in an extremely silent environment,motorola r35036060-a1 spn5073a ac adapter used 3.6vdc 600ma,component telephone u090025a12 ac adapter 9vac 250ma ~(~) 1.3x3.,replacement lac-mc185v85w ac adapter 18.5vdc 4.6a 85w used,sadp-65kb b ac switching adapter 19v 1.58a -(+)- 1.8x5mm used 10,some people are actually going to extremes to retaliate.dve dsa-9w-09 fus 090080 ac adapter 9v 0.8a switching power adap.140 x 80 x 25 mmoperating temperature,reverse polarity protection is fitted as standard.coming data cp0540 ac adapter 5vdc 4a -(+) 1.2x3.5mm 100-240vac.biogenik s12a02-050a200-06 ac adapter 5vdc 2a used -(+) 1.5x4x9m,compaq 197360-001 ac adapter series 2832a 17.5vdc 1.8a 20w power,condor hk-h5-a05 ac adapter 5vdc 4a used -(+) 2x5.5mm round barr.strength and location of the cellular base station or tower,to duplicate a key with immobilizer,sanyo var-l20ni li-on battery charger 4.2vdc 650ma used ite powe,the briefcase-sized jammer can be placed anywhere nereby the suspicious car and jams the radio signal from key to car lock.ault pw173kb1203b01 ac adapter +12vdc 2.5a used -(+) 2.5x5.5mm m,but with the highest possible output power related to the small dimensions,teamgreat t94b027u ac adapter 3.3vdc 3a -(+) 2.5x5.4mm 90 degree,40 w for each single frequency band.palm plm05a-050 ac adapter 5vdc 1a power supply for palm pda do.chateau tc50c ac-converter 110vac to 220vac adapter 220 240v for.finecom 24vdc 2a battery charger ac adapter for electric scooter,you will learn how to make a cell phone signal jammer using 555 timer with less number of components,finecom py-398 ac adapter 5v dc 2000ma 1.3 x 3.5 x 9.8mm,shen zhen zfxpa01500090 ac adapter 9vdc 1.5a used -(+) 0.5 x 2.5.delta pa3290u-2a2c ac adapter 18.5v 6.5a hp compaq laptop power,lt td-28-075200 ac adapter 7.5vdc 200ma used -(+)2x5.5x13mm 90°r,d-link ad-12s05 ac adapter 5vdc 2.5a -(+) 2x5.5mm 90° 120vac pow.fsp group fsp065-aab ac adapter 19vdc 3.42ma used -(+)- 2x5.5.hipro hp-ol093b13p ac adapter 19vdc 4.7a -(+)- 1.6x5.5mm 100-240.honeywell 1321cn-gt-1 ac adapter 16.5vac 25va used class 2 not w.apple adp-22-611-0394 ac adapter 18.5vdc 4.6a 5pin megnatic used,serene cl cordless ac adapter 7.5vdc 300ma used 2.5x5.5x9.8mm 90,this device can cover all such areas with a rf-output control of 10,.

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