An SVM-Based Snow Detection Algorithm for GNSS-R Snow Depth Retrievals

—The signal-to-noise ratio (SNR) is important observations in global navigation satellite system-reﬂectometry (GNSS-R) technology. The oscillation frequency in the SNR arc is sensitive to different reﬂecting surfaces and can be used to build height model totrackthevariationofsnowdepth.However,itisdifﬁculttoobtainretrievalresultswithsnowdepthofzerointheactualsnowdepthre-trievalexperimentsbasedonGNSS-Rtechnology,whichindicatesthattheclassicalmodelhasnonnegligibleretrievalerrorsinthe snow-freestate.Thisstudyaimstorealizethedetectionofgroundtruthinformationbeforesnowdepthretrieval,i.e.,classiﬁcation ofsnow-freestateandsnow-coveredstate.MachinelearningwasintroducedtoachievetheaforementionedpurposeandtheSNRarc wasusedastheinputdata.Comparedwiththecurrentmainstreamtopographycorrectionalgorithms,thealgorithmproposedinthis studydoesnotrelyonanypriorigroundmeasureddataandhastheoreticaluniversality.Thedetectionresultscanconstrainthe retrievalsnowdepthinthesnow-freestateand,thus,improvetheretrievalaccuracy.Theexperimentalresultsforthe2014seasonal snowpackatP351stationinIdaho,USA,showthatthedetectionresultsobtainedbasedonsupportvectormachinesagreewellwith themeasuredsnowdepthprovidedbytheSNOTELnetwork,andtheoveralldetectionaccuracycanreachabout96%.Thedaily snowpackstateisdeterminedbythemajorityofSNRarcsdetectedduringthedayandisonlyconsideredreliableifthepercentage exceeds75%.Onlyonedayofthedetectionresultswasinaccurateandonly8days(8/365)didnotreachthesetthresholdof75%. Withthehelpofthedetectionresults,theroot-mean-squareerrorofsnowdepthretrievalcanbereducedfrom20cmintheclassical algorithmto15cm,whichresultsina25%improvementinretrievalaccuracy.Moreover,thisstudybroadenstheapplicationvalueof GNSSsignalsandprovidesareferencefortheapplicationofSNRinthedetectionﬁeld.

An SVM-Based Snow Detection Algorithm for GNSS-R Snow Depth Retrievals Yuan Hu, Xintai Yuan , Wei Liu , Qingsong Hu, Jens Wickert , and Zhihao Jiang Abstract-The signal-to-noise ratio (SNR) is important observations in global navigation satellite system-reflectometry (GNSS-R) technology.The oscillation frequency in the SNR arc is sensitive to different reflecting surfaces and can be used to build height model to track the variation of snow depth.However, it is difficult to obtain retrieval results with snow depth of zero in the actual snow depth retrieval experiments based on GNSS-R technology, which indicates that the classical model has nonnegligible retrieval errors in the snow-free state.This study aims to realize the detection of ground truth information before snow depth retrieval, i.e., classification of snow-free state and snow-covered state.Machine learning was introduced to achieve the aforementioned purpose and the SNR arc was used as the input data.Compared with the current mainstream topography correction algorithms, the algorithm proposed in this study does not rely on any priori ground measured data and has theoretical universality.The detection results can constrain the retrieval snow depth in the snow-free state and, thus, improve the retrieval accuracy.The experimental results for the 2014 seasonal snowpack at P351 station in Idaho, USA, show that the detection results obtained based on support vector machines agree well with the measured snow depth provided by the SNOTEL network, and the overall detection accuracy can reach about 96%.The daily snowpack state is determined by the majority of SNR arcs detected during the day and is only considered reliable if the percentage exceeds 75%.Only one day of the detection results was inaccurate and only 8 days (8/365) did not reach the set threshold of 75%.With the help of the detection results, the root-mean-square error of snow depth retrieval can be reduced from 20 cm in the classical algorithm to 15 cm, which results in a 25% improvement in retrieval accuracy.Moreover, this study broadens the application value of GNSS signals and provides a reference for the application of SNR in the detection field.Index Terms-Detection, global navigation satellite systemreflectometry (GNSS-R), signal-to-noise ratio (SNR), snow depth, support vector machine (SVM).

I. INTRODUCTION
S NOW is one of the important sources of water resources and a sensitive and important factor in climate change.Therefore, monitoring snowpack is of great significance to climate prediction, hydrological research, and snow disaster prevention.Affected by topography, snowpack also exhibits great spatial variability.In addition, snowpack ablation is also nonuniform due to temperature, wind, and radiation [1].Usually, snow data can be obtained from ground stations and satellite remote sensing.The snowdrift telemetry (SNOTEL) network [2], with nearly a thousand stations distributed in the United States, can provide data, such as snow depth, snowfall, and snow water equivalent (SWE).However, the measurement area of each site is only about 9 m 2 , which cannot adequately express the current status of in-situ snowpack.Besides, other classical snow monitoring methods, such as satellite remote sensing [3] and synthetic aperture radar [3], have certain limitations, such as spatial and temporal resolution, high cost, and susceptibility to external environmental influences.Under these conditions, there is a demand for a method that can measure large areas of snowpack at low cost to complement snow monitoring.
Global navigation satellite system-reflectometry (GNSS-R) technology is a new branch of GNSS that has been gradually developed since the 1990's and is also one of the research hot spots in the field of remote sensing.Multipath signals are often suppressed as a source of error in high accuracy applications [4].However, multipath signals actually carry much geometric and physical information from the reflecting surface that can be used in GNSS-R technology.The signal-to-noise ratio (SNR) data received by the GNSS antenna are formed by the interference of the direct and reflected signals and is a measure of the signal strength.Meanwhile, the SNR data are the important observation for GNSS-R technology.Martin-Neira [5] revealed the interference phenomenon between the direct satellite signal and the reflected signal.Bilich and Larson [6] further proposed the SNR power spectral maps for multipath evaluation and, thus, found a mapping relationship between SNR and multipath environment.It was also shown that the oscillation frequency in a robust SNR time series is a function of the distance to the reflected object.Jacobson [7] also demonstrated that GPS signal power correlates well with snow depth and can be used to track the variability of snow depth.Larson et al. [8] tried to retrieve the snow depth through the SNR data of the standard GPS receiver on the basis of the previous research, in preparation for the SWE measurement.Since then, the GNSS-R snow depth retrieval technology based This work is licensed under a Creative Commons Attribution 4.0 License.For more information, see https://creativecommons.org/licenses/by/4.0/ on SNR data has received wide attention [9]- [13].The existing classical snow depth retrieval model based on SNR data is a height model obtained by empirical derivation.In principle, the height model uses the oscillation frequency to solve for the reflector height, i.e., the distance from the antenna to the reflecting surface.However, it is difficult to see retrieval results with a snow depth of zero in the actual snow depth retrieval experiment.In other words, the classical model cannot or is difficult to detect snow-free state, and even the retrieval results will be affected by the topography and produce immeasurable errors between the measured snow depth [14]- [17].
Currently, most topography correction methods are based on known a priori information.Tabibi et al. [18] proposed to attenuate the effect of partial topography bias by changing the fixed reflector height reference to improve the overall accuracy.Li et al. [19] used the antenna phase center correction model to redefine the antenna height to reduce the effect of topography slope on the retrieval results.Although modifying the reflector height reference can improve the retrieval accuracy, the effect of topography correction is limited.The correction of snow-free states does not seem to be suitable for snow-covered states, and topography correction relies on known topography measurement data [20].
In this study, we still focus on the retrieval error in the snowfree state, but the focus is not on the antenna height instead on detecting the snow state on the ground.As the existing studies indicate, there is a difference between the SNR arcs collected in snow-free state and snow state.We propose to introduce support vector machine (SVM) and use SNR arcs as input samples to detect the ground truth state.When the detection result is snowfree state, the snow depth is zero by default, otherwise the snow depth is retrieved with the help of classical algorithms.This article is structured as follows.Section II introduces the snow depth detection method based on SVM.Next, in Section III, experimental validation and discussion are presented.Finally, Section IV concludes this article.

II. SNOW DETECTION ALGORITHM BASED ON SVM
As the GNSS signal is gradually expanding its coverage, a large number of geodetic receivers are being installed.Since 1994, the International GNSS Service (IGS) Center has made publicly available high-quality GNSS data and products [21] that have been used in a variety of fields, such as earth science research.Besides, the EarthScope Plate Boundary Observation (PBO, http://pbo.unavco.org)program has built hundreds of permanent GPS stations and can provide GPS observations with 15-s temporal resolution.The receivers record observations, including SNR, which can be decomposed into a slowly varying trend term and a high-frequency varying multipath oscillation term.Assuming a planar and leveled reflecting surface, the latter affected by multipath can be modeled as [22] where E is the satellite elevation angle; A is the amplitude; and ϕ is the phase delay between the direct and reflected signals.f is the oscillation frequency, which is not an ordinary temporal frequency, in hertz.The strength of the SNR depends on the shape and dielectric constant of the reflector, which indicates that there are differences in the SNR received by the GNNS antenna for different reflector objects [23], [24].The oscillation frequency f can often be used to track changes in snow depth.
The geometric relationship of the established height model is schematically shown in Fig. 1(a), where H is the antenna height, and h is the reflector height, i.e., the distance from the antenna to the reflecting surface.The relationship between frequency and reflector height can be expressed as where λ is the wave length.As shown in Fig. 1(b), it can be seen that the two SNR arcs collected from snow-free state and snowcovered state obviously show different oscillation frequencies.Actually, there are more differences between them, and machine learning was introduced to solve this problem.In view of the mapping relationship between SNR arcs and reflecting surfaces, SVM can be used to perform machine learning on the collected SNR arcs and then output the detection results to determine whether the reflecting surface is snow-free state or snow-covered state.The SVM [25] is a machine learning algorithm for binary classification of input samples in a supervised learning manner, and its decision boundary is based on the input samples using the structure minimization principle to establish the globally optimal maximum margin hyperplane, the principle of which is shown in Fig. 2. The blue circles and red squares represent different types of samples.The solid line Y represents the optimal hyperplane found, that is, the decision boundary, where w and b are the normal vector of the hyperplane and displacement terms, respectively.The dashed lines Y1 and Y2 are the interval boundaries of each type and margin is the classification interval indicating the sample differentiation.
As in practice, in most cases, the data are not linearly separable, i.e., it is difficult to distinguish the samples with a straight line in the two-dimensional plane.In this case, the hyperplane satisfying the condition simply does not exist, and SVM can solve the problem by introducing kernel functions [26].Specifically, SVM first completes the computation in the low-dimensional space, then maps the input space to the high-dimensional Hilbert space through the kernel function, and finally constructs the optimal separation hyperplane in the high-dimensional feature space, so as to separate the nonlinear data that are not well separated on the plane itself.The advantage of the kernel function is that it can be computed in low dimensions, whereas the substantial classification effect is expressed in high dimensions, avoiding the explicit computation of the inner product in high dimensions.Considering the complexity of the data in this article and the generality of the kernel function, the radial basis kernel (RBF) function is selected where the parameter g is self-contained by the RBF kernel function, which affects the degree of fit of the model and, thus, the generalization ability of the model.In addition, the penalty coefficient c, which affects the degree of fit of the model and, thus, the generalization ability of the model.

A. Station Introduction and Data Selection
The P351 station in Blaine County, ID, USA (43.87441 °N, 114.71916 °W, Elevation 2692.6 m) is one of the observation stations of the PBO network and includes a standard TRIMBLE NETRS receiver and Trimble TRM 29659.00antenna.The antenna is about 2 m above the ground and records GPS observations at a sampling interval of 15 s.In principle, it is possible to collect GPS signals in an area of nearly 10 000 m 2 around the antenna.Different satellites produce different ground tracks, i.e., the sampling area.Usually, the effective multipath signal is considered to be obtained from the first Fresnel zone [14].Furthermore, the GPS signal acquisition also needs to consider the influence of the surrounding environment.As shown in Fig. 3(a), the area of P351 station is sparsely vegetated and free of buildings, so the influence of shading can be ignored.In addition, due to the antenna gain pattern, the oscillation amplitude of SNR data decreases with increasing elevation angle, i.e., the multipath effect is more obvious at low elevation angles.We used SNR data from 5°-25°elevation angle to expect better results.And the azimuth angle range was selected from 0°-360°.
The area where P351 station is located experienced snowpack accumulation-ablation-accumulation in 2014, satisfying the requirement to perform a complete cycle of detection of snow-free state and snow-covered state.As shown in Fig. 3(b), the Galena Summit station (43.87497 °N, 114.71363 °W, Elevation 2676 m) of the SNOTEL network, located about 0.5 km in a straight line from P351 station, recorded many in-situ snow data, which provided reference data for validating the experiments.

B. GNSS-R Snow Depth Retrieval Experiments Combined With SVM
In the classical algorithm, the least squares fitting (LSF) method and the Lomb-Scargle periodogram (LSP) [27], [28] spectral analysis method were used to retrieve the snow depth.The LSF method was used to separate the low-frequency trend terms from the high-frequency oscillation terms, and the LSP spectral analysis method was able to extract the frequencies in the oscillation terms for the subsequent snow depth retrieval.The results of snow depth retrieval for P351 station in 2014 based on the classical algorithm are shown in Fig. 4(a).The horizontal coordinates indicate time and the vertical coordinates indicate snow depth.The snow depth retrieval based on the classical algorithm is highly consistent with the in-situ snow depth provided by the SNOTEL network, but seems to show large variations in some local areas.From the error maps, it can be observed that the main retrieval errors are mainly distributed in the thick snow depth range and snow-free state.Figs. 5  and 6 show the topography around the station and the spatial distribution of snow depth retrieval results, respectively.It can be clearly seen that the retrieval results are difficult to get the retrieval results with snow depth of zero.On the one hand, when the snow depth is close to the height of the antenna, the low-frequency trend term and high-frequency oscillation term will be difficult to separate the spectrum and the size of the Fresnel zone will be decreased.On the other hand, the snow depth retrieval in snow-free state and shallow snow state is also affected by ground cover and electromagnetic penetration bias [29], [30].However, if the ground truth information can be determined, it is possible to transform the snow depth retrieval problem into a ground state detection problem.When the ground is snow-free state, the snow depth retrieval result is set to zero by default, which seems to avoid retrieval errors.Additionally, we observed a blank area in Fig. 6, which may be due to the fact that no qualified SNR data were collected in this area.
As mentioned in Section II, different reflecting surfaces will lead to variability in the SNR.Essentially, the SVM classification model is used to detect satellite signals collected in different snow conditions.The 20 000 SNR arc samples from different snow depths collected at P351 station in 2014 were used as input predictors for the SVM classification model, which contained 10 000 snow-covered state samples set as positive class (DOY 1-148, 295-365) and 10 000 snow-free state samples set as negative class (DOY 149-294).The ratio of training dataset and test dataset is 4:1.It should be noted that the input SNR arcs are constrained to be in the elevation angle range of 5°-25°.In addition, the parameter g and the penalty coefficient c are two key independent parameters of the SVM classification model that need to be considered.In this experiment, c and g were

TABLE I CONFUSION MATRIX OF CLASSIFICATION RESULTS OF SVM
CLASSIFICATION MODEL set to 2 and 0.5, respectively, via the cross-validation and grid search algorithms.Combined with the in-situ snow depth, the detection accuracy of test dataset can reach about 96% overall, with the true positive rate and true negative rate of about 97% and 95%, respectively, as shown in Table I.The area under curve area is approximately 0.96.Statistically, the SVM classification model can well  identify SNR arcs from different reflecting surfaces and detect ground truth information.It should be noted that in this study, the ground state was divided into two states of no snow with zero snow depth and a snow-covered state with snow depth higher than zero.In addition, since the proposed algorithm is applied in GNSS-R snow depth retrieval experiments, the snow depth is recorded at a frequency of 1 d, so for the detection results, we are concerned with the final conclusion of each day.During the experiment, the daily accuracy achieved good performance.The daily ground state detection conclusions consist of the detection results of multiple SNR arcs for the day, and we consider the detection results reliable when a particular result exceeds 75% of the sample size for the day.Combined with the measured snow depth, Fig. 7(a) shows the distribution of the error rate of the daily detection results compared to the real ground state during the experimental period.The statistical results show that out of 365 days in the experimental period, only eight days (DOY 147-149, 167, 294, 296, 298, 304) exceeded the set threshold, and almost all of these 8 days were found to be concentrated in the snow state transition period by comparing with the actual snow depth.In fact, if we set the threshold value to 50%, i.e., adopt the majority principle, then only one day of detection results in this experiment does not meet the requirements, and the improvement for the accuracy of the final snow depth retrieval will be more obvious on this basis.
In order to perform a more in-depth analysis of the performance of the proposed detection algorithm in different snow depth ranges, especially the transition period between snow-free state and snow-covered, we set three transition snow depth ranges: [0, 5], [0, 10], and [0, 20].As shown in Fig. 7(b), the horizontal coordinates represent the range of snow depths for the different transition periods delineated.The ordinates represent the detection accuracy for different snow depth ranges under different delineated intervals.It can be seen that the detection accuracies of both snow-free state and snow-covered state after excluding the set transition period are above 95%, but the detection accuracy of the transition period is not ideal.Taking [0, 5] as an example, the detection accuracies of the snow-free state and the snow-covered state are 95% and 99%, respectively.However, the detection accuracy in the transition period was only 76%, which may be related to the spatial heterogeneity of snow distribution and temperature.The detection results are introduced into the snow depth retrieval to optimize the initial snow depth retrieval results, as shown by the blue dots in Fig. 4(b).The statistics  II.The root-mean-square error (RMSE) of the snow depth retrieval results combined with the SVM classification model is about 15 cm, which is about 25% less than the 20 cm of the classical algorithm.It can be seen that the scheme proposed in this article is feasible, which can effectively reduce the retrieval error in snow-free state and improve the accuracy of snow depth retrieval.

C. Error Source Discussion
Differences in snowfall and topography between GNSS stations and recording stations will affect the retrieval accuracy.In the snow depth retrieval experiment, we use the daily average snow depth data provided by the SNOTEL network as the reference data source to evaluate the retrieval results.Although the distance between the two places is very close, the snowpack has temporal and spatial variability.After all, the snow data of the two places are not completely consistent, which will become an error source for snow depth retrieval.
Snow depth, as a slowly changing meteorological data, has a seasonal snowpack accumulation cycle of accumulationablation-accumulation unless a blizzard is encountered.During the alternating periods of accumulation and ablation states, snowpack is subject to external influences, such as temperature or wind, that may lead to rapid changes in the state of snow-free and snow-covered on the ground.In special cases, SNR arcs collected on the same day may contain ground information of both snow-free state and snow-covered state, which makes retrieval more challenging.

IV. CONCLUSION
In this study, the SNR arcs were used for snow depth retrieval experiments and the feasibility of snow detection on the ground based on SVM and the effect of improving the retrieval accuracy in the snow-free state are analyzed.This study has the following contributions.
1) Since the SNR arcs collected by the GNSS antenna in the snow-free state and the snow-covered state are different, SVM can be used to detect the ground state.The detection results are highly consistent with the measured snow depth data, the detection accuracy of the samples can reach 96%, and the detection accuracy of the daily snow state during the experiment can reach 98% within the set threshold range.2) With the aid of daily detection of snow states on the ground, it is possible to achieve constraints on the initial snow retrieval results, especially in the snow-free state.
The RMSE of the optimized snow depth retrieval results is reduced from 20 to 15 cm, which is 25% less than the initial results.
3) Compared with current topography correction algorithms, the algorithm proposed in this article does not rely on any priori ground measurement data.The SVM classification model can learn the topography environment of the retrieved region from historical SNR data to improve the matching with each other.Therefore, the algorithm is theoretically universal and applicable to different snow scenarios.Moreover, this study broadens the application scope of GNSS signal and provides a reference for the subsequent application of SNR in the detection field.

Fig. 1 .
Fig. 1.Classical GNSS-R snow depth retrieval model.(a) Diagram of the geometric relationship of GNSS-R altimetry.(b) Model predictions for GPS S1C multipath from snow-free state (black) and snow-covered state (red).

Fig. 3 .
Fig. 3. Introduction to the surrounding environment of the station.(a) Environment map of the northern area of P351 station.(b) Environment map of the northern area of Galena Summit station.

Fig. 4 .
Fig. 4. Analysis of GNSS-R snow depth retrieval results for GPS S1C SNR at P351 station.(a) Results of GNSS-R snow depth retrieval based on classical algorithm.(b) Results of GNSS-R snow depth retrieval based on SVM+classical algorithm.

Fig. 7 .
Fig. 7. Analysis of GNSS-R snow depth retrieval results combined with SVM classification model.(a) Statistics of detection results based on SVM classification model.(b) Accuracy of different transitional period division standards.

TABLE II STATISTICS
OF THE RETRIEVAL ACCURACY OF DIFFERENT ALGORITHMS of the retrieval accuracy of different algorithms are recorded in Table