Low Cost and Compact FMCW 24 GHz Radar Applications for Snowpack and Ice Thickness Measurements

Monitoring the evolution of snow on the ground and lake ice—two of the most important components of the changing northern environment—is essential. In this paper, we describe a lightweight, compact and autonomous 24 GHz frequency-modulated continuous-wave (FMCW) radar system for freshwater ice thickness and snow mass (snow water equivalent, SWE) measurements. Although FMCW radars have a long-established history, the novelty of this research lies in that we take advantage the availability of a new generation of low cost and low power requirement units that facilitates the monitoring of snow and ice at remote locations. Test performance (accuracy and limitations) is presented for five different applications, all using an automatic operating mode with improved signal processing: (1) In situ lake ice thickness measurements giving 2 cm accuracy up to ≈1 m ice thickness and a radar resolution of 4 cm; (2) remotely piloted aircraft-based lake ice thickness from low-altitude flight at 5 m; (3) in situ dry SWE measurements based on known snow depth, giving 13% accuracy (RMSE 20%) over boreal forest, subarctic taiga and Arctic tundra, with a measurement capability of up to 3 m in snowpack thickness; (4) continuous monitoring of surface snow density under particular Antarctic conditions; (5) continuous SWE monitoring through the winter with a synchronized and collocated snow depth sensor (ultrasonic or LiDAR sensor), giving 13.5% bias and 25 mm root mean square difference (RMSD) (10%) for dry snow. The need for detection processing for wet snow, which strongly absorbs radar signals, is discussed. An appendix provides 24 GHz simulated effective refractive index and penetration depth as a function of a wide range of density, temperature and wetness for ice and snow.


Introduction
In northern regions where communities rely on winter transport for their food and fuel supply, safety on ice roads is a major concern. Improved methods for monitoring ice thickness are important in the context of climate warming impacts on the cryosphere. Between 1991 and 2000, an average of 27 snowmobilers died each year from breaking through the ice of frozen lakes and rivers [1].

Fundamentals
The principle of FMCW radar has been well known since the 1970s and was described in detail by [26,29] (and the references included in those papers). We only recall here the main practical principle for its use. This type of sensor emits a wave at variable frequencies centered on a reference frequency. When the radar receives an echo from a target, the frequency difference between the emitted and reflected signals can be measured. Since the frequency change rate is known, it becomes possible to measure the time between the emission and the reception of the echo so that the radar-target distance can be calculated (in a manner similar to impulse radars).
For a semi-transparent medium such as snow or ice, the radar wave is partly transmitted, attenuated and reflected (backscattered). The received power is related to the dielectric contrast within the medium, as well as the losses due to volume scattering, attenuation, and spreading effects. The total loss, expressed by the extinction coefficient κ e , corresponds to the sum of the absorption coefficient κ a and the scattering coefficient κ s . In radiative transfer theory, the extinction coefficient is related to the effective medium permittivity ε e f f via Equation (1) [52]: where the complex effective permittivity ε e f f = ε e f f + j ε e f f includes a real (ε e f f ) and an imaginary part (ε e f f ) of the effective medium permittivity, j = √ −1 and k o represent the free-space propagation Sensors 2020, 20, 3909 4 of 28 constant. ε e f f is linked to the wave propagation, while ε e f f is the dielectric loss factor. The transmitted signal in the medium is also partly reflected when large changes in dielectric properties occur. In the simplified case of the boundary between two media of effective permittivity i and i + 1, the magnitude of the reflection at perpendicular incidence is proportional to the elementary reflectivity r i , given by: √ ε e f f ,i + √ ε e f f ,i+1 (2) The radar in FMCW mode measures the transit time of the microwave signal in the medium. This transit time (t) is proportional to the thickness (h) of the medium multiplied by the speed (v) of the electromagnetic wave in the medium, such as for a two-time way retrieval, i.e., a propagation time from the transmitter to the receiver: where υ x = c/n x ; c is the speed of light in air; n x is the effective real refractive index; and ε x is the effective permittivity of the medium (x) for ice x = i, water x = w, dry snow x = sd and wet snow x = sw. The real refractive index can be expressed by the real (ε x ) and imaginary (ε x ) part of the medium, as in Equation (3b). We report all theoretical simulated refractive index values (n x ) at 24 GHz in Appendix A. When pointing the radar vertically downwards at the ice or snow cover (Figure 1), this transit time is converted into the "radar distance" (h radar ) between the radar and the target through the different media: h radar = h air n a + l h x,l √ ε x,l = h air + l h x,l √ ε x,l (4b) l h s,l = h s or l h i,l = h i (4c) where h o,air and h o,x are the radar distance in the air and medium, respectively (x = i, sd, or sw) ( Figure 1). If the medium is not homogeneous, it can be considered as consisting of l layers Equation (2a). All radar distances can be translated to real distances by considering the refractive index (n ) or the permittivity (ε l ) Equation (4b). As the permittivity of air is ε a = 1, h o,air = h air . The radar distance in the medium (h o, x ) can thus be expressed as a function of the sum of each snow or ice layer depth (h x,l ) weighted by the square of the effective permittivity (ε x,l ) of the layer (l) Equation (4b).
The summation over all of the (l) layers of the medium corresponds to the total depth of the medium, i.e., the "snow depth" (h s ) or "ice thickness" (h ice ) Equation (4c). Assuming a homogeneous medium, Equation (4b) for snow becomes: where ε s is the effective permittivity of the whole snowpack and h s is the total snow depth. For ice detection, the radar distance to be considered (h radar,ice ) is the distance between the radar and the bottom of the ice, i.e., at the water interface. Equation (4b) for ice then becomes: where ε i is the ice effective permittivity and h i is the total ice thickness.
The system of Equations (4)- (6) includes undetermined problems (more unknowns than equations). It is possible to measure ε x using an FMCW radar if an independent measurement of snow depth (h s ) or ice thickness (h i ) is available, or inversely, one can measure snow depth or ice thickness if the Sensors 2020, 20, 3909 5 of 28 mean medium permittivity is known. For wet snow, there is a third variable to be considered, that is, its liquid water content (see Discussion).
Sensors 2020, 20, x FOR PEER REVIEW 6 of 29 . Figure 1. Schematic illustration of the radar retrieval. On the left, the radar is at a height hair above the snow, that is at a height (hr) above the ground, given a measured snow depth of hs = 117 cm. On the right, the measured radar signal expressed in "radar distance" is shown, with a series of peaks linked to different layers within the snowpack. The measured total radar distance is 188 cm between the radar and the last peak (i.e., the bottom). Knowing hs, one can retrieve the mean snow refractive index or permittivity(Equation (11)).
The final relationship for estimating the dry snow water equivalent (SWE) from FMCW radar measurements, considering the known snow depth (hs), is solving Equation (9): = ℎ × = ℎ × −1.7 + 2.89 + 2.8( − 1) 1.4 (11) where is derived from Equation (8), and ℎ , is the radar distance between the top and the bottom of the snowpack (Figure 1). Note that Equation (11) is derived from Equation (9) and is only valid for dry snow; Equation (11) is thus not valid for wet snow analysis (see Discussion).

Sensor Description
The low cost compact commercial radar module tested in this study is the K-band 24 GHz IMST sentire™ sR-1200 Series FMCW manufactured by the IMST company, (Kamp-Lintfort, Germany) [51]. The main specifications of this radar are summarized in Tables 1 and 2 [51] and the hardware is shown in Figure 2. We only used its FMCW mode for our snow and ice characterization application. A simplified link budget is provided in Appendix B. Schematic illustration of the radar retrieval. On the left, the radar is at a height h air above the snow, that is at a height (h r ) above the ground, given a measured snow depth of h s = 117 cm. On the right, the measured radar signal expressed in "radar distance" is shown, with a series of peaks linked to different layers within the snowpack. The measured total radar distance is 188 cm between the radar and the last peak (i.e., the bottom). Knowing h s , one can retrieve the mean snow refractive index or permittivity(Equation (11)).

Ice Thickness Derivation
For the freshwater ice thickness measurement, the problem (Equation (4)) is solvable, assuming homogeneous solid pure ice at a given temperature (T), which is known. The commonly accepted value of ice refractive index at the frequency used (24 GHz) is n i = 1.78 ± 0.0035 for 0 ≤ T ≤ -40 • C, and n i = √ ε i = √ 3.17 [53] (see Appendix A). Due to the significant dielectric contrast between ice and water, typically with a refractive index of n i = 1.78 and n w = 4.83 at 24 GHz and 0 • C, giving a 46% reflection (Equation (2) from ice to water (see Appendix A), the ice/water interface is generally strongly marked with the FMCW radar used. This leads to the relationship between ice thickness (h i ) and the measured radar distance between the surface of ice and the bottom ice/water interface, from Equation (6): However, lake ice is not always homogeneous [48]. Increased air bubble content in ice decreases ice density and thus relative permittivity of bubbled ice down to 3.0 (-6% in density), depending on the volumetric air bubble content, i.e., the density [54]. Furthermore, snow cover is often present on the ice surface and given the dielectric contrast between snow and ice, typically n s ≈ 1.214 and n i = 1.78 (19% reflection), the snow/ice interface is generally detectable with the FMCW radar.

Snow Water Equivalent (SWE) Derivation
It is possible to measure the snow refractive index (n s ) using an FMCW radar if an independent measurement of snow depth (h s ) is available. An SWE estimate can thus be derived: SWE = h s × ρ s , where ρ s is the mean snow density linked to the permittivity for dry snow. We focus here on the SWE (permittivity) derivation because snow depth can easily be measured with another sensor, such as LiDAR or an acoustic sensor, or simply with an avalanche probe. The derivation of snowpack stratification is a more complex problem that is discussed in the Discussion. Let us consider a dry snowpack with a total snow depth (h s ) characterized by a mean effective permittivity (ε sd ). From Equation (5), we can derive: For a given range of frequency, the effective permittivity of dry snow was found to depend almost solely on density, i.e., it does not depend on snow type, grain size or temperature [53][54][55][56][57]. The mean relative snow density (ρ s = ρ snow ρ w , where ρ w is the water density) can be retrieved from the estimated permittivity Equation (8) by solving the relationship defined by [57] for dry snow at frequencies between 0.85 to 12.6 GHz: Sadiku [58] showed the extreme stability of dry snow permittivity between 0.6 to 300 GHz, so it is assumed that the Tiuri et al. [57] relationship Equation (9) is still valid at 24 GHz. Several authors proposed slightly different relationships, such as ε sd = 1 + 1.83ρ s [59] or Equation (10) [53], the latter giving values on average 3% higher: Here, we used the relationship given in Equation (9) for dry snow permittivity. The final relationship for estimating the dry snow water equivalent (SWE) from FMCW radar measurements, considering the known snow depth (h s ), is solving Equation (9): where ε sd is derived from Equation (8), and h radar,snow is the radar distance between the top and the bottom of the snowpack ( Figure 1). Note that Equation (11) is derived from Equation (9) and is only valid for dry snow; Equation (11) is thus not valid for wet snow analysis (see Discussion).

Sensor Description
The low cost compact commercial radar module tested in this study is the K-band 24 GHz IMST sentire™ sR-1200 Series FMCW manufactured by the IMST company, (Kamp-Lintfort, Germany) [51]. The main specifications of this radar are summarized in Tables 1 and 2 [51] and the hardware is shown in Figure 2. We only used its FMCW mode for our snow and ice characterization application. A simplified link budget is provided in Appendix B.

Parameters Specifications
General   The radar technology is based on a monostatic FMCW radar system with transmitter and receiver channels and I/Q demodulator [26]. The IMST radar module contains two receiving antennas closed together in one module and fed by one source. The output signal thus consists of four values corresponding to the real and imaginary parts of amplitude, the I and Q channels, respectively, for both antennas. We consider the mean as: Sensors 2020, 20, 3909 8 of 28 In the following, we work on A values as the "relative radar signal amplitude". Note that we could also consider the power signal as: 21 is a reference value. We did not use the magnitude of the returned amplitude (power) from reflectors (i.e., ice or snow) because it is much more difficult to interpret than the position of the detected peak.
The maximum possible update rate of measurements depends on many parameters including ramp duration, signal processing time and the amount of transmitted data samples, i.e., the selected maximum detection distance. For our applications, the algorithm we set for measurements optimizes the radar's parameters, giving a maximum acquisition speed of approximately 15 readings per second. We selected a sampling rate optimization by stretching the signal up to the maximum of 513 values (1/2 of 1024 data samples +1, see Table 1) over a distance of 4 m.

Distance Resolution of the Radar System and Offset
The theoretical distinction capability between two reflective surfaces, i.e., the distance resolution of an FMCW radar (δh), is only a function of the wave speed (v) and the radar band width (B) [51]: where v = c/n, c is the speed of light in air, and n x is the refractive index of the medium. In the air, δh = 6 cm with B = 2.5 GHz (Table 1). In ice, δh is 3.4 cm (n i = 1.78), while in dry snow the radar resolution is in the order of 5 cm at a mean density of 275 kg m −3 (down to 4 cm at 500 kg m −3 ). However, the amplitude and shape of the measured echo after reflection off a target at a relatively short distance (<4 m) depends on the frequency ramp duration (Tr, Table 1) and the sampling mode (padding). A high frequency ramp duration decreases the amplitude of the reflected echo. Setting the padding too low (e.g., to 1) produces a flatter peak than when padding is set to 8, leading to a poorer detection of the true peak in the reflected radar echo. It is thus possible to improve the signal definition ("apparent resolution") by optimizing these settings (see Figure 2). We also found that using interpolation techniques in order to find the true maximum between measured neighboring points increases the measurement accuracy. The true maximum near the measured maximum must be found in order to estimate the true distance between the radar and the target. Our best results were achieved by setting Tr = 1 ms and padding to 8. The method that improves the search for the true maximum is to perform a weighted average of distances between measured points, taking the maximum amplitude and its two immediate neighbors to obtain the intermediate position corresponding to this true maximum ( Figure 3).
The last aspect to consider is the offset in radar echo, which is hardware specific. We had to calibrate each model by measuring the echo for variable distance between the radar and a fixed target. Figure 3 illustrates such a calibration process, showing that, in this case, the systematic bias in the measured signal is 11.2 cm with a precision (standard deviation) of ±0.2 cm.
In practice, we found that an accuracy of about 2 cm can be achieved for ice thickness estimates over the radar resolution. An example of the improvement is illustrated in Figure 4, where the radar signal is shown in "optical distance" (i.e., distance relative to air). The mean derived ice thickness by setting the radar at Tr = 1 ms and padding = 8 was 18.2 ± 3.4 cm, which corresponds to using Equation (5) to reach 18.2/1.78 = 10.2 cm-lower than the true measured value. By applying the proposed interpolation method between measured maximums, the derived ice thickness is found to be 21.6 ± 0.5 cm, or using Equation (7): 21.6/1.78 = 12.1 cm, which is closer to the true measured value of 12.5 cm (Figure 4). Sensors 2020, 20, x FOR PEER REVIEW 9 of 29 Figure 3 illustrates such a calibration process, showing that, in this case, the systematic bias in the measured signal is 11.2 cm with a precision (standard deviation) of ± 0.2 cm.
(a) (b) In practice, we found that an accuracy of about 2 cm can be achieved for ice thickness estimates over the radar resolution. An example of the improvement is illustrated in Figure 4, where the radar signal is shown in "optical distance" (i.e., distance relative to air). The mean derived ice thickness by setting the radar at Tr = 1 ms and padding = 8 was 18.2 ± 3.4 cm, which corresponds to using Equation (5) to reach 18.2/1.78 = 10.2 cm-lower than the true measured value. By applying the proposed interpolation method between measured maximums, the derived ice thickness is found to be 21.6 ± 0.5 cm, or using Equation (7): 21.6/1.78 = 12.1 cm, which is closer to the true measured value of 12.5 cm ( Figure 4).   In practice, we found that an accuracy of about 2 cm can be achieved for ice thickness estimates over the radar resolution. An example of the improvement is illustrated in Figure 4, where the radar signal is shown in "optical distance" (i.e., distance relative to air). The mean derived ice thickness by setting the radar at Tr = 1 ms and padding = 8 was 18.2 ± 3.4 cm, which corresponds to using Equation (5) to reach 18.2/1.78 = 10.2 cm-lower than the true measured value. By applying the proposed interpolation method between measured maximums, the derived ice thickness is found to be 21.6 ± 0.5 cm, or using Equation (7): 21.6/1.78 = 12.1 cm, which is closer to the true measured value of 12.5 cm ( Figure 4).

Penetration Depth
The theoretical penetration depth (δP) of microwave radiation in an absorbing medium is linked to the frequency (ν) (wavelength, λ = c/ν) and its complex permittivity, which is temperature-sensitive. This is defined by [60]: The term on the right is an approximation often used when ε ε . Note that the penetration depth corresponds to the distance at which microwave power is reduced to 1/e (e = 2.718) from the ice or snow surface. This is not the maximum detection depth of the sensor.
For a 24 GHz radar through pure ice, if we consider the two-way radar signal time δP r = δP/2, Equation (11) yields δP r = −1.9298E-02 T + 6.0610, where T is the ice temperature (in Kelvin, see Appendix A). Going from 0 to -30 • C, δP r increases from 0.80 m to 1.57 m.
The radar penetration depth (δP r ) of dry snow significantly decreases with density, following a power law, which varies with temperature. At T = 0 • C, δP r decreases from 6.78 to 4.81, 3.26 and 2.05 m for densities of 150, 200, 275 and 400 kg m −3 , respectively. For a medium density of 275 kg m −3 , δP r increases from 3.26 to 4.78 and 6.38 cm at T = 0 • C, −20 • C and −40 • C, respectively (see Appendix A). The case of wet snow, which drastically reduces δP , is discussed in Section 5.

Operating Modes
The radar is generally controlled and operated with a field tough book or laptop loaded with the software provided by IMST. However, for several applications involving snow or ice monitoring over remote regions, we developed a light compact system with our own controller. The different components of the system, which allow on board signal processing, are described in Figure 5.
The term on the right is an approximation often used when ≪ . Note that the penetration depth corresponds to the distance at which microwave power is reduced to 1/e (e = 2.718) from the ice or snow surface. This is not the maximum detection depth of the sensor. For a 24 GHz radar through pure ice, if we consider the two-way radar signal time = /2, Equation (11) yields = −1.9298E-02 T + 6.0610, where T is the ice temperature (in Kelvin, see Appendix A). Going from 0 to -30 °C, increases from 0.80 m to 1.57 m. The radar penetration depth ( ) of dry snow significantly decreases with density, following a power law, which varies with temperature. At T = 0 °C, decreases from 6.78 to 4.81, 3.26 and 2.05 m for densities of 150, 200, 275 and 400 kg m −3 , respectively. For a medium density of 275 kg m −3 , increases from 3.26 to 4.78 and 6.38 cm at T = 0°, −20° and −40°C, respectively (see Appendix A). The case of wet snow, which drastically reduces , is discussed in Section 5.

Operating Modes
The radar is generally controlled and operated with a field tough book or laptop loaded with the software provided by IMST. However, for several applications involving snow or ice monitoring over remote regions, we developed a light compact system with our own controller. The different components of the system, which allow on board signal processing, are described in Figure 5. The radar is connected to a home-made printed circuit board (PCB) using Arduino© or to a Raspberry Pi © microcontroller and data logger. It is loaded with processing software allowing the automatic calculation of snow and ice thickness. Data are recorded on the memory board and/or sent wirelessly (via Bluetooth) to a smartphone or a tablet for real-time visualization of radar profiles and the measured snow water equivalent (SWE) or ice thickness. The system is powered by a small lithium-ion battery and can be switched to a deep sleep state, consuming less than 5 µW between two series of measurements. An audible or visual alarm can be included to warn if the system detects an ice thickness thinner than a critical value. A GPS receiver can be added to include geospatial information in the saved data but is not necessary for calculating SWE or ice thickness. An inclinometer added to the radar unit ensures that it is parallel to the surface target before beginning a series of measurements, and it filters valid data when the radar is moving. The radar is connected to a home-made printed circuit board (PCB) using Arduino © or to a Raspberry Pi © microcontroller and data logger. It is loaded with processing software allowing the automatic calculation of snow and ice thickness. Data are recorded on the memory board and/or sent wirelessly (via Bluetooth) to a smartphone or a tablet for real-time visualization of radar profiles and the measured snow water equivalent (SWE) or ice thickness. The system is powered by a small lithium-ion battery and can be switched to a deep sleep state, consuming less than 5 µW between two series of measurements. An audible or visual alarm can be included to warn if the system detects an ice thickness thinner than a critical value. A GPS receiver can be added to include geospatial information in the saved data but is not necessary for calculating SWE or ice thickness. An inclinometer added to the radar unit ensures that it is parallel to the surface target before beginning a series of measurements, and it filters valid data when the radar is moving.
The low cost of the IMST radar (€800 in 2018) and the use of an Arduino or Raspberry Pi © controller make this extremely reliable system a very cost-effective instrument. All processing is done on board automatically without human interaction. Two operating modes can be distinguished: The manual in situ mode and the continuous autonomous mode. For ice thickness measurements, the processing is the same for both modes with the following sequence: (1) Automatic detection of ice/water interface (last peak); (2) detection of the first peak encountered above the last peak, which corresponds to snow/ice if there is snow or air/ice if there is no snow; (3) detection of the first peak from the radar, which corresponds to the air/snow interface if there is snow, or to the air/ice interface if there is no snow; (4) comparison between (2) end (3) (whether or not there is snow); (5) distance calculation with peak position refinement (see Section 3.2); and (6) ice thickness retrieval.
For the SWE measurement, the processing sequence is different for the two operating modes, since the snow depth must be known. In manual in situ mode, the sequence is as follows: (1) Manually provide snow depth to the radar; (2) automatic detection of the air/snow interface (first reflection peak); (3) automatic detection of the snow/ground interface (last peak) (see Section 2.2); (4) distance calculation with peak position refinement (see Section 3.2); (5) retrieval of the average (bulk) refractive index; and (6) SWE calculation. In the continuous and autonomous measurement mode (snow monitoring station), the processing sequence only differs for the first step, where the measurement of snow depth is provided by a separate sensor (LiDAR or sonic).

Results: Radar Performance Tests
We tested the system performance using five operating modes for different applications, first for ice thickness (Sections 4.1 and 4.2), and then for snow (Sections 4.3-4.5): • In situ ice thickness: Manual in situ lake ice thickness measurements recorded by walking on the lake or from a stationary snowmobile. The system was not been tested on a moving snowmobile, although this is possible in a continuous recording mode.

•
Ice thickness measurements from a remotely piloted aircraft (RPA) system: A preliminary test was conducted to evaluate the potential of measuring ice thickness with the radar mounted on a RPA.

•
In situ SWE: The manual in situ snow water equivalent (SWE) measurement was based on known snow depth value, measured using an avalanche-type snow depth probe.

•
In situ snow density: We tested the system in particular conditions in Antarctica to assess temporal snow surface density fluctuations.

•
Monitoring SWE: Continuous automatic measurements of SWE evolution during the winter at a weather station. In this case, the radar measurements were combined with a synchronized and collocated automatic snow depth sensor (ultrasonic or LiDAR sensor).
Below, we present examples of results for these applications, showing the performance and limitations of the system. In each case, we describe the experimental protocol and the processing procedure to automatically determine the desired relevant parameter.

Shallow Ice Experiment from A Bridge
We first tested the effective resolution of the system for its shallow ice thickness limit. Measurements were performed from a bridge, with the radar pointing downward at approximately 5.5 m above the ice (Magog River bridge, Sherbrooke, QC, Canada, Figure 6). In Figure 6, the first peak at 1.4 m corresponds to an echo of the bridge structure. The distance between the two high peaks around 5.5 m gives an ice thickness estimate of 9 cm. The ice was too thin to be able to safely measure ice thickness exactly within the radar footprint, but ice thickness was confirmed on the riverbank. This experiment remains interesting as it demonstrates the radar's ability to measure ice thickness near the safe limit of around 10 cm (Canadian Red Cross recommendations, https://www.redcross.ca).
Sensors 2020, 20, x FOR PEER REVIEW 12 of 29 Figure 6. Relative radar signal amplitude (Y axis, starting from distance 0) measured from a bridge over ice at a height of 5.5 m. The width of the two peaks detected around 5.5 m correspond to 9 cm ice thickness.

In Situ Ice Thickness Measurements
A series of radar measurements were acquired along with in situ ice thickness measurements (holes in the ice) for a series of frozen lakes in different cold conditions, with and without snow. The

In Situ Ice Thickness Measurements
A series of radar measurements were acquired along with in situ ice thickness measurements (holes in the ice) for a series of frozen lakes in different cold conditions, with and without snow. The radar was pointed toward the ice at a height of 30 to 50 cm above the surface, with or without snow. Due to permittivity differences between media, the typical profile of relative radar signal amplitudes shows two peaks corresponding to the air/ice and ice/water interfaces without snow cover on ice.
In the presence of snow, an additional peak appears before those two peaks, corresponding to the air/snow, snow/ice and ice/water interfaces. An automatic peak detection algorithm was first applied to select all peaks above a threshold to avoid noise. The threshold given by the average of the whole profile gives the best results. We then retrieved the distance between the last peak (usually with the largest amplitude) and the peak before it. From Equation (5), the difference between these peak gives the ice thickness. Figure 7 illustrates the results of fully automatic ice thickness detection. At five different lakes in Québec Province, North-Eastern Canada, we took 35 measurements with collocated holes in the ice, always in cold conditions (dry ice surface). The measurements taken included "test dry ice" experiments (blue diamond symbol in Figure 7) showing deviations from the 1:1 line for some, which may have been caused by several factors such as poor detection of snow depth on the ice, perpendicular misalignment of the radar with the ice surface, or impure ice. Note that one experiment was conducted over ice thickness values of 0.72-0.83 m (Abitibi Lake, Northern Quebec, gray triangle in Figure 7) around (or over, depending on ice temperature) the limit of radar detection. Unfortunately, we observed water lenses in the ice at measured sites that attenuated the signal, i.e., increased the ice refractive index, leading to reduced measured ice thickness (Figure 7). Without these three biased points, the mean accuracy of the radar is confirmed to be 2 cm (root mean square error) with a bias of −0.4 cm (Figure 7).

Limitations of Ice Thickness Detection
When a thin film of liquid water is on the ice surface, the dielectric contrast between the air/water interface is strong, giving a marked first echo, but with strong absorption underneath as water absorbs the signal (high imaginary part of the permittivity). This leads to a weak, even invisible, echo from the bottom of the ice/water interface, making ice thickness measurements impossible. Another point that must be considered is that we assumed the ice was pure in the operational detection process. That will not be always the case, such as for "white" or "snow ice", which is a mix of frozen

Limitations of Ice Thickness Detection
When a thin film of liquid water is on the ice surface, the dielectric contrast between the air/water interface is strong, giving a marked first echo, but with strong absorption underneath as water absorbs the signal (high imaginary part of the permittivity). This leads to a weak, even invisible, echo from the bottom of the ice/water interface, making ice thickness measurements impossible. Another point that must be considered is that we assumed the ice was pure in the operational detection process. That will not be always the case, such as for "white" or "snow ice", which is a mix of frozen snow and ice caused by the freezing of wet snow on the lake ice's surface. White ice forms a less dense layer on top of "black" lake ice. As the refractive index of white ice can be significantly lower than pure ice, the apparent thickness measured by the radar is increased.

Ice Thickness Retrieval from Remotely Piloted Aircraft (RPA)
A remotely piloted aircraft (RPA) system can be very useful for monitoring thin ice at the beginning of the winter or over a large lake ice area. The compactness and low weight of the radar studied here allows it to be deployed on off-the-shelf commercial RPAs. A preliminary test was conducted in order to evaluate the performance of measuring ice thickness using the radar onboard a Phantom 2 ( Figure 8). In this test, the system included a GPS and an inclinometer for recording viewing angle variations ( Figure 5). The weight of the radar system, including battery, GPS, inclinometer and the control system (Arduino) was 480 g. The data were recorded on a micro-SD card. Weather conditions during the test flight were challenging, with a mean wind speed of 20 km/h (gusting up to 35 km/h) and air temperatures of −15°C. Nonetheless, we were able to successfully fly the RPA (Figure 9). A test stationary flight was first carried out at 2.5 m above the ice, giving a radar footprint of 1 m. Four flight lines (L1 to L4) were then followed at a mean altitude of about 5 m (not measured; note that for the IMST Radar Module, the maximum measurement range capability corresponds to = ( ⁄ ) = 30.7 m). Eight holes were drilled through the ice to measure thickness across the studied area to validate the results. Ice thickness varied from 50 cm to 0 cm near the lake's edge. Weather conditions during the test flight were challenging, with a mean wind speed of 20 km/h (gusting up to 35 km/h) and air temperatures of −15 • C. Nonetheless, we were able to successfully fly the RPA (Figure 9). A test stationary flight was first carried out at 2.5 m above the ice, giving a radar footprint of 1 m. Four flight lines (L1 to L4) were then followed at a mean altitude of about 5 m (not measured; note that for the IMST Radar Module, the maximum measurement range capability corresponds to R max = c (1024/4) B = 30.7 m). Eight holes were drilled through the ice to measure thickness across the studied area to validate the results. Ice thickness varied from 50 cm to 0 cm near the lake's edge.
An example of data recorded during the stationary flight is illustrated in Figure 8. It shows significant fluctuations in the retrievals (blue line), including strong drop-out values. These values relate to the difficulties in identifying the right echoes of the ice surface, ice bottom or both. Overlaying the synchronous viewing angle record (orange signal in Figure 10) with the measurements revealed the RPA's relatively important motion variations (pitch, yaw, roll) and the poor correlation between the measured fluctuations in derived ice thickness and the off-nadir viewing angle variation. It was difficult to define an objective data quality threshold. More experiments are needed to better determine the appropriate filters. Here, we applied an arbitrary threshold of 20 • to off-nadir viewing angles and smoothed the retrieval with a median mobile filter (purple line in Figure 8). Weather conditions during the test flight were challenging, with a mean wind speed of 20 km/h (gusting up to 35 km/h) and air temperatures of −15°C. Nonetheless, we were able to successfully fly the RPA (Figure 9). A test stationary flight was first carried out at 2.5 m above the ice, giving a radar footprint of 1 m. Four flight lines (L1 to L4) were then followed at a mean altitude of about 5 m (not measured; note that for the IMST Radar Module, the maximum measurement range capability corresponds to = ( ⁄ ) = 30.7 m). Eight holes were drilled through the ice to measure thickness across the studied area to validate the results. Ice thickness varied from 50 cm to 0 cm near the lake's ede. An example of data recorded during the stationary flight is illustrated in Figure 8. It shows significant fluctuations in the retrievals (blue line), including strong drop-out values. These values relate to the difficulties in identifying the right echoes of the ice surface, ice bottom or both. Overlaying the synchronous viewing angle record (orange signal in Figure 10) with the measurements revealed the RPA's relatively important motion variations (pitch, yaw, roll) and the poor correlation between the measured fluctuations in derived ice thickness and the off-nadir viewing angle variation. It was difficult to define an objective data quality threshold. More experiments are needed to better determine the appropriate filters. Here, we applied an arbitrary threshold of 20° to off-nadir viewing angles and smoothed the retrieval with a median mobile filter (purple line in Figure 8). For the test stationary flight, the mean RPA-based ice thickness was 39.3 cm, compared to the in situ ice thickness of 39 ± 0.5 cm. The results for the four flight lines (L1 to L4) are shown in Figure 11. They clearly show that the RPA captured the spatial variation in ice thickness, from 50 cm along L1 on the lake edge (blue points in Figure 11) to about 25 cm along L2 and L3, and to open water (near the buoy, red star in Figure  11). The mean RMSE between the RPA-based and in situ measurements for seven points (no RPA measurements for one validation point) is 12 cm. However, near the lake's edge at the end of L1, clear disagreements are apparent for two points, where we observed the presence of liquid water trapped in the ice and because the ice extended down to the lake bottom (ice/water interface not detectable). For the test stationary flight, the mean RPA-based ice thickness was 39.3 cm, compared to the in situ ice thickness of 39 ± 0.5 cm.
The results for the four flight lines (L1 to L4) are shown in Figure 11. They clearly show that the RPA captured the spatial variation in ice thickness, from 50 cm along L1 on the lake edge (blue points in Figure 11) to about 25 cm along L2 and L3, and to open water (near the buoy, red star in Figure 11). The mean RMSE between the RPA-based and in situ measurements for seven points (no RPA measurements for one validation point) is 12 cm. However, near the lake's edge at the end of L1, clear disagreements are apparent for two points, where we observed the presence of liquid water trapped in the ice and because the ice extended down to the lake bottom (ice/water interface not detectable).
RPA captured the spatial variation in ice thickness, from 50 cm along L1 on the lake edge (blue points in Figure 11) to about 25 cm along L2 and L3, and to open water (near the buoy, red star in Figure  11). The mean RMSE between the RPA-based and in situ measurements for seven points (no RPA measurements for one validation point) is 12 cm. However, near the lake's edge at the end of L1, clear disagreements are apparent for two points, where we observed the presence of liquid water trapped in the ice and because the ice extended down to the lake bottom (ice/water interface not detectable). Figure 11. Ice thickness spatial distribution (colors) from in situ measurements (squares) and RPAbased radar data (circles) overlaid on a summer aerial photo. The red star shows the buoy that delimited the open water (see Figure 9). L1 to L4 correspond to the four different RPA flights. The Figure 11. Ice thickness spatial distribution (colors) from in situ measurements (squares) and RPA-based radar data (circles) overlaid on a summer aerial photo. The red star shows the buoy that delimited the open water (see Figure 9). L1 to L4 correspond to the four different RPA flights. The experiment was performed off Pointe-Merry Park, on the right, on Lake Memphremagog, Québec, Canada.
Without these two points, the RMSE becomes 1.6 cm with a weak bias of 0.2 cm. This agreement corresponds to the accuracy derived from in situ measurements (previous section). Despite the limited flight time of this test experiment, these results appear very promising. The RPA-based approach allowed ice thickness measurements where it was too thin to support a person's weight (yellow-red zones in Figure 11).

In Situ Snow Water Equivalent (SWE)
In this section we present a series of tests to evaluate the accuracy of the FMCW system when used in fully automatic mode without any intervention in the retrieval of the measured signal. With the radar pointed toward the snow cover (as in Figure 1), preliminary tests showed that it is sometimes difficult to automatically identify the peak corresponding to the snow/soil interface (P max ). Knowing the snow depth measured with a snow depth probe, we improved the retrieval by searching for the approximate distance of P' max assuming a mean permittivity value (first guess). We then located the exact position of P max within a search zone around the first guess (red zone in Figure 1) and derived the true mean permittivity and then calculated the SWE value using Equation (8).
In the following examples, we put a metallic plate on the ground beneath the snowpack to accentuate the snow/soil interface signal, as it increases the snow/plate permittivity contrast. Figure 12 illustrates a measured radar signal over a 237 cm-thick dry snowpack. It is used as an example to describe the automatic retrieval processing. The maximum detection algorithm identified the first peak after 0 as the starting point (position of the radar), the second peak as the air/snow interface and the last peak as the snow/plate interface. The derived radar distance h radar,snow between the top and the bottom of the snowpack allowed the estimation of the mean permittivity when the snow depth was known, and then the snow water equivalent (SWE) was calculated using Equation (11). The radar-based SWE was then compared to the SWE derived from a collocated snowpit with measured density using a 250 cm 3 (5 cm) density cutter, and with samples weighed using an electronic balance with an accuracy of 0.1 g. The accuracy of the density cutter measurements is about 9% [61] giving an approximate relative SWE accuracy of 11-12%. In Figure 10, from the radar distance estimate (298 cm) and measured snow depth (237 cm), we deduced a 738 mm SWE (Equation (11)), compared to 748 mm from the in situ snowpit measurements (−1.3% difference).
the last peak as the snow/plate interface. The derived radar distance ℎ , between the top and the bottom of the snowpack allowed the estimation of the mean permittivity when the snow depth was known, and then the snow water equivalent (SWE) was calculated using Equation (11). The radar-based SWE was then compared to the SWE derived from a collocated snowpit with measured density using a 250 cm 3 (5 cm) density cutter, and with samples weighed using an electronic balance with an accuracy of 0.1 g. The accuracy of the density cutter measurements is about 9% [61] giving an approximate relative SWE accuracy of 11-12%. In Figure 10, from the radar distance estimate (298 cm) and measured snow depth (237 cm), we deduced a 738 mm SWE (Equation (11)), compared to 748 mm from the in situ snowpit measurements (−1.3% difference).

Figure 12.
Measured relative radar amplitude signal over dry snowpack (snow depth of 237 cm). The right-most peak, at a distance of 298 cm (snow/plate interface) from the radar, allowed us to estimate Figure 12. Measured relative radar amplitude signal over dry snowpack (snow depth of 237 cm). The right-most peak, at a distance of 298 cm (snow/plate interface) from the radar, allowed us to estimate the mean snow permittivity when the measured snow depth was known (Equation (8)). Intermediate peaks correspond to layering within the snowpack (see Discussion).
A series of radar measurements over dry snowpack was compared to in situ SWE measurements over a large range of conditions (snow depth and density) in boreal forest (47 • N, 18 points), subarctic taiga (54-56 • N, 32 points) and Arctic tundra (69 • N, 28 points) zones along a North-Eastern Canada latitudinal transect. Results are shown in Figure 13, giving an overall accuracy of 30% (RMSE of 59 mm) and relative error (Abs(Bias)/mean SWE) of 20%. Six obvious outliers (6 points with bias > 2 × mean) correspond to measurements with weak bottom peak detection amplitudes. The misdetection of these peaks was generally due to the inclination of the plate in relation to the radar position. By applying a quality control check based on a threshold on this bottom amplitude peak, we reduced the RMSE to 20% and relative error to 13%, in the range of the relative accuracy of the in situ snowpit measurement.
Sensors 2020, 20, x FOR PEER REVIEW 17 of 29 the mean snow permittivity when the measured snow depth was known (Equation (8)). Intermediate peaks correspond to layering within the snowpack (see Discussion).
A series of radar measurements over dry snowpack was compared to in situ SWE measurements over a large range of conditions (snow depth and density) in boreal forest (47°N, 18 points), subarctic taiga (54-56°N, 32 points) and Arctic tundra (69°N, 28 points) zones along a North-Eastern Canada latitudinal transect. Results are shown in Figure 13, giving an overall accuracy of 30% (RMSE of 59 mm) and relative error (Abs(Bias)/mean SWE) of 20%. Six obvious outliers (6 points with bias > 2 × mean) correspond to measurements with weak bottom peak detection amplitudes. The misdetection of these peaks was generally due to the inclination of the plate in relation to the radar position. By applying a quality control check based on a threshold on this bottom amplitude peak, we reduced the RMSE to 20% and relative error to 13%, in the range of the relative accuracy of the in situ snowpit measurement.
In conclusion, these radar-based automatic SWE retrievals, optimized with a metallic plate beneath the snowpack, were in very good agreement with in situ measurements and achieved the same RMSE. However, it is important to note that, after the first reflection at the air-snow interface (first peak), the metal plate reflector makes it possible to identify the distance from the bottom without ambiguity [32]. Without the plate, the bottom echo is sometimes not visible or very weak, requiring more sophisticated methods of signal recognition or visual checking of each measurement. Figure 13. Radar-based automatic SWE estimates used with a snow depth probe compared to in situ SWE measurements (snowpit) from five field campaigns in North-Eastern Canada over dry snowpack.

In Situ Density Monitoring in Antarctica
An original experiment was carried out in Antarctica with the FMCW radar to monitor, for the first time, the continuous evolution of surface snow density. The deployment was performed in 2018, Figure 13. Radar-based automatic SWE estimates used with a snow depth probe compared to in situ SWE measurements (snowpit) from five field campaigns in North-Eastern Canada over dry snowpack.
In conclusion, these radar-based automatic SWE retrievals, optimized with a metallic plate beneath the snowpack, were in very good agreement with in situ measurements and achieved the same RMSE. However, it is important to note that, after the first reflection at the air-snow interface (first peak), the metal plate reflector makes it possible to identify the distance from the bottom without ambiguity [32]. Without the plate, the bottom echo is sometimes not visible or very weak, requiring more sophisticated methods of signal recognition or visual checking of each measurement.

In Situ Density Monitoring in Antarctica
An original experiment was carried out in Antarctica with the FMCW radar to monitor, for the first time, the continuous evolution of surface snow density. The deployment was performed in 2018, starting on January 6 at the French-Italian Dome Concordia station on the East Antarctica Plateau (Dome C, 75 • S, 123 • E). The mean annual snow accumulation is exceptionally low at Dome C (8-10 cm/yr), with very low short-term snow depth variability in the order of a few cm. The only apparent variations in surface density are linked to wind variability, and year-to-year variability is remarkably low, except for specific short storm events [62].
The radar and a snow depth sensor (Campbell Scientific®, Edmonton, Canada SRAT50) were installed on a horizontal mast at 1.5 m above the snow (Figure 14), giving a radar footprint of approximately 0.64 m. In this experiment, the radar was controlled with an Arduino card because of its lower power consumption when compared to a RaspBerry Pi© controller (Raspberry Pi Foundation, 37 Hills Road, Cambridge, CB2 1NT, UK). The measurements were acquired with a time step of 10 min. Unfortunately, the system began to have operating problems on January 26 and failed when air temperature dropped to −50 • C on April 30, 2018. This failure was likely due to Arduino's operating temperature limit. In situ density measurements were taken regularly in the vicinity of the radar spot, over the first 5 cm surface layer at five nearby sites every day. The mean air temperature during the experiment was −29 • C (from −16 to −44 • C).
Sensors 2020, 20, x FOR PEER REVIEW 18 of 29 approximately 0.64 m. In this experiment, the radar was controlled with an Arduino card because of its lower power consumption when compared to a RaspBerry Pi© controller (Raspberry Pi Foundation, 37 Hills Road, Cambridge, CB2 1NT, UK). The measurements were acquired with a time step of 10 min. Unfortunately, the system began to have operating problems on January 26 and failed when air temperature dropped to −50°C on April 30, 2018. This failure was likely due to Arduino's operating temperature limit. In situ density measurements were taken regularly in the vicinity of the radar spot, over the first 5 cm surface layer at five nearby sites every day. The mean air temperature during the experiment was −29°C (from −16 to −44°C). Figure 15 shows a sample of recorded values over the first month. The mean snow height variation above the plate was 28.5 ± 0.5 cm, with a variation of ± 12 cm between the maximum (34 cm) and minimum (31 cm) in the month of January. These values are slightly higher than mean surface elevation changes measured with a laser scan sensor deployed in 2015 at Dome C [62], giving 10-15 cm for the months of December and January. Differences in snow elevation could be explained by the difference in footprint size between the laser scan (10 × 10 m 2 ) and the radar (less than 1 × 1 m 2 ), with the former possibly smoothing frequent changes in surface shape caused by redistribution.
The mean radar-based density was 346 ± 10 kg m −3 , ranging from 378 to 291 kg m −3 (Figure 15), in agreement with the measured in situ density variation, which had a range of 353 to 285 kg m −3 for the upper 5 cm of the snow surface during the period. The spatial variability of the five measurements per site (±42 kg m −3 ) was slightly higher than the temporal variability (±26 kg m −3 ) over the period analyzed ( Figure 15). This range of variability was also measured in January 2014 along several hectometer scale transects around Dome C. It was shown that the observed surface density variations result from wind-formed features (dunes), alternating between dense/hard (434 kg m −3 ) and light/loose (372 kg m −3 ) snow areas over the first 35 cm [63]. While these observations were not made in the same year, such typical behavior is always present [62].
In conclusion, this preliminary experimental test at Dome C shows very interesting potential for continuous surface snow density monitoring. However, further work is needed to improve the robustness of the system. In the broader context of better knowledge of snow surface processes in Antarctica, such as the unknown trend of surface density change over the East Antarctic Plateau derived from satellite data [64], this approach appears to be a promising cost-effective tool for a network and to achieve year-round monitoring.  Figure 15 shows a sample of recorded values over the first month. The mean snow height variation above the plate was 28.5 ± 0.5 cm, with a variation of ± 12 cm between the maximum (34 cm) and minimum (31 cm) in the month of January. These values are slightly higher than mean surface elevation changes measured with a laser scan sensor deployed in 2015 at Dome C [62], giving 10-15 cm for the months of December and January. Differences in snow elevation could be explained by the difference in footprint size between the laser scan (10 × 10 m 2 ) and the radar (less than 1 × 1 m 2 ), with the former possibly smoothing frequent changes in surface shape caused by redistribution.

Continuous and Autonomous SWE Measurements
A fixed radar station system was developed for automated continuous winter SWE monitoring and was installed in a boreal environment at Forêt Montmorency research station (NEIGE-FM) (47°19′0′′N; 71°9′5′′W). This snow research station is part of the World Meteorological Organization (WMO) Global Cryosphere Watch (GCW) Surface Network CryoNet (WMO ID: 71212) [5]. The setup requirements included a precise fixed distance between the radar and the reference target (plate) on the ground, and an additional sensor to measure the snow depth as close as possible to the radar footprint. Snow depth measurements were acquired by an SR50AT sonic sensor from Campbell Scientific Canada® (Edmonton, AB, Canada). The radar was placed at a height of 3 m in an assembly with the plate welded to the mast (rigid frame) to maintain a constant distance between them, even when freeze/thaw effects caused ground heaving. The radar footprint was 1.3 m, but a plate size of 0.60 × 0.60 m was enough to enable a clear bottom echo. In this experiment, the radar time acquisition frequency was set at 6 h to optimize the power consumption from its lead battery (no solar panels were used). The radar-based SWE values, processed by the in-system processor, were automatically transferred along with other data (snow depth, radar profile, air temperature-Tair) every day via a cellular telephone connection. In order to validate the radar measurements, a gamma ray SWE sensor was installed at about 3 m from the radar (GMON-CS725 sensor from Campbell Scientific Canada ® , with a footprint of 7-10 m and a time acquisition frequency of 6 h) [16,65]. Snowpit and snow core measurements were also performed throughout the winter in the vicinity of the sensors. Figure 16 shows a comparison of a sample time series of SWE variation retrieved from the radar and GMON sensors. Results show strong agreement between these sensors during the dry snow period, and both were in the range of in situ measurements. In situ measurements showed high variability due to spatial variation of the snowpack in the area surrounding the GMON-radar site. For the dry snow period (identified with negative mean daily maximum air temperature, red line in Figure 16), the observed radar-based SWE fluctuations can be explained by several factors: Radar The mean radar-based density was 346 ± 10 kg m −3 , ranging from 378 to 291 kg m −3 (Figure 15), in agreement with the measured in situ density variation, which had a range of 353 to 285 kg m −3 for the upper 5 cm of the snow surface during the period. The spatial variability of the five measurements per site (±42 kg m −3 ) was slightly higher than the temporal variability (±26 kg m −3 ) over the period analyzed ( Figure 15). This range of variability was also measured in January 2014 along several hectometer scale transects around Dome C. It was shown that the observed surface density variations result from wind-formed features (dunes), alternating between dense/hard (434 kg m −3 ) and light/loose (372 kg m −3 ) snow areas over the first 35 cm [63]. While these observations were not made in the same year, such typical behavior is always present [62].
In conclusion, this preliminary experimental test at Dome C shows very interesting potential for continuous surface snow density monitoring. However, further work is needed to improve the robustness of the system. In the broader context of better knowledge of snow surface processes in Antarctica, such as the unknown trend of surface density change over the East Antarctic Plateau derived from satellite data [64], this approach appears to be a promising cost-effective tool for a network and to achieve year-round monitoring.

Continuous and Autonomous SWE Measurements
A fixed radar station system was developed for automated continuous winter SWE monitoring and was installed in a boreal environment at Forêt Montmorency research station (NEIGE-FM) (47 • 19 0 N; 71 • 9 5 W). This snow research station is part of the World Meteorological Organization (WMO) Global Cryosphere Watch (GCW) Surface Network CryoNet (WMO ID: 71212) [5]. The set-up requirements included a precise fixed distance between the radar and the reference target (plate) on the ground, and an additional sensor to measure the snow depth as close as possible to the radar footprint. Snow depth measurements were acquired by an SR50AT sonic sensor from Campbell Scientific Canada ® (Edmonton, AB, Canada). The radar was placed at a height of 3 m in an assembly with the plate welded to the mast (rigid frame) to maintain a constant distance between them, even when freeze/thaw effects caused ground heaving. The radar footprint was 1.3 m, but a plate size of 0.60 × 0.60 m was enough to enable a clear bottom echo. In this experiment, the radar time acquisition frequency was set at 6 h to optimize the power consumption from its lead battery (no solar panels were used). The radar-based SWE values, processed by the in-system processor, were automatically transferred along with other data (snow depth, radar profile, air temperature-T air ) every day via a cellular telephone connection. In order to validate the radar measurements, a gamma ray SWE sensor was installed at about 3 m from the radar (GMON-CS725 sensor from Campbell Scientific Canada ® , with a footprint of 7-10 m and a time acquisition frequency of 6 h) [16,65]. Snowpit and snow core measurements were also performed throughout the winter in the vicinity of the sensors. Figure 16 shows a comparison of a sample time series of SWE variation retrieved from the radar and GMON sensors. Results show strong agreement between these sensors during the dry snow period, and both were in the range of in situ measurements. In situ measurements showed high variability due to spatial variation of the snowpack in the area surrounding the GMON-radar site. For the dry snow period (identified with negative mean daily maximum air temperature, red line in Figure 16), the observed radar-based SWE fluctuations can be explained by several factors: Radar acquisition is instantaneous every 6 h, while GMON has an integrated value over 6 h, thus the former captures short snow variations particularly during snowfall or strong wind events (e.g., the significant decrease in snow depth on January 29, 2017); the slight differences in location between GMON and radar positions could produce snow depth differences; and the formation of ice crust caused by wet snow refreezing on top of the snowpack after rain events. These short fluctuations can be smoothed over one or two days. Throughout the dry snow period, the SWE root mean square difference (RMSD) between radar and GMON sensors was 25.4 mm (10%), with a mean relative bias of 13.5%.
Sensors 2020, 20, x FOR PEER REVIEW 20 of 29 captures short snow variations particularly during snowfall or strong wind events (e.g., the significant decrease in snow depth on January 29, 2017); the slight differences in location between GMON and radar positions could produce snow depth differences; and the formation of ice crust caused by wet snow refreezing on top of the snowpack after rain events. These short fluctuations can be smoothed over one or two days. Throughout the dry snow period, the SWE root mean square difference (RMSD) between radar and GMON sensors was 25.4 mm (10%), with a mean relative bias of 13.5%. However, as soon as the snow became wet relative to the maximum air temperature, stronger attenuation in the microwave signal occurred, and the radar retrieval was biased, leading to radarbased SWE underestimation. This is clearly apparent during warm episodes (February 22 to March 1) and at the end of the season (melting onset on April 1, 2017) ( Figure 16). While the melting onset could be flagged and eliminated when Tair becomes positive, the retrieval algorithm for wet snow could also be improved (see Discussion). In conclusion, automatic radar-based SWE monitoring of dry snowpack can be achieved with common standard accuracy-typically 10-15%-with the set-up described above, particularly when combined with a snow depth sensor (ultrasonic or LiDAR) and a metallic plate on the ground to increase the snow/plate permittivity contrast. The strong limitation to the continuous winter-long use of the radar is that melting snow can be flagged with coincident temperature measurements. However, as soon as the snow became wet relative to the maximum air temperature, stronger attenuation in the microwave signal occurred, and the radar retrieval was biased, leading to radar-based SWE underestimation. This is clearly apparent during warm episodes (February 22 to March 1) and at the end of the season (melting onset on April 1, 2017) ( Figure 16). While the melting onset could be flagged and eliminated when T air becomes positive, the retrieval algorithm for wet snow could also be improved (see Discussion).
In conclusion, automatic radar-based SWE monitoring of dry snowpack can be achieved with common standard accuracy-typically 10-15%-with the set-up described above, particularly when combined with a snow depth sensor (ultrasonic or LiDAR) and a metallic plate on the ground to increase the snow/plate permittivity contrast. The strong limitation to the continuous winter-long use of the radar is that melting snow can be flagged with coincident temperature measurements.

Discussion
One of the main limitations of the radar is the presence of liquid water on ice or in the snowpack. Liquid water strongly absorbs the radar signal, leading to a high reflectivity at the air/water or air/wet snow interface and a weak transmissivity. When the liquid water content (LWC, in volume fraction, %) in snow increases, the effective refractive index of wet snow (n sw ) increases, but the two-way radar penetration depth (δP r , m) decreases abruptly from 2 m (dry snow) to 0.05 m for LWC ≈0.5% at a density of 400 kg m −3 ( Figure A3 in Appendix A). In order to analyze the radar response during the beginning of a melting period (Figure 17), we simulated SWE (orange dots) decreasing with LWC (%, bottom axis), and overlaid it with the radar-based (blue cross) and GMON-based (black dots) SWE measurements according to the thawing degree-days (TDD) (sum of positive maximum air temperature computed from the maximum measured SWE) (top horizontal axis). TDD values start at 30 degree-days corresponding to the continuous melting onset (Figure 17). No LWC measurements were available. This comparison between measured and simulated SWE during the melting period can be explained by the fact that LWC is not homogenously vertically distributed over the snowpack, as assumed in simulations. Results suggest that a threshold could be applied on radar measurements based on TDD to detect the onset of the melting period. Further studies (in progress) are needed to quantify the LWC effects on radar response and to improve early snow melting detection, i.e., LWC < 1%. Theoretical values of the wet snow refractive index and radar penetration depth as a function of LWC given in Appendix A could be useful for this purpose.
Another limitation is the formation of an ice crust resulting either from short episodes of warmth (thawing/freezing of snow surface) or from rapid refreeze after rain-on-snow events or freezing rain events. These weather episodes, which are becoming increasingly frequent with global warming, bias the radar signal retrieval. A high-density ice crust could generate a strong wave reflection and mask the bottom of the snowpack. Furthermore, internal reflectors, such as refrozen melt water, can be embedded in the ice and result in an ice lens that reduces wave propagation, thus altering the retrieval [66].
Lastly, the snowpack is usually stratified in several layers of different densities, creating a series of clearly visible echoes at each interface with a higher permittivity than the layer above (see examples in Figures 1 and 12). This makes it possible to analyze the stratification of the mantle, a particularly interesting application for avalanche prediction (e.g., [32,37,44,46]).
were available. This comparison between measured and simulated SWE during the melting period can be explained by the fact that LWC is not homogenously vertically distributed over the snowpack, as assumed in simulations. Results suggest that a threshold could be applied on radar measurements based on TDD to detect the onset of the melting period. Further studies (in progress) are needed to quantify the LWC effects on radar response and to improve early snow melting detection, i.e., LWC < 1%. Theoretical values of the wet snow refractive index and radar penetration depth as a function of LWC given in Appendix A could be useful for this purpose. Another limitation is the formation of an ice crust resulting either from short episodes of warmth (thawing/freezing of snow surface) or from rapid refreeze after rain-on-snow events or freezing rain events. These weather episodes, which are becoming increasingly frequent with global warming, bias the radar signal retrieval. A high-density ice crust could generate a strong wave reflection and mask the bottom of the snowpack. Furthermore, internal reflectors, such as refrozen melt water, can be embedded in the ice and result in an ice lens that reduces wave propagation, thus altering the retrieval [66].
Lastly, the snowpack is usually stratified in several layers of different densities, creating a series of clearly visible echoes at each interface with a higher permittivity than the layer above (see examples in Figures 1 and 12). This makes it possible to analyze the stratification of the mantle, a particularly interesting application for avalanche prediction (e.g., [32,37,44,46]).
Within a multilayer (multi-reflectors) snowpack, the amplitude Â of the measured beat signal of the i-th interface is proportional to the magnitude | | of the i-th reflection coefficient, which also depends on the reflection coefficients of the i − 1 preceding interfaces and on the transmission loss factor : For thin layers, reflectivity is a function of frequency due to constructive and destructive interferences. In our case, the FMCW radar operated from 23 to 25.5 GHz, i.e., in a range of wavelengths from 1.1 to 0.97 cm in snow. For layers that are much thicker than the wavelength, the Within a multilayer (multi-reflectors) snowpack, the amplitude Â of the measured beat signal of the i-th interface is proportional to the magnitude |r i | of the i-th reflection coefficient, which also depends on the reflection coefficients of the i − 1 preceding interfaces and on the transmission loss factor L i : For thin layers, reflectivity is a function of frequency due to constructive and destructive interferences. In our case, the FMCW radar operated from 23 to 25.5 GHz, i.e., in a range of wavelengths from 1.1 to 0.97 cm in snow. For layers that are much thicker than the wavelength, the reflectivity depends only on the relative dielectric contrast at the interface, while for layers which have a thickness much smaller than the wavelength, the reflectivity depends upon the layer thickness. Further analyses with special attention to frequency, absorption and propagation velocity within those multiple reflections are needed to interpret such signal features.

Summary and Conclusions
We presented a low cost, compact and lightweight (under 500 g with battery) 24 GHz FMCW radar, commercialized by IMST (IMST, 2019). Plugged into a Raspberry Pi© or Arduino controller, and with a wireless connection to a mobile phone or a handheld PC, this near-turnkey system is easy to implement and is highly adaptable for several uses. Improved distance detection was obtained by optimizing radar settings and applying simple signal processing based on finding the true maximum around the measured maximum (weighted average calculation of the distance between the maximum and its two closest neighbors). The capabilities of the FMCW radar for ice thickness and snow cover monitoring have long been known, but retrievals have rarely been automated. Here, we tested the performance and limitations of this small IMST radar in five different operational applications with different operating modes: (1) In situ lake ice thickness measurements give a 2 cm accuracy above a 4 cm resolution limit and can measure up to 1 m of ice. The safety limit to support a man on ice is approximately 10 cm. These results were obtained assuming pure ice and for dry ice with and without a dry snow cover.
However, as soon as water is present, detection is no longer possible, which is a well-known limitation of the radar system at these high frequencies.
(2) We show that this radar can be put onboard a light remotely piloted aircraft (here a Phantom 2 quadcopter) for lake ice thickness measurements from low-altitude flight (5 m). This enables surveys of, for example, unsafe thin ice and long river transects.
(3) In situ radar measurements were carried out with a joint measurement of snow depth (e.g., with an avalanche probe) to derive the mean density and the snow water equivalent (SWE) for a dry snowpack. For sets of very different snow measurements (boreal, subarctic and arctic snow), a very good overall average accuracy of 13% (RMSE 20%) was achieved by putting a metallic plate on the ground beneath the snow to increase bottom detection. Without this plate, the snow/ground interface was less detectable, which makes SWE estimation much less efficient, making more refined peak detection algorithm necessary. We showed that this radar is capable of dry SWE measurements of snowpacks up to 3 m thick (SWE up to 800-1000 mm).
(4) In the unique conditions of the Eastern Antarctic Plateau, where snow height variations are extremely low through the year (snow accumulation < 10 cm), we successfully tested continuous and automatic tracking of surface snow density over the first 30 cm. This original experiment gave a relative bias of 15 kg m −3 (4%) when compared to only five validation points with significant spatial variability (13%) over a period of one month. Further studies are needed to validate this experiment.
(5) The last experiment we tested was continuous and autonomous winter-long SWE monitoring with a collocated and synchronized snow depth sensor (ultrasonic or LiDAR sensor). Results show a low 13.5% bias and 25 mm RMSD (10%) for the dry snow period, compared to a gamma ray SWE sensor (GMON-CS725 sensor from Campbell Scientific Canada ® ). It must be noted, however, that since SWE data is biased by wet snow, a snowmelt detection algorithm is needed. Numerical simulations of SWE variations according to the liquid water content in snow show the high sensitivity of the radar to the melting process.
In controlled manual operating mode, we conclude that the observed capabilities of this radar in different applications and environments, including arduous climatic conditions, make this an extremely reliable system and cost-effective instrument. However, in an autonomous and continuous operating mode, unfavorable operational conditions outside the limits of radar use may occur, such as for ice and wet snow conditions. In these cases, care must be taken to avoid misinterpretation of the measured signal. Table A1. Relationship between the refractive index and radar penetration depth for ice, dry snow and wet snow. Fits were derived based on SMRT code permittivity values [67]. Note that some of them are unit dependent. See Figures A1-A3

Appendix B. FMCW Radar Simplified Link Budget
The simplified link budget for the snow-to-air reflection is defined here for a homogenous snowpack with an ideal smooth surface. The received power were estimated by the radar equation: where G is the antenna gain, hi is the reflection distance, λ is the wavelength and σ is the radar cross-section. We used the permittivity of dry snow density provided in Appendix A and calculated the reflection coefficients r i for the snow/air interface using Equation (2), expressed in dB: Their corresponding return losses resulted in −29 dB and −15.4 dB for snow density values of 100 kg m −3 and 500 kg m −3 , respectively.
The radar cross section can be derived from the relation (A4) [69]: where the incidence angle α(h i ) is estimated by tan 2 (α(h i )) ≈ δh 2h i with the distance resolution δh (Equation (10)). For a mean transmitted frequency of 24 GHz and a reflection distance of 1 m, the resulting cross section is ≈12.4 m 2 . Considering the RF power between 0 dBm to 9 dBm and antenna gains G of 10 dB, the P RX i power is -40 dB to -31 dB including the free space loss.
The total estimated budget including losses from snow reflection is therefore in the range of −69 dB (worst case) to −46.4 dB (best case). However, this link budget is valid for clear atmospheric conditions and homogeneous snowpack.