Three intensive measurement periods were conducted during the 2013 winter season in the James Bay area, Québec (8–12 January: JBJan; 12–17 February: JBFeb; 19–23 March: JBMar; Tables 1, 2 and 3). The sites were in a typical boreal forest environment, but most of the measurements were conducted in clearings with minimal influence of the environment (topography, vegetation) on the measured TB. However, 15 measurements, spanning across the three campaigns, were conducted in forested areas and were treated separately to specifically investigate the contribution of vegetation on the ground-based measurements (Table 4). Several snow excavation experiments (denoted SEex) were also conducted where snow was removed to measure frozen ground emission. During SEex, large snow pits were dug (about 3 m × 3 m wide) and the snow walls removed to eliminate snow wall emission reflected on the ground. At all sites, the soil (described below) was frozen at least to a depth of 10 cm.

During the JBJan campaign, 16 open-area sites were measured where the mean ρsnow (weighted by snow layers thickness excluding ice lenses) of all snow pits was 218.3 kg m-3 and the mean Ropt (weighted by snow layers thickness excluding ice lenses) was 0.17 mm (Table 1). Snow pits JBJan-1 to JBJan-5 were located in forest clearings where the soil composition mainly consisted of organic matter. On 9 January, a transect of 11 snow pits (JBJan-6.1 to JBJan-6.11, each separated by 3 m) was conducted in an old gravel pit (mostly mineral soil). Five SEex were also conducted in the 30 m transect. One to two ice lenses of about 0.5 to 1 cm were observed in all snow pits, buried at depths of 10 and 30 cm.

Nine snow pits were dug during the February campaign (Table 2), with a mean ρsnow of 225.2 kg m-3 and a mean Ropt of 0.18 mm. All snow pits were conducted in clearings with frozen organic soil. On 15 February, for a transect of seven snow pits, a complete set of measurements was taken for each snow pit. An ice lens at a depth of 30 cm was observed at each snow pit. In addition to snow pit measurements, two SEex were conducted in the transect and two others in JBFeb-1 and JBFeb-2.

During the March campaign, five snow pits with a mean ρsnow of 278 kg m-3 and mean Ropt of 0.26 mm were dug (Table 3). There is a clear increase (70 %) of grain size in March, linked to a strong temperature gradient metamorphism regime typical of such environments. On 22 March, a transect of three snow pits was conducted in a clearing with frozen organic soil.

Measurements were also conducted in a forested area (Table 4), where the emission of the trees that is reflected on the ground contributes to the measured TB (Roy et al., 2012). For these reasons, these snow pits were treated separately and used to better understand the influence of tree emission on ground-based radiometric measurements. On 10 January, a transect of eight snow pits was conducted in a forested area as well as transects of three snow pits on 14 February and 21 March. In addition to the usual snow pit observations, fisheye pictures (Fig. 2) were taken during the January and February campaigns to quantify vegetation density. The pictures were binarized to distinguish sky pixels from tree pixels allowing the estimation of the proportion of pixels (fraction) occupied by vegetation (χveg).

An intensive measurement campaign was conducted in January 2014 (21–28 January) in the region of Umiujaq. All the measurements were conducted in a tundra environment except for the Umi-3 site, which was located in a clearing (Table 5). The tundra sites were characterized by typical dense snow drift layers near the surface that fall into the bridging limits of 0.4 and 0.6 for the ice fraction as defined by Dierking et al. (2012) (see Sect. 2.2.2). Furthermore, one to two ice lenses were observed at the UMI-1, UMI-2 and UMI-4 sites.

The microwave signal is very sensitive to ice lens formation within a snowpack at H-pol (Montpetit et al., 2013; Rees et al., 2010; Lemmetyinen et al., 2010). To simulate the ice lenses present in this study's database (see Tables 1–5) using DMRT-ML, snow layers with a high density of 900 kg m-3 close to the density of pure ice (917 kg m-3) and a null snow grain size were integrated into the snowpack input file where ice lenses were observed. The value of 900 kg m-3 was chosen because only pure ice lenses were observed. To keep the same total snow depth, the adjoining layers were adjusted by removing 0.5 cm of the layer above and below the ice layer. However, an analysis of the effect of ice lens density on TB simulations will be conducted in Sect. 3.2.4. Because coherency (Mätzler, 1987) is neglected in DMRT-ML, the ice lens thickness has a negligible effect on simulated TB. Hence, because no precise measurements of ice lens thickness were performed in the field, ice lens thickness was set to 1 cm in DMRT-ML.

It has been shown that DMRT theory is in agreement with numerical solutions of the 3-D Maxwell equations up to a density of 275 kg m-3 (ice fraction of 0–0.3) (Tsang et al., 2008), which is a relatively low density for snow. Although most of the applications of DMRT theory concern snow, DMRT can be applied to other dense media such as bubbly ice (Dupont et al., 2014). In this case, the background is pure ice, and the scatterers are air spheres to represent bubbles. To the best of our knowledge, no validity tests have been done in this configuration; but if we assume a similar range of validity in terms of volume fraction of scatterers, the DMRT theory would be valid in the range 0.7–1 for the ice fraction, that is 642–917 kg m-3. Even in this case, a large range of intermediate densities remains for which the absorption and scattering coefficients might not be accurate. Following Dierking et al. (2012), an empirical extrapolation of these coefficients from a spline fitted in both validity ranges was implemented to calculate coefficients for a layer with an ice fraction between 0.4 (ρsnow=367 kg m-3) and 0.6 (ρsnow=550 kg m-3) (Fig. 3). As an example, the bridging leads to a decrease of TB at 37 GHz for high snow density (> 350 kg m-3) related to the increase of scattering (Fig. 4). In the following, this approach is denoted as “bridging” and the limits will be set at 0.4 and 0.6 for the ice fraction following the study of Dierking et al. (2012).

The implementation of the snow pit bridging was evaluated with James Bay and Umiujaq snow pit data that include at least one snow layer with an ice fraction of more than 0.4 (Tables 2 and 5). Because ρsnow is relatively low in boreal regions due to weakening of the wind by trees, we also evaluated this approximation using a tundra data set to increase the number of high-density snow layers for the specific validation of the bridging. The database acquired at the Churchill Northern Studies Center (58∘44′ N, 93∘49′ W) (Roy et al., 2013; Derksen et al., 2012) from the winter 2010 campaign is composed of 13 sites with at least one layer in the bridging range.

Soil reflectivity models are included in DMRT-ML to account for the soil contribution to the measured TB. In this paper, the Wegmüller and Mätzler (1999) soil reflectivity model improved for frozen soil by Montpetit et al. (2015) is used. The Wegmüller and Mätzler (1999) model for incidence angles lower than 60∘ is described by Γf,H-pol=Γf,HFresnelexp⁡(-(kσ)-0.1cos⁡θ),Γf,V-pol=Γf,Hcos⁡θβ, where Γf,p is the rough soil reflectivity at a frequency f and polarization p(H-pol or V-pol) by its smooth Fresnel reflectivity in H-Pol (Γf,H), which depends on the incidence angle (θ) and the real part of the soil permittivity (ε′), weighted by an attenuation factor that depends on the standard deviation in height of the surface (soil roughness, σ), the measured wave number (k) and a polarization ratio dependency factor (β). The values of ε′, σ and β at 11, 19 and 37 GHz inverted by Montpetit et al. (2015) for frozen soil (Table 6) were used in this study. Montpetit et al. (2013) used independent snow-free ground-based radiometer angular measurements taken at James Bay site in 2013 (same campaign). The parameters were also validated over Umiujaq (same campaign) from snow removal experiment.

Simulations including observed ice lenses were conducted on all snow pits (Fig. 6), leading to a strong decrease in simulated TB H-pol (up to 40 K). At H-pol, the RMSEs are thus improved by 15.4, 23.4 and 9.3 K at 11, 19 (initially > 35 K) and 37 GHz (initially > 20 K), respectively. The ice lenses also slightly decrease the bias measured at V-pol for all frequencies leading to a RMSE improvement of 3–4 K. These results show that a simple ice lens implementation in DMRT-ML helps to simulate the strong reflection component of ice lenses (decrease of snowpack emissivity), leading to improved simulations of TB.

However, a large variability (190–245 K) in TB observations at H-pol at 11 and 19 GHz is not reproduced by the simulations (dotted black line in Fig. 6). This feature suggests some limitations of ice lens and/or snow layering modeling in DMRT-ML that can be related to the fact that coherence effect is not taken into account. Note that this underestimation of TB spatial variability is not related to the soil as it is demonstrated in Sect. 3.2.1. The modeling uncertainties related to ice lenses will be discussed more specifically in Sect. 3.2.4.

To test the bridging parameterization (see Sect. 2.2.2), we used 13 tundra sites from the Churchill tundra database (Roy et al., 2013), 4 from Umiujaq and 2 from the James Bay snow pits. In each case, at least one snow layer with a snow density higher than 367 kg m-3 (ice fraction of 0.4: Dierking et al., 2012) is used. For each of the 19 sites studied, simulations at 37 GHz (the most sensitive frequency to snow) with and without the bridging implementation were conducted (all input parameters kept the same). The bridging has a relatively modest impact on simulations with an improvement in the RMSEs of between 2 and 4 K at tundra sites (Umiujaq and James Bay). The greatest improvements are found for deep drifted tundra snow pits where there is a very thick wind slab with high ρsnow and small rounded grains are present at the top of the snowpack.

The analysis of small-scale soil variability in modeling the TB of snow-covered surfaces is conducted using the SEex from the transect during the JBJan (mineral soil) and JBFeb campaigns (organic soil). The JBJan SEex data represent the variability within a 30 m transect in a relatively homogeneous mineral soil area (quarry). The JBFeb SEex were conducted at four different locations in clearings with organic soil and within about 1 km from each other. The strategy behind the evaluation of the small-scale spatial variability on snow-covered TB is to first calculate the soil emission variability (optimization of σ) from SEex measurements. This variability is then introduced in the simulations with snow-covered surfaces to evaluate the sensitivity of TB to variability in the emission of frozen soil.

For each SEex measurement, the surface roughness parameter σwas optimized using the three frequencies and both polarizations for bare soil measurements. The σ value was changed by increments of 0.01 cm, up to 1 cm (Eqs. 3 and 4) and the associated RMSEσ was calculated as a function of the measured TB (TB,mes) and simulated TB (TB,sim) in V-pol and H-pol as follows: RMSEσ=∑j=13∑i=1N(TB,sim;ijV-Tb,mes;ijV)2+(TB,sim;ijH-TB,mes;ijH)26N, where j corresponds to the frequencies (j=1,2,3, respectively, for 11, 19 and 37 GHz) and i corresponds to the sites. The optimal σ was determined by the lowest RMSEσ (Eq. 5) value for all sites at JBJan and JBFeb.

The optimization was also done for each site individually to estimate the spatial variability in σ. The results presented in Fig. 7 show that a clear minimum in the RMSEσ can be found at every site. Figure 7 (right) shows that the optimal σ at JBJan-transect values are located between 0.22 and 0.54 cm, while 0.31 is found for all five sites. The variability can be explained by the variation of the gravel size that affects the surface roughness. For JBFeb, the observed spatial variability is more significant with variations ranging between 0.195 cm and 1.987 cm with an optimized σ=0.411 cm for all four sites (Fig. 7 left). However, one should be careful in interpreting these results as the optimization could also compensate for uncertainties in the permittivity of frozen ground. Nevertheless, because the minimal and maximal values of optimized σ are taken, this does not affect our main goal, which is to estimate the variability in snow-covered TB introduced by the soil in the model. Furthermore, as mentioned in Sect. 2.2.3, the permittivity used in this study were retrieved at the same site as this study.

We evaluated the small-scale spatial variability of soil emissivity resulting from the observed roughness variability. For the sites with observations taken with snow on the ground (Tables 1–3 and 5, for both campaigns), we simulated the TB with DMRT-ML considering the lowest and highest optimized σ (see Fig. 7). Note that we have not used the standard deviation of σ that would have led to negative values. Figure 8 (left) shows that the TB sensitivity to the variation of soil roughness is very weak. TB variations of 0.5 and 1.3 K were observed at the JBJan-transect site where the soil properties were more homogeneous (mineral soil), while a variation of 0.7 to 3.8 K was measured at the JBFeb site with organic soil (Table 8). The sensitivity is higher at 11 and 19 GHz because the soil emission is less attenuated by snow grain scattering. We also performed the same calculation without the ice lens implementation where results are similar (less than 1 K change), suggesting that, despite a potential low transmissivity, ice lenses are not responsible for the attenuation of the soil upwelling emission.

The results show that the soil small-scale spatial variability is much lower than the RMSEs for most of the frequencies and polarizations (Tables 7 and 8). However, for 11 and 19 GHz at V-pol, the soil-induced variability calculated during JBFeb campaign leads to ΔTB values (Table 8) similar to the measured RMSEs (Table 7). Hence, the modeling error cannot be solely explained by small-scale variability in the emissivity of frozen soil, except possibly for 11 and 19 GHz at V-pol. However, these conclusions are only valid for frozen soils, but the higher dielectric contrast of thawed soil would have a greater impact on the emissivity of snow-covered surfaces.

To test the sensitivity of the simulations to the grain size (SSA) measurement errors, the simulations considered an error of 12 % in SSA when using the shortwave infrared reflection measurement approach as reported in Gallet et al. (2009). Hence two simulations were conducted: one with all SSA data along the profile increased by 12 % (TB,SSA+12%), and one with all SSA data decreased by 12 % (TB,SSA-12%). From these two simulations, the variation of TB related to SSA errors (ΔTB,SSA:TB,SSA+12%-TB,SSA-12%) was calculated, keeping in mind that this should be the maximum ΔTB error, since the variations in SSA are all in the same direction for the whole profile. The soil parameterization is kept the same for all sites (see Table 6).

Figure 9 shows the error bars related to a variation of +12 % in SSA (upper bars: higher SSA leads to smaller grains and less scattering) and -12 % (lower bars: lower SSA leads to larger grains and more scattering). The results show that 37 GHz is the most sensitive to the grain size with variations between 16.2 and 27.4 K (Table 9). The variations are generally higher at V-pol, which has a higher penetration depth with less sensitivity to stratification and ice lenses. As such, 37 GHz is more influenced by large depth hoar grains at the bottom of the snowpack. Hence, because the relationship between the scattering and the particle size reaches a maximum sensitivity within the particle range (Picard et al., 2013), the variation of 12 % for depth hoar SSA will cause a higher increase of ΔTB,SSA. In all cases, ΔTB,SSA are higher than the RMSEs (Table 7), suggesting that grain size can explain the uncertainty in the TB simulations.

At 19 GHz, there is an increase in ΔTB,SSA of about 7 K at V-pol and H-pol during the three James Bay campaigns. This increase of ΔTB,SSA is linked to snow grain metamorphism (Colbeck, 1983) that tends to increase the particle size through the winter (see Tables 1–3). With a higher sensitivity on the particle range and the dependence of scattering to the particle size, the variation of large grains will increase ΔTB,SSA. This phenomenon shows that at 19 GHz, the effect of SSA measurement uncertainty on TB depends on the type of grains. For small snow grains in January, the error in SSA is small compared to the RMSE, which is not the case in March when the error is closest to the RMSE in the presence of larger grains. A very small increase of ΔTB,SSA is also seen at 11 GHz but with much lower ΔTB,SSA (less than 1 K). These results show that scattering is negligible at 11 GHz for seasonal snow, even with large grains such as depth hoar.

We assessed average variation in TB resulting from 100 runs with random error between ±12 % applied to SSA for each layer and snow pit. As expected, the results show that the variations between initial simulation and simulation with random error on SSA are significantly lower than those shown in Table 9. With random error applied on SSA measurements, the variations are lower than 1 K at 11 and 19 GHz and between 2 and 3 K at 37 GHz. These values give the lower limits of TB error related to SSA uncertainties, while values in Table 9 give the highest limit of the variation in TB.

A similar analysis was conducted to evaluate the TB sensitivity to an error in ρsnow of ±10 % (TBρsnow+10% and TBρsnow-10%). The ice lens density was left at 900 kg m-3 and the variations in TB related to the ρsnow error (ΔTBρsnow:TBρsnow+10%-TBρsnow-10%) were calculated.

The highest sensitivity to ρsnow is seen at 37 GHz (Fig. 10). The ΔTBρsnow are about 13 K during the JBJan campaign and increase to 20 K for JBMar (Table 10). Again, this increase is explained by the growth in snow grain size due to snow metamorphism that leads to lower density values. In the given range of sphere sizes and ρsnow at 37 GHz, the impact of ρsnow on TB increases with a larger grain size (Fig. 3). These results show that the effect of ρsnow at 37 GHz on DMRT-ML simulations depends on grain size and evolves throughout the winter due to snow metamorphism. It should, however, be noted that if the ice fraction limits of the bridging (Sect. 3.1.2) were extended to a lower ice fraction density, the impact for high ρsnow would be lower or even the opposite because of the increase in scattering due to bridging. Table 10 shows that ΔTBρsnow are of the same magnitude as RMSE. Hence, depending on the grain size, ρsnow can explain part of the error in the simulations.

At 11 and 19 GHz, the highest ΔTBρsnow are found at H-pol with values around 7 K (Table 10). These highest values are related to the change in the permittivity discontinuity between layers, mostly at interfaces around the ice lenses, leading to a change in the reflectivity at the different interfaces (Montpetit et al., 2013). Because V-pol is less affected by horizontal layering, the effect is smaller. Hence, the effect of ρsnow uncertainty on TB is lower than the measured RMSEs at 11 and 19 GHz but has a significant impact on TB at H-pol. These results are in agreement with studies that show that the microwave polarization ratio (H-pol / V-pol) can potentially be used for snow density retrievals (Champollion et al., 2013; Lemmetyinen et al., 2016).

While including ice lenses in DMRT-ML significantly reduces the RMSE (Sect. 3.1.1), the underestimation of TB variability remains strong at 11 and 19 GHz. Given that the remaining bias cannot be explained by the soil, grain size or ρsnow (Sects. 3.3.1, 3.3.2 and 3.3.3), we further explore here the role of ice lenses. The ice lens density (ρIL) variations can explain part of the variability as the density of ice influences the internal reflection (Durand et al., 2008; Rutter et al., 2013). In fact, ice lenses can be snow crusts with a density as low as 630 kg m-3 (Marsh and Woo, 1984). However, measuring the density of such layers is challenging and it was not attempted during our campaigns. The sensitivity was evaluated for a range of ice density between 700 kg m-3 (TBρIL700) and 917 kg m-3 (TBρIL917) for all snow pits with ice lenses. The variation of TB related to ρIL uncertainties (ΔTBρIL:TBρIL917-TBρIL700) was then calculated (all other parameters being constant).

Figure 11 shows that ρIL variations have a significant impact on H-pol TB mostly at 11 and 19 GHz. The low ΔTBρIL at 37 GHz (Table 11) is not related to the insensitivity of 37 GHz to ice lenses but rather to the attenuation owing to snow grains dominating the effect of ice lenses. In fact, Table 11 shows that the effect of the variation of ice lens density decreases throughout the winter at James Bay because of increasing attenuation related to grain size metamorphism. It should be noted that no scattering occurs in these layers in the model because the Reff was kept null. Hence, ρIL can explain only the underestimation of TB, not the overestimation. Part of the error could be explained by the coherence that is not taken into account in DMRT-ML. The coherence is caused by multiple reflections within a thin layer and associated interference when the thickness of the ice lenses is less than a quarter of the wavelength (λ/4) (Mätzler et al., 1987; Montpetit et al., 2013). Since DMRT-ML does not take into account the coherence, the thickness of the ice layer has a negligible impact on TB and was kept at 1 cm. However, simulations with MEMLS accounting for coherence have shown that variation in the ice lens thickness can change TB by up to 100 K at H-pol at 19 and 37 GHz (Montpetit et al., 2013). Also, in this study, only the main ice lenses were noted and inserted in DMRT-ML. Many other melt/refreeze thin snow crusts were present but not recorded, and they can have a large impact on TB observations (see Rutter et al., 2013). These thin crusts (less than 2 mm) with a high density (over 600 kg m-3) can also have significant coherence effects (less than λ/4).

During the JBJan campaign, at the transect, two ice lenses were observed at three consecutive snow pits (JBJan-6.7, JBJan-6.8 and JBJan-6.9). The simulations at these sites show the three lowest simulated TB at 11 and 19 GHz at H-pol (Fig. 11). The second observed ice lens inserted in DMRT-ML significantly decreases the simulated TB. Including the second observed ice lens allows an improvement in the TB simulation at JBJan-6.8 (Table 1), while the accuracy decreases for the two other snow pits, especially at 11 GHz. These results show the importance of small-scale spatial variability in the distribution of ice lenses. In this case, since the SBR footprint is not exactly where the snow pit was dug, the 11 GHz measured the two ice lenses at JBJan-6.8, but not at JBJan-6.7 and JBJan-6.9. Rutter et al. (2013) showed that such small-scale discontinuities in ice lenses have a strong impact on TB.

In a forested area, tree emission reflected by the snowpack can significantly contribute to the measured TB on the ground (Roy et al., 2012). An analysis was conducted on 18 site measurements taken in a forest during the three James Bay campaigns (Table 4) to quantify the forest contributions to measured TB using DMRT-ML. A first simulation, neglecting the emission coming from the trees in the downwelling TB (TB,down) reflected by the surface was conducted. Figure 12 shows a clear underestimation (biases ≈40 K at H-pol) of simulated TB at all frequencies, except for 11 and 19 GHz at V-pol. Table 12 shows that these biases are much greater than the uncertainties induced by the snow cover in open areas, showing that the tree emission reflected by the surface significantly increased the measured TB. The low influence of vegetation (low biasforest: Table 12) at 11 and 19 GHz V-pol is explained by the fact that the reflectivity of the surface at these frequencies is very low because the volume scattering is weak and the reflectivity at the interfaces is close to 0 near the Brewster angle.

To quantify the forest contribution, the TB,down was inverted with DMRT-ML. From the simulated TB neglecting the forest contribution (Fig. 12), an iteration process was performed to find the TB,down value that minimized the RMSEveg between simulated and measured TB at V-pol and H-pol for each frequency independently: RMSEveg=∑i=1N(TB,sim;ifV-TB,mes;ifV)2+(TB,sim;ifH-TB,mes;ifH)22N where f is the frequency.

Table 13 shows that the averaged optimized TB,down are 147, 120 and 110 K, respectively, at 11, 19 and 37 GHz. The optimized TB,down, however, decrease with frequency, which is opposite to what was shown in other studies (Kruopis et al., 1999; Roy et al., 2012, 2014). This is probably related to the inherent error in the snow surface TB simulation in DMRT-ML (Table 7), which induces error in the calculation of the reflectivity of the snow-covered surface.

Table 13 also shows that there are large variations between the different snow pits with a standard deviation between 43 and 74 K. The average TB,down of the three frequencies was calculated for each site and compared with χveg obtained from fisheye pictures taken at the 12 JBveg sites in January and February (fisheye pictures were not taken in March). Figure 13 shows that there is a good correlation (R2=0.75) between averaged TB,down (mean for the three frequencies) and χveg. These results confirm that the optimized TB,down are related to the tree emission reflected by the surface (see an example of variations in Fig. 2). For comparison, the calculated atmospheric downwelling contributions were around 6 K at 11 GHz and 25 K at 37 GHz. It also shows the potential of using fisheye pictures to quantify tree microwave emission in boreal forests. However, further considerations are necessary to improve the method. Because of the non-Lambertian component of the snow reflection and the non-homogeneity of the trees surrounding the site measurements, the direction (azimuth) in which the SBR is pointing has an important influence on the signal (Courtemanche et al., 2015). DMRT-ML assumed that the TB,down is isotropic and does not take into account these specular components. For example, the TB will be higher if the SBR is pointing in the direction of a large trunk close to the snow pit instead of pointing in the direction of a forest opening.