The MACSSIMIZE field campaign took place in Trail Valley Creek (TVC), NWT, Canada, in March 2018 as part of the Year of Polar Prediction, an international, cross-disciplinary programme of polar science studies coordinated by the Polar Prediction Project of the World Meteorological Organization (WMO). TVC consists of a mix of wind-blown open tundra areas and valleys with snow drifts and shrub vegetation, typical of Arctic tundra regions. The stratigraphy at the bottom of tundra snowpacks tends to be controlled by shrubs, underlying topography and strong temperature gradients, while layers above this are influenced by wind-driven processes .

Measurements focused on eight areas of interest (AOIs) as described in , the locations of which are shown in Fig. . The AOIs were chosen to capture the range of topographies, aspects and vegetation characteristics of TVC. Figure also shows a map of broad topographic classifications for TVC: flat upland plateau, flat valley bottom and slopes . Between 14–22 March, in situ snowpack measurements on the ground were co-located with flights of the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146 research aircraft. This paper uses data from three flights (C087, C090 and C092) flown on 16, 20 and 22 March. The locations of snow pits where ground-based measurements were made, along with example flight tracks within the AOIs, are also shown in Fig. .

Precipitation and wind during the campaign caused changes in surface snow conditions between flights. Snowfall between flights C087 and C090 introduced a low-density fresh snow layer, which was evident in pits dug around this time. Increased wind speed before the third flight then redistributed the surface snow, altering snowpack stratigraphy. Freezing rain earlier in the season also introduced an ice layer to most snowpacks. Figure  shows how air temperature, precipitation, wind speed and wind direction changed during the campaign, as well as a wind rose demonstrating the prevailing wind direction. The vertical lines show the time of each flight.

Airborne Tb measurements were made using the Microwave Airborne Radiometer Scanning System (MARSS; ) and the International Submillimetre Airborne Radiometer (ISMAR; ) on board the FAAM aircraft. Both instruments are along-track scanning radiometers containing dual-sideband heterodyne receivers measuring between 89 and 664 GHz. The position of these instruments on the side of the aircraft allows both upward and downward observations to be made. On flights discussed in this paper, instruments were configured to make only downward-viewing observations during AOI overpasses to increase the number of observations made over ground sites. The zenith and calibration views were obtained in regions outside the AOIs.

Tb measurements at 89, 157 and 183 GHz from MARSS and 118 and 243 GHz from ISMAR allowed for the retrieval of emissivity spectra. Frequencies above 243 GHz are not considered because the high atmospheric opacity means that satellite observations at higher frequencies have little surface sensitivity, and emissivity retrievals can have large errors. The emissivity retrieval is based on the methods described in , where observations of upwelling and downwelling brightness temperature close to the surface are used to determine both emissivity and effective surface temperature using the relationship 1Tb,up,surf=ϵTs,eff+(1-ϵ)Tb,down,surf, where Tb,up,surf and Tb,down,surf are surface upwelling and downwelling brightness temperatures, Ts,eff is the effective surface temperature, and ϵ is emissivity. Tb,up,surf and Tb,down,surf are determined from aircraft-level observations by correcting for absorption and emission from the atmospheric layer between the aircraft and the surface. An effective Lambertian value of Tb,down,surf was derived from airborne observations at multiple zenith angles , as a Lambertian surface assumption has been shown to better represent snow surfaces at microwave frequencies over a specular assumption . Observations from multiple channels centred on a gaseous absorption line (e.g. water vapour line at 183 GHz or oxygen line at 118 GHz) share the same emissivity and effective temperature but will have different values of Tb,up,surf and Tb,down,surf. This means both ϵ and Ts,eff can be determined. By assuming that Ts,eff is approximately independent of frequency, Eq. () is used to calculate ϵ at window channel frequencies. To ensure consistent viewing geometry, Ts,eff at 183 GHz is used to calculate ϵ for the MARSS channels (89, 157 and 183 GHz) and Ts,eff at 118 GHz to calculate ϵ for the ISMAR channels (118 and 243 GHz).

MARSS and ISMAR scan patterns are not synchronised, so observations from the two radiometers do not correspond to exactly the same ground locations. Retrieved emissivities from the two instruments were mapped onto locations of ISMAR observations by spatially averaging all observations where the beam centre location was within 50 m of each ISMAR data point. This resulted in 1916 observed emissivity spectra. An evaluation of the sensitivity of emissivity retrievals to errors in observed brightness temperatures (of ±1 K) and of assumed parameters, such as temperature and humidity of the atmospheric layer between the aircraft and the surface, suggests that the retrieval error is approximately 0.01 for frequencies between 89 and 157 GHz and 0.02 for frequencies between 183 and 243 GHz. The larger error at higher frequencies is due to increased sensitivity to the amount of water vapour in the atmospheric layer below the aircraft. These values are used as observation errors in the SCEM-UA retrievals (Sect. ). These errors do not include uncertainty due to frequency-dependent changes in Ts,eff, which would have the greatest impact at 89 GHz, increasing uncertainty by a maximum of 0.004. This corresponds to a maximum error in Ts,eff of ±3 K, based on differences between 118 and 183 GHz Ts,eff, and an average variability in observed snowpack temperature of 2.9 K. This is not expected to have a significant impact on the SCEM-UA retrievals.

Retrieved emissivities were grouped using k-means clustering to give eight emissivity spectra, which are used as observations in the SCEM-UA retrievals. The number of clusters was chosen to represent variability in the retrieved emissivity while providing distinct spectra from a significant number of observations. Figure  shows the eight emissivity spectra (coloured lines), which are the centroids of the eight clusters and are referred to as observations throughout the rest of the paper, and all the observed spectra used to generate them (grey lines). The range of spectral shapes reflects the variability in snow properties observed during the three flights. Clusters 0 and 2 were the only spectra where emissivity increased between 89 and 243 GHz, although all clusters show a slight decrease in emissivity at 183 GHz. Emissivity values ranged from 0.55 to 0.80, with the lowest emissivity values associated with cluster 2 and the highest with cluster 7, which had a peak at 118 GHz. Tests were carried out to determine if this peak was caused by the Lambertian surface assumption in the emissivity retrieval; however, running the retrieval for a specular surface produced a similar spectrum. Given the steep change in emissivity, it may be difficult for SMRT to simulate this spectra.

Ground-based measurements of snow microstructure were made in 29 snow pits across eight AOIs. The snow pit locations were aligned with the aircraft flight tracks, as shown in Fig. . Vertical profile measurements of density (ρsnow in kg m-3), specific surface area (SSA in m2 kg-1) and temperature (K) were made at 3 cm vertical resolution in each of the snow pits, using techniques described in . In pits where two vertical profiles of density and SSA were measured, the average of two samples at each vertical position in the profile was used.

Individual layers within each snow pit were classified into three microstructure types, surface snow, wind slab and depth hoar, based on their properties and through visual inspection . Snow properties were averaged across the main microstructure types to quantify the properties of each snowpack layer. All of the snow pits had a depth hoar layer, most contained wind slab and several also had a fresh snow layer. Ice lenses were also present in most pits and were included in simulations in , either by splitting layers or by adding the ice lens between layers depending on where they occurred in the vertical profile. However, because this resulted in four- or five-layer snowpacks, this strategy would be too complex to introduce into the MCMC methodology, which is already computationally intense; therefore, ice lenses are not included in simulations in this paper. The mean difference in simulated Tb of snow pits from MACSSIMIZE with and without ice lenses was 1.88 K at 89 GHz, decreasing with frequency to 0.024 K at 243 GHz, so the impact of excluding ice lenses on emissivity simulations is expected to be minimal. The snow pit SSA, thickness, density and temperature observations for surface snow (SS), wind slab (WS) and depth hoar (DH) were used as input to SMRT, as described in the following sections.

SMRT was used to generate emissivity simulations, using sets of snow parameters generated during the MCMC retrieval as input (see Sect. ) for two- and three-layer snowpacks based on the three main observed snow layers. Three layers captured the main variations in snow profiles and observed stratigraphy and matched the layers simulated in . The underlying soil surface is assumed to be flat, with a temperature of 258.15 K, as used in and based on .

SMRT requires layer thickness, density, temperature and a measure of grain size or microstructure depending on the microstructure model chosen. For this paper, SMRT was configured to use the discrete ordinate radiative transfer (DORT) solver, the improved Born approximation (IBA) electromagnetic model, and the exponential autocorrelation microstructure model. Although IBA is typically limited to lower frequencies than those in this paper, suggested that the applicability of IBA could be extended to higher frequencies, and this was supported by good agreement between SMRT simulations and observations of Tb at higher frequencies in . The exponential correlation length (lex) was used as the microstructure parameter and was derived using observed SSA and density according to the modified Debye relationship : 2lex=αdb4(1-ρsnow/ρi)SSAρi, where ρsnow is snow density, ρi is density of pure ice (916.7 kg m-3) and αdb is the Debye modification parameter. A value of 0.75 is used for αdb for surface snow and wind slab, a value proposed by . For depth hoar, an αdb value of 1.2 is used, as proposed by and discussed in .

SMRT does not directly simulate emissivity; therefore, emissivity was retrieved by simulating upwelling brightness temperature at the surface (Tbsmrt) for a viewing angle of 5∘, with different values for atmospheric downwelling (Tbdown) according to Eq. (). This is preferable to simply dividing Tbsmrt by the physical snowpack temperature, as snowpacks are not isothermal, and microwave penetration depths vary. This method is also used to derive emissivity in MEMLS . 3ϵ=1-Tbsmrt(Tbdown=100K)-Tbsmrt(Tbdown=0K)100K

SCEM-UA is a global optimisation routine, used to generate probability distributions of the parameters of a model through random sampling using MCMC methods. SCEM-UA evolves multiple parallel Markov chains, using the sequence evolution metropolis (SEM) algorithm, which decides at each step in the Markov chain how likely a parameter value is to contribute to the posterior probability distribution. SCEM-UA uses complex shuffling to share information about the parameter space between chains to improve the efficiency and adaptability of the search compared to other MCMC samplers .

SCEM-UA requires an estimation of the physical limits of parameters of interest (range of observed snow parameters; Table ), a set of observed values to match (observed emissivity spectra; Fig. ), an estimate of measurement error (0.01 from 89 to 157 GHz and 0.02 from 183 to 243 GHz; Sect. ) and a model for which the parameters are being estimated (SMRT). SCEM-UA searches within parameter limits for parameter sets that give model simulations that match observed emissivity values within measurement uncertainty. During this search, SCEM-UA maps the probability distributions of the parameters being searched. The returned posterior parameter distributions give an indication of parameter uncertainty associated with simulations and indicate the sensitivity of simulations to different snow parameters.

SCEM-UA was coupled to SMRT, and three experiments were run to assess the sensitivity of simulations to the different snow parameters. The experiments were also split for two- and three-layer snowpacks, whereby two-layer snowpacks did not have a surface snow layer, to reflect the different stratigraphy observed during MACSSIMIZE. Table provides an overview of the three experiments, including the parameters being searched in each snowpack layer (top panel) and the SCEM-UA setup for each experiment (bottom panel). More details on how the experiments were split are given in Sect.  and .

In each experiment, SCEM-UA was set up to run 10 parallel chains, with 50 initial samples per chain. The initial samples are random values from a distribution between the minimum and maximum of the observed parameter range. The number of iterations per chain varied between 10 000 and 20 000, depending on the number of parameters and snowpack layers allowed to vary in the retrieval and how many iterations were needed for the chains to converge. Convergence was assessed using a combination of the rank-normalised R^ convergence criteria and autocorrelation. The rank-normalised R^ convergence diagnostic compares variance between chains V^ to variance within each chain W and is computed by 4R^=V^W. When R^ reaches 1.0, the between-chain and within-chain variance are equal, and the chains have successfully converged; however, a value of less than 1.01 is deemed sufficient to indicate convergence. Samples taken before R^ is below 1.01 are removed from the beginning of the evolution, and the number of iterations this takes is given by the burn-in number in Table . Samples taken after the chains have converged represent samples from the posterior distribution of parameter sets, which are presented in Sect. . Each parameter set within the posterior distribution is then used to calculate a spectrum using SMRT. The means and standard deviations of these spectra are presented in Sect. . Comparisons of simulated and observed emissivity spectra allowed an assessment of SMRT's ability to reproduce the emissivity spectra within observed parameter limits, while the sensitivity of simulations to each parameter was assessed based on the posterior parameter distributions.

The mean SMRT-simulated emissivity spectra for parameter sets retrieved after the chains had converged are shown in Fig.  (standard deviation shown by error bars) for the three experiments, along with observed emissivity spectra for each cluster. Table  gives the mean absolute error (MAE) and mean absolute percentage error (MAPE; MAE as a percentage of the mean observed emissivity across the spectra) between the observed and mean simulated spectra for each cluster in each experiment.

When only correlation length was varied by SCEM-UA in the first experiment, only clusters 1 and 5 had mean simulated emissivities which fell within the observation error at all frequencies (green lines in Fig. ). For clusters 3, 4, 6 and 7, SMRT reproduced the shape of the spectra reasonably well; for example, both observed and simulated emissivity decreased overall between 118 and 243 GHz for clusters 3, 6 and 7 and increased between 89 and 118 GHz for clusters 4 and 7. However, mean simulated emissivities fell outside observation error at some frequencies (89 GHz for cluster 3, 157 GHz for cluster 4, 183 GHz for cluster 6 and 118 GHz for cluster 7). For cluster 7, this relates to the peak in the observed spectrum mentioned in Sect. . SMRT was not able to simulate observed spectra of clusters 0 and 2 when only correlation length was allowed to vary. The slope of the simulated spectrum of cluster 0 was opposite to that of the observed spectrum up to 183 GHz, and although the shape of the cluster 2 spectrum was similar to observations, emissivity values were too high, with an MAE of 0.063.

MAE (MAPE) averaged across all clusters and frequencies decreased from 0.018 (3.0 %) to 0.0078 (1.2 %) when layer thickness was also accounted for. Simulated emissivities were within the observation error at all frequencies for clusters 0, 1, 3, 4, 5 and 6, compared to only clusters 1 and 5 in the first experiment. The biggest improvement was for clusters 0 and 2, where SMRT was not able to reproduce the observed spectra with correlation length alone. Only clusters 2 and 7 had mean simulated emissivities which fell outside the observation errors at 183 and 243 GHz for cluster 2 and 118 GHz for cluster 7. Clusters 2 and 7 also had the largest MAE (MAPE) in the second experiment at 0.011 (1.94 %) and 0.012 (1.62 %) respectively. The only case where the standard deviation of the simulation did not overlap with the observation error was cluster 7 at 118 GHz. Although mean simulated emissivity at 118 GHz increased slightly when layer thickness (and density in the third experiment) was accounted for, this was still not enough to reproduce the peak in the observed spectrum.

Overall MAE did not change much between the second and third experiment when density was also varied. Most clusters had simulated emissivities within the observation error at all frequencies, except cluster 6, where simulated emissivity at 183 GHz was just outside the upper observation error, and cluster 7. Most changes in simulated emissivity in the third experiment were seen at 243 GHz, indicating sensitivity to density in the surface snow due to the shallower penetration depth at this frequency. For clusters 0, 2, 3 and 5, simulated emissivities at 243 GHz were a better match to observations in the third experiment, most notably for cluster 2, where simulations at 183 and 243 GHz previously fell outside the observation error (although the shape of the spectra was a worse match for observations at lower frequencies). For clusters 1, 4 and 7, there was slightly less agreement between simulations and observations. However, these changes in emissivity were relatively small, and the standard deviation of the simulations was larger at 243 GHz than in previous experiments, shown by larger error bars in Fig. . This could be due to 243 GHz being outside the limit of applicability of the IBA electromagnetic model (see Sect. ). Overall, Fig.  suggests that SMRT is capable of simulating a variety of emissivity spectra between 89 and 243 GHz and demonstrates the importance of representing at least the correlation length and thickness of different snow layers. In the last two experiments, the MAE for most clusters was smaller than the lower observation error of 0.01 (Sect. ).

The probability distributions for parameter sets retrieved by SCEM-UA after chains had converged in each experiment are shown in Figs. –. Table  gives the retrieved mean and standard deviation for these distributions. As described in Sect. , the simulations for clusters 0, 1, 2, 4 and 7 were run as two-layer snowpacks and clusters 3, 5 and 6 as three-layer snowpacks; hence, surface snow parameters are only given for clusters 3, 5 and 6.

Figure shows the distributions for correlation length in the first experiment. Several clusters had narrow distributions with a low standard deviation for surface snow (cluster 5) and wind slab (clusters 1, 4, 6 and 7), indicating the sensitivity of simulations to correlation length in these layers. In comparison, depth hoar distributions for most clusters were relatively broad and spanned most of the parameter range, with higher standard deviation than the other layers (0.039 to 0.081 mm; Table ), suggesting simulations were less sensitive to depth hoar. Low sensitivity to depth hoar is expected given the relatively shallow penetration depths at higher frequencies and the need for depth hoar emissions to penetrate the layers above. Given this low sensitivity, and the increased number of parameters being searched in subsequent experiments, depth hoar correlation length was fixed at the mean for the three-layer clusters in the second and third experiments (Sect. ).

Several distributions in all three layers were at the upper limits of the parameter ranges, such as the surface snow correlation length of clusters 3 and 6; wind slab correlation length of clusters 0 and 2 (where SMRT was not able to reproduce the observed spectra); and depth hoar correlation length of clusters 0, 2, 3 and 4. This, along with the inability of SMRT to reproduce observed emissivities at all frequencies (Sect. ), suggests that either the correlation length ranges from observed snow parameters were not large enough or varying the correlation length alone is not sufficient to allow SMRT to simulate observations when other parameters are fixed.

Figure shows distributions from the correlation length and thickness experiment. The correlation length distributions for surface snow and wind slab did not change much when thickness was also varied. The exceptions were the wind slab correlation length distributions of clusters 0, 2 and 6. For cluster 2, wind slab correlation length was at the upper limit in the first experiment but was spread across the parameter range in the second, suggesting a low sensitivity to the wind slab layer for this cluster. This can be explained by wind slab thickness for cluster 2 falling at the bottom of the parameter range (mean thickness of 0.0047 m), indicating a very shallow or non-existent layer. Shallow wind slab resulted in increased sensitivity to depth hoar, indicated by a narrow distribution for depth hoar correlation length with a standard deviation of 0.014 mm, much lower than that of the other depth hoar distributions. Greater sensitivity to large-grained depth hoar (larger correlation lengths) caused increased scattering and contributed to the low emissivities of the cluster 2 spectrum, which could not be simulated without representing wind slab thickness.

With the exception of cluster 2, the relatively narrow wind slab thickness distributions of clusters 0, 3, 4, 6 and 7 indicate the sensitivity of simulations to wind slab thickness as well as correlation length. Surface snow thickness distributions had similar standard deviations to wind slab (0.016 to 0.024 m); however, because the observed surface snow thickness range was relatively small (0.03 to 0.12 m; Table ), the distributions spanned the parameter range. Sensitivity to the thickness and correlation length of surface snow and wind slab is expected, as the thickness and scattering strength of layers near the top of the snowpack influence attenuation of emission from lower layers, as seen for cluster 2. Unlike cluster 2, parameter distributions suggested that cluster 7 was associated with a relatively deep wind slab layer (0.14 m) with a relatively low correlation length (0.094 mm). Lower correlation length relates to smaller snow grains, resulting in reduced scattering across a relatively deep layer, which reduced penetration to depth hoar and resulted in higher emissivities across the cluster 7 spectrum.

Depth hoar thickness distributions spanned the full parameter range for all clusters, including cluster 2, and had higher standard deviations than the other layers (0.083 to 0.09 m), again indicating the low sensitivity of simulations to depth hoar thickness. Even for shallow thicknesses, the higher frequencies are unlikely to penetrate through the depth hoar to the bottom of the snowpack, meaning changes in thickness of this layer are less important. Therefore, in the final experiment, depth hoar thickness was fixed at the mean, in addition to the correlation length, to reduce the number of parameters being searched.

Figure shows distributions for the correlation length, thickness and density experiment. Wind slab parameter distributions were broader, with higher standard deviations (Table ) than in previous experiments for most clusters. This is likely due to the complex interaction of snowpack microstructure parameters such as correlation length and density, whereby a range of combinations of density and correlation length could result in similar scattering properties. Simulations were therefore similarly sensitive to both correlation length and density. Wind slab density distributions were also relatively broad, with the standard deviation ranging from 22 to 58 kg m-3, and as in the other experiments, depth hoar distributions spanned the parameter ranges.

Surface snow correlation length and density distributions had lower standard deviations than wind slab. For all three-layer clusters, surface snow correlation lengths were at the upper end of the parameter range, with mean retrieved values between 0.088 and 0.096 mm, similar to the lowest wind slab correlation lengths of clusters 6 and 7. These distributions did not change much between the three experiments. Surface snow density distributions were at the lower end of the range, with mean retrieved density between 86 and 120 kg m-3 (Table ). Clusters with surface snow at the top of the snowpack (3, 5 and 6) had lower emissivities at 183 and 243 GHz than those with wind slab at the top of the snowpack (except cluster 2). For example, clusters 6 (three-layer) and 7 (two-layer) had a similar emissivity at 89 GHz (0.72 and 0.73) due to similar wind slab scattering properties, but at 243 GHz the emissivity of cluster 6 (0.56) was lower than cluster 7 (0.72). Low density and relatively low correlation lengths in the surface snow layer should result in less scattering and higher, rather than lower, emissivity at the higher frequencies. Another explanation for the differences in emissivity caused by surface snow is boundary effects caused by dielectric contrasts between layers of different density; this is discussed further in Sect. .