Snow density and ground permittivity retrieved from L ...

RSE-09717; No of Pages 15 Remote Sensing of Environment xxx (2016) xxx–xxx

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Snow density and ground permittivity retrieved from L-band radiometry: Application to experimental data Juha Lemmetyinen a,⁎, Mike Schwank b,c, Kimmo Rautiainen a, Anna Kontu a, Tiina Parkkinen a, Christian Mätzler c, Andreas Wiesmann c, Urs Wegmüller c, Chris Derksen d, Peter Toose d, Alexandre Roy e, Jouni Pulliainen a a

Finnish Meteorological Institute, FI-00101 Helsinki, Finland Swiss Federal Research Institute WSL, CH-8903 Birmensdorf, Switzerland c Gamma Remote Sensing AG, CH-3073 Gümligen, Switzerland d Environment Canada, M3H 5T4 Toronto, Ontario, Canada e Université de Sherbrooke, J1K 2R1 Sherbrooke, Québec, Canada b

a r t i c l e

i n f o

Article history: Received 22 June 2015 Received in revised form 13 January 2016 Accepted 2 February 2016 Available online xxxx Keywords: Microwave radiometry Retrieval Snow density Ground permittivity SMOS SMAP

a b s t r a c t The potential of retrieving the bottom layer snow density and soil permittivity under dry snow cover conditions from L-band passive microwave observations was analyzed using multi-angular brightness temperatures measured at horizontal and vertical polarization over two test sites in northern Finland. The near-continuous time series of L-band brightness temperatures covers a total of six winter seasons, over both dry mineral soil in a forest clearing, and organic soil over a wetland site. Detailed measurements of snow and soil conditions are available from both sites. Complementing a previous theoretical study, we show that dry snow cover influences the observed L-band brightness temperatures as a result of both impedance matching and changes in the refraction angle at the snow–soil interface. Exploiting these effects, we demonstrate the retrieval of the bottom layer snow density and the influence of dry snow cover on simultaneously retrieved soil permittivity — a consideration which is currently not accounted for in Soil Moisture and Ocean Salinity (SMOS) retrievals of soil permittivity in the presence of dry snow. Depending on season, the mean bias error between retrieved and in situ snow density measured in the lower snow layers was between −6 kg m−3 and 15 kg m−3 for the forest clearing site, and between 37 kg m−3 and 90 kg m−3 for the wetland site, demonstrating the feasibility of the retrieval approach at the plot scale. In winter conditions, the ground permittivity retrieved without considering the impact of dry snow on L-band emission was, on average, 35% lower for both test sites, which indicates possible errors in current SMOS ground permittivity retrievals under dry snow conditions. The application of SMOS data to simultaneously retrieve dry snow density and ground permittivity is a complex task due to heterogeneous land cover and snow/ soil conditions within SMOS pixels (≈45 km resolution). An approach that considers land cover variations and the spatial variability of snow cover is required to fully determine the feasibility of the methodology to aid e.g. improving estimates snow water equivalent from other sensors, and to take into account effects of dry snow in SMOS-based retrievals of ground permittivities. The results should also be applicable to other L-band sensors in space, such as the recently launched NASA Soil Moisture Active Passive (SMAP) mission. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Components of the terrestrial cryosphere, including seasonal snow cover and soil freeze/thaw (F/T) state play a key role for hydrological, climatological, and ecological processes in northern latitudes. For example, changes in the seasonal cycle of soil-snow states have a major impact on the annual carbon balance (Melaas et al., 2013; Xu et al., 2013; Schuur et al., 2015) and vegetation growth (Kim, Kimball, Zhang, & McDonald, 2012), while snow cover, influences the large scale energy

⁎ Corresponding author.

budget through albedo feedbacks (Fletcher, Zhao, Kushner, & Fernandes, 2012), controls insulation of the soil (Gouttevin et al., 2012) and contributes to river runoff in large areas of the Northern hemisphere (Barnett, Adam, & Lettenmaier, 2005). Observing elements of the terrestrial cryosphere using remote sensing is an appealing option, in particular due to the typically sparse in situ observation networks available in Arctic and sub-Arctic regions, including the northern boreal forest zone. A method for estimating snow water equivalent (SWE) using an assimilation scheme combining passive microwave observations with in situ measurements of snow depth was introduced by Pulliainen (2006). The method applies satellite measurements of brightness

http://dx.doi.org/10.1016/j.rse.2016.02.002 0034-4257/© 2016 Elsevier Inc. All rights reserved.

Please cite this article as: Lemmetyinen, J., et al., Snow density and ground permittivity retrieved from L-band radiometry: Application to experimental data, Remote Sensing of Environment (2016), http://dx.doi.org/10.1016/j.rse.2016.02.002

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J. Lemmetyinen et al. / Remote Sensing of Environment xxx (2016) xxx–xxx

temperatures at Ku and Ka bands (≈19 and ≈37 GHz) in an iterative inversion of the Helsinki University of Technology (HUT) snow emission model (Pulliainen et al., 1999). The implementation of the algorithm in an operational context within the ESA GlobSnow project is described by Takala et al. (2011). The GlobSnow SWE retrieval algorithm assumes spatially and temporally constant values for air-, snow- and vegetation temperatures, snow density, soil surface roughness and soil permittivity (Takala et al., 2011; Lemmetyinen et al., 2015). The consideration of the spatio-temporal dynamics of snow density and ground permittivity through independent satellite retrievals could improve the retrieval of SWE. The SMOS (Soil Moisture and Ocean Salinity) mission, the second in a series of Earth Explorer Opportunity missions by the European Space Agency (ESA), was launched in November 2009 (Kerr et al., 2010). Originally designed to provide global information on near-surface soil moisture and ocean salinity, the SMOS application range was expanded recently to the observation of a number of state variables relevant for the cryosphere, including the detection of thin sea-ice (Kaleschke, Tian-Kunze, Maaß, Mäkynen, & Drusch, 2012) and the monitoring of soil F/T processes (Rautiainen et al., 2012, 2014). Retrievals of landscape F/T state is also a goal of the National Aeronautics and Space Administration (NASA) SMAP (Soil Moisture Active Passive) mission (Entekhabi et al., 2010), launched in January 2015. Recent theoretical and model-based analyses (Schwank et al., 2014; Schwank et al., 2015) indicated the distinct sensitivity of L-band microwave emission with respect to dry snow. While causing virtually no scattering and very low absorption at L-band, dry snow cover affects brightness temperatures observed from above the snow surface through impedance matching and refraction near the snow–soil interface. Impedance matching by dry snow reduces dielectric gradients and consequently increases thermal emission of the scene. This is because in a typical case, the permittivity of snow (1 b εS b 2 for snow density 0 b ρS b 500 kg m−3) is lower than the permittivity of fully frozen ground (εG ≈ 5), while still being larger than the permittivity of air (εair = 1). On the other hand, refraction caused by the snow-layer in contact with the ground surface leads to a steeper incidence angle at the ground surface in comparison with the observation angle (Snell's law). Because emission from the ground beneath the dry snow is the dominant source of L-band emission, refraction increases emission at horizontal polarization, while emission at vertical polarization is decreased. These instances imply that both impedance matching and refraction increase emission at horizontal polarization, while for vertical polarization the effects are partly compensatory. As proposed by Schwank et al. (2015), these emission processes offer the potential to use passive L-band observations to estimate the effective density ρS of the dry snow layer in contact with the ground. The thickness of this sensitive bottom layer is given by the lower limit of ≈10 cm where coherent effects can be disregarded for L-band observations. Although snow density may vary rapidly with increasing snow height, this novel remote sensing information on dry snow cover has the potential to improve satellite-based retrievals of SWE (e.g. Kelly, Chang, Tsang, & Foster, 2003; Takala et al., 2011) which currently rely on physical modeling or climatological values for snow density. In addition, the theoretical study of Schwank et al. (2015) indicates the significant impact of dry snow on retrieved ground permittivity εG. This has potential implications for current SMOS ground permittivity retrievals performed over areas covered with dry snow (Kerr, Waldteufel, Richaume, Ferrazzoli, & Wigneron, 2011). In this investigation, we attempt to evaluate the feasibility of the approach proposed by Schwank et al. (2015) for the simultaneous retrieval of snow density (ρS) and ground permittivity (εG) from multi-angular (θk), dual-polarization (p = H, V) L-band brightness temperatures TpB(θk) as measured by SMOS. A near-continuous dataset of towerbased TpB(θk) measured with ESA's ELBARA-II radiometer (Schwank et al., 2010) are applied. With a focus on winter periods, the available dataset extends for six full seasons. Corresponding brightness

temperatures TpB(θk) were measured over a dry mineral soil site located in a forest clearing as well as over an open wetland site representing organic soil. These two sites can be considered to represent common land cover and soil types in the northern boreal forest zone. A comprehensive dataset of both automated and manual in situ snow and soil observations are used to validate the two-parameter retrievals P = (ρS, εG) derived from the measured TpB(θk). 2. Datasets 2.1. Test site Experimental data used in this study was collected at the Finnish Meteorological Institute Arctic Research Centre (FMI-ARC) in Sodankylä, Finland. The site is located in the northern boreal forest zone. The surrounding landscape is a mosaic of conifer-dominated forests (scots pine), forested and non-forested bogs (wetlands), and small lakes. Elevation above sea level varies between 180 and 240 m; however, small mountain regions (fjells) are typical of the surrounding region. Tower-based observations of L-band brightness temperatures TpB(θk) at polarization p = H,V and incidence angle θk were collected from two test sites, representative of the two most common soil types in the region. The test sites were located ≈ 1 km apart from one another. Soil at the forest clearing test site consisted of sand (70%), silt (29%) and clay (1%), with a bulk density of 1300 kg m− 3 and a thin organic surface-layer (2–5 cm) with sparse ground vegetation typical for northern latitudes, consisting mainly of lichen and heather. The wetland test site was located over an open bog exhibiting a thick and highly variable layer of organics (from 3 to 10 m of peat) on top of bedrock. Surface vegetation consisted of moss, grass and small shrubs, with occasional small trees (pine and birch). During autumn and spring months, the wetland site was typically inundated with water, with water levels often exceeding the height of local surface vegetation in some areas. 2.2. Microwave radiometer measurements From October 2009 to August 2012, the L-band radiometer ELBARAII was operated at the forest clearing site (Fig. 1a). It was deployed on a 4.1-meter platform allowing for elevation scans covering the range of incidence angles 35° ≤ θk ≤ 180° (= zenith). However, our analysis uses TpB(θk) measured for the restricted range of incidence angles 40° ≤ θk ≤ 65°, because steep measurements TpB(θk b 40°) are expected to be influenced by the tower structure, and TpB(θk N 65°) measured for shallow angles θk were affected by the emission from trees facing the instrument. The experimental setup was similar for the wetland site (Fig. 1b), where ELBARA-II was operated from August 2012 to February 2015. However, a modification of the platform design allowed a slight extension of the elevation scans to θk ≥ 30°. Analysis and retrievals based on observations TpB(θk) at the wetland site proved problematic in particular during late autumn, when the soil-surface in the radiometer field of view was partially saturated with water. Local-scale variability in the soil elevation and vegetation height caused the ELBARA-II footprints to include areas with open water (ponds) and areas with vegetation protruding above the local water level. These instances limited the usable incidence angles that provided TpB(θk) suitable for testing the retrieval at the wetland site. At both sites, the ELBARA-II measurements TpB(θk) were composed of automated elevation scan sequences, fixed incidence angle observations, and zenith (sky) measurements for calibration purposes. At both sites elevation scans were made in 5° steps. During the first year of operation at the forest clearing site, elevation scans were performed every three hours. For the following years a four-hour interval was applied. At the bog site, a four-hour interval was used for the duration of the experiment. The measurement duration for each individual



Fig. 1. Experimental setup at the forest clearing (a) and at the wetland site (b) in snowfree conditions. Positions of ELBARA-II footprint center-points at incidence angles 30° ≤ θk ≤ 70° are indicated, as well as approximate −9 dB footprints (θk ± 12°) for the measured incidence angle (θk = 60° and θk = 30° for (a) and (b), respectively). Location of snow pit and manual soil permittivity measurements are indicated, as well as the location of ‘SO11’ stations and ‘SM_A/B′ sensors measuring soil permittivity and temperature.

incidence angle θk was 150 s, with an integration time of 3 s leading to a measurement accuracy of TpB(θk) better than ± 1 K (Schwank et al., 2012). Measurements of downwelling sky brightness temperatures were made every 24 h around midnight in order to verify the stability of the instrument. ELBARA-II was calibrated using internal calibration targets; these consist of a resistive noise source thermally stabilized to the instrument internal temperature (ranging from 10 °C in winter to 35 °C in summer) and an active cold source (ACS) at ≈40 K. The exact value of the ACS noise temperature was calibrated using zenith observations Tsky = TpB(θk = 180°) of sky radiance which is well known and stable (≈5 K) at the L-band (Pellarin et al., 2003). Observations of Tsky showed a standard deviation of less than 0.4 K at both polarizations throughout the entire campaign, indicating the good stability of the instrument. As is described by Schwank et al. (2010) and Schwank et al. (2012), thermal emission of the lossy feed-cables connecting the antenna ports to the receiver was compensated based on a priori characterization of cable losses and cable temperature measured in situ.

2.3. Reference measurements Automated and manual measurements of soil and snow properties were made at the two test sites. The time series of daily averages of TpB(θk = 50°), air and ground temperature (Tair and TG, respectively), in situ soil permittivity (εG) and snow depth (SD) are shown in Fig. 2 for the two test sites. TpB for the forest clearing site were characterized by

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high variability during summer following changes in temperature and soil permittivity. During winter TpB were much more stable in time and reach a seasonal maximum with decreased polarization difference. For the wetland site, the response of TpB can immediately be seen to be more variable, even during winter periods. This is consistent with the high variability of in situ measured εG at wetland site even during winter. At the forest clearing site, surface soil permittivity data were collected from two locations (labeled SM_A and SM_B) using Delta-T Devices ML2x sensors, installed horizontally at a depth of ≈2 cm beneath the organic surface layer; no measurements were taken of the above organic layer. The sensors measure the permittivity of soil at the frequency of 100 MHz. For this study, these in situ measured permittivities are considered to be valid also at L-band, which is a reasonable assumption considering the typical frequency response of the permittivity of mineral soils and water in the 100 MHz–1 GHz range (e.g. Heimovaara, de Winter, van Loon, & Esveld, 1996; Robinson et al., 2008). Both sensors were located at a distance of ≈15 m from the footprints observed by the ELBARA-II radiometer. A temperature sensor at 2 cm depth was also installed at SM_B location. In the summer of 2011, additional permittivity and temperature sensors were deployed at the site. This socalled SO11 station (Fig. 1a), equipped with Decagon 5TM sensors, measured soil permittivity and temperature profile at the depths of 5, 10, 20, 40 and 80 cm; three sensors at 5 cm depths were used to assess the spatial variability of near-surface soil conditions. The measurement location was adjacent to the ELBARA-II footprints, but again, none of the sensors were directly within the radiometer footprints to avoid disturbances while still providing representative in situ information on the scenes observed by the radiometer. The measured permittivity, obtained at 70 MHz, was again assumed to be valid for L-band. In addition to soil measurements, snow depth (SD) at the forest clearing was measured with a Campbell Scientific SR50 acoustic sensor adjacent to the ELBARA-II footprints. The representativeness of the SM_A and SM_B sensors versus ground conditions within the ELBARA-II footprints was investigated by means of manual measurements using a ML2x sensor, alongside the ELBARA-II footprints (Fig. 1a). Ten to twelve measurement locations at 1 m intervals were sampled; 10 individual measurements were made at each location. A total of 78 manual in situ measurements were performed during autumn 2009 and during summer and autumn of 2010. The manually measured εG showed a bias of ≈+34% in comparison with the average ground permittivities measured with the automated sensors SM_A and SM_B. Consistent with this finding, the average εG measured by SO11 sensors showed a bias of ≈+20% compared to εG measured with the SM_A and SM_B sensors, with increasing bias for high values. As a consequence of the extended sensitive volume of the in situ sensors it is expected that readings εG of the shallow sensors buried at 2 cm depth were affected by air and snow above the ground surface, reducing the apparent permittivity measurements. This effect was compensated by using an exponential fit to relate the values of SM_A and SM_B sensors to that of the SO11 sensors:

εG;SO

11 ðt Þ

D E ¼ a∙ exp b∙ εG;SMA ðt Þ : B

ð1Þ

Thereby, 〈εG , SO_11(t)〉 and 〈εG , SM A/B(t)〉 are averaged values of the three SO11 sensors and two SM_A/B sensors at time t, respectively. Using data collected between September 6, 2011, and April 1, 2012, the fit yielded the parameter values a = 2.08 and b = 0.21. Values 〈εG , SM A/B(t)〉 were adjusted accordingly, and the fitted values were used in the subsequent analysis. At the wetland site, ground permittivity and temperature were measured in situ using a SO11 station at three locations at depths of 5, 10, and 20 cm. These three sets of sensors were placed at a distance of 5, 10 and 15 m from the ELBARA-II tower, respectively. As at the forest clearing site, the sensors were placed adjacent to the radiometer


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Fig. 2. Daily averages of measured TpB(θk = 50°) (a), air and ground temperature (Tair and TG) (b), soil permittivity (εG) (c), and snow depth (SD) (d) for the forest clearing (left) and wetland (right) test sites. Average values for TG and εG from sensors SM_A and SM_B at 2 cm depths and average of three SO11 sensors at 5 cm depths (one sensor for wetland site). Manual measurements shown with error bars corresponding to standard deviation of ≈100 samples. Uncorrected values of εG for SM_A and SM_B are shown. Note differing vertical axes for forest clearing and wetland sites in (c).

footprints. At the wetland site, the interpretation of in situ sensor readings was critical during very wet ground conditions, as on occasion some sensors indicated saturation in the measured permittivity (indicating values close to the permittivity of water), while other adjacent sensors indicated lower values. These features reflected the high spatial variability of soil moisture across the wetland site, in particular during late autumn when the water level at the site was at the seasonal maximum. As explained later in Section 4.4, data from only one sensor best matching ELBARA-II observations was used in the analysis. In addition to soil measurements, snow depth was measured with a SR50 acoustic sensor at ≈50 m from the radiometer. During the snow season, regular snow pit observations were made at both sites adjacent to the radiometer footprints, at a distance of ≈20 m (forest clearing) and ≈50 m (wetland) (Fig. 1). Snow density profiles at vertical resolution of 5 cm were measured using a 250 cm3 manual cutter; however, in 2009–2010, a Snow fork (Sihvola & Tiuri, 1986) was used in place of a manual cutter for measuring density profiles at 10 cm resolution. In addition, bulk snow properties (depth and density) were measured separately using a large snow scale. The snow pit measurements were performed twice a week for the period of 2009–2010, once a week until spring 2014, and once every two weeks for the period of 2014–2015. Snow pits were made at a minimum distance of 1 m from the previous pit location to avoid disturbance from the previous pit. The snow pit information thus includes also the influence of small scale spatial variability on observations, which can be significant for natural snowpacks at the meter scale (Sturm & Benson, 2004). 2.4. Snow removal experiment A snow removal experiment was conducted at the wetland test site at the end of the campaign in February 2015, in the measurement area

used for continuous measurements (Fig. 1b). The purpose for the manual removal of the snowpack was to demonstrate the sensitivity of Lband brightness temperatures TpB(θk) with respect to dry snow cover, while being able to quantify the density of the snowpack removed from the radiometer footprints at each incidence angle θk. Moreover, the removal of the snowpack provided reference measurements TpB(θk) of the frozen ground without the influence of snow cover. For the continuous time series, the snow-free reference was only obtained in thawed soil conditions. For the experiment, the naturally accumulated snowpack was first characterized over the ELBARA-II footprints at 30° ≤ θk ≤ 60°. The vertical and horizontal variability of snow density was measured from three adjacent snow profiles at the center of each footprint (seven locations as shown by the footprint center points in Fig. 1b). A total of 21 density profiles were thus measured. Next, the snow was removed using a snow blower and a brush from an area covering at least the −9 dB footprints of ELBARA-II, allowing for a ≈ 0.5 m margin on both sides, and a margin of several meters at the far end θk = 60° footprint. Due to the hard-frozen and mostly even soil surface at the wetland site, the snow removal could be made without provoking serious disturbance to surface roughness properties. 3. Retrieval approach 3.1. Forward model The microwave emission model introduced by Schwank et al. (2015) was used to simulate L-band brightness temperatures TpB(θk) over a rough ground surface, covered by a dry snowpack. The model uses parts of the ‘Microwave Emission Model for Layered Snowpacks’ (MEMLS; Wiesmann & Mätzler, 1999; Mätzler & Wiesmann, 1999) to model propagation in snow by means of a two stream approach, and



parts of the ‘L-band Microwave Emission of the Biosphere’ (L-MEB) model (Wigneron et al., 2007), developed for SMOS, to simulate Lband emission of land surfaces. The resultant microwave emission model, specific for L-band, is rather simple because absorption and volume scattering in dry snow can be neglected implying that the upwelling emission of the ground beneath dry snow is the dominant source of upwelling L-band emission. As a consequence the emission model requires only a small number of input parameters associated with atmospheric, ground- and snow states to simulate L-band TpB at polarization p = H, V and at the observation angle θk relative to nadir. The required parameters are given in Table 1. The simplicity of the model and the small number of input parameters used make the emission model suitable for its application in a retrieval scheme (Section 3.2). The thickness of the sensitive bottom snow-layer is ≈10 cm (≈half observation wavelength), corresponding to the minimal thickness of a snow-layer which is expected not to provoke coherent effects. Sensitivity of L-band TpB with respect to the state of dry snow-layers overlaying the sensitive bottom layer is not expected because of negligible absorption and volume scattering at L-band frequencies. These considerations imply that it is not even necessary to know the depth, the temperature, or the microstructure (e.g. grain size or correlation length) of a dry snowpack to simulate TpB at L-band frequencies, providing that snow depth exceeds the approximate limit of ~10 cm, after which coherence effects arise. A schematic of the forward model setup is given in Fig. 3. The model used to estimate the effective permittivity εS of the sensitive bottom snow-layer with mass density ρS, and the models applied to estimate reflectivities spG (p = H, V) of the rough ground-snow interface and the reflectivities spS of the specular snow–air interface are provided in Appendix A. Once the interface reflectivities spG and spS are known, the Kirchhoff coefficients apG = (1 − spG)(1 − spS) / (1 − spG ∙ spS) and apsky = 1 − apG (Eq. (9) in Schwank et al. (2015)) associated with a single (snow) layer above an infinite half-space (ground) are computed to derive brightness temperatures as TpB = TG ⋅ apG + Tsky ⋅ apsky (Eq. (10) in Schwank et al. (2015)). The two-stream Kirchhoff coefficients inherently include effects of multiple reflections across the sensitive bottom snow-layer, and downwelling sky radiance (Pellarin et al., 2003 and Eqs. (1)–(3) in Schwank et al. (2015)) is TB,sky↓ ≈ 5 K. Fig. 4 demonstrates the effect of snow cover on the microwave signature by comparing simulated reflectivities spG and spS at layer interfaces as a function of snow density ρS. To highlight the effect of impedance matching separately from the effect of refraction in snow, spG is given also for a case where the refraction is artificially omitted and θS = θk. When including the effect of refraction (θS b θk), sH G is seen to drop notably with increasing ρS, while sVG remains relatively stable. On the other hand, when omitting refraction in snow, purely the effect of impedance matching causes sVG to drop more rapidly while the decrease in sH G is less prominent. At the air–snow interface, increasing ρS rapidly also inV creases sH S , while for sS the effect is minimal. Fig. 5 shows an example of simulated TpB(θk) (lines) in comparison with tower-based ELBARA-II observations (symbols) performed at the FMI-ARC test site in Sodankylä, Finland, on March 8th 2012 (forest

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Fig. 3. Schematic of forward model depicting calculation of TpB above snow–ground system.

clearing site). Simulations of TpB(θk) (solid lines for p = H, dashed lines for p = V) are shown for ρS = 100 kg m− 3 (orange), 200 kg m− 3 (blue), 300 kg m− 3 (green), 400 kg m− 3 (red). Measured values of εG = 4.3 and TG = −2.4 °C from SO11 station sensors were applied in the simulation. Ground roughness parameters SDS = 0.5 cm and LC = 1.0 cm estimated from visual site observations yield reasonable agreement between simulated and measured TpB(θk) for the forest clearing site. Measured snow density of the bottom 10 cm of the snowpack on this date was ρS,obs,10cm = 225 kg m−3. As can be seen in Fig. 5, the relatively low sensitivity of TVB (θk) (dashed lines) for 40° ≤ θk ≤ 60° with respect to snow density ρS becomes obvious from the simulations. This is due to the partial compensation of refraction and impedance matching at vertical polarization caused by the snow. At horizontal polarization TH B (θk) (solid lines) are clearly more sensitive with respect to ρS within the angular range 40° ≤ θk ≤ 60° because effects of snow refraction and impedance matching are always supportive. It is exactly this angular and polarization dependent sensitivity of TpB(θk) (p = H, V) that poses a prerequisite for the successful retrieval of dry snow density ρS on the basis of multi-

Table 1 Input parameters required for forward model. Medium

Parameter Description

Atmosphere TB,sky↓a Snow Soil

ρS TG εG SDS LC

Downwelling atmosphere brightness temperature including cosmic background Density of bottom snow layer Soil temperature Soil relative permittivity Standard deviation of soil surface height Autocorrelation length of soil surface

Units K kg/m3 K – cm cm

a Only downwelling TB,sky needs to be considered for tower-based observations (below atmosphere).

Fig. 4. Simulated reflectivities at air snow (spS; dots) and snow–ground interfaces (spG; lines) as a function of snow density ρS. Reflectivity spG at snow–ground interface given both including (θS b θk; solid lines) and omitting (θS = θk; dashed lines) effect of refraction. All interfaces are considered specular.


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The retrieval technique makes use of the method of least squares to minimize the cost function CF(εG, ρS) of model predictions TpB,mod, (θk, εG, ρS)against observations TpB,obs (θk) to retrieve the two free parameters P = (ρS, εG) simultaneously: CF ðεG ; ρS Þ ¼

2 p p; T ð θ Þ−T ð θ ; ε ; ρ Þ : G k k S B;obs B; mod p¼H;V

Xθn X θk ¼θ

ð2Þ

Thereby, the summation is carried out over the available observation angles θk = θ1,…,θn, and over the two polarization states p = H, V. As outlined in Section 2.2 the range of incidence angles applied was selected separately for each test site based on limitations imposed by the ELBARA-II tower platform, vegetation (trees in the forest clearing site) or heterogeneity of the observed scene (standing water in the wetland site). A graphical representation of the minimization process is provided by Schwank et al. (2015; Fig. 4). 4. Results

Fig. 5. Simulated (lines) and measured (symbols) L-band brightness temperatures TBp(θk) (p = H, V) as function of the incidence angle θk (solid lines: horizontal polarization (p = H); dashed lines: vertical polarization (p = V). Simulations using the indicated snow densities ρS are shown in comparison with tower-based ELBARA-II observations (triangles) performed at the forest clearing site. All simulations were made for the indicated ground permittivity εG and ground temperature TG measured from SO11 sensors at 5 cm depth. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

angular brightness temperatures TpB,(θk) at polarization p = H, V. However, it is equally clear that with increasing density, the sensitivity to changes in ρS is quickly reduced and distinguishing between e.g. ρS = 300 kg m−3 and ρS = 400 kg m−3 is difficult even at horizontal polarization. Moreover, for large incidence angles θk, the sensitivities of TpB(θk) with respect to ρS becomes even reversed. However, by applying observations TpB(θk) from a wide range of θk and from both orthogonal polarizations p = H, V, unique retrieval solutions P = (ρS, εG) of the parameters of interest can still be found as it was demonstrated in Schwank et al., 2015 by means of synthetic brightness temperatures TpB(θk) and as will be demonstrated with corresponding ELBARA-II measurements.

In the following sections we present first comparisons between brightness temperatures simulated with the outlined emission model (Section 3.1) against ELBARA-II observations (Section 2.2), as well as parameters P = (ρS, εG) retrieved (Section 3.2) from ELBARA-II measurements (Section 2.2) in comparison with in situ reference measurements (Section 2.3). Observations performed during the snow removal experiment (Section 2.4) are used for the initial forward simulations shown in Section 4.1, because these measurements provide the most reliable information on the snow at the plot scale used to drive the emission model. The approach applied to initialize the ground roughness parameters (SDS, LC) considered as constants for the two-parameter retrievals P = (ρS, εG) is described in Section 4.2. Examples of retrievals P = (ρS, εG) for the two test sites are presented in Section 4.3. Finally, timeseries of retrievals P = (ρS, εG) in comparison with synchronous in situ reference measurements are shown in the Sections 4.4 and 4.5. 4.1. Snow removal experiment Brightness temperatures measured before (solid triangles) and after (hollow triangles) the removal of the dry snow are shown in Fig. 6,

3.2. Two-parameter retrieval The emission model outlined above is used to simulate upwelling Lband brightness temperatures TpB,mod (θk εG, ρS) over a ground with permittivity εG covered with a dry snowpack exhibiting the mass density ρS at the sensitive bottom layer. The only additional model parameters involved are the effective ground temperature TG and the parameters used to characterize ground roughness (standard deviation SDS of the surface height and autocorrelation length LC). From a technical point of view, the simplicity of the emission model (small number of model parameters and simple mathematical structure) makes it suitable for use in an inversion scheme. Furthermore, its significant and distinguishable sensitivities with respect to εG and ρS, in terms of their impact on polarization and angular dependence, suggest the possibility to simultaneously retrieve the two-parameters P = (ρS, εG) on the basis of multiangular observations TpB,obs (θk). A corresponding retrieval technique was proposed by Schwank et al. (2015); the sensitivity of the technique to the quality of observations was explored by means of synthetic observations corresponding to typical SMOS data-quality (see Fig. 5 by Schwank et al., 2015). In this study we apply this two-parameter retrieval approach for the first time to real brightness temperature observations TpB,obs (θk) made with the ELBARA-II radiometer.

Fig. 6. Simulated (lines and shaded areas) and measured (triangles) TpB(θk) for the snowcovered footprints at the wetland site and for the corresponding footprints after snow clearing. Extent of snow clearance indicated with vertical dashed lines.



along with corresponding simulations performed for ρS = 233 kg m−3 − 304 kg m−3 (measured range of snow densities before snow removal) and ρS = 0 kg m−3 (bare ground after snow removal). The whole range of observed and simulated TpB(θk) up to θk = 70° is depicted in Fig. 6, while the vertical dashed lines indicate the angular range 30° ≤ θk ≤ 60° of −9 dB footprints which were bare ground after the snow clearance. Simulations were made with measured ground permittivity εG, taken from measured values at 5 cm depth. Measured TG indicated a temperature of 0 °C; however, a temperature of − 1 °C was applied in the simulations, as the ground was observed to be frozen solid. SDS and LC, indicated in Fig. 6, were used to optimize the simulations for 35° ≤ θk ≤ 55° in terms of agreement with the measurements. The average in situ measured ρS of the bottom 10 cm of the snowpack (the layer expected to affect measured TpB) varied between 233 kg m−3 and 304 kg m−3, with an average of 266 kg m−3 and a standard deviation of 13 kg m− 3. Simulations of TpB(θk) representing the snow covered scene (before removal of the snow) were performed for the whole measured range 233 kg m− 3 ≤ ρS ≤ 304 kg m−3 yielding the simulated TpB(θk) indicated as shaded areas in Fig. 6. For the range 35° ≤ θk ≤ 55° of observation angles (slightly smaller than 30° ≤ θk ≤ 60° expected to be within the snow-cleared area) the observed TpB(θk) are consistent with the simulations, while at θk = 30° and θk ≥ 60° the measurements TH B (θk) are increased. This behavior was consistent for the winter of 2015 from January, until the end of the experiment, indicating possible differences in either snow or ground conditions affecting the horizontally polarized signal. The influence of the snow removal is minimal at vertical polarization, in particular at around θk = 50°. This finding implies that the effect of the dry snowpack on L-band emission is minimal for vertical polarization at θk = 50°, as predicted by the model. At this angle, the contrary effects of refraction angle change and impedance matching exactly cancel each other out. For observations with a small θk the comparison between the measurements at vertical polarization performed over the snow-covered and the snow-free footprints clearly show that the impact of dry snow remains small (1–3 K), consistent with the simulations. Unlike at vertical polarization, measurements at horizontal polarization were not angular dependent (if the differing behavior for θk ≥ 60° is disregarded). These experimental findings corroborate the theoretical finding on the L-band propagation effects in dry snow presented in Schwank et al. (2014) and Schwank et al. (2015). To recap, these theoretical studies predicted that the effects of impedance matching and refraction caused by dry snow should largely compensate for each other at vertical polarization, particularly at θk = 50°, with consistent, angular independent sensitivity at horizontal polarization. Using the optimized ground parameters indicated in Fig. 6, model estimates for the snow covered scene agreed with observations to within 0.5 K at vertical polarization, and 2.7 K at horizontal polarization on average for 35° ≤ θk ≤ 55°. The horizontally polarized brightness temperature measured for θk ≥ 60° over the undisturbed snow covered footprint was possibly affected by differing snow and soil properties. As indicated by the simulations over the measured range of snow densities, however, snow conditions as represented by the in situ measurements are solely not sufficient to explain the differing level of brightness temperatures TpB,(θk N 60°), compared to lower incidence angles. 4.2. Optimization of ground parameters Retrievals P = (ρS, εG) using ELBARA-II data were performed for observations ranging from October 2009 to August 2012, and from September 2012 to February 2015, for the forest clearing and the wetland site (Fig. 1), respectively. Thereto, the optimal ground roughness parameters SDS = 0.5 cm and LC = 1 cm were determined yielding the best agreement between simulated and TpB,obs,(θk) observed at θk = 40°, 45°,…,60° and p = H, V at the forest clearing site during late

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autumn (snow free) in 2010. In the least square sense these roughness parameters yielded the best agreement between observations TpB,obs,(θk) and modeled TpB,mod,(θk) when using in situ measured εG and TG to drive the emission model. Accordingly, the optimized values SDS = 0.5 cm and LC = 1 cm were applied for all retrieval tests at the forest clearing site. For the wetland site, the optimization of the ground roughness parameters SDS and LC was more problematic; the local surface roughness changed over the year due to rising and decreasing water levels. For example, for footprints with standing water during late autumn, the ground permittivity of εG ≈ 86 (L-band water permittivity) and the assumption of an perfectly smooth ground surface (LC = SDS = 0 cm) gave the best model fit with respect to measurements, while for dry summer months best model fit was achieved for SDS ≈ 0.8 cm and LC = 1 cm. For winter months, the optimal fit to observations was achieved with values falling somewhere in between these extremes (0 cm b SDS, LC b 1 cm). Moreover, optimum values even for winter periods were not annually consistent; from the relatively poor fit of the model to observations when using optimal parameters obtained for one season to the other two, it became obvious that the subnivean conditions at the wetland site differed from one season to another. Finally, roughness parameters SDS = 0.6 cm and LC = 1 cm were applied, as these gave a reasonable fit to multi-angular observations during all three winter seasons. Better retrieval results P = (ρS, εG) for the wetland site could have been achieved with annually variable roughness parameters. However, such an advanced approach would probably not be realistic at the satellite scale, hence we assumed temporally constant ground roughness parameters just as it is assumed in current SMOS soil moisture retrievals (Kerr et al., 2011). For the purposes of this study, finding fit parameters for both sites in snow-free conditions would have been ideal, as this increases confidence in the forward model to account for snow cover effects. However, because a reliable snow-free reference could not be obtained for the wetland site, the differing approach based on the winter season was implemented. 4.3. Retrieval examples Fig. 7 shows examples of observed brightness temperatures T pB;obs; (θ k )in comparison with simulations T pB,mod,(θ k , εG, ρS) using optimized ground roughness parameters (Section 4.2) and the retrieved parameters P = (εG,ret , ρS,ret) for the forest clearing and the wetland site. The minimized values CFmin = CF(εG,ret, ρS,ret) of the cost function CF(εG, ρS) achieved for the retrievals P = (εG,ret, ρS,ret ) are also shown (in units K 2 ). The overall goal of the data shown in Fig. 7 is to demonstrate the versatility and limits of the two-parameter retrievals when applied to different situations (forest clearing and wetland during summer and winter). Fig. 7a shows observations TpB,obs,(θk) (triangles) and TpB,mod,(θk, εG, ρS) (lines) modeled for retrievals P = (εG,ret, ρS,ret) at the forest opening site (August 22, 2011; no snow was present, thus ρS = 0 kg m−3). Due to the mentioned disturbances of TpB,obs,(θk) measured at steep (θk b 40°, effect of tower structure) and shallow (θk N 60°, effect of trees in the farrange) observation directions only measurements performed for θk = 40°, 45°, 50°, 55°, 60° and p = H, V (a total of ten measurements), were used for the retrievals P = (εG,ret, ρS,ret) over the forest clearing site. The retrieved εG,ret = 5.7 represents a typical value for unfrozen dry sandy soil as it was the case during these observations; measured permittivity from SM_A/B sensors at 2 cm depth was εG,obs = 4.6. Modeled TpB,mod,(θk, εG = 5.7, ρS = 0 kg m− 3) follow observations T pB;obs; (θk) reasonably at vertical polarization; at horizontal polarization some discrepancy can be noted, which explains the relatively high value of CFmin = 446 K2. For the winter-time case (January 18, 2012, Fig. 7b), modeled brightness temperatures reproduce observations well at both polarizations, as exhibited also by the small value


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Fig. 7. Examples of simulated (lines) and observed (triangles) brightness temperatures TpB(θk) using the indicated retrieved parameters P = (εG,ret, ρS,ret). Forest clearing site for summer (a) and winter (b); wetland site for late autumn (c) and winter (d). Observation angle ranges of 40° ≤ θk ≤ 60° and 50° ≤ θk ≤ 60° used for retrievals over the forest clearing and wetland sites, respectively. Hollow triangles indicate snow free conditions, filled triangles indicate presence of snow.

CFmin = 120 K2. The corresponding retrieved parameters take the values P = (εG,ret, ρS,ret) ≈ (5.1, 281 kg m−3) which reflect typical winter time conditions; in situ measured reference values were εG,obs = 4.3 and ρS,obs,10cm = 288 kg m−3 for the snow density in the sensitive bottom (≈10 cm) snow-layer. The effect of vegetation facing the instrument can be seen as increased brightness temperatures observed at shallow incidence angles (θk N 60°) in both Fig. 7a and b. For the wetland site, an example of a late autumn retrieval for September 21, 2012 (Fig. 7c) where no snow was present (ρS = 0 kg m−3), reflects the saturated moisture conditions the large heterogeneity at the site. This explains the relatively low brightness temperatures, as well as the pronounced variability of the measurements TpB,obs,(θk) even for 40° ≤ θk ≤ 60° considered as observations not disturbed by the tower structure or trees in the far-range. Accordingly, when using the ten measurements TpB,obs,(θk) (θk = 40°, 45°, 50°, 55°, 60° and p = H, V) we retrieved the value εG,ret ≈ 46 for the ground permittivity of the correspondingly very wet and partly saturated ground state. However, even higher ground permittivity εG,ret, close to the value of liquid water, is retrieved when further restricting the observation angles to θk = 30°, 35°. This can be expected already from the low TpB,obs,(θk) measured for these steep angles. Furthermore, webcam imagery from the site confirmed that the water level exceeded the height of surface vegetation for these low angles, while measurements at 40° ≤ θk ≤ 45° represent ‘mixed pixels’. Compared to the late autumn,

the winter observations performed on March 23, 2013 shown in Fig. 7d reveal clearly higher values with less angular variability in both measured and modeled brightness temperatures. The retrieved parameters P = (εG,ret, ρS,ret) ≈ (4.2, 250 kg m− 3) compare reasonably well with the corresponding in situ reference observations ρS,obs,10cm = 244 kg m− 3 for bottom-layer snow density. The retrieved permittivity is underestimated compared to in situ εG,obs = 6.6 measured by the SO11 sensor at 5 cm depth. These values retrieved for the winter state of the wetland site closely match the winter retrievals of the forest clearing shown in Fig. 5b. These results indicate that once the saturated soil at the wetland site freezes completely, the retrievals between sites bear close resemblance. The incidence angle range of 50° ≤ θk ≤ 60° was used in all retrievals at the wetland site until summer 2014. For retrievals in the last season (2014–2015), the range of 45° ≤ θk ≤ 55° was used, as measurements for θk ≤ 60° deviated from lower incidence angles also during winter (see Fig. 6). Overall, these examples demonstrate the versatility of the multiangular retrieval method to represent different situations at the two test sites. The plot scale spatial variability in soil conditions at the wetland site is also highlighted; observed brightness temperatures do not show consistent behavior with incidence angles when subnivean temperatures are above freezing (or during periods of transitions to a frozen state).



4.4. Time series of retrieved ground permittivities In order to quantify the effect of dry snow on ground permittivity retrievals we first performed single-parameter retrievals ε G,ret,inv-snow assuming dry-snow as ‘invisible’ (i.e. as not having any effect on the L-band emission) as it is assumed currently in corresponding SMOS retrievals over snow-covered areas (Kerr et al., 2011). Thus, the brightness temperature above the soil was simply given by (see Fig. 3) T pB = s pG ⋅ T B,sky ↓ + T G ⋅ (1 − s pG ), and s pG was calculated based on Fresnel reflection coefficients between the soil and the atmosphere. Second, two-parameter retrievals P = (εG,ret, ρ S,ret ) were performed, taking into account propagation effects (refraction and impedance matching) in dry snow. Brightness temperatures TpB,obs,(θk) measured exclusively during dry snow conditions (air temperature T air b 0 °C) were applied. Furthermore, to avoid possible coherence effects from shallow snowpacks, the threshold of the in situ measured snow-depth SD applied to distinguish between snow-covered and snow-free situations was set to 10 cm.

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Fig. 8 shows reference in situ ground permittivities εG,obs (black lines) measured at the forest clearing site (panels a)–c); 2009–2012) and at the wetland site (panels d)–f); 2012–2015). Measured soil temperature TG is also shown, Synchronous retrievals of εG,ret,inv-snow (green; single-parameter retrievals assuming dry snow as ‘invisible’) and εG,ret (blue; two-parameter retrievals taking into account snow refraction and impedance matching) derived from TpB,obs,(θk) measured for dry snow conditions are shown for comparison. For the forest clearing site, the reference data εG,obs measured for 2009–2010 and 2010–2011 represent the average of SM_A and SM_B sensors at 2 cm depths (Fig. 8a,b); for 2011–2012 the average of three SO11 sensors at 5 cm depths is also shown (Fig. 8c). For the wetland site (Fig. 8e–g), the spatial and temporal variability in permittivity conditions indicated by the SO11 sensors at 5 cm depth (labeled here a, b, and c) presented difficulties for the analysis. In 2012–2013, sensor SO11a indicated freezing on the same date as retrieved εG,ret. Sensor SO11c indicated freezing two weeks after, and sensor SO11b as late as February 2013. In 2013–2014, sensor SO11b did not indicate freezing at all. Sensor SO11c indicated temporally the same behavior as SO11a,

Fig. 8. Night-time averages of ground permittivities εG,ret,inv-snow (green) and εG,ret (blue) retrieved from TpB,obs,(θk) measured with ELBARA-II during dry snow conditions. Reference ground permittivities εG,obs measured in situ (average of SMA/B sensors at 2 depths and SO11 sensors at 5 cm depth for forest clearing site; readings of individual sensors for wetland site). Measured soil temperature TG from 2 cm depth (forest clearing site) and 5 cm depth (wetland site). Seasons 2009–2010 (a), 2010–2011 (b) and 2011–2012 (c) at the forest clearing site. Seasons 2012–2013 (d), 2013–2014 (e) and 2014–2015 (f) at the wetland site. Sensor SO11c failed in early March 2014, but was replaced for the following season.


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but the permittivity values during the freezing periods differed with a permittivity of ~ 40, compared to values below 20 given by sensor SO11a. There was also a temporal difference of almost two weeks in the timing of melt events indicated by the ELBARA-II retrievals in January and March 2014, and melting detected by these sensors. This can be possibly be explained by the local conditions; the soil surface was frozen solid, resembling e.g. lake ice, which prevented the immediate percolation of melt water to the sensors buried in the organic soil/ice medium. This was confirmed by snow pit observations at the site, which showed a 2–4 cm layer of moisture-saturated snow on top of a solid frozen surface, which coincided with increased permittivity retrieved from ELBARA-II. The moist snow layer had refrozen two weeks after, when in situ sensors reported the thaw events. Possibly, percolation of moisture to the sensor depths was delayed by the solid frozen ground. Another explanation is that the moisture had slowly spread horizontally to finally reach the sensor locations. However, no in situ observations are available to support these assumptions. For the last season of the experiment in 2014–2015, sensor SO11a indicated freezing with εG,ret, but SO11b and c simultaneously indicated freezing with a delay of one week. Based on the temporal behavior, sensor SO11a was assumed to be the most representative of conditions observed by ELBARA-II, and used in the subsequent analysis. Data for all sensors are displayed in Fig. 8. Night-time averages of ground permittivities εG,ret,inv-snow and εG,ret, retrieved between 11 pm to 7 am local time with the two mentioned approaches, are compared against εG,obs in Table 2 in terms of average bias and unbiased root-mean square error (uRMSE) for winter periods, given as percentage of observation mean. The winter period was defined as the surface soil temperature TG being under 0 °C, or ~ 0 °C for the wetland site, with retrieved permittivity also indicating freezing. The night-time averages were used in order to avoid possible sun glint effects and melting of the snow surface. Table 3 shows similar values for the late autumn period at the forest clearing site when snow cover was present but the soil was not fully frozen (2009-10-10 to 2009-1215, 2010-10-25 to 2010-11-24 and 2011-11-20 to 2011-12-15). This period was ambiguous for the wetland site, and precise error values are not given; the retrieval, however, yielded clearly erroneous solutions as can be seen from Fig. 8. A possible reason for the failure of the retrieval during autumn periods at the wetland site is the presence of moisture beneath the dry snow cover due to incomplete freezing of the moist organic soil at the site. At the forest clearing site, retrievals εG,ret,inv-snow achieved under the assumption of ‘invisible’ dry snow were on average 35% and 40% lower than the retrievals εG,ret achieved when propagation in dry snow is considered for winter (frozen soil) and late autumn (thawed soil), respectively. For the winter period, the bias between the retrievals εG,ret and

Table 3 Same as Table 2 but for autumn season at the forest clearing site (unfrozen soil). Values for wetland site not given (all bias errors in excess of −80%). Site

Forest clearing

Season

2009–2010 2010–2011 2011–2012

N

29 25 16

εG,ret

εG,ret,inv-snow

Bias (%)

uRMSE (%)

Bias (%)

uRMSE (%)

14.0 −4.4 10.4

10.8 25.8 6.8

−31.7 −43.7 −31.8

14.7 25.5 4.9

the reference in situ data εG,obs was smallest for the 2009–2010 season, while for the other two seasons, a bias smaller than 17% was reached. For the late autumn periods, the corresponding retrieval bias was less than 14% for all three seasons. It should be noted that the error values provide only an indication of retrieval performance, due to the natural variability at the site, and also due to the L-band emission depth that may deviate from the installation depth of the in situ sensors. This depth-related sensitivity may also explain the temporal differences in permittivity observed and retrieved at the wetland site in the winter of 2013–2014 (Fig. 8e). For the wetland site, retrieved εG,ret match references εG,obs from the sensor SO11a relatively well for the first and third winter seasons, while large discrepancies are noted for the 2013–2014 season. A reason behind this may be the aforementioned mild conditions experienced during that season, which resulted in multiple snow melt-refreeze events already in January–February 2014, and incomplete freezing of the ground, as indicated by the measured permittivity values of the three SO11 sensors (Fig. 8e). In contrast, a sharp freezing was apparent during the following season already in mid-November 2014, with surface probes indicating that the surface soil remained frozen until the snow removal experiment in February 2015. Nevertheless, εG,ret,inv-snow yielded on average 35% lower values than εG,ret. For both test sites, the results confirm predictions given in the synthetic study (Schwank et al., 2015) that ground-surface permittivity retrieved under the assumption that dry snow does not affect L-band emission leads to a systematic and significant underestimation of actual ground permittivity. According to the synthetic analysis, retrieval εG,ret,inv-snow of a ground surface beneath dry snow with density of ρS = 200 kg m−3 underestimates the actual ground permittivity εG by approximately 30%.

4.5. Time series of retrieved snow densities The two-parameter retrievals P = (εG,ret, ρS,ret) derived from the T pB;obs; (θk) measured during dry snow conditions, described in

Table 2 Statistics of night-time averages of retrievals εG,ret,inv-snow (‘invisible’ dry snow) and εG,ret (consideration of propagation in dry snow) against in situ references εG,obs for six winter seasons (frozen soil) at forest clearing and wetland sites. N are the number of cases, bias and unbiased RMSE are given as percentage of εG,obs. For forest clearing site, εG,obs represents the average of sensors SM_A and SM_B. For the wetland site, εG,obs represents sensor SO11a (see Fig. 8 d–f). Site

Forest clearing

Wetland

Season

2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015

N

99 124 103 115 38 68

εG,ret,inv-snow

εG,ret Bias (%)

uRMSE (%)

Bias (%)

uRMSE (%)

10.0 −17.0 14.2 5.2 −62.3 −23.6

5.3 5.9 7.4 24.6 46.3 10.5

−30.1 −43.8 −29.1 −33.9 −57.9 −47.6

2.8 3.3 3.6 36.3 83.5 49.0

Section 4.4, were used to quantify the performance of dry snow density ρS,ret retrieved with respect to in situ observations ρS,obs of snow densities. Fig. 9 shows time-series of retrievals ρS,ret interpreted as the density of the approximately lowest 10 cm of the dry snowpack against manual in situ snow densities observed from snow pits at the two test sites. Both in situ bulk density ρS,obs,bulk and in situ density ρS,obs,10cm observed for the lowest ≈10 cm of the snowpack are shown. In the snow pit observation ρS,obs,10cm there are some uncertainties related to the measurements for the season of 2009–2010, as the density was measured using a Snow fork (Sihvola & Tiuri, 1986), while for later seasons a manual cutter and scale were applied. The uncertainty of snow fork measurements increases for loosely packed, coarse grained snow, which is often present in the lowest part of a snowpack due to depth hoar formation. This can be seen as a large variability of ρS,obs,10 cm shown in Fig. 9a. Similar problems can also be encountered with the manual measurements, specifically due to difficulty in extracting precise samples in



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Fig. 9. Night-time averages of snow densities ρS,ret (blue lines) retrieved from TpB,obs,(θk) measured with ELBARA-II during the selected dry-snow conditions. Reference in situ snow densities ρS,obs,bulk (blue circles) and ρS,obs,10cm (black squares) are shown for comparison. Seasons 2009–2010 (a), 2010–2011 (b) and 2011–2012 (c) at forest clearing site. Seasons 2012–2013 (d), 2013–2014 (e) and 2014–2015 (f) at wetland site. Note differing range of figure vertical axes for forest clearing and wetland sites.

the presence of hard crusts and loose depth hoar layers with ground vegetation. The values measured with the manual scale are nevertheless considered more reliable. A bias of − 60 kg m−3 was observed when

Table 4 Statistics of night-time averages of ρS,ret against in situ observations ρS,obs,bulk and ρS,obs,10cm over six winter seasons (dry snow conditions). Site

Forest clearing

Wetland

Season

2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015

N

22 18 12 16 13 5

ρS,obs,bulk

ρS,obs,10cm Bias (kg m−3)

uRMSE (kg m−3)

Bias (kg m−3)

uRMSE (kg m−3)

15 −11 −6 90 37 52

60 22 30 103 154 43

20 18 31 102 110 45

58 33 73 165 134 117

comparing snow fork densities to density profiles measured using the manual scale; this constant offset was added to all measured values for 2009–2010 to compensate for this bias. Statistics comparing retrieved dry-snow densities ρS,ret against corresponding in situ reference measurements ρS,obs,10cm and ρS,obs,bulk are summarized in Table 4. For the forest clearing site, ρS,ret matched in situ observations ρS,obs,10cm made in the lowest 10 cm of the snowpack for all three seasons to within ≈ 10%. Discrepancies were the largest for the early seasons of 2009–2010 and 2010–2011, while during midwinter retrievals ρS,ret were typically very close to the in situ measurements. Bulk snow densities ρS,obs,bulk measured in situ were typically smaller than retrievals ρS,ret (and likewise ρS,obs,bulk b ρS,obs,10cm). This corroborates the theoretical expectation that L-band emission is most affected by the density ρS,obs,10cm of the snow in contact with the ground; on the other hand it implies that retrieved ρS,ret should not be directly interpreted as the snowpack bulk density ρS,obs,bulk, required to estimate SWE. The in situ snow densities were relatively stable through the dry snow season, and most of the


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variability evident in Fig. 9 can be attributed to spatial variability and measurement uncertainty of the snow pit observations. The standard deviation of bottom layer densities ρS,obs,10cm were 59 kg m− 3, 20 kg m− 3 and 22 kg m− 3 for the first, second and third seasons, respectively. As expected, for the wetland site, bias and RMSE of ρS,ret against ρS,obs,10cm and ρS,obs,bulk were larger than for the forest clearing site. As is apparent from Fig. 9d–f, the retrievals ρS,ret achieved for all seasons exhibited a high degree of variability also during the cold winter period, which is attributed to variability in the subnivean conditions (soil freeze/thaw state), in particular for the 2013–2014 season. For example, the melt event in January 2014 (see Fig. 7e) leads to an increase in ρS,obs,bulk, even exceeding the measured ρS,obs,10cm, followed by a value of almost 500 kg m−3 for ρS,obs,10cm the following week. Large discrepancies between ρS,ret and in situ observations (ρS,obs,10cm and ρS,obs,bulk) were apparent especially during the early winter seasons of 2012–2013 and 2013–2014 (Fig. 9d, e), while for the last season in 2014–2015 the retrievals were relatively stable (Fig. 9f). Retrievals ρS,ret still agreed better with ρS,obs,10cm than with ρS,obs,bulk indicating that also at this site, the retrievals ρS,ret are better correlated with bottom densities ρS,obs,10cm rather than with bulk densities ρS,obs,bulk of a dry snowpack.

5. Discussion The snow removal experiment (Section 4.1) clearly demonstrated that TpB(θk) at L-band are significantly affected by dry snow, known to be almost fully transparent at L-band. The distinct sensitivity of TpB(θk) with respect to the presence of a dry snowpack is predicted by the emission model of Schwank et al. (2015) applied here (Section 3.1). The TH B (θk) measured before and after snow clearance clearly corroborated the model predictions, indicating that the influence of snow cover can be accounted for by the relatively simple emission model, suitable for retrieval purposes. Likewise, the measurements at vertical polarization and θk ≈ 50° confirmed that TVB (θk ≈ 50°) are almost the same and after snow removal, again confirming model predictions. Overall, these qualitative findings clearly demonstrate the necessity to consider radiative transfer processes across the dry snow-layer also at L-band.

Fig. 10. Estimated error of volumetric water content (ΔVWC) as a percentage of reference VWC, assuming 20, 30 and 40% errors (underestimation) in retrieved εG,ret. Conversion of εG,ret to VWC using models by Mironov et al. (2009) and Bircher et al. (2015) for mineral and organic soils, respectively.

This has particular implications also for SMOS soil moisture retrievals over areas affected by seasonal snow cover. Fig. 10 presents the estimated error in retrieved volumetric water content (VWC) as a percentage of the reference value, when the retrieved εG,ret is underestimated by 20, 30 or 40% due to the influence of snow cover (ΔεG,ret = (εG,ret,inv-snow − εG,ret) / εG,ret). Models by Mironov, Kosolapova, and Fomin (2009) and Bircher, Kerr, and Wigneron (2015) are used to convert εG,ret to VWC. In these exemplary simulations, the clay, sand and silt contents for mineral soil were set following measured values from the site (70% sand, 29% silt, 1% clay, with a bulk density of 1300 kg m−3). The sensitivity for other mineral soil compositions will thus differ. For organic soil, the simulations follow an empirical relation derived by Bircher et al. (2015), using samples collected from the organic horizon of several representative sites, including bog sites. The derived relation can be considered to hold for a wide variety of organic soil types (histosols), including the peat and organic surface matter found at the Sodankylä site. With the typical 30% underestimation of εG,ret in this study, VWC at a range of 0.05 to 0.5 will be underestimated from −80 to −30% for the mineral soil type, with increasing error for dry soils. For organic soils, the underestimation ranges from over −100% (zero VWC is estimated) to −20%. In the case of the retrieval time series over the forest clearing site, both the soil permittivity and the density of the bottom snow layer could be estimated to a high degree of accuracy. For the wetland site, results were ambiguous, as the highly variable local soil permittivity prevented a full quantitative evaluation of retrieval performance. Retrievals P = (εG,ret, ρS,ret) at the wetland site exhibited a high degree of variability due to changes in subnivean conditions particularly for the 2013–2014 season, effectively preventing a meaningful comparison between retrievals and in situ measurements. Performing retrieval tests with annually varying roughness conditions (not shown) allowed a better fit of P = (εG,ret, ρS,ret) with in situ observations also for the wetland site. Difficulties may also arise for different snow conditions, such as shallow snow or a thin layer (less than 10 cm) of dense snow or ice at the ground surface (induced by melt events), which may trigger coherence effects which prevent a meaningful retrieval, if the effect covers a significant part of the observation. However, at the spatial scale of passive microwave satellite observations (N10 km), it is presently unclear if such effects can affect the end result in a discernible manner. While these encouraging results were found at the plot scale, it is clear that the application of the two-parameter retrieval approach at the satellite scale presents further challenges regarding land cover and vegetation. The influence of vegetation cover will affect the sensitivity of the retrieval; furthermore, water bodies such as rivers and lakes constitute a highly variable source of brightness temperature in winter, and have to be accounted for in the retrieval. The selection of spatially varying effective surface roughness parameters is another issue. These difficulties are, however, common with any retrieval approach from L-band passive microwave observations over heterogeneous terrain, including the baseline retrieval of soil moisture applied to SMOS measurements. One of the possible applications of the presented methodology to retrieve P = (εG,ret, ρS,ret) from L-band radiometry is to define these values a priori in the retrieval of SWE from higher microwave frequencies, e.g. in the context of the GlobSnow approach (Takala et al., 2011), using space-borne observations of SMOS or equivalent sensors on board other missions (Aquarius, SMAP). At present, the GlobSnow retrieval assumes a fixed soil permittivity of 6–1 ⋅i across all snow covered areas, and applies a static snow density of 240 kg m3 regardless of time and location. SMOS derived estimates of these parameters could be investigated for suitability as dynamic inputs to the SWE algorithm. Despite this potential, it is acknowledged that the retrieved ρS,ret from SMOS describes the density of the bottom snow layer in contact with the ground surface, instead of the bulk density of the entire snowpack required by the SWE retrieval algorithm. Accordingly, the retrieved bottom layer



densities have to be attributed to the full density profile using e.g. a physical snow model, constrained or driven with the retrieved bottom layer density. Spatial heterogeneity in snow density at the scale of a SMOS grid cell is also poorly defined at present, although it has been shown that density is a relatively conservative variable compared to snow depth (Sturm et al., 2010). Applying a temporally and spatially variable εG in the retrieval is more straightforward; however, considerations have to take into account e.g. the differing spatial resolution of satellite instruments used in SWE retrieval (e.g. the Special Sensor Microwave Imager, SSM/I and the Advanced Scanning Microwave Radiometer — Earth Observing System, AMSR-E), compared to SMOS. Furthermore, since effective permittivity is also frequency dependant, εG,ret retrieved at Lband will have to be transferred to higher frequencies using a suitable model for permittivity of frozen soils. Although models exist for thawed soils (e.g. Dobson, Ulaby, Hallikainen, & El-Rayes, 1985; Mironov et al., 2009), a comprehensive model for the permittivity of frozen soils is still missing. However, experimental data (Hallikainen et al., 1985) indicates that the permittivity of frozen soil is highly uniform over a wide range of microwave frequencies, which is to be expected due to the dielectric properties of ice (Mätzler et al., 2006; Rautiainen et al., 2014). 6. Conclusions The approach to retrieve the parameters P = (ρS, εG) of snow density and ground permittivity from L-band passive microwave observations, proposed by Schwank et al. (2015), was demonstrated using tower-based multi-angular brightness temperatures TpB(θk) measured at polarization p = H, V. The applied dataset consisted of a six-year time series of TpB(θk) measured with the L-band radiometer ELBARA-II, overlooking test sites located in a forest clearing and a wetland in Sodankylä, northern Finland. The retrieval of ground permittivity εG was shown to depend on the presence of dry-snow cover. When omitting the influence of dry snow, the retrieved permittivity was lower by ≈35% at both test sites during winter. This has potential implications regarding the present baseline SMOS retrieval algorithm for ground permittivity beneath a dry snow cover (Kerr et al., 2011). In accordance with recent theoretical studies (Schwank et al., 2014; Schwank et al., 2015), retrieved snow density ρS based on TpB(θk) measured with ELBARA-II at the forest clearing site matched the in situ reference densities of the bottom ≈ 10 cm of the snowpack with a bias ranging from − 6 kg m− 3 to 15 kg m−3, while comparison to in situ bulk densities provided a consistent overestimation. At the wetland site, similar results were obtained, albeit variability in the subnivean medium resulted in larger differences and increased variability both inter-annually and within snow seasons. However, the snow removal experiment conducted at the wetland test site showed that measured L-band brightness temperatures TpB(θk) are well in line with simulations performed with the relatively simple microwave emission model proposed by Schwank et al. (2015). At least at the plot scale the retrievals P = (ρS, εG) look promising in comparison with corresponding in situ observations. According to our assessment of the retrieval performance performed by means of tower-based L-band brightness temperatures, we suggest to test the novel two-parameter retrieval with SMOS data measured over northern latitudes. If successful, we consider it prudent to implement the evaluated two-parameter retrieval in a future version of the SMOS processor applied over land to achieve a further step towards the full exploitation of SMOS data.

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imagery for enhanced monitoring of terrestrial cryosphere processes”, (ESA ESRIN Contract No. 4000110696/14/I-BG), and the Finnish Academy Centre of Excellence in Atmospheric Science (FCoE-ATM). FMI Staff in Sodankylä are acknowledged for collection of in situ data and operation of the ELBARA-II radiometer. S. Bircher is acknowledged for providing the relation for soil permittivity and VWC in organic soils. The three anonymous reviewers are acknowledged for providing useful comments and suggestions, which considerably helped to improve this manuscript. Appendix A The computation of the two-stream Kirchhoff coefficients apG and apsky = 1 − apG used to simulate brightness temperatures TpB requires the effective permittivity εS = εS′ + i ∙ εS″ of the snow layer in contact with the ground surface (compare Section 3.1). At L-band frequencies (1–2 GHz) losses in dry snow are known to be very low (εS′ ≫ εS″ ≈ order of 10− 4). Accordingly, εS is assumed as real only, and computed from snow mass-density ρS⁎ (in g cm−3) with the empirical model developed originally for the ‘Microwave Emission Model for Layered Snowpacks’ (MEMLS; Wiesmann & Mätzler, 1999; Mätzler & Wiesmann, 1999):

ε

ρS

( ¼

1 þ 1:5995∙ρS þ 1:861∙ρS 3 for 0:0 g cm3 ≤ρS ≤0:4 g cm3 ðð1 vÞ∙εh þ v∙ε b Þ3 for ρS N0:4 g cm3 ðA1Þ

with v = ρ⁎S /0.917; εh =0.99913; εb = 1.4759. The refraction of radiation at layer interfaces (air–snow; snow– soil) is calculated using Snell's law. Reflectivities spS at polarization p = H, V of the snow–air interface are considered specular, and thus calculated using Fresnel equations. Reflectivities spG (p = H, V) of the snow–soil interface (or, air–soil interface in the case of snow-free ground), are simulated from corresponding (specular) Fresnel reflectivities spG , Fresnel corrected for the impact of ground surfaceroughness characterized by its standard deviation SDS and its autocorrelation length LC. Thereto, we used the H–Q model (introduced by Wang and Choudhury (1981), and modified later by Wang, O'Neill, Jackson, and Engman (1983)) which is the roughness model implemented in the current SMOS Level 2 soil moisture retrieval algorithm (Kerr et al., 2011). Assuming roughness effects as independent on the incidence angle, this assumption is common for L-band (Lawrence, Wigneron, Demontoux, Mialon, & Kerr, 2013) and also considered in current SMOS (Kerr et al., 2011; Wigneron et al., 2007) and SMAP (O'Neill, Chan, Njoku, Jackson, & Bindlish, 2012) retrievals. The roughness model now reads: spG ¼ expðhG Þ∙ spG;Fresnel ð1 qG Þ þ qG ∙sp⊥ ; G;Fresnel

ðA2Þ

where sp⊥ G,Fresnel is the Fresnel reflection coefficient at polarization p = p⊥ orthogonal to the polarization p = H or V. Accordingly, qG is a parameter used to take into account polarization mixing between the two orthogonal polarizations p and p⊥. According to Lawrence et al. (2013) the parameters hG and qG in Eq. (A2) can be expressed with the slope parameter Z ≡ SDS2/LC (in units of cm) defined by the standard deviation SDS of the interface and its autocorrelation length LC:

Acknowledgments

Z hG ¼ 1:762 1− exp − and 1:85 qG ¼ 0:05 hG :

The work was supported by the European Space Agency project “Combined use of multifrequency radiometry (L- to Ka-Band) and SAR

The complete model codes were listed by Schwank et al. (2015), and are available also on demand from the authors.

ðA3Þ


14


Appendix B A list of symbols used in the manuscript and their meaning are summarized below.

permittivity of air εair εG ground permittivity εG,obs observed ground permittivity εG,ret retrieved ground permittivity εG,ret,inv-snow retrieved ground permittivity without consideration of snow cover effects θk incidence angle at air–ground (or air–snow) interface θS incidence angle at snow–ground interface εS permittivity of snow ρS snow density ρS,obs,10cm observed snow density for lowest 10 cm of snowpack ρS,obs,bulk observed bulk snow density ρS,ret retrieved snow density a, b fit parameters apG, apsky Kirchhoff coefficients of snow layer above ground CF cost function LC autocorrelation length of soil surface height p polarization SD snow depth SDS standard deviation of soil surface height spG reflectivity of snow–ground interface at polarization p spS reflectivity of snow–air interface at polarization p Tair air temperature TpB,mod modeled brightness temperature at polarization p TpB,obs observed brightness temperature at polarization p TB,sky↓ downwelling atmosphere brightness temperature including cosmic background TpB brightness temperature at polarization p TG ground temperature VWC volumetric water content Z slope parameter References Barnett, T. P., Adam, J. C., & Lettenmaier, D. P. (2005). Potential impacts of a warming climate on water availability in snow-dominated regions. Nature, 438, 303–309. http:// dx.doi.org/10.1038/nature04141. Bircher, S., Kerr, Y. H., & Wigneron, J. -P. (2015). SMOSHiLat — Microwave L-band Emissions From Organic-rich Soils in the Northern Cold Climate Zone and Their Impact on the SMOS Soil Moisture Product. Final Report, ESA ESRIN Contract No. 4000107338/ 12/I-BG. 76 pp. Dobson, M. C., Ulaby, F. T., Hallikainen, M. T., & El-Rayes, M. A. (1985). Microwave dielectric behavior of wet soil-part II: Dielectric mixing models. IEEE Transactions on Geoscience and Remote Sensing, GE-23(1), 35–46. Entekhabi, D., Njoku, E. G., O'Neill, P. E., Kellogg, K. H., Crow, W. T., Edelstein, W. N., ... Van Zyl, J. (2010). The Soil Moisture Active Passive (SMAP) mission. Proceedings of the IEEE, 98(5), 704–716. http://dx.doi.org/10.1109/JPROC.2010.2043918. Fletcher, C., Zhao, H., Kushner, P., & Fernandes, R. (2012). Using models and satellite observations to evaluate the strength of snow albedo feedback. Journal of Geophysical Research, 117, D11117. http://dx.doi.org/10.1029/2012JD017724. Gouttevin, I., Menegoz, M., Dominé, F., Krinner, G., Koven, C., Ciais, P., ... Boike, J. (2012). How the insulating properties of snow affect soil carbon distribution in the continental pan-Arctic area. Journal of Geophysical Research, 117, G02020. http://dx.doi.org/10. 1029/2011JG001916. Hallikainen, M. T., Ulaby, F. T., Dobson, M. C., El-Rayes, M. A., & Wu, L. -K. (1985). Microwave Dielectric Behavior of Wet Soil - Part I: Empirical Models and Experimental Observations. IEEE Transactions on Geoscience and Remote Sensing, 23, 25–33. Heimovaara, T. J., de Winter, E. J. G., van Loon, W. K. P., & Esveld, D. C. (1996). Frequency dependent dielectric permittivity from 0 to 1 GHz: Time domain reflectometry measurements compared with frequency domain network analyzed measurements. Water Resources Research, 32(12), 3603–3610. Kaleschke, L., Tian-Kunze, X., Maaß, N., Mäkynen, M., & Drusch, M. (2012). Sea ice thickness retrieval from SMOS brightness temperatures during the Arctic freeze-up period. Geophysical Research Letters, 39. Kelly, R. E., Chang, A. T., Tsang, L., & Foster, J. L. (2003). A prototype AMSR-E global snow area and snow depth algorithm. IEEE Transactions on Geoscience and Remote Sensing, 412, 230–242. http://dx.doi.org/10.1109/TGRS.2003.809118.

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