Long-Term Arctic Snow/Ice Interface Temperature from Special Sensor for Microwave Imager Measurements

Article Long-Term Arctic Snow/Ice Interface Temperature from Special Sensor for Microwave Imager Measurements

Sang-Moo Lee 1 , Byung-Ju Sohn 1,* and Christian D. Kummerow 2

1 School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea; [email protected] 2 Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523, USA; [email protected] * Correspondence: [email protected]; Tel.: +82-02-880-8166

Received: 22 August 2018; Accepted: 9 November 2018; Published: 12 November 2018

Abstract: The Arctic sea ice region is the most visible area experiencing global warming-induced climate change. However, long-term measurements of climate-related variables have been limited to a small number of variables such as the sea ice concentration, extent, and area. In this study, we attempt to produce a long-term temperature record for the Arctic sea ice region using Special Sensor for Microwave Imager (SSM/I) Fundamental Climate Data Record (FCDR) data. For that, we developed an algorithm to retrieve the wintertime snow/ice interface temperature (SIIT) over the Arctic Ocean by counting the effect of the snow/ice volume scattering and ice surface roughness on the apparent emissivity (the total effect is referred to as the correction factor). A regression equation was devised to predict the correction factor from SSM/I brightness temperatures (TBs) only and then applied to SSM/I 19.4 GHz TB to estimate the SIIT. The obtained temperatures were validated against collocated Cold Regions Research and Engineering Laboratory (CRREL) ice mass balance (IMB) drifting buoy-measured temperatures at zero ice depth. It is shown that the SSM/I retrievals are in good agreement with the drifting buoy measurements, with a correlation coefﬁcient of 0.95, bias of 0.1 K, and root-mean-square error of 1.48 K on a daily time scale. By applying the algorithm to 24-year (1988–2011) SSM/I FCDR data, we were able to produce the winter-time temperature at the sea ice surface for the 24-year period.

Keywords: snow/ice interface temperature; SSM/I; microwave measurement; fundamental climate data record; apparent emissivity; Arctic sea ice

1. Introduction The increasing emission of man-made greenhouse gases has caused global warming of 0.8 ◦C since 1900 [1–3], but the temperature increase is not the same everywhere over the globe. Especially, over the Arctic polar region, where snow and ice cover the ocean, the increase in the near-surface is nearly twice that in the tropics–a phenomenon called Arctic ampliﬁcation [4,5]. Such a rapidly rising surface temperature over the Arctic is manifested by changes in the sea ice extent over last three decades. The sea ice extent has been declining at a rate of ≈3.8%/decade [6]. The largest decline is observed in September with an alarming rate of ≈13%/decade, corresponding to more than 30% of sea ice loss compared with the late 1970s [7,8]. The impact of ice loss appears to be profound, not only inﬂuencing the local climate, hydrological cycle, ecosystems, and natural habitats, but also affecting the global weather/climate system. With the declining sea ice, more ocean water will be exposed to cold and windy atmospheric environments,

Remote Sens. 2018, 10, 1795; doi:10.3390/rs10111795 www.mdpi.com/journal/remotesensing Remote Sens. 2018, 10, 1795 2 of 15 probably inducing enhanced evaporation to the cold atmosphere, which can lead to more water vapor, clouds, and more precipitation [9]. The precipitation change in response to the sea ice melt is particularly interesting because the precipitation itself (regardless of snow or rain) has the potential to feedback the climate [10]. As expected, increased precipitation is noted in the Arctic [11], mainly due to the increased local evaporation caused by the sea ice loss [12]. Furthermore, a higher percentage of precipitation throughout the Arctic summer time will be in liquid form, namely rain, due to the warmer low atmosphere, forcing the snow cover to further decline [10]. It is projected that rain will be the dominant form of precipitation in the Arctic by the end of the 21st century [13]. The increased rain, a hydrological response to dramatically decreasing sea ice (or to the warming atmosphere) should lead to a positive feedback to ice melting, through the substantially decreasing surface albedo, establishes a self-feeding cycle where warming temperatures will lead to more rain and ice melt [10] and cause more warming due to even more rain and ice melt. With respect to the influence of the decline of Arctic sea ice on the weather/climate elsewhere, there is cumulating evidence that Arctic warming has been identified as an important element of the variability of mid-latitude, large-scale atmospheric circulation including storm tracks, planetary waves, jet stream, and energy transport [14,15]. It is reported that the atmospheric variability due to Arctic warming is closely linked to more frequent events of atmospheric blocking patterns [16] and increased cold surges with snowy winters in East Asia, Europe, and Northern America [14,17,18]. Central and northern Europe have experienced six years (2007–2012) of extraordinary wet summer, likely due to the southward shift of the summer jet forced by Arctic sea ice loss [19]. More extreme weather may be expected worldwide in the future due to continuous Arctic warming and the associated sea ice loss. Although current monitoring of sea ice extent and understanding of subsequent impacts on climate components are in high confidence, dramatic changes of the Arctic climate system and expected continuous change in the future make it difficult to assess the future evolution of Arctic environments and/or predict global climate change. To facilitate our understanding of Arctic climate change and thus to reduce the uncertainty of future climate change assessment, observations of climate variables, such as the sea ice extent and its depth, snow cover, and depth are needed, in addition to observations of thermal structures throughout the atmosphere-snow-ice column. At least, much needed thermodynamic variables may be the surface air temperature, snow top temperature, and snow-ice interface temperature (SIIT), from which the thermal structure of the snow-ice system can be studied and related to the sea ice melt or sea ice depth change. The SIIT is intriguing because, if ice depth is known, the heat content of an ice column can be calculated by assuming a nearly constant lapse rate within the ice layer, at least during winter. The amount of heat content held by the ice should be the main factor controlling upward heat transfer from the ocean water to the atmosphere. It builds up a preconditioning of how fast the ice melts in spring and summer, or how fast the ice grows in fall and winter. Thus, the SIIT is valuable information, which can lead to better climate monitoring over the Arctic. In fact, the aforementioned sea ice decline, changes in the Arctic hydrological cycle, and influences on the mid-latitude weather are all related to the SIIT because the SIIT is the variable that can give information on the thermal state of the ice. In this study, we propose an algorithm to produce the long-term SIIT from SSM/I microwave (MW) measurements, which can penetrate the snow layer without much interference. A recent study showed that 6.9 GHz brightness temperature (TB) measurements are theoretically related to the sea ice emissivity and temperature [20]. Although the retrieved ice temperature from 6.9 GHz TBs is in good agreement with the buoy-measured SIIT, the acquisition of long-term data may not be possible, because 6.9 GHz TB measurements before the launch of the Advanced Microwave Scanning Radiometer–EOS (AMSR-E) in August 2002 are not available. In reality, long-term global MW observations are available, as shown in the intercalibrated Fundamental Climate Data Record (FCDR) of TBs [21], covering more than 30 years, but without the 6.9 GHz channel. In the higher frequency region, such as 19.4 GHz, it is difficult to apply the Fresnel assumption for the emissivity retrieval due to surface and volume scatterings. However, Remote Sens. 2018, 10, 1795 3 of 15 if the influences of surface and volume scatterings are known and included in the radiative transfer calculation within the sea ice, it may be possible to retrieve the temperature even using higher frequencies. Aiming at producing long-term SIIT over the Arctic sea ice, we develop an algorithm for retrieving the SIIT from SSM/I TB data, by counting surface and volume scattering effects on the measured TBs, which were examined in the previous study [22]. For this objective, we introduce a correction factor to remove surface and volume scattering influences from measured TBs. Subsequently, the radiative transfer equation is solved for the physical emission temperature from SSM/I (or SSMIS alike) TBs only using the correction factor and combined Fresnel equation. Based on this methodology, we attempt to produce long-term sea ice temperature over the Arctic. The obtained long-term SIIT will certainly help to understand how the global warming has influenced the Arctic climate change in the past decades.

2. Used Data

2.1. Passive MW Data In this study, we use FCDR SSM/I 19.4 and 37.0 GHz vertically and horizontally polarized TBs to retrieve the sea ice temperature. The SSM/I sensors have measured MW TBs with a viewing angle near 53◦ since 1987. The sensors aboard different platforms are physically consistent but depend on varying orbital and navigational quantities such as the incident angle, resolution, and observation time. The objective of SSM/I FCDR data is to generate consistent and well-calibrated MW TBs from 1987 onwards by using multiple techniques for intercalibration [21,23]. In this study, these SSM/I FCDR orbital data were converted to 25 km Equal-Area Scalable Earth (EASE)-grid data, on a daily basis, to collocate SSM/I data with gridded AMSR-E TBs and SSM/I bootstrap sea ice concentration data [24]. More information on the SSM/I FCDR dataset can be found in References [21,23] and on the webpage of the Precipitation Research Group of the Department of Atmospheric Science of the Colorado State University (http:/rain.atmos.colostate.edu/FCDR/). The AMSR-E 6.9 GHz TBs are used for retrieving the adjusted real refractive index and emitting layer temperature of Arctic sea ice, adapting a method described in Reference [20]. Level 3 daily TBs at 6.9 GHz were obtained from the Global Change Observation Mission (GCOM) data center site (http://gcom-w1.jaxa.jp/). In addition, bootstrap sea ice concentration data are applied to minimize the inﬂuences of water contamination. When sea ice coexists with open water within the same pixel, a heterogeneous problem arises in the interpretation of the MW brightness temperature, making the retrieval difﬁcult. In this study, we minimized the water contamination effect in the retrieval by imposing 98% of sea ice concentration as a criterion. Sea ice concentration data were downloaded from the National Snow and Ice Data Center (NSIDC) website (http://nsidc.org/)[24].

2.2. CRREL Buoy Measurements To validate the developed algorithm, we compared the pixel-based retrieved sea ice temperature with in situ measurements from U.S. Navy Cold Regions Research and Engineering Laboratory (CRREL) ice mass balance (IMB) buoy measurements at a daily time scale [25]. The buoy incorporates a thermometer string instrument to measure the temperature proﬁle from the near-surface atmosphere, through the sea ice, and to sea water. In addition, the snow depth and sea ice thickness are measured with an acoustic sounder installed at the buoy. Daily averages were taken from 2-hourly measured data, which were downloaded from the CRREL website (http://imb-crrel-dartmouth.org/imb.crrel/). Temperature at zero ice depth (which is also referred to as SIIT but from buoy measurement) is used for the comparison with collocated SSM/I-derived SIIT. Two types of CRREL IMB buoy data are available, i.e., “Provisional Buoy” data and “Archived Buoy” data. The “Provisional Buoy” data were archived without quality control, and thus often abnormal features are found in the “Provisional Buoy” data, i.e., (1) the air temperature is substantially higher than snow/ice interface (or zero ice depth) temperature even during the winter time; (2) a strong Remote Sens. 2018, 10, 1795 4 of 15 inversion layer exists within the sea ice; (3) the air temperature variation is smaller than that of temperature at zero ice depth; and (4) the air/snow interface or at snow/ice interface show no vertical temperature gradient change. The “Archived Buoy” data are quality-controlled, but, even some of “Archived Buoy” data show abnormal features similar to that found in the “Provisional Buoy” data, although there are relatively few cases. In this study, we only used “Archived Buoy” data for the comparison because of the abnormal features found in “Provisional Buoy” data. However, more control checks are necessary even for “Archived Buoy” data, and we apply quality assurance checks (1)–(4) to “Archived Buoy” data before the comparison. Details of the quality checks are provided in Section4.

3. Theoretical Background and Methodology The theoretical background for the algorithm development was developed and introduced in a previous study ([22], this reference, (Lee, Sohn, and Shi, 2018), is now referred to as LSS18). Here, we provide a summary of the theoretical backgrounds used in that study, and an algorithm development for SSM/I measurements. Detailed explanations are provided in AppendixA.

3.1. Simple Snow/Ice Model for Radiative Transfer In this study, sea ice used for the radiative transfer is composed of three layers, i.e., a snow layer at the top, surface ice layer (or freeboard sea ice layer) in the middle below the snow layer, and congelation ice layer as the lowest layer [26]. The snow layer (top layer) and upper part of the surface ice layer (middle layer) are presumed to be the volume scattering layer that attenuates the radiation emanating from the emission layer below. The model has one emission layer with temperature and related emissivity (TE and ε, respectively). The emission layer is located below the volume scattering layer and composed of the lower part of the surface ice layer and/or upper part of the congelation ice layer (see Figure 1 in Reference [22]). For the radiative transfer, surface and volume scatterings occurring above the emission layer are treated independent of the emission layer, not allowing interactions between the two layers. If TBsfc is deﬁned as an upwelling TB at the snow top, then the radiative transfer through the snow-ice layer can be expressed as follows:

−τsca TBs f c = εTEe (1) where τsca is the optical thickness associated with the snow/ice volume scattering.

3.2. Apparent Emissivity

We deﬁned the apparent emissivity (ε A) by taking the ratio between TE and TBsfc:

TBs f c ε A = (2) TE

Apparent emissivities at the SSM/I 19.4 GHz channels are obtained by taking the ratio of SSM/I 19.4 GHz TBsfc to the sea ice emission temperature (TE), according to Equation (2). TBsfc here is from the measured TB after removing atmospheric effects, which are calculated using the line-by-line radiative transfer model of the Satellite Data Simulator Unit (SDSU)-version 2.1 [27] with inputs of atmospheric temperature and humidity proﬁles from European Centre for Medium-Range Weather Forecasts Reanalysis (ERA)-Interim data [28]. The collocated TE is obtained from the AMSR 6.9 GHz retrieved SIIT, based on the ﬁnding that its emission weighting function is similar to that for 19.4 GHz. Figure1 shows the spatial distributions of the apparent emissivities for both polarizations at 19.4 GHz on 1 January 2004. The obtained apparent emissivities are used for calculating the so-called “correction factor” described in Section 3.3. Remote Sens. 2018, 10, 1795 5 of 15

The apparent emissivity can also be related to scatterings, as shown in Equation (1): Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 15 ε A = ε exp(−τsca) (3) By using known εA distributions in Figure 1, we try to solve the unknowns on the right-hand side ofBy Equation using known (3). εA distributions in Figure1, we try to solve the unknowns on the right-hand side of Equation (3).

Figure 1. Geographical distributions of the retrieved (a) vertically and (b) horizontally polarized Figureapparent 1. Geographical emissivities at distributions 19.4 GHz of SSM/Iof the onretrieved 1 January (a) 2004.vertically and (b) horizontally polarized apparent emissivities at 19.4 GHz of SSM/I on 1 January 2004. 3.3. Correction Factor 3.3. CorrectionSince ε inFactor Equation (1) represents the emissivity for a rough surface, we needed to express ε withSince an emissivityε in Equation for (1) the represents smooth surface the emissivity (εs). This for isa rough because surface, the emissivity we needed characteristics to express ε with of a smooth surface based on the Fresnel equations are well understood, and thus we intended to use the an emissivity for the smooth surface (εs). This is because the emissivity characteristics of a smooth surfacecombined based version on the of the Fresnel Fresnel equations equation [are29, 30well] to solveunderstood, the unknowns. and thus In LSS18,we intended a concept to regardinguse the combinedthe surface version roughness of the effect Fresnel was developedequation [29,30 by relating] to solve the smooththe unknowns. surface emissivity In LSS18, to a theconcept rough regardingsurface emissivity: the surface roughness effect was developed by relating the smooth surface emissivity to the rough surface emissivity: ε = εsF (4)

where F is the roughness parameter. Based on the concept in Equations (3) and (4), F and τsca at  s F (4) SSM/I 19.4 GHz frequency can be determined by introducing a two-dimensional surface roughness wheremodel F andis the using roughness the adjusted parameter. real refractive Based on indexthe concept obtained in Equations together with (3) andTE from(4), F AMSR-Eand τsca at 6.9 SSM/I GHz 19.4TB measurements.GHz frequency Thecan be detailed determined method by including introducing the a two-dimensional two-dimensional surface surface roughness roughness model model to andestimate usingF theand adjustedτsca for areal given refractiεA canve beindex found obtained in LSS18. together with TE from AMSR-E 6.9 GHz TB measurements.The correction The factordetailed (CF method) can be deﬁnedincluding as thethe ratiotwo-dimensional between the apparent surface emissivityroughness andmodel smooth to estimatesurface emissivity.F and τsca for Since a given the smooth εA can be surface found emissivity in LSS18. is altered by the surface roughness and volume scatteringThe correction extinction factor in the (CF constructed) can be defined model, CFas canthe beratio written betw as:een the apparent emissivity and smooth surface emissivity. Since the smooth surface emissivity is altered by the surface roughness ε A and volume scattering extinction in theCF constructed= = F model,exp(− τCFsca )can be written as: (5) εs

 A After solving F and τsca for 19.4CF GHz with F givenexp( εA,sca the ) correction factor CF for 19.4 GHz(5) is calculated using Equation (5). The CF data for s 19.4 GHz are constructed over the Arctic sea ice region for the December–January–February (DJF) period of 2003–2011 (AMSR-E period). We present the CF After solving F and τsca for 19.4 GHz with given εA, the correction factor CF for 19.4 GHz is calculateddistribution using on 1Equation January (5). 2004 The in CF Figure data2a. for 19.4 GHz are constructed over the Arctic sea ice region for the December–January–February (DJF) period of 2003–2011 (AMSR-E period). We present the CF distribution on 1 January 2004 in Figure 2a. The Equation (5) can be written for two polarized components (vertical (V) and horizontal (H) components for CF, εA, εs, and F). Thus, with the help of the combined Fresnel equation for emissivity given in Equation (6), εs can be obtained by solving Equation (5) [30].

Remote Sens. 2018, 10, 1795 6 of 15

The Equation (5) can be written for two polarized components (vertical (V) and horizontal (H) componentsRemote Sens. 2018 for, 10CF, x FOR, εA ,PEERεs, and REVIEWF). Thus, with the help of the combined Fresnel equation for emissivity6 of 15 given in Equation (6), εs can be obtained by solving Equation (5) [30].

2  1/2−1/2 !2 1[11+ [1 −sHε, s, ]H] cos2cos 2θ εs,V =11[1− [1 − εs,H ]] (6) (6) sV,, sH + [ − 1/2]1/2 1[111 sH,εs, ]H cos2cos 2θ

So far,far, εεAAand andCF CFdistributions distributions are are constructed constructed for for the the winter winter (DJF) (DJF) of the of2003–2011 the 2003–2011 period period during whichduring AMSR-Ewhich AMSR-E and SSM/I and SSM/I data coexist, data coexis to developt, to develop an SSM/I-only an SSM/I-only algorithm. algorithm.

Figure 2. Geographical distributions of (a) directly calculated CF and (b) regression-based CFR at Figure 2. Geographical distributions of (a) directly calculated CF and (b) regression-based CFR at 19.4 19.4 GHz (explained in detail in Section 3.4) on 1 January 2004. GHz (explained in detail in Section 3.4) on 1 January 2004. 3.4. Development of the SSM/I-Only Algorithm for the Correction Factor 3.4. Development of the SSM/I-Only Algorithm for the Correction Factor The retrieval of long-term sea ice TE data from SSM/I FCDR data beyond the AMSR-E period dependsThe onretrieval how we of canlong-term obtain thesea CFicefrom TE data SSM/I from measurements SSM/I FCDR alone.data beyond For that the purpose, AMSR-E we period utilize a ﬁndingdepends of on strong how we linear can relationshipobtain the CF between from SSM/I the CF measurementsand spectral alone. gradient For ratiothat purpose, (GR in Equation we utilize (7)). Here,a finding we of attempted strong linear to develop relationship a regression between algorithm the CF and determining spectral gradientCF at 19.4ratio GHz(GR in using Equation SSM/I TB(7)). measurements. Here, we attempted to develop a regression algorithm determining CF at 19.4 GHz using SSM/I TB measurements. Now we relate the estimated CF (in Figure2a) to collocated SSM/I TBs and GR between 19.4 and Now we relate the estimated CF (in Figure 2a) to collocated SSM/I TBs and GR between 19.4 and 37.0 GHz at vertical polarization: 37.0 GHz at vertical polarization:

TB37V − TB19V GR19V,37V =TB37VV TB 19 (7) GR19VV ,37  TB37V + TB19V (7) TB37VV TB 19 R = + + + CF R a0 a1TB19V a2TB37V a3GR19V37V (8) CF a0 a 1 TB 19VV  a 2 TB 37  a 3 GR 19 VV 37 (8) where ai (i = 0, 1, 2, and 3) are regression coefficients (Table1), which are obtained using daily CF andwhere TBs ai ( datai = 0, for1, 2, DJF and months 3) are regression of the 2003–2011 coefficients period, (Table except 1), which for 2004,are obtained over the using area daily with CF a sea and ice concentrationTBs data for DJF >98%. months of the 2003–2011 period, except for 2004, over the area with a sea ice concentration >98%. Table 1. Regression coefficients at two polarizations in Equation (8). Table 1. Regression coefficients at two polarizations in Equation (8). Coefficients a0 a1 a2 a3 V-polarizationCoefficients 0.48253852a0 0.00204367a1 a 0.00005565372 a3− 0.50878161 H-polarizationV-polarization 0.492235960.48253852 0.00204367 0.00201050 0.0000556537−0.0000576901 −0.50878161−0.52647698 H-polarization 0.49223596 0.00201050 −0.0000576901 −0.52647698

It is noted that the obtained coefficients are slightly different between polarizations, but spatial distributions and magnitudes of CFR at both polarizations are nearly identical (not shown). It is thought that the surface scattering influence on the apparent emissivity appears to be minor for sea ice in the case of the 19.4 GHz frequency, in spite of surface scattering capable of affecting the

Remote Sens. 2018, 10, x FOR PEER REVIEW 7 of 15

Remotepolarization Sens. 2018, 10 state, 1795 [22]. By applying the regression equation, geographical distributions of CFR are 7 of 15 obtained for 1 January 2004 (Figure 2b), which can be compared with the AMSR-derived CF in Figure 2a. The figure shows that they are in good agreement, with small regional differences within 0.05 overIt is the noted Arctic that Ocean the obtained (Figure 3a). coefficients The scatterplot are slightlybetween differentCF and CF betweenR for one month polarizations, (January but2004) spatial R distributionsalso clearly and shows magnitudes that regression-based of CF at both SSM/I polarizations CFR retrievals are are nearly comparable identical to the (not direct shown). CF, It is thoughtshowing that thea correlation surface scattering coefficient influence of 0.98. The on thebias apparent and RMSE emissivity in this comparison appears to are be − minor0.0004 forand sea ice in the0.0053, case ofrespectively. the 19.4 GHz In order frequency, to examine in spite the ofrobust surfaceness scattering of the regression capable Equation of affecting (8), regressions the polarization statewere [22]. performed By applying with the different regression combinations equation, of geographical 8 years in the distributions 2003–2011 period. of CFR Eachare obtained year’s for R 1 Januarycomparison 2004 (Figure between2b), CF which and CF can indicated be compared that there with exists the a AMSR-derived clear linear relationshipCF in Figure between2a. Thethose figure two, with correlation coefficients above 0.97, regardless of the year given in Table 2. This suggests shows that they are in good agreement, with small regional differences within 0.05 over the Arctic that the regression coefficients obtained in this study work well for other years. Because of this, we Ocean (Figure3a). The scatterplot between CF and CFR for one month (January 2004) also clearly shows apply the coefficients in Table 1 to the whole SSM/I period. R that regression-basedConsequently, the SSM/I resultsCF demonstrateretrievals that are the comparable CF can be predicted to the direct from EquationCF, showing (8) with a correlationSSM/I coefficientTBs only. of 0.98.Therefore, The bias by incorporating and RMSE in CF thisR into comparison Equation (5), are ε−A 0.0004can be andcalculated 0.0053, by respectively. applying CF Into order to examineεs. Once theεA is robustness available, it of is thestraightforward regression Equationto estimate (8), the regressions emitting layer were temperature performed TE from with TB differentsfc combinationsusing Equation of 8 (2). years in the 2003–2011 period. Each year’s comparison between CF and CFR indicated that there exists a clear linear relationship between those two, with correlation coefficients R above 0.97,Table regardless 2. Correlation of the coefficients year given between in Tabledirectly2 .obtained This suggests CF and modeled that theCF for regression each year. coefficients obtained in this study2003 work2004 well 2005 for other2006 years. 2007 Because 2008 of this, 2009 we apply2010 the coefficients2011 in Table1 to the whole SSM/I0.9811 period. 0.9839 0.9901 0.9798 0.9859 0.9745 0.9848 0.9897 0.9777

R FigureFigure 3. (a 3.) Geographical(a) Geographical distributions distributions ofof difference between between CFCF andand CFCFR for verticalfor vertical polarization polarization at at R 19.4 GHz19.4 GHz on 1 on January 1 January 2004. 2004. (b )(b Scatterplot) Scatterplot between betweenCF CFand and CFCFR for January January 2004. 2004. Bin Bin sizes sizes are are 0.01 0.01 for bothfor axes, both and axes, statistics and statistics are provided are provided in the in the scatterplot. scatterplot.

R 4. SSM/ITable Snow/Ice 2. Correlation Interface coefﬁcients Temperature between (SIIT) directly obtained CF and modeled CF for each year.

Since2003 the emissivities 2004 for 2005 the smooth 2006 surface and 2007 regressed 2008 CFR values 2009 are now 2010 available 2011for SSM/I RR 19.4 GHz,0.9811 the apparent 0.9839 emissivities 0.9901 can 0.9798 be calculated 0.9859 from 0.9745Equation (5), 0.9848 i.e.,As 0.9897CF . The 0.9777 spatial distributions of regression-based apparent emissivities are given in Figure 4. The distributions are almostConsequently, the same theas that results for the demonstrate directly calculated that the apCFparentcan emissivity be predicted in Figure from 1, Equation demonstrating (8) with that SSM/I R apparent emissivity can be estimated byR solely using SSM/I measurements. Because  is now TBs only. Therefore, by incorporating CF into Equation (5), εA can be calculated by applyingA CF to available for the given SSM/I measurements, the emission temperature TE can be estimated. However, εs. Once εA is available, it is straightforward to estimate the emitting layer temperature TE from TBsfc usingbecause Equation TE is(2). in fact the temperature between snow and ice layers, as expressed in Reference [11], the obtained emission temperature is also referred to as SIIT. 4. SSM/I Snow/Ice Interface Temperature (SIIT)

Since the emissivities for the smooth surface and regressed CFR values are now available for SSM/I R R 19.4 GHz, the apparent emissivities can be calculated from Equation (5), i.e., ε A = CF εs. The spatial distributions of regression-based apparent emissivities are given in Figure4. The distributions are almost the same as that for the directly calculated apparent emissivity in Figure1, demonstrating R that apparent emissivity can be estimated by solely using SSM/I measurements. Because ε A is now Remote Sens. 2018, 10, 1795 8 of 15 available for the given SSM/I measurements, the emission temperature T can be estimated. However, Remote Sens. 2018, 10, x FOR PEER REVIEW E 8 of 15 because TE is in fact the temperature between snow and ice layers, as expressed in Reference [11], theRemote obtained Sens. 2018 emission, 10, x FOR temperature PEER REVIEWis also referred to as SIIT. 8 of 15

Figure 4. Geographical distributions of the obtained apparent emissivities based on CFR for (a) vertical Figure 4. Geographical distributions of the obtained apparent emissivities based on CFR for (a) vertical and (b) horizontal polarizations at 19.4 GHz on 1 January 2004. andFigure (b) 4. horizontal Geographical polarizations distributions at 19.4 of GHzthe obta onined 1 January apparent 2004. emissivities based on CFR for (a) vertical and (b) horizontal polarizations at 19.4 GHz on 1 January 2004. Figure 5 shows the geographical distributions of the SIIT retrieved from AMSR-E 6.9 GHz and Figure5 shows the geographical distributions of the SIIT retrieved from AMSR-E 6.9 GHz SSM/I 19.4 GHz measurements for 1 January 2004. Note that the spatial distributions of both and SSM/IFigure 19.45 shows GHz the measurements geographical for distributions 1 January 2004.of the NoteSIIT retrieved that the spatial from AMSR-E distributions 6.9 GHz of both and temperatures are similar, indicating that the retrieval method developed in this study works well for temperaturesSSM/I 19.4 GHz are similar,measurements indicating for that1 January the retrieval 2004. methodNote that developed the spatial in thisdistributions study works of wellboth SSM/I measurements. Both distributions show relatively colder temperatures over the central Arctic fortemperatures SSM/I measurements. are similar, indicating Both distributions that the retr showieval relatively method developed colder temperatures in this study over works the well central for Ocean and Canadian Archipelago where multiyear sea ice is prevalent. Relatively warmer ArcticSSM/I Oceanmeasurements. and Canadian Both distributions Archipelago show where relative multiyearly colder sea icetemperatures is prevalent. over Relatively the central warmer Arctic temperatures are shown in the Laptev, East Siberian, and Chukchi seas, where first-year sea ice is temperaturesOcean and Canadian are shown Archipelago in the Laptev, where East Siberian,multiyea andr sea Chukchi ice is seas,prevalent. where Relatively ﬁrst-year seawarmer ice is likely present. The geographical distributions of the temperature difference between AMSR-E and likelytemperatures present. are The shown geographical in the Laptev, distributions East Siberi of thean, temperature and Chukchi difference seas, where between first-year AMSR-E sea ice and is SSM/I are shown in Figure 6a for 1 January 2004. The temperature difference distributions may be SSM/Ilikely present. are shown The in geographical Figure6a for distributions 1 January 2004. of the The temperature temperature difference difference between distributions AMSR-E may and be attributed to the difference distributions between CF and CFR because the unexplained CF variance attributedSSM/I are toshown the difference in Figure distributions 6a for 1 January between 2004.CF Theand temperatureCFR because difference the unexplained distributionsCF variance may be in in the regression should be propagated into the temperature difference. The two difference maps theattributed regression to the should difference be propagated distributions into thebetween temperature CF and difference.CFR because The the two unexplained difference CF maps variance show show very similar features (i.e., Figures 3a and 6a). It is noted that the temperature difference is veryin the similar regression features should (i.e., be Figures propagated3 and6 ).into It isth notede temperature that the temperaturedifference. The difference two difference is generally maps generally within 1.5 K regardless of the ice type. withinshow very 1.5 K similar regardless features of the (i.e., ice type.Figures 3a and 6a). It is noted that the temperature difference is generally within 1.5 K regardless of the ice type.

Figure 5. Geographical distributions of the (a) AMSR-E 6.9 GHz and (b) SSM/I 19.4 GHz-retrieved sea iceFigure temperature 5. Geographical for 1 January distributions 2004. of the (a) AMSR-E 6.9 GHz and (b) SSM/I 19.4 GHz-retrieved sea ice temperature for 1 January 2004. Figure 5. Geographical distributions of the (a) AMSR-E 6.9 GHz and (b) SSM/I 19.4 GHz-retrieved sea ice temperature for 1 January 2004. A scatterplot of the temperature difference between two for January month of 2004 is provided in Figure 6b. Most of the pairs are near the one-to-one line, implying that both temperatures have a strong A scatterplot of the temperature difference between two for January month of 2004 is provided in Figure 6b. Most of the pairs are near the one-to-one line, implying that both temperatures have a strong

Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 15 linear relationship. The corresponding statistics show a high correlation coefficient of 0.97 and bias (RMSE) of 0.007 K (1.01 K). It is noted that some points off the 1:1 line are in the boundary area between seaRemote ice Sens.and 2018open, 10 water,, 1795 where water exposure often contaminates the MW measurement scene. 9 of 15

FigureFigure 6. 6. (a) (Geographicala) Geographical distributions distributions of difference of difference between between AMSR-E AMSR-E 6.9 GHz 6.9andGHz SSM/I and 19.4SSM/I GHz- retrieved19.4 GHz-retrieved sea ice temperature sea ice temperature for 1 January for 2004. 1 January (b) Scatterplot 2004. (b) between Scatterplot two between temperatures two temperatures for January 2004for January with bin 2004 size with of 0.4 bin K sizefor both of 0.4 axes. K for St bothatistics axes. are Statisticsprovided are in providedthe scatterplot. in the scatterplot. A scatterplot of the temperature difference between two for January month of 2004 is provided in Validation against the Buoy Snow/Ice Interface Temperature Figure6b. Most of the pairs are near the one-to-one line, implying that both temperatures have a strong linearValidating relationship. the developed The corresponding algorithm, statistics retrieved show SSM/I a high sea correlationice temperatures coefﬁcient are compared of 0.97 and with bias CRREL(RMSE) IMB of 0.007 drifting K (1.01 buoy K). measurements It is noted that someover the points Arct offic thesea 1:1ice linearea are [19]. in theFor boundary the comparison, area between grid- basedsea ice SSM/I-retrieved and open water, temperatures where water are exposure collocated often wi contaminatesth buoy data the by MWapplying measurement the following scene. steps: (1) Is the center point of any given SSM/I target with 25 km × 25 km resolution target located within aValidation 12.5 km againstdistance the from Buoy Snow/Icethe buoy Interface location Temperature at a given time? (2) Are the corresponding sea ice concentrationsValidating greater the developed than 98%? algorithm, (3) Are the retrieved selected SSM/I satellite sea pixels ice temperatures entirely covered are comparedby sea ice? with (4) SelectCRREL a closest IMB drifting target buoy value measurements if multiple SSM/I over thetargets Arctic satisfy sea ice conditions area [19]. For (1), the(2), comparison, and (3). Although grid-based the buoySSM/I-retrieved data pass the temperatures above-mentioned are collocated criteria, with the buoydata are data rejected by applying if snow/ice the following interface steps: information (1) Is the iscenter not provided point of anyor if given the data SSM/I failed target the withquality 25 assurance km × 25 km criteria resolution given target in Section located 2.2. within The remaining a 12.5 km measurementsdistance from thealong buoy 13 deployed location at tracks a given are time?taken (2)for Arethe thevalidation. corresponding The observation sea ice concentrations periods and startgreater and than end 98%?latitudes (3) Areand thelongitu selecteddes are satellite given pixels in Table entirely 3. Among covered the by13 buoy sea ice? tracks, (4) Select 8 were a closestfound intarget the northern value if multiple Beaufort SSM/I Sea and targets 5 were satisfy found conditions in the Central (1), (2), Arctic and (3).Ocean, Although as shown the in buoy Figure data S1 pass in thethe Supplementary above-mentioned Material. criteria, the data are rejected if snow/ice interface information is not provided or if theFigure data failed 7a shows the quality a scatterplot assurance of the criteria buoy-measured given in Section SIITs 2.2and. Thecorresponding remaining measurementsSSM/I values along along all13 13 deployed buoy tracks, tracks with are taken a correlation for the validation. coefficient The of 0.86, observation bias of periods-0.36 K, andand startRMS and error end of latitudes 3.42 K. The and plotlongitudes shows area scattered given in pattern, Table3. Amongin which the the 13 daily buoy variation tracks, 8 wereis greater found than in the 7 K. northern Except Beaufortfor the blue Sea dots,and 5a werelarge foundbundle in of the black Central points Arctic is located Ocean, along as shown the 1:1 in line. Figure It is S1noted in the that Supplementary the scattered blue Material. dots are associatedFigure7a showswith three a scatterplot buoys (#2, of the #6, buoy-measured and #8 in Table SIITs 3) in and which corresponding temperature SSM/I variations values at along the snow/iceall 13 buoy interface tracks, withare greater a correlation than 7 coefﬁcientK for some of data 0.86, points. bias of Close -0.36 K, examination and RMS error of those of 3.42 data K. Thereveals plot thatshows such a scatteredlarge variations pattern, are in not which due the to dailythe shallo variationw ice isdepth greater or ice than type 7 K. (not Except shown). for theIt is blue thought dots, thata large they bundle are likely of black due to points problems is located related along to th thee buoy 1:1 line. instruments It is noted themselves. that the scattered Rationally blue thinking, dots are suchassociated large temperature with three buoys variations (#2, #6, within and #8 the in Tableice may3) in not which be acceptable temperature such variations that 7 K at is the subjectively snow/ice appliedinterface as are a criterion greater thanto remove 7 K for such some buoy data measurements. points. Close examination of those data reveals that such largeBecause variations of those are not reasons, due to thewe shallowexclude icethe depthblue dots or ice in type Figure (not 7a shown). from the It ispaired thought data that set theyfor the are comparison.likely due to Comparison problems related results to theobtained buoy instruments after applying themselves. quality Rationallyassurance thinking,checks indicate such large a correlationtemperature coefficient variations of within 0.95, bias the iceof 0.15 may K, not and be acceptableRMS error suchof 1.48 that K 7(Figure K is subjectively 7b). It is important applied as to a notecriterion that tothe remove SSM/I-derived such buoy measurements.physical temperature of the sea ice surface shows a good 1:1 correspondence to buoy-measured SIIT, indicating that the temperature obtained for SSM/I in this

Remote Sens. 2018, 10, x FOR PEER REVIEW 10 of 15 study represents the temperature near the snow/ice interface defined using buoy measurements in which the typical emitting layer lay in MW frequencies.

Remote Sens. 2018, 10, 1795 10 of 15 Table 3. Used data periods and starting/ending points of buoys used for validation.

# Period Starting Point Ending Point Table 3. 1 1 DecemberUsed data 1993–28 periods February and starting/ending 1994 74.81°N, points 138.55°W of buoys used 74.38°N, for validation. 154.19°W #2 22 December 1997–28 Period February 1998 75.34°N, Starting 150.05°W Point 75.11°N, Ending 159.66°W Point 13 1 1 December December 1993–281997–28 February February 1994 1998 76.14°N, 74.81◦N, 138.55147.46°W◦W 75.11°N, 74.38◦ N,159.59°W 154.19◦W 24 1 22 December December 1997–282003–29 February February 1998 2004 75.24°N, 75.34◦N, 150.05135.07°W◦W 74.89°N, 75.11◦ N,141.07°W 159.66◦W 35 1 1 December December 1997–282006–28 February February 1998 2007 77.43°N, 76.14◦N, 147.46139.35°W◦W 76.74°N, 75.11◦ N,139.14°W 159.59◦W ◦ ◦ ◦ ◦ 46 1 December 2003–29 2006–2 February February 2004 2007 85.03°N, 75.24 N, 135.07128.78°EW 86.98°N, 74.89 N, 125.96°E 141.07 W ◦ ◦ ◦ ◦ 57 11 1 December 2006–28 2007–27 February February 2007 2008 79.87°N, 77.43 N, 139.35155.15°WW 80.85°N, 76.74 N,151.78°W 139.14 W 6 1 December 2006–2 February 2007 85.03◦N, 128.78◦E 86.98◦N, 125.96◦E 78 1 11 December December 2007–272007–28 February February 2008 2008 77.20°N, 79.87◦N, 155.15135.27°W◦W 74.64°N, 80.85◦ N,135.14°W 151.78◦W 89 12 1 December 2007–28 2007–23 February February 2008 2008 83.90°N, 77.20◦N, 135.27112.91°W◦W 84.00°N, 74.64◦ N,109.63°W 135.14◦W 910 1112 December 2007–23 2007–28 February January 2008 2008 81.98°N, 83.90◦N, 112.91119.61°W◦W 82.01°N, 84.00◦ N,119.76°W 109.63◦W ◦ ◦ ◦ ◦ 1011 1 11 December December 2008–18 2007–28 JanuaryFebruary 2008 2009 82.57°N, 81.98 N, 119.61115.30°WW 82.09°N, 82.01 N,114.50°W 119.76 W 11 1 December 2008–18 February 2009 82.57◦N, 115.30◦W 82.09◦N, 114.50◦W 1212 1 1 December December 2010–282010–28 February February 2011 2011 77.02°N, 77.02◦N, 149.28149.28°W◦W 76.23°N, 76.23◦ N,146.66°W 146.66◦W 1313 1 1 December December 2010–282010–28 February February 2011 2011 75.32°N, 75.32◦N, 142.39142.39°W◦W 74.10°N, 74.10◦ N,142.60°W 142.60◦W

Figure 7. (a) Scatterplots between CRREL IMB buoy-measured snow/ice interface temperature (x-axis) andFigure SSM/I-derived 7. (a) Scatterplots temperature between (y-axis), CRREL from IMB (a buoy-mea) all 13 buoys,sured and snow/ice from ( binterface) buoys aftertemperature the quality (x- checkaxis) and is applied. SSM/I-derived temperature (y-axis), from (a) all 13 buoys, and from (b) buoys after the quality check is applied. Because of those reasons, we exclude the blue dots in Figure7a from the paired data set for the comparison.As previously Comparison discussed, results we intended obtained to after produce applying long-term quality assuranceSSM/I-derived checks temperature indicate a correlationinformation coefficient over the ofArctic 0.95, biassea ice of 0.15area. K, Since andRMS we developed error of 1.48 an K algorithm (Figure7b). to It retrieve is important the SIIT, to note we thatgive the an SSM/I-derivedattempt to produce physical 24 years temperature of SSM/I of SI theIT. sea For ice demonstration surface shows purposes, a good 1:1 we correspondence generated the tomean buoy-measured December SIIT SIIT, from indicating 1988 to that 2011 the and temperature the results obtained are given for SSM/Iin Figure in this8. The study figure represents clearly theindicates temperature that the near temperature the snow/ice is significantly interface defined colder usingin the buoyearly measurementsyears of the period, in which suggesting the typical that emittingthe Arctic layer sea ice lay had in MW experienced frequencies. a rapid temperature rise during the 1988–2011 period. This type of dataAs provides previously important discussed, information we intended about the to evolut produceion of long-term climate change SSM/I-derived over the Arctic temperature Ocean in informationthe last decades, over theif we Arctic extend sea this ice area.effort Since to incl weude developed the SSMIS, an which algorithm effect toively retrieve replaces the SIIT, the weSSM/I. give an attempt to produce 24 years of SSM/I SIIT. For demonstration purposes, we generated the mean December SIIT from 1988 to 2011 and the results are given in Figure8. The figure clearly indicates that the temperature is significantly colder in the early years of the period, suggesting that the Arctic sea ice had experienced a rapid temperature rise during the 1988–2011 period. This type of data provides important information about the evolution of climate change over the Arctic Ocean in the last decades, if we extend this effort to include the SSMIS, which effectively replaces the SSM/I.

Remote Sens. 2018, 10, 1795 11 of 15 Remote Sens. 2018, 10, x FOR PEER REVIEW 11 of 15

Figure 8. (a–x) Retrieved December Arctic snow/ice interface temperature from SSM/I FCDR data Figure 8. (a–x) Retrieved December Arctic snow/ice interface temperature from SSM/I FCDR data from 1988 to 2011. from 1988 to 2011. 5. Discussion and Conclusions 5. Discussion and Conclusions Aiming at producing a long-term temperature record over the Arctic sea ice area, we developed an algorithmAiming at to producing retrieve the a long-term wintertime temperature SIIT over thereco Arcticrd over Ocean the Arctic from sea SSM/I ice area, FCDR we data. developed In so doing,an algorithm a simple to radiativeretrieve the transfer wintertime model SIIT was over set up,the inArctic which Ocean the snow-ice from SSM/I is composed FCDR data. of threeIn so layersdoing, (i.e., a simple snow radiative layer, volume transfer scattering model was ice layer,set up, and in which emitting the icesnow-ice layer, fromis composed the top). of In three the model, layers the(i.e., emitting snow layer, radiation volume from scattering the emission ice layer, layer and is attenuatedemitting ice via layer, volume from scatterings the top). In from the model, snow/ice the layersemitting above radiation as well from as bythe ice emission surface layer scattering. is attenuated By using via the volume collocated scatterings AMSR-E from 6.9 snow/ice GHz derived layers SIITabove as as an well emission as by temperatureice surface scattering. for SSM/I By 19.4 using GHz, the the collocated apparent AMSR-E emissivity 6.9 was GHz determined derived SIIT from as SSM/Ian emission 19.4 GHz temperature TBs. The for obtained SSM/I 19.4 apparent GHz, emissivitythe apparent was emissivity then related was to determined volume scattering from SSM/I and surface19.4 GHz roughness TBs. The to obtained examine apparent how these emissivity parameters wa cans then be related related to to the volume correction scattering factor (i.e., and the surface ratio betweenroughness apparent to examine emissivity how these at the para surfacemeters and can specular be related emissivity to the atco therrection emission factor layer). (i.e., Thenthe ratio the correctionbetween apparent factor was emissivity deﬁned and at the predicted surface from and aspec combinationular emissivity of SSM/I at the TBs emission (i.e., TB19V layer). and Then TB37V). the Thecorrection correction factor factor was from defined SSM/I and measurements predicted from can a be combination used to predict of SSM/I the corresponding TBs (i.e., TB19V apparent and emissivityTB37V). The from correction the combined factor Fresnelfrom SSM/I equation. measurements It is straightforward can be used to estimateto predict the the SIIT corresponding from SSM/I 19.4apparent GHz measurementsemissivity from once the thecombined correction Fresnel factor equa is determinedtion. It is straightforward from SSM/I measurements. to estimate the SIIT fromThe SSM/I developed 19.4 GHz algorithm measurements has been once successfully the correction implemented factor foris SSM/Idetermined TB measurements from SSM/I availablemeasurements. from July 1987. The retrieved temperatures were validated against the temperatures at the snow-iceThe developed interface algorithm (or the temperature has been atsuccessfully the top of theimplemented ice layer) from for CRRELSSM/I TB IMB measurements drifting buoy measurements.available from July The 1987. validation The retrieved results indicated temperatur thates the were SSM/I-derived validated against SIITs the are temperatures in good agreement at the withsnow-ice drifting interface buoy measurements(or the temperature of the at SIIT the (temperature top of the ice at layer) the zero from ice CRREL depth), IMB with drifting a correlation buoy coefﬁcientmeasurements. of 0.95, The bias validation of 0.1 K, results and RMS indicated error of th 1.48at the K onSSM/I-derived a daily time SIITs scale. are These in good results agreement suggest thatwith adrifting long-term buoy ice measurements temperature record of the canSIIT be(tempe producedrature by at applyingthe zero ice the depth), developed with algorithma correlation to well-calibratedcoefficient of 0.95, long-term bias of FCDR0.1 K, dataand RMS composed error of SSM/I1.48 K on and a SSMISdaily time data scale. spanning These over results thirty suggest years. that a long-term ice temperature record can be produced by applying the developed algorithm to well-calibrated long-term FCDR data composed of SSM/I and SSMIS data spanning over thirty years.

Remote Sens. 2018, 10, 1795 12 of 15

It should be mentioned that caution should be exercised if the developed algorithm is applied for thin ice because the penetration depth of the MW spectrum of interest in this study can penetrate deeper to reach the ocean water below the ice layer if the ice depth is less than approximately 16 cm, which is twice the penetration depth for first-year sea ice at 6.9 GHz with typical dielectric constant of 3.3–i0.15 [31]. In other words, a portion of the signal may be from underlying water although the magnitude is expected to be small. Additionally, the algorithm is only valid for high-concentrated sea ice pixels because the regression coefficients for the correction factor are based on TB data over the ice area with an ice concentration >98%. Therefore, when the sea ice concentration (SIC) decreases with melt ponds on the sea ice during the summer ice melt, the current approach may produce erroneous results. Furthermore, the regression coefficients for CFR may depend on the SIC products because we tried to remove possible water-contaminated pixels. We used 98% of the SIC obtained from National Snow Ice Data Center (NSIDC) product based on the National Aeronautics and Space Administration (NASA)’s bootstrap algorithm as a criterion to remove such pixels. It is known that different algorithms for the SIC (e.g., Ocean and Sea Ice Satellite Application Facility (OSI SAF), NASA Team, and Bristol algorithms among others) result in different SIC distributions with respect to seasons and regions [32–35]. However, considering that the water contamination should be largely confined within the marginal sea ice area during the winter time which we focus on in this study, the use of different data sets may provide results that do not significantly deviate from the current one. Nonetheless, it may be worthwhile to examine how different SIC data give different results, especially over the marginal sea ice area.

Supplementary Materials: The following are available online at http://www.mdpi.com/2072-4292/10/11/ 1795/s1, Figure S1: Tracks of the 13 selected buoys deployed in the Arctic sea. Colors indicate different buoy tracks, and numbers correspond to deployed buoys defined in Table3. Three rejected buoys (#2, #6, and #8) are underlined in the labels. Author Contributions: Conceptualization, S.-M.L. and B.-J.S.; Methodology, S.-M.L. and B.-J.S.; Software, S.-M.L.; Validation, S.-M.L. and B.-J.S.; Formal Analysis, S.-M.L.; Investigation, S.-M.L. and B.-J.S.; Resources, B.-J.S.; Data Curation, S.-M.L., B.-J.S., and C.D.K.; Writing-Original Draft Preparation, S.-M.L.; Writing-Review and Editing, B.-J.S. and C.D.K.; Visualization, S.-M.L.; Supervision, B.-J.S.; Project Administration, B.-J.S.; Funding Acquisition, B.-J.S. Funding: This research was funded by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2016R1A2B4009551). Acknowledgments: Authors would like to thank three anonymous reviewers for their constructive and valuable comments which led to an improved paper. Authors also thank to the GCOM-W data center of Japanese Aerospace Exploration Agency (JAXA) for AMSR-E 6.9 GHz polarized brightness temperatures and NSIDC for SSM/I bootstrap sea ice concentration data. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A Here, the method to estimate the surface roughness and volume scattering effects on the apparent emissivity is reviewed in detail. The snow-ice layer schematically simpliﬁed for the radiative transfer calculation is composed of two different layers; upper layer for volume scattering and lower layer for emission. Once MW emission occurs in the lower emission layer with emission temperature TE and corresponding rough surface emissivity (εr), the emitted TB at the surface (TBsfc), after experiencing volume scattering extinction, can be written as:

−τsca TBs f c = εrTEe (A1) where τsca is the optical depth due to volume scatterings by snow and surface ice. Because of εr for rough surfaces, it can be expressed in terms of the smooth surface emissivity (εs) scaled by the roughness factor, F, i.e., εr = εsF. Applying the roughness factor F to Equation (A1), we obtain:

−τsca TBs f c = εsFTEe (A2) Remote Sens. 2018, 10, 1795 13 of 15

By introducing the apparent emissivity (εA) concept described in Section 3.2, the following equation is obtained, TB s f c −τsca ε A = = εsFe (A3) TE To solve Equation (A3), the smooth surface emissivity and roughness factor on the right-hand side should be parameterized in terms of basic parameters, such as the refractive index and surface roughness, using physical theory or modeling. In the case of smooth surface emissivity, Fresnel reﬂection theory [30] is followed:

q 2 2 2 2 Nr cos θ − Nr − sin θ εs,V (Nr) = 1 − q (A4) 2 2 2 Nr cos θ + Nr − sin θ

q 2 2 2 cos θ − Nr − sin θ εs,H(Nr) = 1 − q (A5) 2 2 cos θ + Nr − sin θ where εs,V and εs,H are the vertically and horizontally polarized smooth surface emissivities, respectively; Nr is the adjusted real refractive index; and θ is the satellite zenith angle. Therefore, the smooth surface emissivity can be obtained if the refractive index is known. To parameterize the roughness effect in Equation (A3), a two-dimensional roughness model was introduced [36–38]. This model assumes that there are no multiple reﬂections on the surface and slopes of numerous rough facets that follow the Gaussian probability. There are three different factors to parameterize the rough surface emissivity: (1) locally polarized emissivity for numerous facets with different emission angles (εs,local), (2) a ratio between the area of local facets and the projected area perpendicular to the emission direction (g), and (3) an illumination function (S). Therefore, the rough surface emissivity εr can be expressed as an ensemble average of the smooth surface emissivity of numerous facets [36]: εr(Nr, σ) = εs,local gS (A6) Since the parameters of g and S are expressed as Gaussian probability density function with a root-mean-square (RMS) slope of the surface (σ), the rough surface emissivity can be calculated if Nr and σ are known. Subsequently, F can be calculated as follows:

εr(Nr, σ) F(Nr, σ) = = εs,local gS (A7) εs(Nr)

Based on Equations (A4)–(A7), Equation (A3) can be expressed as:

−τsca ε A = εs(Nr)F(Nr, σ)e (A8)

Equation (A8) consists of two parts for each polarization and three unknowns (Nr, σ, and τsca). In order to solve Equation (A8), information on one of three unknowns should be ready. In this study, we employ Nr calculated in accordance with Reference [20] by assuming a spectral invariance of Nr in the MW frequencies especially for Arctic sea ice [39]. At this point, σ and τsca can be obtained from Equation (A8) if the apparent emissivity is known.

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