Incidence Angle Dependencies for C-Band Backscatter From Sea Ice During Both the Winter and Melt Season

Incidence angle normalization is used to reduce the radiometric ambiguity within or between synthetic aperture radar (SAR) images. For sea ice, incidence angle normalization is typically constrained to winter months because of the difficulty of capturing the rapidly changing backscatter values during the melt season. Here, we make use of high-temporal-resolution RADARSAT Constellation Mission (RCM) SAR images to quantify incidence angle dependencies (slopes) for first-year ice (FYI), second-year ice (SYI), and multi-year ice (MYI) during several stages of melt. We apply a new successive image differencing method to mitigate the rapid changes in backscatter during the melt season. Slopes for SYI are shown, for the first time, for winter, and for most melt season periods. Time series of slopes are shown, also for the first time, at intervals as short as 30 min. Slopes for the early melt period (FYI: −0.230; SYI: −0.191; and MYI: −0.175 dB/1°) are similar to those for winter (FYI: −0.235; SYI: −0.208; and MYI: −0.167 dB/1°). During the snowmelt period, slopes remain similar to winter for FYI (−0.235 dB/1°) but become steeper for SYI (−0.241 dB/1°) and MYI (−0.240 dB/1°). All ice types reach their maximum slope steepness during the ponding period (FYI: −0.308; SYI: −0.283; and MYI: −0.289 dB/1°) and then become shallower again during the drainage period (FYI: −0.198; SYI: −0.207; and MYI: −0.240 dB/1°). We show that the melt-season-specific slopes provide important improvements for the visual interpretation of SAR imagery and in backscatter consistency for automated classification algorithms.


Incidence Angle Dependencies for C-Band
Backscatter From Sea Ice During Both the Winter and Melt Season Torsten Geldsetzer and Stephen E. L. Howell Abstract-Incidence angle normalization is used to reduce the radiometric ambiguity within or between synthetic aperture radar (SAR) images.For sea ice, incidence angle normalization is typically constrained to winter months because of the difficulty of capturing the rapidly changing backscatter values during the melt season.Here, we make use of high-temporal-resolution RADARSAT Constellation Mission (RCM) SAR images to quantify incidence angle dependencies (slopes) for first-year ice (FYI), second-year ice (SYI), and multi-year ice (MYI) during several stages of melt.We apply a new successive image differencing method to mitigate the rapid changes in backscatter during the melt season.Slopes for SYI are shown, for the first time, for winter, and for most melt season periods.Time series of slopes are shown, also for the first time, at intervals as short as 30 min.Slopes for the early melt period (FYI: −0.230; SYI: −0.191; and MYI: −0.175 dB/1 • ) are similar to those for winter (FYI: −0.235; SYI: −0.208; and MYI: −0.167 dB/1 • ).During the snowmelt period, slopes remain similar to winter for FYI (−0.235 dB/1 • ) but become steeper for SYI (−0.241 dB/1 • ) and MYI (−0.240 dB/1 • ).All ice types reach their maximum slope steepness during the ponding period (FYI: −0.308; SYI: −0.283; and MYI: −0.289 dB/1 • ) and then become shallower again during the drainage period (FYI: −0.198; SYI: −0.207; and MYI: −0.240 dB/1 • ).We show that the melt-season-specific slopes provide important improvements for the visual interpretation of SAR imagery and in backscatter consistency for automated classification algorithms.

I. INTRODUCTION
T HE decline in Arctic sea ice, together with the increase in shipping activity [1], [2], [3], underscores the need for the continued operational monitoring of sea ice in order to avoid marine disasters.C-band synthetic aperture radar (SAR) satellite imagery at HH polarization is the most widely used for operational ice monitoring; however, the effect of incidence angle remains a challenge for visual interpretation (e.g., operational ice chart production) and ice type separability Torsten Geldsetzer resides in Calgary, AB T2N 3H2, Canada (e-mail: Torsten.Geldsetzer@gmail.com).
Stephen E. L. Howell is with the Climate Research Division, Environment and Climate Change Canada, Toronto, ON M3H 5T4, Canada (e-mail: Stephen.Howell@ec.gc.ca).
To perform incidence angle normalization on satellite-based SAR imagery, the incidence angle dependency (slope) of the surface feature(s) must be known.The slope is usually expressed as a magnitude change in backscatter (in dB) per 1 • of incidence angle.Slopes for sea ice are estimated using either the direct or differencing method [7].The direct method collates all backscatter incidence angle observations and uses a simple linear regression to obtain the slope [8].A variant of the direct method calculates a slope using all backscatter incidence angle observations for an individual ice location and then averages those slopes for many locations [6].The differencing method obtains a slope from the difference in backscatter over a change in incidence angle for the same ice location, employing image pairs at different viewing geometries [5].
The incidence angle dependency during the winter months at C-band HH polarization has been well-studied for seasonal first-year ice (FYI) and multi-year ice (MYI) [5], [6], [7], [8], whereas incidence angle dependency during the melt season has received less attention.However, various studies have reported slope values for various melt season periods or range of periods (see Table I).Although the particular period(s) used in previous studies can be ambiguous, we allocate them to one or more melt season periods based on their descriptions of snow and meteorological conditions.For example, Onstott [9] reports slopes (valid for incidence angles in the range of 20 • -26 • ) for various ice types and melt season periods (late spring, early summer, midsummer, and late summer).The first two periods correspond to the early melt and melt onset periods, whereas the latter two periods correspond with the snowmelt and ponding periods.Mäkynen et al. [4] report HH slopes for FYI under moist and wet snow conditions, but these are for low salinity sea ice in the Baltic Sea and may not apply to the common case of saline FYI.However, if the scattering is confined to the upper snow layer, then salinity may not be a significant factor.Their moist snow class is for snow wetness > 0% and <1% and likely falls into the early melt period.Their wet snow class is for wetness > 1%, while there is snow on the ice and, therefore, likely extends from the beginning of the melt onset period to the end of the snowmelt.Mäkynen et al. [10] report HH slopes for MYI during the melt period, providing monthly averages for June, July, and August.June appears to extend from winter through snowmelt; therefore, the mean June slope may be an average of diverse conditions.July is their main ponding period.August begins with some ponds, but drainage is prevalent, putting it primarily into the drainage period.Park et al. [11] report general slopes representing a mix of ice types on a monthly basis; however, the meteorological or ice conditions are not described, preventing placement of these into one or more of the melt periods.Finally, Mäkynen and Karvonen [5] observe greater slope variability during the melt season and report a mean HH slope for rough FYI for an amalgam of the snow-covered melt periods from melt onset to the end of the snowmelt.
To quantitatively summarize the literature, during winter, FYI slopes range from −0.27 to −0.20 dB/1 • , and MYI slopes range from −0.10 to −0.20 dB/1 • (see Table I).General slopes (−0.19 to −0.21 dB/1 • ) can be used for winter situations when both FYI and MYI exist in the same scene [6].We note that no winter slopes are found in the literature for second-year ice (SYI).FYI slopes during early melt (−0.21 to −0.22 dB/1 • ) are consistently reported.These are within the range of winter values (−0.20 to −0.27 dB/1 • ) and will likely be indistinguishable from winter.For MYI during the early melt, one value exists, showing that an increase in slope may already be occurring compared to winter (−0.27 versus −0.10 to −0.20 dB/1 • ); this needs corroboration.No early melt slope values exist for SYI.Reported slopes during the snowmelt periods appear to be relatively consistent (−0.26 to −0.34 dB/1 • ).The similarity in the FYI, SYI, and MYI slopes suggests that the dominant scattering mechanism is the same, likely volume scattering within the snow cover due to increasing snow moisture.For the ponding period, FYI slopes are only reported at small incidence angles and may not be generally applicable.The range of MYI slopes during ponding is large (−0.25 to −0.60 dB/1 • ).The steeper value for MYI is also at small incidence angles and may not be generally applicable.No ponding slope values exist for SYI.For the drainage period, only a single slope for MYI is reported (−0.20 dB/1 • ); this needs corroboration.Slopes for FYI and SYI have not been reported during drainage.General slopes as steep as −0.28 dB/1 • are reported early in the melt season [11].
Despite the variability in melt season slopes over various ice types, winter slopes are often used for this period, e.g., [12] and [13].However, this proxy may not be appropriate given that backscatter from sea ice changes significantly during the melt season, as the scattering mechanisms and scattering centers undergo profound changes [14], [15], [16].Accordingly, there is a need for a comprehensive investigation of incidence angle dependence for FYI, SYI, and MYI during the melt season.The use of winter slopes during the melt season can be partly attributed to a lack of high-temporalresolution SAR imagery available to capture and characterize the dependence of rapidly changing backscatter in the melt season.The recent launch of the RADARSAT Constellation Mission (RCM), which is a trio of C-band SAR satellites that can provide subdaily temporal resolution over the high Arctic, provides a new opportunity to characterize incident angle dependence during the melt season.
The primary objective of this article is to present a comprehensive set of new HH slope values for FYI, SYI, and MYI for four melt season periods: early melt, snowmelt, ponding, and drainage, as well as for winter.This will provide missing slope values and corroborate existing values.The full range of common SAR incidence angles is used to avoid bias.Our second objective is to present, for the first time, time series of slope values from winter through drainage for FYI, SYI, and MYI.We begin by providing detailed background information about snow and ice geophysical properties during the melt season and the effects of these changing properties on microwave backscatter.We then describe the study area, the study periods, and the sample selection, followed by the SAR processing, the sampling procedure, and the slope calculation methods.We then report on a time series of slopes from winter through the melt seasons.We then present slopes for winter and for each melt season period.We conclude by showing the impact of the new slopes on melt season backscatter observations relative to the use of winter slopes.

II. DATA
RCM SAR images (n = 1004) in various image beam modes [17] are the primary data source.RCM imagery is freely available online at Natural Resources Canada's Earth Observation Data Management System (https://www.eodmssgdot.nrcan-rncan.gc.ca).Only HH Ground Range Detected (GRD) RCM products are used.These have an estimated number of looks (ENL) from ∼3.6 to 7.2 (see Table SI in the Supplementary Material).The images are calibrated to sigma nought and speckle filtered using a refined Lee filter [17] with a 5 × 5 window.Orthorectification uses the Canadian Polar Stereographic WGS84 coordinate system (EPSG:5937).
The various RCM beam modes have different system noise levels.To reduce the effects of varying system noise on backscatter and the analyses, noise values are obtained from each scene's metadata and subtracted from the measured backscatter prior to use.
Mean backscatter and incidence angle values are calculated for a 200 m radius around each sample site.Samples encompass ∼56-733 pixels, depending on beam mode, with over 73% of samples each encompassing ∼270 pixels.Given the image ENL and subsequent filtering, these many pixels reduce the standard deviation due to residual speckle to <0.2 dB in all cases, reasonably permitting the mixing of samples from the different beam modes.The total number of samples is 3439.The incidence angle range of the samples is 19.1 • -57.7 • (see Fig. 1).The mean incidence angle is 39.3 • ± 7.6 • .The near-infrared (NIR) band (∼835 nm) of Sentinel-2 Level 1C optical imagery was used to identify the transitions to ponding and drainage.Cloud-free conditions over the sample sites are confirmed via visual inspection.Sentinel-2 imagery is available at the Copernicus Open Access Hub (https://scihub.copernicus.eu/dhus/#/home).
National Centers for Environmental Prediction (NCEP) Climate Forecast System Version 2 data (https://doi.org/10.5065/D61C1TXF)are used to obtain 6-h averages of the 2-m surface air temperature and the 10-m u-and v-components of the wind for each site.These data have a spatial resolution of 22 264 m and are available at https://rda.ucar.edu/datasets/ds094.0/.

III. STUDY AREA AND SAMPLE SITE SELECTION
The study area encompasses the Queen Elizabeth Islands region of the Canadian Arctic Archipelago (see Fig. 2).Sample sites are selected based on their RCM observation frequency, which is greatest for sites farther north [19] together with the availability of supporting NIR imagery.All sites are landfast until at least July 10, 2021.Therefore, we end the analysis for all sites on this date to facilitate comparison.There are six FYI sites, five for SYI sites, and seven for MYI sites.Sample site details are provided in Table SII in the Supplementary Material.
Initial site selection was made using the Canadian Ice Service ice chart on March 8, 2021.Potential sites are first identified in weekly regional ice charts by the designation of landfast (immobile) ice.Polygons with large proportions of MYI, SYI, or FYI are selected for closer examination.Specific site selection is done by referencing RCM SAR imagery using backscatter, ice floe morphology, texture, and association to identify each ice type.The samples purposefully represent a diversity of ice characteristics for each ice type.For the SYI sites, the relevant ice floe is tracked and monitored backward until the end of the previous summer to ensure that it was FYI that survived the summer.Site breakup dates are identified when the ice becomes mobile, as observed in RCM SAR imagery.

IV. METHODOLOGY A. Stages of Melt Determination
Livingstone et al. [14] describe distinct periods during the annual cycle for which specific microwave backscatter signatures are related to the geophysical properties of sea ice and its snow cover.These periods are identified as freezeup, winter, early melt, melt onset, and advanced melt.Onstott and Gogineni [15] describe the advanced melt period as having four subperiods, starting with the snow cover melting (snowmelt), then the initial formation of melt ponds (pond onset), increasing pond coverage (ponding), and then pond drainage (drainage).This is followed by ice decay and, finally, breakup.For this study, we divide the melt season into four periods: 1) early melt; 2) melt onset through snowmelt (henceforth snowmelt); 3) pond onset and ponding (henceforth ponding); and 4) drainage.We amalgamate the melt onset and snowmelt periods because, without in situ snow wetness measurements, it is difficult to establish when the transition occurs.We also amalgamate pond onset and ponding, as the transition generally occurs rapidly, and the scattering mechanisms are the same.We also include the winter period as a reference (baseline) period.Except for winter, we identify the transitions from one period to the next based either on air temperature, backscatter changes, or NIR values, as specified in the following.The period timing is estimated separately for each site.
1) Winter: Our winter period is between January 1, 2021, and March 31, 2021, when sea ice is characterized by low solar input and cold snow on cold thick sea ice that facilitates a stable backscatter.Backscatter from FYI is low due to its dielectrically lossy nature caused by high snow and ice salinity [9].It exhibits minor fluctuations attributed to thermodynamic changes in the basal snow layer [20] when brine volume increases for brine-wetted snow grains and potentially coincident grain growth [21].In contrast to FYI, winter backscatter from SYI and MYI is high and stable [16], [22], [23], [24], with surface scattering and volume scattering both contributing significantly at the C-band [25].Lacking significant brine in the snow or upper ice layers, SYI and MYI are less susceptible to thermodynamically induced variation.
We do not extend the winter period right up to the beginning of early melt to avoid possible late winter instabilities due to early, usually short-term, warming events.
2) Early Melt: Early melt commences with a diurnal cycle of solar input.This leads to dynamic changes in the snow cover, with increased snow grain metamorphism associated with melt-freeze cycles [14], [16], [25], [26].Backscatter from FYI during early melt is a combination of volume scattering from the brine-wetted basal snow layers and surface scattering from the ice surface.The diurnal increase in solar input and temperature leads to observable diurnal changes in backscatter, caused by increasing the brine volumes in the brine-wetted snow layer and the upper ice layer [9], [16], [21], [27], [28].Backscatter from MYI during early melt remains high and stable, with the potential for minor diurnal fluctuations as snow moisture temporarily increases [16], or with short-term backscatter decreases caused by short-term warming events [29].We identify the beginning of early melt as the first occurrence of air temperatures exceeding −5 • C for the first time lasting 48 consecutive hours.This temperature threshold is chosen to capture possible changes in brine movement for the sea ice [30].
3) Snowmelt: The snowmelt period is characterized by the consistent presence of meltwater in at least part of the snow cover, increased brine volumes due to higher temperatures, and continued snow grain metamorphism [14], [21].The transition from the beginning of melt onset to the end of snowmelt can occur rapidly (3-10 days), especially for thin snow covers, while thicker snow covers can delay the transition [27], [31].
Backscatter from FYI exhibits a sharp increase in backscatter as the beginning of melt onset [12], [16], [22], [24], [31].This increase is attributed to increased volume scattering from greater brine volumes in the basal snow layer, as well as from larger snow grains formed through melt-freeze metamorphism, plus an increase in snow surface scattering when the snow moisture becomes high enough [15], [16].For MYI, increased snow moisture and increased hummock ice wetness mask the strong volume scattering from the underlying ice, resulting in a dramatic decrease in backscatter [12], [15], [16], [23], [26], [29].
The convergence of FYI and MYI backscatter values during snowmelt is a usual occurrence [15], [22], [26].Backscatter values converge between approximately −13 and −17 dB [22].However, this convergence may be short-lived, with MYI exhibiting lower backscatter than FYI during late snowmelt [9], a reversal from winter.We identify the beginning of snowmelt when FYI backscatter increases rapidly for smooth FYI, or dips briefly before increasing for rough FYI, or decreases dramatically for MYI.This is usually associated with an air temperature >∼−3.5 • C [12], [27].
4) Ponding: At melt pond onset, the sea ice is a mix of snow-covered ice, a shoreline region made up of saturated snow adjacent to ice covered by shallow (2 cm) water, and melt ponds [32], [33].The proportions of each surface type vary considerably during the early stages of ponding.Barber et al. [22] report unsaturated snow fractions ( f s ) of approximately 0.52 for FYI and 0.62 for MYI; shoreline fractions ( f sh ) of 0.38 for FYI and 0.21 for MYI; and melt pond fractions of 0.1 for FYI and 0.17 for MYI.As melt progresses, the melt pond fraction increases to a general maximum of 0.75 for FYI and 0.45 for MYI, before drainage [33].
Backscatter from FYI during ponding is dominated by surface scattering from wet ice surfaces and melt ponds, with decreasing backscatter from ice areas later in the ponding period due to erosion of its surface roughness and its increased wetness [15].Potentially high backscatter variability can be observed.If melt ponds are calm, specular scattering occurs, and a backscatter decrease is observed [15]; however, when melt ponds are wind-roughened, a higher backscatter is observed [20].For MYI, the melt ponds and the wet ice or snow continue to mask the volume scattering from the underlying old ice layers, keeping backscatter relatively lower than during winter [15].However, a rapid backscatter increase from melt onset levels is generally observed if the melt ponds are wind roughened [16], [29].
To identify pond onset, we use Sentinel-2 NIR images because they show a strong contrast between snow/ice and melt ponds.The NIR albedo (α) for melting snow is ∼0.65, for saturated snow ∼0.25, for deteriorated ice ∼0.37, for shallow early melt ponds ∼0.1, and for mature melt ponds ∼0.07 [32], [35], [36].Using a mixture model, we estimate the expected NIR albedo for sea ice at pond onset where α NIR shore is the mean of the saturated snow and shallow early melt pond albedos (0.18).f s and f sh are the fractions of the snow and shore areas, respectively.This produces sea ice albedo values at pond onset of 0.41 for FYI and 0.45 for MYI.Because pond fractions during pond onset are unknown for SYI, we use the mean of the FYI and MYI pond onset albedo values, 0.43.Imputation of NIR albedo values for missing Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
days is done using a linear weighted moving average with a window size of five.We identify the date when α NIR seaice reaches the pond onset value for the sea ice type.NIR observation density varies from site to site due to cloud cover; however, all selected sites have sufficient density to enable reasonable imputation of missing values for estimating pond onset (see Table SIII in the Supplementary Material).
5) Drainage: At pond drainage, the sea ice transitions from a mix of bare deteriorated ice and mature melt ponds to bare deteriorated ice [15], [36].For FYI, the drainage of melt ponds usually leads to a reduction in backscatter [16].For MYI, partial drainage of the melt ponds occurs in the latter stage of advanced melt before refreezing occurs.Drainage of hummock surface wetness can lead to an increase in backscatter through greater volume scattering; however, the drainage of melt ponds usually leads to a reduction in backscatter [16].
We identify the transition to pond drainage as an increase in NIR albedo from the NIR albedo minimums (<∼0.2) caused by maximums in pond fraction.We estimate the expected NIR albedo for sea ice at the transition to drainage to be where α NIR ice is the albedo for deteriorated ice and α NIR ponds is the albedo for mature ponds.We use f p of 0.2 for FYI, SYI, and MYI, which loosely corresponds to the downward inflections in f p for MYI [34].This produces a sea ice NIR albedo value of 0.31 at the transition to pond drainage.Manual adjustment of the pond drainage transition date is done in cases that do not have clearly defined NIR evolutionary signatures, as is often the case for MYI (see Table SII in the Supplementary Material).

B. Incidence Angle Normalization
We apply the differencing method [5] to calculate incidence angle dependence instead of the direct method [8] because, during periods of high variation in backscatter due to meteorological forcing during the melt season, the direct method will be impacted by a greater range of backscatter values [7].Specifically, this will decrease the coefficient of determination (R 2 ) values and increase the residual standard error, reducing confidence in slope values.This applies to both the bulk direct method and the per-site direct method.The differencing method mitigates higher backscatter variation by only using the change in backscatter ( σ 0 ) and change in incidence angle ( θ) observations between image pairs.The closer image pairs are in time, the lesser will be the influence of backscatter changes due to meteorological forcing.Furthermore, differences in backscatter within an ice type are reduced because the backscatter magnitude is no longer relevant.This method produces higher R 2 and lower residual standard error [4], increasing confidence in slope values.
For time-series analysis and to reduce the effect of temporal backscatter variation and trends, we apply the differencing method on a per-site basis.The slope is calculated between each observation in a time series and the next observation (successive differencing).When two or three of the RCM trio of satellites image an area on the same pass, the time between observations may be as short as ∼30 min.In other cases, observations may be several days apart.There is no set frequency of observation.Geographic location and competing interests for RCM imagery dictate the acquisition dates and times.The mean of the successive differencing slopes, over a particular period, is used as the per-site slope measure.We also calculate the bulk difference, which collates all σ 0 and θ for successive observations for all sites, for a particular ice type, for a particular period, and apply a simple linear regression to find the slope.
A caveat for the differencing method is that slopes calculated from two observations that have similar incidence angles can result in unreasonably large slopes [5].This occurs because small variations in backscatter (in one or both observations), due to radiometric error, residual speckle, or natural variability, will have an increasingly disproportionate effect on the slope as θ becomes smaller.For example, σ 0 of 2 dB (e.g., from 10 to 12 dB) over θ of 10 • will produce a slope of 0.2 dB/1 • .If the first measurement has a small radiometric error (e.g., 10.1 dB instead of 10 dB), then the resulting slope will be 0.19 dB/1 • .This error is relatively inconsequential.Similarly, given σ 0 of 0.2 dB (e.g., from 10 to 10.2 dB) over θ of 1 • will also produce a slope of 0.2 dB/1 • .However, if the same radiometric error of 0.1 dB occurs in the first measurement, then the resulting slope will be 0.10 dB/1 • .The effect of the error is obviously much greater.
To establish at what value of θ slopes become unreliable, we use the winter slope data for all ice types from January 1, 2021, to March 31, 2021 (see Fig. 3).Under the assumption that winter slopes are relatively stable and that large values of θ provide reliable results, we first find the standard deviation of the slopes (sm) for θ > 10 • ; this is sm baseline (±0.068 dB/1 • ).Then, on a 1 • basis, we assess at what absolute θ value the sm for the 1 • slice exceeds twice sm baseline .This criterion is met when 6 • < θ < 7 • .Therefore, we only use successive observations with θ > 6 • ; the rest are omitted.
Finally, incidence angle normalization is performed using where σ 0 hh is the original backscatter at θ, θ norm is the desired normalized incidence angle, and m is the appropriate slope for the ice type(s) and meteorological/surface conditions.

A. Temporal Evolution of Incidence Angle Dependence
Time series of slope values for selected sites from successive observations (differencing method) illustrate the increase in variability during the melt season for FYI, SYI, and MYI (see Figs. 4-6).The gaps between the slope points are not due to a lack of temporal resolution; their sparsity, relative to the backscatter observations, is a function of the minimum θ criterion for successive observations (i.e., θ > 6 • ).
FYI displays the largest range in slope values during early melt (between the green and purple vertical lines), as expected given the influence of temperature-sensitive brine volume on backscatter (see Fig. 4), whereas SYI and MYI are more stable (see Figs. 5 and 6).The beginning of melt onset (the purple vertical line) is characterized by a distinct upturn in backscatter for FYI and a distinct downturn for SYI and MYI.For FYI, SYI, and MYI, the slope variance increases substantially, which persists until the time series ends.
The Sentinel-2 NIR observations, and imputed values, provide a reasonably robust indication of pond onset using (1) (the vertical red line).The high slope variability persists in prepond and postpond onsets.There is a general trend toward more negative slopes for SYI and MYI from melt onset through pond drainage.The NIR identification of the pond drainage transition (the cyan vertical line) is provided as a rough estimate.
To evaluate the slopes quantitatively, data from winter and the four melt periods are grouped, and slopes are calculated using both the bulk differencing and the per-site successive differencing methods.The bulk differencing slopes are summarized in Table II.Each period is then examined in detail.The per-site method is included to assess the relative spatial (within ice type) variability and temporal variability inherent in the samples.
1) Winter: The mean backscatter values in winter (see Table II) provide an indication of the sea ice roughness.For FYI, the mean −20.34-dB value indicates relatively smooth ice.The winter slope for FYI using the bulk differencing method is −0.235 dB/1 • with RSE of 1.246 dB/1 • [see Table II and Fig. 7(a)].
The omission of samples between −6 • and 6 • on the θ xaxis is the result of the minimum θ criterion for successive observations (i.e., θ > 6 • ).Although we could have included all samples for the bulk differencing, we chose to omit the ±6 • θ samples for consistency with the time-series plots and the per-site statistics, for which they are omitted in order to reduce the variance.For the individual FYI sites, slopes range from −0.131 to −0.296 dB/1      A general all-ice-type slope for winter, based on the mean of the FYI, SYI, and MYI bulk differencing slopes, is −0.203 dB/1 • ; this is similar to the −0.19 dB/1 • value reported by Mahmud et al. [6].
2) Early Melt: The FYI slope for the early melt period (−0.230 dB/1 • ) [see Fig. 8(a) and Table II] is similar to the previously reported range (−0.21 to −0.22 dB/1 • ) and is also similar to the winter slope (−0.235 dB/1 • ), as expected from previous studies (see Table I).The RSE is reduced from winter values.The between-sites standard deviation remains the same as for winter (see Table SV in the Supplementary Material).The standard deviation of backscatter is also reduced relative to winter (from 2.26 to 1.32 dB).This suggests that the scattering from snow is becoming more dominant, likely due to increasing brine volumes in the basal snow layer.II].The between-sites standard deviation (0.016 dB/1 • ) is also similar to winter, and the temporal variability, with a mean of 0.064 dB/1 • , is slightly reduced from winter (see Table S5 in the Supplementary Material).
3) Snowmelt: The FYI slope of −0.235 dB/1 • remains very similar to winter (−0.235 dB/1 • ) and early melt (−0.230 dB/1 • ) (see Table II).However, the variance is higher, as shown by the lower R 2 and higher RSE values [see Fig. 9(a) and Table II].The higher variance likely stems, at least in part, from the rapid changes in backscatter as the snow moisture increases.The elevated variance may also be caused by the small number of samples for FYI due to the often-rapid transition from melt onset to the end of snowmelt for this ice type.The FYI slope is somewhat lower than the previously reported range (−0.26 to −0.34 dB/1 • ; Table I); however, three of our FYI sites do fall within this range (see Table SVI in the Supplementary Material).The mean per-site standard deviation of 0.202 dB/1 • indicates a substantially higher temporal variability relative to winter (0.081 dB/1 • ) and early melt (0.077 dB/1 • ).Although the differencing method mitigates the effects of changes in backscatter magnitude, a higher temporal resolution may be needed to fully compensate for the rapid change.
The SYI slope increases in this period, to −0.241 dB/1 • , from the early melt slope of −0.191 dB/1 • [see Fig. 9(b) and Table II].The moist snow is likely reducing the dominance of the volume scattering from the underlying ice, with increasing surface scattering from the snow surface, or from the snow-ice interface.As with FYI, the relatively high variance is a function of the rapid changes in backscatter.
The MYI slope also increases in this period, to −0.240 dB/1 • , from the early melt slope of −0.175 dB/1 • [see Fig. 9(c) and Table II].This is lower than the −0.33-dB/1 • value of [9], which is likely related to their use of small incidence angles.As for SYI, the moist snow is likely reducing ice volume scattering and increasing surface scattering to produce a steeper slope.The relatively high variance for MYI is a function of the rapid changes in backscatter.
The moist snow produces very similar slopes for all three ice types.A general all-ice-type slope for the snowmelt period is −0.239 dB/1 • (see Table II).
4) Ponding: During ponding, the FYI slope increases substantially for the first time, to −0.308 dB/1 • , under the partial influence of steeper slopes for water [see Fig. 10(a) and Table II].The variance is higher as well, with R 2 of 0.64 and an RSE value of 2.894 dB/1 • , likely caused by changing pond fractions and changing wind speeds.The very high slopes of [9] are not observed, likely a function of our larger range of incidence angles.Nevertheless, site FYI_EAD_1 reaches −0.483 dB/1   II].The variance is also high with an RSE of 2.182 dB/1 • , likely caused by the changing pond fractions and changing wind speeds.From the per-site perspective, the steepest slope is for site SYI_D_2 at −0.361 dB/1 • , and this is the SYI site with the lowest winter backscatter (see Table SVII in the Supplementary Material), suggesting a relatively smoother surface, which would facilitate a larger pond fraction.The temporal variability for SYI is lower than for FYI but relatively high compared to MYI.This suggests that pond fractions on although our per-site range does straddle this value.The temporal variability is relatively low, suggesting that the topographical constraints for melt ponds on MYI are more entrenched than for SYI.The greater relief of MYI topography constrains the melt pond coverage, reducing pond size and pond fraction relative to FYI [15].
A general all-ice-type slope for the ponding period is −0.293 dB/1 • (see Table II).
5) Drainage: Once the majority of the melt ponds have drained, the sea ice is dominated by bare deteriorating ice.Occasional early cold temperatures may freeze the remaining melt pond surfaces, and new snow may cover the ice (see Figs. [4][5][6]. The FYI slope decreases to its ice type minimum of −0.198 dB/1 • [see Fig. 11(a) and Table II].The deteriorating ice is porous, which can increase volume scattering, likely resulting in a lower slope.The variance is high with an RSE of 2.164 dB/1 • , which is related to the large range in slopes from the individual sites (−0.109 to −0.448 dB/1 • ).
The SYI slope decreases to −0.207 dB/1 • , back to its winter value [see Fig. 11(b) and Table II].The variance is moderate although the per-site range is still relatively large (−0.164 to −0.304 dB/1 • ).
The MYI slope decreases to −0.240 dB/1 • , back to its snowmelt value [see Fig. 11(c) and Table II).Although steeper than that reported by Mäkynen et al. [10] (−0.20 dB/1 • ), the 0.05 dB/1 • decrease from ponding is the same.In contrast to the FYI and SYI sites, the per-site MYI slopes are very uniform (−0.219 to −0.279 dB/1 • ) (see Table SVIII in the Supplementary Material).For the ponding period, the temporal variability is relatively low, supporting the notion of more entrenched topographical constraints.
A general all-ice-type slope for the drainage period is −0.215 dB/1 • .

B. Application of Incidence Angle Dependency During the Melt Season
Using time series for representative sites for FYI, SYI, and MYI, we show which melt periods benefit the most from period-specific slope normalization, relative to winter slope normalization.We also present examples of image normalization to illustrate the improvements gained when using period-appropriate slopes.We conclude with a discussion of the implications for classification approaches more generally.
The time-series applications of incidence angle normalization for FYI, SYI, and MYI are shown in Figs.12-14, respectively.The blue points and line are the normalized backscatter adjusted for each period's slope.For comparison, the purple points are normalized using the winter slope; the open black circles are the unnormalized backscatter.
An incidence angle normalized FYI time series is minimally affected (i.e., the points overlap) during early melt and during snowmelt, as expected given the slopes for these periods [see Fig. 12 and Table II].However, during ponding, the steeper period-adjusted slope (−0.308 versus −0.235 dB/1 • ) results in backscatter values up to 1.4 dB different.Once drainage begins, the slope difference is less, but the points still diverge.Winter slope values can thus be used for FYI until the end of the snowmelt without encountering significant deviation; as of ponding, period-specific slopes should be used.
An incidence angle normalized SYI time series shows a minor difference between winter normalization and period-specific normalization during the early melt period (see Fig. 13).However, with melt onset, the difference increases due to the steepening slope (−0.241 versus −0.208 dB/1 • ) and increases again in the ponding period due to an even steeper slope (−0.283 dB/1 • ).The difference in backscatter between applications of winter or period-specific slopes can reach 1.1 dB.An incidence angle normalized MYI time series shows similar results (see Fig. 14).The difference in backscatter between applications of winter or period-specific slopes can reach 1.2 dB for MYI.These time series and the slope values  in Table II show that winter slopes for SYI and MYI can only be used until the end of early melt; as for snowmelt, periodspecific slopes should be used.
The value of appropriate incidence angle normalization is demonstrated in Fig. 15.The winter image [see Fig. 15(a)] shows a region encompassing a mix of FYI, SYI, and MYI, necessitating the use of general period slopes.The general winter slope (−0.203 dB/1 • ) applied to this image produces an even tone throughout its 22 • range.The ponding period image in Fig. 15(c) is unnormalized, showing the strong radiometric gradient as the incidence angle changes throughout its 22 • range.The challenges for visual or automated classification using such unnormalized imagery are obvious.The ponding period image, normalized using the general winter slope [see Fig. 15(d)], shows a significant improvement in the evenness of tone throughout the image; however, a gradient is still discernable.The ponding period image normalized using the general ponding slope [see Fig. 15(e)] produces the most even tone throughout, facilitating consistent visual interpretation of ice types.
The detail images [see Fig. 15(f)-(k)] are used to quantify the improvements in radiometric normalization as the winter, and then, the ponding slopes are applied.We select two MYI floes near the extremes of the image incidence angle range that has similar backscatter ( σ 0 = 0.7 dB) and texture in the winter image.These floes are within the mixed ice areas  The general winter slope reduces the difference, but σ 0 of 1.1 dB may still be too large for robust classification.The general slope for the ponding period is effective in reducing σ 0 to 0.01 dB, facilitating consistent visual interpretation and classification potential.
The implications of our findings for sea ice classification are varied.For approaches that estimate per-class slopes during classification, e.g., [37] and [38], the rapidly changing slopes, as one transitions from one melt stage to the next, will likely add significant complexity, as they will only be valid for a short period and could be spatially diverse.However, given that the slope differences between sea ice types are reduced during the melt stages (as low as 0.005 dB/1 • ), the use of general per-melt stage slopes may be sufficient, with little if any additional classification accuracy to be achieved using per-class slope calculations.The substantial changes in even the general slope values, as the melt season progresses, imply that classification approaches need to either be able to ascertain the melt stage transitions in order to apply appropriate slope corrections or be able to calculate new slopes at each time step.

VI. CONCLUSION
We applied a new successive differencing method to obtain valuable incidence angle slope information needed for normalization to account for the rapid changes in SAR image backscatter during the melt season over Arctic sea ice.The result is a comprehensive set of C-band HH backscatter incidence angle dependencies (i.e., slopes) for sea ice for both the winter and melt seasons.They encompass FYI, SYI, and MYI sea ice types for the winter, early melt, snowmelt, ponding, and drainage periods.Many of these slopes were presented for the first time, and their respective time series from winter through drainage for individual sites provided significant insight as to when incidence angle correction is most beneficial.
We demonstrated that early melt slopes do not differ from winter slopes, allowing winter slopes to be used until melt onset for SYI and MYI.The moist snow of the snowmelt period produces very similar slopes for all three ice types; however, SYI and MYI slopes become appreciably steeper during snowmelt, while the FYI slope remains similar to winter.This allows winter slopes to be used for FYI until pond onset occurs.The ponding period produces substantially steeper slopes for all ice types due to the influence of melt ponds.FYI exhibits the highest temporal variability in slopes during ponding, due to the greater range of melt pond fractions, relative to SYI and MYI, which are more constrained by their ice topography.The drainage period exhibits a high spatial variability in slopes for all ice types; however, slope values become shallower with fewer melt ponds.
Our new set of backscatter slopes includes a diversity of sites for FYI, SYI, and MYI.However, they represent only a single year's melt progression.Repeating this sampling in other years may produce slightly different values, but the basic geophysical changes of moistening snow and melt pond formation should result in similar values.The use of the differencing method for calculating slopes mitigates large changes in absolute backscatter values.Future melt season research should include estimating slopes for younger ice types and differentiate between smooth (level) and rough (deformed) FYI types to be more comprehensive.A further logical next step for this work is to focus on assessing the impact of our melt season slope values within the context of improving ice type separability for operational ice chart production and in automated classification algorithms.

Fig. 2 .
Fig. 2. Study site locations in the Queen Elizabeth Islands of the Canadian Arctic Archipelago.The land is gray.Site details are provided in Table SII in the Supplementary Material.

Fig. 3 .
Fig. 3. Slope (dB/1 • ) versus change in incidence angle ( • ) for successive observations between January 1, 2021, and March 31, 2021, for all ice types n = 989.The y-axes do not extend to the full range of slope values (the full range is −23.6 to 24.9 dB/1 • ).Red lines indicate the standard deviation × 2 for data with changes in incidence angle > 10 • .The dashed vertical green line indicates the 6 • cutoff.

Fig. 4 .
Fig. 4. Site FYI_Eureka_1 time series of RCM backscatter slope as a function of incidence angle (blue points and lines), with the FYI winter slope (horizontal blue dashed line).HH backscatter (purple) normalized to an incidence angle of 35 • using the winter slope with a seven-sample running mean (purple dashed line).NCEP 6-h air temperature (green line) and 6-h wind speed (brown line).Sentinel-2 NIR observations (red points) with imputed values (red dashed line).Vertical lines indicate the beginning of early melt (green), melt onset (purple), pond onset (red), and pond drainage (cyan).

Fig. 5 .
Fig. 5. Site SYI_EAF_1 time series of RCM backscatter slope as a function of incidence angle (blue points and lines) with the SYI winter slope (horizontal blue dashed line).HH backscatter (purple) normalized to an incidence angle of 35 • using the winter slope with a seven-sample running mean (purple dashed line).NCEP 6-h air temperature (green line) and 6-h wind speed (brown line).Sentinel-2 NIR observations (red points) with imputed values (red dashed line).Vertical lines indicate the beginning of early melt (green), melt onset (purple), and pond onset (red).Pond drainage occurs after the time-series end date.

Fig. 7 (
Fig. 7(c) and Table II].The individual MYI sites range from −0.151 to −0.172 dB/1 • , with a mean of −0.163 dB/1 • , and a smaller between-sites standard deviation of 0.008 dB/1 • (see Table SIV in the Supplementary Material).The temporal variability has a mean of 0.062 dB/1 • .These slope values are within the previously reported winter range of −0.10 to −0.20 dB/1 • (see Table I).A general all-ice-type slope for winter, based on the mean of the FYI, SYI, and MYI bulk differencing slopes, Fig. 7(c) and Table II].The individual MYI sites range from −0.151 to −0.172 dB/1 • , with a mean of −0.163 dB/1 • , and a smaller between-sites standard deviation of 0.008 dB/1 • (see Table SIV in the Supplementary Material).The temporal variability has a mean of 0.062 dB/1 • .These slope values are within the previously reported winter range of −0.10 to −0.20 dB/1 • (see Table I).A general all-ice-type slope for winter, based on the mean of the FYI, SYI, and MYI bulk differencing slopes,

Fig. 6 .
Fig. 6.Site MYI_D_1 time series of RCM backscatter slope as a function of incidence angle (blue points and lines) with the MYI winter slope (horizontal blue dashed line).HH backscatter (purple) normalized to 35 • incidence using the winter slope with a seven-sample running mean (purple dashed line).NCEP 6-h air temperature (green line) and 6-h wind speed (brown line).Sentinel-2 NIR observations (red points) with imputed values (red dashed line).Vertical lines indicate the beginning of early melt (green), melt onset (purple), pond onset (red), and pond drainage (cyan).

Fig. 7 .
Fig. 7. Change in backscatter versus change in incidence angle during winter for (a) FYI, (b) SYI, and (c) MYI.The dashed lines are linear regressions.The θ ± 6 • gap is described in Section IV-B.

Fig. 8 .
Fig. 8. Change in backscatter versus change in incidence angle during the early melt period for (a) FYI, (b) SYI, and (c) MYI.The dashed lines are linear regressions.The θ ± 6 • gap is described in Section IV-B.

Fig. 9 .Fig. 10 .
Fig. 9. Change in backscatter versus change in incidence angle during the snowmelt period for (a) FYI, (b) SYI, and (c) MYI.The dashed lines are linear regressions.The θ ± 6 • gap is described in Section IV-B.

Fig. 11 .
Fig. 11.Change in backscatter versus change in incidence angle during the drainage period for (a) FYI, (b) SYI, and (c) MYI.The dashed lines are linear regressions.The θ ± 6 • gap is described in Section IV-B.

Fig. 12 .
Fig. 12.Time series for site FYI_Eureka_1 with unnormalized backscatter (open circles), winter slope normalization (purple), and period-adjusted slope normalization (blue); the latter two are both normalized to an incidence angle of 35 • .The dashed lines are seven-sample running means.Vertical lines indicate the beginning of melt onset (purple), pond onset (red), and pond drainage (cyan).

Fig. 13 .
Fig. 13.Time series for site SYI_EAF_1 with unnormalized backscatter (open circles), winter slope normalization (purple), and period-adjusted slope normalization (blue); the latter two are both normalized to an incidence angle of 35 • .The dashed lines are seven-sample running means.Vertical lines indicate the beginning of melt onset (purple) and pond onset (red).

Fig. 14 .
Fig. 14.Time series for site MYI_D_1 with unnormalized backscatter (open circles), winter slope normalization (purple), and period-adjusted slope normalization (blue); the latter two are both normalized to an incidence angle of 35 • .The dashed lines are seven-sample running means.Vertical lines indicate the beginning of melt onset (purple), pond onset (red), and pond drainage (cyan).

Fig. 15 .
Fig. 15.Examples of image normalization: (a) RCM SC100MA HH descending image for March 23, 2021, normalized using the general winter slope (−0.203 dB/1 • ), with incidence angle range indicated; (b) green rectangle is the region shown in the main images; (c) RCM SC50MB HH ascending image for June 23, 2021, without incidence angle normalization, with incidence angle range indicated; (d) same image normalized using the general winter slope; and (e) using the general ponding slope (−0.293 dB/1 • ); (f)-(h) details of the red region for the respective normalizations; and (i)-(k) orange region.The backscatter values in the detail images are for their respective yellow subregions, representing similar MYI floes.All images are scaled from −5 to −25 dB.The main region is ∼350 × 160 km, the red detail is 19 × 18 km, and the orange detail is 32 × 30 km.

TABLE I PREVIOUSLY
REPORTED C-BAND HH BACKSCATTER INCIDENCE ANGLE DEPENDENCIES FOR SEA ICE

TABLE II SLOPE
STATISTICS FOR THE BULK DIFFERENCING METHOD FOR SEA ICE DURING THE MELT PERIODS.ALL SLOPES ARE SIGNIFICANT AT p < 0.001.RSE IS THE RESIDUAL STANDARD ERROR.DF IS THE DEGREE OF FREEDOM Material).Site FYI_Eureka_2 has relatively low backscattering ice, and there is no obvious cause for the relatively low slope.Similarly, site FYI_EAI_2 presents no obvious clues for its relatively high slope (see Table SIV in the Supplementary Material).This natural variability for FYI is reflected in the between-sites standard deviation of 0.056 dB/1 • .The temporal variability of the FYI per-site slopes ranges from standard deviations of 0.054 to 0.101 dB/1 • , with a mean of 0.077 dB/1 • .The bulk differencing slope and the mean of the per-site differencing slopes are within the previously reported winter range of −0.27 to −0.20 dB/1 • (see Table I).The winter slope for SYI using the differencing method is −0.208 dB/1 • with an RSE of 0.810 dB/1 • [see Fig. 7(b) and Table II].The individual SYI sites range from −0.194 to −0.225 dB/1 • , with a mean of −0.205 dB/1 • and a smaller between-sites standard deviation of 0.015 dB/1 • (see Table SIV in the Supplementary Material).The temporal variability has a mean of 0.081 dB/1 • .These SYI findings are new, as SYI slopes have not been previously reported for winter.SYI slopes are approximately midway between those for FYI and MYI, as expected.
The winter slope for MYI using the bulk differencing method is −0.167 dB/1 • with an RSE of 0.745 dB/1 • [see Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.