1. Introduction
The Arctic has undergone rapid change over recent decades [
1,
2]. Sea ice in the Arctic is decreasing at an accelerated rate [
3,
4], shifting from multiyear ice to younger ice [
5,
6]. Snow is the primary atmospheric source input to Arctic sea ice, and it is highly sensitive to climate change [
7]. The snow cover on sea ice possesses several typical characteristics, such as a high albedo and low thermal conductivity, which influences the heat transfer between the ocean and the atmosphere [
8,
9,
10]. Furthermore, snow depth (SD) on sea ice is vital to understanding the overall heat exchange occurring in the Polar Regions, and also important variables in the fresh water budget of the oceans. Additionally, accurate estimation of the snow depth is essential for calculating sea-ice thickness and volume [
11,
12]. Research has shown that a SD uncertainty of 5 cm could lead to estimation errors of 35 cm in the ice thickness [
13].
The Special Sensor Microwave/Imager (SSM/I) and the Special Sensor Microwave Imager/Sounder (SSMIS) on Defense Meteorological Satellite Program (DMSP) satellites provide brightness temperature (TB) data for the retrieval of SD on sea ice at a large spatial and temporal scale [
8,
10]. These data make it possible to study the spatiotemporal variability of SD on Arctic sea ice. However, the agreement and consistency of the TB measurements are affected by the differences in satellite sensors and platforms, which lead to discrepancies in the derived long-term SD on sea ice.
Inter-calibration and validation are fundamental assurances for the application of remote sensing data [
14,
15]. Cross-platform calibrations have been performed between the SSM/I carried on the DMSP-F8, DMSP-F11 (SSM/I) and DMSP-F13 (SSM/I). Abdalati et al. [
16] examined the correlation between F8 and F11 SSM/I TB, and a further study by Stroeve et al. [
17] indicated that the differences among F8, F11, and F13 data are sufficiently large to affect analyses of sea-ice extent and area time-series data. Meier et al. [
18] and Cavalier et al. [
19] used the full-year F13 SSM/I and F17 SSMIS overlap TB data, to obtain consistent sea ice extent and area information based on intercalibration processing. Dai et al. [
20] inter-calibrated TB data obtained from different passive microwave satellite sensors, and assessed the consistency of terrestrial snow depth retrievals in China. However, there has been no adequate comparison and evaluation between the retrieved SDs from F13 SSM/I and F17 SSMIS, and the intercalibration effects in terms of SD retrievals on the Arctic sea ice during their overlap period.
In this paper, the differences between the estimated SDs based on the original F17 SSMIS TB and the calibrated F17 SSMIS TB using the F13 SSM/I TB as the baseline are assessed through comparing with the Operation IceBridge (OIB) SD measurements. We also analyzed the performance of different inter-calibration models according to the method of Cavalieri and Dai, and made the assessment of OIB SD data which were resampled to a pixel size of 25 km on first-year sea ice.
4. Results
4.1. Inter-Calibration Models
The overlap period of 2007 was selected for both F13 SSM/I and F17 SSMIS data to establish calibration models using F13 as the baseline with the linear regression relationship in two ways.
Table 3 shows the CA models and the DA models for the four channels. All the models were statistically significant at the 0.05 alpha level using F-test.
As shown in
Table 3, the slope values are within 0.04 of 1 and the intercepts of 19H are close to −2 K for both models. Moreover, intercept values of 19V and 22V are less than intercept of the other channels. Comparison of the RMSE for the CA and the DA models show that there are relatively higher values for DA models than that for the CA models for the 19H, 19V and 22V channel, whereas those values of CA models are higher than the DA models for the 37V channel. When considering the overall effect, we used CA models to correct the inter-sensor bias using F13 as the baseline, and obtained the calibrated data denoted as F13C.
4.2. OIB Snow Depth Resampling in 25 km Pixel
The spatial coverage for the OIB snow depth includes Beaufort Sea, North of the Canadian archipelago and Greenland in Arctic with the track resolution of 40 m, and the snow depth of OIB measures were distributed not only on first-year ice, but on multiyear ice.
In this study, we selected OIB SD measurements which are distributed in the 25 km pixels of the 100% first-year sea ice regions according to the NT algorithm. Although OIB SD measurements have a higher spatial resolution, it is important to evaluate OIB SD transect across the resampling pixel. If there are no less than two OIB transects within a pixel along different routes in one day, we then analyzed the differences of OIB SDs within the pixel.
On 15 March 2012, there are two pixels over first-year sea ice (P1 and P2,
Figure 3a). The mean SD varies about 1 cm in both pixels between the top transect and the bottom transect. On 17 March 2012, only one pixel with two OIB SD transects on first-year sea ice (P3,
Figure 3b), the differences of the mean SDs is 2 cm. Therefore, there is 1–3 cm SD deviation for two transects in different locations in P1-P3 pixels (
Table 4).
4.3. Comparison with OIB Snow Depth
The F17 SSMIS (2009–2013) TB were calibrated using F13 TB as the baseline, and the calibrated F17 TB data were denoted as F13C TB data, which were used to calculate F13C SD. Furthermore, the original F17 SD and F13C SD were compared with the OIB SD during 2009–2013.
Figure 4 shows the difference between the F17 SD, the F13C SD and the OIB SD on first-year sea ice. The Bias and RMSE can be calculated using the following formulas:
, and
, where
refers to the value of F17 (F13C) SD for each pixel, and
refers to the value of OIB SD for the same pixel,
n is the number of pixels. The values of Bias and RMSE between the F17 and the OIB SDs are −9 cm and 10 cm, respectively. These values are larger than those that were obtained by comparison of the F13C SD with the OIB SD, indicating that F17 SSMIS calibrated to F13 SSM/I is more suitable for obtaining a long-time series SD.
Table 5 shows the yearly bias and RMSE values of the F13C SD to the OIB SD from 2009 to 2013. The absolute Bias and RMSE of the F13C-OIB SD are much smaller than the F17-OIB SD.
5. Discussion
F13 SSM/I sensor’s feature is similar to F17 SSMIS, with the mean biases of measured brightness temperatures for the channel of 19V, 19H, 22V and 37V vary from 0.8K to 1.7K in 2007. These minor discrepancy of TB lead to 0.5% bias for the calculated sea ice concentration, and have a profound impact on
GRV (ice) in SD retrieval algorithm, finally resulting in −6.7 cm bias for the calculated SD (
Table 6), in addition,
Figure 5 shows the significant differences of derived SD from F13 TB and the uncorrected F17 TB, despite the SD retrieval algorithm breaks down in summer due to the snow is wet or exists a certain liquid water fraction. Therefore, the inter-calibration processing between F13 TB and F17 TB is necessary for deriving long-term snow depth.
The F13C TB were the result that F17 TB calibrated to F13 TB using CA models according to Cavalieri et al. [
19]. When comparing with F17 to F13, there are lower biases for sea ice concentration, GRV (ice) and SD between F13C and F13. The bias of −6.6 cm exists between F17 SD and F13 SD, and −0.4 cm between the F13C SD and F13 SD, which mean that F13C SD is about 6.2 cm higher than F17 SD. Moreover, the 6.2 cm bias is as the same as the F13C cloud points seem to be higher than that of F17 cloud points in
Figure 4. In the similar way, we derived SD from the TB which originates from the TB result of F17 TB calibrated to F13 TB using DA models, and then compared with F13 SD in 2007. The bias, RMSE and MRE between the two SD are −0.5 cm, 0.8cm and −6.2%, respectively. It can be concluded that CA models seem a little better than DA models when inter-calibrating F13 TB and F17 TB for the snow depth retrieval purpose.
The calibration method following Cavalieri et al. [
19] was ultimately used in this paper, due to the smaller RMSE values when comparing to that of the method from Dai et al. [
20] (
Table 3) and the SD retrievals using CA models were better agree with F13 SD. Furthermore, DA models according to Dai et al. [
20] is used for terrestrial snow cover and the Cavalieri method is used specifically for sea ice. The linear coefficients were obtained through the relationship between the F13 TB and F17 TB for each channel for the entire year in DA models, and the daily sample points will affect the regression coefficients directly. However, the linear regression coefficients between the F13 TB and F17 TB were obtained for each day on each channel, and then the daily coefficients values were averaged to produce coefficient values as the final coefficient in CA models. This processing reduced the direct impact of daily sample points on the final coefficient value, but increased the amount of calculations.
The OIB SD variability within a 25 km pixel in this paper is different from the values reported by Brucker et al. [
10], who analyzed the two 12.5 km pixels of the two OIB SD transects over multiyear ice, with the mean SDs differing by 2–4 cm on 18 March 2011, whereas, the mean SDs differing by 1–3 cm on first-year sea ice was found in this study. The RMSE of F13C SD when compared with OIB SD is 5 cm, which is less than that in Brucker et al. [
10], with the RMSE of 7 cm for the comparison of SDs that was acquired by the AMSR-E with the OIB SD.
Through comprising the F17 SDs, F13 SDs with the OIB SDs, we conclude that it is more suitable to choose the F13 SSM/I TB as the baseline for the SD retrieval purpose on the Arctic sea ice. However, Dai et al. [
20] recommended using the F17 SSMIS TB as the reference to improve the consistency between F13 SSM/I TB and F17 SSMIS TB when comparing the retrieved snow depth over Tibetan Plateau. We conclude that the calibration option should be adjusted according to the different retrieval parameters for different regions.
The change of Arctic sea ice to a thinner and seasonal one, may result in a smaller and faster moving ice cover and snow-ice formation than just a decade ago [
30,
31]. Wet snow and melt-ice will bring large retrieval error based on the existing SD empirical algorithm [
8], which may influence the inter-calibration option of SSM/I and SSMIS TB data. It is necessary to reconstruct the SD retrieval model using the field-derived SD measurements. Some international Arctic research initiatives like the MOSAiC science plan [
32] are broadly motivated by the dramatic changes in the Arctic climate system. More snow depth measurements on first-year sea ice could be collected to build a robust new snow depth algorithm based on passive microwave satellite data, for obtaining more consistent snow depth information over Arctic first-year ice.
6. Conclusions
This paper attempted to construct a consistent time-series data set of brightness temperatures through establishing the calibration models for the four channels. We further compared SDs on Arctic first-year sea ice that was derived from passive microwave satellite observations of the SSM/I and SSMIS with the OIB SDs.
Inter-calibration model analysis show that the RMSE of the DA models are higher than that of the CA models for the channel of 19H, 19V, 22V, whereas the RMSE of CA models is higher than that of DA models for the 37V channel. Taking into account of the overall effect, the CA models are recommended to correct the inter-sensor bias.
The variations of OIB SD are 5–7 cm while examining the OIB transect across the 25 km pixel on 15 and 17 March 2012, with 1–3 cm SD deviation for two transects in different locations.
Based on CA models, the biases between the retrieved F17 SDs and F13C SDs when compared to the OIB SDs are both around −8~−2 cm. In addition, the F13C SDs perform smaller RMSE (5 cm) than F17 (10 cm). It can be concluded that TB observations from F17 SSMIS calibrated to F13 SSM/I as the baseline should be recommended when performing the sensors’ biases correction for snow depth purpose based on the existing algorithm.
Snow depth over Arctic sea ice is an important parameter for calculating ice thickness. Inter-sensor calibration can reduce the systematic errors that are introduced by the use of various passive microwave sensors, and it can improve the consistency of SD time-series data that are used for long-term trend analyses. However, the calibration models in different Arctic sea regions could also be considered for future studies in order to obtain SD information with greater accuracy and consistency. Currently, NASA MEaSUREs program produces an improved, enhanced-resolution, gridded passive microwave data set [
33], it means that higher-resolution PM data can be used for future studies of obtaining accurate SD information, as well as Arctic sea ice thickness.
It should be noted that the SD empirical algorithm may influence the inter-calibration option, however, there are no other SD algorithms expect for the Markus’s empirical algorithm published in 1998 based on DMSP SSM/I-SSMIS TB data until now. More in-situ SD measurements over first-year sea ice should be collected to construct a robust new SD algorithm in future work. However, this paper provided an inter-calibration option about obtaining more consistent SD information based on the existing algorithm.