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  • View in gallery

    AMSR-E SD on 4 Apr 2009, as well as locations of the 2009–11 OIB flights measuring SD used in this paper. Blank area represents missing data of SD.

  • View in gallery

    SD differences between the AMSR-E and OIB products during 2009–11. Filled triangle represents overlapping part of OIB flight route in different years.

  • View in gallery

    AMSR-E SDs verses OIB SDs. The red and black dashed lines are the dividing lines with deviations less than 5 and 10 cm, respectively.

  • View in gallery

    MAEs of different methods for 20 groups of experiment.

  • View in gallery

    Contour distribution of SD in Arctic scale obtained by (left) QPF, (center) PF78, and (right) TPF24 on (top) 5 Apr 2009, (middle) 21 Apr 2010, and (bottom) 25 Mar 2011. The averaged OIB SD in these days is also shown.

  • View in gallery

    Point comparisons of fitting SDs verses OIB SDs. (a)–(c) Results for 5 Apr 2009, 21 Apr 2010, and 25 Mar 2011, respectively.

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Acquiring the Arctic-Scale Spatial Distribution of Snow Depth Based on AMSR-E Snow Depth Product

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  • 1 Physical Oceanography Laboratory, Qingdao Collaborative Innovation Center of Marine Science and Technology, Ocean University of China, and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
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Abstract

Snow on sea ice is a key variable in Arctic climate studies and thus plays an important role in geophysics. However, snow depths (SDs) derived from passive satellite remote sensing data are missing on multiyear ice due to the limitation of algorithm. We interpolate the SDs using the polynomial fitting (PF) method, trigonometric polynomial fitting (TPF) method, and multiquadric function interpolation method, and NASA’s Operation IceBridge (OIB) SD product is used to assess errors. Results show that TPF with the highest degree in x direction equaling 2 and the highest degree in y direction equaling 4 (TPF24) is the most satisfactory method, which has a deviation of 7.19 cm from OIB SD. Although PF with the highest degree in x and y directions being 7 and 8, respectively (PF78), also performs well in terms of error (7.22 cm), unreasonable value will be obtained at the edge due to its high degree. Results of TPF24 show a thicker SD area located in the north of Greenland, which is in good agreement with the actual situation.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xianqing Lv, xqinglv@ouc.edu.cn

Abstract

Snow on sea ice is a key variable in Arctic climate studies and thus plays an important role in geophysics. However, snow depths (SDs) derived from passive satellite remote sensing data are missing on multiyear ice due to the limitation of algorithm. We interpolate the SDs using the polynomial fitting (PF) method, trigonometric polynomial fitting (TPF) method, and multiquadric function interpolation method, and NASA’s Operation IceBridge (OIB) SD product is used to assess errors. Results show that TPF with the highest degree in x direction equaling 2 and the highest degree in y direction equaling 4 (TPF24) is the most satisfactory method, which has a deviation of 7.19 cm from OIB SD. Although PF with the highest degree in x and y directions being 7 and 8, respectively (PF78), also performs well in terms of error (7.22 cm), unreasonable value will be obtained at the edge due to its high degree. Results of TPF24 show a thicker SD area located in the north of Greenland, which is in good agreement with the actual situation.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xianqing Lv, xqinglv@ouc.edu.cn

1. Introduction

The crucial role of snow on sea ice in the climate system is well recognized. Because of its high surface albedo and low thermal conductivity, snow on sea ice is pivotal for the regulation of heat transfer between ocean, sea ice, and atmosphere (Maykut 1978). In the course of past decades, interest in the spatial and temporal variations of snow distribution over sea ice has increased due to its importance to the retrieval of sea ice thickness from airborne and spaceborne altimeters (Kwok and Cunningham 2008; Giles et al. 2007). Moreover, snow depth (SD) on sea ice is an important indicator of polar precipitation and thus can be used as a proxy for the amount of freshwater entering the ocean.

However, due to the wide coverage of snow cover, the data of SD measured in situ are incomplete, at low resolution, and extremely scarce (Shalina and Sandven 2018). On this account, Markus and Cavalieri (1998) developed an algorithm to derive SD on seasonal sea ice from spaceborne passive microwave measurements, for example, from Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). Their algorithm shows good accuracy and the results are consistent with in situ measurements (Cavalieri et al. 2014). Nevertheless, the distribution of SD across the Arctic is still unavailable because of the algorithm is unsuitable for the retrieval of SD over multiyear ice (MYI) (Comiso et al. 2003).

Additionally, between 2009 and 2013, NASA’s Operation IceBridge (OIB) Mission measured SD on Arctic sea ice in March and April by using an airborne snow radar. The OIB SD data were evaluated with in situ measurements located at the north of Greenland and were found to be accurate (Farrell et al. 2012). Brucker and Markus (2013) verified the SDs measured by OIB as well as derived by AMSR-E data and found the deviation between them is within an acceptable range.

Knowledge of the thickness and spatial distribution of snow on sea ice is essential for estimating sea ice thickness and volume (Kurtz and Farrell 2011; Webster et al. 2014), improving the accuracy of dynamic–thermodynamic sea ice models (Peter et al. 1997) and atmospheric models (Comiso et al. 2003), and studying climate change (Holland and Bitz 2003). Many scholars have studied the spatial distribution of SD in the Arctic.

Warren et al. (1999, hereafter W99) analyzed the large-scale Arctic SD distribution by using two-dimensional quadratic polynomial fitting (QPF), based on the SD data measured by Soviet Union drifting stations between 1954 and 1991. Based on the OIB SD products, Webster et al. (2014) found that the snowpack was thinning by using the same method as W99. However, the OIB SD data are basically available only in the western Arctic region, and therefore, the fitted SD field does not represent the whole Arctic situation. Castro-Morales et al. (2015) used a regional model configuration for the Arctic with the Massachusetts Institute of Technology General Circulation Model (MITgcm) and followed a simple snow parameterization to analyze the changes of SD between 2000 and 2013 at the regional scale, and their results also show a thinning trend of SD.

In this study, we use polynomial fitting (PF) method, trigonometric polynomial fitting (TPF) method, and multiquadric interpolation method to estimate the missing data of AMSR-E SD, and the QPF method is used for comparison. The OIB SD product is used to evaluate the error of each method, before which the correlation between the AMSR-E and the OIB SD products are checked. For PF and TPF, the optimal degree is determined by comprehensive consideration of mean absolute error (MAE) and variance, and the distribution of SD in the Arctic is obtained at last.

This study is organized as follows. Section 2 shows the correlation between the AMSR-E and the OIB SD data at the grids where both of them are available. SD fitting methods are given in section 3. Result analysis and conclusions are presented in section 4 and section 5, respectively.

2. Data and correlation analysis

a. AMSR-E snow depth data

The AMSR-E dataset used here is the AMSR-E/Aqua Daily L3 12.5 km brightness temperature and sea ice concentration, version 3, product (Cavalieri et al. 2014), which is mapped to a polar stereographic grid at 12.5 km spatial resolution. To minimize variability resulting from weather effects, the product provides a 5-day running averaged SD, which is based on the current and the previous 4 days excluding Arctic perennial ice regions. Temporal coverage is from 1 June 2002 to 3 October 2011.

Because of the inapplicability of passive microwave SD algorithm on MYI or melting snow region, the AMSR-E SD product has a large number of missing data. Taking 5 April 2009 as an example (Fig. 1), the missing data are mostly distributed in the Arctic basin. Additionally, the upper limit for SD retrieval is 50 cm, which is a result of the limited penetration depth at 18.7 and 36.5 GHz.

Fig. 1.
Fig. 1.

AMSR-E SD on 4 Apr 2009, as well as locations of the 2009–11 OIB flights measuring SD used in this paper. Blank area represents missing data of SD.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

b. Operation IceBridge data

To evaluate the accuracy of the Arctic SD spatial distribution fitting methods, the IceBridge L4 Sea Ice Freeboard, SD, and Thickness (IDCSI4) product are used here as a reference (Kurtz et al. 2015). From 31 March 2009 to 25 April 2013, the NASA’s OIB Mission conducted 45 flights in March and April, before the onset of melt, and measured SD on Arctic sea ice by using the University of Kansas’s frequency modulated continuous-wave (FMCW) snow radar which has a nominal sweep from 2 to 8 GHz and a usable bandwidth of about 4.5 GHz (Kurtz et al. 2009). To reduce speckle noise when using the SD retrieval algorithm (Kurtz and Farrell 2011; Kurtz et al. 2013), the OIB SD product has the spatial resolution reduced to 40 m.

Farrell et al. (2012) found that there is a bias of about 0.01 m and a correlation of r = 0.7 between the mean OIB SDs and in situ measurements over first year ice. By using 610 satellite grid cells where both satellite SD retrievals and OIB data were available, Brucker and Markus (2013) found the difference between these two SD products is 0.00 ± 0.007 m.

Both AMSR-E data and OIB data can be downloaded from the National Snow and Ice Data Center (NSIDC) website (https://nsidc.org/data).

c. Correlation between AMSR-E data and OIB data

Preliminary validation of the correlation between AMSR-E and OIB SD products is required before we use OIB SDs to evaluate the error of various methods in obtaining the spatial distribution of Arctic SDs.

From 2009 to 2011, there were 28 days in total when both OIB SD data and AMSR-E SD data were available, and we finally select 20 days of them considering that the amount of missing AMSR-E SDs should be moderate to ensure completeness of Arctic SDs (the specific dates for these 20 days are listed in Table 1). Since AMSR-E SDs were less accurate (|ΔSD| = |SDOIB − SDAMSR-E| > 10 cm) in the regions with low ice concentration (Brucker and Markus 2013), we removed SDs on the grids where ice concentration lower than 90%. Then, there are 522 satellite grid cells in total where both kinds of SD dataset were available, and the results show a 4.59 cm mean absolute deviation (MAD) between them (Table 1). Moreover, Fig. 2 illustrates the spatial distribution of SD differences, and as it shows, the less accurate AMSR-E SDs were mainly located in the Nares Strait (during the 25 April 2009 and the 26 March 2010 flights), and the central Arctic basin (during the 12 April 2010 flight).

Table 1.

Statistics of the difference between AMSR-E SDs and OIB SDs during 2009–11. Variable N represents the number of pixels that OIB flight passed where AMSR-E SD exist.

Table 1.
Fig. 2.
Fig. 2.

SD differences between the AMSR-E and OIB products during 2009–11. Filled triangle represents overlapping part of OIB flight route in different years.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

AMSR-E SDs verses OIB SDs is demonstrated in Fig. 3. Overall, 88.7% of the AMSR-E SDs are within ±10 cm of the OIB SDs, and 71.5% within ±5 cm. There are 59 pixels where the difference is larger than 10 cm, and in order to obtain more accurate fitting results, these AMSR-E SDs are also removed.

Fig. 3.
Fig. 3.

AMSR-E SDs verses OIB SDs. The red and black dashed lines are the dividing lines with deviations less than 5 and 10 cm, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

3. Methodology and experiments

a. Fitting methods

SD datasets are denoted by (xi, yi, zi), i = 1, 2, …, I, where x and y are rectangular coordinates converted from longitudes and latitudes using the Stereographic map projection, z is the SD observation, and I is the total number of the data.

The estimated SDs z˜i(i=1,2,,I) calculated by PF method are
z˜i=k=0Kmaxs=0Smaxβk,s×xik×yis,
where βk,s (k = 0, 1, …, Kmax, s = 0, 1, …, Smax) represent the constant coefficients and can be solved by the least squares method. In the study of W99 and Webster et al. (2014), they set Kmax + Smax ≤ 2, which is called QPF.
Considering the periodicity and diversity, TPF method is used in our study, and the estimated SDs calculated by TPF method are
z˜i=k=0Kmaxs=0Smax(CCk,s,CSk,s,SCk,s,SSk,s)×Fk,s(xi,yi),
where
Fk,s(xi,yi)=[cos(2πkxi/T)×cos(2πsyi/T)cos(2πkxi/T)×sin(2πsyi/T)sin(2πkxi/T)×cos(2πsyi/T)sin(2πkxi/T)×sin(2πsyi/T)],
represents base functions, T is the horizontal wavelength, and CCk,s, CSk,s, SCk,s, SSk,s are constant coefficients that also can be solved by the least squares method.

b. Interpolation methods

Since radial basis function (RBF) interpolation has been widely used in the scatter data interpolation (Franke 1982), the multiquadric function interpolation method is considered in this study.

The multiquadric function interpolation is a linear combination of multiquadric functions centered at known data points (Hardy 1971). We figure out all coefficients αj, j = 1, 2, …, I by solving equations
zi=j=1Iαj×D(dij),i=1,2,,I,
where D(dij)=1+(ε|dij|)2, dij is Euclidean distance between (xi, yi) and (xj, yj) points, and ε indicates the inverse of a critical radius, which is set to be the average distance between the nodes in this paper.

c. Experimental process

It’s critical for both PF and TPF methods to determine the maximum degrees of base functions in the x direction and y direction, that is, Kmax and Smax. Due to the scarcity of SD measurements, fitting results are very sensitive to individual data when Kmax + Smax ≥ 3 in the study of W99. However, resolution of the satellite data is 12.5 km × 12.5 km and there are about 40 thousand available data per day, thus we need to find the optimal combination of Kmax and Smax. The accuracy of the OIB SD data and its consistency with the AMSR-E SD product (with a bias of 4.59 cm) enables it to be used to evaluate the errors of various methods. Here we define the MAE as MAE=i=1N|z˜iz¯i|/N, where z¯i represents the averaged OIB SD in the ith satellite pixel, z˜i is the calculated SD value at the intermediate point of the OIB track in the same pixel, and N is the total number of pixels.

All the combinations of Kmax = 0, 1, …, 9 and Smax = 0, 1, …, 9 are tested when we fit every day’s AMSR-E SD data by using PF and TPF methods, and mean MAE MAE¯ and variance Var=n=120(MAEnMAE¯)2/20 of these 20 groups of experiments for each combination are given in Tables 25.

Table 2.

Mean MAE of PF method. The unit is centimeters.

Table 2.
Table 3.

Variance of PF method. The unit is centimeters.

Table 3.
Table 4.

Mean MAE of TPF method. The unit is centimeters. A value of more than 50 cm is considered unreasonable and is indicated by a slash.

Table 4.
Table 5.

Variance of TPF method. The unit is centimeters. A value of more than 50 cm is considered unreasonable and is indicated by a slash.

Table 5.

4. Result analysis and discussion

As shown in Tables 25, for PF method, both MAE¯ and Var are significantly reduced when Kmax = 7 and Smax = 8, while for TPF method, MAE¯ reaches the minimum and Var is acceptable when Kmax = 2 and Smax = 4. In that way, the optimal degree of PF and TPF is found, and we donated them by PF78 and TPF24, respectively.

The MAEs of 20 experiments with different kinds of methods are illustrated in Fig. 4, while MAE¯ and Var are listed in Table 6. Comparing the results of these methods, it can be clearly seen that TPF24 method has both the minimum MAE¯ and Var, which means that TPF24 is not only the most accurate, but also the most stable method. On the contrary, the result of multiquadric interpolation method shows a MAE of more than 9 cm, as well as a variance of 32.65 cm. Obviously, it is not reliable. It can be seen from Eq. (4) that I equations will be solved when we use RBF interpolation method. Once the amount of data is too large, the computational resources required will increase accordingly. Therefore, another drawback of RBF interpolation method is the huge computation load. In addition, because the interpolant passes through each data point precisely, errors of SDs derived from satellite data will be included.

Fig. 4.
Fig. 4.

MAEs of different methods for 20 groups of experiment.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

Table 6.

Mean MAE and variance of each method in the 20 groups of experiments. The unit is centimeters.

Table 6.

Finally, PF78 and TPF24 are selected to fit AMSR-E SD data on the Arctic scale, while QPF method is used for comparison. The contour maps of SDs on 5 April 2009, 21 April 2010, and 25 March 2011 are shown in Fig. 5 since OIB aircraft’s tracks are relatively long in these days. Results of TPF24 show that the fitting values well match with the OIB SD distribution, while neither QPF nor PF78 can reflect the characteristics of OIB SD changes.

Fig. 5.
Fig. 5.

Contour distribution of SD in Arctic scale obtained by (left) QPF, (center) PF78, and (right) TPF24 on (top) 5 Apr 2009, (middle) 21 Apr 2010, and (bottom) 25 Mar 2011. The averaged OIB SD in these days is also shown.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

Additionally, PF78 performs better than QPF since the latter provides an unrealistic north-to-south gradient. A clearer fitting effect on the OIB track is shown in Fig. 6. It can be clearly seen that the results of QPF are almost a straight line, which cannot effectively reflect the characteristics of SD distribution. However, the biggest drawback of PF78 is the high degree on both x and y directions (Kmax = 7 and Smax = 8), which leads to unreal values at the edge (higher than 50 cm or lower than 0 cm), and this shortcoming is related to the nature of the polynomial function itself.

Fig. 6.
Fig. 6.

Point comparisons of fitting SDs verses OIB SDs. (a)–(c) Results for 5 Apr 2009, 21 Apr 2010, and 25 Mar 2011, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 36, 10; 10.1175/JTECH-D-18-0217.1

Since AMSR-E SD values are more likely to be underestimated where the OIB SD is larger than 30 cm (Fig. 3), TPF24 has a lower fitting value at some points (Fig. 6), but this does not affect the superiority of the method. Actually, this method is computational inexpensive in comparison with numerical model products (Castro-Morales et al. 2015) yet can produce reliable SD.

In this study, we only fitted SDs in the spring of 2009–11 because AMSR-E and OIB data are both available only in these days. However, it is unclear whether the best fitting function (TPF24) performs well in other seasons. For more knowledge of SD over MYI, it is necessary to have more datasets that can be used to detect the fitting effect.

5. Conclusions

This study has shown that the TPF method with Kmax = 2 and Smax = 4 is the most satisfactory method in the fitting of AMSR-E SD product in the Arctic. The errors of different methods are evaluated with the OIB SD. The results of all 20 experiments show that TPF24 method has the minimum mean MAE and variance among QPF, PF78 and multiquadric function interpolation methods. By using TPF24, thick SD in some areas is reproduced, which is in good agreement with the thicker SD over MYI (Blanchard-Wrigglesworth et al. 2015). PF78 also recovers some characteristics of the spatial distribution, however, unreasonable values will be obtained at the edges due to its high degree. Meanwhile, RBF interpolation methods are considered inappropriate to construct the SD on MYI because of the larger errors and instability.

The TPF24 method proposed in this study may be beneficial to the study of interdecadal variation of Arctic snow cover, to the comprehension of the relationship between snow thickness and climate change, and to providing reference for model results. Moreover, once the data are complete in time, the space–time complete product of the Arctic SD will be obtained, which is of great benefit to the study of Arctic sea ice and climate change.

Acknowledgments

This work is supported by Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology through Grant 2017A05, the National Key Research and Development Plan of China (Grant 2016YFC1402705 and 2016YFC1402304), the National Natural Science Foundation of China (Grant 41606006). Both AMSR-E and OIB snow depth data are obtained from the National Snow and Ice Data Center (NSIDC, https://nsidc.org/data).

REFERENCES

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    • Crossref
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  • Brucker, L., and T. Markus, 2013: Arctic-scale assessment of satellite passive microwave-derived snow depth on sea ice using Operation IceBridge airborne data. J. Geophys. Res. Oceans, 118, 28922905, https://doi.org/10.1002/jgrc.20228.

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  • Castro-Morales, K., R. Ricker, and R. Gerdes, 2015: Snow on Arctic sea ice: Model representation and last decade changes. Cryosphere Discuss., 9, 56815718, https://doi.org/10.5194/tcd-9-5681-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cavalieri, D. J., T. Markus, and J. C. Comiso, 2014: AMSR-E/Aqua daily L3 12.5 km brightness temperature, sea ice concentration, and snow depth polar grids, version 3. NASA National Snow and Ice Data Center Distributed Active Archive Center, accessed 23 August 2018, https://doi.org/10.5067/AMSR-E/AE_SI12.003.

    • Crossref
    • Export Citation
  • Comiso, J. C., D. J. Cavalieri, and T. Markus, 2003: Sea ice concentration, ice temperature, and snow depth using AMSR-E data. IEEE Trans. Geosci. Remote Sens., 41, 243252, https://doi.org/10.1109/TGRS.2002.808317.

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