SCIENCE CHINA Earth Sciences • RESEARCH PAPER •
doi: 10.1007/s11430-017-9023-8
Spatial and temporal variability of sea ice deformation rates in the Arctic Ocean observed by RADARSAT-1 XIE Tao1,2,3*, William PERRIE 3, FANG He1, ZHAO Li1,2, YU WenJin1,2 & HE YiJun1,2 1
School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China; 2 Jiangsu Engineering Technology Research Center of Marine Environment Detection, Nanjing 210044, China; 3 Fisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth B2Y 4A2, Nova Scotia, Canada Received February 8, 2017; accepted February 23, 2017; published online March 22, 2017
Abstract Sea ice deformation parameters are important for elucidation of the properties and characteristics of ice-ocean models. Observations of sea ice motion over 11.5 year period (November 1996–April 2008) are used to calculate ice motion divergence and shear rates, and thus, to construct total deformation rate (TDR) estimates with respect to spatial and temporal variability in the Arctic Ocean. Strong sea ice deformation signal (SDS) rates are identified when TDR>0.01 day‒1, and very strong SDS events, when TDR>0.05 day‒1. These calculations are based on measurements made by the RADARSAT-1 Geophysical Processer System (RGPS). Statistical analysis of the SDS data suggest the following features: (1) Mean SDS and the SDS probability distributions are larger in “low latitudes” of the Arctic Ocean (less than 80°N) than in “high latitudes” (above 80°N), in both summer and winter; (2) very high SDS probabilities distributions and mean SDS values occur in coastal areas, e.g. the East Siberian Sea, Chukchi Sea and Beaufort Sea; (3) areas with relatively low TDR values, in the range from 0.01 day‒1 to 0.05 day‒1, cover much of the Arctic Ocean, in summer and winter; (4) of the entire TDR dataset, 45.89% belong to SDS, with summer the SDS percentage, 59.06%, and the winter SDS percentage, 40.50%. Statistically, the summer mean SDS, SDS percentage and very strong SDS are larger than corresponding values in the winter for each year, and show slight increasing tendencies during the years from 1997 to 2007. These results suggest important constraints for accurate simulations of very strong SDS in ice-ocean models. Keywords Sea ice deformation, RGPS, SAR, Arctic Ocean, Arctic amplification Citation:
Xie T, Perrie W, Fang H, Zhao L, Yu W J, He Y J. 2017. Spatial and temporal variability of sea ice deformation rates in the Arctic Ocean observed by RADARSAT-1. Science China Earth Sciences, 60, doi: 10.1007/s11430-017-9023-8
1. Introduction The advent of satellite observations of sea ice since 1979 reveals the significant variability and reduction in the Arctic ice coverage area since the 1980s (e.g., Cavalieri and Parkinson, 2008; Sha et al., 2015; Bian et al., 2016). Recognizing the important linkage and contribution of sea-ice changes to the global climate system, sea-ice modelling is an essential component of the climate and earth system models. Sea-ice observations, from both in situ and remote sensing, are im* Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2017
portant for evaluating sea-ice models and for guiding their improvement (Wang et al., 2005; Bai et al., 2011; Wang et al., 2012). Common aspects of sea-ice analysis and model evaluation include ice extent, thickness and drift. Recently, new research areas haven developed, including ice melt ponds, snow properties, pack ice, and fast ice, etc. (e.g., Proshutinsky et al., 2016). On the other hand, sea-ice deformation (related to shear, divergence/convergence and vorticity of ice motions) is another important aspect of ice characteristics that has been observed by satellite remote sensing (Kwok, 2001). The treatment of ice deformation by models influences how the kinetic energy balance of sea-ice is represented (Bouchat and Tremblay, 2014). Thus, deriving characteristics earth.scichina.com link.springer.com
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of sea-ice deformation is important for both model validation and improvement. Synthetic aperture radar is an useful tool to observe globe ocean features (Marsan et al., 2004; Kwok, 2001, 2006; Xie et al., 2015). Owing to their high spatial resolution, satellite images from the RADARSAT-1 Geophysical Processor System (RGPS) enable various statistics of variability of ice deformation to be derived (Marsan et al., 2004; Kwok, 2001, 2006; Weiss, 2008; Stem and Lindsay, 2009; Herman and Glowacki, 2012). Subsequently, the statistics derived from observations and models have been compared, and significant discrepancies have been identified (Kwok et al., 2008; Girard et al., 2009). Thus, statistics of ice deformation derived from satellite remote sensing, such as the RGPS product, provide a useful metric for the evaluation of ice models. For this purpose, a starting point might be for models to simulate the general spatial and temporal variations of the observed ice deformation. In this study, we derive characteristics of the spatial and seasonal variations of ice deformation in the Arctic, from analysis of the RGPS data during a period of 11.5 years. In particular, we separate the strong ice deformation signal (SDS) from the whole dataset. To our knowledge, such simple statistics have not been reported by previous studies.
the RGPS at JPL, another RGPS called the Alaska SAR Facility (ASF) in Fairbanks was also established. Input data are the Scan synthetic aperture radar (SAR) images in the Arctic Ocean, as collected by RADARSAT-1 C band (5.3 GHz) SAR, with a swath of 460 km with resolution of 100 m×100 m per pixel. RGPS products include Lagrangian motion trajectories, backscatter histograms, ice deformation, ice age and thickness distributions, winter multiyear ice concentrations, summer open water areas, Eulerian ice motion, and the dates of melt onset and freeze up (Kwok et al., 2000; Kwok and Cunningham, 2014). To retrieve the sea ice motion in meridional and zonal velocities and, multiple RADARSAT-1 SAR swaths covering the Arctic Ocean were used to produce time series products specific to a number of sea ice motions. Using the maximum cross correlation (MCC) method (Emery et al., 1986; Ninnis et al., 1986) in the same area, the displacement of small regions of patterns from one template sub-window in SAR image (initial sub-window) to that in later one can be calculated. Then the ice motion velocity can be derived as input data of the RGPS. Polar stereographic projection was used in RGPS, which is also used by gridded SSM/I products. The Cartesian grid origin for the polar stereographic projection is the North Pole, and 70°N is the reference latitude, with ordinate and abscissa defined by 135°E and 45°E meridians. RGPS products cover the entire Arctic every 3 days. We use the shear and divergence data products for the ice deformation dataset. The grid size of the products is 12.5 km×12.5 km. The data is from November 10, 1996 to April 29, 2008, available at (http://rkwok.jpl.nasa.gov/radarsat/3daygridded.html). Details regarding the RGPS ice deformation data are given in Table 1.
2. RGPS dataset RADARSAT-1 was launched at 14:22 UTC on November 4, 1995, from Vandenberg AFB in California, into a sun-synchronous orbit (dawn-dusk) above the Earth with an altitude of 798 km and inclination of 98.6°. Shortly thereafter, the RGPS was developed at the Jet Propulsion Laboratory (JPL) in Pasadena, California, USA. As a complementary system to
Table 1 Days of missing RGPS data, for the entire dataset (10 November, 1996–29 April, 2008) Year
January
February
April
May
June
1996 4–23 2–12
15–19
October
November
December
August 1 to November 4
2–15
1999
Jul 28 to November 2
3–10
2000
August 4 to November 3 May 3 to November 9
2001
10–17
2002
August 2 to November 10 August 3 to December 31
April 29 to May 21
2003 2004
September
Data starts on November 10, 1996
1997 1998
August
July
2–16 6–10
17–18
August 1 to December 9
12–28
27–29
7–11
4–20
August 2 to December 4
2006
2–24
August 3 to December 8
2007
3–19
August 1 to December 6
2005
2008 a) Underline the data means no data
August 16 to November 18
Data end on: April 29, 2008
5–6
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3. Method 3.1 Total sea ice deformation rate Following Kwok and Cunningham (2014), we focus on the sea ice motion products: Lagrangian ice motion, backscatter, ice age/thickness, ice deformation, area/open water fractions, Eulerian ice motion, melt onset/freeze up. The ice deformation products consist of ice motion divergence, vorticity and shear rates. Marsan et al. (2004) and Girard et al. (2009) define the total deformation rate (TDR), based on divergence and shear of the sea ice motion. Let ux, uy, vx, vy, represent the spatial gradients of ice motion, calculated using a line integral around the boundary of each measurement cell, respectively. Thus, the divergence and shear rates are: (1) d = u x + vy, s
=
(u x
2
vy) 2 + (u y + vx) ,
The “locations”, of corresponding values of TDR, and proportions of different area samples in all samples of the whole dataset, are shown in Table 2. The entire dataset is defined in five areas by different gradient values for TDR, i.e., L1, L2, L3, L4 and L5. From Figure 2 and Table 2, samples fall into area L1 whose TDR is larger than 0 and less than 0.001 day−1. Similarly, TDR of L2, L3, L4 and L5 fall into intervals of (0.001, 0.01) day−1, (0.01, 0.05) day−1, (0.05, 0.10) day−1 and (0.10, 58.10) day−1, respectively. Relative to 15948148 TDR samples, the proportion of samples in each area (L1, L2, L3, L4 and L5) are 8.48%, 45.77%, 36.01%, 8.99% and 0.75%, respectively. Recall the first question in introduction: What is SDS? We define SDS here. In order to obtain the TDR minimum, which can still be regarded as a strong sea ice deformation signal in the dataset, two criteria should be satisfied. One is that in or-
(2)
respectively, and the TDR is defined as: t
=
2 d
+
2 s
(3)
.
The TDR, t , contains both the intensity of the strain rate and information about the shear. The divergence rate and the shear rate are calculated following eqs. (1) and (2), and TDR is calculated based divergence and shear rates with eq. (3) above. 3.2 Strong sea ice deformation signal Based on the 3-day intervals, and gridded products of divergence and shear rates from November 10, 1996 to April 29, 2008, TDR data are calculated following eq. (3). There are 871 images comprising effectively 15948148 data samples for each type of product, and for the TDR data. The maximum TDR is 58.104 day−1 while the minimum is 0 day−1. Figure 1 shows TDR values, sorted by ascending sequences; in order to enhance the graphical presentation, the maximum TDR is cut off at 0.60. Therefore, the TDR can be sorted into different linear segments, implying that the entire dataset can be classified into a small number of sub-sets, by slopes of different linear line segments. The TDR gradients for ascending satellite passes, corresponding to data in Figure 1, are shown in Figure 2. It is notable that there are five distinct areas for gradient values, with boundaries identified by A, B, C and D, respectively.
Ascending Figure 1 sequences of TDR for 15948148 effective samples derived from gridded RGPS data from 871 SAR images based on 3 day intervals.
Gradients Figure 2 of TDR corresponding to Figure 1.
Table 2 “Locations”, for TDR, the proportion of different area samples in all samples of the whole dataset Boundaries name
First data
A
B
C
D
Last data
Sample “locations” in index number
1
1330648
8629671
14475592
15910352
15948148
TDR (day−1)
0
0.001
0.01
0.05
0.10
58.10
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der to avoid loss in generality, the resulting percentage of filtered data samples in the total dataset should not be too small. The second is that the SDS absolute value should not be too small else too many weak signals are included as “noise”. Following these 2 criteria, we find that the TDR for locations A and B are good candidates to define SDS in Table 2 (also in Figure 2). However, the TDR for B is better than that of A, because the overall mean TDR for the entire dataset is 0.02 day−1. Therefore, we select 0.01 day−1 as the critical SDS value. In other words, samples whose TDR values are larger than 0.01 day−1 are included in the SDS dataset to study the spatial distribution and temporal variability of SDS in the Arctic Ocean from November 1996 to April 2008 (this data is denoted the “whole dataset” hereafter). Thus, in this paper, SDS values are defined as samples whose TDR values are no less than 0.01 day−1.
4. Results and discussion A statistical analysis was conducted of SDS values for different temporal periods, for each grid, to show spatial distributions as well as the statistical relations among the data, including “small deformation rates signals”, whose values are less than the critical value 0.01 day−1. The occurrence probability of SDS for each grid was also calculated, based on time series analysis. We find that the mean TDR of the whole dataset in winter is 0.0181 day−1, and in summer, 0.0264 day−1. By comparison, the mean SDS is 0.0390 day−1, whereas in winter it is 0.0399 day−1, and in summer, 0.0415 day−1. Thus, the summer mean values of TDR and SDS are larger than those in winter. A statistical analysis of the TDR probability density functions (PDF) in different seasons and for the whole dataset is shown in Figure 3, showing the variation of PDF with TDR for the whole dataset, as well as the variations of PDF in summer and winter. Figure 3 suggests that the peak PDF values are 0.098 when TDR is 0.001 day−1 in winter and 0.046 when TDR is 0.004 day−1 in summer. The maximum PDF of the whole dataset is 0.083 at 0.001 day−1. The PDF distributions for the summer, winter, and the whole datasets are chi-square distributions. For the winter dataset and the whole dataset, the PDF values decrease with increasing TDR. For the summer dataset, the PDF values decrease with increasing TDR, when TDR is larger than 0.004 day−1. The vertical dashed line in Figure 3, occurring when TDR is 0.01 day−1 corresponds to PDF value 0.033 and separates all PDF curves into two parts. The first part includes TDR samples which are defined as SDS (with TDR value>0.01 day−1), on the right side of the vertical dashed line in Figure 3. Therefore, for this portion of the distributions, the PDF of SDS in summer is larger than that of winter. The other part occurs on the left side of the vertical dashed line, showing the opposite results, i.e., the PDF of TDR in winter is larger than that of in summer. Possible
Variation Figure 3 of probability density function distributions with TDR, for the whole dataset (black line), for summer (red line) and for winter (blue line).
reasons for these results are the differences in temperature, ice thickness, and other differences between summer and winter. For example, summer Arctic temperatures are higher than those of winter, melting some of the ice, and reducing ice thickness, which suggests that sea ice is more easily broken, leading to larger TDR values in summer than in winter. 4.1 Spatial and probability distributions of SDS To elucidate the spatial distribution characteristics of SDS, we calculate the spatial and probability distributions of SDS in both summer and winter. Summer and winter spatial distributions of mean SDS are shown in Figures 4a and c, and SDS probability distributions, in Figures 4b and d, respectively. Therefore, we find that SDS has four spatial distribution characteristics: (1) Mean SDS for the whole dataset in the “low latitudes” (less than 80°N) of the Arctic Ocean are larger than those of in high latitudes (larger than 80°N), in both summer and winter, as shown in Figures 4a and c. (2) The SDS probability distribution in the Arctic Ocean has similar characteristics to those of mean SDS, i.e., higher SDS probability distributions in “low latitudes” compared to those in “high latitudes”, in both summer and winter. (3) Much higher SDS probability distributions in summer, than in winter, as shown in Figures 4b and d. (4) Very high SDS probability distributions and mean SDS probability distributions in coastal areas (E. Siberian Sea, Chukchi Sea and Beaufort Sea). To study the spatial distribution characteristics of different signal intensities, the TDR dataset is divided into four sub-interval ranges, i.e., 0–0.01, 0.01–0.05, 0.05–0.10 and >0.10 day−1, as presented in Figure 5. The TDR time averages at each grid point is calculated, as shown in Figures 5a and b. The spatial distributions of the four interval ranges, from the TDR time averages for each grid, in summer and winter, are shown in Figures 5a and b, respectively. By comparison, Figures 5c and d show results for all TDR samples (not from TDR
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Spatial Figure 4 and probability distributions of SDS: (a) mean of SDS in summer; (b) probability distribution of SDS in summer; (c) mean of SDS in winter; (d) probability distribution of SDS in winter.
time averages at each grid, but from the whole dataset), as counted and classified in the four interval ranges. From Figures 5a and b, we find that the TDR time average for most of the Arctic Ocean is in the range of 0.01–0.05 day−1 (cyan in Figure 5) whether in summer or in winter, whereas red area (>0.10 day−1) covers the smallest area percentage of the four interval ranges. Red areas are embedded within the yellow areas, in both summer and winter. Red and yellow areas occur adjacent to the coastal areas, as also shown in Figure 4, implying that very strong signals occur in these areas. Figures 5c and d show the percentages of samples whose TDR values fall within the four interval respective ranges. Therefore, percentages of weak signals, with TDR values in the range of 0–0.01 day−1 (blue in Figure 5) are 41% in summer and 59% in winter. From Figures 5a and b, areas with weak signals (<0.10 day−1) occupy a very small percentage of the Arctic Ocean. These weak signals mainly occur near shallow coastal waters such as around the New Siberian Islands, East Siberian Sea Coast and the Queen Elizabeth Islands. There are two factors that might generate this spatial behaviour. One factor is that these are “low latitude” areas
of the Arctic Ocean, with no ice when water temperatures are above freezing temperature. The other factor is that ocean currents tend to be weak and thus ice motions are small in shallow nearshore coastal waters, compared to deeper waters, e.g. at the shelf edge. By comparison, the relatively large area (blue in Figure 5), where 0.01
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Spatial Figure 5 distributions of the four interval ranges from TDR time averages at each grid in summer (a) and in winter (b); the pie chart of percentages of samples in the whole dataset in summer (c) and in winter (d). Colours Blue, Cyan, Yellow and Red represent TDR samples whose values are in interval 0–0.01, 0.01–0.05, 0.05–0.10 and >0.10 day−1, respectively.
both summer and winter. (2) Very strong SDS samples (>0.05 day−1) occur near coastal areas. (3) Percentages of SDS samples in total dataset of summer are larger than those of winter, except for the weakest interval, 0–0.01 day−1. 4.2 Temporal variability of SDS To study the temporal variability of SDS, yearly and seasonal mean SDS values and percentages of SDS on different time scales (e.g. mean of whole dataset, yearly mean TDR, winter, summer) are calculated. From our statistical results from Figure 3, there are 45.89 % samples in the whole dataset that belong to the SDS set. The percentage of SDS is 59.06% in summer, which exceeds the percentage of SDS in winter (40.50%) by 18.46%. In another words, there are 18.46% samples of the whole dataset whose TDR values are larger than 0.01 in the summer than is the case in winter. This result implies that the ice velocity, divergence, shear and total deformation rates in summer are more than those in winter which is in accord with the results shown in Figure 4. Results for yearly and seasonal variations of mean SDS, percentage of SDS and very strong SDS (>0.05 day−1) are shown in Figures 6a–c, for the period from 1997 to 2007 (except 2000 owing to very few samples in that year), respec-
tively. The total original data is defined as yearly and seasonal mean SDS, or percentage of SDS, and very strong SDS for the selected 10-year interval used here. All data, including total original data, summer original data and winter original data are used to show the yearly and seasonal variations and trends of mean SDS, percentage of SDS and very strong SDS, respectively. Using these averages, Figure 6a shows that the maximum summer SDS is 0.0346 day−1 in 2007 and the maximum winter SDS is 0.0208 day−1 in 2005. The minimum values for SDS are 0.0213 day−1 in summer in 2005 and 0.0147 day−1 in winter in 1999. From Figure 6b, percentages of SDS in summer are between 50.22% in 2005 and 65.05% in 2002, whereas the maximum and minimum percentages of SDS in winter are 35.81% and 44.53% respectively. In Figure 6c, maximum percentages of very strong SDS in summer and winter are 18.89% and 9.17% while minimum percentages are 9.51 % and 5.71%, respectively. Figure 6 shows that values for summer mean SDS, percentage of SDS and very strong SDS are larger than the corresponding values of these variables for winter, for the 10-year period. This result indicates that the foregoing statistical results from Figure 3, for the whole dataset, can be extended in accord with yearly and seasonal statistical results. Moreover, fitted curves of year-to-year variations of yearly mean SDS, in Figure 6a, percentage of SDS, in Figure 6b, and very strong
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Temporal Figure 6 variability of yearly and seasonal (a) mean SDS; (b) percentage of SDS larger than 0.01 day−1; (c) percentage of SDS larger than 0.05 −1 day , where data in 2000 were not used owing to very few samples in that year.
SDS, in Figure 6c, have the same tendencies, i.e., they are increasing as time progresses, from 1997 to 2007; similar tendencies are evident for corresponding fitted curves, on both yearly and seasonal variation timescales. For example, fitted curves for (1) summer mean SDS and (2) percentage of very strong SDS, increase from 1997 to 2001, decrease from 2001 to 2004, and then increase after 2004. In winter, the trends for mean SDS and percentage of very strong SDS are almost opposite to the trends in summer, i.e., values of winter SDS and percentage of very strong SDS decrease from 1997 to 2001, decrease from 2001 to 2005, and then decrease after 2005. These results suggest that very strong SDS values are strongly affected by mean SDS characteristics. These results may be important to sea ice model development. When simulating sea ice motion, care must be taken in situ ations with very strong SDS, i.e., when TDR values are larger than 0.05 day−1.
5. Conclusions RGPS ice motion products were retrieved by RADARSAT-1 SAR images covering the time from November 10, 1996 to April 29, 2008. Based on products of divergence and shear of sea ice motion, the TDR products are calculated and used for statistical analysis of the spatial distribution and temporal variability of strong sea ice deformation estimates in the Arctic Ocean. Firstly, statistical results show that the spatial distributions of SDS have the following features: (1) Both mean SDS and the probability distribution of SDS for the whole dataset in “low latitude” areas (< 80°N) in the Arctic Ocean are larger than those in “high latitude” areas (>80°N), both in summer
and winter. (2) SDS probability distributions in summer are much higher than those in winter, in all intervals of SDS, except the lowest, 0–01 day−1. (3) Both very high SDS probability distributions and very high mean SDS distributions occur in coastal areas (E. Siberian Sea, Chukchi Sea and Beaufort Sea). (4) Samples whose TDR values fall into the interval range of 0.01–0.05 day−1 dominate the Arctic Ocean area in both summer and winter. (5) Very strong SDS samples (>0.05 day−1) occur near coastal areas. (6) Percentages of SDS samples in the total summer dataset are larger than those in the winter. Secondly, there are 45.89 % samples in the whole dataset that belong to SDS, whereas the percentage is 59.06% when only samples in summer are counted. This portion is 18.46% more than the percentage in winter (40.50%), that belongs to SDS. In another word, there are 18.46% more samples whose TDR values are larger than 0.01 in the summer than in winter. The results from yearly statistical analysis for the temporal variability of SDS and very strong SDS indicate that summer mean SDS, percentage of SDS and very strong SDS are larger than winter mean SDS, percentage of SDS and very strong SDS for each year. Mean SDS, percentage of SDS and percentage of very strong SDS tend to increase very slowly in magnitude, during the years from 1997 to 2007. This tendency may be connected with the observed climate change whereby Arctic sea ice cover is experiencing gradual overall decline during these years. Finally, comparing the temporal variability of SDS (Figure 6), with values in the intervals 0.01–0.05 day−1, and very strong SDS (>0.05 day−1), temporal variability is strongly affected by that of the mean SDS. This result may be important for validation and comparisons to ice-ocean model simulations. The behaviour for very strong SDS, i.e., observed TDR
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values larger than 0.05 day−1 is particularly notable, in this regard. Acknowledgements This
work was supported by the Global Change Research Program of China (Grant No. 2015CB953901), the National Key Research and Development Program of China (Grant No. 2016YFC1401007), the Canadian Program on Energy Research and Development (OERD), the Office of Naval Research (Code 322, “Arctic and Global Prediction”, Grant Number and Principal Investigator: William Perrie, Grant No. N00014-15-1-2611).
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