Simulating sea ice dynamics at high resolution

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(1)Simulating sea ice dynamics at high resolution Martin Losch. with contributions from Nils Hutter (AWI), Dimitris Menemenlis (JPL, NASA), and Jean-François Lemieux (EC).

(2) Animation by T. Agnew. Arctic Sea ice from space.

(3) Sea Ice Deformation Multiple scales of Introduction. sea ice deformation. Linear Kinematic Features (LKFs):. ⇠ 170 km. ⇠ 170 km. ⇠ 2000 km. What induces the stress in the ice cover? Wind Tides, Swell & Ocean Circulation N. Hutter. -. Viscous Plastic Sea Ice Models at Very High Resolution. 6.

(4) A different kind of satellite. MITgcm at <1km grid spacing, Simulation: D. Menemenlis (JPL).

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(6) this talk • are these new high-res simulations with old VP-rheology useful? realistic? (Hutter et al. 2018) • explore properties of high-res VP dynamics: example land-fast ice.

(7) Motivation vation Why sea ice at high resolution?. Climate Modeling: ateIModeling: Sea ice acts as an insulator between Heat loss Climate Modeling: atmosphere Ice growth a ice•ocean acts asand anacts insulator Heat loss Sea ice as anbetween insulator Al anIand atmosphere Leads enable direct contact Ice growth between ocean and Albedo ch atmosphere adsIenable direct Leads cover contact 5% of area but change ofarea heat but loss •accommodate Leads cover 5% ads cover 5% of area50% butof Brine rejection Biological ac accommodate 50% ommodate 50% of heat lossof heat Brine rejection Biological activity loss. Economic interest: Economic interest: I Starting Economic interest: exploration of natural • exploration/exploitation of I Starting resources exploration of natural natural resources I Intensifying shipping in the Arc resources • intensified shipping in the ocean I Intensifying Arcticshipping in the Arctic oceanI Possibility of forecast? • LKF forecast? I Possibility of forecast?.

(8) Motivation vation Why sea ice at high resolution?. Climate Modeling: ateIModeling: Sea ice acts as an insulator between Heat loss Climate Modeling: atmosphere Ice growth a ice•ocean acts asand anacts insulator Heat loss Sea ice as anbetween insulator Al anIand atmosphere Leads enable direct contact Ice growth between ocean and Albedo ch atmosphere adsIenable direct Leads cover contact 5% of area but change ofarea heat but loss •accommodate Leads cover 5% ads cover 5% of area50% butof Brine rejection Biological ac accommodate 50% ommodate 50% of heat lossof heat Brine rejection Biological activity Christof Lüpkes, AWI loss. Economic interest: Economic interest: I Starting Economic interest: exploration of natural • exploration/exploitation of I Starting resources exploration of natural natural resources I Intensifying shipping in the Arc resources • intensified shipping in the ocean I Intensifying Arcticshipping in the Arctic oceanI Possibility of forecast? • LKF forecast? I Possibility of forecast?.

(9) Sea Ice Deformation. • RADARSAT sequence in the Beaufort Sea with focus on SHEBA camp (1997/1998).

(10) Sea Ice Deformation. Sea Ice Deformation Introduction Linear Kinematic Features (LKFs):. ⇠ 170 km. ⇠ 170 km. ⇠ 2000 km. What induces the stress in the ice cover? Wind Tides, Swell & Ocean Circulation N. Hutter. -. Viscous Plastic Sea Ice Models at Very High Resolution. 6.

(11) Sea ice as a quasi-continuous fluid with Viscous-Plastic (VP) rheology 2D momentum equations for sea ice (Hibler 1979): Du m = m f k ⇥ u + ⌧a ⌧o + m g rH + r · Dt <latexit sha1_base64="wgA80Ou5AZ4DBdkjVlEzHb//T6o=">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</latexit>. requires relation between internal stress tensor and velocity vector Rheology (✏) <latexit sha1_base64="G3s/E3PgWD6pBSw0ULd7kIcRC4Y=">AAACEnicbZDNSsNAFIUn9a/Wv6g73QwWoW5KIoK6K7pxWcHYQhPKZDpph85MwsxEKCHgS/gKbnXvStz6Am59EqdpFtp6YODj3Hu5d06YMKq043xZlaXlldW16nptY3Nre8fe3btXcSox8XDMYtkNkSKMCuJpqhnpJpIgHjLSCcfX03rngUhFY3GnJwkJOBoKGlGMtLH69oEf8sxXdMhR3iiYJIqyWOQnfbvuNJ1CcBHcEuqgVLtvf/uDGKecCI0ZUqrnOokOMiQ1xYzkNT9VJEF4jIakZ1AgTlSQFX/I4bFxBjCKpXlCw8L9PZEhrtSEh6aTIz1S87Wp+W8t5HObdXQRZFQkqSYCzxZHKYM6htOA4IBKgjWbGEBYUnM7xCMkEdYmxpoJxZ2PYBG80+Zl07k9q7euynSq4BAcgQZwwTlogRvQBh7A4BE8gxfwaj1Zb9a79TFrrVjlzD74I+vzB7EznoI=</latexit>. Material properties of sea ice: • weak in tension (divergence) • strongest in compression (convergence) • strong in shear Collection of plastic ice floes leads to on average viscous behavior (Hibler, 1977).

(12) principle stress plane e=2, kt=0. 0.4. e=2, kt=0.2 0.2. e=1.5, kt=0. tension. 0. σ. p2. maximum −0.2. /P. shear. p. −0.4 −0.6 −0.8 −1. maximum compression −1.2 −1.2. −1. −0.8. −0.6. −0.4. −0.2. σp1 / Pp. 0. 0.2. 0.4.

(13) Motivation Motivation Increasing the resolution. (a) resolution: (a) resolution: 27 km27 km. (b) resolution: (b) resolution: 4.5 km4.5 km. Figure: Figure: Sea ice Seathickness ice thickness (color) (color) and sea and ice seaconcentration ice concentration (contour (contour lines)lines) from from sea ice sea ice model model (Losch (Losch etthickness al.,et2014) al., 2014) Sea ice (color) and sea ice concentration (contour I. lines) from a sea ice model (Losch et al., 2014). I Increasing Increasing resolution resolution resolves resolves those those linear linear features features.

(14) trajectories for this comparison, which are initialized every 7 days on the EGPS grid and last 14 days.. Broadly speaking, model results and observations agree on the order of magnitude of the deformation, but the observed deformation rates are slightly higher (Figure 5). The spatial scaling exponent of the EGPS data ranges from 0.09 (s51 day) to 0.06 (s514 days). For the same temporal scales, the scaling exponents of the model data are around 0.06 and show no clear dependence on the temporal scale. Although the model. 1km-model snapshots on Sep21, 2011. ✓. ◆. Figure 4. (a) Sea ice concentration, (b) divergence rate, and (c) shear rate of the LLC4320 run for 21 September 2011, 2 pm. The deformation rates concentrate along the leads seen in the sea ice concentration and mark Linear Kinematic Features (LKF).. 1 @ui @uj strain rate tensor ✏˙ij = + HUTTER ET AL. components SEA ICE DEFORMATION MODELS 2 IN VP@x @xi j divergence rate shear rate <latexit sha1_base64="aNkqi/bpfa6EO4UmNpLgQsK1rKg=">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</latexit>. = ✏˙11 + ✏˙22 q = (✏˙11 ✏˙22 )2 + 4✏˙212. 678.

(15) Spacial Scaling ofIceSea Ice Deformation Spacial Scaling of Sea Deformation (a) 170 km (b) 85 km (c) 42.5 km (d) 21.25 km Results. Figure: LANDSAT 8 false color image showing sea ice in the Beaufort Sea in spring (U.S. Geological Survey). (a) 170 km. N. Hutter -. (b) 85 km. I. Multi fractal characteristics. I. Spatial scaling laws (Marsan et al., 2004):. he˙L i ⇠ L. H. with H = 0.20 ± 0.01. (3). (d) 21.25 km 16. Viscous Plastic Sea Ice Models at Very High Resolution. (c) 42.5 km.

(16) comparison to EGPS rnal in of Geophysical Research: Oceans. data10.1002/2017JC013119. Hutter et al. (2018). Figure 1. Model domain, region of EGPS data, and the coastline filter. The analysis regions are shaded (blue for model-only analysis and green for model-observation comparison).. for Medium-Range Weather Fo converted to surface fluxes usin ice model (Losch et al., 2010). forcing for the 16 most signific 1! Ponte et al. (2015). A 24 LLC sim simulation is initialized on 10 S ! 1 from the 48 LLC simulation, her cap. The LLC4320 simulation is hourly intervals. At the time of t 2012.. Published model-data comparis (Rocha et al., 2016a), which com ler Current Profiler data, and a upper ocean stratification and study is the first to examine the a little below 1 km. Bathymetry sion 2.23 (Jakobsson et al., 2008 2010). Ocean and sea ice param ing modifications: (1) the salt-p transport term in the K-Profile P stepping uses Crank-Nicolson i ary conditions; (5) lead closing 27.5 kN m21 instead of 22.6 kN in any way to fit observations; order to make the LLC4320 inte HUTTER ET AL.. Figure 5. Spatial-temporal scaling properties of model output compared to EGPS data. The comparison is confined to the area of the EGPS composite for each day and to the period of 1 January 2012 to 31 March 2012.. • heterogeneity OK for large (10day) time scales reproduces the spatial scaling characteristics observed from EGPS for large temporal scales, there is no cou• low intermittency (Hutter et al., 2018). SEA ICE DEFOR.

(17) ferent ice conditions and the seasonal cycle of sea ice deformation. In addition, the model-only analysis includes scales as small as L 5 1 km and s 5 1 h. A spatiotemporal scaling analysis tests the effect of reproduced leads on the scaling characteristics of sea ice deformation. We apply the LSE method described in section 3.1 to all data between 1 December 2011 and 30 April 2012 in the entire model domain. To define the LSE boxes, we integrate trajectories of virtual. Pan-Arctic model data. Figure 7. Spatiotemporal scaling of total deformation of the model output in the period between December and April 2012. Total deformation for different spatial and temporal scales is indicated by dots. Power-law fits to this data are presented as lines in the left plots (a) and (c). The right plots (b) and (d) show the powerlaw exponents of the fit with respect to the spatial scale and the temporal scale, respectively. The error bounds of the scaling exponents are determined by the minimum and maximum slope between successive points of the power-law fit.. • coupling of spatial and temporal scaling (Hutter et al., 2018).

(18) Summary so far • Sea ice deformation localizes along lines in high-resolution viscous-plastic sea ice models • The model reproduces spatial scaling properties as observed in satellite data (heterogeneity OK) • The model underestimates temporal scaling compared to satellite data (intermittency of deformation events too low).

(19) Land-fast ice at high resolution Martin Losch (AWI) Jean-François Lemieux (EC). • What is land-fast ice? Why is it important? • land-fast ice and models, problems and solutions • parameterizations and resolution.

(20) What is fast ice? Why is it important?. Sketches by Lusilier - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22893504 and https://commons.wikimedia.org/w/index.php?curid=29853839.

(21) Animation by T. Agnew. Arctic Sea ice from space.

(22) Fast ice example Greenland's east coast near Zachariae and 79N Glaciers (Source: Arctic Sea ice blog).

(23) False Polynyas ASAR satellite image (30 April 2008), south-eastern Laptev Sea (from Rozman et al. 2011).

(24) It matters: example fluxes. Photo: Christof Lüpkes, AWI.

(25) False Polynyas matter ITKIN ET AL.: LANDFAST ICE AND ARCTIC HALOCLINE. Arctic Itkin Ocean stratification winter processes maintaining et vertical al. (2015): position ofand false polynya in Laptev Sea has th an effect on the water mass distribution in the central Arctic ..

(26) mechanisms • grounding (in shallow shelf seas) • static arching (pinned between coastlines and islands or shallows?). • how much of this is in standard viscoplastic models (Hibler 1979)? • (usually models don’t get it right).

(27) Observations and model. NIC observations. http://nsidc.org/data/docs/noaa/g02172_nic_charts_climo_grid/.

(28) Observations and model numerical model (MITgcm) 36km grid spacing. Frequency of occurrence of land-fast ice for January-May for the years 2005, 2006 and 2007, reproducing Lemieux et al. (2016).. NIC observations. http://nsidc.org/data/docs/noaa/g02172_nic_charts_climo_grid/.

(29) Sea ice as a quasi-continuous fluid with Visous-Plastic (VP) rheology 2D momentum equations for sea ice (Hibler 1979): Du m = m f k ⇥ u + ⌧a ⌧o + m g rH + r · Dt <latexit sha1_base64="wgA80Ou5AZ4DBdkjVlEzHb//T6o=">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</latexit>. requires relation between internal stress tensor and velocity vector Rheology (✏) <latexit sha1_base64="G3s/E3PgWD6pBSw0ULd7kIcRC4Y=">AAACEnicbZDNSsNAFIUn9a/Wv6g73QwWoW5KIoK6K7pxWcHYQhPKZDpph85MwsxEKCHgS/gKbnXvStz6Am59EqdpFtp6YODj3Hu5d06YMKq043xZlaXlldW16nptY3Nre8fe3btXcSox8XDMYtkNkSKMCuJpqhnpJpIgHjLSCcfX03rngUhFY3GnJwkJOBoKGlGMtLH69oEf8sxXdMhR3iiYJIqyWOQnfbvuNJ1CcBHcEuqgVLtvf/uDGKecCI0ZUqrnOokOMiQ1xYzkNT9VJEF4jIakZ1AgTlSQFX/I4bFxBjCKpXlCw8L9PZEhrtSEh6aTIz1S87Wp+W8t5HObdXQRZFQkqSYCzxZHKYM6htOA4IBKgjWbGEBYUnM7xCMkEdYmxpoJxZ2PYBG80+Zl07k9q7euynSq4BAcgQZwwTlogRvQBh7A4BE8gxfwaj1Zb9a79TFrrVjlzD74I+vzB7EznoI=</latexit>. Material properties of sea ice: • weak in tension (divergence) • strongest in compression (convergence) • strong in shear Collection of plastic ice floes leads to on average viscous behavior (Hibler, 1977).

(30) previous work 0.4. e=2, kt=0 e=2, kt=0.2. 0.2. e=1.5, kt=0. 0. σ. p2. −0.2. /P. p. −0.4 −0.6 −0.8 −1 −1.2 −1.2. −1. −0.8. −0.6. −0.4. −0.2. σp1 / Pp. 0. 0.2. 0.4.

(31) previous work 0.4. e=2, kt=0 e=2, kt=0.2. 0.2. e=1.5, kt=0. 0. σ. p2. −0.2. /P. e=a/b. p. −0.4 −0.6. a. b. −0.8 −1 −1.2 −1.2. −1. −0.8. −0.6. −0.4. −0.2. σp1 / Pp. 0. 0.2. 0.4.

(32) previous work • tensile strength (Dumont et al. 2007, Itkin et al 2015, Olason 2016) σ - uniaxial (param e) - isotropic (param kt). p2. 0.4. e=2, kt=0 e=2, kt=0.2. 0.2. e=1.5, kt=0. 0 −0.2. /P. p. −0.4 −0.6 −0.8 −1 −1.2 −1.2. −1. −0.8. −0.6. −0.4. −0.2. σp1 / Pp. 0. 0.2. 0.4.

(33) s term due to grounded ridges, σ is the internal ice stress tensor. previous work. = σxx , σ22 = σyy and σ12 = σxy , g is the gravity and Ho the sea surfa. • tensile strength (Dumont et al. 2007, Itkin et al 2015, Olason 2016) σ /P the advection of momentum is neglected. In our implementation, th - uniaxial (param e) e formulated as in Roy et al. [2015]. - isotropic (param kt) Following Lemieux et al. [2015] 0.4. e=2, kt=0. e=2, kt=0.2. 0.2. e=1.5, kt=0. 0. −0.2. p2. p. −0.4 −0.6 −0.8 −1. iven by. −1.2 −1.2. −1. −0.8. −0.6. −0.4. −0.2. σp1 / Pp. • bottom drag (Lemieux et al 2015) τb =. !. 0 " if h ≤ hc , # −u −αb (1−A) k2 |u|+u (h − h ) exp if h > hc , c 0. 0. 0.2. 0.4.

(34) Observations and model. NIC observations. http://nsidc.org/data/docs/noaa/g02172_nic_charts_climo_grid/.

(35) Observations and model numerical model (MITgcm) 36km grid spacing. Frequency of occurrence of land-fast ice for January-May for the years 2005, 2006 and 2007, simulation without and with explicit parameterization of grounding (Lemieux et al., 2015), reproducing Lemieux et al. (2016). NIC observations. http://nsidc.org/data/docs/noaa/g02172_nic_charts_climo_grid/.

(36) Observations and model numerical model (MITgcm) 36km grid spacing. Frequency of occurrence of land-fast ice for January-May for the years 2005, 2006 and 2007, simulation without and with explicit parameterization of grounding (Lemieux et al., 2015), reproducing Lemieux et al. (2016). NIC observations. http://nsidc.org/data/docs/noaa/g02172_nic_charts_climo_grid/.

(37) 4.5km VP simulations.

(38) 4.5km VP simulations.

(39) Resolution (w/out parameterization) 4.5 km. 18 km. 9 km. 36 km. NIC observations.

(40) Resolution (w/out parameterization) 4.5 km. 18 km. 9 km. 36 km. NIC observations.

(41) Islands in the Kara Sea.

(42) speculative explanation. thickness. shear stress.

(43) Conclusions: Fast ice • Parameterizations can improve land fast ice • resolution of VP model also improves the land fast ice representation probably because of increased “effective shear strength”, and resolved topography (islands) • results depend on regions implying different mechanisms in different regions: - topographic anchors ‣ bottom (grounding) ‣ islands (arching) - static arching: ‣ shear strength of sea ice ‣ general strength of sea ice (changes with resolution?).

(44) Conclusions challenges high resolution sea ice modeling: • continuity assumption • VP-rheology assumptions (new rheologies) • more nonlinearity: solvers don’t converge but: • simulations more realistic in comparison to observations • for the right/wrong reasons? • ….

(45)