Numerical simulation for cutoff draft of sea ice ridge keels based on a novel optimal modeling with nonlinear-statistical constraints

Xingang Zhang; Bing Tan; Peng Lu; Bin Cheng; Ting Wang; Chunchun Gao; Zhijun Li; Xingang Zhang; Bing Tan; Peng Lu; Bin Cheng; Ting Wang; Chunchun Gao; Zhijun Li

doi:10.3934/era.2022086

Electronic Research Archive

2022, Volume 30, Issue 5: 1708-1722. doi: 10.3934/era.2022086

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Numerical simulation for cutoff draft of sea ice ridge keels based on a novel optimal modeling with nonlinear-statistical constraints

1.
School of Mathematics and Statistics, Nanyang Normal University, No. 1638, Wolong Road, Wolong District, Nanyang, MO 473061, China
2.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2, Linggong Road, Ganjingzi District, Dalian, MO 116024, China
3.
Finnish Meteorological Institute, Erik Palménin aukio 1, Helsinki, MO FI-00560, Finland

Received: 28 December 2021 Revised: 20 February 2022 Accepted: 15 March 2022 Published: 25 March 2022

Optimal identification and numerical models are powerful tools that have been widely used in geoscience research for many years. In this study, we proposed a novel optimal method to simulate a key parameter (cutoff draft) of the ridge keels due to dynamic deformation of sea ice at bottom. The sea ice ridges were measured in the Northwestern Weddell Sea of Antarctic, by a helicopter-borne electromagnetic-induction (EM) system. An optimal model with nonlinear-statistical constraints was developed, by taking deviations between the theoretical and measured keel draft (spacing) distributions as the performance criterion, and cutoff draft as the identified parameter. The properties of the optimal model and the existence of the optimal parameter were demonstrated. We identified that the optimal cutoff draft was 3.78 m via an optimal numerical algorithm, this value was then employed to separate the ridge keels from the ice bottom. Finally, the relationship between the mean keel draft and frequency (number of keels per km) was analyzed, and the result showed that this relationship was modeled well by a logarithmic function with a correlation coefficient of 0.7. The present optimal modeling method will provide a new theoretical reference for separating accurately the ridge keels from undeformed sea ice bottom, and analyzing the relationship between the morphologies of sea ice surface and bottom and the inversions of sea ice bottom draft and ice thickness by the surface height.
- optimal modeling,
- nonlinear-statistical constraint,
- numerical simulation,
- cutoff draft,
- ridge keel
Citation: Xingang Zhang, Bing Tan, Peng Lu, Bin Cheng, Ting Wang, Chunchun Gao, Zhijun Li. Numerical simulation for cutoff draft of sea ice ridge keels based on a novel optimal modeling with nonlinear-statistical constraints[J]. Electronic Research Archive, 2022, 30(5): 1708-1722. doi: 10.3934/era.2022086

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Abstract

Optimal identification and numerical models are powerful tools that have been widely used in geoscience research for many years. In this study, we proposed a novel optimal method to simulate a key parameter (cutoff draft) of the ridge keels due to dynamic deformation of sea ice at bottom. The sea ice ridges were measured in the Northwestern Weddell Sea of Antarctic, by a helicopter-borne electromagnetic-induction (EM) system. An optimal model with nonlinear-statistical constraints was developed, by taking deviations between the theoretical and measured keel draft (spacing) distributions as the performance criterion, and cutoff draft as the identified parameter. The properties of the optimal model and the existence of the optimal parameter were demonstrated. We identified that the optimal cutoff draft was 3.78 m via an optimal numerical algorithm, this value was then employed to separate the ridge keels from the ice bottom. Finally, the relationship between the mean keel draft and frequency (number of keels per km) was analyzed, and the result showed that this relationship was modeled well by a logarithmic function with a correlation coefficient of 0.7. The present optimal modeling method will provide a new theoretical reference for separating accurately the ridge keels from undeformed sea ice bottom, and analyzing the relationship between the morphologies of sea ice surface and bottom and the inversions of sea ice bottom draft and ice thickness by the surface height.

References

[1]	Q. Yang, S. N. Losa, M. Losch, X. Tian-Kunze, L. Nerger, J. Liu, et al., Assimilating SMOS sea ice thickness into a coupled ice-ocean model using a local SEIK filter, JGR: Oceans, 119 (2014), 6680–6692. https://doi.org/10.1002/2014JC009963 doi: 10.1002/2014JC009963
[2]	Q. Bai, R. Li, Z. Li, M. Leppäranta, L. Arvola, M. Li, Time-series analyses of water temperature and dissolved oxygen concentration in Lake Valkea-Kotinen (Finland) during ice season, Eco. Inf.s, 36 (2016), 181–189. https://doi.org/10.1016/j.ecoinf.2015.06.009 doi: 10.1016/j.ecoinf.2015.06.009
[3]	L. Zhou, J. Gao, D. Li, An engineering method for simulating dynamic interaction of moored ship with first-year ice ridge, Ocean Eng., 171 (2019), 417–428. https://doi.org/10.1016/j.oceaneng.2018.11.027 doi: 10.1016/j.oceaneng.2018.11.027
[4]	R. Lei, D. Gui, P. Heil, J. K. Hutchings, M. Ding, Comparisons of sea ice motion and deformation, and their responses to ice conditions and cyclonic activity in the western Arctic Ocean between two summers, Cold Reg. Sci. Technol., 170(2020), 102925. https://doi.org/10.1016/j.coldregions.2019.102925 doi: 10.1016/j.coldregions.2019.102925
[5]	T. Martin, Comparison of different ridge formation models of Arctic sea ice with observations from laser profiling, Ann. Glaciol., 44 (2006), 403–410. https://doi.org/10.3189/172756406781811132 doi: 10.3189/172756406781811132
[6]	K. V. Høyland, Consolidation of first-year sea ice ridges, JGR: Oceans, 107 (2002), 15-1–15-16. https://doi.org/10.1029/2000JC000526 doi: 10.1029/2000JC000526
[7]	R. Lei, M. Leppäranta, B. Cheng, P. Heil, Z. Li, Changes in ice-season characteristics of a European Arctic lake from 1964 to 2008, Clim. Change, 115 (2012), 725–739. https://doi.org/10.1007/s10584-012-0489-2 doi: 10.1007/s10584-012-0489-2
[8]	Y. Zu, P. Lu, M. Leppäranta, B. Cheng, Z. Li, On the form drag coefficient under ridged ice: Laboratory experiments and numerical simulations from ideal scaling to deep water, JGR: Ocean, 126 (2021), e2020JC016976. https://doi.org/10.1029/2020JC016976. doi: 10.1029/2020JC016976
[9]	M. Leppäranta, The drift of sea ice, 2^nd edition, Springer, Berlin, (2011), 347. https://doi.org/10.1007/978-3-642-04683-4_4
[10]	C. Haas, A. Friedrich, Z. Li, M. Nicolaus, A. Pfaffling, T. Toyota, Regional variability of sea ice properties and thickness in the northwestern Weddell Sea obtained by in-situ and satellite measurements, in Peter Lemke, The Expedition of the Research Vessel "Polarstern" to the Antarctic in 2006 (ANT-XXX Ⅲ/7), Reports on Polar and Marine Research, 586 (2009), 36–74.
[11]	C. Haas, J. Lobach, S. Hendricks, L. Rabenstein, A. Pfaffling, Helicopter-borne measurements of sea ice thickness, using a small and lightweight, digital EM system, J. Appl. Geophys., 67 (2009), 234–241. https://doi.org/10.1016/j.jappgeo.2008.05.005 doi: 10.1016/j.jappgeo.2008.05.005
[12]	R. Lei, X. Tian-Kunze, B. Li, P. Heil, Z. Tian, Characterization of summer Arctic sea ice morphology in the 135°-175°W sector using multi-scale methods, Cold Reg. Sci. Technol., 133 (2017), 108–120. https://doi.org/10.1016/j.coldregions.2016.10.009 doi: 10.1016/j.coldregions.2016.10.009
[13]	B. Tan, L. Wang, P. Lu, Z. Li, A novel strategy to analyze the form drag on pressure ridges and air-ice drag coefficient in northwestern Weddell Sea, Appl. Math. Model., 58 (2018), 158–165. https://doi.org/10.1016/j.apm.2017.09.046 doi: 10.1016/j.apm.2017.09.046
[14]	R. B. Guzenko, Y. U. Mironov, R. May, V. S. Porubaev, P. А. Tarasov. Morphometry and internal Structure of ice ridges in the Kara and Laptev Seas, Int. J. Offshore Polar, 30 (2020), 194–201. https://doi.org/10.17736/ijope.2020.jc784 doi: 10.17736/ijope.2020.jc784
[15]	O. Ekeberg, K. Høyland, E. Hansen, Ice ridge keel geometry and shape derived from one year of upward looking sonar data in the Fram Strai, Cold Reg. Sci. Technol., 109 (2015), 78–86. https://doi.org/10.1016/j.coldregions.2014.10.003 doi: 10.1016/j.coldregions.2014.10.003
[16]	T. M. O. Jeffries. Morphology of deformed first-year sea ice features in the southern ocean, Cold Reg. Sci. Technol., 36 (2003), 141–163. https://doi.org/10.1016/S0165-232X(03)00008-9 doi: 10.1016/S0165-232X(03)00008-9
[17]	B. Tan, Z. Li, P. Lu, C. Haas, M. Nicolaus, Morphology of sea ice pressure ridges in the Northwestern Weddell Sea in winter, JGR: Oceans, 117 (2012), C06024. https://doi.org/10.1029/2011JC007800 doi: 10.1029/2011JC007800
[18]	H. Eicken, W. Tucker, D. Perovich, Indirect measurements of the mass balance of summer Arctic sea ice with an electromagnetic induction technique, Ann. Glaciol., 33 (2001), 194–200. https://doi.org/10.3189/172756401781818356 doi: 10.3189/172756401781818356
[19]	A. Renner, S. Hendricks, S. Gerland, J. Beckers, C. Haas, T. Krumpen, Large-scale ice thickness distribution of first-year sea ice in spring and summer north of Svalbard, Ann. Glaciol., 54 (2013), 13–18. https://doi.org/10.3189/2013AoG62A146 doi: 10.3189/2013AoG62A146
[20]	B. A. Lange, J. F. Beckers, J. A. Casey, C. Haas, Airborne observations of summer thinning of multiyear sea ice originating from the lincoln sea, JGR: Oceans, 124 (2019). https://doi.org/10.1029/2018JC014383 doi: 10.1029/2018JC014383
[21]	A. P. Worby, P. W. Griffin, V. I. Lytle, R. A. Massom, On the use of electromagnetic induction sounding to determine winter and spring sea ice thickness in the Antarctic, Cold Reg. Sci. Technol., 29 (1999), 49–58. https://doi.org/10.1016/S0165-232X(99)00003-8 doi: 10.1016/S0165-232X(99)00003-8
[22]	C. Haas, Evalation of ship-based electromagnetic-inductive thickness measurements of summer sea-ice in the Bellingshausen and Amundsen seas, Antarctica, Cold Reg. Sci. Technol., 27 (1998), 1–16. https://doi.org/10.1016/S0165-232X(97)00019-0 doi: 10.1016/S0165-232X(97)00019-0
[23]	J. E. Reid, A. Pfaffling, A. P. Worby, J. R. Bishop, In situ measurements of the direct-current conductivity of antarctic sea ice: implications for airborne electromagnetic sounding of sea-ice thickness, Ann. Glaciol., 44 (2006), 217–223. https://doi.org/10.3189/172756406781811772 doi: 10.3189/172756406781811772
[24]	J. Guo, S. Bo, G. Tian, The application of electromagnetic-induction on the measurement of sea ice thickness in the Antarctic, Appl. Geophys., 4 (2007), 214–220. https://doi.org/10.1007/s11770-007-0024-9 doi: 10.1007/s11770-007-0024-9
[25]	C. Wang, J. Negrel, S. Gerland, D. V. Divine, P. Dodd, M. A. Granskog, Thermodynamics of fast ice off the northeast coast of greenland (79°n) over a full year (2012-2013), JGR: Oceans, 125 (2020). https://doi.org/10.1029/2019JC015823 doi: 10.1029/2019JC015823
[26]	W. D. Hibler, W. F. Weeks, S. J. Mock, Statistical aspects of sea ice ridge distributions, JGR, 77 (1972), 5954–5970. https://doi.org/10.1029/JC077i030p05954 doi: 10.1029/JC077i030p05954
[27]	P. Wadhams, A comparison of sonar and laser profiles along corresponding tracks in the Arctic Ocean, in Sea Ice Processes and Models, University of Washington Press, (1980), 283–299.
[28]	P. Wadhams, T. Davy, On the spacing and draft distributionfor pressure ridge keels, JGR, 91 (1986), 10697–10708. https://doi.org/10.1029/JC091iC09p10697 doi: 10.1029/JC091iC09p10697
[29]	H. B. Granberg, M. Leppäranta, Observations of sea ice ridging in the Weddell Sea, JGR: Oceans, 104 (1999), 25735–25745. https://doi.org/10.1029/1999jc900160 doi: 10.1029/1999jc900160
[30]	N. R. Davis, P. Wadhams, A statistical analysis of arctic pressure ridge morphology, JGR: Oceans, 100.C6 (1995), 10915. https://doi.org/10.1029/95JC00007 doi: 10.1029/95JC00007
[31]	K. M. Obert, T. G. Brown, Ice ridge keel characteristics and distribution in the northumberland strait, Cold Reg. Sci. Technol., 66 (2011), 53–64. https://doi.org/10.1016/j.coldregions.2011.01.004 doi: 10.1016/j.coldregions.2011.01.004

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