Data fusion and data assimilation of ice thickness observations using a regularisation framework
By: Nazanin Asadi, Andrea Scott and David A. Clausi
References
- Akaike
, H. 1980. Likelihood and the Bayes procedure. Trab. Estadística Invest. Oper. 31, 143– 166. doi: 10.1007/BF02888350. - Andersen
, M. S., Dahl, J.and Vandenberghe, L. 2013. Cvxopt: A python package for convex optimization, version 1.1. 6. Online at: cvxopt. org. - Auclair
, J.-P., Lemieux, J.-F., Tremblay, B.and Ritchie, H. 2017. Implementation of Newton’s method with an analytical Jacobian to solve the 1d sea ice momentum equation. J. Comput. Phys. 340, 69– 84. doi: 10.1016/j.jcp.2017.02.065. - Batrak
, Y.and Müller, M. 2018. Atmospheric response to kilometer-scale changes in sea ice concentration within the marginal ice zone. Geophys. Res. Lett. 45, 6702– 6709. - Budd
, C., Freitag, M. A.and Nichols, N. 2011. Regularization techniques for ill-posed inverse problems in data assimilation. Comput. Fluids, 168– 173. doi: 10.1016/j.compfluid.2010.10.002. - Calvetti
, D., Reichel, L., Sgallari, F.and Spaletta, G. 2000. A regularizing Lanczos iteration method for underdetermined linear systems. J. Comput. Appl. Math. 115, 101– 120. doi: 10.1016/S0377-0427(99)00298-8. - Carrieres
, T., Buehner, M., Lemieux, J.-F.and Pedersen, L. 2017. Sea Ice Analysis and Forecasting. Cambridge University Press, Cambridge, UK. - Caya
, A., Buehner, M.and Carrieres, T. 2010. Analysis and forecasting of sea ice conditions with three-dimensional variational data assimilation and a coupled ice-ocean model. J. Atmos. Oceanic Technol. 27, 353– 369. doi: 10.1175/2009JTECHO701.1. - Chambers
, J. M. 1983. Graphical Methods for Data Analysis. CRC Press, Boca Raton, FL. - Daley
, R. 1993. Atmospheric Data Analysis. Number 2. Cambridge University Press, Cambridge, UK. - Ebtehaj
, A. M.and Foufoula-Georgiou, E. 2013. On variational downscaling, fusion, and assimilation of hydrometeorological states: A unified framework via regularization. Water Resour. Res. 49, 5944– 5963. - Ebtehaj
, A. M., Foufoula-Georgiou, E., Lerman, G.and Bras, R. L. 2015. Compressive earth observatory: An insight from AIRS/AMSU retrievals. Geophys. Res. Lett. 42, 362– 369. - Ebtehaj
, A. M., Zupanski, M., Lerman, G.and Foufoula-Georgiou, E. 2014. Variational data assimilation via sparse regularisation. Tellus Dyn. Meteorol. Oceanogr. 66, 21789. doi: 10.3402/tellusa.v66.21789. - Flato
, G. M. 1998. The thickness variable in sea-ice models. Atmos. Ocean, 29– 36. doi: 10.1080/07055900.1998.9649604. - Foufoula-Georgiou
, E., Ebtehaj, A., Zhang, S.and Hou, A. 2014. Downscaling satellite precipitation with emphasis on extremes: A variational l1-norm regularization in the derivative domain. Surv. Geophys. 35, 765– 783. doi: 10.1007/s10712-013-9264-9. - Freedman
, D.and Diaconis, P. 1981. On the histogram as a density estimator: L 2 theory. Z Wahrscheinlichkeitstheorie Verw. Gebiete, 453– 476. doi: 10.1007/BF01025868. - Freitag
, M. A., Nichols, N. K.and Budd, C. J. 2010. L1-regularisation for ill-posed problems in variational data assimilation. Proc. Appl. Math. Mech. 10, 665– 668. doi: 10.1002/pamm.201010324. - Freitag
, M., Nichols, N.and Budd, C. 2013. Resolution of sharp fronts in the presence of model error in variational data assimilation. Q. J. Royal Meteorol. Soc. 139, 742– 757. doi: 10.1002/qj.2002. - Fu
, H., Ng, M. K., Nikolova, M.and Barlow, J. L. 2006. Efficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration. SIAM J. Sci. Comput. 27, 1881– 1902. doi: 10.1137/040615079. - Gaspari
, G.and Cohn, S. E. 1999. Construction of correlation functions in two and three dimensions. Q. J. Royal Meteorol. Soc. 125, 723– 757. doi: 10.1002/qj.49712555417. - Girard
, L., Bouillon, S., Weiss, J., Amitrano, D., Fichefet, T. and co-authors. 2011. A new modeling framework for sea-ice mechanics based on elasto-brittle rheology. Ann. Glaciol. 52, 123– 132. doi: 10.3189/172756411795931499. - Golub
, G. H.and Von Matt, U. 1997. Tikhonov regularization for large scale problems. Workshop on Scientific Computing, Springer, New York, pp. 3– 26. - Haas
, C., Hendricks, S., Eicken, H.and Herber, A. 2010. Synoptic airborne thickness surveys reveal state of Arctic sea ice cover. Geophys. Res. Lett. 37, L09501. - Haas
, C.and Howell, S. E. 2015. Ice thickness in the Northwest Passage. Geophys. Res. Lett. 42, 7673– 7680. - Haas
, C., Lobach, J., Hendricks, S., Rabenstein, L.and Pfaffling, A. 2009. Helicopter-borne measurements of sea ice thickness, using a small and lightweight, digital EM system. J. Appl. Geophys. 67, 234– 241. doi: 10.1016/j.jappgeo.2008.05.005. - Hansen
, P. C. 1992. Analysis of discrete ill-posed problems by means of the l-curve. SIAM Rev. 34, 561– 580. doi: 10.1137/1034115. - Hansen
, P. C., Nagy, J. G.and O’Leary, D. P. 2006. Deblurring Images: matrices, spectra, and Filtering, Vol. 3. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. - Hansen
, P. C.and O’Leary, D. P. 1993. The use of the l-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14, 1487– 1503. doi: 10.1137/0914086. - Hibler
, W. D. 1979. A dynamic thermodynamic sea ice model. J. Phys. Oceanogr. 9, 815– 846. doi: 10.1175/1520-0485(1979)009<;0815:ADTSIM>2.0.CO;2. - Johnson
, C., Nichols, N.and Hoskins, B. 2005. Very large inverse problems in atmosphere and ocean modelling. Int. J. Numer. Meth. Fluids, 759– 771. doi: 10.1002/fld.869. - König Beatty
, C.and Holland, D. M. 2010. Modeling landfast sea ice by adding tensile strength. J. Phys. Oceanogr. 40, 185– 198. doi: 10.1175/2009JPO4105.1. - Kubat
, I., Sayed, M.and Babaei, M. H. 2013. Analysis of besetting incidents in Frobisher Bay during 2012 shipping season. In: Proceedings of the International Conference on Port and Ocean Engineering Under Arctic Conditions, Sweden, POAC. - Kullback
, S.and Leibler, R. A. 1951. On information and sufficiency. Ann. Math. Statist. 22, 79– 86. doi: 10.1214/aoms/1177729694. - Lahoz
, W., Khattatov, B.and Menard, R. 2010. Data assimilation and information . In: Data Assimilation: Making Sense of Observations(eds. W., B., and R.). Springer, Berlin Heidelberg, pp. 3– 12. - Lawson
, C. L.and Hanson, R. J. 1995. Solving Least Squares Problems. SIAM, Philadelphia, PA. - Laxon
, S. W., Giles, K. A., Ridout, A. L., Wingham, D. J., Willatt, R. and co-authors. 2013. Cryosat-2 estimates of Arctic sea ice thickness and volume. Geophys. Res. Lett. 40, 732– 737. - Lemieux
, J.-F., Knoll, D. A., Losch, M.and Girard, C. 2014. A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics. J. Comput. Phys, 375– 392. doi: 10.1016/j.jcp.2014.01.010. - Lemeiux
, J., Tremblay, B., Thomas, S., Sedláček, J.and Mysak, L. 2008. Using the preconditioned Generalized Minimum RESidual (GRMES) method to solve the sea-ice momentum equation. J. Geophys. Res. 113, 1– 12. - Lipscomb
, W. H., Hunke, E. C., Maslowski, W.and Jakacki, J. 2007. Ridging, strength, and stability in high-resolution sea ice models. J. Geophys. Res. Oceans, C03S91. - Loptien
, U.and Axell, L. 2014. Ice and AIS: ship speed data and sea ice forecasts in the Baltic Sea. Cryosphere, 2409– 2418. doi: 10.5194/tc-8-2409-2014. - Lorenc
, A. C. 1986. Analysis methods for numerical weather prediction. Q. J. Royal Meteorol. Soc. 112, 1177– 1194. doi: 10.1002/qj.49711247414. - Meier
, W., Hovelsrund, G., van Oort, B., Key, J., Kovaks, K. and co-authors. 2014. Arctic sea ice in transformation: A review of recent and observed changes and impacts on biology and human activity. Rev. Geophys. 51, 185– 217. - Mohammadi-Aragh
, M., Goessling, H., Losch, M., Hutter, N.and Jung, T. 2018. Predictability of Arctic sea ice on weather time scales. Sci. Rep. 8, 6514. doi: 10.1038/s41598-018-24660-0. - NSIDC (National Snow and Ice Data Center).
. Submarine upward looking sonar ice draft profile data and statistics, version 1. doi: 10.7265/N54Q7RWK. - Pizzolato
, L., Howell, S. E. L., Dawson, J., Laliberté, F.and Copland, L. 2016. The influence of declining sea ice on shipping activity in the Canadian Arctic. Geophys. Res. Lett. 43, 12,146– 12,154. 2016GL071489. - Rainwater
, S., Bishop, C.and Campbell, W. 2015. The benefits of correlated observation errors for small scales. Q. J. Royal Meteorol. Soc. 141, 3439– 3445. doi: 10.1002/qj.2582. - Renner
, A. H., Gerland, S., Haas, C., Spreen, G., Beckers, J. F. and co-authors. 2014. Evidence of Arctic sea ice thinning from direct observations. Geophys. Res. Lett. 41, 5029– 5036. - Rothrock
, D.and Thorndike, A. 1980. Geometric properties of the underside of sea ice. J. Geophys. Res. 85, 3955– 3963. - Stonebridge
, G., Scott, K. A.and Buehner, M. 2018. Impacts on sea ice analyses from the assumption of uncorrelated ice thickness observation errors: Experiments using a 1D toy model. Tellus Dyn. Meteorol. Oceanogr. 70, 1445379. doi: 10.1080/16000870.2018.1445379. - Sturges
, H. A. 1926. The choice of a class interval. J. Am. Atatistic. Assoc. 21, 65– 66. doi: 10.1080/01621459.1926.10502161. - Thomas
, M., Geiger, C.and Kambhamettu, C. 2008. High resolution (400 m) motion characterization of sea ice using ERS-1 SAR imagery. Cold Reg. Sci. Technol. 52, 207– 223. doi: 10.1016/j.coldregions.2007.06.006. - Tikhonov
, A. N., Arsenin, V. I.and John, F. 1977. Solutions of Ill-Posed Problems, Vol. 14. Winston, Washington, DC. - Wahba
, G. 1990. Spline Models for Observational Data. SIAM, Philadelphia, PA. - Wahba
, G.and Wendelberger, J. 1980. Some new mathematical methods for variational objective analysis using splines and cross validation. Mon. Wea. Rev. 108, 1122– 1143. doi: 10.1175/1520-0493(1980)108<;1122:SNMMFV>2.0.CO;2.
DOI: https://doi.org/10.1080/16000870.2018.1564487 | Journal eISSN: 3035-9554
Language: English
Page range: 1564487 - 1564487
Published on: Jan 1, 2019
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
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© 2019 Nazanin Asadi, Andrea Scott, David A. Clausi, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.