Stochastic Parameterization Using Compressed Sensing: Application to the Lorenz-96 Atmospheric Model
References
- Anosov, DV. 1969. Geodesic flows on closed Riemann manifold with negative curvature. Volume 90 of Trundy ordena Lenina Mathematicheskogo Instituta imeni V.A. Steklova. American Mathematical Society.
- Arnold, HM, Moroz, IM and Palmer, TN. 2013. Stochastic parametrizations and model uncertainty in the Lorenz ‘96 system Philosophic Transactions of the Royal Society A, 371: 1991. DOI: 10.1098/rsta.2011.0479
- Asch, M, Bocquet, M and Nodet, M. 2016. Data assimilation: methods, algorithms, and applications. Society for Industrial and Applied Mathematics. DOI: 10.1137/1.9781611974546
- Beeson, R and Sri Namachchivaya, N. 2020. Particle filtering for chaotic dynamical systems using future right-singular vectors. Nonlinear Dyn, 102: 679–696. DOI: 10.1007/s11071-020-05727-y
- Bengtsson, T, Bickle, P and Li, B. 2008. Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems. IMS Collections: Probability and Statistics Essays in Honor of David A. Freedman, 2: 316–334. DOI: 10.1214/193940307000000518
- Bishop, CM. 2006. Pattern Recognition and Machine Learning. Springer.
- Brunton, SL, Proctor, JL and Kutz, JN. 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15): 3932–3937. DOI: 10.1073/pnas.1517384113
- Candès, EJ, Romberg, JK and Tao, T. 2005. Decoding by linear programming. IEEE Transactions on information theory, 51(12): 4203–4215. DOI: 10.1109/TIT.2005.858979
- Candès, EJ and Tao, T. 2006. Near-optimal signal recovery from random projections: Universal encoding strategies. IEEE Transactions on Information Theory, 52(12): 5406–5425. DOI: 10.1109/TIT.2006.885507
- Candès, EJ and Wakin, MB. 2006. An introduction to compressed sampling. IEEE signal processing magazine, 25(2): 21–30. DOI: 10.1109/MSP.2007.914731
- Chen, SS, Donoho, DL and Saunders, MA. 2003. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1): 33–61. DOI: 10.1137/S1064827596304010
- Devaney, RL. 1989. An Introduction to Chaotic Dynamical Systems. Addison-Wesley.
- Donoho, DL. 2006. Compressed sensing. IEEE Transactions on information theory, 52(4): 1289–1306. DOI: 10.1109/TIT.2006.871582
- Eckmann, P and Ruelle, D. 1985. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys., 57(3): 617–656. DOI: 10.1103/RevModPhys.57.617
- Evensen, G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 99: 10143–10162. DOI: 10.1029/94JC00572
- Evensen, G. 2003. The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean dynamics, 53(4): 343–367. DOI: 10.1007/s10236-003-0036-9
- Gagne, DJ, Christensen, H, Subramanian, A and Monahan, AH. 2020. Machine learning for stochastic parameterization: Generative adversarial networks in the lorenz ‘96 model. Journal of Advances in Modeling Earth Systems, 12(3). DOI: 10.1029/2019MS001896
- Gordon, NJ, Salmond, DJ and Smith, AFM. 1993. Novel approach to nonlinear/non-gaussian Bayesian state estimation. IEEE Proceedings, F(2): 107–113. DOI: 10.1049/ip-f-2.1993.0015
- Kalman, RE. 1960. A new approach to linear filtering and prediction problems. DOI: 10.1115/1.3662552
- Kullback, S and Leibler, RA. 1951. On Information and Sufficiency. The Annals of Mathematical Statistics, 22: 79–86. DOI: 10.1214/aoms/1177729694
- Law, K, Stuart, A and Zygalakis, K. 2015.
Data assimilation . 214. Cham, Switzerland: Springer. DOI: 10.1007/978-3-319-20325-6 - Lorenz, EN. 1995. Predictability: A problem partly solved. ECMWF Seminar Proceedings on Predictability, ECMWF.
- Majda, A, Abramov, R and Grote, M. 2005. Information Theory and Stochastic for Multiscale Nonlinear Systems (CRM Monograph Series), 25. New York: American Mathematical Society. DOI: 10.1090/crmm/025
- Mukherjee, A, Aydogdu, Y and Ravichandran, T. 2021. Stochastic Parameterization using Compressed Sensing: Application to the Lorenz-96 Atmospheric Model. GitHub Repository.
https://github.com/amartyamukherjee/StochasticParameterization-ApplicationToLorenz96 . - Pawar, ASE and San, O. 2020. A Hands-On Introduction to Dynamical Data Assimilation with Python. Fluids, 5(4): 225. DOI: 10.3390/fluids5040225
- Pesin, YB. 2004. Lectures on partial hyperbolicity and stable ergodicity. EuropeanMathematical Society. DOI: 10.4171/003
- Pindyck, RS and Rubinfeld, DL. 1991. Forecasting with Time-Series Models. Econometric Models & Economic Forecasts 3rd ed., 516–535.
- Sinai, YG. 1977.
Introduction to ergodic theory . Volume 18 of Mathematical Notes. Princeton University Press. - Skokos, Ch. 2010. The Lyapunov Characteristic Exponents and Their Computation. Lect. Notes Phys., 790: 63–135. DOI: 10.1007/978-3-642-04458-8_2
- Snyder, C, Bengtsson, T, Bickel, P and Anderson, J. 2008. Obstacles to high-dimensional particle filtering. Monthly Weather Review, 136(12): 4629–4640. DOI: 10.1175/2008MWR2529.1
- Tibshirani, R. 1996. Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1): 267–288. DOI: 10.1111/j.2517-6161.1996.tb02080.x
- Wilks, DS. 2005. Effects of stochastic parameterizations in the Lorenz ‘96 system. Royal Meteorological Society, 131: 389–407. DOI: 10.1256/qj.04.03
- Wolf, AS, Swinney, JB and Vastano, HL. 1985. Determining Lyapunov exponents from a time series. Physica, 16D: 285–317. DOI: 10.1016/0167-2789(85)90011-9
- Yeong, HC, Beeson, R, Sri Namachchivaya, N and Perkowski, N. 2020. Particle Filters with Nudging in Multiscale Chaotic Systems: with Application to the Lorenz-96 Atmospheric Model. Journal of Nonlinear Science, 30: 1519–1552. DOI: 10.1007/s00332-020-09616-x
- Young, LS. 1998. Statistical properties of dynamical systems with some hyperbolicity. The Annals of Mathematics, 147(3): 585–650. DOI: 10.2307/120960
DOI: https://doi.org/10.16993/tellusa.42 | Journal eISSN: 3035-9554
Language: English
Page range: 300 - 317
Submitted on: Feb 21, 2022
Accepted on: Feb 21, 2022
Published on: Apr 26, 2022
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 2022 A. Mukherjee, Y. Aydogdu, T. Ravichandran, N. Sri Namachchivaya, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.