参考文献
Amari, S., 1967: A theory of adaptive pattern classifiers. IEEE
Transactions on Electronic Computers, EC-16,
299–307, https://doi.org/10.1109/PGEC.1967.264666.
Amari, S., 1998: Natural gradient works efficiently in learning.
Neural Comput., 10, 251–276, https://doi.org/10.1162/089976698300017746.
Ancell, B., and G. J. Hakim, 2007: Comparing adjoint- and
ensemble-sesitivity analysis with applications to observation targeting.
Mon. Wea. Rev., 135, 4117–4134, https://doi.org/10.1175/2007MWR1904.1.
Anderson, J. L., 2001: An ensemble adjustment Kalman filter
for data assimilation. Mon. Wea. Rev., 129,
2884–2903, https://doi.org/10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.
——, 2003: A local least squares framework for ensemble filtering.
Mon. Wea. Rev., 131, 634–642, https://doi.org/10.1175/1520-0493(2003)131<0634:ALLSFF>2.0.CO;2.
Arakawa, A., 1966: Computational design for long-term numerical
integration of the equations of fluid motion: Two-dimensional
incompressible flow Part I. J. Comput.
Phys., 1, 119–143.
Bishop, C. H., and Z. Toth, 1999: Ensemble transformation and adaptive
observations. J. Atmos. Sci., 56, 1748–1765,
https://doi.org/10.1175/1520-0469(1999)056<1748:ETAAO>2.0.CO;2.
——, J. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the
ensemble transform Kalman filter. Part
I: Theoretical aspects. Mon. Wea. Rev.,
129, 420–436, https://doi.org/10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2.
Bowler, N. E., J. Flowerdew, and S. R. Pring, 2013: Tests of different
flavours of EnKF on a simple model. Quart. J. Roy.
Meteor. Soc., 139, 1505–1519, https://doi.org/10.1002/qj.2055.
Broyden, C. G., 1970: The convergence of a class of double-rank
minimization algorithms 1. General considerations. IMA
J. Appl. Math., 6, 76–90, https://doi.org/10.1093/imamat/6.1.76.
Burgers, G., P. J. van Leeuwen, and G. Evensen, 1998: Analysis scheme in
the ensemble Kalman filter. Mon. Wea. Rev.,
126, 1719–1724, https://doi.org/10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2.
Butcher, J. C., and G. Wanner, 1996: Runge-Kutta methods:
Some historical notes. Appl. Numer. Math., 22,
113–151, https://doi.org/10.1016/S0168-9274(96)00048-7.
Chase, R. J., D. R. Harrison, A. Burke, G. M. Lackmann, and A. McGovern,
2022: A machine learning tutorial for operational meteorology.
Part I: Traditional machine learning. Wea.
Forecast., 37, 1509–1529, https://doi.org/10.1175/WAF-D-22-0070.1.
——, ——, G. M. Lackmann, and A. McGovern, 2023: A machine learning
tutorial for operational meteorology. Part II:
Neural networks and deep learning. Wea. Forecast.,
38, 1271–1293, https://doi.org/10.1175/WAF-D-22-0187.1.
Duc, L., T. Kawabata, and D. Hotta, 2023: On the foundation and
different interpretations of ensemble sensitivity. Mon. Wea.
Rev., 151, 1689–1697, https://doi.org/10.1175/MWR-D-22-0273.1.
Eckert, P., D. Cattani, and J. Ambühl, 1996: Classification of ensemble
forecasts by means of an artificial neural network. Meteor.
Appl., 3, 169–178, https://doi.org/https://doi.org/10.1002/met.5060030207.
Enomoto, T., W. Ohfuchi, H. Nakamura, and M. A. Shapiro, 2007: Remote
effects of tropical storm Cristobal upon a cut-off cyclone
over Europe in August 2002. Meteor. Atmos.
Phys., 96, 29–42, https://doi.org/10.1007/s00703-006-0219-2.
——, S. Yamane, and W. Ohfuchi, 2015: Simple sensitivity analysis using
ensemble forecasts. J. Meteor. Soc. Japan, 93,
199–213, https://doi.org/10.2151/jmsj.2015-011.
Evensen, G., 1994: Sequential data assimilation with a nonlinear
quasi-geostrophic model using Monte Carlo
methods to forecast error statistics. J. Geophys. Res.: Oceans,
99, 10143–10162, https://doi.org/10.1029/94JC00572.
Fletcher, R., 1970: A new approach to variable metric algorithms.
The Computer Journal, 13, 317–322, https://doi.org/10.1093/comjnl/13.3.317.
Fukushima, K., 1980: Neocognitron: A self-organizing neural
network model for a mechanism of pattern recognition unaffected by shift
in position. Biological Cybernetics, 36,
193–202, https://doi.org/10.1007/BF00344251.
Golub, G. H., and C. F. Van Loan, 2013: Matrix computations - 4th
edition. fourth. Johns Hopkins University Press,.
Griewank, P. J., M. Weissmann, T. Necker, T. Nomokonova, and U. Löhnert,
2023: Ensemble-based estimates of the impact of potential observations.
Quart. J. Roy. Meteor. Soc., 149, 1546–1571,
https://doi.org/10.1002/qj.4464.
Hacker, J. P., and L. Lei, 2015: Multivariate ensemble sensitivity with
localization. Mon. Wea. Rev., 143, 2013–2027,
https://doi.org/10.1175/MWR-D-14-00309.1.
Hamill, T. M., C. Snyder, and J. S. Whitaker, 2003: Ensemble forecasts
and the properties of flow-dependent analysis-error covariance singular
vectors. Mon. Wea. Rev., 131, 1741–1758, https://doi.org/10.1175//2559.1.
Houtekamer, P. L., and H. L. Mitchell, 1998: Data assimilation using an
ensemble Kalman filter technique. Mon. Wea. Rev.,
126, 796–811, https://doi.org/10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2.
Huang, X.-Y., and X. Yang, 1996: Variational data assimilation with
the Lorenz model. HIRLAM,.
Kalnay, E., 2003: Atmospheric modeling, data assimilation and
predictability. Cambridge University Press,.
Kassinos, S., and A. Alexiadis, 2024: Beyond language:
Applying MLX transformers to engineering
physics. https://doi.org/10.48550/arXiv.2410.04167.
Kohonen, T., 1982: Self-organized formation of topologically correct
feature maps. Biol. Cybern., 43, 59–69, https://doi.org/10.1007/BF00337288.
Langland, R. H., M. A. Shapiro, and R. Gelaro, 2000: Initial condition
sensitivity and error growth in forecasts of the 25 January
2000 East Coast snowstorm. Mon. Wea.
Rev., 130, 957–974, https://doi.org/10.1175/1520-0493(2002)130<0957:ICSAEG>2.0.CO;2.
Liu, D. C., and J. Nocedal, 1989: On the limited memory
BFGS method for large scale optimization. Math.
Programming, 45, 503–528, https://doi.org/10.1007/BF01589116.
Lorenc, A. C., 1986: Analysis methods for numerical weather prediction.
Quart. J. Roy. Meteor. Soc., 112, 1177–1194.
Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos.
Sci., 20, 130–141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
——, and K. A. Emanuel, 1998: Optimal sites for supplementary weather
observations: Simulation with a small model. J. Atmos. Sci.,
55, 399–414, https://doi.org/10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2.
Matsueda, M., M. Kyouda, Z. Toth, H. L. Tanaka, and T. Tsuyuki, 2011:
Predictability of an atmospheric blocking event that occurred on 15
December 2005. Mon. Wea. Rev.,
139, 2455–2470, https://doi.org/10.1175/2010MWR3551.1.
Milne, A. A., 1926: Winnie-the-pooh.
Project Gutenberg,.
Nakashita, S., and T. Enomoto, 2021: Factors for an abrupt increase in
track forecast error of Typhoon Hagibis
(2019). SOLA, 17A, 33–37, https://doi.org/10.2151/sola.17A-006.
Nishii, K., and H. Nakamura, 2010: Three-dimensional evolution of
ensemble forecast spread during the onset of a stratospheric sudden
warming event in January 2006. Quart. J. Roy. Meteor.
Soc., 136, 894–905, https://doi.org/10.1002/qj.607.
Nocedal, J., 1980: Updating quasi-Newton matrices with
limited storage. Math. Comput., 35, 773–782,
https://doi.org/10.2307/2006193.
——, and Stephen J. Wright, 2006: Numerical
Optimization. 2nd ed. Springer,.
Rabier, F., E. Klinker, P. Courtier, and A. Hollingsworth, 1996:
Sensitivity of forecast errors to initial conditions. Quart. J. Roy.
Meteor, Soc., 112, 121–150, https://doi.org/10.1002/qj.49712252906.
Rodgers, C. D., 2000: Inverse methods for atmospheric sounding:
Theory and practice. World Scientific,.
Rumelhart, D. E., G. E. Hinton, and R. J. Williams, 1986: Learning
representations by back-propagating errors. Nature,
323, 533–536, https://doi.org/10.1038/323533a0.
Sakov, P., and P. R. Oke, 2008: A deterministic formulation of the
ensemble Kalman filter: An alternative to ensemble square
root filters. Tellus A, 60, 361–371, https://doi.org/10.1111/j.1600-0870.2007.00299.x.
Sasaki, Y., 1958: An objective analysis based on the variational method.
J. Meteor. Soc. Japan, 36, 77–88, https://doi.org/10.2151/jmsj1923.36.3_77.
Schaback, R., and H. Wendland, 2006: Kernel techniques:
From machine learning to meshless methods. Acta
Numerica, 15, 543–639, https://doi.org/10.1017/S0962492906270016.
Shanno, D. F., 1970: Conditioning of quasi-Newton methods
for function minimization. Math. Comput., 24,
647–656, https://doi.org/10.1090/S0025-5718-1970-0274029-X.
Snyder, C., 1996: Summary of an informal workshop on adaptive
observations and FASTEX. Bull. Amer. Meteor. Soc.,
77, 953–961, https://doi.org/10.1175/1520-0477-77.5.953.
Takemura, K., T. Enomoto, and H. Mukougawa, 2021: Predictability of
Enhanced Monsoon Trough
Related to the Meandered Asian
Jet and Consequent Rossby
Wave Breaking in Late
August 2016. J. Meteor. Soc. Japan,
99, 339–356, https://doi.org/10.2151/jmsj.2021-016.
Talagrand, O., 1991: Adjoint models. Reading, UK, European Centre for
Midium-Range Weather Forecasts, 73–91 https://www.ecmwf.int/sites/default/files/elibrary/1991/12548-adjoint-models.pdf.
——, and P. Courtier, 1987: Variational assimilation of meteorological
observations with the adjoint vorticity equation. I:
Theory. Quart. J. Roy. Meteor. Soc.,
113, 1311–1328, https://doi.org/10.1002/qj.49711347812.
Tippett, M. K., J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S.
Whitaker, 2003: Ensemble square root filters. Mon. Wea. Rev.,
131, 1485–1490, https://doi.org/10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2.
Tsuyuki, T., and T. Miyoshi, 2007: Recent progress of data assimilation
methods in Meteorology. J. Meteor. Soc. Japan.,
85B, 331–361, https://doi.org/10.2151/jmsj.85B.331.
Vaswani, A., N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez,
L. Kaiser, and I. Polosukhin, 2023: Attention Is
All You Need. https://doi.org/10.48550/arXiv.1706.03762.
Vetra-Carvalho, S., P. J. V. Leeuwen, L. Nerger, A. Barth, M. U. Altaf,
P. Brasseur, P. Kirchgessner, and J.-M. Beckers, 2018: State-of-the-art
stochastic data assimilation methods for high-dimensional
non-Gaussian problems. Tellus A,
70, 1–43.
Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation
without perturbed observations. Mon. Wea. Rev.,
130, 1913–1924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.
Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and
observation availability on convective-scale data assimilation with an
ensemble Kalman filter. Mon. Wea. Rev.,
132, 1238–1253, https://doi.org/10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.
榎本剛., 2021: 自己組織化マップを用いた大気循環パターンのクラスタ解析.
京都大学防災研究所年報. B, 64, 313–316.
——, and 中下早織., 2022: 準地衡流モデルへの決定論的アンサンブルデータ同化.
京都大学防災研究所年報. B, 65.
甘利俊一., 1968: パターン認識の理論. 計測と制御,
7, 180–189, https://doi.org/10.11499/sicejl1962.7.180.
——, 2001: 自然勾配学習法-学習空間の幾何学. 計測と制御,
40, 735–739, https://doi.org/10.11499/sicejl1962.40.735.
赤穂昭太郎, 2008:
カーネル多変量解析―非線形データ解析の新しい展開. 岩波書店,.