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References

Foundational DA texts

  1. Daley, R. (1991). Atmospheric Data Analysis. Cambridge University Press.
  2. Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press.
  3. Asch, M., Bocquet, M., & Nodet, M. (2016). Data Assimilation: Methods, Algorithms, and Applications. SIAM.
  4. Carrassi, A., Bocquet, M., Bertino, L., & Evensen, G. (2018). Data assimilation in the geosciences: An overview of methods, issues, and perspectives. WIREs Climate Change 9(5), e535.

Optimal Interpolation / BLUE (chapter 4)

  1. Lorenc, A. (1981). A global three-dimensional multivariate statistical interpolation scheme. MWR 109(4).
  2. Eliassen, A. (1954). Provisional report on calculation of spatial covariance and autocorrelation of the pressure field. Inst. Weather and Climate Res., Acad. Norway.
  3. Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. (Ch. 2.7 for the GP-as-OI view.)

3DVar and 4DVar — strong constraint (chapters 5, 6)

  1. Lorenc, A. C. (1986). Analysis methods for numerical weather prediction. QJRMS 112(474).
  2. Talagrand, O., & Courtier, P. (1987). Variational assimilation of meteorological observations with the adjoint vorticity equation. QJRMS 113(478).
  3. Le Dimet, F.-X., & Talagrand, O. (1986). Variational algorithms for analysis and assimilation of meteorological observations. Tellus A 38(2).
  4. Errico, R. M. (1997). What is an adjoint model? BAMS 78(11).
  5. Talagrand, O. (1997). Assimilation of observations, an introduction. JMSJ 75(1B).

Weak-constraint 4DVar (chapter 7)

  1. Trémolet, Y. (2006). Accounting for an imperfect model in 4D-Var. QJRMS 132(621).
  2. Fisher, M., Leutbecher, M., & Kelly, G. A. (2005). On the equivalence between Kalman smoothing and weak-constraint four-dimensional variational data assimilation. QJRMS 131(613).
  3. Daescu, D. N., & Todling, R. (2010). Adjoint sensitivity of the model forecast to data assimilation system error covariance parameters. QJRMS 136(653).

Incremental 4DVar with CVT (chapter 8)

  1. Courtier, P., Thépaut, J.-N., & Hollingsworth, A. (1994). A strategy for operational implementation of 4D-Var, using an incremental approach. QJRMS 120(519).
  2. Lorenc, A. C. (1997). Development of an operational variational assimilation scheme. JMSJ 75(1B).
  3. Bannister, R. N. (2017). A review of operational methods of variational and ensemble-variational data assimilation. QJRMS 143(703).
  4. Bannister, R. N. (2008). A review of forecast error covariance statistics in atmospheric variational data assimilation. QJRMS 134(637).

4DVarNet (chapter 9)

  1. Fablet, R., Amar, M. M., Febvre, Q., Beauchamp, M., & Chapron, B. (2021). End-to-end physics-informed representation learning for satellite ocean remote sensing data. ISPRS Annals V-3-2021, 295–302.
  2. Fablet, R., Chapron, B., Drumetz, L., Mémin, E., Pannekoucke, O., & Rousseau, F. (2021). Learning variational data assimilation models and solvers. JAMES 13(10).
  3. Fablet, R., Febvre, Q., & Chapron, B. (2023). Multimodal 4DVarNets for the reconstruction of sea surface dynamics from NADIR and wide-swath altimetry. IEEE TGRS 61.
  4. Bolte, J., Pauwels, E., & Vaiter, S. (2023). One-step differentiation of iterative algorithms. NeurIPS 36. arXiv:2305.13768.
  5. LeCun, Y., Chopra, S., Hadsell, R., Ranzato, M., & Huang, F. (2006). A tutorial on energy-based learning. Predicting Structured Data 1(0).

Amortized inference (chapter 10)

  1. Cranmer, K., Brehmer, J., & Louppe, G. (2020). The frontier of simulation-based inference. PNAS 117(48).
  2. Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S., & Lakshminarayanan, B. (2021). Normalizing flows for probabilistic modeling and inference. JMLR 22(57).
  3. Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., & Poole, B. (2021). Score-based generative modeling through stochastic differential equations. ICLR.
  4. Cohen, S., Amos, B., & Lipman, Y. (2023). Score-based diffusion meets annealed importance sampling. NeurIPS.

Adjoint methods (chapter 12)

  1. Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. (2018). Neural ordinary differential equations. NeurIPS.
  2. Kidger, P. (2021). On neural differential equations. PhD thesis, University of Oxford. (diffrax author; Ch. 5 on adjoints.)
  3. Blondel, M., Berthet, Q., Cuturi, M., Frostig, R., Hoyer, S., Llinares-López, F., Pedregosa, F., & Vert, J.-P. (2022). Efficient and modular implicit differentiation. NeurIPS.

Posterior + ensemble methods (chapter 13)

  1. Cressie, N., & Wikle, C. K. (2011). Statistics for Spatio-Temporal Data. Wiley.
  2. Talts, S., Betancourt, M., Simpson, D., Vehtari, A., & Gelman, A. (2018). Validating Bayesian inference algorithms with simulation-based calibration. arXiv:1804.06788.
  3. Evensen, G. (2003). The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dynamics 53.

Examples (chapters 15–17)

  1. Lorenz, E. N. (1963). Deterministic nonperiodic flow. JAS 20(2).
  2. Lorenz, E. N. (1996). Predictability — a problem partly solved. ECMWF Seminar.
  3. Le Guillou, F., et al. (2023). Mapping altimetry in the forthcoming SWOT era by back-and-forth nudging a one-layer quasigeostrophic model. JTECH 40(1). (OceanBench reference.)
  4. Ubelmann, C., Klein, P., & Fu, L.-L. (2015). Dynamic interpolation of sea surface height and potential applications for future high-resolution altimetry mapping. JTECH 32.
  5. Jacob, D. J., et al. (2022). Quantifying methane emissions from the global scale down to point sources using satellite observations of atmospheric methane. ACP 22(14).
  6. Varon, D. J., et al. (2019). Quantifying methane point sources from fine-scale satellite observations of atmospheric methane plumes. AMT 12(10).
  7. Cusworth, D. H., et al. (2021). Multisatellite imaging of a gas well blowout enables quantification of total methane emissions. GRL 48(2).

Ecosystem libraries

  • somax — geophysical fluid models
  • plumax — atmospheric transport + RTM (methane)
  • gaussx — structured linear operators, Matérn factorisation
  • lineax — linear solvers, AbstractLinearOperator
  • optimistix — optimisers + adjoints
  • diffrax — ODE / SDE integration + adjoints
  • filterax — ensemble methods
  • pipekit + pipekit-cycle — operator composition + DA cycle protocols

Predecessors