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Data Assimilationactivities atIMT AtlantiqueWorkshop on Data AssimilationIMT Atlantique Brest - Feb 22, 20191Pierre Tandeo - [email protected]

OutlineI- DA applications at IMT AtlantiqueII- Mathematical formulation of DAIII- Analog DAIV- Uncertainty quantification in DAV- Conclusions and perspectives

I- Data Assimilation applications at IMT AtlantiqueSynergy in spatial oceanography Satellite observations from differentsensors Various observed variables(temperature, salinity, currents) Different spatial and temporalresolutions Observations only at the surface.3

I- Data Assimilation applications at IMT AtlantiqueNumerical simulations of the ocean Integration of physical equations (atdifferent depths) Consistency between variables Same spatial and temporal resolution Useful to get forecasts but we need agood initial condition4

II- Mathematical formulation of Data AssimilationBridge between observations and simulations5

II- Mathematical formulation of Data AssimilationNonlinear state-space model6Estimation ofp(x y) usingEnsemble Kalman

III- Analog Data AssimilationGeneral concept7

III- Analog Data AssimilationMathematical formulation8

III- Analog Data AssimilationModel-driven VS Data-driven9Both methods areequivalent for largeenough catalog

III- Analog Data AssimilationComparison with other data-driven methods (model is unknown) Exact interpolator: linear, cubic or splines no error in observations Smoothers: Optimal Interpolation (OI) or AnDA errors in observations need historical data to learn temporal dependencies10

III- Analog Data AssimilationComparison with other data-driven methodsRealistictrajectory usinganalogsAdaptiveuncertaintiesusing analogs11

III- Analog Data AssimilationApplications in spatial oceanographyExample for the interpolation of along-track SSH:12

IV- Uncertainty quantification in Data AssimilationGeneral variances

IV- Uncertainty Quantification in Data AssimilationMathematical formulation14

IV- Uncertainty Quantification in Data AssimilationApplications in spatial oceanography15Bad modelspecificationStrongsatelliteerrorsExample for the interpolation of infrared SST:

V- Conclusions and perspectivesConclusions and references Data-driven methods in DA: use historical data from observations or numerical simulations use machine learning for the emulation of the model use statistical algorithms for uncertainty quantification Analog DA: Lguensat, R., Tandeo, P., Ailliot, P., Pulido, M., & Fablet, R. (2017). Theanalog data assimilation. Monthly Weather Review, 145(10), 4093-4107. Uncertainty quantification in DA: Dreano, D., Tandeo, P., Pulido, M., Ait‐El‐Fquih, B., Chonavel, T., &Hoteit, I. (2017). Estimating model‐error covariances in dtheexpectation–maximization algorithm. Quarterly Journal of the RoyalMeteorological Society, 143(705), 1877-1885.

V- Conclusions and perspectives17Other activities and perspectives Joint estimation of Q and R in DA: 1st collaboration betweenRIKEN and IMT Atlantique review paper in revision with T. MiyoshiNowcasting of extreme rainfalls: 2st collaboration between RIKENand IMT Atlantique use deep learning methods with T. Miyoshi and S. Otsuka (talk) Others applications at IMT Atlantique: use neural network in DA (S. Ouala talk) image processing and optimization techniques (L. Drumetz talk)

Thank you!Any questions?18

Workshop on Data Assimilation IMT Atlantique Brest - Feb 22, 2019 1. I- DA applications at IMT Atlantique II- Mathematical formulation of DA III- Analog DA IV- Uncertainty quantification in DA V- Conclusions and perspectives Outline. ... and IMT Atlantique use deep learning methods