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Multiscale Data Assimilation

Multiscale Data Assimilation. Multiscale Dimensionality Reduction for Rainfall Fields. Eulerian vs. Lagrangian Perspectives. Some Difficulties in Rainfall Assimilation. truth. truth. model. precipitation. model. y. x. time. Rainfall Errors at a Point:

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Multiscale Data Assimilation

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  1. Multiscale Data Assimilation Multiscale Dimensionality Reduction for Rainfall Fields Eulerian vs. Lagrangian Perspectives

  2. Some Difficulties in Rainfall Assimilation truth truth model precipitation model y x time • Rainfall Errors at a Point: • Non-Gaussian, Non-smooth (Atomic Probability Mass) • Non-stationary • Mis-located rainfall cells/clusters; (2) Mis-timed events; (3) Missing/excessive cells/events. • Chatdarong’s Approach from a Lagrangian Perspective • Position Errors (shift detection by MRA) • Scale (Intensity) Errors • Timing Errors

  3. Eulerian and Lagrangian Representations Rasterization – Easy! Storm cell/cluster identification/ tracking (Quantization) – Difficult! Eulerian Perspective Lagrangian Perspective c1 c4 c3 y c2 cluster1 x • Clusters/cells, and their locations, shapes, sizes, intensities, life cycles, ... • Low-dimensional, compact • Less complicated errors • Explicit multiscale structures • No observation data in this format so far • Sequence of raster images (time series of points) • High-dimensional, sparse • Complicated errors • Implicit multiscale structures • Most data available in this framework

  4. Assimilation on an Implicit Multiscale Structure Implicit Multiscale Structure (from Chatdarong’s Thesis)

  5. Assimilation on an Explicit Multiscale Structure Explicit Multiscale Structure Large Scale Features Storm Cells Radar Resolution

  6. Available Storm Identification and Tracking Techniques NOAA: Storm Cell Identification and Tracking algorithm (SCIT) UCAR: Thunderstorm Identification Tracking Analysis and Nowcasting (TITAN)

  7. RCR Model Developed at MIT

  8. Storm Cell/Cluster Identification/Tracking

  9. Storm Cell/Cluster Identification/Tracking

  10. Storm Cell/Cluster Indentification/Tracking

  11. Storm Cell/Cluster Indentification/Tracking

  12. In Progress • Low dimensional representation and restoration. • Unsupervised algorithms. • Construction of likelihood function (error measure) for data assimilation.

  13. End Thank You!

  14. Backups from here on

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