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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 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: • 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
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
Assimilation on an Implicit Multiscale Structure Implicit Multiscale Structure (from Chatdarong’s Thesis)
Assimilation on an Explicit Multiscale Structure Explicit Multiscale Structure Large Scale Features Storm Cells Radar Resolution
Available Storm Identification and Tracking Techniques NOAA: Storm Cell Identification and Tracking algorithm (SCIT) UCAR: Thunderstorm Identification Tracking Analysis and Nowcasting (TITAN)
In Progress • Low dimensional representation and restoration. • Unsupervised algorithms. • Construction of likelihood function (error measure) for data assimilation.
End Thank You!
