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Multiscale Data Assimilation

Multiscale Dimensionality Reduction for Rainfall Fields

Eulerian vs. Lagrangian Perspectives

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Some Difficulties in Rainfall Assimilation

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Rainfall Errors at a Point:

• Non-Gaussian, Non-smooth (Atomic Probability Mass)

• Non-stationary

(1) 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

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Eulerian and Lagrangian Representations

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• Sequence of raster images (time series of points)

• High-dimensional, sparse

• Complicated errors

• Implicit multiscale structures

• Most data available in this framework

Eulerian Perspective Lagrangian Perspective

• 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

Storm cell/cluster identification/ tracking (Quantization) – Difficult!

Rasterization – Easy!

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Assimilation on an Implicit Multiscale Structure

Implicit Multiscale Structure (from Chatdarong’s Thesis)

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Assimilation on an Explicit Multiscale Structure

Large Scale Features

Storm Cells

Radar Resolution

Explicit Multiscale Structure

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Available Storm Identification and Tracking Techniques

NOAA:Storm Cell Identification and Tracking algorithm (SCIT)

UCAR:Thunderstorm Identification

Tracking Analysis and Nowcasting (TITAN)

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RCR Model Developed at MIT

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Storm Cell/Cluster Identification/Tracking

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Storm Cell/Cluster Identification/Tracking

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Storm Cell/Cluster Indentification/Tracking

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Storm Cell/Cluster Indentification/Tracking

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In Progress

• Low dimensional representation and restoration.

• Unsupervised algorithms.

• Construction of likelihood function (error measure) for data assimilation.

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End

Thank You!

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