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

2. Some Difficulties in Rainfall Assimilation
truth
truth
model
model
precipitation 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
Eulerian Perspective
Lagrangian Perspective
Rasterization – Easy! c1 c4 c3 y c2
Storm cell/cluster identification/
tracking (Quantization) – Difficult!
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
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!

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