Multiscale Data Assimilation
Multiscale Dimensionality
Reduction for Rainfall Fields
Eulerian vs. Lagrangian Perspectives
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Some Difficulties in Rainfall Assimilation
model
y
precipitation
truth
truth
model
x
time
Rainfall Errors
a Point: Perspective
Chatdarong’s Approach
from a at
Lagrangian
•
Non-Gaussian, Non-smooth (Atomic Probability Mass)
•
• Position Errors (shift detection by MRA)
Non-stationary
• Scale
(Intensity)
Errors(2) Mis-timed events; (3) Missing/excessive
(1) Mis-located
rainfall
cells/clusters;
cells/events.
• Timing Errors
2
Eulerian and Lagrangian Representations
Eulerian Perspective
Lagrangian Perspective
Rasterization – Easy!
c1
y
Storm cell/cluster identification/
tracking (Quantization) – Difficult!
c2
c4
c3
cluster1
x
• Sequence of raster images
(time series of points)
• Clusters/cells, and their
locations, shapes, sizes,
intensities, life cycles, ...
• High-dimensional, sparse
• Low-dimensional, compact
• Complicated errors
• Less complicated errors
• Implicit multiscale structures
• Explicit multiscale structures
• Most data available in this
framework
• No observation data in this
format so far
3
Assimilation on an Implicit Multiscale Structure
Implicit Multiscale Structure (from Chatdarong’s Thesis)
4
Assimilation on an Explicit Multiscale Structure
Explicit Multiscale Structure
Large Scale Features
Storm Cells
Radar Resolution
5
Available Storm Identification and Tracking Techniques
NOAA:
Storm Cell Identification and
Tracking algorithm (SCIT)
UCAR:
Thunderstorm Identification
Tracking Analysis and
Nowcasting (TITAN)
6
RCR Model Developed at MIT
7
Storm Cell/Cluster Identification/Tracking
8
Storm Cell/Cluster Identification/Tracking
9
Storm Cell/Cluster Indentification/Tracking
10
Storm Cell/Cluster Indentification/Tracking
11
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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Backups from here on
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