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Jidong Gao, Kristin Kuhlman,Travis Smith, David Stensrud
3DVAR Storm-scale assimilation in real-
time
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Convective-scale Warn-on-Forecast Vision
Probabilistic tornado guidance: Forecast looks on track, storm circulation (hook echo) is tracking along centerline
of highest tornadic probabilities
Radar and Initial Forecast at 2100 CST Radar at 2130 CST: Accurate Forecast
MostLikelyTornadoPath
T=2120 CST
T=2150
T=2130T=2140
70%
50%
30%
T=2200 CST
Developing thunderstorm
MostLikelyTornadoPath
T=2120 CST
T=2150
T=2130T=2140
T=2200 CST
An ensemble of storm-scale NWP models predict the path of a potentially tornadic supercell during the next 1 hour. The ensemble is used to create probabilistic tornado guidance.
70%
50%
30%
Stensrud et al. 2009 (October BAMS)
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Probabilistic convective-scale analysis and forecast
system
• High-resolution 3-d analysis produced every 5 min
• 1-h ensemble forecasts produced every 5 min– Provides probabilities of hazardous weather
• Assimilation of all available observations
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Multiple sensors
4
Radar #1
Radar #2
Radar #3
+ Denser Observations!
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Example: Multi-sensor data fields
Show physical relationships between data fields from multiple sensorsStorm tracks and trends can be generated at any spatial scale, for any data fieldsFuture state predicted through extrapolation shows skill out to about an hour
Near-surface reflectivity
Reflectivity @ -20 C
(~6.5 km AGL)
Total Lightning Density
Max Expected Size of Hail
55
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Courtesy Lou Wicker
A better alternative?Radar #1 Radar #1
Radar #2 Radar #2
Radar #3 Radar #3
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Single analysis
that can also be used to initialize forecast modelsfor Warn-on-Forecast
3D Wind (U/V/W)
Solve vorticity equation
Not limited by edge of echo
Pres/Temp/RH
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Radar Data Assimilation
Dowell and Wicker (2009)
Tornado Tracks
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Real-time assimilation / Hazardous Weather
Testbed (Spring 2012)
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Getting started: R & D goals for Spring 2012
To create realtime weather-adaptive 3DVAR analyses at high horizontal resolution and high time frequency with all operationally available radar data from the WSR-88D network.
To use the analysis product to help detect supercells and determine if these analyses can improve forecasters awareness of the hazardous weather event.
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3D-Var: An Introduction
Given a set of observations and a model of some physical parameters, what does knowledge of observations tell us about the model state?
3D-Var finds the optimal analysis that minimizes the distance to the observations weighted by the inverse of the error variance
J(x) (x x b )TB 1 (x x b ) (y0 H(x))TR 1(y0 H(x))
J(x) = cost function (to be minimized such that x = xa: )
Xa= optimal analysis of field of model variablesXb= background field Y0= observationsH matrix transforms vectors in model space to observation
spaceB = background error covariance R = observational error
covariance
xJ(xa )0
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3D-Var: An IntroductionThe minimum is found by numerical minimization, which is typically an iterative process
Fig. from ECMWF (Bouttier & Courtier)
Schematic of the cost function minimization in two dimensions.
The minimum is found by performing several searches to move the control variable to areas where the cost-function is smaller, usually by looking at the local slope (the gradient) of the cost-function.
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3D-Var: Advantages
The essence of the 3D-Var algorithm is to rewrite a least-squares problem as the minimization of a cost-function. The method was introduced in order to remove the local data selection in the Optimal Interpolation algorithm, thereby performing a global analysis of the 3-D meteorological fields, hence the name.
For 3D-Var: Observations and model variables can be non-linearly related
There is no data selection – all available data used simultaneously (no jumpiness in boundaries between regions)
4D-Var is generalized as 3D-var for observations that are distributed in time.
4D-Var is more complex: needs linearized perturbation forecast model and its adjoint to solve the cost function minimization problem efficiently
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Real-time system
• 1pm to 9pm daily
• 4 floating domains (user-controlled)
• 1 km res
• 31 vertical levels
• 200x200 grid points
• 5-min updates
• Near-real-time (<5 min latency)
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Real-time system
NAM forecast is used for the background field
• interpolated to the 3DVAR analysis time
Uses Reflectivity and Radial Velocity from all nearby WSR-88D radars
• Cloud analysis
• 3DVAR Wind analysis
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User-controlled domain w/ MRMS domains
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3D Wind field
Max updraft Simulated Reflectivity & 3D Wind Vector
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Vertical Vorticity
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Vorticity Tracks
3DVAR assimilation vorticity track0-3 km MSL
KTLX azimuthal shear track0-3 km MSL
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May 10, 2010
Courtesy NWS-Norman
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May 10 – Stanley Draper EF4
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Vorticity Track / Max Updraft Track – Apr 30,
2010
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Hail Size (MR/MS) versus updraft intensity: May 16,
2010
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May 10 – Stanley Draper EF4
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April 14, 2011 – floating domains working together
Updraft Track (6-hour) Vorticity Track (6-hour)
Floating Domain
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May 16 Hail Storm / OKC
Assimilation simulated reflectivity
KTLX Reflectivity
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Notes
20 prior cases (from 2010, all of which are supercells) showed:
• max W range: 15 to 25 m/s
• max Vorticity range: 0.012 to 0.032 s-1
• values seem to vary based on range from radar
• More study is needed, here
• Trends of vorticity match azimuthal shear
• Updraft intensity frequently trends w/ MESH
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A typical session
You will use the 3DVAR analysis to help with warning decision assistance.
• AWIPS / WarnGen; WDSS-II for some displays
Feedback:
• real-time observation / discussion (recorded to EWP blog)
• web-based surveys
• daily post-mortem discussion
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Things to ponder this week
•Look long-term (5-10-15 years into the future).
•Think about how the 3DVAR storm structure and morphology compare to how you would analyze the data during typical forecast/warning operations in your office.
•Consider how storm-scale ensemble prediction will affect warning decision-making and communication of warning information in 10-15 years.
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In Conclusion
You are getting the first look at these real-time data!
It’s the start of a > 10-year journey.
Web archive / real-time images:
•http://www.nssl.noaa.gov/users/jgao/public_html/analysis/RealtimeAnalysis.htm
•http://tiny.cc/3DVAR