Jidong Gao, Kristin Kuhlman,Travis Smith, David Stensrud

3DVAR Storm-scale assimilation in real-

time

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)

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

Multiple sensors

4

Radar #1

Radar #2

Radar #3

+ Denser Observations!

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

Courtesy Lou Wicker

A better alternative?Radar #1 Radar #1

Radar #2 Radar #2

Radar #3 Radar #3

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

Radar Data Assimilation

Dowell and Wicker (2009)

Tornado Tracks

Real-time assimilation / Hazardous Weather

Testbed (Spring 2012)

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.

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

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.

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

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)

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

User-controlled domain w/ MRMS domains

3D Wind field

Max updraft Simulated Reflectivity & 3D Wind Vector

Vertical Vorticity

Vorticity Tracks

3DVAR assimilation vorticity track0-3 km MSL

KTLX azimuthal shear track0-3 km MSL

May 10, 2010

Courtesy NWS-Norman

May 10 – Stanley Draper EF4

Vorticity Track / Max Updraft Track – Apr 30,

2010

Hail Size (MR/MS) versus updraft intensity: May 16,

2010

May 10 – Stanley Draper EF4

April 14, 2011 – floating domains working together

Updraft Track (6-hour) Vorticity Track (6-hour)

Floating Domain

May 16 Hail Storm / OKC

Assimilation simulated reflectivity

KTLX Reflectivity

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

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

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.

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