The Development of a Wave Packet Tracking Algorithm: Preliminary Climatological and

Model Verification Results

Matthew Souders, Brian Colle, Edmund ChangNROW-12: November 3-4, 2010

School of Marine and Atmospheric SciencesStony Brook University

SBU CSTAR

Motivation● Wave packets linked with

weather disasters, regime changes and predictability issues (e.g. Archambault et al. 2009)

● Evidence that some errors in NWP propagate like wave packets (e.g. Langland and Shapiro, 2002)

● To date, there has been no comprehensive Rossby wave packet climatology

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March 2, 2009 – New York City

Talk Outline

● Defining Rossby Wave Packets● Extracting Rossby Wave Packet Envelopes● Filtering Wave Packet Amplitude (WPA) and

Tracking Wave Packets● Preliminary Climatological Results● Examining Days with Large Medium Range

Error in GFS Forecasts for East Coast Cyclones● Preliminary Conclusions

What is a Rossby Wave Packet?

A A B

A BWave Packet Amplitude (m s-1)

300 hPa Meridional Wind (m s-1)

Data and Methods● Wave Packet Tracking Climatology

– 2.5 degree NCEP/NCAR Reanalysis, global coverage– 4 times daily 300 hPa wind and height fields (1948-2009)

● Analysis of Large Cyclone Errors in GFS Forecasts– Archived 2.5 degree grids from operational GFS forecasts

for cold season (October-March) west Atlantic cyclone events which were relatively poorly forecast from 2003-2007

– Used large SLP error events in the GFS (Charles and Colle, 2010 – WAF Accepted)

– 300 hPa wind and height fields every 24 forecast hours out to H+96

Extracting Wave Packet Envelopes• Implemented the Hilbert

transform technique described by Zimin et al. (2003) to extract wave packet envelopes

• 300 hPa meridional wind used as a measure of wave energy

• 14-day running mean 300 hPa wind used to establish the wave guide

GFS Forecast from 00 UTC 29 OCT, 2010: An Example of a Rossby Wave Packet

Filtering Wave Packet Amplitude (WPA)

Synoptic Scale Disturbance

Goals of Filtering: Make local maxima

easier to find Deemphasize WPA

signals encompassing

a single eddy

Filter Specifications:● Longitude-wrapped

Butterworth Filter● Zonal wave numbers

0-8 retained● Meridional wave

numbers 0-10 retained

TRACK Program• Maxima in WPA is used to track wave packets• Objects were only tracked if their maximum WPA exceeded 16

m s-1 (the climatological average WPA value in the storm tracks) over at least 1,000,000 km2.

• TRACK program uses a cost optimization routine to fit a smooth track through feature points as they move in time (e.g. Hodges, 1995 & Konig, 1993)

• The track smoothness required to continue tracking a feature may be adjusted to account for that feature’s propagation speed (faster moving packets should follow smoother tracks, e.g. Hodges, 1999)

• Running TRACK on filtered WPA produces raw tracks that are ~95% accurate based on two-month hand tracked sample (Northern Hemisphere NCEP/NCAR Reanalysis JAN-FEB 2009)

Track Post-Processing• Track Discontinuities

• Hodges’ method may be confused by mountain barrier crossings, ultra-

fast propagation or multiple maxes in one envelope.

• Likely-related tracks were merged by temporal and geographical

proximity – this reduced distinct NCAR tracks roughly 25%

• Significant Tracks vs. Noise• About 51% of NCAR wave packet tracks failed to last at least two days

and reach a minimum intensity of 20 m/s and were discarded

• Non-significant tracks accounted for only 14.8% of all objects located

by TRACK (the most important 49% of the tracks represent 85% of the

data)

Wave Packet Tracking AnimationJAN 30 – FEB 22, 2009 – Long-lived Wave Packet

Preliminary Climatology: Wave Packet Formation and Dissipation Densities

Formation of significant wave packets favored areas known to be active storm tracks (West Pacific, Atlantic, near the Alps)

Wave packet dissipation heavily influenced by the Tibetan High Plateau

Formation (# per 5 degrees) Dissipation (# per 5 degrees)

Track Density: El Nino vs. La Nina

During El Nino months, wave packets over Central Asia with fewer over the Pacific

During La Nina months, wave packets more frequent in the Eastern Pacific and over North America and less frequent over Asia

Tracks within 5 degrees per Month MEI Index > 0.5

Tracks within 5 degrees per Month MEI Index < -0.5

Wolter, K., 1987: The Southern Oscillation in surface circulation and climate over the tropical Atlantic,

Eastern Pacific, and Indian Oceans as captured by cluster analysis. J. Climate Appl. Meteor., 26, 540-558

Wave Packets and the Operational GFS● Charles and Colle (2008) verified the forecast position

and intensity of cyclones by the GFS.● Examined west Atlantic cyclones which were very

poorly forecast by the GFS at H+96 – interested in large errors in the minimum central MSLP

● 50 largest errors in minimum MSLP selected– 25 too weak (error average: +11.8 hPa)– 25 too strong (error average: -10.3 hPa)

● WPA composites from NCAR dataset and GFS forecasts for these events were compared every 24 hours (initialization to event at H+96)

Composite of WPA (Day 4 GFS Cyclone too Weak)

NCAR Dataset GFS - NCAR

H+00

H+48

H+96

Event

m s-1

NCAR Dataset GFS - NCARm s-1

H+00

H+48

H+96

Event

Composite of WPA (Day 4 GFS Cyclone too Strong)

Preliminary Conclusions● An automated tracking algorithm for Rossby wave

packets has been implemented for reanalysis and model gridded datasets. The tracking scheme is ~95% successful in identifying well defined packet events.

● Wave packets are a very common occurrence - a new significant wave packet forms approximately once per day somewhere on Earth. A few circle the globe 2 or 3 times before they decay!

● Wave packet formation is favored in the storm track regions, while the largest dissipation region occurs near the Tibetan Plateau.

● Compared to El Nino months, wave packets during La Nina events are more pronounced on average fot the north-central Pacific and Canada, while they are weaker in central Asia.

● For events with relatively large GFS cyclone errors (day 4), there are relatively large wave packet errors around day 2 along the west coast of North America (GFS wave packets typically too strong there).

Preliminary Conclusions