Using Standardized Anomaly Data in Operational

Forecasting

Mike Bodner

NCEP/HPC

Development Training Branch

September 2011

Training Outline

• Overview of standardized anomalies and statistical methods in forecasting

• Methodology and computational information behind operational standard deviations

• Application of standardized anomalies in forecasting

• Case Study – Tennessee Flood – Spring 2010

Statistical or stochastic based tools already being used in forecasting…

• MOS output

• Ensembles

• Bias corrected model data

Standardized anomalies are another tool to add to your forecaster tool

chest…

• Assess a meteorological feature based on 60 years of climatology

• Can be applied to model forecast output

• Fields can be compared to record breaking or extreme weather events from the past

• Can use for model diagnostics and evaluation

• Help discern pattern changes in medium range

How are standardized anomalies generated?

• Daily averages and standard deviations (variances) are computed for several meteorological parameters using NCAR/NCEP Reanalysis data from 1948-2009

• A 15-day centered averaging is then applied to the daily data set

• The 15-day filtered data is then subtracted from the model forecast, then divided by the standard deviation to get the standardized anomaly

Note that the standardized or normalized data is “unit-less”. Therefore teleconnections can be derived between anomalies of different parameters.

Example using 500 hPa heights…

Standard deviation or σ is computed by the following formula..

σ = square root of the average of Z2 - average Z2 / # years in data sample

The number of standard deviations from the climatology or standardized anomaly is computed by subtracting the 60 year average height Z' from the model forecast or observed height Z, then dividing by the standard deviation σ

Standardized Anomaly =  (fcst height - average height) ÷ σ

Things to be mindful of when looking at standardized anomalies in forecasting…

• Be aware of the standard deviation or variance pattern for your forecast data

• Climatological variances are not as large over the southern latitudes, particularly during  the warm season

An example of the computed standard deviations for 500 hPa heights forAn example of the computed standard deviations for 500 hPa heights forJuly 4. Notice how the variance increases proportionally with latitude. Also noteJuly 4. Notice how the variance increases proportionally with latitude. Also notehow the largest standard deviations occur over the North Pacific and North Atlantic. how the largest standard deviations occur over the North Pacific and North Atlantic.

Let’s apply the SD data from the July 4 image in the previous slide…

• At Atlanta, GA. The average 500 hPa height for July 4 is 588 dm, and the standard deviation for 500 hPa height over Atlanta is 3 dm

• A forecast value of 3 standard deviations from normal or -3 would suggest a  forecast height of 579 dm which is 9 dm below climatology

• At Seattle, WA. The average 500 hPa height for July 4 is about 570 dm, and the standard deviation for 500 hPa height over Seattle is 9 dm

• A forecast value of 3 standard deviations from normal or -3 would suggest a  forecast height of 543 dm or 27 dm below climatology.

Central U.S. Heat Wave 1980

A prolonged heat wave gripped the central U.S. during the summer of 1980. The pattern featured a closed anti-cyclonic circulation at 500 hPa over the south central U.S. and 850 hPa temperatures 2-2.5 standard deviations above climatology.

The charts displayed on the left are for July 14, 1980.

Sample Application

Record Cold Northeast U.S 19-21 January 1994

Temperatures remained below zero for over 50 hours in Pittsburgh and many other sections of Pennsylvania, Ohio New York and New England during 19-21 January 1994.

500 hPa height fields for 19 January 1994 show a deep trough over eastern North America, but the significant departure from climatology as depicted by the standard deviation fields illustrated the extent of the low level cold air.

850 hPa Moisture FluxHeavy Rain Event over CA

October 2009

GFS 120HR Forecast

GFS 000HR forecast

+6.0 Sigma

Based on normal Gaussian distribution, the number of standard deviations (σ) are depicted along with

the probability of occurrence with respect to climatology.

# of Standard Deviations Probability of Occurrence Based on Climatology

1σ 0.6826895 2σ 0.2718076 3σ 0.0428032

4σ 0.0026364

5σ 0.0000628

A standard PDF curve based on Gaussian distribution. The values A standard PDF curve based on Gaussian distribution. The values plotted on the standard "bell curve" depict percent probability of a plotted on the standard "bell curve" depict percent probability of a standard deviation being above or below the climatological mean standard deviation being above or below the climatological mean (essentially these values are half of the probabilities sited in the (essentially these values are half of the probabilities sited in the above chart). above chart).

However, meteorological fields are not Gaussian distributed…therefore

• Standardized anomaly data can NOT be used to determine the probability of the occurrence of an event

• Data can NOT be used to estimate a 100 year or 500 year magnitude event

Disclaimer

Disclaimer

Estimating a PDF for a specific variable Since meteorological data does not typical fall in line with a Gaussian distribution, the ideal frame of reference for the standardized anomalies is a PDF for a given meteorological parameter on the respective model or reanalysis grid.

Therefore we consider estimating a climatological probability using the Chebyshev Inequality.

This is a probability theorem which states that in any data sample or probability distribution, nearly all the values are close to the mean values and provides a quantitative description of “nearly all” and “close to”

Where

σ = standard deviationk = standardized anomalyμ = meanX = random variable (height, temperature or other meteorological parameter)

Therefore, no more than 1/k2 of the values are more than k standard deviations (where k is the value of the standardized anomaly) away from μ (the mean).

• If the GFS suggests a 120 hour forecast of 500 hPa Heights at -6.0 standard deviations below climatology, we can compute a climatological probability by taking the inverse reciprocal of the normalized anomaly value

• Squaring this value

• Multiplying the squared value by 1/2 (to account for both sides of the median)

• Convert result to a percent

• Therefore >> 1/62 = 1/36, 1/36 * ½ = 1/72, which = 0.0138 or 1.4%

Let’s look at an example

In other words, the probability that the 500 hPa heights will differ from the climatological mean by more than 6 standard deviations is <= to 1.4%. Likewise the probability that the 500 hPa height will lie within 6 standard deviations of the mean is >= 98.6%

500 hPa height forecast with standardized

anomalies and climatological probabilities

• Please be mindful that we are using model forecast data, and the various problems and biases of each model

• This method accounts for climatological variance and provides a more reasonable climatological probability than extracting sigma values from a Bell Curve.

Sample of Precipitable Water, standardized anomalies, climatological probabilities

Tennessee FloodsMay 1-3, 2010

Rainfall Observations

24hrs ending

1200 UTC May 2

24hrs ending

1200 UTC May 3

Total Precipitable Water

1200 UTC May 1, 2010 1200 UTC May 2, 2010

500 hPa Geopotential Height

Normalized Anomalies (GFS Analysis)

• Deep western U.S. trough

• Anomalous Ridge along

eastern seaboard

• Favorable pattern for deep

tropical moisture infusion

into the Tennessee Valley

region.

Precipitable Water

Normalized Anomalies (GFS Analysis)

• Deep western U.S. trough

• Anomalous Ridge along

eastern seaboard

• Favorable pattern for deep

tropical moisture pooling into

the Tennessee Valley region.

GFS 500mb Height Anomalies Initial VT 1200 UTC May 1, 2010

- 3 standard dev (sigma)

- 5 standard dev (sigma)

DRY MOIST

====

====

====

====

====

====

==

====

==

GOES Water Vapor 1215 UTC May 1, 2010

GFS Precip Water Anomalies Initial VT 12 UTC May 1, 2010

+2 sigma

+ 4 sigma

Blended TPW Percent of Normal 1215 UTC May 1, 2010

> 200% of

normal ~ 175% of

normal

subtropical j

et

850 hPa Moisture Flux (v * q)

Normalized Anomalies (GFS Analysis)

• Deep western U.S. trough

• Anomalous Ridge along

eastern seaboard

• Favorable pattern for deep

tropical moisture infusion into

the Tennessee Valley region.

850 hPa V-Flux (meridional wind * q)

Normalized Anomalies (GFS Analysis)

• Depiction of tropical

moisture originating in the

deep tropics during high

amplitude flow regime• Favorable assessment of “q”

due to lower magnitudes of

v-wind

• Possible diagnostic for

PRE events during the warm

season

Midwest floods of 1993 and 2008

Normalized anomalies applied over a two week period

To sum up, when using standardized anomalies in the operational environment, always be mindful that…

• It’s a statistical tool and not to be used to find an analogue from a “similar” past event, or assign a historical ranking to an event

• Standardized anomalies are not a substitute for sound meteorological analysis, diagnosis and an informed forecast process

• The tool is not to be used to assign a probability of occurrence for a specific weather event

• Extreme SA values can be an indicator that a particular model solution may be going astray.

• Although 850 hPa temperatures are below ground level in the west, the SAs correlate well with record events.

References

Bodner, M.J., N.W. Junker, R.H. Grumm, R.S. Schumacher, 2011: Comparison of the 2008 Midwest floods to the historic 1993 floods: Atmospheric Circulation and Processes. Paper Accepted by National Weather Digest, February 2011.

Kalnay, E., and Coauthers , 1996: The NCEP/NCAR 40-year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437-471.

Wilks, Daniel S., Statistical Methods in the Atmospheric Sciences, 2nd Edition, 2006.

ResourcesTo view standardized anomaly data in real time, go to

http://www.hpc.noaa.gov/training/SDs http://eyewall.met.psu.edu/ensembles

To compute and display standardized anomaly data for specific a specific date(s) over your RFC/CWA, the web site below is an excellent reference.

http://www.hpc.ncep.noaa.gov/ncepreanal

Additional significant cases, including several on a more national scale can be found at the reference and training web site for using standard deviations. The web address is

http://www.hpc.noaa.gov/training/

If you have questions or comments, please email

mike.bodner@noaa.gov