Using Standard Deviation Data in Using Standard Deviation Data in

Operational ForecastingOperational Forecasting

Mike BodnerMike Bodner

NCEP/HPCNCEP/HPC

Development Training BranchDevelopment Training Branch

Fall 2004Fall 2004

OutlineOutline

Overview of standard deviations and Overview of standard deviations and statistical methods in forecastingstatistical methods in forecasting

Methodology and computational information Methodology and computational information behind operational standard deviationsbehind operational standard deviations

Application of standard deviationsApplication of standard deviations

Look at significant casesLook at significant cases

We are already using tools that We are already using tools that apply stochastic methods in apply stochastic methods in

operational forecasting…operational forecasting…

MOS outputMOS output

EnsemblesEnsembles

SREFsSREFs

Standard deviations can be another Standard deviations can be another tool to add to the chest…tool to add to the chest…

Based on 50 years of climatologyBased on 50 years of climatology

Can be applied to a model forecast outputCan be applied to a model forecast output

Fields can be compared to record breaking Fields can be compared to record breaking or extreme events from past datesor extreme events from past dates

Can help discern how whether or not model Can help discern how whether or not model forecast is way off the mark or notforecast is way off the mark or not

How are standard deviations generated?How are standard deviations generated?

Daily averages and variance are computed Daily averages and variance are computed for 500 hPa heights and 850 hPa for 500 hPa heights and 850 hPa temperatures from NCAR/NCEP Reanalysis temperatures from NCAR/NCEP Reanalysis data from 1950-2001 data from 1950-2001

Variance is the mean or expected value of Variance is the mean or expected value of the squared deviations from the mean itself the squared deviations from the mean itself or by the expressionor by the expression

var(x) = MEAN{[x-MEAN(x)]**2}var(x) = MEAN{[x-MEAN(x)]**2}

Another way of looking at it using 500 Another way of looking at it using 500 hPa heights…hPa heights…

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

σ = square root of the average of heights 2 - average height2

The number of standard deviations from the climatology is computed by subtracting the 50 year average height from the model forecast or observed height then dividing by the standard deviation.

# of standard deviations =  (fcst height - average height) ÷ σ

Keep in mind when looking at standard Keep in mind when looking at standard

deviation data in an operational setting..deviation data in an operational setting.. Whenever the models are forecasting the number of standard Whenever the models are forecasting the number of standard

deviations to be 3 units of more from climatology, a significant deviations to be 3 units of more from climatology, a significant or extraordinary event is being suggested or extraordinary event is being suggested

A record breaking temperature or precipitation scenario is A record breaking temperature or precipitation scenario is possiblepossible

Typically 3-4 standard deviations from normal during the cold Typically 3-4 standard deviations from normal during the cold season and 2-3 in the warm seasonseason and 2-3 in the warm season

Forecast values of 5 and 6 are of extremely low probability and Forecast values of 5 and 6 are of extremely low probability and should be closely scrutinized if displayed in model forecast should be closely scrutinized if displayed in model forecast datadata

Surprise October 1996 snow event in Kansas City metro area..4 SDs lower Surprise October 1996 snow event in Kansas City metro area..4 SDs lower than climatologythan climatology

Other items to be aware of when using Other items to be aware of when using this toolthis tool

It’s beneficial to be aware of the standard deviations It’s beneficial to be aware of the standard deviations or at least the SD pattern for your forecast dataor at least the SD pattern for your forecast data

The climatological standard deviations are not as The climatological standard deviations are not as large over the southern latitudes, particularly during  large over the southern latitudes, particularly during  the warm season the warm season

The probability of the heights and temperatures do The probability of the heights and temperatures do not follow a normal distribution in southern and not follow a normal distribution in southern and tropical latitudes where heights or temperatures are tropical latitudes where heights or temperatures are more likely to exceed 1 standard deviation more likely to exceed 1 standard deviation

Here’s an example of the computed standard deviations for 500 hPa heights forHere’s an 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 variance occurs over the North Pacific and North Atlantic. how the largest variance occurs over the North Pacific and North Atlantic.

Let’s apply the SD data from the July 4 image in the previous slide…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 At Atlanta, GA. The average 500 hPa height for July 4 is 588 588 dmdm, and the standard deviation for 500 hPa height over Atlanta , and the standard deviation for 500 hPa height over Atlanta is is 3 dm3 dm

A forecast value of A forecast value of 3 standard deviations3 standard deviations from normal or from normal or -3-3 would suggest a  forecast height of would suggest a  forecast height of 579 dm579 dm which is which is 9 dm9 dm below climatologybelow climatology

At Seattle, WA. The average 500 hPa height for July 4 is about At Seattle, WA. The average 500 hPa height for July 4 is about 570 dm570 dm, and the standard deviation for 500 hPa height over , and the standard deviation for 500 hPa height over Seattle is Seattle is 9 dm9 dm

A forecast value of A forecast value of 3 standard deviations3 standard deviations from normal or from normal or -3-3 would suggest a  forecast height of would suggest a  forecast height of 543 dm 543 dm or or 27 dm27 dm below below climatology.climatology.

As mentioned several slides earlier, height and temperature regimes As mentioned several slides earlier, height and temperature regimes depicted as 3 or more standard deviations from climatology are very depicted as 3 or more standard deviations from climatology are very

rare. rare.

# of Standard Deviations# of Standard Deviations Probability of Occurrence Probability of Occurrence

Based on ClimatologyBased on Climatology 11σσ 0.68268950.6826895 22σσ 0.27180760.2718076 33σσ 0.0428032 0.0428032

44σσ 0.0026364 0.0026364

55σσ 0.00006280.0000628 The number of standard deviations are displayed with probability of occurrence of the number of standard deviations from climatology based on a standard probability density function (PDF) curve. The values include both above and below normal conditions.

The values plotted on the standard "bell curve" depict percent The values plotted on the standard "bell curve" depict percent probability of a standard deviation being above or below the probability of a standard deviation being above or below the climatological mean (essentially these values are half of the climatological mean (essentially these values are half of the probabilities sited in the above chart). As you can see, there is probabilities sited in the above chart). As you can see, there is extremely low probability for forecast events greater than 3 standard extremely low probability for forecast events greater than 3 standard deviations from climatology.deviations from climatology.

Let’s take a look a few regional heat cases…Let’s take a look a few regional heat cases…

Northeast U.S. Heat Wave – July 1966Northeast U.S. Heat Wave – July 1966

Central U.S. Heat Wave – July 1980Central U.S. Heat Wave – July 1980

Southwest U.S. Extreme Heat – June 1990Southwest U.S. Extreme Heat – June 1990

44thth of July Heat Wave over of July Heat Wave over

the Northeast U.S.the Northeast U.S.

Triple digit temperatures were noted over many Northeast locations during the 3 day period 3-5 July 1966.

The 500 hPa charts for this record breaking heat event over the Northeast do not depict a pattern typical of a severe heat wave. 500 hPa heights are 2 standard deviations above climatology but the next slide depicts the 850 hPa thermal field which ended up being the driver in this pattern.

850 hPa temperatures 850 hPa temperatures and standard deviationsand standard deviations

The high 850 temperatures were 2.5 standard deviations above normal. The anomalously warm thermal field coupled with down sloping were primary contributors to the record breaking heat of 3-5 July, 1966.

Central U.S. Heat Wave 1980Central 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.

Southwest U.S. – Extreme Heat Southwest U.S. – Extreme Heat 19901990

A pre-monsoon 500 hPa anti-cyclone became established over the southwest U.S. in late June 1990. During the period June 25-28, numerous records were set. On June 26, Phoenix, AZ recorded a record maximum temperature of 122F and Downtown Los Angeles a record 112F.  Both 500 hPa heights and 850 hPa temperatures were 2 SDs above climatology near the center of the upper high.

Applying this tool to extreme cold at the Applying this tool to extreme cold at the regional scale…regional scale…

Northeast U.S. – January 1994Northeast U.S. – January 1994

Central U.S. – November 1991Central U.S. – November 1991

Western U.S. – February 1989Western U.S. – February 1989

Record Cold Northeast U.S Record Cold Northeast U.S 19-21 January 199419-21 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. Moreover fresh snow cover increased the potential for an exceptionally cold boundary layer.

Record Cold over Central U.S. Record Cold over Central U.S. November 1991November 1991

Within days after the “perfect storm” churned up the western Atlantic and caused extensive damage to the Northeast coast, another intense cyclone resulted in an early season heavy snow event across the upper Mississippi Valley.

In the aftermath of this storm, a full latitude trough delivered a record cold air mass to the plains states. Significant negative temperature anomalies were noted at 850 hPa.

The images to the right show 500 and 850 hPa fields for 3 November 1991. This was the initial surge of arctic air into the central U.S. during a record breaking cold week.

Record cold over Western U.S. Record cold over Western U.S. February 1989February 1989

A very large arctic air mass moved into the western U.S. in early February 1989. The coldest anomalies both at 850 hPa and the surface were noted over the Great Basin region. Eventually the cold migrated to the central and southern plains.

On the graphics for 6 February 1989, note the anomalously large ridge over the Gulf of Alaska at 500 hPa and full latitude trough over the western states to delivery the cold air. Also note the strong negative standard deviations at 850 hPa over the west.

February records were set at Reno, NV, -15F, -30F at Ely, NV and 31F at San Francisco, CA on 6 February 1989.

When using standard deviations in the operational environment, always When using standard deviations in the operational environment, always be mindful that…be mindful that…

It’s a statistical tool and not to be used to find an It’s a statistical tool and not to be used to find an analogue from a “similar” past eventanalogue from a “similar” past event

Standard deviation data is not a substitute for Standard deviation data is not a substitute for meteorological analysis, diagnosis and an informed meteorological analysis, diagnosis and an informed forecast processforecast process

Like the mass fields or other diagnostic fields, standard Like the mass fields or other diagnostic fields, standard deviation based on model forecast output will lose it’s deviation based on model forecast output will lose it’s skill with time. In other words SDs will likely go astray skill with time. In other words SDs will likely go astray more at 72 hours and beyond than at 12-48 hours.more at 72 hours and beyond than at 12-48 hours.

Extreme SD values can be a clue that a particular Extreme SD values can be a clue that a particular model may be going a stray.model may be going a stray.

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.ncep.noaa.gov/training

If you have any questions or comments, please email

mike.bodner@noaa.gov