Using Standard Deviation Data in Operational Forecasting

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Using Standard Deviation Data in Operational
Forecasting

• Mike Bodner
• NCEP/HPC
• Development Training Branch
• Winter 2005

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Outline

• Overview of standard deviations and statistical
  methods in forecasting
• Methodology and computational information behind
  operational standard deviations
• Application of standard deviations
• Look at significant cases

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

• MOS output
• Ensembles
• Short Range Ensemble Forecasts
• (SREFs)

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Standard deviations can be another tool to add to
the chest

• Based on 50 years of climatology
• Can be applied to a model forecast output
• Fields can be compared to record breaking or
  extreme events from past dates
• Can help discern how whether or not model
  forecast is way off the mark or not

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How are standard deviations generated?

• Daily averages and standard deviations
  (variances) are computed for 500 hPa heights and
  850 hPa temperatures from NCAR/NCEP Reanalysis
  data from 1950-2001

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Another way of looking at it using 500 hPa
heights
Standard deviation or s is computed by the
following formula.. s 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) s
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Keep in mind when looking at standard deviation
data in an operational setting..

• Whenever the models are forecasting the number of
  standard deviations to be 3 units of more from
  climatology, a significant or extraordinary event
  is being suggested
• A record breaking temperature or precipitation
  scenario is possible
• Typically 3-4 standard deviations from normal
  during the cold season and 2-3 in the warm season
  
• Forecast values of 5 and 6 are of extremely low
  probability and should be closely scrutinized if
  displayed in model forecast data

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Rather benign day with not much going on
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Surprise October 1996 snow event in Kansas City
metro area..4 SDs lower than climatology
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Other items to be aware of when using this tool

• Its beneficial to be aware of the standard
  deviations or at least the SD pattern for your
  forecast data
• The climatological standard deviations are not as
  large over the southern latitudes, particularly
  during  the warm season
• The probability of the heights and temperatures
  do not follow a normal distribution over the far
  southern tier of the U.S. and tropical latitudes
  where heights or temperatures are more likely to
  exceed 1 standard deviation

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Heres an example of the computed standard
deviations for 500 hPa heights forJuly 4. Notice
how the variance increases proportionally with
latitude. Also note how the largest standard
deviations occur over the North Pacific and North
Atlantic.
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Lets 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.

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As mentioned several slides earlier, height and
temperature regimes depicted as 3 or more
standard deviations from climatology are very
rare.
of Standard Deviations Probability of Occurrence Based on Climatology
1s 0.6826895
2s 0.2718076
3s 0.0428032
4s 0.0026364
5s 0.0000628
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.
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The values plotted on the standard "bell curve"
depict percent probability of a standard
deviation being above or below the climatological
mean (essentially these values are half of the
probabilities sited in the above chart). As you
can see, there is extremely low probability for
forecast events greater than 3 standard
deviations from climatology.
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Lets take a look a few regional heat cases

• Northeast U.S. Heat Wave July 1966
• Central U.S. Heat Wave July 1980
• Southwest U.S. Extreme Heat June 1990

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4th of July Heat Wave over 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.
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850 hPa temperatures and 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.
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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.
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Southwest U.S. Extreme Heat 1990
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, a record maximum
temperature of 122F was recorded at Phoenix, AZ.
In Downtown Los Angeles a record 112F was
observed.  Both 500 hPa heights and 850 hPa
temperatures were 2 SDs above climatology near
the center of the upper high.
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Applying this tool to extreme cold at the
regional scale

• Northeast U.S. January 1994
• Central U.S. November 1991
• Western U.S. February 1989

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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. Moreover fresh snow
cover increased the potential for an
exceptionally cold boundary layer.
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Record Cold over Central U.S. November 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.
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Record cold over Western U.S. February 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.
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Late July cold front into southern Texas
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Look at model forecast
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Early August cold front into Florida
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Look at model forecasts
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When using standard deviations in the operational
environment, always be mindful that

• Its a statistical tool and not to be used to
  find an analogue from a similar past event
• Standard deviation data is not a substitute for
  meteorological analysis, diagnosis and an
  informed forecast process
• Like the mass fields or other diagnostic fields,
  standard deviation based on model forecast output
  will lose its skill with time. In other words
  SDs will likely go astray more at 72 hours and
  beyond than at 12-48 hours.
• Extreme SD values can be a clue that a particular
  model may be going astray.
• 500 and 850 hPa SD data does not take into
  account local boundary layer conditions (i.e.
  snow cover)

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More Operational Rules of Thumb

• For a significant or record breaking event, a SD
  threshold of 2 is a guide for the warm season,
  and 3 for the cold season.
• SDs gt 5 are more an indication of model failure
  than an extreme event.
• When applying SDs to significant temperature
  scenarios, focus more on 850 hPa temperatures
  than 500 hPa heights.
• Although SDs at 850 are below ground in the west,
  they do correlate well with record events.

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Resources
To view standard deviation data in real time, go
to http//eyewall.met.psu.edu
/ensembles/avn.html To compute and display
standard deviation for specific a specific
date(s) over your 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
any questions or comments, please email
mike.bodner_at_noaa.gov