Local 3 Month Precipitation Outlook

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Local 3 Month Precipitation Outlook Downscaling
Climate Variable Downscaling Inferring climate
variations on smaller spatial/temporal scales
than resolution of source climate
model/forecast Marina Timofeyeva, 1UCAR and
NWS/NOAA Contributors Jenna Meyers, NWS WR HQ
and Dave Unger, CPC
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Outline

• Requirements for downscaling success
• Challenges with precipitation downscaling
• Precipitation downscaling methods
• Results
• Product presentation and expected timeline

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Downscaling Requirements

• Model Simplicity Increased number of predicted
  variables increase model uncertainty may lead
  to type 1 error (we reject when we do not need
  to)
• Validity of Distribution If the distribution is
  not appropriate, the statistical results cannot
  be interpreted correctly and this may lead to
  type 2 error (we do not reject when we ought to)
• Existence of potential predictability If there
  is no potential predictability in the downscaling
  source, no matter how good the downscaling model
  is, we will end up with poor downscaled
  information type 2 error in the model
  applications

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Downscaling Precipitation Forecasts

• Source for Downscaling CPC forecasts
• Questions to be answered
• Why downscale?
• What distribution is appropriate?
• Is there potential predictability?
• How do we do it?
• What is the outcome? discussed in previous
  section

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Why L3MPO?

• CPC 3 month precipitation forecast uses forecast
  tools calibrated for 102 forecast regions or
  large scale grids and, therefore, inherit the
  resolution of the tools
• Numerous requests from customers after L3MTO
  launched
• L3MTO methodology cannot be instantly used for
  L3MPO

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Challenges Precipitation Distribution
Temperature is a normally distributed variable,
therefore the downscaling method based on
regression can provide good estimates
Precipitation (right chart) is too skewed for
normal distribution. The regression would
require a transformation of this variable.
Compositing can be used for Precipitation
forecasts because it does not employ regression
analysis.
Mean 0.30 St. Dev. 0.38 Median 0.19 Mode
0.01 Skewness 3.11 Kurtosis 14.67
NOT a good fit
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Challenges Precipitation Distribution
Distributions of seasonal precipitation totals
are too skewed
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Challenges Precipitation Distribution

• Which distribution is an appropriate assumption
  for precipitation?
• Data 1960 2005 3 month (DJF, OND) total
  precipitation for 87 locations in NWS WR
• Kolmogorov-Smirnoff GOF test of Distributions
  Normal, Lognormal and Gamma
• Mapping CPC forecast potential predictability on
  fit of an assumed distribution

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Challenges Precipitation Distribution
Which distribution is an appropriate assumption
for precipitation?
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Challenges Precipitation Distribution

• What does it mean?
• Linear regression cannot be used because
  distribution assumptions, used by regression
  tests, are not met in many cases
• Several alternatives
• Variable transformation, e.g. sqrt, ln, etc.
• Normal Quantile transformation
• Special Case, zero precipitation amounts, require
  the use of two model forecast systems
• forecast probability of precipitation chance and
• forecast probability of precipitation amount

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Challenges Predictability of CPC Forecast

• Is there Potential Predictability in CPC
  Precipitation Forecasts?
• Useable national-scale skill entirely confined to
  Fall/Winter strong ENSO years in short to medium
  leads
• Otherwise skill is statistically
  indistinguishable from zero

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Challenges Predictability of CPC Forecast
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Challenges Predictability of CPC Forecast
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L3MTO Methodology in Application to L3MPO

• Precipitation
• A discrete climate variable
• Or
• Bounded at zero
• Continuous climate variable (above zero)

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L3MTO Methodology in Application to L3MPO

• To ensure precipitation is bounded at 0,
  regression is one parametric intercept is zero
• Trend is adjusted by changing the intercept if
  the difference between station and Forecast
  Region for the last 10 years is statistically
  significant

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L3MTO Methodology in Application to L3MPO

• Verification of 1994-2005 hind-cast provides
  assessment of the L3MTO methodology goodness for
  L3MPO
• All leads have been used in computation of Heidke
  skill for each forecast target season
• 75 confidence defined cutoff for forecast
  improvement over climatology (HSS4.22)
• Analysis of spatial distribution and overal
  statistic follow

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L3MTO Methodology in Application to L3MPO
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L3MTO Methodology in Application to L3MPO

• In average 24 of tested station indicated an
  improvement of climatology at 75 confidence
  level
• The actual number of such station is great (59)
  if to subtract the station in the area with no
  CPC predictability

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L3MTO Methodology in Application to L3MPO

• About 60 of station in CPC predictability area
  that indicated L3MTO methodology allows L3MPO
  improvement over climatology
• There were in average 11 of stations will good
  expectations for L3MTO methodology to work, but
  no L3MTO improvement
• About 10 of station showed a need for different
  distribution assumption

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Alternatives to L3MTO method

• Several alternatives
• Variable transformation, e.g. sqrt, ln, etc.
• Normal Quantile transformation
• Special Case, zero precipitation amounts, require
  the use of two model forecast systems
• forecast probability of precipitation chance and
• forecast probability of precipitation amount
• This complicated the forecast model significantly

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Alternatives to L3MTO method
Warning To apply a nonlinear transformation we
must ensure a straightforward procedure to
transform the downscaled predictions back to
physical units. For example, log transformation
has a relationship between parameters in
transformed (a,ß) and untransformed (µ,s) domains
(Aitchison and Brown, 1957)
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Alternatives to L3MTO method
Parameters of the linear regression are quantiles
of standard normal distribution
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Summary

• We got reasonable results using L3MTO approach
  for L3MPO
• We feel that the normal quantile transformation
  might improve the forecast model for stations
  with significantly skewed distributions
• This research may be completed by October 2007
  when we test this methods among peers at CDPW

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Summary

• We need to apply the best method for entire
  country Dec 2007
• L3MPO will be designed in the same way as L3MTO
• Internal review can be available as early as
  February 2008
• To implement this experimentally we need to
  incorporate WFO feedback (May 2008)
• To implement operationally we need to incorporate
  customer feedback (August 2008)