DOWNSCALING

1
DOWNSCALING

• Bo Cui , Yuejian Zhu, Zoltan Toth
• Environmental Modeling Center
• NOAA/NWS/NCEP
• Ackn.
• Steve Lord, Geoff DiMego, Ken Mitchell
• http//wwwt.emc.ncep.noaa.gov/gmb/ens/index.html
  

2
FORECASTING, BIAS CORRECTION, DOWNSCALING

• Forecasting
• Projection (extrapolation) of events in time into
  the future
• Assessed by measures of statistical resolution
• Numerical modeling techniques dominate
• Model drift causes lead-time dependent
  systematic error (forecast bias)
• Statistical bias correction possible
• Finite resolution in time, space, variables due
  to limited computational resources
• Increasing resolution has limited return in
  statistical resolution
• Downscaling possible
• Statistical bias correction in numerical modeling
• Estimate/eliminate lead-time dependent systematic
  error from forecasts
• Primary choice is improving numerical model
• Make forecasts statistically look like initial
  (analyzed) fields
• Improved statistical reliability
• Feedback to numerical modeling
• Downscaling
• Projection (interpolation) of coarse resolution
  info onto finer scales
• Needed due to computational resource limitations
• Interpolation in

3
FORECASTING, BIAS CORRECTION, DOWNSCALING - 2

• Example Global forecast integration out to 16
  days on 1x1 degree grid
• Forecast part is done
• Resolution cannot be improved via statistical
  post-processing etc
• Fidelity (statistical resolution) can be
  improved by either
• Bias correction of eg 10-day forecast on model
  grid
• Make 1x1 degree forecast look like 1x1 degree
  analysis
• Downscaling
• Make 1x1 degree analysis (or bias-free fcst) look
  like 5x5 km analysis
• Relationship between bias correction and
  downscaling
• Common
• Both intend to improve statistical reliability
• Difference
• Lead-time dependent correction
• Bias correction
• Enhanced spatial resolution
• Downscaling
• Joint/mixed application
• Often two goals addressed with same algorithm
• Potential benefits if treated separately

4
DOWNSCALING

• Goal
• Establish relationship between coarse and fine
  resolution data
• Assume difference between low hires analysis is
  systematicreproducible
• Entire difference is deterministic
• Hires numerical model could capture difference
• Performance objectives
• Systematic error reduced enhanced statistical
  reliability
• Random errors not increased maintained
  statistical resolution
• Approaches/methods with various levels of
  sophistication
• Climatological downscaling
• Eg, difference in climate mean low hires
  analysis fields
• Smart Init effect of topography, etc (any
  case dependent adjustments?)
• Regime dependent
• Eg, time mean difference in recent low hires
  analysis fields
• Bo Cui, decaying averaging difference
• Gridded MOS, Analog approaches, etc
• Case dependent
• Physics considered (INFORM) simplified
  numerical models
• Hybrid ensemble (Jun Du others), dual
  resolution 3/4DVAR or ens-DA

5
CHARACTERISTICS OF RELIABILITY RESOLUTION

• Reliability
• Related to form of forecast, not forecast content
• Fidelity of forecast
• Reproduce nature when resolution is perfect,
  forecast looks like nature
• Not related to time sequence of forecast/observed
  systems
• How to improve?
• Make model more realistic
• Also expected to improve resolution
• Statistical bias correction Can be statistically
  imposed at one time level
• If both natural forecast systems are stationary
  in time
• If there is a large enough set of
  observed-forecast pairs
• Link with verification
• Replace forecast with corresponding fdo
• Resolution
• Related to inherent predictive value of forecast
  system
• Not related to form of forecasts
• Statistical consistency at one time level
  (reliability) is irrelevant
• How to improve?

6
STATISTICAL RELIABILITY TEMPORAL AGGREGATE
STATISTICAL CONSISTENCY OF FORECASTS WITH
OBSERVATIONS

• BACKGROUND
• Consider particular forecast class Fa
• Consider frequency distribution of observations
  that follow forecasts Fa - fdoa
• DEFINITION
• If forecast Fa has the exact same form as fdoa,
  for all forecast classes,
• the forecast system is statistically consistent
  with observations gt
• The forecast system is perfectly reliable
• MEASURES OF RELIABILITY
• Based on different ways of comparing Fa and fdoa

7
STATISTICAL RESOLUTION TEMPORAL EVOLUTION
ABILITY TO DISTINGUISH, AHEAD OF TIME, AMONG
DIFFERENT OUTCOMES

• BACKGROUND
• Assume observed events are classified into finite
  number of classes, like Oa
• DEFINITION
• If all observed classes (Oa, Ob,) are preceded
  by
• Distinctly different forecasts (Fa, Fb,)
• The forecast system resolves the problem gt
• The forecast system has perfect resolution
• MEASURES OF RESOLUTION
• Based on degree of separation of fdos that
  follow various forecast classes
• Measured by difference between fdos climate
  distribution
• Measures differ by how differences between
  distributions are quantified

FORECASTS
OBSERVATIONS
EXAMPLES
8
FORECAST SYSTEM ATTRIBUTES

• Abstract concept (like length)
• Reliability and Resolution
• Both can be measured through different statistics
• Statistical property
• Interpreted for large set of forecasts
• Describe behavior of forecast system, not a
  single forecast
• For their definition, assume that
• Forecasts
• Can be of any format
• Single value, ensemble, categorical,
  probabilistic, etc
• Take a finite number of different classes Fa
• Observations
• Can also be grouped into finite number of
  classes like Oa

9
CHARACTERISTICS OF FORECAST SYSTEM ATTRIBUTES

• RELIABILITY AND RESOLUTION ARE
• General forecast attributes
• Valid for any forecast format (single,
  categorical, probabilistic, etc)
• Independent attributes
• For example
• Climate pdf forecast is perfectly reliable, yet
  has no resolution
• Reversed rain / no-rain forecast can have perfect
  resolution and no reliability
• To separate them, they must be measured according
  to general definition
• If measured according to traditional definition
• Reliability resolution can be mixed
• Function of forecast quality
• There is no other relevant forecast attribute
• Perfect reliability and perfect resolution
  perfect forecast system
• Deterministic forecast system that is always
  correct
• Both needed for utility of forecast systems