Statistical Downscaling Approach

1
Statistical Downscaling Approach its
Application

• Bo Cui1, Zoltan Toth2, Yuejian Zhu2
• Stéphane Beauregard3, David Unger4 , Richard
  Wobus1
• 1SAIC at Environmental Modeling Center, NCEP/NWS
• 2Environmental Modeling Center, NCEP/NWS
• 3Canadian Meteorological Centre, Meteorological
  Service of Canada
• 4Climate Prediction Center, NCEP/NWS
• Acknowledgements
• Richard Verret, Poulin Lewis CMC/MSC
• Dingchen Hou EMC/NCEP/NWS/NOAA
• David Michaud, Brent Gorden, Luke Lin
  NCO/NCEP/NWS/NOAA
• Valery J. Dagostaro MDL/NWS/NOAA

2
Statistical Post-Processing Issues

• Goal
• Improve reliability while maintaining resolution
  in NWP forecasts
• Reduce systematic errors (improve reliability)
  while
• Not increasing random errors (maintaining
  resolution)
• Retain all useful information in NWP forecast
• No variation added on finer scales (spatial,
  temporal and across variables covariance)
• Approach
• Bias Correction estimate/eliminate lead-time
  dependent bias on model grid
• Working on coarser model grid
• Feedback on systematic errors to model
  development
• Downscaling project ( interpolate ) coarse
  resolution info onto finer grid
• Needed due to computational resource limitations
• Interpolation in space, time, across variables
• Not directly related to numerical models
• Relationship 2-step processing
• Common
• Both intend to improve statistical reliability
• Difference
• Bias correction

3
Downscaling

• Goal
• Establish relationship between coarse and fine
  resolution data
• Assume difference between low hires analysis is
  systematicreproducible
• Not dependent on lead time
• Downscaling approaches
• Climatological downscaling
• Eg, difference in climate mean low hires
  analysis fields
• Regime dependent
• Eg, time mean difference in recent low hires
  analysis fields
• Bo Cui, decaying averaging difference
• Gridded MOS, Analog approaches, etc
• Case dependent
• Hybrid ensemble (Jun Du others), dual
  resolution 3/4DVAR or ens-DA
• Compare high-low res control forecasts
• Adjust all ensemble members by difference
• Physics considered (INFORM) simplified
  numerical models
• One-way coupled LAM integrations most costly

4
Statistical downscaling for NAEFS forecast

• Proxy for truth
• RTMA at 5km resolution
• Variables (surface pressure, 2-m temperature, and
  10-meter wind)
• Downscaling vector
• Interpolate GDAS analysis to 5km resolution
• Compare difference between interpolated GDAS and
  RTMA
• Apply decaying weight to accumulate this
  difference downscaling vector
• Downscaled forecast
• Interpolate bias corrected 11 degree NAEFS to
  5km resolution
• Add the downscaling vector to interpolated NAEFS
  forecast
• Application
• Ensemble mean, mode, 10, 50(median) and 90
  forecasts

5
Downscaling Method with Decaying Averaging
Algorithm

• True high resolution analysis
• Operational North American Real-Time Mesoscale
  Analysis (RTMA)
• 5x5 km National Digital Forecast Database (NDFD)
  grid (e.g. G. DiMego et al.)
• 4 variables available surface pressure, T2m, 10m
  U and V
• Other data can also be used
• Downscaling method apply decaying averaging
  algorithm

Downscaling Vector5km (t0) (1-w) prior
DV5km (t-1) w (GDAS5km(t 0) RTMA5km(t0))

• GDAS5km GDAS 1x1 analysis interpolated to
  RTMA5km grids by bilinear interpolation
• 4 cycles, individual grid point, DV5km
  Downscaling Vector on 5km grids
• choose different weight 0.5, 1, 2, 5, 10

• Downscaling Process

Downscaled Forecast5km(t) Bias-corrected
Forecast5km(t) DV5km (t0)

• Bias-corrected Forecast5km interpolated to
  RTMA5km grids by bilinear interpolation
• subtract DV5km from bias-corrected forecast5km
  valid at analysis time

6
GEFS bias-corr. down scaling fcst.
GEFS raw forecast
12hr 2m T forecast Mean Absolute Error w.r.t
RTMA for CONUS Average for September
NAEFS forecast
7
NCEP/GEFS raw forecast
4 days gain from NAEFS
NAEFS final products
From Bias correction (NCEP, CMC) Dual-resolution
(NCEP only) Down-scaling (NCEP,
CMC) Combination of NCEP and CMC
8
NCEP/GEFS raw forecast
8 days gain
NAEFS final products
From Bias correction (NCEP, CMC) Dual-resolution
(NCEP only) Down-scaling (NCEP,
CMC) Combination of NCEP and CMC
9
Summary and Future Plan

• Downscaling NAEFS products has been implemented
  in NCEP by
• December 4th 2007 1200UTC
• CONUS only
• 4 variables only
• Surface pressure, 2m temperature and 10m u and v
• Downscaling NAEFS products
• Reduced mean absolute errors (by 4 days)
• Improved probabilistic skills (by 8 days)
• This method could apply to SREF, too.
• Apply statistical downscaling method to other
  regions, Alaska, Hawaii, Puerto Rico and Guam,
  when RTMA is available
• Needed in support of Alaska Desk, etc
• Following after RTMA implementation
• Add new variables to NDFD grids, such as wind
  speed/direction, maximum/minimum temperature,
  2-meter dew point temperature etc
• Enhance products by
• Improvements to RTMA
• Bias correction of forecast first guess using
  recursive algorithm
• Under testing