Statistical Downscaling Approach

1
Statistical Downscaling Approach its
Application

• Bo Cui1, Zoltan Toth , Yuejian Zhu
• Environmental Modeling Center, NCEP/NWS
• 1SAIC at Environmental Modeling Center, NCEP/NWS
• Acknowledgements
• Steve Lord, Geoff DiMego, Ken Mitchell, Manuel
  Pondeca

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
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 (1-w) prior DV5km
w (GDAS5km RTMA5km)

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

• Downscaling Process

Downscaled Forecast5km Bias-corrected
Forecast5km DV5km

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

5
2m Temperature RTMA Analysis
6
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 (1-w) prior DV5km
w (GDAS5km RTMA5km)

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

• Downscaling Process

Downscaled Forecast5km Bias-corrected
Forecast5km DV5km

• Bias-corrected Forecast5km interpolated to
  RTMA grids by using copygb
• subtract DV5km from bias-corrected forecast5km
  valid at analysis time

7
Downscaling Application

• Experiment design
• control 1 interpolated operational GEFS ensemble
  (using copygb)
• control 2 interpolated NAEFS bias corrected
  ensemble (using copygb)
• 5 downscaled ensembles 0.5, 1, 2, 5, 10
  weights when calculating DV5km
• Application period
• 08/11/2006 current, off-line experiments
• Verification
• Evaluation before and after downscaling
• Metrics bias, continuous ranked probability
  score (CRPS), RMSE, etc.
• Issues addressed
• Effect of downscaling
• on different variables 2m temperature, 10m U V
• on lead time forecasts, including
• on low resolution analysis
• Effect of different weighting

8
Summary of Downscaling Application

• Result examination
• Maps comparison for bias (before and after)
• domain averaged bias (absolute values)
• ensemble mean forecast bias at 00 hr and 24 hr
• predict high res analysis based on low res
  analysis
• Statistics for
• continuous ranked probability score (CRPS)
• RMSE and ensemble spread
• Downscaling Vector comparison
• Conclusions
• Bias reduced (up for 70)
• RMS errors improved by 10-25
• Probabilistic forecast
• Improved for all lead time by 10-30

9
2m Temperature Accumulated Bias Before/After
Downscaling

• Domain average bias on fine grid
• bias range comparison
• control 1 1.1- 1.7
• control 2 1-1.6
• 1 0.5-0.6
• 2 0.3- 0.5
• 10 0.2-0.4
• downscaling can effectively reduce systematic
  forecast errors on fine grid
• 10 weighting has the best performance, 70
  of systematic errors are reduced
• 00 hr bias comparison create fine res
  information based on coarse res fields.
  Possibility to predict high res analysis from
  low-res analysis

1
2
10
Black- control 1, operational ensemble mean
Red - control 2, NAEFS bias corrected ensemble
mean Blue- downscaled bias corrected
ensemble mean, 1 Green- downscaled bias
corrected ensemble mean, 2 Yellow- downscaled
bias corrected ensemble mean, 10
10
10m U Wind Accumulated Bias Before/After
Downscaling

• bias range comparison
• control 1 0.7-0.85
• control 2 0.6-0.8
• 1 0.4-0.45
• 2 0.3-0.35
• 10 0.2-0.3
• 10 weighting has the best performance

0.7
1
2
10
0.2
Black- control 1, operational ensemble mean
Red - control 2, NAEFS bias corrected ensemble
mean Blue- downscaled bias corrected
ensemble mean, 1 Green- downscaled bias
corrected ensemble mean, 2 Yellow- downscaled
bias corrected ensemble mean, 10
11
Analysis 00hr Ensemble Mean Bias
Before/After Downscaling 10
2m Temperature
10m U Wind
Before
Before
After
After
12
Fcst 24hr Ensemble Mean Bias Before/After
Downscaling 10
Before
Before
After

• Left top operational ens. mean and its bias wrt
  RTMA
• Right top bias corrected ens. mean and its bias
  wrt RTMA
• Left bottom bias corrected downscaled ( 10 )
  ens. mean and its bias wrt RTMA
• After Downscaling
• Bias reduced, especially high topography areas
• More detailed forecast information

13
Fcst 24hr Ensemble Mean Bias Before/After
Downscaling 10
Before
Before
After
14
2m Temperature Continuous Ranked Probability
Score (CRPS) Average for 20070212 to 20070404

• Preliminary results
• Downscaled bias-corrected ensemble forecasts
  have significant improvements compared with raw
  calibrated forecast for all lead time
• 10 weighting is better than 2 and 5 weighting
  in short range. 30 improvement with 10
  weighting for d0-d4. The 2, 5 and 10 weighting
  curves are close for long range. Will add more
  high weights for comparison.
• Limitation
• small samples
• more samples needed

Before downscaling
After downscaling
15
2m Temperature Ensemble Mean RMSE and Ensemble
Spread Average for 20070212 to 20070404

• Preliminary results
• RMSE downscaled forecasts have reduced ensemble
  mean RMSE compared with the raw and
  bias-corrected forecasts
• 10 - 25 of RMS errors reduced
• the space between RMSE and spread decrease with
  forecast lead time

RMSE Before

RMSE After
Ensemble Spread
16
Summary Future Plan

• Summary
• systematic (time mean) error downscaling method
  with decaying averaging algorithm can effectively
  reduce systematic forecast errors. The 10 weight
  has the best performance, 70 of T2m, 10m U and
  V wind systematic errors are reduced
• more detailed forecast information available in
  the downscaled forecast
• CRPS show that the downscaled bias-corrected
  ensemble forecasts have been improved compared
  with the raw and bias corrected ensembles, 30
• RMSE downscaled forecasts have reduced ensemble
  mean RMSE compared with the raw and
  bias-corrected forecasts, 10 - 30 of RMS
  errors reduced
• Future Plan
• more weight factor tests choosing 20 and do
  comparison with 10
• study on systematic and random error components,
  respectively
• add downscaled 10-50-90 percentile forecast
  values for selected variables
• downscaled method scheduled to be implemented
  later in 2007
• combine high res control ensemble (hybrid
  idea, case dependent downscaling , Jun Du
  others)
• NAM/SERF application

17
Background !!!!!
18
Bias Before/After Bias Correction ( NCEP NH)
500hPa height
850hPa temperature
Before bias correction (1x1)
After bias correction (1x1)
2m Temperature
Sea level pressure
before downscaling (5x5 km)
after downscaling (5x5 km)
before bc. (1x1)
after bc. (1x1)
19
24hr Downscaled Ensemble Bias Comparison 2, 5
10
2
5
10

• Bias corrected downscaled ensemble mean and
  its bias left wrt RTMA T2m
• more bias are reduced with 10 weighting
• lakes have different bias from surrounding
  areas, 10 weighting can eliminate some of the
  cold bias

20
GDAS Analysis Downscaling Vector ( 10 )
21
Fcst 24hr Ensemble Mean Bias Before/After
Downscaling 10
Before
Before
After

• Left top operational ens. mean and its bias wrt
  RTMA
• Right top bias corrected ens. mean and its bias
  wrt RTMA
• Left bottom bias corrected downscaled ( 10 )
  ens. mean and its bias wrt RTMA
• After Downscaling
• Bias reduced, especially high topography areas
• More detailed forecast information

22
Fcst 24hr Ensemble Mean Bias Before/After
Downscaling 10
Before
Before
After

• Left top operational ens. mean and its bias wrt
  RTMA
• Right top bias corrected ens. mean and its bias
  wrt RTMA
• Left bottom bias corrected downscaled ( 10 )
  ens. mean and its bias wrt RTMA
• After Downscaling
• Bias reduced, especially high topography areas
• More detailed forecast information

23
Downscaling Application Verification
Experiments

• Experiment design
• control 1 interpolated operational GEFS ensemble
  (using copygb)
• control 2 interpolated NAEFS bias corrected
  ensemble (using copygb)
• 5 downscaled ensembles 0.5, 1, 2, 5, 10
  weights when calculating DV5km
• Application period
• 08/11/2006 current, off-line experiments
• Verification experiment design
• Purpose
• evaluation before and after downscaling
• Approach
• accumulated bias calculation, derived from 7
  experiments wrt RTMA 2

Accumulated Bias5km (1-w) prior accumulated
bias5km w ( mean forecast5km RTMA5km)

• mean forecast control 1, 2 and 5 downscaled
  ensemble mean5km , respectively