Statistical Downscaling Approach

1
Statistical Downscaling Approach its
Application in EMC

• Bo Cui1, Zoltan Toth2, Yuejian Zhu2
• 1SAIC at Environmental Modeling Center, NCEP/NWS
• 2Environmental Modeling Center, NCEP/NWS
• Acknowledgements
• Ken Mitchell, EMC/NCEP
• Manuel Pondeca, EMC/NCEP

2
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 Vector (1-w) prior DV w
(GDAS RTMA)

• four cycles, individual grid point, DV
  Downscaling Vector
• GDAS analysis interpolated to RTMA grids
• regime (not flow) dependent
• choose different weight 0.5, 1, 2, 5, 10

• Downscaling Process

Downscaled Forecast Bias-corrected Forecast
Downscaling Vector

• subtract DV from bias-corrected forecast valid
  at analysis time
• bias-corrected forecast interpolated to RTMA
  grids

3
Downscaling Application Verification

• Experiments
• control 1 operational GEFS ensemble after
  interpolated to RTMA grids
• control 2 NAEFS bias corrected ensemble after
  interpolated to RTMA grids
• 5 downscaled ensembles 0.5, 1, 2, 5, 10
  weights when calculating DV
• Application
• off-line experiments starting from 08/11/2006,
  different decaying weights
• baseline for evaluating other sophisticated flow
  dependent downscaling methods
• Verification
• Domain averaged bias (absolute values)
  comparison before after downscaling
• Accumulated bias are derived from 7 experiments
  against RTMA with 2 weight

Accumulated Bias (1-w) prior accumulated bias
w ( mean forecast RTMA)

• mean forecast from control 1, 2 and 5 downscaled
  ensemble mean, respectively
• Ensemble mean bias comparison before
  after downscaling 00 hr, 24 hr
• Continues Ranked Probability Scores (CRPS)
• Ensemble mean RMSE and ensemble spread
• Downscaling Vector comparison

4
2m Temperature Accumulated Bias Before/After
RTMA Downscaling
1.7
1
2
10
0.2
Black- control 1, operational ensemble mean,
bias range 1.1- 1.7 Red - control 2, NAEFS
bias corrected ensemble mean, bias range
1-1.6 Blue- downscaled bias corrected
ensemble mean, 1, bias range 0.5-0.6 Green-
downscaled bias corrected ensemble mean, 2,
bias range 0.3- 0.5 Yellow- downscaled bias
corrected ensemble mean, 10, bias range 0.2-0.4
5
10m U Wind Accumulated Bias Before/After RTMA
Downscaling
0.7
1
2
10
0.2
Black- control 1, operational ensemble mean,
bias range 0.7-0.85 Red - control 2, NAEFS
bias corrected ensemble mean, bias range
0.6-0.8 Blue- downscaled bias corrected
ensemble mean, 1, bias range 0.4-0.45 Green-
downscaled bias corrected ensemble mean, 2,
bias range 0.3-0.35 Yellow- downscaled bias
corrected ensemble mean, 10, bias range 0.2-0.3
6
10m V Wind Accumulated Bias Before/After RTMA
Downscaling
Black- control 1, operational ensemble mean,
bias range 0.6-0.8 Red - control 2, NAEFS
bias corrected ensemble mean, bias range
0.55-0.65 Blue- downscaled bias corrected
ensemble mean, 1, bias range 0.4-0.5 Green-
downscaled bias corrected ensemble mean, 2,
bias range 0.3-0.4 Yellow- downscaled bias
corrected ensemble mean, 10, bias range 0.2-0.25
7
00hr GEFS Ensemble Mean Bias Before/After
Downscaling 10
2m Temperature
10m U Wind
Before
Before
After
After
8
24hr Ensemble Mean Bias Before/After RTMA
Downscaling 10
Before
Before
After

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

9
24hr Ensemble Mean Bias Before/After RTMA
Downscaling 10
Before
Before
After

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

10
24hr Downscaled Ensemble Bias Comparison 2, 5
10
2
5
10

• Bias corrected downscaled ensemble mean and
  its bias left vs. RTMA T2m
• more bias are reduced for 10 test
• lakes have different bias from surrounding
  areas.
• 10 can eliminate most of the cold bias.
• Downscaling vectors display the similar bias
• over lakes. Which system is doing the poor job
  of
• analysis over lake? GFS analysis or RTMA?

11
GDAS Analysis Downscaling Vector ( 10 )
12
GDAS Analysis Downscaling Vector ( 5 )
13
GDAS Analysis Downscaling Vector ( 2 )
14
2m Temperature Continuous Ranked Probability
Scores (CRPS) Average for 20070212 to 20070305
Before downscaling
After downscaling
15
CRPS 2m Temperature
CRPS 10m U
CRPS 10m V

• Preliminary results
• 2, 5 10 have significant improvements
  compared with raw calibrated fcst. till day 7
• 10 is better than 2 and 5 in short range, 2,
  5 and 10 are close for long range
• Limitation
• small samples, 22 cases
• more samples in short range than long range

16
2m Temperature Ensemble Mean RMSE and Ensemble
Spread Average for 20070212 to 20070305
17
2m Temperature
10m U
10m V

• Preliminary results
• downscaled forecast have reduced RMSE compared
• with raw bias-corrected forecast
• small ensemble spread changes for different
  tests
• distance between RMSE and ensemble spread has a
  decreasing tendency with forecast lead time. The
  ens. mean RMSE and spread curves are becoming
  close for long lead time

18
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.
• RMSE downscaled forecasts have reduced ensemble
  mean RMSE compared with the raw and
  bias-corrected forecasts, 10 - 20 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.

19
Background !!!!!
20
Introduction

• Definition of downscaling for this discussion
  (there are other ways to define)
• Relationship between coarse fine resolution
  geo-science information
• How we create fine resolution info based on
  coarse resolution fields
• In space and/or in time
• Related to finite spatial/temporal resolution
• Not directly related to any numerical model
• Eg, relationship between low and high resolution
  analyses How can we predict hires from low-res?
• Definition of forecast bias correction
• Removal of systematic (time mean) error from
  forecast
• On original forecast grid
• Related to drift of numerical model forecast
• Relationship between bias correction
  downscaling
• They are orthogonal
• Different problems, different methods can (or
  should?) be used
• Benefit from understanding differences between
  forecast bias correction downscaling
• Some studies address both forecast bias
  correction downscaling with same method
• Objectives for downscaling
• Systematic (time mean) errors on fine scale
• Want to eliminate

21
Statistical Post-Processing Issues

• Statistical Downscaling Method
• Regression MOS techniques Bayesian technique
• PDF matching (aka CDF matching)
• Matching cumulative probability density functions
  (frequency of occurrence)
• Neural Networks
• Analog Methods Tom Hamill and Jeff Whitaker
  Self Organizing Maps (SOMs)
• Downscaling Vectors (DV) with decay averaging
  algorithm
• requires an independent hi-res analysis (e.g.
  RTMA applied to GFS forecast)
• derive static DV for past N times subtract
  hi-res anal from low-res fcst valid at anal time
• averaged DV apply decreasing weights to past N
  static DVs (above bullet)
• Canonical Correlation Analysis CCA
• e.g. widely used in CPC (Huug Van den Dool)
• Redundacy Analysis a variant of CCA
• Singular Value Decomposition a variant of CCA
• Bias Correction vs. Downscaling
• Bias Correction remove lead-time dependent bias
  on model grid
• Working on coarser model grid allows use of more
  complex methods
• Feedback on systematic errors to model
  development
• Downscaling downscale bias-corrected forecast to
  finer grid

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Downscaling Some basic preliminariesby Ken
Mitchell

• Definition
• Any method to represent a global or regional
  models atmospheric, oceanic or land analysis or
  forecast at substantially finer resolution than
  the original product
• Common Motivation
• Represent the influence of finer scale topography
• Main Types of Methods
• Dynamical predictive models, with temporal
  evolution
• imbed finer scale predictive model inside parent
  global or regional model
• often the most expensive approach to develop,
  execute and maintain
• Physical no temporal predictive element
• Kinematic includes adjustment of large scale
  wind and pressure field to finer scale topography
• Static usually applied 1-D in vertical, without
  spatial adjustment of wind and pressure field to
  finer terrain
• Statistical analog techniques, neural networks,
  others
• The broadest category, usually requires long
  archive of parent model prediction
• Combination combination of two or more of above
• Prediction Range
• short-range (1-3 days), medium-range (1-15 days),
  sub-seasonal (1-6 weeks) or seasonal to annual
  (1-12 months)

25
Bias Correction Method Application

• Bias Correction Techniques array of methods
• Estimate/correct bias moment by moment (e.g., D.
  Unger et al.).
• Simple approach, implemented partially
• May be less applicable for extreme cases
• Bayesian approach (e.g., Roman Krzysztofovicz)
• Allows simultaneous adjustment of all modes
  considered, under development
• Moment-based method at NCEP apply adaptive
  (Kalman Filter type) algorithm

decaying averaging mean error (1-w) prior
t.m.e w (f a)
For separated cycles, each lead time and
individual grid point, t.m.e time mean error

• Test different decaying weights.
• 0.25, 0.5, 1, 2, 5 and
• 10, respectively
• Decide to use 2 ( 50 days)
• decaying accumulation bias
• estimation

6.6
3.3
1.6
Toth, Z., and Y. Zhu, 2001
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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)
27
24hr Ensemble Mean Forecast Bias Left 2,5
10
2
5
10

• Bias corrected downscaled ensemble mean and its
  bias left vs. RTMA 10m U
• more bias are reduced for weight 10 test

28
24hr Downscaled Ensemble Mean Bias Comparison
2,5 10
2
5
10

• Bias corrected downscaled ensemble mean and
  its bias left vs. RTMA T2m
• more bias are reduced for weight 10 test
• lakes have different bias from surrounding
  areas. 10 can eliminate most of the cold bias.
  Downscaled vectors also display this bias. Which
  system is doing the poor job of t2m analysis over
  lake? The GFS analysis or RTMA?