# Presentation: 098135

##  Statistical Downscaling Approach & its Application  

**Bo Cui****1****, 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

**Notes:**
Bo is 2nd

## 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
lead-time dependent correction, cheap on model grid
Downscaling
enhance “spatial” resolution, not dependent on lead time  
downscaling vector ( large file ) is for each time of day, cheap for transition

- 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
- lead-time dependent correction, cheap on model grid
- Downscaling
- enhance “spatial” resolution, not dependent on lead time
- downscaling vector ( large file ) is for each time of day, cheap for transition

-  Statistical Post-Processing Issues

**Notes:**
First is statistical pp issues

## Goal  
Establish relationship between coarse and fine resolution data 
Assume difference between low & hires analysis is systematic=reproducible
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

**Goal  **
- Establish relationship between coarse and fine resolution data
- Assume difference between low & hires analysis is systematic=reproducible
- 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

**Notes:**
For the bias correction technique    implemented last year

## 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**5km** = (1-*w*) * prior DV**5km** + *w* * (GDAS**5km** – RTMA**5km**)

* **GDAS**5km**: GDAS **1x1** analysis interpolated to RTMA**5km** grids by using copygb command*
* **4 cycles, individual grid point, DV**5km** = Downscaling Vector on 5km grids*
* **choose different weight: 0.5%, 1%, 2%, 5%, 10%*

-   Downscaling Process

-  Downscaled Forecast**5km** = Bias-corrected Forecast**5km** – DV**5km**

- 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

*  **Bias-corrected Forecast**5km: **interpolated to RTMA**5km** grids by using** **copygb  *
* **subtract DV**5km** from bias-corrected forecast**5km** valid at analysis time*

**Notes:**
Here is the detail of downscaling method

## 2m Temperature: RTMA Analysis  

**Notes:**
Rtma anal of 2m temp

## 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**5km** = (1-*w*) * prior DV**5km** + *w* * (GDAS**5km** – RTMA**5km**)

* **GDAS**5km**: GDAS **1x1** analysis interpolated to RTMA**5km** grids by using copygb command*
* **4 cycles, individual grid point, DV**5km** = Downscaling Vector on 5km grids*
* **choose different weight: 0.5%, 1%, 2%, 5%, 10%*

-   Downscaling Process

-  Downscaled Forecast**5km** = Bias-corrected Forecast**5km** – DV**5km**

- 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

*  **Bias-corrected Forecast**5km: **interpolated to RTMA grids by using** **copygb  *
* **subtract DV**5km** from bias-corrected forecast**5km** valid at analysis time*

**Notes:**
Now look at downscaling method:   5x5km ndfd

## 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

**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

**Notes:**
The downscaling application, exp design

## 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%

**Notes:**
In the following will show some results

## 2m Temperature: Accumulated Bias Before/After Downscaling  

- 10%

- 1%

- 2%

- 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

**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%**

**Notes:**
First look at cumulative bias  before/after             zoltan comment

## 10m U Wind: Accumulated Bias Before/After Downscaling  

- 10%

- 2%

- 1%

- 0.2

- 0.7

**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%**

-  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

**Notes:**
Here is another variable   (U)

##  Analysis: 00hr  Ensemble Mean & Bias Before/After Downscaling 10%  

- _  __2m Temperature_

- _  __10m U Wind_

- Before

- After

- Before

- After

**Notes:**
Now we look at how ens mean & bias change

## 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

**Notes:**
Now look at 24hr ens mean/bias

## Fcst: 24hr Ensemble Mean  & Bias Before/After Downscaling 10%

- Before

- Before

- After

**Notes:**
This is the small area plot

## 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_

**Notes:**
Now lets look at continuous ranked prob score

## 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

- _Ensemble Spread_

- _RMSE Before_

- _RMSE After_

**Notes:**
Here is the rmse & ens spread

## 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

- 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

- Summary & Future Plan

**Notes:**
Summary & future                            suru, jeff

## Background !!!!!

**Notes:**
Stop here

##   Bias Before/After Bias Correction ( NCEP NH)

-   Bias Before/After Bias Correction ( NCEP NH)

- _500hPa height_

- _850hPa temperature_

- _Sea level pressure_

- _2m Temperature_

*Before bias correction (1*x*1**)*

*After bias correction (1*x*1)*

- before downscaling (5x5 km)

- after downscaling (5x5 km)

*before bc. (1*x*1**)*

*after bc. (1*x*1)*

## 24hr Downscaled Ensemble Bias Comparison : 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

- 2%

- 5%

- 10%

## GDAS Analysis & Downscaling Vector  ( 10% )

## Fcst: 24hr Ensemble Mean  & Bias Before/After Downscaling 10%

- Before

- After

- Before

-  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

## Fcst: 24hr Ensemble Mean  & Bias Before/After Downscaling 10%

- Before

- After

- Before

-  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

## 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%

- 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 Bias**5km** = (1-*w*) * prior accumulated bias**5km** + *w* * ( mean forecast**5km** – RTMA**5km**)

-  *mean forecast: control 1, 2 and 5 downscaled ensemble mean**5km** , respectively*