# Presentation: 897613

## Young-Kwon Lim, D.W. Shin, S. Cocke, T. E. LaRow, J. J. O’Brien, and E. P. Chassignet Center for Ocean-Atmospheric Prediction Studies, Florida State University, Tallahassee, FL, USA 

**Statistical Downscaling of the NCEP CFS Retrospective forecasts (precipitation) ****over the SE US**

## Background and Motivation

**Global NCEP/CFS : 1) Retrospective forecasts longer than 20 year period (1981-2006), 2) Widely used in many studies, 3) the low seasonal predictive skill (e.g., precipitation for growing season) in certain areas.**
**Question: Can we successfully downscale the CFS data which have 2.5 degree resolution and the low skill over several regions?**

## Why downscaling over the SE USA?

**Extremely high temperature and heavy rainfall**** ****with severe storms during summer, resulting in potential**** ****property damage and injuries.**
**The largest areas of**** ****agricultural farms**** ****in the nation.**
** **
**An accurate**** ****forecast with higher spatial resolution is essential**** ****to adapt management, increase profits, reduce production risks, and mitigate damages.**

## Regional climate simulation in FSU/COAPS

**FSU/COAPS Global Spectral Model**** ****(FSU/COAPS GSM) has been downscaled to the**** ****20km grid**** ****resolution by**** ****FSU/COAPS nested regional spectral model**** ****(FSU/COAPS NRSM) over the southeast US. ******** *****Dynamical Downscaling***

**Statistical downscaling model ****has been also developed. (****CSEOF, multiple regression, and stochastic PC generation**** are used.)**

## Training 

**Training **

**Predictor : model output**

**Predictand : observation**

**&**

**CSEOF analysis**

**Regression**

**Observation**

**NCEP CFS**

**CSEOF PC generation**

**Downscaled data construction**

**(for the prediction period)**

**Regressed eigenfunctions of CFS runs used**

- 0.2° 0.2° (~20km res.)

- 2.5° 2.5° (~250km res.)

**Eigenfunctions of the Obs. over training period and the Generated PC used**

**Prediction period **

**Withholding different year for ****Cross-validation**

- Output

## Data (Obs. & CFS) and period

**Variables : ****Daily precipitation**
** **
**Period : ****1987 ~ 2005 (Spring (MAM) ~ Summer (JJA) each year (daily))**
**Observed data source :**
**      ****National Weather Service Cooperative Observing Program surface data over the southeast US : ~20km×20km**
**Large-scale data to be downscaled :**
**     ****NCEP/CFS retrospecitve forecasts : 2.5°×2.5°, 10 members with lagged initial conditions. Seasonal integrations starting from February each year. **

## Results

**2-d seasonal**** ****mean field (****CFS, Downscaled data, and Observation****)**** **
**Time series ****over ~20 years**** (Interannual variation)**** ****for three states**** (****Tallahassee, Jacksonville, Orlando, Miami, Atlanta, Tifton, Birmingham, and Montgomery****)**
**Error variance and correlations**** **
**Categorical Predictability**** ****for above/below seasonal climatology**
**Extremes: Frequency of ****heavy rainfall events**** per season**
**Extremes: Frequency of ****dry spells**** per season**
**Application**** of downscaled data: ****agricultural model**
**Realtime forecast**** (2008 winter)**

## Biased NCEP/CFS fields (comparison with Obs.)

**CFS**

**Obs.**

**Overestimation (largest: Georgia)**

**MAM**

**JJA**

**East > West**

**Florida is not the wettest region in summer. **

**Problems?**

## Seasonal mean field (before and since 2000)

**Seasonal mean field (before and since 2000)**

**NCEP/CFS**

**Downscaling**

**Observation**

**Little change in rainfall amount**

**Similar regional distribution**
**Rainfall increase**
**Reduction in bias**

## 
Observed variation is better captured by downscaling.
Several poor captures are found (e.g., before 1990, and 94~97).
CFS overestimates the observed variation.
Anomaly time series : CFS data show smaller amplitude variation.

**Black : Observation**
**Red : Downscaling**
**Blue : CFS**

**Observed variation is ****better captured by downscaling****.**
**Several poor captures are found (e.g., before 1990, and 94~97).**
**CFS overestimates**** the observed variation.**
**Anomaly time series : CFS data show smaller amplitude variation.**

**Interannual variation at coarse scale **
**(all area averaged seasonal anomaly)**

## 
Better capture of observed variation since 1999.

Several poor captures in the early period (e.g., before 1990, and 1994).

**Blue : Downscaling**

**Better capture of observed variation since 1999.**
**Several poor captures in the early period (e.g., before 1990, and 1994).**

**Interannual variation at regional scale **
**(seasonal anomaly time series)**

**Florida Pan.**

**Southern****Florida**

**Central Florida**

**NE ****Florida **

**Northern****Alabama **

**Southern****Georgia **

**Northern ****Georgia **

**Southern****Alabama **

## 
Localized seasonal forecast with a slight increase in Corr.

Reduction in Relative error variance (REV) (≈ 2  0.6~1.4)

**Error variance and Seasonal Anomaly Correlation**

**Localized seasonal forecast with a slight increase in Corr.**
** **
**Reduction in Relative error variance (REV) (≈ 2 ******** 0.6~1.4)**
**     **

**REV**

**Corr.**

**Corr. (0.3~0.4)**

**Corr. (0.4~0.6)**

**REV > ****2.0**

**REV < 1**

## Categorical predictability (HSS) for 

**Categorical predictability (HSS) for **
**Seasonal anomaly**

**Downscaling**

**Rescaling (OA) from the CFS with bias-correction**

**CFS**

**Downscaling: Positive on most grid points (0~0.5)**
**Skill in overall: Downscaling > CFS and Rescaling (OA)**
**     **

**0.2~0.45**

**0.1~0.2**

**0.0~0.1**

## 
Observed variation is captured reasonably by downscaling.
Several poor captures are found in early period (before 1995).
Rescaling overestimates the observed variation.

**Red : Downscaling**
**Blue : Rescaling from the CFS**

**Observed variation is captured reasonably by downscaling.**
**Several poor captures are found in early period (before 1995).**
**Rescaling overestimates the observed variation.**

**Extremes (Frequency of daily heavy rainfall events)**

**Threshold : exceeds 1 std. + climatology**

## Categorical predictability (HSS) for 

**Categorical predictability (HSS) for **
**the frequency of rainfall extremes**

**Downscaling**

**Difference (Down. - Rescaling)**

**Rescaling (OA) from the CFS**

**Downscaling:**
**    ****Florida and S. Georgia : > 0.1,  Alabama and C. Georgia : -0.1 ~ 0.2, **
**Rescaling: -0.2 ~ 0.2 **
**     **

**1 std. + climatology**

**0.1~0.5**

**-0.2 ~ 0.1**

**≥****0.1**

## 
Downscaled data are closer to the observation.

Rescaled data have serious underestimation problem with little amplitude fluctuation.

**Red : Downscaling**
**Blue : Rescaling from the CFS**

**Downscaled data are closer to the observation.**
**Rescaled data have serious underestimation problem with little amplitude fluctuation.**

**Extremes (Frequency of Subseasonal dry spells)**

**Threshold : a week average < 0.1mm/day**

## Categorical predictability (HSS) for 

**the frequency of dry spells**

**HSS (Downscaling)**

**Downscaling:**
**     ****Better prediction in Georgia and Alabama than Florida : -0.1 ~ 0.4, **
**Rescaling: no skill in terms of HSS. ****    **

**Threshold : a week < 0.1mm/day**

**0.0~0.4**

## Application example: Downscaled atmospheric data to the crop model 

- Maize Yields

- Precipitation

**Tifton (GA) Crop Yields and Precipitation**

- Red (CFS) Black (Observed) Green (Bias-corrected downscaled CFS)‏

## CFS

**Application example: Realtime seasonal forecasts (2008 winter) **

**CFS**

**Downscaling**

## Concluding remarks

**Precipitation for growing season ****from NCEP/CFS (~2.5****° res.) run have been**** ****downscaled to local scale of ~20km for the SE US.**
**Downscaling**** simulates the regional-scale seasonal precipitation with reduction in wet biases****.**
**Correlation, categorical predictability**** for seasonal anomaly ****has been improved**** from the coarsely resolved NCEP/CFS.**
**Heavy rainfall events: ****In overall, downscaling**** better produces the interannual frequency variation**** than bias-corrected rescaling. **
**Subseasonal dry spells:**** Rescaled data show significant underestimation with much smaller amplitude variation than observation.**
**Application**** to crop model and realtime forecast.**

## Statistical downscaling procedure (1)

**1. Cyclostationary EOF analysis for the model output and the observation :**
-    **CSEOF (Kim and North 1997) : analysis technique for extracting ****the spatio-temporal evolution of physical modes (e.g., seasonal cycle, ENSO, ISOs, etc.) and their long-term amplitude variations.**** **
-                                ***P*****(*****r*****,*****t*****)=∑*****n***** *****S******n*****(*****t*****) *****B******n*****(*****r*****,*****t*****)**
***    ******B******n*****(*****r*****,*****t*****) : time-dependent eigenfunctions, *****S******n*****(*****t*****) : PC time series.**
**    **
**    ****In this study, CSEOF is conducted on both observation and FSUGSM runs over the training period.**

## Statistical downscaling procedure (2)

**2. Multiple regression between the model output and the observation :**
**    ****CSFOF PC time series of the first significant modes of ****a predictor variable (FSUGSM data) are regressed onto a certain PC time series of the target variable (observation)**** in the training period.**
***                                ******PCT******n*****(*****t*****)=∑*****i******α******n******i*****·*****PCP******i*****(*****t*****)+*****ε*****(*****t*****)     *****i*****=1,2,...10**
***    ******PCT******n*****(*****t*****): target PC time series, *****α******n******i*****: regression coefficient**
***    ******PCP******i*****(*****t*****): predictor PC time series**
**    ****Relationship between model output and the observation is extracted from CSEOF and multiple regression.**** **

## Result of multiple regression

-     **PC time series**

-     **Eigenfunction (****from Observation**)

-     ***Regressed***** Eigenfunction (****model****)**

-                   **Both are physically consistent.**

-     **(training period)**

**?**

-     **forecast period**

## Result of multiple regression

-     **Eigenfunction (****from Observation**)

-     ***Regressed***** Eigenfunction (****model****)**

## Statistical downscaling procedure (3)

**3. Generating CSEOF PC of the model data over the forecast period from the regressed fields in the training :**
**    ****CSFOF PC time series of the model data are generated for the prediction period. ****Modeled data and the regressed eigenfunctions identified from training are used****.**
***                                 ******PC******n*****(*****t*****)=∑*****g******P*****(*****g*****,*****t*****)·*****B******n*****+****(*****g*****,*****t*****)**
***    ******PC******n*****(*****t*****): the *****n*****th mode PC time series for the prediction period**
**    *****g***** : large-scale grid point**
***    ******B******n*****+****(*****g*****,*****t*****) : regressed CSEOF eigenfunctions**
***    ******P*****(*****g*****,*****t*****): global model anomaly over the prediction period**

## Statistical downscaling procedure (4)

**4. Downscaled data construction from the eigenfunctions of the observation and the generated CSEOF PC time series :**
**            *****                        ******D*****(*****s*****,*****t*****)=∑*****n******PC******n*****(*****t*****)·*****B******n*****o****(*****s*****,*****t*****)**
***  ******	******PC******n*****(*****t*****) : generated PC time series from the previous step**
***	******B******n*****o****(*****s*****,*****t*****): CSEOF eigenfunctions of the observation (training ****	****     period)**
***    ******D*****(*****s*****,*****t*****) : downscaled output**
**5. Generating downscaled output for the entire period (9yrs) by cross-validation framework **

## 
Observed variation is captured by downscaling to a certain extent.
Several peaks are not captured well (e.g., 1998 in Florida).
Rescaled data with bias-correction oscillates near zero (significant underestimation).

**Red : Downscaling**
**Blue : Rescaling from the CFS**

**Observed variation is captured by downscaling to a certain extent.**
**Several peaks are not captured well (e.g., 1998 in Florida).**
**Rescaled data with bias-correction oscillates near zero (significant underestimation).**

**Extremes (Frequency of Subseasonal dry spells (anomaly))**

**Threshold : a week average < 0.1mm/day**