# Presentation: 797792

## Assessing the skill of an all-season statistical forecast model of the Madden-Julian Oscillation

**Xian-an Jiang, Duane E. Waliser**
*Jet Propulsion Laboratory/California Institute of Technology, Pasadena, CA*
**Matthew C. Wheeler**
*Bureau of Meteorology Research Centre, Melbourne,* *Australia*
**Charles Jones**
*Institute for Computational Earth System Science, UCSB, CA*
**Myong-In Lee, and Siegfried D. Schubert**
*Global Model and Assimilation Office**, **NASA/GSFC, MD*

## Motivation:

- Provide a more realistic benchmark for numerical forecast models;
- Provide assessment of a statistical model for the *real-time* forecast of the MJO;
- ...see next page

**Why Subseasonal Variability / Madden-Julian Oscillation?**

**Why empirical model?**

**Why current study (****real-time scheme; Wheeler and Hendon 2004)****?**

**Dynamical models**: skill only up to lead times of about **7-10** days.

**Empirical models****:** **15** days (rainfall/OLR), **20-25** days for dynamical fields.

-  (e.g., von Storch and Xu,1990; Waliser et al.,1999; Lo and Hendon, 2000; Jones et al., 2004; Wheeler and Weickmann, 2001; Mo, 2001; and others)

***Time-filtering***

**Weather**
**(~days)**

**Interannual**
**(~seasons)**

**Subseasonal (~weeks)**

***Real-time application***

**?**

-  (e.g., Waliser et al.,1999, 2004; Hendon et al.,2000; Jones et al, 2000; Seo et al, 2005; and others.)

## Hybrid Forecast: Empirical + Dynamical

- Provide a near-term means to improve extended-range predictions;
- Motivate the need to improve intrinsic capability in MJO prediction in the dynamical models.

_**Motivation (cont’d)**_

## MJO Index

- (15oS-15oN ; Wheeler and Hendon 2004)

_**MJO Index**_

**NCEP-DOE2 Reanalysis **
**Daily, 1983-2004**

**Annual cycle removed;**
**Interannual variability (ENSO) removed:**
**Regression pattern of each variable against the PC of SST rotated EOF1 (ENSO);**
**120-day mean of previous 120 days.**

- EOF 1 (11%)

- EOF 2 (10%)

**Model construction (I)**

## Time series of Combined EOF

- Combined Amplitude

_**Time series of Combined EOF**_

- PC1

- PC2

**Model construction (II)**

**Strong MJO**

**Weak MJO**

## Lagged regression Model

- Seasonal dependent

_**Lagged regression Model**_

- Variable A at particular grid point at forecast lead ndt: *A(x,y,p,t**0**+ndt)*

**KEY: How to get ***PC**1**(t**0**)*** and ***PC**2**(t**0**)*** (the real-time MJO index)? **

- Time at forecast point: *t**0*

***A(x,y,p,t******0******+ndt) ******= ******reg******1******(x,y,p,ndt) ******× ******PC******1******(t******0******)  +  ******reg******2******(x,y,p,ndt) ******× ******PC******2******(t******0******)***

*reg**1**(x,y,p,ndt) **and** **reg**2**(x,y,p,ndt):*

**Model construction (III)**

## Real-time forecast flow chart

**u850,u200**

***PC******1******(t******0******), PC******2******(t******0******)***

**Lag Regression Forecast Model**

***A(x,y,p,t******0******+ndt)***

**SST**

**SST’**

**PC****sst**

**Project to SST EOF1**

**Remove**

**annual cycle**

**Remove**

**annual cycle**

**Regression pattern to PC****sst**** based on historical dataset**

**Remove previous 120-day mean**

**OLR’, **
**u850’,u200’**

**OLR’*, **
**u850’*,u200’***

**Project to CEOF 1 & 2**

**Lag Regression pattern for each variable against PC1 & 2 based on historical dataset**

***A: u, v, t, q & OLR, SLP.***

**IAV of OLR, **
**u850,u200**

_**Real-time forecast flow chart**_

*reg**1**(x,y,p,ndt),** **reg**2**(x,y,p,ndt)*

- Real-time Observations at t0

**Remove IAV**

## Cross-validation:

**1983**

**1984  1985  1986  ...... ****...... ......**** 2002 2003  2004**

- Construct lag-regression coefficients

- Forecast/validation

**1983**

**1985  1986 ****...... ...... ......**** 2002 2003  2004**

**1984**

**2004**

**1983 1984 1985 ......  2001 2002**

**2003**

**1983 1984 1985   ......   2001 2002 2003**

**2004**

**......****..**

**Forecast starting date: 1****st****, 6****th****, 11****th****, 16****th****, 21****st****, and 26****th**** of each month.**
**Summer****: Forecasts with the starting date during ****Jun, Jul, Aug****.**
**Winter****:  ****Nov, Dec and Jan****.**

**1**

**2**

**21**

**22**

**...****..**

## Predictive Skills

_**Predictive Skills**_

**OLR**

- Pattern correlation (Forecast vs EOF filtered Observations)
- (30oS-30oN, global longitudes)

- 0.36

- 0.19

## Temporal Correlation (against EOF filtered OBS)

**OLR**

**5d**

**10d**

**15d**

**20d**

## Pattern Correlation (against unfiltered OBS anomalies)

## 850mb u-wind

- OLR

- Correlation (vs. unfiltered OBS)

**5d**

**10d**

**15d**

**20d**

- Winter

## 200mb u-wind

- Correlation (vs. unfiltered OBS)

**5d**

**10d**

**15d**

**20d**

- Winter

## Sensitivity Tests (I)

_**Sensitivity Tests (I)**_

- Advantage by using seasonal-dependent regression coefficients

## Sensitivity Tests (II)

- Including more PCs in the regression model

- 2PCs

- 5PCs

- Winter

- Summer

_**Sensitivity Tests (II)**_

## Sensitivity Tests (III)

- More lagged information in the regression model

_**Sensitivity Tests (III)**_

## Sensitivity Tests (V)

- Impact of MJO status at the initial forecast time

_**Sensitivity Tests (V)**_

**Strong MJO (172)**

**Weak MJO (115)**

**Total: 396**

**OLR**

## Correlation vs unfiltered OBS at 20d

- Ctrl_exp

- Strong MJO

**OLR**

**u850**

**u200**

**Winter**

## OLR (15oS-15oN)

- Nov/03

- Dec/03

- Jan/04

- Feb/04

- Mar/04

- May/04

- Apr/04

- Jun/04

**Obs**

**5d**

**10d**

**15d**

**OLR (15****o****S-15****o****N)**

_**Hindcast ’03~’04 Winter**_

## Conclusions

- The current real-time forecast model exhibits useful extended-range skill for real-time MJO forecast with correlation skill of 0.3 (0.5) between predicted and observed unfiltered (EOF-filtered) fields at a lead time of 15d.
- The predictive skill is increased significantly when there are strong MJO signals at the initial forecast time.
- Predictive skill for the upper-tropospheric winds is relatively higher than for the low-level winds and convection signals.

- Bureau of Meteorology Research Centre, Australia
- http://www.bom.gov.au/bmrc/clfor/cfstaff/matw/maproom/rmm