# Presentation: 424691

## Introduction

- The Climate Forecasting System (CFS) ensemble (Wang et al., 2005) is a seasonal forecast system based on the NCEP global model (GFS) and the GFDL ocean model (MOM3).  The CFS ensemble uses the “lagged-average” method for generating ensemble members.  For this study, we will only consider the problem of how to dynamically weight the CFS ensemble for the problem of forecasting NINO 3.4 SSTs (5S-5N, 120W-170W).
- For many ensembles, one has little information about the quality of individual ensemble members so one has to weight them equally when trying to get the single best forecast.  However, the problem of forecasting NINO 3.4 is different as we can use statistical methods to get an idea about the quality of individual ensemble members and consequently derive weights for each member.
- Theory
- Schematically we can draw the the PDF of the 1-month forecast (lead 0) from CFS ensemble as the black line (Fig. 1).  If we have a better forecast for lead 0 (perhaps a combination of statistical and dynamical methods), we would have a different PDF (red line).  We want to weight the ensemble so that it resembles the red PDF.  One can easily show that the appropriate weighting of the ensemble members changes from 1/N to PDFNEW/(N•PDFCFS).   Assuming a perfect model, the weights calculated for the lead-0 forecast can be used for longer leads (t=n).
- Since it's impossible to calculate the PDF, need to make assumptions about the PDF; i.e.,
- 		PDFCFS(x) = PCFS(x') Q(x*)
- 		PDFNEW(x) = PNEW(x') Q(x*)
- 		x= state vector
- 		x' = NINO 3.4 index, for example
- 		x* = x - x'
- 		note, P is proportional to the probability forecast of NINO 3.4
- After making the above assumption, the ensemble weighting is just the ratio of the CFS and new probability forecasts of NINO 3.4 (with a factor of 1/N).
- Details
- Need a better forecast of NINO 3.4 to calculate PDFNEW
- 	take better of persistence and extrapolation of NINO 3.4 anomaly
- 		(simple is better for preliminary studies)
- 	convert to a probability forecast by assuming Gaussian and the mean is determined by
- 	    the deterministic forecast and the variance is constant and determined by historical skill
- 	convert CFS ensemble mean to probability forecast by assuming Gaussian distribution and
-    	    variance is constant and determined by historical skill
- 	combine CFS and statistical probability forecasts by PNEW = constant•PSTAT PCFS-mean
- CFS ensemble converted to probability forecast (PCFS) by assuming Gaussian with mean
- 	determined by ensemble mean and variance by the ensemble spread.
- Ensemble weights are proportional to PNEW/PCFS
- 	(also did normalization and pruning to improve accuracy, problem of small ensemble size)
- Procedure
- Used CFS hindcasts to evaluate ensemble weighting
- 	1979-2003
- 	cross validated
- 	used 15 member ensemble
- 	bias removal

- Results: x' = NINO 3.4 SST
- Fig 2. shows the results when weighting the ensemble.  As seen, the weighted ensemble (solid line) usually shows improved or similar skill to the equally weighted ensemble (dashed line).  The forecast for lead-0 = October was difficult as the combined model was less skillful than the CFS ensemble.  The forecasts for late Summer were also difficult as persistence scored very well relative to the model.
- Results: x' = Equatorial Subsurface Temperature
- ENSO is a coupled system and obviously the equatorial subsurface temperature is important.   Since x' could, in theory, be any variable, we let x' be the average subsurface Equatorial temperature for the Central Pacific (0-200 meters, 160E-140W).  The domain corresponds to two of the legs of the TOGA-COARE array circa 1986.  As expected (Fig. 3), weighting the ensemble by “good” subsurface temperatures doesn't have an immediate effect on the NINO 3.4 forecast.  However, many forecasts are improved at longer leads.
- Results: x' = (NINO 3.4, Equatorial Subsurface Temperature)
- Weighting the ensemble by the using forecasts of NINO 3.4 and equatorial subsurface temperature improves the forecast skill as shown in Fig. 4.  This produces a weighting that is better 51% of the time for leads 0-2.
- Conclusion
- By combining simple statistical models and the CFS ensemble mean, we were able to produce an one month forecast (lead-0) of NINO 3.4 SST that was often better then the CFS ensemble mean.    We used this combined forecast to weight the ensemble members and used these weights for all leads.   Usually the weighted ensemble showed either better or similar skill to the ensemble mean.    By including forecasts of the equatorial subsurface temperature, we were able to improve the forecast skill.
- This procedure was designed as a “test study” as a better statistical forecast would expected to improve the results.
- References
- Wang, W, S. Sara, H. Pan, S. Nadiga, G. White, 2005: Simuation of ENNSO in the new NCEP Coupled Forecast System Model (CFS03), Mon. Wea. Rev, **133**, 1574-1593.
- Saha, S. et al, 2005: The NCEP Climate Forecast System, Submitted to J. Climate.

- Fig 2.  shows the skill of the persistence (dotted line), ensemble mean (dashed
- line) and the weighted ensemble mean (solid line) for forecasts of the monthly
- NINO 3.4 SST.  The top left plot shows the forecasts made in December and
- the verifying skill for January (lead 0) through September.  The next plot shows
- the skill of the forecasts made in January.  x' = NINO 3.4 SST (Reynold's OI2)

- Fig. 3, like Fig. 2 except x' = equatorial subsurface temperature (0-200 m, 16OE-140W) from GODAS.

- Fig. 4, like Fig. 2 except x' = (NINO 3.4 SST, ave. equatorial subsurface temperature)

- Fig. 1,  PDFCFS is from CFS ensemble after 1 month, PDFNEW is from a better forecast (only available at t=1).