1. Daiwen Kang 1, Rohit Mathur 2, S. Trivikrama Rao 2 1 Science and Technology Corporation 2 Atmospheric Sciences Modeling Division ARL/NOAA NERL/U.S. EPA 5 th Annual CMAS Conference, Chapel Hill, NC, October 16 – 18, 2006 APPLICATION OF BIAS ADJUSTMENT TECHNIQUES TO THE ETA-CMAQ AIR QUALITY FORECASTS

2. Outline Overview of air quality forecast system Bias adjustment forecast techniques Results for O 3 forecasts Results for PM 25 forecasts Summary and Conclusions

3. Model Configuration Model Forecast Model Configuration Eta derived meteorology CBIV chemical mechanism Emissions processed using SMOKE 12 km horizontal grid cell size 22 Vertical Layers between surface and 100 mb 48 Hr. Forecast for O 3 and 24 Hr. Forecast for PM 25 Simulation Analysis Period 1 July – 30 September 2005 for O 3 4 January – 31 December 2005 for PM 25

4. Forecast Domain and Monitoring Locations (AIRNOW network) Continental US domain for O 3 forecast and the eastern US domain (dashed) for PM 25 forecast.

5. Forecast and observed time series The model consistently over-predicts O 3, but simulates the day-to-day variability quite well, suggesting that the forecast guidance could be improved by combining observations with forecast biases

6. Bias Adjustment Forecasts (1) Hybrid Forecast (HF): HF t+Δt = O t + (M t+Δt – M t ) where O t are observations at time t, M t+Δt and M t are forecasts at time t+Δt and t, respectively. The rationale: Model forecasts are based on unknown initial conditions, but a good model should be able to predict the change over time (dC/dt) correctly.

7. Bias Adjustment Forecasts (2) Kalman Filter Predictor Bias Adjustment (KF): x t+Δt|t = x t|t-Δt + β t|t-Δt (y t – x t|t-Δt ) KF t+Δt = F t+Δt - x t+Δt|t where: y t = F t – O t ; F t and O t are forecast and observed values; β t|t-Δt = (p t-Δt|t-2Δt + σ 2 η )/(p t-Δt|t-2Δt + σ 2 η + σ 2 ε ); p t|t-Δt = (p t-Δt|t-2Δt + σ 2 η )(1 - β t|t-Δt ), σ 2 η and σ 2 ε are the noise and error variances associated with previous bias and forecast errors. P is the expected mean square error. KF is a recursive algorithm to estimate a signal from noisy measurements in which information from recent past forecasts and observations is used to revise the estimate of the current raw forecast.

8. Evaluation Metrics: RMSE can be separated into systematic and unsystematic components based on the linear-regression model (Willmott, 1981): Where a and b are the intercept and coefficient for the linear regression of model concentrations (C P ) on observation concentrations (C O ), respectively.

9. Evaluation Metrics: Index of Agreement is also calculated to evaluate the results of bias adjustment results, which is defined as (Willmott, 1981): Where:

10. Two ways to apply KF for calculation of max. 8-hr O 3 and daily mean PM 25 : (1) Apply KF to hourly data, then calculate max. 8-hr O 3 or daily mean PM 25 ; (2) Calculate max. 8-hr O 3 or daily mean PM 25 from hourly data, then apply KF. Method 2 Method 1 Method 2 Method 1 Daily Mean PM 25 (ug/m 3 ) Max. 8-hr O 3 (ppb)

11. Max. 8-hr O 3 distribution KF distribution is most close to that of observation, and Hybrid distribution is better than the original model forecasts

12. Time Series for max. 8-hr O 3 at a monitoring location in Raleigh NC

13. RMSE Monthly Boxplots for max. 8-hr O 3

14. Bias Adjustment Error Split for Max. 8-hr O 3 RMSE RMSE_Sys RMSE_Unsys RMSE are calculated for each site for the entire study period (July 1 to September 30, 2005)

15. Index of Agreement for Max 8-hr O 3 CMAQKalman Filter Hybrid

16. Daily Mean PM 25 distribution Both KF and HF distribution are better than that of original model forecasts and the effects of the two are similar

17. Time Series for daily mean PM 25 at a monitoring location in NC Winter Summer

18. RMSE Monthly Boxplots for daily mean PM 25

19. RMSERMSE_SysRMSE_Unsys Bias Adjustment Error Split for Daily PM 25 RMSE are calculated for each site for the entire study period (January 4 to December 31, 2005)

20. Index of Agreement for daily mean PM 25 CMAQKalman FilterHybrid

21. Conclusions Both Kalman filter predictor bias adjustment and the simple hybrid bias adjustment can significantly improve forecast skills Kalman filter forecasts perform better than hybrid forecasts for max. 8-hr O 3 forecasts, but the two approaches perform similar for daily mean PM 25 forecasts. Both bias adjustment techniques can significantly reduce systematic errors, but have little effect on unsystematic errors. In max. 8-hr O 3 forecasts, both techniques even have increased unsystematic errors compared with the model forecasts. A seasonal cycle in modeled PM25 RMSE is noted with winter and summer highs, autumn and spring lows. Additional analysis of speciated data over annual cycle is needed to determine the possible reasons for these trends.

22. Future Work Further research on Kalman filter predictor bias adjustment approach for different locations (different σ 2 η / σ 2 ε ratios for different locations) Implement the bias adjustment approaches to real time forecast guidance. Investigate use of spatial statistical techniques to cover whole forecast domain at locations where no observations are available.

23. Disclaimer: The research presented here was performed under the Memorandum of Understanding between the U.S. Environmental Protection Agency (EPA) and the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration (NOAA) and under agreement number DW13921548. This work constitutes a contribution to the NOAA Air Quality Program. Although it has been reviewed by EPA and NOAA and approved for publication, it does not necessarily reflect their views or policies. Acknowledgement The authors are grateful to Luca Delle Monache and Roland Stull for providing their original Kalman Filter source codes for our reference. Thanks also go to the air quality forecast team both at NCEP NWS and ARL, RTP for producing the Eta-CMAQ forecast data.