Daiwen Kang1, Rohit Mathur2, S. Trivikrama Rao2

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APPLICATION OF BIAS ADJUSTMENT TECHNIQUES TO THE
ETA-CMAQ AIR QUALITY FORECASTS

• Daiwen Kang1, Rohit Mathur2, S. Trivikrama Rao2
• 1Science and Technology Corporation
• 2Atmospheric Sciences Modeling Division
• ARL/NOAA
• NERL/U.S. EPA
• 5th Annual CMAS Conference, Chapel Hill, NC,
  October 16 18, 2006

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Outline

• Overview of air quality forecast system
• Bias adjustment forecast techniques
• Results for O3 forecasts
• Results for PM25 forecasts
• Summary and Conclusions

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Model Configuration

• 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 O3 and 24 Hr. Forecast for
  PM25
• Simulation Analysis Period
• 1 July 30 September 2005 for O3
• 4 January 31 December 2005 for PM25

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Forecast Domain and Monitoring Locations (AIRNOW
network)
Continental US domain for O3 forecast and the
eastern US domain (dashed) for PM25 forecast.
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Forecast and observed time series
The model consistently over-predicts O3, but
simulates the day-to-day variability quite well,
suggesting that the forecast guidance could be
improved by combining observations with forecast
biases
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Bias Adjustment Forecasts (1)

• Hybrid Forecast (HF)
• HFt?t Ot (Mt?t Mt)
• where Ot are observations at time t, Mt?t and
  Mt are forecasts at time t?t 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.

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Bias Adjustment Forecasts (2)

• Kalman Filter Predictor Bias Adjustment (KF)
• xt?tt xtt-?t ßtt-?t(yt xtt-?t)
• KFt?t Ft?t - xt?tt
• where yt Ft Ot Ft and Ot are forecast and
  observed values ßtt-?t (pt-?tt-2?t
  s2?)/(pt-?tt-2?t s2? s2e )
• ptt-?t (pt-?tt-2?t s2?)(1 - ßtt-?t),
  s2? and s2e 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.

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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
(CP) on observation concentrations (CO),
respectively.
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Evaluation Metrics
Index of Agreement is also calculated to evaluate
the results of bias adjustment results, which is
defined as (Willmott, 1981)
Where
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Two ways to apply KF for calculation of max. 8-hr
O3 and daily mean PM25 (1) Apply KF to hourly
data, then calculate max. 8-hr O3 or daily mean
PM25 (2) Calculate max. 8-hr O3 or daily mean
PM25 from hourly data, then apply KF.
Daily Mean PM25 (ug/m3)
Max. 8-hr O3 (ppb)
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Max. 8-hr O3 distribution
KF distribution is most close to that of
observation, and Hybrid distribution is better
than the original model forecasts
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Time Series for max. 8-hr O3 at a monitoring
location in Raleigh NC
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RMSE Monthly Boxplots for max. 8-hr O3
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Bias Adjustment Error Split for Max. 8-hr O3
RMSE are calculated for each site for the entire
study period (July 1 to September 30, 2005)
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Index of Agreement for Max 8-hr O3
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Daily Mean PM25 distribution
Both KF and HF distribution are better than that
of original model forecasts and the effects of
the two are similar
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Time Series for daily mean PM25 at a monitoring
location in NC
Winter
Summer
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RMSE Monthly Boxplots for daily mean PM25
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Bias Adjustment Error Split for Daily PM25
RMSE are calculated for each site for the entire
study period (January 4 to December 31, 2005)
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Index of Agreement for daily mean PM25
CMAQ
Kalman Filter
Hybrid
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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 O3 forecasts, but
  the two approaches perform similar for daily mean
  PM25 forecasts.
• Both bias adjustment techniques can significantly
  reduce systematic errors, but have little effect
  on unsystematic errors. In max. 8-hr O3
  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.

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Future Work

• Further research on Kalman filter predictor bias
  adjustment approach for different locations
  (different s2? / s2e 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.

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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.
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 Commerces
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.