ESTIMATION OF THE MODELLING UNCERTAINTY RELATED WITH STOCHASTIC PROCESSES

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Diane Sutton
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Portugal ESTIMATION OF THE MODELLING UNCERTAINTY

1 International Technical Meeting Air Pollution Modelling and its Application September 24-28, 27, Aveiro - Portugal ESTIMATION OF THE MODELLING UNCERTAINTY RELATED WITH STOCHASTIC PROCESSES O. Tchepel, A. Monteiro, C. Borrego

2 Presentation outline Introduction Objectives Methodology Application example Results Conclusions

3 Introduction Quantification of uncertainties Modelling results Monitoring data Model physics/chemistry Data inputs Stochastic variations Calibration error Imperfections in measurement techniques Sampling error

4 Introduction Quantification of uncertainties Are we comparing the comparable data? Modelling results Grid cell Monitoring data Point measurements Short-term stochastic fluctuations!!!

5 Objectives Developing of a methodology for quantification of modelling uncertainty related with short-term fluctuations 1) spectrum analysis of the data Contribution of different frequencies to the variance 2) decomposition of the time series Remove the short-term variations 3) Validation of modelling results

with frequencies {f } j and random amplitudes {A } j and {B }: j X t

6 1) spectrum analysis of the data Methodology a time series X t of length N is presented as a linear combination of harmonic functions with frequencies {f } j and random amplitudes {A } j and {B }: j X t = µ + [ N / 2] j= 1 [ A cos ( 2π f t) + B sin ( 2π f t) ] j j j FFT j,

7 Methodology 2) decomposition of the data Data filtering Low-pass filter Kolmogorov-Zurbenko filter Multiple-pass moving average filter: The KZ(m,k) filter of the original time series is computed as a simple moving average of m points applied k times (number of iterations) 6 π 1 1 / 2 k w c 2 1 / 2 k m (1 / (1 / 2) 2) separation frequency C(t)=C B (t)+c S (t)

8 3) Validation of modelling results Original Measurement data Methodology Original Modelling results Baseline Short-term fluctuations Baseline Short-term fluctuation Statistical parameters

9 Application: modelling system Meteorological model MM5 Boundary conditions Climatological Model MOZART, GOCART Emissions anthropogenic biogenic CHIMERE Gaseous chemistry 44 species, 116 reactions Transport horizontal vertical diffusion Aerosol module Gas/aerosols deposition dry wet Pollutants concentration gas/aerosols Pollutants deposition gas/aerosols 1-year of CHIMERE model predictions

10 Application European domain CHIM-EUR 58ºN Portugal domain CHIM-PT 35ºN 58 km 14ºW 5x5 km 2 25ºE 1x1 km 2 29 km

11 Application: monitoring data Urban traffic Urban traffic Regional background Lisbon-Benfica Urban background Porto-Boavista Suburban background Lisbon Region-Chelas Pollutants: O 3 NO NO 2 Lisbon-Chelas Porto-Vila N.T Completeness >9% Year:24

12 Results: original time series Measurement data Modelling results ln(concentration) % 1% 75% 25% Median Chamusca_NO Chelas_NO Benfica_NO Benfica_NO2 Chelas_NO2 Vila N.T._NO2 Chamusca_NO2 Boavista_O3 Vila N.T._O3 Chamusca_O3 99% 1% 75% 25% Median ln(concentration) -8 Chamusca_NO Chelas_NO Benfica_NO Benfica_NO2 Chelas_NO2 Vila N.T._NO2 Chamusca_NO2 Boavista_O3 Vila N.T._O3 Chamusca_O3

13 Results: spectrum analysis Urban traffic station (Benfica, NO 2 ) Measurement data Modelling results 1 month 1 week 24 hours 12 hours 1 month 1 week 24 hours 12 hours periodogram frequency f (h -1 ) frequency (h -1 )

14 O 2 Measurements Modelling Urban traffic Urban background Suburban background Regional background periodogram periodogram periodogram periodogram ITM, September , 27,.1 Aveiro.1 - Portugal 1 f frequency (h -1 ) periodogram periodogram periodogram periodogram f (h -1 ) frequency (h -1 )

15 ln(no2) ln(no2) g p Results: data filtering Original measurement data Baseline component ln(no2) hours Short-term fluctuations f=.95 h -1 T= 1/f 11 h KZ 3,3

16 Results Short-term fluctuations Measurement data Modelling results ln (Concentration) % 1% 75% 25% Median Chamusca_NO Chelas_NO Benfica_NO Benfica_NO2 Chelas_NO2 Vila N.T._NO2 Chamusca_NO2 Boavista_O3 Vila N.T._NO2 Chamusca_O3 99% 1% 75% 25% Median ln (Concentration) -2.5 Chamusca_NO Chelas_NO Benfica_NO Benfica_NO2 Chelas_NO2 Vila_N.T._NO2 Chamusca_NO2 Boavista_O3 Vila N.T._O3 Chamusca_O3

17 Results Model validation using original and filtered hourly concentration data - NO 2 example RMSE µg/m 3 urban traffic urban background suburban background regional background original urban after traffic filtering urban background suburban background regional background Pearson Correlation Coefficient original after filtering

18 Conclusions The proposed approach contributes to better understanding of the model prediction uncertainty The analysis of the measurement data in frequency domain shows the contribution of short- and long-term components to the total variability The model validation methodology based on the pre-filtered data allows to separate the estimation of the model error in predicting the baseline concentration from the error in predicting the short-term variations

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