Kalman Filter in Real Time URBIS

1. Kalman Filter in Real Time URBIS Richard Kranenburg 06-01-2010

2. Introduction • TNO – Technisch Natuurwetenschappelijk Onderzoek • Kerngebied – Bouw en Ondergrond • Business Unit – Milieu en Leefomgeving Introduction - Uncertainty analysis - Kalman filter - Application on population

3. Introduction • Accompanists • Michiel Roemer (TNO) • Jan Duyzer (TNO) • Arjo Segers (TNO) • Kees Vuik (TUDelft) Introduction - Uncertainty analysis - Kalman filter - Application on population

4. Problem • Current situation • Real Time URBIS model gives one value for the concentration NOx in the DCMR area • Wanted situation • Uncertainty interval for the concentration NOx • Uncertainty interval dependent of the place in the domain Introduction - Uncertainty analysis - Kalman filter - Application on population

5. DCMR-area Introduction - Uncertainty analysis - Kalman filter - Application on population

6. 11 emission sources Traffic CAR Zone Cards Road near Road far Background Abroad Rest of the Netherlands DCMR-area Shipping Ship sea Ship inland Industry Industry Rest Winddirections North East South West Wind speeds 1.5 m/s 5.5 m/s Total 88 standard concentration fields for the concentration NOx URBIS model Introduction - Uncertainty analysis - Kalman filter - Application on population

7. Real Time URBIS • Gives for every hour an expected concentration NOx for the whole DCMR-area, based on input parameters • Wind direction (φ) • Wind speed (v) • Temperature (T) • Month (m) • Weekday (d) • Hour (h) • State equation: Introduction - Uncertainty analysis - Kalman filter - Application on population

8. Measurement locations • DCMR-Stations • Schiedam • Hoogvliet • Maassluis • Overschie • Ridderkerk • Rotterdam Noord • RIVM-Stations • Schiedamsevest • Vlaardingen • Bentinckplein Introduction - Uncertainty analysis - Kalman filter - Application on population

9. Uncertainty Real Time URBIS • Compare Real Time URBIS simulations with the observations on the nine measurement locations • Both observations and model simulations have a log-normal distribution Introduction - Uncertainty analysis - Kalman filter - Application on population

10. Log-normal distributions Introduction - Uncertainty analysis - Kalman filter - Application on population

11. Correction of the model • Differences between model and measurements plotted with respect to 6 input parameters • h: hour of the day • φ: wind direction Introduction - Uncertainty analysis - Kalman filter - Application on population

12. Uncertainty of the model • Standard deviation of the differences between the corrected model and the observations • v: wind speed Introduction - Uncertainty analysis - Kalman filter - Application on population

13. Result of uncertainty analysis Introduction - Uncertainty analysis - Kalman filter - Application on population

14. Kalman filter • Smooth random errors in the model of a dynamical system • In a real time application, measurements on time k are directly available to filter the state on time k. • Two results after application • New expected concentration NOx • Uncertainty interval for the concentration NOx • New state equation: Introduction - Uncertainty analysis - Kalman filter - Application on population

15. Kalman filter equations • Forecast • Analysis Introduction - Uncertainty analysis - Kalman filter - Application on population

16. Kalman filter on emission source ‘Background’ • In the vector all values are equal to zero, except the entries corresponding with the source ‘background’ • Linearization of the Kalman filter equations • Matrix A estimated with measurements in Schipluiden and Westmaas • Matrix R estimated with measurements at Bentinckplein Introduction - Uncertainty analysis - Kalman filter - Application on population

17. Kalman filter on emission source ‘Background’ • Screening criterion: • Pfabs,k : Model uncertainty after forecast step • Rabs,k: Uncertainty of the measurements Introduction - Uncertainty analysis - Kalman filter - Application on population

18. Kalman filter on emission source ‘Background’ Introduction - Uncertainty analysis - Kalman filter - Application on population

19. Kalman filter on all emission sources • State equation: • Screening Criterion Introduction - Uncertainty analysis - Kalman filter - Application on population

20. Kalman filter on all emission sources • Matrix A estimated with measurements in Schipluiden, Westmaas, Overschie, Ridderkerk, Maassluis, Vlaardingen • Matrix R estimated with measurements at Bentinckplein Introduction - Uncertainty analysis - Kalman filter - Application on population

21. Kalman filter on all emission sources Introduction - Uncertainty analysis - Kalman filter - Application on population

22. Connection with population • Each grid cell, every hour a certainty interval • Annual mean of the width of these intervals per grid cell • Amount of large widths of these intervals per grid cell • Number of postal zipcodes per grid cell • Population density 1.99 people per grid cell • Number of people per grid cell Introduction - Uncertainty analysis - Kalman filter - Application on population

23. Connection with population Introduction - Uncertainty analysis - Kalman filter - Application on population

24. Connection with population Introduction - Uncertainty analysis - Kalman filter - Application on population

25. Connection with population Introduction - Uncertainty analysis - Kalman filter - Application on population

26. Connection with population Introduction - Uncertainty analysis - Kalman filter - Application on population

27. Conclusions • The differences between the observations and the model simulation are not only caused by inaccuracies in the background • Uncertainty interval has large width in the industrial region around Pernis and on the main roads • The application of the Kalman filter makes it possible to correct the model values every hour, with help of the observations

28. Further investigation • Add measurement stations to reduce uncertainty of the Kalman filter results • State optimal setting of measurement stations • Increase time scale (Day, Week or Month)