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. URBIS model 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 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:  P f abs,k : Model uncertainty after forecast step  R abs,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)