Forecasting of daily PM10 concentrations in Brno and Graz

Transcription

1 Forecasting of daily PM10 concentrations in Brno and Graz Ernst Stadlober Graz University of Technology Zuzana Hüberová, Jaroslav Michálek Brno University of Technology June 5,

2 Contents Situation in Graz and Brno Meteorological and anthropogenic factors Measuring stations in Graz and Brno Statistical Prediction Models Multiple Linear Regression Generalized Linear Model Quality of the Models Measuring stations Graz-Mitte and Zvona ka in Brno Winter Season 2013/14 Quality of Forecast in Graz-Mitte and Graz-Süd 2

3 The general Situation Graz (263k inhabitants): Basin Area Low wind velocities, low precipitation, temperature inversion Trac, domestic fuel Brno (430k inhabitants): Open Basin Area Concentration of industry, motor trac, heating plants Temperature inversion Consequence Treshold value daily mean PM10 50µg/m 3 exceeded regularly (PM10: particulate matter with diameter < 10µm = 0.01mm) Graz: exceedances in winter seasons Brno: exceedances 3

4 Stations in Graz Forecast: Graz-Mitte (trac area), Graz-Süd (industrial zone) Precipitation: Graz-Nord Temperature inversion: Kalkleiten Kalkleiten Nord Mitte Süd km 4

5 Graz-Mitte: Inversion and Weekend Eect Figure: Graz-Mitte: Five winter seasons 02/0306/07 No Inversion: 40% lower than Inversion Sun/Holiday: 30% lower than Working Day 5

6 Stations in Brno Forecast: Arboretum (botanical garden) šidenice (heavy trac street), Zvona ka (trac spot) 6

7 Training Data and Test Data for Graz Model ts on Training Data Graz-Mitte: 7 winter seasons ( ) Graz-Süd: 6 winter seasons ( ) All models are tted on observed covariates Predictions (one-day forecasts) on Test Data Graz-Mitte,Graz-Süd: 1 winter season ( ) 7

8 Covariates for Graz Ap t : daily mean PM10 day t T t : mean temp di to test point Kalkleiten day t V t : mean wind speed day t (Graz Mitte for Graz Süd) Prec t : 1 = prec., 0 = no prec. on day t (Graz Nord) Ap lag : mean of PM10 (12.30 (t 2) to (t 1)) T lag : categorized mean (temp means: (t 2) to (t 1)) (= 0 temp>0, = 1 temp 0) (Graz Mitte for Graz Süd) saturday: (0 1) sunday: (0 1) febr: (0 1) march: (0 1) 8

9 Training Data and Test Data for Brno Model ts on Training Data Arboretum: 2 winter seasons 11/0603/07, 10/0703/08 Zidenice, Zvonar ka: 1 winter season 11/0703/08 All models are tted on predicted covariates Predictions (one-day forecasts) on Test Data Arboretum, Zidenice, Zvonar ka: 1 winter season ( ) 9

10 Covariates for Brno Ap t : daily mean PM10 day t V t sin D t (pred): mean of 4 predictions (=velocity sin(direction)) (0.00, 6.00, 12.00, day t) V t cos D t (pred): mean of 4 predictions (=velocity cos(direction)) T t (pred): mean of 4 predictions of temperature Cover t (pred): mean of 4 predictions of coverage (values 1:10) Ap lag : mean of PM10 (13.00 (t 2) to (t 1)) T lag : mean of 4 measurements of temperature (18.00 (t 2), 0.00, 6.00, (t 1)) 10

11 Covariates for Brno - 2 HS t : activity of heating plants day t (Oct: 0.08, Nov: 0.14, Dec: 0.17, Jan; 0,19, Feb: 0.16, Mar: 0.14) weekend: (0 1) sunday: (0 1) febr: (0 1) march: (0 1) 11

12 Multiple Linear Regression Dependent variable Ap t Model assumption x (i) t (i = 1, 2,..., m) metric input variables d (j) t (j = 1,..., p) dummy (0 1) input variables at day t Linear model for Ap t : Apt = β 0 + m i=1 β i x (i) t + p j=1 where ɛ t iid N(0, σ 2 ). β m+j d (j) t + ɛ t (1) 12

13 Multiple Linear Regression: Graz-Mitte Variables ordered according importance Variables x or d beta sd(beta) t-value const T t Ap lag V t T lag sunday march saturday Prec t febr R 2 se n

14 Multiple Linear Regression: Zvona ka in Brno Variables x or d beta sd(beta) t-value const V t sin D t Cover t march T lag T t weekend Ap lag V t cos D t β S 103 R 2 se n HS t, sunday, febr not signicant 14

15 GLM model with gamma distribution and log link Dependent variable Ap t is gamma distributed Model assumption x (i) t (i = 1, 2,..., m) metric input variables d (j) t (j = 1,..., p) dummy (0/1) input variables Ap t has Gamma(φµ t, 1/φ) distribution, φ dispersion ln(µ t ) = ln (E(Ap t S t )) = β 0 + m i=1 β i x (i) t + p j=1 β m+j d (j) t, (2) E(Ap t S t ) cond. expect. of Ap t for given set S t of variables 15

16 GLM with gamma log link: Graz-Mitte Variables x or d beta sd(beta) const T t ln(ap lag ) V t T lag sunday march saturday Prec t febr χ 2 ans f 1189 n

17 GLM with gamma log link: Zvona ka in Brno Variables x or d beta sd(beta) const V t sin D t T lag Cover t march T t weekend febr V t cos D t ˆβ S 0.13 S 101 χ 2 ans f 125 n 134 Ap lag, HS t, sunday not signicant 17

18 Quality of forecasting Training data set to compute estimates ˆβ i, ˆβ j+m Model LM applied to test data yield estimates Ap t Âp t = ( Ap t ) 2 Model GLM applied to test data yield estimates Âp t = exp( ln(ap t )) ln(apt ) 18

19 Quality of forecasting - 2 Quality function Q(x, y): (x = observation, y = forecast) 0 Q(x, y) 1 for each pair (x, y) Values close to 1 signify very good forecasts { } x y Q(x, y) = 1 min 10d, 1 with d = x 50 + y (IA + 10I B ) where A = {x 50, y 50}, B = {x 100, y 100}, I E is indicator function: I E = 1 if E is valid, I E = 0 otherwise. Scoring system Q(x, y) [0.8, 1.0] (1: excellent), Q(x, y) [0.6, 0.8) (2: good) Q(x, y) [0.4, 0.6) (3: satisfactory), Q(x, y) [0.2, 0.4) (4: bad) Q(x, y) [0, 0.2) (5: very bad) 19

20 Quality of forecasting - 3 Quality function Q(x, y): (x = observation, y = forecast) Quality: 5 levels green (1=excellent) to red (5=very bad) 20

21 Practical performance and comparison: Graz-Mitte Predictions based on a sufficient LM for Graz Mitte Predictions based on a sufficient GLM for Graz Mitte Predicted PM10 (µg/m 3 ) excellent good satisfactory bad very bad Predicted PM10 (µg/m 3 ) excellent good satisfactory bad very bad Observed PM10 (µg/m 3 ) Observed PM10 (µg/m 3 ) Figure: Graz-Mitte: Quality function of LM and GLM 21

22 Practical performance and comparison: Graz-Mitte Comparison of predictions for Graz Mitte Predictions of PM10 (µg/m 3 ) by LM Predictions of PM10 (µg/m 3 ) by GLM Figure: Graz-Mitte: Forecasts Âp t of GLM vs LM 22

23 Practical performance and comparison: Graz Mitte - 3 Quality of prediction of PM10 (µg/m 3 ) by LM Comparison of qualities of predictions for Graz Mitte Quality of prediction of PM10 (µg/m 3 ) by GLM Figure: Graz-Mitte: Quality function GLM vs LM 23

24 Practical performance and comparison: Graz Mitte - 4 Table: Contingency table Graz-Mitte: Quality of GLM (rows) vs LM (columns), number and percentage of quality 1 to 5 GLM/LM sglm % cum % slm % cum %

25 Practical performance and comparison: Zvona ka Predicted PM10 (µg/m 3 ) Predictions based on a sufficient LM for Zvonarka excellent good satisfactory bad very bad Predicted PM10 (µg/m 3 ) Predictions based on a sufficient GLM for Zvonarka excellent good satisfactory bad very bad Observed PM10 (µg/m 3 ) Observed PM10 (µg/m 3 ) Figure: Zvona ka: Quality function of LM and GLM 25

26 Practical performance and comparison: Zvona ka Comparison of predictions for Zvonarka Predictions of PM10 (µg/m 3 ) by LM Predictions of PM10 (µg/m 3 ) by GLM Figure: Zvona ka: Forecasts Âp t of GLM vs LM 26

27 Practical performance and comparison: Zvona ka - 3 Quality of prediction of PM10 (µg/m 3 ) by LM Comparison of qualities of predictions for Zvonarka Quality of prediction of PM10 (µg/m 3 ) by GLM Figure: Zvona ka: Quality function GLM vs LM 27

28 Practical performance and comparison: Zvona ka - 4 Table: Contingency table Zvona ka: Quality of GLM (rows) vs LM (columns), number and percentage of quality 1 to 5 GLM/LM sglm % cum % slm % cum %

29 Practical Experience Graz-Mitte and Graz-Süd Multiple linear regression for Ap t Daily predictions of PM10 for 10 winter seasons: 2004/05 to 2013/14 Meteorological forecasts by ZAMG Styria till 11 in the morning PM10-Prediction during 1 and 3 PM at Daily update: comparison of predictions with measured values (day t 2) with excel-le to Environmental Department of Graz 80 93% of the predictions at least satisfactory 29

30 Quality of Prediction Graz-Mitte 2013/14 1: 55%, 2: 33.7%, 3: 4% 92.7% 18 days with observed exceedances (PM10 50) 30

31 Predictions and Observations Graz-Mitte 2013/14 31

32 Quality of Prediction Graz-Süd 2013/14 1: 53%, 2: 22.5%, 3: 9.3% 84.8% 39 days with observed exceedances (PM10 50) 32

33 Predictions and Observations Graz-Süd 2013/14 33

34 Graz-Süd 2013/14: 9 observed days PM10 > 75µg/m 3 3 days: Prediction PM10 > 75µg/m 3 5 days: Prediction PM10 > 50µg/m 3 1 day: Prediction PM10 < 50µg/m 3 34

35 Graz-Süd 2013/14: 11 predicted days PM10 > 75µg/m 3 Good prediction, if observed PM10 > 50µg/m 3 3 predicted values too high 35

36 Conclusion LM and GLM models suitable for daily PM10 forecasts Results of models similar and comparable Brno: 1 or 2 seasons for training data, test data 2008/09 Graz: 6 or 7 seasons for training data, test data 2009/10 Brno: no measures for precipitation and inversion for each site specic selection of covariates Graz: all 9 covariates are signicant Very Good quality: Arboretum (98% satisfactory) Good quality: Graz-Mitte, Graz-Süd (85%) Moderate quality: Zvona ka, šidenice (74%) 36

37 Literature Hörmann S., B. Pfeiler, E. Stadlober (2005), Analysis and Prediction of Particulate Matter PM10 for the Winter Season in Graz, Austrian Journal of Statistics 34, Hrdli cková Z., Michálek J., Kolá r M. and Veselý V. (2008), Identication of factors aecting air pollution by dust aerosol PM10 in Brno City, Czech Republic, Atmospheric Environment 42, Stadlober E., S. Hörmann, B. Pfeiler (2008), Quality and Performance of a PM10 Daily Forecasting Model, Atmospheric Environment 42, Stadlober E., F. Moser (2013), Ermittlung von saisonbereinigten PM10-Mittelwerten des Winterhalbjahres auf Basis der Daten 2003/ /2013, Endbericht im Auftrag der Stadt Graz Stadlober E., Hübnerová Z., Michálek J., Kolá M. (2012), Forecasting of Daily PM10 Concentrations in Brno and Graz by Dierent Regression Approaches, Austrian Journal of Statistics 41,4,