Prediction of daily averaged PM 10 concentrations by statistical time-varying model K.I. Hoi, K.V. Yuen, K.M. Mok * Department of Civil and Environmental Engineering, University of Macau, Av. Padre Toma ´s Pereira Taipa, Macau SAR, China article info Article history: Received 3 October 2008 Received in revised form 4 February 2009 Accepted 6 February 2009 Keywords: Air quality prediction Artificial Neural Network Kalman filter Coastal city Macau PM 10 abstract In this study, a time-varying statistical model, TVAREX, was proposed for daily averaged PM 10 concen- trations forecasting of coastal cities. It is a Kalman filter based autoregressive model with exogenous inputs depending on selected meteorological properties on the day of prediction. The TVAREX model was evaluated and compared to an ANN model, trained with the Levenberg–Marquardt backpropagation algorithm subjected to the same set of inputs. It was found that the error statistics of the TVAREX model in general were comparable to those of the ANN model, but the TVAREX model was more efficient in capturing the PM 10 pollution episodes due to its online nature, therefore having an appealing advantage for implementation. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction In the present study, a time-varying autoregressive model with exogenous input (TVAREX) was developed for daily PM 10 concen- tration prediction of coastal cities. The Kalman filter algorithm (Kalman, 1960; Kalman and Bucy, 1961) was implemented on the model to perform state estimation. The model was tested in a typical coastal city, Macau, with Latitude 22  10’N and Longitude 113  34’E. The data were provided by the Macau Meteorological and Geophysical Bureau from an ambient air quality monitoring station that has an altitude of 158.2 m, hence its air quality and meteoro- logical measurements are considered to be representative of the general background conditions for the whole city. The prediction results of the TVAREX model were compared with those by artifi- cial neural network algorithm (Gardner and Dorling, 1998; Mok and Tam, 1998; Jiang et al., 2004; Hooyberghs et al., 2005; Grivas and Chaloulakou, 2006). 2. Kalman filter based TVAREX model In this section, the model was formulated according to the nature of a typical coastal city, Macau. However, it is believed that this model is applicable to other coastal cities with slight modifi- cation of the model inputs as they are also influenced by similar physical processes. The time-varying autoregressive model with exogenous inputs is proposed: x k ¼ Â f 1;k1 x k1 þ f 2;k1 x 0 k1 þ f 3;k1 expð au k  bjq k jÞ Ã exp À  f 4;k1 r k Á þ f k (1) In this model the symbols x k1 and x 0 k1 denote the daily averaged PM 10 concentration of yesterday and the hourly averaged PM 10 concentration before midnight, respectively. It is used to reflect the initial condition of PM 10 concentration on the next day. In addition, the symbols u k and jq k j denote the magnitude and the absolute angle of the resultant wind velocity vector. The resultant wind velocity vector is obtained by the sum of the hourly wind velocity vectors on the day of prediction. The magnitude u k is associated with the dispersion condition of the kth day. It becomes low under the conditions of low wind speed, occurrence of reversal in the prevailing wind directions, or a combination of both. When the wind speed is low, the atmosphere becomes stagnant. The partic- ulates generated from the local sources or transported from the upwind areas are trapped in the boundary layer and are hardly removed through advection. When there is a reversal of the prevailing wind directions, the particulates which are located downwind of Macau may be transported back due to the directional swing. This condition can also enhance the buildup of PM 10 concentrations on the day of prediction. The absolute angle of the * Corresponding author. Tel.: þ86 (853)83974350; fax: þ86 (853)28838314. E-mail addresses: kihoi@umac.mo (K.I. Hoi), kvyuen@umac.mo (K.V. Yuen), kmmok@umac.mo (K.M. Mok). Contents lists available at ScienceDirect Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv 1352-2310/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2009.02.020 Atmospheric Environment 43 (2009) 2579–2581