Development of Bayesian Maximum Entropy Method Toolbox on Quantum GIS—An Application of Long-term Exposure Estimation of Particulate Matter in Taiwan

本研究發展Quantum GIS上時空統計函式–貝氏最大熵法–的插件軟體 (Quantum Bayesian Maximum Entropy Toolbox, QtBME)，可應用於非定常非同質時空過程之推估與繪圖。在時空過程可分成高頻與低頻之假設下，利用核心平滑法將原時空過程分離為定數的低頻趨勢與定常且同質之高頻時空隨機過程，並用粒子群最佳化演算法與AIC準則客觀選取適合高頻時空隨機過程之巢狀共變異數，進而利用貝氏最大熵法推估欲推點的資料特性。藉由Quantum GIS的圖形運算能力與內建地理資訊系統函式，QtBME能輕鬆地展現向量式與網格式二種地理資料格式推估的結果。本研究應用QtBME推估台灣地區從2004至2008年的空氣懸浮粒子PM10濃度，結果顯示，北部、雲嘉南、高屏等地為PM10濃度聚集的區域。花東、宜蘭則有較低的濃度。另外，暴露在高濃度( >50μg/m3 )懸浮粒子下的機率有週期性。一般來說，在3月開始下降到7月後，再由8月上升至隔年2月。交叉驗證的結果顯示，QtBME預測的相對誤差大部份落在 20%之內，偶有較高的誤差，為該測站特性與附近所提供的資訊較少所造成。This study developed the Quantum Bayesian Maximum Entropy Toolbox (QtBME), which is a spatiotemporal statistics function, can be applied to estimate and map a non-stationary and non-homogeneous spatiotemporal process under the platform of Quantum GIS (QGIS) software. Kernel smoothing method is used to divide the original process into a deterministic trend and a stationary and homogeneous spatiotemporal process, assuming that a spatiotemporal process can be divided into high and low frequency. The covariance model of the process of high frequency is selected objectively by particle swarm optimization (PSO) method and Akaike''s information criterion (AIC). Bayesian maximum entropy method is then applied to spatiotemporal mapping of the variable of interest. By means of ability of geoprocessing as well as graphical computing and mapping in QGIS libraries, QtBME can display the results easily with two types of geographical data format, i.e., raster and vector formats. This study evaluated the long-term township-based exposure estimation of particulate matter (PM10) from 2004 to 2008 in Taiwan. Results showed that PM10 concentration are higher in Taipei, Tainan, and Kaohsiung, and lower in Taidon and Ilan. Moreover, the probability of the high PM10 exposure (i.e., higher than 50μg/m3) has strong seasonality; in general, it decreases from March to July and then increases from August to February. The results of cross validation show that QtBME provides satisfactory predictions for the PM10 with relative errors less than 20%. High relative error seldom occurred because of the particular characteristic of certain stations and lack of information provided from the stations in the estimation neighborhoods