Analýza znečištění ovzduší prachovými částicemi PM10 založená na zobecněném lineárním modelu s maticí plánu silně neúplné hodnosti

Analysis of PM10 Air Pollution In Brno Based on Generalized Linear Model With Strongly Rank-Deficient Design Matrix

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An analysis of air pollution by suspended particulate matter PM10 in Brno, the second largest urban agglomeration of the Czech Republic, based on generalized linear model (GLM) is presented. Average daily concentrations coming from PM10 monitoring for the period 1998-2005 have been processed. The measured meteorological factors: air temperature and humidity, direction and wind speed were considered as covariates along with some additional seasonal factors. A family of complex (generalized) linear models has been suggested exhibiting strong rank-deficiency in the design matrix to allow for more precise modeling involving identification of significant air pollution sources, among others. From each of them the parameter estimates were obtained using both standard estimation procedure and a new sparse parameter estimation technique based on BPA4 – a four-step modification of the Basis Pursuit Algorithm originally suggested in [Chen S. S., Donoho D. L., Saunders M. A.. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput., 20(1):33--61, 1998.] for time- scale analysis of digital signals. As the standard estimation algorithms often fail due to numerical instability caused by strong overparametrization, we have applied this new computationally intensive approach allowing us to reliably identify nearly zero parameters in the model and thus to find numerically stable sparse solutions. The goal of the analysis was to identify the model and algorithm yielding most precise one-day forecasts of the level of pollution by PM10 with regard to the meteorological and seasonal covariates.

Byla navržena třída komplexních zobecněných lineárních modelů vykazujících silnou neúplnost hodnosti matice plánu v důsledku snah o dosažení zvýšené přesnosti modelu, který umožňuje (kromě jiného) i identifikovat významné zdroje znečištění. Pro každý model byly nalezeny odhady parametrů jak standardním postupem tak i novou estimační technikou pro hledání řídkých odhadů založenou na BPA4 – čtyřkrokové modifikaci algoritmu "Basis Pursuit" [Chen {S. S.}, Donoho {D. L.}, Saunders {M. A.}.Atomic decomposition by basis pursuit. SIAM J. Sci. Comput., 20(1):33-61,1998.]. Cílem analýzy je nalezení modelu a algoritmu, který dává nejpřesnější jednodenní předpovědi znečištění částicemi PM10 v závislosti na meteorologických a sezónních faktorech.

An analysis of air pollution by suspended particulate matter PM10 in Brno, the second largest urban agglomeration of the Czech Republic, based on generalized linear model (GLM) is presented. Average daily concentrations coming from PM10 monitoring for the period 1998-2005 have been processed. The measured meteorological factors: air temperature and humidity, direction and wind speed were considered as covariates along with some additional seasonal factors. A family of complex (generalized) linear models has been suggested exhibiting strong rank-deficiency in the design matrix to allow for more precise modeling involving identification of significant air pollution sources, among others. From each of them the parameter estimates were obtained using both standard estimation procedure and a new sparse parameter estimation technique based on BPA4 – a four-step modification of the Basis Pursuit Algorithm originally suggested in [Chen S. S., Donoho D. L., Saunders M. A.. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput., 20(1):33--61, 1998.] for time- scale analysis of digital signals. As the standard estimation algorithms often fail due to numerical instability caused by strong overparametrization, we have applied this new computationally intensive approach allowing us to reliably identify nearly zero parameters in the model and thus to find numerically stable sparse solutions. The goal of the analysis was to identify the model and algorithm yielding most precise one-day forecasts of the level of pollution by PM10 with regard to the meteorological and seasonal covariates.

Air Pollution; Dust Aerosols PM10; Generalized autoregressive linear model; sparse estimator; Basis Pursuit Algorithm

2009

07.12.2009

John Wiley & Sons

Chichester

1180-4009

Environmetrics

20

6

676–698

23