**3.2. Calculated PM2.5 concentrations**

It is impossible for the public and governmental officers to accept the membership grade kriging maps. Therefore, kriging maps of every year PM2.5 concentrations (collected and estimated together) must be constructed. The conversion formula is

$$\tilde{\mathbf{x}}\_{\circ} = \frac{\sqrt{6}m}{\pi} \ln \left( \frac{2 - \hat{\mathbf{e}}\_{\circ}}{\hat{\mathbf{e}}\_{\circ}} \right). \tag{11}$$

Kriging maps with "completed" of every year PM2.5 data {*xij* , *i* =1,2,...,13, *j* =1,2,...,113}. Com‐ parison of kriging maps with the "completed" data can now be performed. See Figure 4. A complete dataset is now available, the 113 observation sites now have the full 13 year PM2.5 concentration, containing 1469 data records. The 13 ordinary kriging prediction maps are generated, and one can clearly observe the changes in PM2.5 year by year.

2005 2006 2007

2008 2009 2010

2011

1999 2000 2001

2002 2003 2004

As one can observe from Figure 3, central California regions have very low membership

It is impossible for the public and governmental officers to accept the membership grade kriging maps. Therefore, kriging maps of every year PM2.5 concentrations (collected and

> <sup>6</sup> <sup>2</sup> <sup>ˆ</sup> ln . <sup>ˆ</sup> *ij*

parison of kriging maps with the "completed" data can now be performed. See Figure 4. A complete dataset is now available, the 113 observation sites now have the full 13 year PM2.5 concentration, containing 1469 data records. The 13 ordinary kriging prediction maps are

1999 2000 2001

2002 2003 2004

2005 2006 2007

2008 2009 2010

2011

*<sup>m</sup> <sup>e</sup> <sup>x</sup>* p *e* æ ö - <sup>=</sup> ç ÷

*ij*

% (11)

, *i* =1,2,...,13, *j* =1,2,...,113}. Com‐

ç ÷ è ø

grades, and the rest of Calfornia have higher membership grades.

estimated together) must be constructed. The conversion formula is

*ij*

generated, and one can clearly observe the changes in PM2.5 year by year.

Kriging maps with "completed" of every year PM2.5 data {*xij*

**3.2. Calculated PM2.5 concentrations**

320 Current Air Quality Issues

**Figure 4.** Kriging maps of completed estimated PM2.5 concentrations for California 1999-2011

One can now observe and compare the year by year changes of PM2.5 concentration, and note the regions of high and low PM2.5 concentration. The dark brown colours represent high PM2.5 concentrations, and light yellow colours represent areas with low PM2.5 concentrations. Note that central California shows to have continual high levels of PM2.5 concentration, year after year.
