**6. Prediction of** *PM*<sup>10</sup> **values**

8 Current Air Quality Issues

up to a maximum number of eight values.

been validated using the *GSLib* program "KT3D".

estimated ones (b) Diagram of *PM*<sup>10</sup> residuals towards the estimated ones

been used with the aim to estimate *PM*<sup>10</sup> daily measurements.

**5. Estimation of missing values**

and the deseasonalized values.

concentrations,

daily residuals.

[20, 21, 30, 31].

• at the same day of two years before and/or later, (*t* − 2*d*) and (*t* + 2*d*), with *d* = 365 and

The variogram model (6), which describes the temporal correlation for *PM*<sup>10</sup> residuals, has

(a) (b)

**Figure 4.** Scatter plots between observed and estimated values. (a) Diagram of *PM*<sup>10</sup> daily concentrations towards the

In this section the reconstruction of *PM*10, by using the kriging technique, has been discussed

The reconstruction of temporal data is required if a time series is incomplete. This problem could be due to a malfunction of the monitoring station or the presence of invalid data.

With this aim, six consecutive *PM*<sup>10</sup> values from the 12th to the 17th of June 2011, have been considered as missing, both for the observed time series with a 365-day periodic behavior

Kriging daily estimations for these missing values have been obtained using, alternatively

1. the periodic variogram model (5), which describes the temporal correlation for *PM*<sup>10</sup> daily

2. the nonperiodic variogram model (6), which describes the temporal correlation for *PM*<sup>10</sup>

Since the time series of the observed values is characterized by a periodic behavior, *GSLib* routine "KT3DP", properly modified in order to define an appropriate neighborhood, has

some days before and/or later, (*t* − 2*d* ± *k*) and (*t* + 2*d* ± *k*), with *k* = 1, 2, 3,

In this section, predictions for the variable under study in time points after the last available data are discussed [23, 24, 28].

The periodic variogram model (5) of *PM*<sup>10</sup> concentrations and the nonperiodic variogram model (6) of *PM*<sup>10</sup> residuals, have been used in order to predict six time points after the last available data, i.e. the 31st of December 2013. In particular, kriging predictions have


*a* Results obtained by using the periodic variogram model (5) *b* Results obtained by using the nonperiodic variogram model (6)

**Table 2.** Kriging estimations of a sequence of 6 missing values, from the 12th to the 17th of June 2011 and corresponding errors for periodic and nonperiodic variogram models

been computed for the period ranging from the 1st to the 6th of January 2014, by using, alternatively


**Figure 6.** Time plot of *PM*<sup>10</sup> predicted values and *PM*<sup>10</sup> daily concentrations (*µg*/*m*3), from the 1st to the 6th of January 2014

2013 to the 6th of January 2014 is shown together with the predicted *PM*<sup>10</sup> values for the period ranging from the 1st to the 6th of January 2014. Note that the kriging procedure using the nonperiodic variogram model (6) related to *PM*<sup>10</sup> residuals has produced overestimates of the pollution levels.

Moreover, in Table 3 some results of the performance of the prediction procedure are presented. The mean value of the kriging standard error is lower if the periodic variogram model is used, compared with the case of kriging based on the nonperiodic variogram model.


*a* Results obtained by using the periodic variogram model (5) *b* Results obtained by using the nonperiodic variogram model (6)

**Table 3.** Kriging predictions of a sequence of six days, from the 1st to the 6th of January 2014 and corresponding errors for periodic and nonperiodic variogram models

It is important to highlight that in the period 1-5 January 2014 predicted values greater than 50 *µg*/*m*<sup>3</sup> (i.e. the limit value fixed by the National Law) have been obtained.

Note that in the period 1-4 January 2014, *PM*<sup>10</sup> values greater than this threshold have been measured. On the other hand, at day 5th, the kriging procedure produces overestimate of the variable under study.
