Improving of local ozone forecasting by integrated models

Abstract

This paper discuss the problem of forecasting the maximum ozone concentrations in urban microlocations, where reliable alerting of the local population when thresholds have been surpassed is necessary. To improve the forecast, the methodology of integrated models is proposed. The model is based on multilayer perceptron neural networks that use as inputs all available information from QualeAria air-quality model, WRF numerical weather prediction model and onsite measurements of meteorology and air pollution. While air-quality and meteorological models cover large geographical 3-dimensional space, their local resolution is often not satisfactory. On the other hand, empirical methods have the advantage of good local forecasts. In this paper, integrated models are used for improved 1-day-ahead forecasting of the maximum hourly value of ozone within each day for representative locations in Slovenia. The WRF meteorological model is used for forecasting meteorological variables and the QualeAria air-quality model for gas concentrations. Their predictions, together with measurements from ground stations, are used as inputs to a neural network. The model validation results show that integrated models noticeably improve ozone forecasts and provide better alert systems.

Appendix A: Performance measures

The following are performance measures used in the study.

• The root-mean-square error – RMSE:

  $$ \text{RMSE} = \sqrt{\frac{1}{N}\sum\limits_{i=1}^{N} (E(\hat{y}_{i})-y_{i})^{2}}, $$

  (2)

  where y _i and $\hat {y}_{i}$ are the observation and the prediction in the i-th step, respectively, E(⋅) denotes the expectation, i.e., the mean value, of the random variable, and N is the number of used observations.

• The standardised mean-squared error – SMSE

  $$ \text{SMSE}=\frac{1}{N}\frac{{\sum}_{i=1}^{N}(E(\hat{y}_{i})-y_{i})^{2}}{{\sigma_{y}^{2}}}, $$

  (3)

  where ${\sigma _{y}^{2}}$ is the variance of the observations.

• The Pearson’s correlation coefficient – PCC:

  $$ \text{PCC}=\frac{{\sum}_{i=1}^{N}(E(\hat{y}_{i})-E(\hat{\mathbf{y}}))(y_{i}-E(\mathbf{y}))}{N\sigma_{y}\sigma_{\hat{y}}}, $$

  (4)

  where $E(\hat {\mathbf {y}})$ is the expectation, i.e., the mean value, of the vector of predictions, and $\sigma _{y},\sigma _{\hat {y}}$ are the standard deviations of the observations and the predictions, respectively.

• The mean fractional bias – MFB:

  $$ \text{MFB}=\frac{1}{N}\sum\limits_{i=1}^{N}\frac{E(\hat{y}_{i})-y_{i}}{\frac{1}{2}(E(\hat{y}_{i})+y_{i})}. $$

  (5)

• The factor of the modelled values within a factor of two of the observations – FAC2:

  $$ \mathrm{FAC2}=\frac{1}{N}\sum\limits_{i=1}^{N}n_{i}~~~\text{with}~~~n_{i}= \left\{\begin{array}{ll} 1 & \text{for} ~~0.5\le|\frac{E(\hat{y}_{i})}{y_{i}}|\le 2,\\ 0 & \text{else}. \end{array}\right. $$

  (6)

RMSE and SMSE are frequently used measures for the accuracy of the predictions’ mean values, which are 0 in the case of perfect model. SMSE is the standardised measure with values between 0 and 1. PCC is a measure of associativity and is not sensitive to bias. Its value is between −1 and +1, with ideally linearly correlated values resulting in a value 1. MFB is the measure that bounds the maximum bias and gives additional weight to underestimations and less weight to overestimations. Its value is between −2 and + 2, with the value 0 in the case of a perfect model. FAC2 indicates the fraction of the data that satisfies the condition from Eq. 6. Its value is between 0 and 1, with the perfect model resulting in a value of 1.