Supplementary material 1
Particle size distribution of cultivable airborne microbes and inhalable particulate matter in a waste water treatment plant facility
E. Katsivela1[1], E. Latos2, L. Raisi1, V. Aleksandropoulou2 and M. Lazaridis2
1Department of Environmental and Natural Resources Engineering, Technological Educational Institute of Crete, Romanou 3, 73133 Chania, Crete, Greece
2Department of Environmental Engineering, Technical University of Crete, Polytechneioupolis, 73100 Chania, Crete, Greece
*To whom correspondence should be addressed:
Dr. Eleftheria Katsivela
Associate Professor
Technological Educational Institute of Crete
Department of Environmental and Natural Resources Engineering
P.O. Box 89, Anapavseos St. 10, 73135 Chania, Crete, Greece
Tel. +30 28210 23071, Fax. +30 28210 23003
E-mail:
Calculation of root mean square error and Index of agreement
Τhe root mean square error (RMSE) is one of the commonly used statistical indices for overall model performance. It is calculated by the equation (1):
(1)
where Oi and Pi are the observed and predicted values at data point i (i=1 - N), and N is the number of data points. RMSE values of 0 indicate a perfect fit and it is generally accepted the lower the RMSE value the better the model performance. Specifically, Singh et al. (2004) suggested that RMSE values lower than half the standard deviation of the measured data, are appropriate for model evaluation. Nevertheless, for the model evaluation also the systematic (RMSEs) and unsystematic (RMSEu) portions of RMSE should be analyzed (). The RMSEs represents the error related to additive and proportional problems of the model, whereas the RMSEu the random effects on predicted values. They are estimated by the equations (2):
and (2)
where Pi=a+bOi, and a and b are regression coefficients. For a good model, the systematic RMSE value should approach 0, while the value of the RMSEu should be much larger than the systematic.
The index of agreement (d) is a measure of the degree of model prediction error on a scale from 0 to 1. The value of 1 indicates a perfect fit. It is calculated by the equation (3) (Willmott, 1981):
(3)
where Pi'=Pi+O, Oi'=Oi+O, and O is the mean value of observations. The values of d should be better examined in conjunction with difference measures such as the RMSEs and RMSEu (Willmott, 1982).
[1] Corresponding author (e-mail: )