## 6 Concluding Remarks  
This work deals with the accuracy of acoustical measurements and prediction models related to the ancient open-air theatre of Syracusae. Measurements based on ISO 3382-1 were conducted in unoccupied conditions. Firecrackers were used, because of the relatively high background noise level. The acoustical parameters described in the ISO 3382-1 standard, that is, Reverberation Time (T\({}_{20}\)), Clarity (C\({}_{80}\)), and Sound Strength (G), were obtained from the IRs measured at each receiver position. The uncertainty contributions due to the input values of sound absorption and scattering coefficients, \(\alpha_{\mathrm{w}}\) and s, have also been calculated with two simulation tools, that is, Odeon, version 13.02, and CATT-Acoustic, version 9. The models have been calibrated on the basis of the best match between the simulated and measured parameter values. Other sources of uncertainties, that is, the run-to-run variations and number of rays, have also been analysed and the obtained results have all been found to be under or at commonly accepted limit values of the Just Noticeable Differences (JNDs). The variability of the results is related to the algorithms used to approximate the acoustic phenomenon of the absorption and scattering. This kind of software are based on geometric acoustic principles, which rely on a statistical approach used to include diffuse sound scattering and predict the reverberant tail of an impulse response [22; 23].  
The following main results have been found from the uncertainty analysis that was conducted on the simulations of the Syracusae theatre:  
* The uncertainty, due to the input variability of \(\alpha_{\mathrm{w}}\) and s, is lower than the JND for T\({}_{20}\) and C\({}_{80}\), when the Odeon software is considered, and for G when both types of software are considered;
* Apart from T\({}_{20}\), Odeon software is more sensitive to variation of sound absorption than of sound scattering, while the opposite occurs for CATT-Acoustics;
* Comparable behaviour of the simulated values of G has been shown for both types of software; G has been found to be the most suitable parameter for the calibration of the open-air theatre model;
* A good agreement with the measured values has been found, at the limit of the JNDs, in the calibrated model for all the parameters, in spite of the limitation of the GA software that has emerged in this case study, for both types of software.  
Future studies will be conducted on a larger number of case studies, considering the influence of the architectural state of conservation, completeness, and dimensions on the acoustic field. Moreover, more suitable parameters for the acoustical characterisation of the open-air theatres than those described in ISO 3382-1 standard are the subject of continuous research [49].  
[PERSON] and [PERSON] conceived and designed the data collection campaigns and simulations; [PERSON] collected data on site and performed the simulations with Odeon together with [PERSON], [PERSON] performed the simulations with CATT. [PERSON] and [PERSON] collaborated for the statistical analysis of the uncertainties. F.A. offered support on the applicability of the ISO standard. All authors wrote and revised the paper.  
This research was funded through a Ph.D. scholarship awarded to the first author by the Politecnico di Torino (Turin, Italy).  
The authors are grateful to [PERSON], [PERSON], and [PERSON] from the Acoustics Laboratory of Politecnico di Torino for their technical contribution to this project, as well as to [PERSON] and [PERSON] from ODEON support team. The authors would like to thank also Soprintendenza BB.CC.AA di Siracusa, Istituto Nazionale Dramma Antico and [PERSON] for their support during the measurements in the theatre. Finally, the authors are grateful to [PERSON] and [PERSON] from the Univeristy of Ferrara, [PERSON] from the University of Parma, and [PERSON], from KU Leuven, for their suggestions and advice.  
The authors declare no conflicts of interest.