## 5 Conclusions  
This study explores the application of data assimilation techniques, focusing on operational atmospheric state forecasting. The use of variational methods, particularly WRF-DA 3D-Var, demonstrates potential in refining the WRF model using real-time data. Despite the small observed improvements over the control case, several factors such as discretization errors and localized accumulation of errors in the covariance matrix may contribute to the  
Figure 7: Visualization of the DTO application results of (**a**) a ship routing application simulating the Heraklion to Chania port route and (**b**) surface oil spill concentration (grey color: tonnes/km\({}^{2}\)) and beached oil concentration (colored circles) forecasted after 35 h of hypothetical spill release; test case above Heraklion, Greece. Both visuals are available through Geomachine.com (accessed on 28 October 2024).  
limited effectiveness of the 3D-Var correction. Furthermore, the observed improvements with 3D-Var underscore the model's potential for enhancing forecast accuracy.  
The small percentage of improvement for WRF-DA can be attributed to several reasons. Firstly, discretization errors may play a role, stemming from the mismatch between model grid points and observation locations, where the nearest neighbor algorithm has been used for direct comparison, and this discrepancy can lead to inaccuracies in the comparison of gridded model data with localized meteorological station data. Secondly, localized accumulation of errors in the covariance matrix B, calculated over a finite time period, may influence the effectiveness of the 3D-Var correction. This suggests a need for further refinement in the estimation of covariance matrices, potentially through prolonged observation periods or enhanced data preprocessing techniques. Lastly, the location of the observation points for assimilation into the model and the validation stations plays a significant role, as implied by [20].  
This improved atmospheric model can serve as a foundation for correcting the wave and currents models, illustrating the interconnectedness between atmospheric and sea state modeling. A thorough comparative analysis of the results obtained by the corrected wave model with real-time buoy and in situ meteorological station data will guide the choice of the most suitable approach for operational wave forecasting and atmospheric state data assimilation. This test case, explored in the wider region of the island of Crete, showcases the potential of these refined models in practical applications, thereby contributing to the development of a high-resolution digital twin for ocean applications, demonstrating an on-demand service of optimal ship routing that aids in minimizing CO\({}_{2}\) emissions.  
Conceptualization, A.P.; methodology, A.P., V.M. and G.V.K.; software A.P. and V.M.; validation, A.P. and V.M.; formal analysis, A.P.; investigation, A.P. and V.M.; resources, A.P., V.M. and G.V.K.; data curation, A.P.; writing--original draft preparation, A.P., V.M. and G.A.; writing--review and editing, A.P., V.M., G.V.K., N.A.K. and G.A.; visualization, A.P. and V.M.; supervision, A.P. and N.A.K.; project administration, A.P., N.A.K. and G.A.; funding acquisition, N.A.K. All authors have read and agreed to the published version of the manuscript.  
This project has received funding from the European Commission's Horizon 2020 Research and Innovation programme under grant agreements no. 101037643.  
Data Availability StatementData are available from the corresponding author upon request.  
Data acquisition was from Cretaweather.gr, and computational time was granted by Meluxina under ID u100862 and AWS EC2 server under the GRNET-EDYTE Amazon grant. We acknowledge the help of IIlad Partner [PERSON] for access and setting up the visualizations through Geomachine.  
The authors declare no conflicts of interest.