## 3 Results  
We here introduce and comment on the results, firstly validating the dynamical downscaling control case study that featured the implementation of the WRF. Results of the application of 3D-Var to the case study are discussed, for a test case consisting of a time period of 92 days with a forecast horizon of 3 days each. The respective dates cover a summer case from 15 July 2024 to 15 October 2024 in order to show the improvement and highlight the challenges associated with this task. For consistency purposes, this time window is also used to compare the impact that the atmospheric DA has on wave and hydrodynamic modelling when used as alternative forcing.  
This study presents the implementation of the 3D-Var technique within a WRF-DA model framework, focusing on a case study encompassing the region around the island of Crete. The model is configured to correct daily runs of 3-day forecasts over a 3-month period. A notable challenge highlighted in Section 2 is the substantial computational burden associated with this approach, necessitating intricate parameter optimization. Specifically, the computational demands are exemplified by a customized WRF run, where the initial 27 km input forcing undergoes dynamical downscaling to spatial resolutions of 9 km and 3 km through consecutive one-way nesting procedures. This process, executed on an Intel Xeon cluster with 64 cores, requires approximately 5 h to complete. Subsequently, real-time data acquisition, transformation into \"littleR\" format files, and functional minimization entail an additional half-hour on the same cluster. The subsequent assimilated run demands another 5 h of computational time, employing MPI parallelization between the CPU cores.  
To achieve reliable results, a significant number of daily runs, specifically 92, was considered in this study in order to mitigate statistical errors. Furthermore, there are many tunable parameters in this methodology that are case specific, for example, VAR_SCALING,a multiplier to the background error parameter since it is seen to be often underestimated, was proposed in the work of [20] as equal to 3, but in our case, this showed a deterioration of the results, indicating that the background error was not overestimated in our case. Fine-tuning these parameters was performed solely through trial and error, requiring significant computational resources and time. While only small differences were observed, the best configuration was selected for operational use in our tests. It is important to note that model calibration is an ongoing process, and most forecast data providers continuously perform and update their calibrations to enhance their services. Additionally, the reliable selection of observation points that provided a continuous stream of observations without missing values was of the essence, and the only way to overcome this burden is with continuous testing and validation through observational data.  
This validation poses additional challenges, notably the discretization error arising from the fact that observation points and model nodes do not typically coincide. The proximity of meteorological stations to model grid points influences the validation process, with errors persisting unless a more refined model is introduced, which introduces additional points in the finer grid and reduces the distance from the model's grid point to the observational one. This approach increases the computational cost and time, which can become a computational burden when considering operational forecasting systems that run on a continuous schedule.  
To ensure that the model approximates the real atmospheric conditions and is able to forecast without the resolution handicapping the forecasting skill, we performed a comparative analysis between the 27 km spatial resolution forcing used to initialize the WRF model and the 3 km dynamically downscaled model, which is then mentioned as the control case in our subsequent step of data integration within the WRF-DA model.