## 4 Simulation and Experimental Results and Discussion
### WRF Simulation Analysis
This conclusion is strengthened by the absence of wind direction forecasts lower than \(200^{\circ}\), which are present in the observations. The WRF1 simulation also overestimates wind velocity and direction, which also illustrates that the simulated wind is more northerly than the observations. Figure 6: Measured versus simulated wind direction scatterplot with point density for the (**a**) WRF1 simulation and (**b**) WRF9. The x-axis shows measured direction, and y-axis simulated direction (degrees). The color map shows data point density, and each subfigure includes the regression line equation, \(r^{2}\), and \(p\) value. The diagonal black line indicates the 1:1 ratio between the simulation and measurement, and the red line is the regression line. The generation process of 2D linear regression for wind direction can be a challenging task. This is because degree units exhibit a circular characteristic; for example, 2\({}^{\circ}\) and 358\({}^{\circ}\) would appear at different edges along the axis, although they represent the equivalent wind direction. However, in our examined data, this did not pose a problem because there were no observations or simulated wind from the north. The WRF9 wind velocity simulation was unable to resolve the wind velocity patterns. The simulation was always close to 5 knots, while the observations ranged between 2 and 14 knots. The WRF1 simulated wind velocity, which is illustrated in Figure 7a, is an overestimate compared with the measurements. While the slope of the regression line is 0.77, so the deviation overestimate decreases as wind velocity increases, the intercept of the regression line is 4.9 knots, so the overestimate in the lower wind range is high. The maximum wind measured at the station reaches only 16 kts, whereas the simulated velocity contains numerous predictions for 15-20 kts as well as a few days of predicted 20 kts, although those may be interpreted as artifacts. Both observations and simulations show two prevalent wind velocity modes, which are illustrated by the two hotspots in Figure 7a,b. The prevalent low wind mode is at wind velocities of about 1.5-4.5 kts in the observations and about 4-9 kts in the simulations (left yellow patches). The higher velocity mode is at about 9-12 kts for the measurements and about 12-15 kts for the WRF1 forecast (right light blue patches). We assume that the wind modes in both the forecast model and the observations are due to the lower morning lake breeze and the stronger afternoon wind. Systematic deviations, such as those we previously described, can potentially be recognized by ML methods to improve the prediction of the simulation model. There are multiple possible explanations for the low prediction accuracy of the WRF, all of which result from our decision not to optimize the WRF simulation. One possibility is that the data derived from the initial conditions of the GFS-27 model (27 km resolution) may not be entirely suitable for our research site. Another potential factor could be that the terrain characteristics supplied to the model within the WRF model might not have been of a high enough resolution for accurate predictions. Furthermore, a more accurate parameterization scheme for subgrid processes using a different parameterization scheme for processes such as convection could achieve better forecasting. In this research, we intentionally avoided optimizing the WRF simulation at the cost of lower WRF accuracy in order to test ML postprocessing as an alternative to optimizing the WRF simulation. The goal was to emphasize the use of the ML model, shifting the focus away from WRF reconfiguration. The use of high-resolution simulation, especially when focusing on competitive sailing forecasts, is expected to yield better results. However, the high-resolution simulation is not a good fit for this application.