## 3 Combined Numerical Forecast Model and Machine Learning
### Research Site  
Lake Kinneret, also known as the Sea of Galilee and shown in Figure 3, is the world's lowest freshwater lake, with an altitude range of 208-215 m below sea level. It is located in the northern part of the Dead Sea rift, between the Galilee and Golan Mountain regions (N 35\({}^{\circ}\)35, E 32\({}^{\circ}\)50). The average daily annual air temperatures range between 17 and 18 \({}^{\circ}\)C in the winter and up to 40 \({}^{\circ}\)C during the summer, whereas the lake's average surface water temperatures are 15-16 \({}^{\circ}\)C in the winter and reach 31 \({}^{\circ}\)C in the summer. The Kinneret's surface area is about 166 km\({}^{2}\), with a maximum length and width of 22 and 12 km, respectively [58; 59; 60]. The Kinneret wind system during the summer is characterized by strong westerly winds in the afternoons, which makes it a popular sailing site. The daily wind cycle starts with the morning's lake breeze, from approximately 07:00 to 11:00, blowing from the lake  
Figure 3: Map of the study site: **(a)** location of the research site in the Eastern Mediterranean. The green box illustrates the largest physical simulation domain (WRF9, low-resolution simulation), the red box illustrates the second physical simulation domain, and the orange pentagon in **(c)** illustrates the meteorological measurement’s location (Kfar Nahum, 35.579\({}^{\circ}\) E, 32.883\({}^{\circ}\) N), and the two purple grid points in **(b,c)** that were used for studying WRF output: the western point is WRF1 (35.583\({}^{\circ}\) E, 32.883\({}^{\circ}\) N, 351 m east of Kfar Nahum) and the eastern point is WRF9 (35.610\({}^{\circ}\) E, 32.901\({}^{\circ}\) N, 3570 m northeast of Kfar Nahum). The blue box in **(b)** illustrates the high-resolution domain. The region topography is illustrated in **(b)**; brown lines are 10 m contours, and black lines are contours at elevations of 0, 500, 1000. Figure 2: Research model system flowchart: Part I is the training phase of the model, during which GFS data are used as initial conditions for a WRF simulation, which produces an initial wind prediction (output). This output serves as an input to train the ML model with the IMS observation dataset. Part II is the validation of the trained ML model forecasts. In this phase, the output of the physical prediction (WRF) is used as an input to the trained ML model in conjunction with the IMS validation dataset to measure the model prediction accuracy on unrecognized input data. toward the shores and usually light, up to 4-5 m/s [61]. The mechanism that drives the afternoon winds is the westerly Mediterranean Sea breeze, which develops in the morning to early noon and blows toward Lake Kinneret. The high prevalence of the Mediterranean Sea breeze is a local phenomenon that relies on the stable presence of the Persian trough that dominates during summer [62]. When the westerlies originating from the Mediterranean reach the lake, they blow significantly stronger, reaching velocities of 8-15 m/s [63; 64]. The wind velocity enhancement process in the Kineret is substantial, and whereas seasonal average winds at the Mediterranean are in the 4-6 m/s range [63], they increase approximately threefold when reaching the Kinneret. Due to the lake's shape, the westerly wind reaches the lake first at the west bank, at the area of Vadi Arbel, where the strongest winds are experienced. The wind gradually decreases toward the middle of the lake and the eastern coast. Three factors affect the temporal and geographic distribution of the Kinneret's wind. The primary factor is the downslope wind. The westerly Mediterranean breeze (~45 km west of the Kinneret) climbs the Galilee Mountains and then blows downward toward the rift. This process is intensified by differences in air temperature between the colder, humid, and mountain-descending air and the warm, dry rift air. Furthermore, the pressure gradient is intensified by the afternoon deepening of the Persian trough [65].