The Battle of Megiddo is Thutmose III’s first major victory in Palestine. It began when all Canaan, from Yurza (Tell Jemmeh, 31°23’14″N, 34°26’43″E) to the legendary marshes of the Euphrates revolted against Egypt after Hatshepsut’s death. Thutmose first came to Tjaru, located at Tell Hebua I, at 30°56’9″N, 32°22′E, and Tell Hebua II, located less than a mile to the ESE of the former, on roughly April 19. This identification is confirmed by a votive statue found at the site. Tell Hebua I was located on a coastal strip just north of a lagoon, called the Shihor (“Waters of Horus”) by the Egyptians, and possibly the “tongue of the sea of Egypt” in Isaiah 11:15, which was an estuary of Pelusiac I, and is today shown clearly as a gray area in Google Maps, set in Terrain mode. The body of water north of Tell Hebua I in the 2nd millennium B.C. and earlier was the Mediterranean, as shown in Hoffmeier’s map of the region (http://www.bibleorigins.net/MVC-128S.JPG). The Plain of Pelusium was formed by silt coming from Qantir. Lake Menzaleh, meanwhile, is of no earlier than the Islamic Period, formed by tectonic movements lowering parts of the Northern Delta at the rate of up to four meters every thousand years, as confirmed by Glen Fritz and Strabo.
Thutmose then arrived at Gaza (31°30’17″N, 34°27’50″E) on roughly the 28th of April, traveling over 140 miles in 9 days, about 15.6 miles every day. After leaving a day later, he traveled around 9 miles per day, a perfectly feasible rate of travel, to reach Yehem (modern Yama, Israel) around May 10th, where he head that the king of Kadesh had come into Megiddo. There were three routes to Megiddo: 1. The Jokneam route, bypassing Megiddo 2. The Aruna route, going straight to Megiddo, but easily open to attack and 3. The route splitting off from Yehem to go through the Wadi Masim to Dothan, Ibleam, and Taanach. The routes beside the Aruna were well guarded by the Canaanites. The Taanach route, excellently watered, was considered the preferable route by the commanders, and the Jokneam route Thutmose chose the direct route.
On around May 13, Thutmose came to the city of Aruna, modern Ar’ara, and took it. The arrival just south of Megiddo took place one day later. The Brook Kina is now partially transformed into a canal at 32°34’40″N, 35°11’31″E. Thutmose III, attacking from the northwest and southeast, almost captured the kings of Kadesh and Megiddo, but the army wasted time plundering. The siege beginning the day after Thutmose arrived at Megiddo lasted considerable time. I would recommend Nelson’s “The Battle of Megiddo” for further information.