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Jordan borders Syria, Iraq, Saudi Arabia and Israel. In the south around Aqaba there is a small coastline across the Gulf of Aqaba to the Red Sea.
Basically, the climate in Jordan is not uniform. Jordan is hilly in the northwest, here is the rainiest part of the country, at higher altitudes there is an average of 800mm of precipitation per year. The period between November and March is the rainiest. Here it is also comparatively cold in winter. Typical would be the table for Amman. In the west of this chain of hills, the Jordan River flows in a low-lying bed. Here the winters are mild and the summers quite hot. There is comparatively little rain. Clearly assigned to the desert climate are the south and east of the country. In the south, the heat is usually intense in midsummer, with extreme drought. Temperatures can rise to 40°C and more. Then one can actually only think of a beach vacation. The west is completely different. Here a kind of Mediterranean climate prevails. The summers from May to October are dry and hot. Winters from November to April are mild and relatively humid.
By the way, the winter months in Jordan bring rain surprisingly often. This is at least true for the north and the center of the country as well as the region around Petra. Especially around Petra, it can rain heavily from time to time, even in October and November, so heavily that flooding can occur from time to time. In January and February snow can fall in Jordan (e.g. in Amman, Ajlun or Petra), in the winter months Petra is often not accessible. Winter temperatures can drop below freezing in the highlands of Jordan.
On the other hand, the Dead Sea, Aqaba and Jordan Valley have more than pleasant temperatures in winter. Water temperatures in winter are usually still around 20 degrees. The Dead Sea is special in every point. Due to its location (the lowest point in the world) and the abundance of salt, the sea acts as a heat reservoir. This leads to practically constant pleasant temperatures throughout the year. Snow and cold are almost unknown here, and extreme heat is also rare.
The seasons are hardly noticeable in Jordan. It is either summer or winter. Summer usually ends when a kind of rainy season begins. Then there can be heavy rainfall from the Jordanian mountains to Amman and around Petra. There is a rough formula for rainfall in Jordan: rainfall decreases from west to east and from north to south. Rainy is the western mountainous area, relatively dry the middle mountainous area and very dry the desert areas.
The best time for the whole country is between March and May and October to November. But: due to the experiences of the last years one must expect violent precipitations in October and November e.g. around Petra. Perhaps the region around the Dead Sea would be good to visit all year round. This is also true for Aqaba, but the summers here are very hot. As I said, you can also go to other parts of the country in high summer, especially to the north. Also in winter you can basically make a vacation in Jordan. Then, for example, the regions around the Dead Sea, Aqaba or the Jordan Valley are ideal.