What are the reasons for the permissibility of tayammum which are agreed upon by the Muslim jurists?

Tayammum is permissible for the one in the condition of minor or major ritual impurity, while he is a resident or a traveler, if one of the following reasons is present:
If someone doesn’t find water, does not find sufficient water, or if he needs the water he has for a present or future need to drink, or for others to drink (humans or animals).
If someone finds water but is unable to reach it, or does not find the right place to bathe.
If someone finds water but has a wound or is ill and he fears that water may increase his illness or delay the cure.
If someone finds water, but it is too cold and he does not have the means to heat the water, or if using that water will harm him.