Describe the long profile and changing cross profile of a river and its valley.

The long profile of a river illustrates its gradient from source to mouth, typically showing a steep gradient in the upper course, which gradually decreases towards the lower course. The cross profile, on the other hand, reveals the shape of the river valley at different points along its length. In the upper course, valleys are often V-shaped due to vertical erosion, while in the middle and lower courses, they become wider and flatter, reflecting processes of lateral erosion and deposition. Understanding these profiles helps explain how rivers shape the landscape over time.