To complement Christophe's answer, you can also use SOURCES, especially if you need to control the discharge. You can choose a node downstream of your inflows, not too close to your boundary segment, and discharge on dry as a SOURCE.
Because SOURCEs are added in the (water) mass conservation, it is easier to take them into account when you start with dry land.
Also, if you are more worried about level at your upstream boundary, you can add a small reservoir (part of the mesh), deep enough not to be dry. You can then set the level and the water will spill over into your dry land.
Hope this helps.
Sébastien