Carl measures the temperature of the water at different depths of the lake to see if there is a relationship.

independent variable:

dependent variable:

Independent variable - Water depth

The independent variable is something that is purposely changed in order to see the effects of change on the dependent variable. So since Carl wants to measure the temperature of water at different depths we will purposely change the depth of the water in order to observe how this would affect the temperature. 

Dependent variable - Temperature of the water 

The dependent variable is something that is dependent on the independent variable and is assumed to change as the independent variable changes. So we can determine that the temperature of the water is the independent variable as Carl expects it to change with the depth of the water. Another reason we can determine this is the dependent variable is because Carl can change the depth of the water measured but not the temperature of the water depths.