To find out how much water is flowing in a stream or river, USGS personnel have to go out and make a "discharge measurement." USGS uses the term "discharge" to refer to how much water is flowing, and discharge is usually expressed in "cubic feet per second" (think of a cube of water one foot on a side, and how many of those move past a point in one second). To do this, we often have to go out and stand in the creek, measure the depth and how fast the water is moving at many places across the creek. By doing this many, many times, and at many stream stages, over the years we can develop a relation between stream stage and discharge. Stream stages are not always cooperative, so its not uncommon for someone to have to go measure a stream at 2:00 in the morning during a storm, sometimes in freezing conditions! Also, the stream can be uncooperative in that it changes -- a big storm may come along and scour out bottom material of a creek, or lodge a big log sideways in the creek, or sometimes do both at the same time. These kind of changes result in changes in the relation between stage and discharge.
SOURCE: USGS Water-Resources