Measuring a river should be an easy task. But rivers and watersheds are in a constant state of change, so any measurement we take is simply a "snapshot" that is true for an instant of time.
Rivers pulse in reflection of the seasons. When there is snowmelt and during rainy seasons, the total volume of water in the river increases. As water in the river channel rises, islands and riverbanks that are usually exposed are submerged. Increased levels of water scour the land it flows over and increases the amount of sediment carried with the current. The process is reversed in the dry season. Land that was submerged is exposed, less water and slower current allow particles to settle out of the water and be deposited on the riverbed itself. Year after year this cycle is repeated.
Measuring the river, then, actually means sampling the river at a specific point in time. If we are talking about water volume, we would measure it every day, or week, or month. These measurements can be averaged to give a reasonable picture of the amount of water carried in a river channel. But then, we would have to decide over what period of time is the average calculated? Ten years? Twenty years? Thirty? Each average would give a different result.
When we talk about the length of a river, we must also take a snapshot. Rivers are notorious for finding new channels, for cutting across a curve in the river which would result in a shortening of the river. Rivers also build land. At the mouth of rivers, sediment carried from throughout the watershed is deposited. That sediment, also called alluvium, builds to become dry land. Deposited at the mouth or end of the river, the additional land increases the length of the river. On the other hand, as sea levels rise and submerge coastal alluvium, the length of the river would decrease.
Nevertheless, the measurements we have, while not exact over time, are important. It is important to know that the Mississippi is the third largest watershed in the world. It meaningful to know that the combined length of the Mississippi and the Missouri make it the fourth longest river in the world after the Nile River of Africa, the Amazon River of South America and the Yangtze of Asia. It is important to know that the Mississippi carries close to a half a million pounds of sediment with it every day of the year.
The thing to remember about river measurements is that the measurement you read is not the last word in the story, the river reserves that right to itself.