Just as the continents have shifted and broken apart to take the shapes we know today, so has the source of fresh water changed location and direction as it flows from higher and colder places to lower and warmer ones. Rivers are frequently formed from snow and ice melt, and due to what we now perceive as global warming, we can be sure some rivers will indeed disappear.
There are some rivers that are fed by underground springs, or the overflow of fresh water lakes. Any of these rivers can potentially dry up and disappear as well. Rivers may disappear permanently, although it may be we will not be around long enough to view their rebirth when the climate changes yet again.
The course of a great river can hardly remain exactly the same over a very long period of time, as the power of its flow eventually changes it to some degree. The more rain, or snow and ice melt,the more powerful the flow of water, the more potential it has for changing the direction of its flow in one place or another. There are drought conditions that can severely diminish their volume. In that scenario, they can fade away to a trickle and then disappear.
The presence and flow of the fresh water visible in great river systems and lakes across the earth, in particular because the water is nearly as old as the planet itself. The cycle of water being lifted into the sky and released as rain to once again fill aquifers and river systems, along with snow and glacier melt to be sure, is what enables us to survive. With global warming a definitive interruption to critical supply systems, it is impossible to predict how long the current patterns will sustain us.
It is a fascinating side trip to consider the water that sated a dinosaur may have been recycled millions of times to end up as a celebrative bottle of Budweiser!
Some years ago there was a study done of reservoirs where it was discovered their very existence had gently changed the axis of the earth itself by several hundreds of a degree. That doesn't seem like much, but the very notion it is possible provides an insight into changes that affect the planet itself. The article also pointed out these reservoirs have conserved trace minerals and released them into more limited ecosystems which have enhanced the global spread of red tides.
If we consider that river systems are merely runoff of extra water from somewhere on its way to somewhere else, it's clear unexpected events can change the volume of water they carry. What will happen when the glaciers on Mount Kilimanjaro have disappeared? Where will the rivers begin in that region? What if the warming trends and climate changes begin to limit water available at the source of river systems that begin in the Himalayas? Many millions of people will be affected.
Maintaining an expansive water supply to keep the rivers gurgling and bubbling does seem to come back to global warming and population control. We need to address and adjust energy sources that give us what we need without adding to the global warming phenomenon. Population control is a critical part of this picture, and at least as challenging as the uses of petroleum.
Recently, the personal effluence of drug use was discovered to be present in some of the water in California. This is a harbinger of things to come unless we act to prevent it. Ozonation might be one way to purify water without chemicals. It should be at least considered where possible.
We don't really know how big the window of opportunity is. If we don't act immediately, the river systems of earth and the populations that depend on them will surely pay the ultimate price.