Most of the hikes in Denali follow braided river valleys up towards their glaciers. A braided river is very different from our usual image of a river. Its icy meltwater flows out from beneath the snout of the glacier, laden with the broken rock fragments of its home mountains. The water carries so much bedload and suspended grit that the water is opaquely gray.
Almost immediately, the stream starts dropping some of its bedload which clogs up the channel which forces some of the water to find a new path to flow along, a process that can happen fast enough to make me move while I’m eating a snack beside the stream. The river splits into multiple channels, hence the name, a braided river. (The Yukon River did the same thing in the Yukon Flats and for the same reason.) The whole length of the glacial valley — once carved by its glaciers into a broad U shape — is now being filled in as the clogging-up channels split and snake back and forth, burying the valley with a nearly level accumulation of gravel a half-mile wide and probably a hundred feet deep. For the hiker, the braided streams create a wonderfully level, broad, vegetation-free path to follow up into the glaciated Alaska Range.
https://www.nps.gov/dena/planyourvisit/images/10-a.jpg
However, because of the braiding, I have to cross these streams several times in order to reach the spectacular glacial country at the head of the valley. The meltwater of glaciers is icy cold; my feet ache and start going numb in a few minutes. The water carries so much silt of ground-up mountains that I can’t see beneath the surface. The bottom remains invisible; the depth unseeable. If I slip on an invisible rock or if the current sweeps me off my feet (especially with a backpack on), I am in trouble. This makes stream crossings challenging.
Hiking Denali is where I mastered the Stream Discharge Equation. Discharge is the measure of how much water is flowing in a stream. (In the United States, we measure this in cubic feet per second (cfs).) A simplified equation for calculating discharge is “width x depth x speed = discharge”. The wider the stream, the more water per second can be flowing down it. The deeper the stream, the more water per second can be flowing down it. The faster the stream, the more water per second can be flowing down it. Multiply the three together to calculate the stream’s discharge. This equation is over-simple because the stream channel is not of uniform depth and speed is not uniform across its width. But this simple formula gets us to the heart of river crossings (and much else that will follow).
A channel’s shape changes along its length. The current slows or quickens as it flows. But if no other side streams enter, the same amount of water is flowing through these variations in channel. Therefore, the discharge remains the same. Therefore, the width x depth x speed at one place in the stream must equal the width x depth x speed at another place. The three variables at the first place multiplied together must equal those three variables at the other place multiplied together.
For example, a stream that is 16 feet wide and one foot deep flowing at one foot per second at one place (16 x 1 x 1 = 16 cfs) could, in another place, be four feet wide and two feet deep flowing at two feet per second (4 x 2 x 2 = 16 cfs; the narrowing stream speeds up and deepens).
A dramatic example of this is a draining bathtub. The water in the tub itself (place one) is so broad and deep that its speed is almost undetectable while the water going through the very narrow drain (place two) goes so fast that it exerts a tremendous suction that fascinated me as a kid.
A consequence of this relationship is that if the glacial river speeds up at some place, then the only way to keep its discharge the same is to have either the width or the depth (or both) decrease proportionally. Or if, instead, the width at some place increases, then either the depth or speed (or both) must decrease. It’s mathematically inevitable. It’s natural law. It’s not a sometimes; it’s an always. The stream discharge equation acts as my fourth rule of flow.
This changeability of a stream’s current is known to boaters and fisherman and children who send sticks floating down the current. It should also be learned by hikers crossing glacial rivers. What I have to avoid is crossing where the current is either so deep or so fast that I am swept off my feet. The only way to minimize both depth and speed is to maximize the width. The wider the current, the slower and shallower it has to be.[1]
[1] A second aspect of a river crossing is that crossing the channel is different from crossing the current. The rules of discharge apply to the current. There are places in a stream where the current crosses from one side of the channel to the other. In these places, the current flows “sideways” so that the width of the current is wider, thus shallower, than the channel. At these convenient locations, one crosses the channel on an angle.
So when I see ahead that I will need to cross the glacial river, the first thing I look for is a place where the braided river has broken into multiple channels. Then I look along each of these channels for the widest part. Lots of times I am walking back and forth, upstream and downstream, as I strategically cross first one channel at its widest point and then the next. As I cross, I read the surface of the water. I can’t see the bottom but I can see how the water is moving on the surface. I don’t want quiet places because they are deep. I don’t want narrow, fast water because that is both deep and fast. What I’m looking for is wide, splashy water all the way across the stream; this indicates a riffle. The riffles offer broad paths of shallow water.
Looking down on a braided river where the river splits into multiple strands.
River is flowing from left to right. Brown is abandoned channels. Opaque greenish-gray is active channels.
Each glacial river crossing is an act of deepening confidence in the stream discharge equation. I once described this as an act of “faith in” and someone objected that it was an act of “confidence in”. The word choice is worth thinking about. In our culture we tend to have a religion vs. science attitude. Thanks to the stream discharge equation, I stepped into a possibly life-threatening situation hundreds of times. Was that faith or confidence? And faith or confidence in what?
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heather rangel
Faith or confidence? This is a beautiful contemplation! I have been paying close attention to the role of confidence in dogs as they greet each other, especially since lack of confidence in one dog can create an incredible reactive situation that can escalate to violence quickly with dogs. I wonder whether ( I assume, actually) confidence is something that is baked into personality (for dogs and humans!) at early imprinting years and how much work it takes to develop confidence once that imprinting door mostly closes. The work to slowly practice building confidence is an upward spiral that brings more opportunities to create life giving moments.
admin
Your comment took me back to some of my memories. In some, I know I exude solid confidence such as a glacial stream crossing or teaching math to middleschoolers. In other areas, I lack confidence such as many social occasions. So I think probably each one of us is a palette of mixed colors in terms of confidence.