Long & Cross Profiles

By Alex Jackson

A River’s Course

The course a river takes is split into three stages, the upper, middle and lower stage. In the upper stage, the river is close to its source and high above its base level (the lowest point the river can erode to1). In the lower stage the river is far away from its source, close to the mouth and not far above its base level. In the middle stage, it’s somewhere in between.

The total energy that a river possesses varies from one stage to another because of changes in the river’s height, gradient and speed. In the upper course, the gradient of the river is steep and the river is high above sea level giving it a large amount of gravitational potential energy that can be converted to kinetic energy later on. In the middle course, the river’s gravitational potential energy gets converted to kinetic energy and the gradient begins to level out resulting in the river’s velocity increasing. By the time the river reaches its lower stage, it has next to no gravitational potential energy but lots of kinetic energy resulting in a high velocity.

The Long Profile

The long profile shows how a river’s gradient changes as it flows from its source to its mouth. You can draw a diagram of a river’s long profile either by drawing a quick sketch based on some previous knowledge or by plotting the height of the river above sea level at various points in its course. A sketch of a long profile would look something like this:

The long profile shows how, in the upper stage of a river’s course, the river’s gradient is steep but it gradually flattens out as the river erodes towards its base level. One thing to note is the presence of knickpoints in the long profile. These are points where the gradient of the river changes suddenly and can be caused by landforms like waterfalls or lakes, where the lithology of the river changes and differential erosion takes place. Knickpoints can also be the result of rejuvenation, where the base level of the river falls giving it some extra gravitational potential energy to erode vertically.

Throughout the long profile of a river, deposition and erosion are balanced meaning that, given enough time, the river’s long profile would become a smooth, concave, graded profile and all the knickpoints would be eliminated as they are either eroded or filled in by deposition. It would take a long time for a river’s long profile to become a graded profile though so the idea of a graded profile is, essentially, theoretical as it doesn’t really occur in nature. It’s not too hard to imagine what a graded profile would look like but here’s a sketch of one anyway:

If you needed to describe the graded profile you could describe it as a smooth, concave profile in dynamic equilibrium.

Changing River Processes

If there’s one key thing to take away from everything that’s been discussed so far it’s that the energy of a river changes as it flows through its course. As we’ve already discussed when we talked about river processes, rivers do stuff because they have energy and what they do depends on how much of a certain type of energy they have. Logically, this means that the processes that a river carries out changes throughout its course as it moves from one stage to another.

Processes in the Upper Course

In the upper course, the river has a lot of gravitational potential energy so it has a lot of energy to erode vertically. The bed of the river is eroded greatly while the banks aren’t eroded as much. The river mainly transports large pieces of angular rock and does so by traction because it doesn’t have enough kinetic energy to move the load in any other way. This increases erosion of the bed by corrasion as a result of the load being dragged along the bed of the river. Vertical erosion is further increased by the rough nature of the channel in the upper course which increases the water’s turbulence and its ability to erode. Erosion and transportation only takes place in large quantities in the upper course when the river’s discharge is high after periods of heavy precipitation. When the river’s discharge falls the river stops transporting the large boulders its transporting and deposits them.

Processes in the Middle Course

In the middle course, the river has less gravitational potential energy and more kinetic energy so erosion shifts from vertical to lateral erosion. Corrasion is still the main erosive process as large particles are transported by saltation. The average load size has decreased in the middle course, so more load is being transported in suspension. In the middle course, the river can flood and in doing so, it deposits gravel and sand sized particles onto its flood plain.

Processes in the Lower Course

In the lower course, the river has next to no gravitational potential energy so erosion is almost exclusively lateral. There isn’t much erosion though because the channel is smoother resulting in less turbulent flow. The main place where erosion takes place is where the river meanders. The average particle size is very small now, another reason for the reduction in erosion. The river’s load is mainly composed of silts and clays and it is transported in suspension or even solution. Like in the middle course, when the river floods it deposits its load but deposition now also takes place at the mouth of the river where the river meets the sea or a stationary body of water.

River Cross Profiles

River cross profiles show you a cross-section of a river’s channel and valley at certain points in the river’s course. The cross profile of a river changes as it moves from the upper to lower course as a result of changes in the river’s energy and the processes that the river carries out.

In the upper course, the valley and channel are narrow and deep as a result of the large amount of vertical erosion and little lateral erosion. The sides of a river’s valley in the upper course are very steep earning these valleys the nickname “V-Shaped Valley” since they look like a letter V. The river’s valley can be anything from a few meters to a few hundred metres in width depending on the lithology but the channel rarely more than 5m or 6m wide.

In the middle course, the valley has increased in width due to the increase in lateral erosion but its depth hasn’t changed significantly because vertical erosion has slowed down. Similarly, the channel’s width has increased but it’s still roughly the same depth. The land to either side of the channel in the valley is now the river’s floodplain and the valley’s sides are much more gentle.

In the lower course the valley is now very wide (often several kilometres) and the floodplain has increased greatly in size. The channel is a little wider but not much deeper.

Channel Efficiency & Velocity

The speed that a river flows at is affected by the efficiency of a river’s channel. The efficiency of a river’s channel is, in turn, dependent on a few factors. The less friction between the water and the bed & banks the higher the channel’s efficiency so to increase the channel’s efficiency you can do one of two things. Either a) Make the channel smoother to reduce friction or b) Reduce the amount of water that’s in contact with the bed and banks.

Hydraulic Radius

The efficiency of a channel can be quantified as the channel’s hydraulic radius. The hydraulic radius shows you how efficient a channel is. The larger the hydraulic radius, the higher the channel’s efficiency. The hydraulic radius can be calculated using the following formula:

\[ R_h = \frac{A}{P} \]

Where \(R_h\) is the hydraulic radius, \(A\) is the cross-sectional area of the channel and \(P\) is the wetted perimeter of the channel. The wetted perimeter is the length of the river’s bed and banks that is in contact with the water.

A large hydraulic radius is more efficient because it means that a smaller proportion of the river’s water is in contact with the bed & banks so there is less friction. The ideal channel shape for a large hydraulic radius would be a narrow and deep channel. Wide and shallow channels are less efficient and have a smaller hydraulic radius.

Here’s an example of calculating the hydraulic radius. Consider the two channel cross-sections below:

The cross-sectional area of channel A is 20m2 and its wetted perimeter is 14m so its hydraulic radius is 1.4. For channel B, the cross-sectional area is 16m2 and its wetted perimeter is 12m meaning that its hydraulic radius is 1.3. Channel A has the larger hydraulic radius so it’s the more efficient channel. We could have guessed that channel A is the more efficient channel without working out the hydraulic radius because it’s deeper and narrower than channel B.

Channel Roughness

Leading on from the hydraulic radius of the channel is the roughness of the channel. If the channel is rough with lots of large, angular boulders sticking out, it’s going to impede the flow of the river and increase its wetted perimeter, reducing the river’s efficiency. This will, in turn, increase the hydraulic radius of the river. Rough channels will, however, increase the turbulence of a river, increasing the river’s ability to transport and erode material.

The roughness of a river’s channel (and hence its efficiency) changes between different stages in a river’s course. In the upper course, the channel is very rough so velocity and discharge are low except after heavy precipitation. In the lower course, the channel is much smoother so the river’s efficiency is greater and the velocity and discharge are much higher.

Channel Velocity

The average flow velocity of a river increases along its long profile. This makes sense; along the profile, more potential energy is converted to kinetic energy, increasing the velocity. This is only the average velocity however; a cross-section of a river shows that the velocity varies from one side to the other. The lowest velocities are found where the river is shallow and so friction is greatest. The maximum velocity is found near the river’s surface where the channel is deep. At this point, friction with both the air and the channel is minimal. This point is often directly above the river’s thalweg.

A line running along a river’s profile linking its deepest points. A river’s fastest flow normally runs along it.

The velocity at different points along a channel’s cross-section is shown using isovels. That’s just a fancy name for contour lines that link areas of equal velocity.

An example cross-section of a river channel with isovels drawn on. The shape of the isovels will vary with the shape of the channel.

  1. Nine times out of ten, this will be sea level.