Picture a mountain stream. It is narrow, shallow and full of boulders. Water splashes and foams around the rocks, so it looks very fast.
Now picture the same river near the sea. It is wide, deep and smooth, and the surface looks calm and slow. Most people would say the mountain stream flows faster.
The surprise is that, in most rivers, the calm lower course is flowing faster. This lesson explains why. It also gives you a model that predicts how a river changes along its whole length.
The Bradshaw model is a simple summary of how river characteristics change from the source to the mouth. It builds on the long profile idea from the last lesson: a river runs from its source in the upper course to its mouth in the lower course.
Key terms:
| Characteristic | Source to mouth |
|---|---|
| Discharge | Increases 📈 |
| Occupied channel width | Increases 📈 |
| Channel depth | Increases 📈 |
| Mean velocity | Increases 📈 |
| Load quantity | Increases 📈 |
| Load particle size | Decreases 📉 |
| Channel bed roughness | Decreases 📉 |
| Gradient | Decreases 📉 |
Quick reminder from the first lesson: discharge is the volume of water passing a point each second (in cumecs), found by width x depth x velocity, and velocity is how fast the water moves in m/s.
Five things go up and three go down. Learn the pattern, then learn the reasons. The reasons earn the marks.
Discharge increases because more tributaries join the river, and more land drains into it, so more water is added along the way. With more water, the river cuts a bigger channel, so width and depth increase. A big river needs a big channel to hold all that water.
Mean velocity increases because the channel becomes bigger, smoother and more efficient. A smaller share of the water is rubbing against the bed and banks, so there is less friction to slow it down. The river flows faster even though the gradient is gentler.
Load particle size decreases because pieces of load knock against each other and the bed, and break into smaller, rounder pieces. This process is called attrition, and you will study it in the lesson on erosion, transportation and deposition. Smaller, smoother stones on the bed also mean that channel bed roughness decreases.
Load quantity increases because the river picks up more material along its length, from its banks, its bed and its tributaries. Gradient decreases because the river starts high up in the hills and gradually loses height, so the land it flows over becomes flatter near the sea.
In the mountains the water is shallow, so a large share of it is touching the rough bed and banks. Boulders break up the flow and slow it, even though the slope is steep. The foam and splashing make it look quick, but the water is held back by friction.
Near the sea the channel is deep and the bed is smooth. Most of the water is away from the bed and banks, so friction has much less effect. The result is a higher mean velocity. This is why velocity increases downstream even though the gradient falls.
Explanations score well when they are chains. For velocity: more water, so a bigger channel, so less of the water touches the bed and banks, so less friction, so faster flow.
It is simple, so it is easy to learn and remember. It gives the expected pattern for a typical river, which lets us make predictions. It also gives us something to compare real measurements with, which is useful in fieldwork.
It is a generalisation, so real rivers do not always follow it. A dam can cut discharge and velocity downstream. Hard rock can make a river steeper in places. People may straighten a channel or line it with concrete, which changes depth, velocity and roughness. Measurements at only a few sites may miss these changes.
You may be given measurements taken at sites along a river. Follow these steps:
A river has a velocity of 0.5 m/s at site 1 and 0.4 m/s at site 2 (nearer the mouth). The model says that velocity should increase, so this result is an anomaly. A possible reason is that a weir or dam just before site 2 slowed the water. Always back this kind of answer with the figures.
Saying that the river is faster in the mountains because it is steeper. Steeper does not mean faster once friction is included. Another mistake is saying that width increases with no mention of more water, so always start with discharge. Finally, remember that load size gets smaller, but the total amount of load gets bigger.
Fig. 1.1 shows measurements taken at three sites on the River Alvo (made-up data).
| Site | Distance from source (km) | Width (m) | Mean depth (m) | Mean velocity (m/s) | Median pebble length (mm) |
|---|---|---|---|---|---|
| A | 3 | 2 | 0.3 | 0.6 | 180 |
| B | 30 | 9 | 1.1 | 0.9 | 60 |
| C | 80 | 25 | 3.0 | 1.3 | 8 |
(a) Describe how the width of the river changes between Site A and Site C. [2 marks]
(b) Calculate the discharge at Site B. Show your working. [2 marks]
(c) Explain why the size of the load decreases downstream. [3 marks]
(d) To what extent do the data in Fig. 1.1 support the Bradshaw model? [6 marks]
(a) The width increases from 2 m at Site A (1) to 25 m at Site C (1).
(b) Discharge = width x depth x velocity = 9 x 1.1 x 0.9 (1) = 8.9 cumecs (1).
(c) Pieces of load hit each other and the bed as the river carries them (1). This wears them down and breaks them into smaller pieces (1). The further they travel, the more time this has to happen, so the load is smaller towards the mouth (1).
(d) Top level answer (5-6 marks): The data support the model strongly. Width increases from 2 m to 25 m, depth from 0.3 m to 3.0 m and velocity from 0.6 m/s to 1.3 m/s, as the model predicts (1-2). Pebble size falls from 180 mm to 8 mm, which also matches (1). Discharge rises from about 0.4 cumecs at A to about 98 cumecs at C, which fits more water being added by tributaries (1). The model also predicts that gradient and bed roughness decrease, but these are not measured, so they cannot be checked (1). The model is a generalisation and only three sites were used, so a dam or a change in rock between sites could be missed (1). Overall the data fit the model well for every variable shown.
In a "to what extent" answer, give figures for the points that fit, then say what the data cannot show, and end with a judgement.
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