Does the river Alyn follow Bradshaw's model?

This is described by hydraulic radius. This is the ratio between the cross sectional area of a river and its wetted perimeter. For example if two rivers have an equal cross-sectional area the river with the greater wetted perimeter will have more friction and so the velocity will be less. River A River B Both river A and B have a cross sectional area of 60 m. However river A has a wetted perimeter of 62 metres where as river B has only has 22 metres of wetted perimeter.

In river A the ratio between cross sectional area and wetted perimeter is very low which means the river flows slowly. In river B the ratio is much greater which means the river flows faster.

In general the larger the cross sectional area in comparison to the wetted perimeter the faster the river flows. This ratio is usually greater the further you go downstream and so the river flows faster. Discharge is the volume of water flowing in a river at a given point and is measured in cubic metres per second (cumecs).

Discharge increases downstream due to a number of factors. Firstly there are more streams and tributaries entering the river the further you go along a river. Velocity also causes discharge to increase downstream. The faster the velocity the greater the amount of water flowing past a point in a given time span.

Another factor that causes discharge to increase downstream is an increase in surface run-off. In the lower part of the profile there are normally more buildings and less vegetation than in the upper part.

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This means there is less interception from trees and more impermeable surfaces the further you go downstream. Consequently there is a greater surface run-off and a greater amount of water entering the river causing a greater discharge. Seasonal variations in rainfall and temperature mean that varying amounts of water enter and leave the river resulting in a varying discharge. Discharge decreases as more water is taken from the river for domestic purposes. Also water used for irrigation of farmland can lead to a decrease in discharge.

The importance of Hydraulic Geometry. Being able to measure the hydraulic geometry, particularly discharge and velocity in a river is important. Knowing how river variables change can be useful in predicting how the river will react to heavy rainfall which can help with flood prediction and protection. Being able to measure the velocity and discharge at a point on a river is important when building dams so that your dam can provide the optimum amount of hydroelectric power. It is also important that you know the geometry of the river in built up areas so that you can predict how the rivers course, size, or flow might change and take action.

Location The river on whi h I am investigating velocity and discharge is the river Alyn. It is found in North Wales approximately 25 miles southwest of Liverpool. Its source is found in Llanferres in the Llanddegla Moors. The particular site I will be working at will be Loggerheads, which is found roughly 2 miles west of a residential area called Mold. Methodology – Sampling Sampling is where you select and test part of an area as opposed to sampling the whole thing.

Sampling is carried out to test ideas and see if theories are correct or to find out information for the first time so that theories can me made. Sampling is obviously less accurate than testing a whole population but it saves a lot of time and can still help to show general trends and relationships. The larger you can make the sample the more accurately it is likely to reflect the whole population. When sampling, it is important to try not to introduce any bias as this will give misleading results. There are a number of different types of sampling including random, stratified and systematic. We carried out the systematic method of sampling where samples are taken at agreed intervals.

In this case we tested the river every 30 metres for 450 metres. This is an unbiased method of sampling but it is possible that we may have introduced bias without knowing it. For example it may have been that by coincidence every 30 metres the river changed completely randomly which would cause biased results. The method used to pick the 4 points on the river where we would sample was biased as these areas were picked to try and show certain trends in pollution levels. The areas I tested, Loggerheads, wasn’t chosen at random which means that there may be some bias in my results.

Below are some photographs showing the methods we used when sampling. Data Analysis Having gathered the data, I need to analyse it in a way that will answer the key questions: ‘Does discharge increase downstream?’ and ‘Does velocity increase downstream?’ Therefore my first graphs plot velocity and discharge against the distance along the profile of the river. If Bradshaw’s model is correct these graphs should show a positive correlation. However, the results of both graphs were completely random and showed no correlation.

For example the graph of discharge against profile had the least discharge of 0.17 cumecs at 240 m and the most discharge of 2.07 cumecs at 180 m. The graph of velocity of against profile had the least discharge (0.24m/s) at 420 m and the greatest velocity (1.1m/s) at 30 m. This shows exactly how random the results were as greatest velocity was at the start of the profile and the least velocity was at the end.

Although the results appeared quite random at first, I thought there may have been an overall trend. In order to try and show this I used an averaging method in which I took the 2 adjacent readings and calculated their average. After doing this for each pair of readings I plotted the averages against the length along the profile. Although this helped to eliminate the peaks and troughs and produce a less variable graph it still failed to show a positive relationship with the distance along the profile. As there was no relation shown between distance downstream and velocity / discharge it was necessary to examine the measurements I had taken of other river variables known to affect velocity and discharge.

I plotted each river variable against river profile. For each river variable the results were as follows: Width- There was no relationship between the width of the river and the distance downstream. The measurements showed no correlation with the river being widest at 300m along the site when the width was 14.6 m, and it was least wide further down the profile at 390 m when the width was just 4.4 m Depth – From graph 5 you can see how the depth of the river changes. We can see that the depth varies from just 12 cm to 42 cm, but we can see from the shape of the graph that the variation in depth has no link with the distance along the profile as the shallowest point of the river was at 420 m which was at the very end of the profile when you would expect it to be deeper.

Cross-sectional Area The pattern shown by the graph is random. This was obvious as the cross-section area is determined by the depth and width of the river and these were also completely random. The greatest cross-sectional area was 3.19mat 180 metres, whilst the least was 0.74 m again at 450 metres. Hydraulic Radius – Again there is no relationship between hydraulic radius and the distance along the profile. The greatest value was 0.355 at 180m and the least was 0.07 at 450 m and 270m Wetted Perimeter – The results for wetted perimeter were completely random. The largest reading of 16.3m was at 300m, the lowest ( 6.08m ) at 30m. The readings had a range of 10.22m. There was not much difference between first  and last (10m ) readings along the river profile.

It is quite obvious that none of the river variables tested had any positive correlation with the river profile in any way that would be expected if Bradshaw’s model were correct. An assumption could be made that the only reason velocity and discharge have not correlated is due to the fact that the river variables which affect them haven’t correlated. This needs investigating further by relating each variable to velocity and discharge because there could be other factors accounting for the absence of positive correlation. For example it cannot be assumed that a point of non- correlation between velocity and river profile will match a point of non-correlation of river depth and profile for example. To investigate these relationships I plotted scatter graphs for the different variables so that I could use Spearman’s Rank to obtain a numerical value for the quality of the relationship between each set of variables. The results were as follows.