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 (graph3). 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 (graph 4)- 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 (graph 5) – 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 (graph 6) – 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 3.19m ² at 180 metres, whilst the least was 0.74 m² again at 450 metres.
Hydraulic Radius (graph 7) – 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 (graph 8) – 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 (11.7m ) 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.
Data Analysis
Width v Velocity (graph 10) – This graph came out with a slightly negative value for the correlation. This means that as the width increased the velocity decreased. This is due to the fact that when there is increased width there is more area in contact with the water causing greater friction and slowing the water down.
Width v Discharge (graph 11)– This graph came out with a value of 0.26 this shows that there was some positive correlation between these 2 river variables. As width increased so did discharge. This is because as the width increases there is a greater volume of water in the river and so more water is discharged each second.
Wetted Perimeter v Velocity (graph 12)– This graph had virtually no correlation with a value of – 0.05. I would have expected more of a negative correlation as the greater the wetted perimeter the more friction there would be and the slower the river would flow.
Wetted Perimeter v Discharge (graph 13)– As with width this graph had a very small positive correlation of 0.12. This means that for a few values as the wetted perimeter increased so did the discharge. In some cases where there was a larger wetted perimeter the river channel would be larger and would allow a larger volume of water through. However at other places a larger wetted perimeter could have caused more friction slowing the water down and meaning that less volume of water was passing through each second.
Depth v Discharge (graph 14) – The graph for depth against discharge showed a definite positive correlation. As the depth increased the discharge increased. Again this was due to the fact that as the depth increased there was a greater volume of water and so more water could pass through at that point. Because the river is wider than it is deep changes in depth as opposed to changes in width have a greater effect on the cross-sectional area and consequently cause greater changes in the discharge.
Depth v Velocity (graph 15) – The results for this graphs gave a value of 0.13 this shows that there was a very small positive correlation. It is difficult to see how depth would affect velocity as there are so many other factors to take into account. For example when the river got deeper the gradient may have been less, which would mean that there wasn’t that much change in velocity.
Cross-sectional Area v Discharge (graph 16) – This showed a good positive correlation of 0.56. This isn’t surprising as discharge is made up of cross-sectional area and velocity and so when cross sectional area increases there is only one other factor that can counteract it. When the cross-sectional area increases there is a greater volume of water and so obviously the discharge increases.
Cross- sectional Area v Velocity (graph 17) – This had a negative correlation of - 0.23 that means that when the cross-sectional area increased the velocity decreased. This could be because for there to be an increase in cross-sectional area there probably would have to be an increase in the wetted perimeter which would cause more friction and slow the water down.
Hydraulic Radius v Discharge (graph 18) – The correlation between Hydraulic Radius and Discharge was 0.5 which shows quite a strong positive correlation. This means that as the value for the hydraulic radius went up so did the discharge. As hydraulic radius is a measure of velocity it follows that as the hydraulic radius increases the water is flowing faster and so more is discharged each second from a certain point.
From these results I can see that the main things that affected Discharge were Cross-sectional area, hydraulic radius and depth as these all had quite strong positive correlations that is when they increased so did the discharge. Cross- sectional Area had the greatest influence whilst wetted perimeter had the least correlation and the least influence. It was much harder to pinpoint the factors that affect the velocity, as there were more things that could affect it. This means there were more factors that could counteract the effect of increases in other variables. For example river width may increase which should lead to an increase in velocity, but if simultaneously depth and gradient were to reduce then the increase in river width would appear to have no effect on velocity. Consequently there wasn’t a strong correlation between velocity and the other variables. Depth had the best correlation with 0.14 and Cross sectional area had the worst correlation with – 0.23.
Data Representation
In this section I have presented my data in using a variety of graphical techniques so it is easier to understand and compare. This should also make it easier to identify any links between data and therefore will make the data easier to analyse.
Although my key questions were looking at velocity and discharge I didn’t actually take measurements of these but I was able to take measurements which allowed me to calculate values for these two variables.
To work out velocity I used the formula Speed = Distance/ Time. The distance in every case was 10 metres and the time was the average flow reading for that particular site.
To find the discharge I used the formula Discharge = Cross-sectional Area x Velocity. To find the velocity I multiplied the Channel Width by the Channel Depth.
To find the Hydraulic Radius I simply divided the cross sectional area by the wetted perimeter.
Conclusion and Evaluation
The aim of my investigation was to see if the river Alyn followed Bradshaw’s model in terms of the questions does velocity increase downstream and does discharge increase downstream.
From the results we can see that although there was no relationship between discharge, velocity or any of the other river variables measured and the distance along the profile, there is still a relationship between some of the variables as would be expected. So we might uphold the assumption that velocity and discharge didn’t increase downstream because the other variables with which they have a relationship didn’t increase downstream. Therefore the evidence suggests that the theory on which Bradshaw’s model is based is true: that is the relationship between different variables exists as predicted. However Bradshaw’s model itself, that the river variables increase downstream, has not been shown to be true in this case. Although Bradshaw’s model didn’t have any similarities with my results this only proves that the section of the river I tested didn’t follow Bradshaw’s model. Over the course of the whole river Bradshaw’s model might prove to be true. I also think that if I had done this experiment at any point on the river I would still have obtained random results for how discharge and velocity change. However I expect that the further downstream I conduct the experiment the higher the average discharge and velocity of these random results would be and so this would therefore give the effect of discharge and velocity increasing downstream.
Even though the investigation didn’t produce the results I expected I still consider measuring velocity and discharge worthwhile as the results did show the relationships between the river variables. I found that the cross sectional area of the river appeared to have the biggest effect on how discharge and velocity changed. I am quite confident that this is an accurate finding because it had a spearmans rank value of 0.57. This shows that for most cases a change in cross-sectional area produced a change in discharge and velocity and the bigger the change in cross sectional area the bigger the change in velocity and discharge. I also found depth had a considerable effect on discharge with a value of 0.46 for spearmans rank. This may have only been true for the part of the river I tested because it was quite wide but very shallow which meant that any changes in depth produced quite a large change in the cross sectional area which we have already discovered has a large influence on discharge and velocity.
I think the main reason that my investigation didn’t provide evidence to support Bradshaw’s model was caused by the methods I selected when collecting data and the implementation of these methods.
The first area that caused problems was the sample size and area tested. When carrying out the testing I didn’t take nearly enough samples to get accurate results. Although I was able to draw a conclusion from the data I collected that the river did not follow Bradshaw’s Model, this could be completely wrong a I took too few samples over too small an area. Greater sampling would have given me greater confidence that my final conclusion was accurate.
On reflection the way in which I actually took the measurements was inaccurate. For example when measuring the flow of the river I timed how long it took a twig to travel 10 metres. Several factors made this method inaccurate. Firstly the instrument used to measure river flow was a twig. In practice this was not accurate scientific equipment. Apart from the possibility of water logging that would affect speed of travel, different twigs were used at different points, so different speeds may have been recorded even if the river flow had actually been the same. The distance from the bank of the river where each twig was put in could also affect the speed at which it travelled as some parts of the river flow faster than others due to the helicoidal flow. These factors could have had a significant influence on the accuracy of the readings which we obtained for the velocity of the river and the discharge.
When calculating the cross-sectional area the measurements we took were very inaccurate. Again a number of factors contributed to this: firstly some measurements were only taken to the nearest 10 cm whilst some were taken to the nearest centimetre or millimetre. Although the odd centimetre may not seem that important it can have a large affect when it is multiplied to find the cross-sectional area and then multiplied again to find the discharge. There were also potential errors with the equipment we used. It is possible that sometimes there might have been some slack in the tape measure giving us an overestimate of the actual widths. Also, the measurements for width may not have been in a straight line perpendicular to the riverbank. If a slightly diagonal route was taken when measuring to the opposite bank this would increase the distance measured. When measuring depth we only took 3 measurements to try and gain an average for the whole of the channel. Although this is better than taking just one measurement it is still gives quite an inaccurate reflection of the actual depth.
Other problems with my investigation include the fact that I only tested the area at one time of year. At different times during the year the discharge of the river changes, but we can’t tell if the whole rivers discharge would rise or fall by the same proportion. For example in the summer the part of the river nearest the source might lose 10% of its water but further down the river it might lose that 10% and a further 10% due to other tributaries drying up, This means the discharge would change by different amounts at different parts of the river.
Although the investigation would have been more accurate if carried out over a larger section of river I did not have suitable resources or equipment for measuring on a large scale. It would have taken a considerable length of time to record data for a large enough sample.