Subsequent to the data collection, the statistics then had to be studied, tested for relationships/reliability. To establish any relationship between the data, the results were put through the calculations of the Spearman’s Rank Correlation Coefficient theory to determine the value of ‘r’. To decipher the extent of the data reliability, the ‘r’ value was placed upon the ‘Significance of the Spearman rank correlation coefficients and degrees of freedom’ graph. This graph then conveys the likelihood of the correlation occurring by chance. These methods have been chosen, as they are both well-established geographical tests and have been used in prior investigations.
Results Analysis
Hypothesis One: Discharge will increase further downstream.
At eight of the twelve sites shown in Figure 3.1, the discharge is between 500 and 1000 cumecs, with no obvious linear trend. Measurements at site numbers three, seven and twelve indicate an increase in discharge downstream. The scatterplot as a whole does not show a clear relationship between site number and discharge. This is confirmed by a Spearman’s Rank Correlation Coefficient (SRCC) of r = 0.147 (shown in Fig 4.1), with a significance level (0.649) that far exceeds the 0.05 confidence level. i.e. there is virtually no correlation between the two variables and a high likelihood that the coefficient has occurred by chance.
On this basis, hypothesis one cannot be accepted. i.e. discharge does not increase further downstream. This is going against well-established geographical theory that discharge does increase further downstream due to the following reasons. A greater accumulation of water via catchment area input such as (i) throughflow – water will flow laterally underground (ii) surface run-off – if the soil becomes saturated, then excess water will over the surface (iii) groundwater flow – water being transferred laterally from the water table. In addition to these transfers, the further downstream, the more confluences with tributaries occur and so increase the river’s capacity, the river then compensates for the extra water by increasing the size of the channel, i.e. a greater volume of water is able to flow downstream.
Hypothesis Two: Cross-Sectional Area will increase further downstream.
At site numbers four, five, six and eleven the cross sectional area has been measured at around 20mm². Similarly, a reading of around 60mm² has been taken at site numbers eight to ten. Measurements at the remaining sites suggests an increase in distance downstream, increases the cross sectional area. The scatterplot as a whole gives little indication of any relationship between the two variables, cross sectional area and site number. Once again, the SRCC reinforces this conclusion, r = -0.021. As does the significance level (0.948), this surpasses the 0.05 confidence level considerably. i.e. there is virtually no relationship between the two variables and a high probability that the coefficient has occurred by chance.
In conclusion, hypothesis two cannot be accepted. i.e. cross sectional area does not increase further downstream. Geographical theories suggest that the hypothesis should be accepted, due to several reasons. Firstly, both the catchment area input (through processes such as surface runoff) and tributary input increases further downstream, the channel is eroded and made larger so to accommodate for the increased volume of water in the channel.
The reasons for the results not corresponding with geographical theories, as well as problems and solutions encountered, for scatterplots showing site number against both discharge and cross sectional area, are in the following paragraph.
Firstly, the stretch of the river Lyd that the study was carried out did not contain any confluences with tributaries. As mentioned above, the input from tributaries is a main contribution to an increase in discharge downstream, without any tributaries in the data collection zone, the volume of the river or the discharge will not increase.
The lack of tributaries affect the cross sectional area as well, as the more water in the channel the larger the cross sectional area will be. Also, the size of the river channel will not increase due to the lack of erosion taking place (as there is not a large quantity of water), as a larger river channel (providing it is full) means a larger cross sectional area.
As shown in Figure 1.1, Parkend (nearest town to where the study was completed) is about half way along the Lyd’s course and the stretch extended to just before Bream; therefore it is not surprising that there is not a large increase in discharge in this small section of the river. To overcome this, the course should be divided into several sections and an average discharge then calculated. These new results would represent the discharge far better. When these results are plotted on a scatterplot, a more clear correlation may be visible.
Hypothesis Three: The larger the wetted perimeter, the greater the discharge.
On four occasions while the wetted perimeter is between 150 – 250mm, the discharge is slightly below one thousand cumecs. The remaining eight points show a strong positive correlation, indicating that an increase in wetted perimeter also means an increase in discharge. Four of the eight points in this correlation are clustered when the wetted perimeter is 50mm and the discharge is 1000 cumecs. Figure 3.3 as a whole provides an indication of a fairly strong correlation between wetted perimeter and discharge. Due to the relatively high ‘r’ value of 0.734, the SRCC also suggests that there is relationship between the two values. The significance level (0.007) is significantly below the 0.05 confidence level. i.e. there is 95% chance that the relationship between the two variables has occurred not by chance and because there is a correlation. If the study were to be undertaken again, a similar set of results would be collected.
In conclusion, hypothesis three is can be accepted. i.e. the larger the wetted perimeter, the greater the discharge. Geographical theory states the above hypothesis should be accepted. This is because the bigger the river channel, the water capacity of the channel also increases meaning more water can flow downstream, this is displayed in Figure 2.5. If the channel size i.e. wetted perimeter is bigger, then a greater volume of water can be transferred downstream at a quicker rate and hence discharge is greater.
As 4.1 demonstrates a possible reason for one of the weaker points in the correlation (site number 10) is the fact that a natural barrier/dam had built up in the river. This could have been due to debris not being able pass a certain obstacle during flood conditions or for another reason.
Paired Variables CSA&Site No. WP&Discharge Discharge&Site No. Correlation Coefficient -0.021 0.734 0.147
Significance Level 0.948 0.007 0.649
Number of Sites 12 12 12
Correlation Coefficient – A statistical representation of the extent of how the two variables are related, it tests linear association.
Significance Level – Refers to the probability of the correlation being correct and statistically significant.
N – Number of observations, in this case, the number of sites.
Calculations for the figures on the previous page are shown in Figure 4.2.
Problems and Solutions
During the study, inevitably problems were encountered; these are described below as well as possible solutions to these difficulties.
Problem: This problem only applies to hypotheses one and two. As mentioned in the above paragraphs, the stretch of the river Lyd in which the study was undertaken is approximately a quarter of the length of the whole river. The results therefore do not represent the whole river but merely one quarter of it. Although geographical theories for both hypotheses one and two state the two variables (discharge and cross sectional area) should increase as the river makes its way downstream, these concepts suggest that there should be a significant increase in the two variables between the source and the mouth. On this basis, should we have measured the variables at each end of the river, a considerable difference may have occurred.
Solution: The course could be divided into various sections, in each section at twelve equally spaced sites; the measurements would then be taken. Averages would then be calculated to establish the mean measurement of the variable within each section, a represented sample of each section of the course would then be shown, and this may then demonstrate a stronger more reliable correlation.
Problem: It is extremely challenging to measure the velocity of a river, due to the fact that each part of the river flows at varying speeds. For example the water in a channel flows at the greatest speed in the middle of the channel, as this is where least friction is found. Due to the fault in the flowmeter, the second method had to be used to measure the velocity; this method measures the velocity of the surface as the ‘ping pong’ ball floats in water. However, the flowmeter measures the velocity just below the surface and so the results are not consistent in the respect that the same part of the river was not measured at each site. This affects hypothesis one as discharge is calculated using the velocity of the river.
Solution: This problem was unavoidable as it was the fault and the unreliability of the equipment.
Problem: The title of the investigation is fairly general and extensive in respect to the areas in which the study has to cover, although only three hypotheses were chosen there several other hypothesis options available.
Solution: Create another title such as: ‘Investigate changes in river channel morphology’
Problem: This investigation demonstrates the changes of river characteristics in only one way, this being hypothesis three – the larger the wetted perimeter, the greater the discharge.
Solution: Investigate different hypotheses such as, ‘the greater the hydraulic radius, the greater the discharge.’
On this basis, it is difficult to suggest that this study has achieved the aim of its title i.e. ‘How do river characteristics vary downstream?’
However, this may be due to the inappropriate methods of data collection, explained in the first problem.
