MARCO CONCEPTUAL

What constitutes a 'break' in a river long profile depends on what the researcher deems relevant, since boundaries can relate to a changes in profile (slope) and/or in bedform character (wavelength and amplitude). The type and scale of this variation is important, as it influences the nature of the evaluation in terms of'window span' (number of data points included for analysis at a given time) as well as analysis methodology. For example, if change in profile slope is sought, a relatively wide span is required (including many data points) in order to smooth out the influences of a variable bed morphology. Conversely, if a change in bedform character is sought, a relatively narrow span is required (including relatively fewer data points) so as to prevent smaller bedform scale variations being hidden.

To identify breaks in a river profile, a two-window approach can be used. The characteristics identified in one window are then compared to those in the other window. Profile breaks are located in areas where the coefficients suddenly change. A simple analysis methodology for this two-window approach involves comparing the average elevations identified in each window. These can be compared as a ratio, 'a', given by:

a = ( X , / X j ' (3.1)

where;

X, - mean elevation in window 1

%2 = mean elevation in window 2

Unfortunately, ratio measures do not produce consistent results, as a drop of similar magnitude will produce relatively larger coefiBcients in downstream locations where the elevations are lower. For example, an elevation drop from 10m to 8 m (a drop of 2m) produces a ratio of 1.25. However, an elevation drop from 4m to 2 m (also a drop of 2m) produces a ratio of 2. Consequently, similar breaks in gradient will produce larger coefficients in downstream reaches. Subtracting both sides eliminates this 'bias', with a magnitude measure, 'b', given by:

b=(X, -X2)=' (3.2)

where:

Xi - mean elevation in window 1 X2 = mean elevation in window 2

The variation in 'b' for a hypothetical data set is presented in Figure 3.12a. One difficultly associated with this measure is that the breaks in the coefficients will naturally reduce downstream as the gradient reduces. Smaller breaks in low gradient reaches downstream profile breaks may be as morphologically important as larger breaks in upstream reaches, although may not be selected relative to the larger coefficients produced in the upstream reaches. Equation 3.2 is also appropriate to determine breaks in the long profile in some situations where bedform variability exists. For example. Figure 3.12b shows that with a relatively constant bedform character, the break in profile slope can still be determined fi’om equation 3.2. This break is also evident should bedform amplitude decrease on steeper slopes (Figure 3.12c). If, however, bedform amplitudes increase on steeper slopes (Figure 3.12d), the clarity of the breaks is much reduced.

Variations in bedform wavelength also compromise the ability of local boundary hunting to identify breaks in a river profile as it affects the number of bedforms contained within a window span. Bedforms of larger wavelengths can produce more erratic coefficients, and this is evident in Figure 3.8c. This is an important consideration, especially as pool-riffie spacing has been noted to vary fi-om 1 to 21wy in natural river systems (Keller and Melhom, 1978). To remove the impact of such bed features, a relatively large window span is necessary. In contrast, a narrower window span will be required to identify breaks in form character at a smaller scale, such as those associated with pool-riffie bedforms.

To identify breaks in bedform character, single moving window approach can be adopted utilising measures of standard deviation. For example, bedforms of increasing amplitude will produce larger coefficients (Figure 3.8a). Unfortunately, standard deviation measures are also influenced by variations in channel gradient, with steeper profiles dominating values upstream relative to those derived fi*om lower gradient reaches downstream. Similar standard deviation measures can therefore be found with low amplitude bedforms on steep slopes and high amplitude bedforms on shallow slopes (Figure 3.13a). The influence of the profile can be removed through differencing the series (Figure 3.13b). The standard deviation of the differenced series, 'c', given by:

c = SD(Xdi) (3.3)

where:

SD = standard deviation

a)

140

Profile form C oefficient Location o f break

120 1 20 : ^ E 100 : r o c 80 : ' 100 € < 0 20 Distance 40 b) 200 300 ' B 150 : S 100 0 20 Distance 40 c) 200 ^ 150 CO € < 0 20 Distance 40 140 120

I I

Æ -O 80 60 40 20 0 d) 200 150 2 I < 0 20 Distance 40

Figure 3.12 Profile breaks identified by variation in elevation (Equation 3.2) for an artificially generated data set.

a) Simple case with no bedform variability b) Simple case with constant bedform variability.

c) Complex case with reduced bedform variation on steeper slopes. d) Complex case with increased bedform variation on steeper slopes.

a) 200 -B 150 ■2 100 50 0 0 0 _Profile 20 Distance 40 b) L o c a tio n o f b ed fo rm L o c a tio n o f b ed fo rm ro = ? ; J5 w (O T3 200 b re a k s b r e a k s -B 150 50 0 Profile Distance 14 12 % 10 S 8 I

: 1

2 (O 0

Figure 3.13 a) Profile and bedform influence on standard deviation coefficients for an artificially generated data set.

b) Removal of profile variability through differencing the series. Higher

standard deviation coefficients identify greater bedform variability.

The coefficients generated by equation 3.3 are able to identify simple breaks in bedform amplitude (as in Figure 3.8a) as well as in bedform wavelength (Figure 3.8b). Variations in coefficients cannot be simply related to form character as an increase in form amplitude can have the same influence on standard deviation values as a decrease in form wavelength (as in Figures 3.8a and 3.8b). Furthermore, a combination of increasing form amplitude and decreasing form

wavelength downstream (and visa versa) may cancel out any variation in the standard deviation

coefficients (as in Figure 3.8c and Figure 3.9).

Downstream trends in pool-riffie wavelengths also complicate local boundary hunting as it influences the number of data points included in a single window span. Coefficients generated become more erratic with fewer and fewer bedforms. This can be seen in Figure 3.8c where standard deviations calculated over a set distance become more erratic as bedform wavelengths

increase. Consequently, a single window span may not be appropriate for all sections of one

river or as a means to compare different river morphologies as form characteristics can be highly variable.

Instead of trying to adjust the formula and window spans to separate profile from bedform variability, another method combines the two. Webster (1976) describes an index which can be adapted to identify morphological breaks in river systems. This approach combines changes in mean elevation with changes in form variability (equation 3.4). The 'Webster' index, 'd', is given

d = (X |-X ;)^ (3.4) (V," + Vz")

wiicrc.

X] = mean elevation in window 1 X2 = mean elevation in window 2 Vj = mean variance in window 1 V2 = mean variance in window 2

The 'Webster' index tempers the breaks identified in the profile in relation to the morphological characteristics exhibited by the bedforms. In cases Wiere bedform amplitudes are relatively high, the confidence in any break in the profile is reduced, and the coefficients produced are relatively small. However, for a similar drop in profile vdiere the bedform variability is much lower, the confidence in the drop being attributable to an actual reduction in profile is increased, and the coefficient would be relatively large. One complicating factor in equation 3.4 is that the variance parameters will be influenced by profile slope, which reduces downstream. To prevent this, the variance of the differenced series can be used. The adapted Webster index, 'e', is given by:

e = (X .-X ,)^ (3.5)

(Vd,^+Vd2^)

where:

X, - mean elevation in window 1 X2 = mean elevation in window 2

Vd] - variance of the differenced series in window 1 Vd2 = variance of the differenced series in window 2

Due to the nature of the equations, a change in either profile or bedform character will be marked by a sudden rise or fell in the coefficients vffiich then plateau to a new level (as in Figure 3.12 and 3.13). The rises and falls mark the locations whereby the reaches are morphologically distinct. The clarity of these breaks are influenced by the nature of the variability (sudden or gradual) as well as the window span selected (wider spans progressively smoothing smaller scale variability). Spikes in the coefficients may also arise indicating the presence of a localised disturbance. Whilst these disturbances may not indicate a significant and continuing change in morphological character, they will affect the integrity of the bedform identification techniques. For example, if a profile gradient suddenly increases and decreases to its original gradient within a relatively short distance, failure to separate the reaches will seriously compromise the ability to detrend the profile with a single fimction. For the present study, both consistent changes and peaks in the

coefficients are used to segment the reaches. A tolerance value cannot be applied to identify significant breaks due to the progressive nature of profile and bedform variability.

Equations 3.1, 3.2, 3.3 and 3.5 were applied to the centreline profile of the Clyne River to identify breaks in profile and bedform character. A range of window spans were evaluated (4m, 10m, 20m, 50m, 100m, 200m), vyith the most appropriate selected on a purely visual basis. This selection balances the requirements for break clarity (small span) with the need to identify significant changes (larger span). During this analysis, the adapted Webster index (equation 3.5) was further amended as squaring the variance practically removed the dampening effect of bedform variability. Without squaring the variance, clearer associations were produced. The adapted Webster index (2), 'f , is given by;

f = (X ,-X 2 )' (3.6)

(Vd,+Vd2>

where:

X] = mean elevation in window 1

%2 = mean elevation in window 2

Vd] = variance of the differenced series in window 1 Vd2 = variance of the differenced series in window 2

Figure 3.14 shows the variation in the coefficient generated fi-om equations 3.1, 3.2, 3.3 and 3.6 when applied to the Clyne River. The variation is not random, and the river has adjusted into a series of reaches of a few hundred metres within which relatively uniform conditions exist. The reach scale variation in form character is most noticeable in the standard deviation of the differenced series measures (Figure 3.14c). The variability of the profile and bedform coefficients exposes the importance of this type of analysis vdien attempting to identify and characterise bed morphology. Unfortunately, given that form characteristics can be extremely variable between river systems, the functions and window spans derived for the River Clyne may not be easily transferable to other river systems. It is therefore difficult to recommend any of the parameters used here, although they do offer a foundation for fiiture evaluations conducted on other river systems.

The variability between the different coefficients, makes it difficult to select boundaries appropriate to all. For the 2.4 km section, 8 breaks (9 reaches) were selected subjectively through identifying breaks which were common to the 4 equations applied (Figure 3.15). These reaches have already been applied to assess the impact of variations in the data sampling interval (Figure 3.5 and 3.6). These reaches are also used in the following analysis to determine the impact of longitudinal and lateral bedform shape on the bedform identification techniques and associated

20 -1

NB Break in sampling due to access difficulties 500 1000 Distance (m) 1500 2000 O) 0.9 0.7 - 0.6 0.5 500 1000 Distance (m) 1500 2000 I 1000 Distance (m) 500 2000 0.15 % 0.05 - 1000 Distance (m) 1500 0 500 2000 200 1 e)

I

- 150 - 1000 Distance (m) 1 5 0 0 500 2000 Figure 3.14

a) Centreline profile of the Clyne River

b) Elevation change (ratio). Split window (each with 100 metre span, 200 total) Equation 3.1 c) Elevation change (magnitude). Split window (each with 100 metre span, 200 total) Equation 3.2 d) Standard deviation of the differenced series. Single window, 100 metre span. Equation 3.3

e) Elevation change (magnitude) / variance. Split window (each with 100 metre span, 200 total) Equation 3.6

20 1 Reach 1 Reach 2 16 - Reach 3 12 - Reach 4 Break in sampling Reach 5 Reach 6 Reach 7 Reach 8 Reach 9 500 1000 1500 2000 Distance downstream (m)

Location o f the breaks in the centreline profile o f the River Clyne based on the coefficients in F igure 3.14. Figure 3.15

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