Quantifying variability in stream channel morphology



[1] Nine stream channel characteristics (channel unit frequency, channel unit length, pool spacing, depth variability, width variability, large woody debris jam spacing, large woody debris volume, relative roughness, and average bank-full width used as a scale) were measured in 12 reaches in old growth forests on Haida Gwaii and Vancouver Island. They are applied to calculate a Euclidean distance measure of dissimilarity between all possible reach pair combinations. Frequency distributions of the resulting dissimilarity values express the range of variability present in the streams analyzed and enable definition of ranges of favorable and unfavorable comparisons. Reach pairs exhibiting high dissimilarity values have significant differences in several key stream channel characteristics that vary between reach pairs. Those reaches consistently appearing in reach pairs with high dissimilarity values exhibit significant variance from the norm for the group. Dissimilarity distributions provide a basis for appraising the outcome of stream channel manipulation (for example, in channel “restoration” programs) and for selecting channel pairs that are sufficiently similar to act as treatment and control units in experimental manipulations.

1. Introduction

[2] Large variability exists in stream channel morphology. Variability occurs within the same channel type even within a single reach, between tributaries of a single system, and certainly between different stream systems, particularly with respect to sediment storage, channel geometry, and structural features such as large woody debris [Wood-Smith and Buffington, 1996]. Recognizing variability is important when attempting to characterize and/or compare stream channels. It becomes extremely significant when considering the idea of “restoring” streams, a concept that seems to imply an ideal or “target” state. Can a target state (or range of states) be defined, considering the abundant variability that exists in stream channel morphology?

[3] It can be argued that the idea of identifying disturbed stream channels is not properly founded without some measure of the variability that exists in undisturbed channels, so that “disturbance” can be quantitatively appraised. Conversely, the “similarity” between two channels that might be selected for experimental purposes cannot be appraised unless the range of potential variability has been defined. Such measures are not currently available, and this represents a serious constraint to the effectiveness of programs designed to maintain and improve stream habitat. For example, Forest Renewal British Columbia (FRBC) invested more than $300 million in watershed restoration projects [Association of Professional Engineers and Geoscientists of British Columbia (ASPECT), 2000]. The success of this initiative has been seriously questioned, as the project goal (to return watersheds and stream channels to conditions similar to those found in undisturbed watersheds) is not clearly defined or quantified [ASPECT, 2000]. The notion of an ideal or “target” state is essentially connected to the variability of stream channel morphology. That variability is formally explored in this study.

[4] Attempts to compare smaller stream channels commonly focus on characteristics such as the proportions, spacing, slope, and shape of channel units [Keller and Melhorn, 1978; Grant et al., 1990; Montgomery et al., 1995]; and on changes in large woody debris (LWD) [Keller and Tally, 1979; Hogan, 1986, 1989; Andrus et al., 1988; Ralph et al., 1994; Wood-Smith and Buffington, 1996]. Channel units are morphologically distinct portions of a channel, one to a few channel widths in length. They consist of various types of pools, shallows, rapids, and falls that are the basic morphological components of a reach [Grant et al., 1990; Hawkins et al., 1993]. They are important descriptors of aquatic habitat [Bisson et al., 1982; Sullivan, 1986], and changes in their occurrence are often used as indicators of a stream's response to land-use changes [Hogan, 1986]. While the analysis of channel units in morphological studies is clearly helpful, the lack of clarity in defining the range of conditions that may be associated with them remains a limitation. The variability is not obviously structured, nor has it been shown to be systematically associated with disturbance in any simply predictive sense. Yet some measure of the variability is essential to enable meaningful comparison among stream channels and for identifying disturbed ones. This study represents a first attempt to quantify the variability inherent in stream channel morphology.

2. Study Areas and Reach Selection

2.1. Study Areas

[5] The study was conducted in forested watersheds on the coast of British Columbia. The goal is to determine the range of variability that streams, under similar basic governing conditions, hence with presumably similar channel morphologies, possess. Therefore geology, hydrological zone, biogeoclimatic zone, and basin type were all controlled, as they are known to exert considerable influence over the processes that occur in forest streams and hence on stream morphology. The study is further confined to streams located in forested drainage basins which have not experienced a major human disturbance (e.g., logging), so-called “old growth forest streams.”

[6] These requirements imposed significant limitations on the size of the project database. Most of the remaining intact, old growth drainage basins in British Columbia are found in remote locations that are not easily accessed. It is difficult to find a substantial grouping with suitably similar governing conditions. Five intact, old growth watersheds were selected for this study. They represent the largest surveyed group of small- to intermediate-sized streams (upper width limit in the range of 20–30 m) located in the same biogeoclimatic zone. All are located in the “outer coast” hydroclimatic zone, a winter-mild perhumid region (annual precipitation greater than 3000 mm). All are located on volcanic rocks (Karmutsen formation [Sutherland Brown, 1968]) or mixed volcanic and sedimentary rocks of similar age. The contributing drainage basins are characteristically steep and have high drainage density, as one would expect on the outer coast (Table 1). Four of the watersheds (Jason Creek, Inskip Creek, Gregory Creek, and Government Creek) are found on Haida Gwaii (Figure 1). These streams have previously been surveyed as part of the Canada-British Columbia Fish-Forestry Interaction Program (FFIP). The remaining watershed (Carmanah Creek) is located on Vancouver Island (Figure 1).

Figure 1.

Location map.

Table 1. Biogeophysical, Morphometric, and Hydroclimatic Characteristics
 Gov MainGov UMJason UpperJason LowerCarmanah Upper   
  • a

    QCR, Queen Charlotte Ranges; SP, Skidegate Plateau; VIR, Vancouver Island Ranges.

  • b

    K, Karmutsen (mafic volcanics, flow breccia, limestone); Y, Yakoun (shale, siltstone, volcanics, conglomerates); X, heterogeneous group of sedimentary/volcanic rocks.

  • c

    CWH, coastal western hemlock.

  • d

    Steepland is slopes >60%.

  • e

    Valley flat is slopes <7%.

  • f

    P, Podzol.

  • g

    R-P, riffle-pool; S-P, step-pool; C, cascade.

 Basin Characteristics, Uncoupled Reaches   
Contributing area, km216.   
Physiographic zoneaQCRQCRQCRQCRVIR   
Geology (dominant)bKKKKX   
Precipitation, mm/yr>3600>3600>3600>36003140   
Biogeoclimatic zonecCWHCWHCWHCWHCWH   
Steepland area,d %2530625749   
Valley flat area,e %1519167   
Drainage density, km/km20.8370.8960.3460.3581.56   
 Stream Characteristics, Uncoupled Reaches  
Wb, m32.318.522.321.838.9   
Gradient, m/m0.0060.0140.0180.0110.006   
Morphology (dominant)gR-PR-PR-PR-PR-P   
 Gov NBGov NB NFGov NB EFInskip MainInskip NBInskip SBGregory NBGregory UM
 Basin Characteristics, Coupled Reaches
Contributing area, km27.
Geology (dominant)bKKKKKKYY
Precipitation, mm/yr>3600>3600>3600>3600>3600>3600>3600>3600
Steepland Area,d %19029705484024
Valley Flat Area,e %1012210202
Drainage Density, km/km20.9240.9230.9990.4810.4740.4080.3970.443
 Stream Characteristics, Coupled Reaches
Wb, m20.711.718.130.918.519.313.631.7
Gradient, m/m0.0170.0590.0250.0190.0580.0460.0270.013
Morphology (dominant)gR-PS-PR-PR-PCCR-PR-P

[7] Thirteen stream reaches were delimited in the five watersheds. The reaches were initially classified into two general categories by field workers: (1) uncoupled and (2) coupled. Coupled streams receive material directly from the adjacent hillslopes by creep and episodic mass-movement processes [Rice, 1994]. Uncoupled streams are generally flanked by floodplains and receive sediment inputs principally by fluvial sediment transport. The distinction between coupled and uncoupled reaches identifies potentially significant differences in position in the drainage basin and in key processes [Schumm, 1977] that may affect or alter stream channel morphology. In this paper, the coupled/uncoupled distinction will be referred to as “channel setting.”

2.2. Field Survey

[8] Of the five watersheds selected for this study, four have previously been surveyed for the FFIP. Carmanah Creek was surveyed by the senior author and two assistants in August 1999. In order to maintain consistency, the survey technique developed and used in the FFIP studies was employed in Carmanah Creek.

[9] In order to establish a measurement interval, bank-full width (Wb) was estimated for each stream on Haida Gwaii through use of a regional discharge/bank-full width relation. At Carmanah Creek, width was estimated by averaging bank-full width measurements recorded randomly along the candidate reach. Longitudinal profiles were surveyed with an automatic level and stadia rod, and distances were measured with a surveyor's hip chain. Thalweg, water surface, and bar and bank elevations were measured, and surface D95 was estimated, at a set interval of one bank-full width. Morphological features (e.g., breaks separating channel units; the deepest point of a pool) were added as supplementary survey points. The original FFIP surveys covered the entire stream length.

[10] Channel cross sections were surveyed at a set interval of one bank-full width for Carmanah Creek and five bank-full widths for the remaining channels. A fiber tape was strung normal to the right bank and tensioned to horizontal, and bank-full width was measured. Horizontal distances were also recorded at significant points in the cross section (e.g., top of the bank, water surface edge, edge of vegetation). This information, along with the elevation data from the longitudinal profile, was then incorporated into a cross-sectional sketch (Figure 2).

Figure 2.

Carmanah Creek. Scaled diagram (120–240 m) and sketch of cross section at 120 m.

[11] The volume of all LWD jams, steps, and individual pieces was inventoried every bank-full width using procedures established by Hogan [1989] and Hogan and Bird [1998]. The volume of sediment storage associated with LWD jams and LWD jam characteristics was also assessed. Finally, a scaled diagram was assembled which included the position of channel units, position and orientation of LWD, and the position of cross-sectional surveys (Figure 2). The scaled diagram was used as a reference when calculating channel unit lengths and LWD characteristics.

[12] Channel units were identified in the field using topographical, sedimentological, and hydraulic criteria adopted in the FFIP surveys and outlined in Figure 3. Some of the channel unit types listed in Figure 3 are not conventionally defined as channel units. Stone lines and log steps are generally viewed as channel elements within rapid and cascade channel units, respectively. The unit types listed in Figure 3 were selected primarily in order to preserve those morphological units delineated in the FFIP surveys database.

Figure 3.

Channel unit types and their associated characteristics.

2.3. Selection of Stream Channel Characteristics for Analysis

[13] No clear criteria exist for determining which variables best characterize stream channels. The choice of channel characteristics for investigation in this study was limited because much of the data were originally collected for a different project. Table 2 summarizes the available stream channel characteristics selected for study in the project.

Table 2. Stream Channel Characteristics
ParameterUnitMetric Scale
Channel unit frequencynumber of specific unit/number of all units 
Channel unit lengthm/mreach length
Pool spacingm/mmean Wb
Depth variabilitym/mmean bank-full depth (d)
Width variabilitym/mmean Wb
LWD spacingm/mmean Wb
LWD volumem3/m3mean Wb × d × reach length
Relative roughness (D95/d)m/md

[14] The two channel unit characteristics selected for analysis in this project are (1) channel unit frequency by number (e.g., riffle unit frequency = number of riffles/total number of all channel units), and (2) channel unit frequency by length (e.g., riffle length frequency = total length of riffles/total length of reach). Channel unit length (expressed as a percentage of the total channel length) is perhaps not as robust a measure as channel unit frequency, yet it provides important information on the nature of a stream. For example, Jason Lower has a pool unit frequency of 49% (i.e., 49% of the observed channel units in the reach were pools). While this characteristic provides significant information, we can better understand the character of Jason Lower if we also know that 70% of the reach length is occupied by pools.

2.4. Stream Channel Subreach Selection

[15] In the stream morphology literature, the term “reach” is used in different contexts. In the strict sense, a reach is a morphologically homogenous length of channel within which the controlling factors do not change appreciably [Church, 1992]. However, it is common to use the term reach to describe any length of channel being studied. As no standards exist, reach lengths surveyed to characterize channel morphology tend to vary between studies. We consider a reach length of 50–70 Wb to be a conservative measure, based on knowledge that in free-formed pool-riffle reaches, pool-to-pool spacing tends to average 5–7 Wb [Leopold et al., 1964]. This length ensures a well-represented sample of channel units. For forest streams, where pool-to-pool spacing shortens to three to five channel widths, reach lengths of 30–50 Wb would be conservative. However, many studies have considered shorter reach lengths. Montgomery and Buffington [1997] used reach lengths of 10–20 channel widths, and Wood-Smith and Buffington [1996] used reach lengths of roughly 20 channel widths. Hogan [1986] used reach lengths of approximately 30 channel widths but recommended longer reaches for future studies in order that certain channel features, such as LWD clustering, could be investigated more thoroughly.

[16] In order to characterize the variability between streams, the reach lengths and measurement intervals used for a given stream must be representative of that system. Figure 4a illustrates the two sampling lengths in question. For a given quantity of information, there is a direct relation between reach length and measurement interval. The choice of measurement interval within a fixed reach will influence how much local variability is captured. However, there is likely a characteristic reach length within which full systemic variability is expressed. Varying the measurement spacing would vary the resolution at which variability is defined. Lengthening the reach could improve the precision merely because the sample size grows.

Figure 4.

(a) Illustration of the two primary sampling lengths: reach length and measurement interval length. (b) Fitted second-order polynomial regression line superimposed on a longitudinal profile (Jason Lower). (c) Variance plot (horizontal distance versus variance of depth deviation) (Jason Lower). The upstream end of the displayed variance plot shows an abrupt rise at 875 m. This is likely due to the presence of several large LWD jams immediately downstream of this point.

[17] Representative reach lengths were determined by analyzing the variance of depth deviation, over increasing distances. The FFIP channel depth data were selected for this analysis for two reasons: (1) Depths were surveyed over the longest possible distances using a reasonably intensive measurement interval (less than or equal to 1 Wb), and (2) the longitudinal depth profile reflects important structural elements of the channel that are related to channel unit types which, in turn, reflect channel morphology and aquatic habitat quality.

[18] For each reach, longitudinal profiles were constructed. Second-order polynomial regression lines (z = x2 + bx + c) were fitted to the longitudinal profiles to estimate the average thalweg elevation (Figure 4b), and depth deviations (actual thalweg elevation minus estimated thalweg elevation) were calculated. Significant deviations from the regression line represent changes in the sediment supply and storage regime (e.g., sediment wedges associated with LWD jams). The variance of these deviations was then calculated for increasingly extended sets of the data, and the results were plotted (Figure 4c). As can be seen from Figure 4c, the variance of depth deviation generally decreases or stabilizes with longer reach lengths, indicating that the full reach variability has been reached. Similar calculations were carried out for all reaches.

[19] Figure 5 portrays the decision tree followed to select the most representative reach (or subreach) for further analysis. The variance plot of Inskip NB was not stable (Figure 6) and was discarded from the database. Table 3 summarizes the selected subreaches that were used to quantify stream channel variability. The shortest scaled distance is 25 Wb but measures 800 m. The shortest absolute length is 370 m (34 Wb).

Figure 5.

Decision tree for selecting most representative reach.

Figure 6.

Variance plots of candidate reaches.

Table 3. Old Growth Subreach Selection
WatershedReachChannel SettingEntire Reach, mSelected Subreach, mLength (Wb)Final Variance of Depth Deviation
Government CreekGovernment Mainuncoupled0–8000–800250.05
Government UMuncoupled800–2660800–1925600.05
Government NBcoupled800–1593800–1593400.06
Government NB NFcoupled1593–24641593–1963340.05
Government NB EFcoupled1593–22651593–2265400.06
Inskip CreekInskip Maincoupled0–6490–649290.05
Inskip NBcoupled649–919discardedn/an/a
Inskip SBcoupled649–1399902–1399340.14
Gregory CreekGregory UMcoupled3701–58664786–5866500.11
Gregory NBcoupled5866–62865866–6286280.03
Jason CreekJason Loweruncoupled0–12050–860460.07
Jason Upperuncoupled1205–19251205–1925330.05
Carmanah CreekCarmanah Upperuncoupled0–10000–1000260.07

3. A Method for Stream Channel Comparison

[20] The standard techniques used to compare stream channels do not offer a quantitative method incorporating a variety of stream channel characteristics. A method based on the concept of dissimilarity, developed by Cheong [1992] for objective landform comparison, is adapted here for use in stream channels. Stream channel reaches are compared by calculating the dissimilarity between two reaches based on selected stream channel characteristics. A Euclidean distance measure is used to calculate the “proximity” between them [Gordon, 1981]:

equation image

where wk (k = 1, …, p) is a set of weights, k represents the characteristic variable, and i and j represent the first and second objects, respectively, in the individual pairwise comparison. For example, xik represents the value of the kth characteristic variable in the ith stream. Equation (1) yields the weighted root-mean-square distance. The higher the values for δij the greater the dissimilarity between the two objects. It is beyond the scope of this study to define particular weights for stream channel characteristics, which presumably would depend on the particular purposes of an individual analysis; hence we set wk = 1 for all k.

[21] Incompatible units between variables may pose a problem. This can be overcome by standardizing the variables, achieved by dividing each variable by its standard deviation or, for interval measures, range. Standardization also eliminates the possibility for a variable with a relatively large range of values to skew calculations. Hence

equation image

where σk is the standard deviation or the range of x·k.

[22] Application of the dissimilarity measure involves two steps. The first step is to calculate the individual dissimilarity value of each stream channel characteristic for any given reach pair combination. For example, the riffle frequency dissimilarity (squared) between reach i and reach j in a sample of N reaches is calculated using equation (2), where k now represents the riffle frequency characteristic r and σr is the standard deviation of all the riffle frequencies in the sample (i.e., all N reaches). In the second step the total dissimilarity is calculated. For a given reach pair combination, the total dissimilarity is the square root of the sum of all the individual squared dissimilarity values for each stream channel characteristic:

equation image

[23] Table 2 lists the stream channel characteristics, all of which are scale free, used in the dissimilarity calculations in this study. This places the focus on intensive measures of the system. As scale-free variates are dimensionless, it can be argued that the measures need not be standardized. In our case, though, the majority of the stream channel characteristics fall in the range 0 to 1, while LWD spacing values (scaled as multiples of Wb) fall in the range 1 to 10. Hence standardization is necessary to eliminate the effect of one variable with a disparate range.

[24] On the other hand, for some purposes a scale-referenced comparison may be more effective. Then, the complete removal of scale from the calculations may not be appropriate. Mean bank-full width, which relates directly to the physical scale of the system in question, was selected in order to investigate this question. The dissimilarity testing procedure was carried out for two cases: (1) mean bank-full width not standardized, and (2) mean bank-full width standardized. For the case when mean bank-full width is not standardized, it is by far the most influential variate in determining dissimilarity between reach pairs. The values for δij2Wb are so great that all other variates are inconsequential in the calculations. In contrast, when mean bank-full width is standardized (along with all the other variates) it is only occasionally the most influential measure. While standardizing mean bank-full width diminishes the importance of scale in the calculations, it is judged to be the best way to incorporate the scale-reference characteristic into the calculations.

[25] Weights (as shown in equation (1)) might be employed to adjust the effect of unscaled mean bank-full width. As mentioned above, however, individual variate weightings were not applied in this paper. All variates were standardized in the dissimilarity calculations which follow.

4. Results

[26] The relevant stream channel characteristics (as outlined in Table 2 and including mean bank-full width) were extracted from the channel surveys of each reach. These summary data (Table 4) were used to calculate dissimilarity values for various reach pair combinations. It should be noted that all but two of the reaches in our comparisons are pool-riffle channels (Table 1). Government NB NF is a step-pool channel and Inskip SB is classified as a cascade. Definitive comparisons would, for most purposes, be restricted to channels within one of these major morphological types. We have retained the two disparate channels in order to demonstrate the discriminating power of the analysis.

Table 4. Summary Characteristics (xik) for Dissimilarity Calculations (Uncoupled Reaches)
CharacteristicGov MainGov UpperJason LowerJason UpperCarmanah
Riffle unit frequency0.460.340.440.380.39
Riffle length frequency0.
Pool unit frequency0.380.440.490.350.36
Pool length frequency0.700.550.700.420.55
Glide unit frequency0.110.0900.130.24
Glide length frequency0.050.1100.150.24
Log step unit frequency0.
Log step length frequency0.00070.020.010.020
Cascade unit frequency0.030.0100.030
Cascade length frequency0.010.0200.060
Pool spacing (Wb)1.570.891.441.112.14
Width variability, m/m0.4190.2640.1480.4890.199
Depth variability, m/m0.19410.29890.26070.31470.2863
LWD jam spacing (Wb)2.3323.1883.0532.8862.984
LWD volume, m3/m30.0370.0680.0500.0410.011
Relative roughness, m/m0.730.810.741.210.64
Mean Wb, m32.318.518.520.938.9

[27] To illustrate the sensitivity of the method, we discuss some of the results in detail and present detailed calculation results for one reach pair, Carmanah–Inskip SB (Table 5). Three general types of reach pair combinations were constructed: uncoupled versus uncoupled; coupled versus coupled; and channel setting ignored.

Table 5. Detailed Dissimilarity Calculation Results, Carmanah–Inskip SB
Characteristic (k)Carmanah (i)–Inskip SB (j) δijk2
Riffle unit frequency7.22
Riffle length frequency1.03
Pool unit frequency0.09
Pool length frequency1.75
Glide unit frequency4.09
Glide length frequency4.34
Log step unit frequency9.36
Log step length frequency12.15
Cascade unit frequency9.26
Cascade length frequency11.03
Stone line unit frequency6.60
Stone line length frequency4.31
Pool spacing (Wb)1.37
Width variation, m/m9.18
Depth variation, m/m6.86
LWD jam spacing (Wb)0.41
LWD volume, m3/m311.65
Relative roughness, m/m9.11
Mean Wb, m9.51
δij-total2 (= Σ δijk2)119.33
Total dissimilarity (= δij-total2)1/210.92

4.1. Uncoupled Reach Pair Combinations

[28] Total dissimilarity values are presented in Table 6. The range of observed values is 3.96 < δij-total < 7.17 (N = five reaches; n = 10 comparisons) (Figure 7a). The most dissimilar reach pair combination is Jason Upper–Carmanah (δij-total = 7.17), followed by Jason Lower–Jason Upper (δij-total = 6.55). The high total dissimilarity value for the Jason Upper–Carmanah reach pair can be attributed to the high individual dissimilarity values for relative roughness, riffle length, and cascade length. The high value for δ2D/d is likely related to scale. Carmanah has the lowest relative roughness (D/d = 0.63) in the uncoupled database while Jason Upper has the highest (D/d = 1.21). This is expected, as Jason Upper is steeper than Carmanah (Table 1) and steeper channels tend to have larger values of D/d. Jason Lower and Jason Upper differ because Jason Upper has a steeper channel gradient than Jason Lower, so, for example, Jason Lower has no cascades and different pool characteristics.

Figure 7.

Frequency distributions of dissimilarity values: (a) All uncoupled old growth reach pairs (no distribution superimposed due to insufficient sample size). (b) All coupled old growth reach pairs (normal distribution superimposed). (c) All old growth reach pairs (lognormal distribution superimposed).

Table 6. Total Dissimilarity Values (Uncoupled Reaches)
Reach Pair CombinationsDissimilarity
Jason Upper/Carmanah 7.17
Jason Lower/Jason Upper6.55
Gov Main/Jason Upper6.46
Gov Upper/Carmanah6.35
Jason Lower/Carmanah6.16
Gov Main/Gov Upper6.15
Gov Main/Carmanah5.35
Gov Main/Jason Lower4.98
Gov Upper/Jason Upper4.33
Gov Upper/Jason Lower3.96

[29] The most similar reach pair combination is Gov Upper–Jason Lower, followed by Gov Upper–Jason Upper. While there are not many substantial differences between the two most similar reach pairs, the relative roughness characteristic appears to be one of the key discriminators. The value for δ2D/d is 0.09 for Gov Upper–Jason Lower. In contrast, δ2D/d is 3.22 for Gov Upper–Jason Upper. The relative roughness values for Gov Upper and Jason Lower are very similar (0.81 and 0.74, respectively), while the relative roughness for Jason Upper is larger (1.21).

4.2. Coupled Reach Pair Combinations

[30] The range of dissimilarity values is 2.75< δij-total < 8.72 (N = 7; n = 21) (Figure 7b). The least similar reach pair combinations all involve the cascade reach, Inskip SB. Inskip SB has the largest values for LWD volume (LWD volume = 0.165) and log step length frequency (log step length = 0.04). As Inskip SB is a steep, small channel with relatively large amounts of wood present, the higher frequency of log steps is not surprising. The cascade length frequency for Inskip SB is also, of course, significantly higher than all other reaches (cascade length = 0.2).

[31] The most similar reach pair combinations include (in order of increasing dissimilarity): Gov NB EF–Gov NB, Greg Upper–Gov NB, and Inskip Main–Greg Upper. While there are not many substantial differences between Greg Upper–Gov NB and Inskip Main–Greg Upper, the pool spacing characteristic appears to be the key discriminator. Greg Upper has the greatest pool spacing value (2.52) in the set while Gov NB and Inskip Main have small pool spacing values (0.92 and 1.25, respectively). This may be related to Greg Upper's low LWD volume and relatively flat gradient.

[32] Reach pairs involving the step-pool reach, Gov NB NF, exhibit total dissimilarity values greater than or equal to 5.18. In contrast, two thirds of all pool-riffle reach pairs exhibit δij-total < 5.18. If Gov NB NF and Inskip SB are removed from the coupled data set and dissimilarity values are recalculated, the range of observed dissimilarity values is 3.69 < δij-total < 7.36 (N = 5; n = 10), very similar to the range for uncoupled reach pairs.

4.3. All Possible Reach Pair Combinations

[33] The summary dissimilarity results using all possible reach pair combinations yielded a range 2.73 < δij-total < 10.92 (N = 12; n = 66) (Figure 7c), with no notable outliers. The range of observed dissimilarity values is greater than that found in the uncoupled or coupled comparisons. It is also worth noting that the pairwise dissimilarity values differ between the three combination types. For example, Gov Main–Gov Upper Main has a total dissimilarity value of 4.49 in the all-pairs comparison but a total dissimilarity value of 6.15 in the uncoupled calculations. This change is related to the change in sample size, which alters standard deviation values. If sufficiently large sample sizes were available, the standard deviation values would be stable and the changes in dissimilarity values would not likely occur. While the dissimilarity values are different, there are only slight changes in the overall ranking of the reach pairs.

[34] The least similar reach pair is Carmanah–Inskip SB (δij-total = 10.92) (Table 5); this result is expected because it is a comparison between very different reach morphologies (lowest gradient, widest pool-riffle versus steep-gradient cascade). High individual dissimilarity values are exhibited in three morphological stream channel characteristics (LWD volume, δ2LWDvol = 11.65; log step length, δ2lslen = 12.15; and cascade length, δ2clen = 11.03) and two scale-based characteristics (mean bank-full width, δ2Wb = 9.51; and relative roughness, δ2D/d = 9.11).

[35] The Carmanah–Inskip SB reach pair is a good example of differences that arise across extreme variations in scale and channel morphological type. Inskip SB is among the smaller basins in the comparison (Ad = 5.0 km2), whereas Carmanah is the largest (Ad = 35.2 km2). So processes mediated by position in the basin have their greatest effect in comparisons such as this. A critical operational comparison would probably endeavor to hold scale variations well within an order of magnitude.

[36] The high total dissimilarity value for the Jason Lower-Inskip SB reach pair (δij-total = 10.22) can be attributed to differences in channel setting and reach morphology. Jason Lower is an uncoupled, relatively flat pool-riffle reach, while Inskip SB is both coupled and a relatively steep cascade. This is reflected in the sharply different channel unit frequencies. A high value for δ2wvar (11.18) is also recorded because Jason Lower has a relatively low width variability value while Inskip SB has the highest. The high width variability calculated for Inskip SB can be attributed to one unusually high Wb value (Wb = 39.2) at the site of a relatively large channel spanning logjam. It is probable that single exceptional values such as this should be removed from the data since they significantly skew the characterization of the channel. Indeed, when the extreme Wb value is removed from Inskip SB and dissimilarities are recalculated, δ2wvar becomes insignificant (2.27).

[37] Inskip SB is found in three of the four remaining reach pair combinations within the least similar 10%. Overall, Inskip SB emphasizes the importance of topography and processes in mediating comparisons. It also stresses the importance of channel setting and gross morphology as filter factors.

[38] The most similar reach pairs are Gov Upper–Gov NB and Gov NB EF–Gov NB. This outcome raises the question whether the average dissimilarity among reach pairs within the same drainage basin (e.g., Government Creek) is less than that among reach pairs between basins and, by extension, whether reach pairs from within a basin may, in some sense, not be independent. However, an analysis of variance determined that no significant difference exists between average dissimilarity values for within-basin pairs compared to between-basin pairs (F1,43,0.05 = 4.07 > Fobs = 1.47).

[39] To investigate the possibility of a more general relation between geographic proximity and dissimilarity, a Spearman Rank correlation test was performed on all reach pair combinations. The correlation is not significant. In other words, the reach pairs closest in geographical proximity are not necessarily the most similar. Comparisons appear to have value regardless of proximity.

4.4. Summary

[40] The objective of this paper is to quantify the variability of forest stream channel morphology in order to provide a basis for studying dissimilarity or similarity among pairs of channels. This is accomplished by constructing frequency distributions of dissimilarity values based on n-dimensional Euclidean separations for defined groups of channels (e.g., all uncoupled reach pairs, all coupled reach pairs, and all reach pairs).

[41] Relative roughness, LWD characteristics, and certain channel unit characteristics stand out as being influential in our dissimilarity calculations. Differences also arise across extreme variations in scale. Differences between reaches based on these influential stream channel characteristics are often best explained by considering the stream reach position within the watershed. Stream reach position frequently relates to channel setting, gradient, sediment characteristics, and, ultimately, channel morphological type.

[42] The importance of sediment was not assessed in this study (for lack of appropriate information in the precollected database), but its effect on stream channels is undeniable. One of the principal governing conditions for stream channel morphology is the magnitude and time distribution of sediment supplied to the channel from the land surface. The caliber of the sediment is also important, for it determines the mobility of the sediment once in the channel. Thus channel disturbance (or instability) should theoretically be reflected in the bed material.

5. Assigning Statistical Significance

[43] The range of dissimilarity values observed within a set of reaches depends on what characteristics are chosen for analysis and what reaches are included in the set, as is made clear by the results presented above. What constitutes notable dissimilarity (or similarity) remains a value judgment made by the observer in light of the observed range of variation. However, given a sufficiently well behaved distribution of outcomes, we can apply statistical methods to make formal judgments about dissimilarity.

[44] The distributions of dissimilarity values in our examples appear to be sufficiently regular to permit inferential use of them. This idea was tested by comparing them with standard distributions. The dissimilarity values for “all reach pairs” do not deviate significantly from the standard lognormal distribution (chi-square = 1.90, df = 5, p = 0.863) (Figure 7c). The outcome is usual for test data that are distributed away from a limit value (here, zero). The chi-square analysis cannot be used on the other distributions since they have too few cases. A Kolmogorov-Smirnov (K-S) test, which detects gross deviations from a theoretical distribution, can be performed on the coupled reach pairs data set. Results from this test are illustrated in Figure 7b. On the basis of both visual inspection and the K-S test, the distribution for “coupled reach pairs” does not deviate significantly from the theoretical normal distribution. Hence a well-defined frequency distribution of outcomes occurs, given sufficient comparisons. The distribution can be interpreted as the probability distribution for channel pairs to be, in the sense defined by the test characteristics, not significantly different than each other.

[45] It is now possible to go back to the underlying question of this study: Can a target state be defined? Looking at Figure 7, the answer to that question seems to be no, at least in any simple sense. The outcomes of the pairwise comparisons among streams in broadly similar settings are simply too widely distributed for a unique target state to be identified. We observe a substantial range of channel morphologies that are not significantly different, in the statistical sense, given the overall variability in the set. However, the distribution illustrated in Figure 7c may be used to define high dissimilarity, thereby establishing a basis for identifying grossly different states.

[46] Two basic approaches may be taken to define high dissimilarity. Empirically, the uppermost class in Figure 7c (here, for example, δij-total > 9.20) could be identified. This isolates five reach pairs, all involving one reach (Inskip SB). Statistically, the upper 10% (or other limit percentage, e.g., 1%, 5%, representing the usual range of statistical confidence limits) of the reach pairs can be selected. Here this procedure isolates seven pairs whose dissimilarity values are greater than or equal to 8.56. Six out of these seven reach pairs involve Inskip SB.

[47] These outcomes serve to illustrate how dissimilarity testing may be used to identify reaches which are so different that they do not reasonably belong in the set. In the case above, reach pairs involving Inskip SB consistently achieve dissimilarity values judged to be significantly high. Therefore Inskip SB (which we know to be a gross morphological mismatch with the balance of the group) would be a reach of concern in any comparative exercise. In this case, the basis for mismatch appears to lie in drainage basin controls, but it could as easily arise from any other factor governing channel morphology (including disturbance).

[48] The present database serves to illustrate the principle of comparison by dissimilarity, but it does not by any means constitute a reference set for the outer coast region of British Columbia. An ideal reference set would have all reaches meeting strict assessment criteria regarding drainage basin setting, or gross channel classification [e.g., Grant et al., 1990; Montgomery and Buffington, 1997], and a sample size large enough so that the standard deviation values of the stream channel characteristics (used to standardize the variates) would remain stable upon the addition of new reaches. On present experience, we estimate an ideal regional reference set would have a minimum of 20 reaches, enabling 190 pairwise comparisons.

[49] Once a satisfactory reference set is obtained, new reaches (which pass the assessment criteria) could be assessed for similarity. Having defined a basis for comparison through the dissimilarity distribution, one could simply introduce a new reach into this group, recalculate dissimilarity values for all reach pair combinations, and assess the dissimilarity values for reach pairs involving the new reach. If reach pairs involving the new reach consistently achieved dissimilarity values judged to be significantly high in statistical comparison with the range of variability observed in the set, the new reach would be considered to fall outside the range of defined variability and hence to represent, in some sense, a deviant condition.

[50] At the other extreme of the distribution, the most similar reaches in a set become objectively selected candidates for paired treatment and control experiments.

6. Conclusions

[51] In this study, a method of quantifying stream channel variability has been presented. Any stream reach falling at the high end of the range of defined variability can be considered to represent, in some sense, a deviant condition, and hence stream channel disturbance can be effectively quantified. Three preliminary steps were involved in developing this method: (1) selection of suitably similar drainage basin settings, (2) selection of suitable stream channel characteristics; and (3) selection of suitable stream reaches.

[52] Results from the dissimilarity testing procedure are promising. Reach pairs exhibiting high dissimilarity values tend to have significant differences in several key stream channel characteristics. In this study, dissimilarity values varied between reach pairs depending on the reach pair group involved (e.g., uncoupled reaches versus all reaches). This outcome is related to changes in sample size, which subsequently alter the standard deviations used to standardize variables. If sufficiently large samples were available (we estimate at least 20 reaches), the standard deviation values would be stable and the changes in dissimilarity values would not occur. A whole array of regional reference sets could be assembled, reflecting different channel types and governing conditions. Comparing an individual site to a reference group is meaningless if the local context is not suitably controlled. It is important, then, to realize that judgment has not disappeared from the selection process. The comparison set, comparison criteria, and weighting given to them are all based on judgments in the first place.

[53] Reaches consistently appearing in reach pairs with high dissimilarity values can be considered significantly different. Formal statistical criteria can be applied to this decision. Thus the dissimilarity method of comparing stream channel reaches enables definition of deviant states and, prospectively, quantification of land management impact. Conversely, reach pairs with extremely low dissimilarity values can be considered “similar.” Hence the dissimilarity method of comparing stream channel reaches may also be used to identify reaches suitable for experimental treatment/control studies. Between these extremes, the bulk of the range of dissimilarity values defines the normal range of variability that one may expect to observe in stream channel morphology under homogeneous conditions. This range precludes the identification of narrowly specific “target states” for stream management or restoration.


[54] We thank Dan Hogan and Steve Bird for provision of the FFIP database and for advice on stream inventory methods; Tony Cheong for advice on drainage basin comparisons and dissimilarity indices; and Craig Jones and Dave Campbell for assistance in the field. This research was supported by Forest Renewal British Columbia and the Natural Sciences and Engineering Research Council of Canada. This paper has benefited greatly by reviews from John Buffington, David Montgomery, Jack Schmidt, and an anonymous reader.