Influence of step composition on step geometry and flow resistance in step-pool streams of the Washington Cascades

Transcription

1 WATER RESOURCES RESEARCH, VOL. 39, NO. 2, 1037, doi: /2001wr001238, 2003 Influence of step composition on step geometry and flow resistance in step-pool streams of the Washington Cascades William A. MacFarlane 1 and Ellen Wohl Department of Earth Resources, Colorado State University, Fort Collins, Colorado, USA Received 7 February 2002; revised 27 August 2002; accepted 27 August 2002; published 19 February [1] Step-pool streams dissipate flow energy primarily through spill resistance. We compared the geometry, step characteristics, and flow hydraulics of 20 step-pool reaches without large woody debris (LWD) to 20 step-pool reaches with LWD. Non-LWD streams exhibited significantly shallower flows, lower steps, shorter step spacings, greater percentages of water-surface drop created by steps, larger grain sizes, and smaller Darcy- Weisbach friction factors. Grain resistance was negligible in both stream types. Form resistance created by irregularities in the channel shape associated with steps contributed more to the total flow resistance in LWD reaches. Although both stream types showed poor correlation between step height and flow resistance, the significant positive correlation between flow resistance and step height/length ratio in the non-lwd reaches demonstrates the increasing effect of spill resistance with increasing step height. The lack of such a trend in the LWD-loaded reaches suggests that spill resistance was highly influenced by a few large log steps in these reaches. LWD creates deep pools and increases flow resistance along step-pool streams. It thus stabilizes channels and stores sediment in steep headwater streams recently scoured by debris flows. INDEX TERMS: 1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625); KEYWORDS: step-pool, flow resistance, large woody debris, Washington, debris flow Citation: MacFarlane, W. A., and E. Wohl, Influence of step composition on step geometry and flow resistance in step-pool streams of the Washington Cascades, Water Resour. Res., 39(2), 1037, doi: /2001wr001238, Introduction [2] Step-pool sequences are commonly found in mountain streams with gradients greater than 0.02 [Grant et al., 1990]. Channel bed steps are most commonly composed of alluvial boulders, although bedrock and large woody debris (LWD) also frequently create steps. Vertically oriented bed steps with a spacing of one to four bank-full widths [Montgomery and Buffington, 1997] are morphologically and hydraulically significant because they regulate flow resistance and sediment storage by creating hydraulic jumps, velocity fluctuations or reversals, and turbulence as supercritical flow over the steps becomes subcritical in the pools [Wohl and Thompson, 1999]. [3] Flume studies have shown that alluvial steps are created during high flows, which arrange the larger bed material into regularly spaced, channel-spanning steps [Grant et al., 1990; Grant and Mizuyama, 1991]. Field studies indicate that debris flows or extraordinary floods are likely to create a more uniform bed, along which steps and pools form following a series of lower magnitude or normal floods [Gintz et al., 1996; Lenzi et al., 1999; Lenzi, 2001]. [4] Many high-gradient streams in heavily forested areas such as the Washington Cascades incorporate LWD as well 1 Now at USDA Forest Service, Chugach National Forest, Anchorage, Alaska, USA. Copyright 2003 by the American Geophysical Union /03/2001WR ESG 3-1 as alluvial clasts into step-pool sequences. In such streams, LWD improves aquatic habitat by creating deep pools with substrate heterogeneity [Abbe and Montgomery, 1996]; improves water quality and contributes organic nutrients to stream ecosystems [Bisson et al., 1987]; and decreases flood conveyance by increasing channel roughness [Gippel, 1995]. Previous research has shown that step size in steppool streams may be related to the size of the step-forming clasts [Chin, 1999; Chartrand and Whiting, 2000] or the diameter of the step-forming LWD [Wohl et al., 1997]. Furthermore, Keller and Swanson [1979] showed that LWD steps accounted for 30 to 80 percent of the elevation loss in western Oregon streams, dissipating much of the flow energy in only a small portion of the stream length. [5] Flow resistance, the loss of energy caused by interactions between the flow and the channel boundary, is influenced by roughness elements and obstructions such as grains, bed forms, LWD, channel form, and vegetation. As defined by Bathurst [1978], step-pool streams are characterized by large-scale roughness, or relative submergences (R/D 84 ) less than 1.2. In such streams, large grain sizes in relation to flow depths allow form drag, freesurface distortion, and turbulence to be significant hydraulic processes [Mussetter, 1989]. The hydraulics of such streams are difficult to quantify because of the many related and unpredictable factors that contribute to flow energy dissipation. [6] The Darcy-Weisbach friction factor has been used extensively to quantify flow resistance in high-gradient mountain streams, and many researchers have shown that

2 ESG 3-2 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE step-pool streams exhibit extremely high friction factors, ranging from 0.1 to 2645 [Beven et al., 1979; Mussetter, 1989; Bathurst, 1997; Curran and Wohl, 2003]. These high friction factors are a function of the constant state of turbulence and energy dissipation that exist in step-pool streams with sequences of closely spaced vertical steps and plunge pools [Chin, 1989]. Because it was developed for uniform flow conditions, Beven et al. [1979] suggested that the Darcy-Weisbach friction factor may not be accurate in high-gradient step-pool streams with obviously nonuniform flow conditions. Although many empirical semi-logarithmic equations have been developed to predict flow resistance in low-gradient sand and gravel bed rivers [e.g., Keulegan, 1938; Hey, 1979], few of these equations have successfully predicted flow resistance in high-gradient boulder-bed channels [Marcus et al., 1992]. Maxwell and Papanicolaou [2001] used flume data to develop a formula for predicting the friction factor based on form and grain roughness of a gravel bed, but this has not yet been tested against field data. In the absence of a widely accepted equation for flow resistance along step-pool channels, we use the Darcy- Weisbach friction factor as the best available approximation. [7] Headwater streams in the heavily forested Cascade Range of Washington generally contain plentiful LWD, which often creates morphologically and hydraulically significant step-pool sequences. In an analysis of flow resistance in LWD-loaded step-pool streams in the Washington Cascades, Curran and Wohl [2003] measured Darcy-Weisbach friction factors ranging from 5 to 380. They partitioned the total flow resistance into grain resistance, or the shear generated by grains distributed along the flow boundary; form resistance, the result of drag forces or pressure differences between the upstream and downstream sides of an obstacle to flow, such as LWD or local channel expansions and contractions; and spill resistance associated with flow acceleration and deceleration. By partitioning total flow resistance into empirically derived components of grain, form, and spill resistance, Curran and Wohl attributed greater than 90% of the total flow resistance in these streams to spill resistance and unaccountable sources. They showed that step-forming LWD contributed more substantially to flow resistance than individual pieces of LWD that did not form steps, and concluded that LWD is an integral component of step-pool streams for providing flow energy dissipation. Abrahams et al. [1995] also suggested that LWD steps provide extremely high spill resistance in headwater streams, resulting from the interaction between large logs and shallow flows. Despite these findings, no previous research has compared friction factors between step-pool streams containing no LWD and those containing numerous LWD steps. [8] Although lithology, valley confinement, and mass movements such as debris flows also influence step-pool characteristics [Chartrand and Whiting, 2000], we expect step-pool streams that contain no LWD to be morphologically and hydraulically different from those that contain abundant LWD. We examined the flow hydraulics of 20 step-pool reaches in 15 streams in the Washington Cascades that contained little or no LWD, generally as a result of recent debris flow scour. To infer the effects of LWD on step-pool morphology and hydraulics, we made comparisons to the dataset of LWD-loaded step-pool streams from Curran and Wohl [2003]. The streams with and without LWD were similar in terms of lithology, valley confinement, stream order, drainage area, and hydrology. We hypothesize that flow resistance in streams that do not contain LWD is lower than flow resistance in LWD-loaded step-pool streams of similar size and gradient that contain abundant LWD steps. These differences in flow resistance are analyzed with regard to differences in step composition, hydraulic parameters, step geometry, channel characteristics, and the relative contributions of grain, form, and spill resistance between these two step-pool channel types. The results presented in this paper represent conditions of static channel geometry in that the step-pool sequences were stable and minimal bed load transport occurred during the period of measurement. 2. Study Area and Methods [9] Twenty step-pool stream reaches were surveyed on 15 streams on the western slope of the Cascade Range, Washington during July and August Ten reaches were located in the Green River watershed near Stampede Pass, eight were located in the Kapowsin Tree Farm in the Nisqually and Puyallup watersheds, and two were located in Lewis County in the Cowlitz watershed near Mt. St. Helens (Figure 1). The surveyed reaches were located on first-, second-, or third-order headwater streams adjacent to second-growth forests on lands owned by the timber companies of Plum Creek or Champion International. [10] Reach selection was based on a set of criteria similar to that used by Curran and Wohl [2003] in order to study reaches with size, gradient, planform, and hydroclimatic regime comparable to their dataset of LWD-loaded steppool streams. Gradient was between 4 and 18 percent, the approximate range in which step-pool streams are known to exist [Grant et al., 1990; Chin, 1998, 1999; Chartrand and Whiting, 2000]. Straight reaches with few divided channels were selected to minimize form resistance created by channel shape, and reach lengths were approximately ten channel widths long in order to represent the processes that define the channel morphology [Montgomery and Buffington, 1997]. In contrast to the reaches studied by Curran and Wohl [2003], the reaches described in this paper contained little or no in-channel LWD. Many had been recently scoured by debris flows that removed LWD from the channel. Other studies [Sawada et al., 1983; Gintz et al., 1996] suggest that debris flows destroy step-pool sequences, which subsequently re-form under fluvial regimes over a period of months to years. The step-pool sequences described here thus post-date the debris flows. [11] Because flow resistance along step-pool channels decreases with increasing discharge [Beven et al., 1979; Curran, 1999], channel surveys were conducted during the stable low-flow conditions of the latter half of the summer, minimizing the effects of stage fluctuation on flow resistance. This facilitated comparison of flow resistance among streams. The LWD-loaded streams studied by Curran and Wohl [2003] were surveyed during low-flow conditions in the summer of [12] Channel surveys were conducted using a theodolite and stadia rod. Ten cross-sections were surveyed perpendicular to the primary flow direction at equal intervals

3 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE ESG 3-3 flow depths and highly variable velocities. Velocity was calculated based on the thalweg length along the bed surface and the travel time of the salt solution along the same distance. Because the actual thalweg is likely more tortuous than the measured thalweg, velocity may be underestimated. [15] Grain sizes were measured using a random-walk method [Wolman, 1954], with measurements of the intermediate axis of 100 step-forming clasts and 100 poolforming clasts in each reach. The clasts measured in steps and pools were analyzed separately and also combined for a composite grain size distribution. [16] The Darcy-Weisbach friction factor is, Figure 1. Study area location map. The surveyed reaches were located in three general regions on the western slope of the Cascade Range, Washington. throughout each reach, representing steps as well as pools. Cross-sectional data were used to depict the channel geometry and calculate the reach-averaged hydraulic radius, areaweighted when divided channels existed. The channel edges were surveyed to depict the general planimetric shape of each reach, and a longitudinal profile was surveyed along the thalweg of each reach in order to calculate step geometry variables, thalweg length, and gradient. The longitudinal profile included the bed- and water-surface elevations at the crest and base of each step greater than 5 cm high, as well as the thalweg of each cross section. The water-surface gradient from the crest of the first step to the crest of the final step was assumed to approximate the friction slope, although this is a potential source of error as a result of nonuniform flow conditions and highly variable energy gradients. Each step was characterized as a vertical step, a riffle, or a smooth bedrock slide in the form of a bedrock surface inclined from the horizontal. [13] To define step geometry, step height (H) was measured as the vertical distance from the crest to the base of each step, and step spacing (L) was defined as the horizontal distance along the thalweg from the crest of a step to the crest of the next downstream step (Figure 2). The reachaveraged step height to step spacing ratio (H a /L a ) was calculated by dividing the height of each step by the spacing to the next upstream step, and the reach-averaged H a /L a /S a ratio incorporated the reach-averaged water-surface slope. The reach-averaged low-flow width-to-depth ratio (w/r) and relative submergence (R/D 84 ) were also calculated. The coefficients of variation of the hydraulic radius and low-flow width were calculated as a measure of variability in channel geometry. [14] Reach-averaged channel velocity was measured with a salt tracer using a pair of Hydrolab Recorders that measured specific conductance. A salt solution of 50 g of table salt dissolved in 5 10 l of water was instantaneously dumped into the channel approximately 10 channel widths upstream of the beginning of the reach, and the travel time was calculated as the difference between the peak specific conductance measured at the upstream and downstream ends of the reach. This method is comparable to using at-asite velocity meters [Spence and McPhie, 1997], which are less feasible in high-gradient streams because of shallow f ¼ 8gRS V 2 ; ð1þ where f is a dimensionless friction coefficient, g is the gravitational acceleration in m/s 2, R is the hydraulic radius in m, S is the channel slope, and V is the velocity in m/s. The friction factor was calculated for each reach using reachaveraged values of the hydraulic parameters. This equation was used because of its wide use in previous research, its dimensionless property, and its compatibility with empirical flow resistance equations. The grain resistance component of the Darcy-Weisbach friction factor ( f grain ) was calculated using a modified form of the Keulegan equation [Millar and Quick, 1994], f grain ¼ 2:03 log 12:2 R 2 ; ð2þ k s where k s is equal to the median grain size (D 50 ). Because no grain resistance equations have been developed specifically for high-gradient step-pool channels, and the range of applicability of this equation does not include such channels, the calculated grain resistance is only considered an approximation. [17] Statistical analyses were conducted using Statistical Analysis Software [SAS Institute, 2000]. For lognormally distributed variables, log (base 10) transformations were conducted prior to analysis. The level of significance was 0.10 for all analyses. 3. Results 3.1. Stream Descriptions [18] Each of the 20 non-lwd reaches exhibited a steppool configuration, although step composition and geome- Figure 2. Step dimensions in a typical step-pool sequence.

4 ESG 3-4 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE Table 1a. Stream Characteristic Hydraulic Parameters Stream a Drainage Area, km 2 Elevation, m Composite D 50,mm Step D 50,mm Composite D 84,mm Step D 84,mm Slope S, m/m Hyd. Radius R, m Velocity V, m/s Alluvial Bobcat* Caterpillar* Crystal Green* Kellogg (Lower) Main Intake NF Intake (Lower) Pioneer SF Mashel (Lower) Tacoma (Upper)* Tumwater Mixed Busywild Kellogg (Upper) NF Intake (Upper) SF Mashel (Middle) SF Mashel (Upper) Snake* Bedrock McCain Mint* Tacoma (Lower)* Stats Mean (non-lwd) Mean (LWD-loaded) b p-value (t-test) c < < < < a Stream names denoted by asterisk are informal names. b LWD-loaded stream data are from Curran and Wohl [2003]. c Bold p values indicate significant differences between non-lwd and LWD-loaded reaches. try varied considerably. Drainage area ranged from 0.45 km 2 to 5.9 km 2 and elevation ranged from 305 m to 1244 m. Reaches ranged in length from 40.6 m to 71.4 m, each containing between 13 and 30 steps and little or no LWD. The LWD-loaded reaches studied by Curran and Wohl [2003] contained an average of 79 pieces of LWD per 100 meters of stream, with 29% of the steps containing LWD. [19] In this study, 11 of the non-lwd reaches contained alluvial substrates, 3 contained predominantly bedrock substrates, and 6 contained mixed substrates of alluvium and bedrock (Table 1a). Alluvial reaches exhibited regularly spaced step-pool sequences with an average of 94% of the steps composed of boulders and cobbles, and pools composed of finer sediments (Figure 3). Reaches with bedrock substrates, likely as a result of scouring debris flows that removed alluvium to expose the underlying bedrock, often contained irregular and poorly defined steps. These reaches contained an average of 81% bedrock steps, ranging from long, smooth, low-angle bedrock slides with short, shallow pools to steep bedrock ledges with deep pools (Figure 4). Reaches with mixed substrates of alluvium and bedrock exhibited a combination of alluvial steps, bedrock ledges, low-angle bedrock slides, and steps composed of both bedrock and alluvium. [20] Field observations of debris-flow levees, downstream in-channel debris-flow deposits, and associated vegetation suggested that 8 of the surveyed reaches were scoured by debris flows within the past ten years, 9 reaches were likely scoured by debris flows more than ten years ago, and 3 reaches showed no evidence of debris flow occurrence (Table 1a). Although the bedrock and mixed substrate reaches all showed evidence of debrisflow scour, substrate lithology also played a role in determining substrate and step characteristics. Observations of channels formed on volcanic lithologies indicated that these channels were more likely to have smooth surfaces with exposed bedrock, whereas channels formed on sandstone with beds oriented perpendicular to flow were more likely to retain loose clasts and have alluvial steps Grain Size Analysis [21] Analyses of randomly selected grains show that the composite D 50 of the non-lwd reaches ranged from 104 mm to 181 mm, and the composite D 84 ranged from 223 mm to 478 mm (Table 1a). Comparisons between the LWDloaded and non-lwd reaches show that the D 50 and D 84 were both significantly larger in the step-pool streams that did not contain LWD ( p < ) (Figure 5). Additionally, the grains that comprised the steps were significantly larger than those that comprised the pools. This relationship also holds true for the LWD-loaded streams studied by Curran

5 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE ESG 3-5 Figure 3. Typical alluvial step-pool stream (South Fork Mashel River, Lower reach). and Wohl [2003], despite the frequent occurrence of LWDcontrolled steps Hydraulic Parameters [22] The hydraulic parameters used to calculate the Darcy-Weisbach friction factor were analyzed and compared between LWD and non-lwd streams (Table 1a and Figure 6). The reach-averaged water-surface slopes (S) of the non-lwd reaches ranged from to As prescribed by the stream selection criteria, these slopes were fairly similar to the range of slopes in the LWDloaded reaches. The reach-averaged hydraulic radius (R) of the non-lwd reaches ranged from m to 0.14 m. These flow depths were significantly shallower than those of the LWD-loaded reaches ( p = 0.04), which generally had larger pools. Reach-averaged flow velocities (V ) of the non-lwd reaches ranged from m/s to 0.28 m/s and were not significantly different from those of the LWDloaded reaches Channel Geometry [23] Parameters that describe channel geometry were compared between the LWD and non-lwd streams (Table 1b and Figure 7). Although the reach-averaged low-flow channel widths of the two stream types were similar, the ratios of width-to-depth for the non-lwd reaches (range 15 62) were significantly higher than those of the LWDloaded reaches ( p = 0.05). This is a result of the shallower flows of the non-lwd reaches, and the high width-to-depth ratios associated with the long, shallow slides of the non- LWD reaches that contained bedrock substrates. The relative submergences of the non-lwd reaches averaged 0.26, which was significantly smaller than those of the LWDloaded reaches ( p < ) because of shallower flow depths and larger grain sizes. Nevertheless, both stream types are characterized by large-scale roughness, which implies complex, turbulent flows and nonlogarithmic velocity profiles [Jarrett, 1984, 1992] Step Geometry [24] Several step geometry variables were compared between stream types (Table 1b and Figure 8). The average height (H ) of the steps in the non-lwd reaches was 0.30 m, and the average step spacing (L) was 2.6 m. The non-lwd reaches had significantly smaller step heights ( p = 0.03) and significantly shorter step spacings ( p = 0.01), indicating a higher frequency of steps, as well as smaller pools than the LWD-loaded reaches. The H a /L a ratio of the non-lwd reaches averaged 0.17, and the H a /L a /S a ratio averaged Although the non-lwd reaches had shorter steps and smaller pools than the LWD-loaded reaches, the H a /L a ratios of these two types of stream were not significantly different ( p = 0.18). However, the H a /L a /S a ratios of the non-lwd reaches were significantly larger than those of the LWD-loaded reaches ( p = ), indicating different relationships between step geometry and slope. The percentage of the total water-surface elevation loss attributed to steps in the non-lwd reaches averaged 91%. This was significantly higher than the 79% elevation loss attributed to steps in the LWD-loaded reaches ( p = ). This differ-

6 ESG 3-6 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE Figure 4. Typical bedrock step-pool stream (Tacoma Creek, Lower reach). ence is related to the greater frequency of steps and the shorter pools of the non-lwd reaches Flow Resistance [25] Darcy-Weisbach friction factors (equation 1) for the non-lwd reaches ranged from 11 to 101 and averaged 36 (Table 1b). Friction factors measured by Curran and Wohl [2003] in LWD-loaded reaches were significantly higher ( p = 0.10), ranging from 5 to 380 and averaging 85 (Figure 9). The grain resistance component calculated in the non-lwd reaches using the modified Keulegan equation [Millar and Quick, 1994] (equation 2) ranged from 0.26 to 0.55, with an average of This was an insubstantial component, representing between 0.4% and 2.6% of the total flow resistance. Grain resistance coefficients in the LWD-loaded reaches were significantly lower than in the non-lwd reaches ( p < ), averaging 0.14, or 0.5% of the total flow resistance. [26] The non-lwd streams had no component of form resistance created by LWD, whereas non-step-forming LWD comprised up to 15% of the total flow resistance in the LWD-loaded reaches [Curran and Wohl, 2003]. Form resistance created by changes in the channel form was not fully quantified, but variations in the hydraulic radius and low-flow channel width explained 20% of the variation in flow resistance in the non-lwd reaches. [27] Although it cannot be easily or accurately isolated and quantified, spill resistance was estimated by assuming that the total flow resistance is equal to the sum of the grain, Figure 5. Grain size comparisons between non-lwd reaches (n = 20, light shading) and LWD-loaded reaches (n = 20, dark shading). For each box plot the solid box indicates the range between the 25th and 75th percentiles, the solid line indicates the median, the dotted line indicates the mean, the bars and whiskers indicate the 10th and 90th percentiles, and the solid circles indicate outliers.

7 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE ESG 3-7 Figure 6. Comparisons of hydraulic parameters between the non-lwd reaches (n = 20, light shading) and the LWD-loaded reaches (n = 20, dark shading). form, and spill resistance, in addition to any error [Millar and Quick, 1994]. Because of low values of grain and form resistance, spill resistance was assumed to be the dominant component of the total flow resistance in both the LWDloaded and non-lwd reaches. [28] Maxwell and Papanicolaou [2001] developed a formula for total resistance in step-pool channels based on form and grain roughness ways in which each variable contributes to energy dissipation and flow resistance (Table 2) Effects of LWD on Flow Resistance Components [30] LWD in step-pool channels has a different effect on each component of flow resistance. The significantly p ð8=f Þ ¼ 3:73 log ½ð H D84 Þ= ðldþš 0:80; ð3þ where D 84 is the grain size for 84% of the distribution is finer and d is flow depth in m. We found no consistent correlation between f calculated using equations 1 and 3 for either LWD or non-lwd reaches. The ratio f eqn1 to f eqn3 averaged 24 for LWD reaches and 0.1 for non-lwd reaches. This indicates that form and grain parameters produce a very different estimate of flow resistance than the more traditionally used hydraulic parameters, and that form and grain resistance as formulated in equation 3 substantially underestimate friction factor for channels with LWD relative to the Darcy-Weisbach estimation. 4. Discussion [29] The results of this research indicate that step-pool streams in which LWD was incorporated as bed steps provided greater flow resistance than those that contained no LWD. These differences are related to (1) the relative magnitude of each component of flow resistance, (2) the role of LWD on step geometry, (3) the influence of step geometry on flow resistance, and (4) the ways in which step-pool streams re-arrange available bed material to optimize energy expenditure. Correlations between each variable and flow resistance were analyzed to further assess the Figure 7. Comparisons of channel geometry variables between the non-lwd reaches (n = 20, light shading) and the LWD-loaded reaches (n = 20, dark shading).

8 ESG 3-8 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE Table 1b. Channel Geometry and flow resistance Stream a Width to Depth (w/r) Rel. Submerg. (R/D 84 ) Step Height H, m Step Spacing L, m H=L H=L=S Percent Drop by Steps Darcy-Weisbach f Grain Resistance Alluvial Bobcat* Caterpillar* Crystal Green* Kellogg (Lower) Main Intake NF Intake (Lower) Pioneer SF Mashel (Lower) Tacoma (Upper)* Tumwater Mixed Busywild Kellogg (Upper) NF Intake (Upper) SF Mashel (Middle) SF Mashel (Upper) Snake* Bedrock McCain Mint* Tacoma (Lower)* Stats Mean (non-lwd) Mean (LWD-loaded) b p value (t test) c 0.05 < < a Stream names denoted by asterisk are informal names. b LWD-loded stream data are from Curran and Wohl [2003]. c Bold p values indicate significant differences between non-lwd and LWD-loaded reaches. Figure 8. Comparisons of step geometry between the non-lwd reaches (n = 20, light shading) and the LWD-loaded reaches (n = 20, dark shading).

9 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE ESG 3-9 Figure 9. Comparisons of measured flow resistance coefficients between the non-lwd reaches (n = 20, light shading) and the LWD-loaded reaches (n = 20, dark shading). smaller relative submergences of the non-lwd reaches allowed greater turbulence and flow blockage by grains along the bed surface, creating higher grain resistance coefficients as compared to the LWD-loaded reaches. Step-forming LWD contributed to higher relative submergences and lower grain resistance coefficients in the LWDloaded reaches by creating deeper pools that allowed for storage of finer sediment. The significant correlation between grain resistance and total flow resistance in the non-lwd streams (r 2 = 0.23, p = 0.05) suggests that roughness created by alluvial grains had a measurable, although small, influence on the total flow resistance. This relationship was not observed in the LWD-loaded streams (r 2 = 0.01, p = 0.62), likely because of higher relative submergences and increased form and spill resistance created by LWD. However, grain resistance is insignificant in both stream types compared to the dominant spill and, to a lesser extent, form resistance components associated with step-pool streams. These results agree with previous studies indicating that grain resistance is much lower than form resistance along channels with pronounced bed form sequences [Prestegaard, 1983; Maxwell and Papanicolaou, 2001]. [31] No empirical equations are available to quantify form resistance created by channel shape. However, variations in geometry created by channel expansions and contractions were shown to have a larger effect on the LWDloaded reaches than the non-lwd reaches. The coefficients of variation of the hydraulic radius explained 43% of the variation in flow resistance in the LWD-loaded reaches, but only 3% in the non-lwd reaches, perhaps because of less variation in the non-lwd reaches. The coefficient of variation of the low-flow width explained 19% and 17% of the variation in flow resistance in the LWD-loaded and non-lwd reaches, respectively. Expansions and contractions may have significantly contributed to form resistance in the non-lwd reaches as a result of channel width variations associated with the higher frequency of steps. Nevertheless, form resistance is expected to be higher in the LWD-loaded streams as a result of flow blockage created by non-step-forming LWD. Using a method developed by Shields and Gippel [1995], Curran and Wohl [2003] empirically determined that this comprised up to 15% of the total flow resistance in the LWD-loaded step-pool reaches. Form resistance created by non-step-forming LWD was of course absent in the non-lwd reaches. [32] By subtracting the measured grain and form resistance from the total flow resistance, spill resistance was inferred to comprise a majority of the total flow resistance in both stream types. However, spill resistance was not quantified because these values would also include measurement error as well as unaccounted sources of flow resistance, which might be significant in these streams. Because form resistance created by LWD and fluctuations in channel shape was a larger component in the LWD-loaded reaches, and grain resistance, although greater, was still almost negligible in the non-lwd reaches, spill resistance likely comprised a larger percentage of the total flow resistance in Table 2. Linear Regression Against Flow Resistance (log f ) Variable b Non-LWD reaches (n = 20) r 2 LWD-Loaded Reaches (n = 20) a Non-LWD and LWD-Loaded Reaches (n = 40) p p p Value c r 2 Value c r 2 Value c Drainage basin parameters Elevation Drainage area* Hydraulic parameters Hydraulic radius (R) Slope (S ) < Velocity (V ) < < Channel geometry variables Low flow width (w) Width/depth (w/r)* Average step height (H )* Average step spacing (L)* Average H=L* Average H=L=S Percent drop by steps Thalweg sinuosity n/a n/a n/a n/a Coefficient variation R Coefficient variation w Grain size characteristics Composite D Composite D Rel. submergence (R/D 84 ) Grain resistance* a See Curran and Wohl [2003]. b Variables denoted by asterisks were log transformed for statistical analysis. c Bold p values indicate significant correlations.

10 ESG 3-10 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE the non-lwd reaches. To further analyze the effects of LWD on flow resistance, we analyzed the effects of LWD on each factor that contributes to spill resistance, focusing on the relationship between step geometry and energy dissipation Effects of LWD on Step Geometry [33] This research indicates that step-forming LWD contributed to higher and more widely spaced steps, larger pools, and greater flow depths than were found in channels containing no LWD. Step height is generally controlled by the size and type of the step-forming material. Wohl et al. [1997] found that log diameter was related to the size of LWD steps, and Chin [1999] showed that the D 84 grain size of alluvial steps was strongly correlated with step height. Although Curran and Wohl [2003] showed that step height was not significantly correlated with LWD diameter in the LWD-loaded step-pool reaches, there was a significant positive correlation between the D 84 and step height for the LWD-loaded reaches (r 2 = 0.35, p = 0.01) as well as the non-lwd reaches (r 2 = 0.19, p = 0.08). This suggests that the largest alluvial clasts in the channel controlled a majority of the steps in both stream types, and LWD was responsible for creating only a few large steps in the LWD-loaded reaches. [34] Comparing the size of the step-forming material, the D 84 of step-forming clasts was greater in the non-lwd reaches than in the LWD-loaded reaches. In addition, these step-forming clasts in the non-lwd reaches were larger than the average log diameter of the LWD present in the LWD-loaded reaches (Figure 10). However, despite the larger size of the step-forming material in the non-lwd reaches, the LWD-loaded reaches exhibited significantly larger average step heights. This demonstrates that LWD is much more effective than alluvial clasts at creating large steps, as logs can span the entire channel, and multiple logs can form large steps or logjams that create large pools and store sediment. The absence of large wood steps in the non- LWD reaches was associated with shorter steps, shallower pools, and smaller hydraulic radii. [35] Step geometry in the LWD and non-lwd reaches can also be compared to step geometry predicted by formulas for equilibrium step height [Maxwell and Papanicolaou, 2001]: h ðh=dþs 0:5 ¼ 2 Q= p gd 5 i 0:31; ð D50 =dþ 1:5 ð4þ and step length [Maxwell and Papanicolaou, 2001]: L ¼ 7:39 lnðh=sþ 5:52; ð5þ Where s is p (D 84 /D 16 ) and Q is volumetric flow rate in m 3 /s. Using these equations, step height in both LWD and non- LWD reaches is below the predicted equilibrium height. The average ratio of predicted to measured height is 0.3 for the 20 LWD reaches and 0.6 for the non-lwd reaches. However, these formulas were developed for higher flows than we measured in the field, and they were developed for experimental channels with no LWD. Predicted step length, which is not discharge-dependent, showed a different trend than measured step length, with both Figure 10. Comparison of the size of the step-forming material for the non-lwd reaches (light shading) and the LWD-loaded reaches (dark shading). underprediction and overprediction. The average ratio of predicted to measured height is 0.8 for the LWD reaches and 1.1 for the non-lwd reaches. By these criteria, the step geometry in the non-lwd reaches is closer to the predicted equilibrium conditions for step-pool channels without wood. This is important because experimental studies rarely incorporate LWD realistically, and predictive criteria developed from these studies must be applied to natural channels with caution Effects of Step Geometry on Spill Resistance [36] Step-forming LWD significantly contributes to spill resistance by creating hydraulic jumps that dissipate flow energy in the deep pools below LWD steps. Because Curran and Wohl [2003] found that LWD diameter was positively correlated with total flow resistance in the LWD-loaded reaches, it is logical that the non-lwd reaches had lower flow resistance than the LWD-loaded reaches. Curran and Wohl [2002] suggested that a few large steps in each reach were responsible for much of the energy dissipation in the LWD-loaded reaches. With the absence of large log steps and deep plunge pools, the non-lwd reaches had more frequent, but smaller steps with shallower pools, leading to weaker hydraulic jumps, less energy dissipation, and lower spill resistance overall, when compared to LWD reaches. [37] Although the larger steps of the LWD-loaded reaches are associated with higher flow resistance, neither stream type showed a significant correlation between step height and total flow resistance, suggesting that step height alone may not be the most influential factor affecting energy dissipation. However, the significant positive correlation between H a /L a and flow resistance in the non-lwd reaches (r 2 = 0.25, p = 0.03) indicates that spill resistance increases with increasing step height in relation to pool size (Figure 11a). This relationship reflects the increase in energy dissipation as step height, normalized by spacing between

11 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE ESG 3-11 Figure 11. (a) Relationship between the H a /L a ratio and flow resistance for the non-lwd reaches (r r = 0.25, p = 0.03) and the LWD-loaded reaches (r 2 = 0.16, p = 0.08). (b) Relationship between step spacing and flow resistance for the non-lwd reaches (r 2 = 0.20, p = 0.05, negative correlation) and the LWD-loaded reaches (r 2 = 0.10, p = 0.17, positive correlation). steps, increases and hydraulic jumps strengthen. The fact that this relationship does not exist in the LWD-loaded reaches suggests that spill resistance in such streams is controlled predominantly by a few large log steps in each reach. [38] Step spacing had a more significant effect on flow resistance than step height. The non-lwd reaches showed a significant negative correlation between step spacing and flow resistance (r 2 = 0.20, p = 0.05) (Figure 11b), suggesting that flow resistance in these streams increased with greater step frequency and shorter lengths relative to height. However, the LWD-loaded reaches showed a weak positive trend (r 2 = 0.10, p = 0.17). [39] It is not clear why LWD and non-lwd reaches had contrasting trends between step spacing and flow resistance, but the relation between step and pool geometry may be important. The significantly larger step spacings of the LWD-loaded reaches were associated with higher flow resistance, whereas the non-lwd reaches had generally smaller step spacings and lower flow resistance. This suggests that the LWD steps created larger pools that increased flow resistance by allowing greater energy dissipation through decreases in flow velocity and larger hydraulic jumps associated with large log steps. The LWD reaches had more variability in hydraulic radius (Figure 6), primarily associated with the presence of deep pools below tall log steps. Taller steps in the non-lwd reaches did not necessarily occur with deep pools. The greater flow depths in the larger pools of the LWD-loaded reaches are also associated with greater flow resistance in these reaches as compared to the non-lwd reaches, but there is little correlation between hydraulic radius and flow resistance for either stream type. [40] The percentage of the water-surface elevation loss attributed to steps was significantly higher in the non-lwd reaches than in the LWD-loaded reaches, a result of the higher frequency of steps and shorter pools of the non-lwd reaches. Curran and Wohl [2003] showed that the average percent water-surface drop created by steps in the LWDloaded reaches was nearly equal to the percentage of the total flow resistance attributed to spill resistance (80 90%). Although these values of spill resistance may include significant error, the assumption that the non-lwd reaches had a larger component of spill resistance than the LWDloaded reaches is supported by the larger percentage of the water-surface elevation loss attributed to steps in the non- LWD reaches (79 99%). This relationship suggests that energy dissipation and spill resistance in step-pool streams may occur largely through the loss of potential energy at vertical steps, although the high friction factors of the LWDloaded reaches imply that step geometry and form resistance are also important factors Optimization of Energy Expenditure in Step-Pool Streams [41] Channel slope plays an important role in energy dissipation in step-pool streams. The non-lwd reaches exhibited a significant positive correlation between step height and gradient (r 2 = 0.64, p < ), whereas the LWD-loaded reaches showed no correlation (Figure 12). This suggests that these two types of stream have different controls on step geometry. Alluvial steps in the non-lwd reaches tend to adjust their height to reflect the channel gradient and available bed material, whereas step heights in the LWD-loaded streams are largely a function of the random placement of LWD, which can force large steps independently of gradient and grain size. [42] The relationship between the H a /L a ratio and the channel slope characterizes the step tread, or the depth of each pool in relation to the lip of the next downstream step. Because turbulent flows at steps can scour pools to create reverse gradient [Wohl, 2000], the H a /L a /S a ratio is related to energy expenditure in step-pool streams. Abrahams et al. [1995] suggested that step-pool streams adjust their geometry to maximize flow resistance and thereby increase stability. Their model showed that this occurs when H a /L a =1.5S, or the elevation loss at steps is maximized, a reverse slope tread is maximized, and steps are regularly spaced. We tested this model using both step-pool datasets and showed that maximum flow resistance occurred at a H a /L a /

12 ESG 3-12 MACFARLANE AND WOHL: STEP GEOMETRY AND FLOW RESISTANCE However, the values for step height and spacing in both LWD and non-lwd reaches approximated maximum flow resistance as determined in previous studies of variously shaped roughness elements in which maximum resistance is associated with L/H values of approximately 9 10 [Johnson and LeRoux, 1946; Davies, 1980; Wohl and Ikeda, 1998], or H/L values of [Rouse, 1965]. Figure 12. Relationship between step height and slope for the non-lwd reaches (r 2 = 0.64, p < ) and the LWDloaded reaches (r 2 = 0.09, p = 0.21). S a ratio of approximately two in the non-lwd reaches and approximately one in the LWD-loaded reaches (Figure 13). As the model suggests, flow resistance increases with H/L/S in the non-lwd reaches, although there is poor correlation. The lack of a positive trend in the LWD-loaded reaches suggests that a few large log steps were responsible for much of the energy dissipation in these reaches, rather than the average step geometry. [43] Observations of channels scoured by debris flow suggest that step-pool channels incorporate alluvium and LWD into steps until maximum energy expenditure is reached. Debris flows in the Pacific Northwest have been shown to completely scour headwater channels to bedrock, removing any overlying alluvium and debris [Keller and Swanson, 1979; Benda, 1990]. Research from other regions has shown that recently scoured channels are able to reestablish step-pool morphology relatively quickly [Sawada et al., 1983; Gintz et al., 1996], but these channels did not contain substantial LWD. Because debris flows in the Pacific Northwest have recurrence intervals of hundreds to thousands of years [Costa, 1984], and because of gradual recruitment of LWD to the channel following a debris flow, headwater streams in the Washington Cascades exhibit different stages of recovery from debris flows. Most of the non-lwd reaches surveyed for this research were recently scoured by debris flows, and these reaches exhibited significantly lower flow resistance than those containing abundant LWD. (We did not find significant differences in channel and hydraulic characteristics as a function of estimated time since the debris flow.) It is likely that flow resistance will further increase, in the reaches scoured by debris flows, with the addition of LWD from surrounding forests. Large logs within the channel would provide sediment storage sites, eventually forming steps and increasing flow resistance as steps became higher, pools became deeper, and LWD provided increased channel stability. 5. Conclusions [44] This research shows that flow resistance in step-pool streams that do not contain LWD is lower than flow resistance in LWD-loaded step-pool streams that contain abundant LWD steps. The difference in flow resistance between these two stream types is related to the ways in which LWD influences step geometry and how step geometry in turn influences spill resistance. The fact that LWD steps were associated with high spill resistance suggests that LWD is an important component of step-pool streams because it creates deep pools, stores sediment, and dissipates energy in strong hydraulic jumps. Based on the differences in flow resistance and step geometry between step-pool channels with and without LWD, the artificial addition of step-forming LWD could be valuable to steppool streams. LWD may increase channel stability and decrease sediment movement by increasing flow resistance, particularly through the formation of large steps. Larger diameter logs, or debris jams, may be especially important in forming large steps which create pools, cover, and substrate heterogeneity that are beneficial to aquatic organisms. The role of LWD in forming large steps and associated pools is analogous to alterations in pool-riffle channels associated with LWD [Montgomery et al., 1995] and LWD-forced alluvial channel segments [Montgomery et al., 1996], further illustrating the importance of LWD in maintaining channel stability and habitat diversity in headwater streams. Figure 13. Relationship between the H a /L a /S a ratio and friction factor for the non-lwd reaches (r 2 = 0.13, p = 0.12) and the LWD-loaded reaches (r 2 = 0.08, p = 0.23).

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