Rhythmic Spacing and Origin of Pools and Riffles

Rhythmic spacing and origin of pools and riffles

E. A. KELLER Environmental Studies and Department of Geological Sciences, University of California, Santa Barbara, Santa Barbara, California 93106 W. N. MELHORN Department of Geosciences, Purdue University, West Lafayette, Indiana 47907

ABSTRACT be filled at low flow. Riffles or crossings between consecutive pools characteristically have a more symmetrical cross-channel profile, Quantitative analysis of the spacing of pools in bedrock and tend to fill at high flow, and may be scoured at low flow. A pool alluvial stream channels in California, Indiana, Virginia, and North and adjacent riffle, referred to as a pool-riffle sequence, is thought Carolina suggest that the tendency for streams to meander in the to be important in maintaining the quasi-equilibrium of stream vertical (or third) dimension, as in the horizontal plane, is a funda- channels (Dolling, 1968) by minimizing the potential energy loss mental characteristic of many streams that is independent of mate- per unit mass of water (Yang, 1971) or minimizing power expendi- rial type. Simple linear-regression and correlation models reveal ture (Cherkauer, 1973). Pools and riffles are found in both bedrock that approximately 70% of the variability of the spacing of pools and alluvial channels. Compared to ephemeral bed forms such as can be explained by the variability of channel width. Analysis of the ripples and dunes, they tend to be stable over a period of flows. spacing of 251 pools in eleven streams, utilizing the Kolmogorov- Remarkably, Dury (1970) found that essentially no change oc- Smirnov goodness of fit test and one-way analysis of variance curred in 100 yr in the pool-riffle morphology of a bedrock river in suggests that the hypothesis that the data from bedrock and alluvial New South Wales. channels are from the same population cannot be rejected at the 0.05 level of significance. POOL-TO-POOL SPACING Morphologic maps and field observations of stream channels incised in sandstone, limestone, metavolcanic rock, and syenite Because we evaluate here pool-to-pool spacing in alluvial and suggest that although these streams have much in common with bedrock channels, it is important to define the use of the terms alluvial stream channels, there exist considerable differences in cer- "alluvial" and "bedrock." Alluvial streams are those in which the tain aspects of channel morphology. This results because bedrock control of morphology locally may be more significant than the ef- (A) Planimetric view fects of general processes that tend to produce rhythmic channel forms such as pools and riffles. However, local controls tend to ^ meander mask rather than destroy the effects of more general processes that produce the third dimension of meandering streams.

INTRODUCTION

A good deal is known about the meandering streams in the planimetric view, where the straight-line meander wavelength (Fig. 1, A) very roughly averages about eleven times the channel width (Leopold and Wolman, 1960). This relationship between meander wavelength and channel width is remarkably consistent for alluvial and bedrock channels as well as supraglacial streams, suggesting that the relationship represents a characteristic of streams that is independent of material type. Meandering of streams in the third dimension along the bottom (thalweg) is a less well understood phenomenon best delineated at low flow by the occurrence of regularly spaced deeps (pools) with intervening shallows (riffles) (Fig. 1, B). In this paper we critically examine and test the hypothesis that the tendency for streams to develop regularly spaced pools is a fundamental characteristic of many streams that is independent of material type. bank erosion R riffle area Pools in meandering and straight channels are topographic low thalweg (crossing) areas, usually on the order of several channel widths long, produced by scour at high flow. Pools are commonly associated with P pool area /^TT^S point bar an adjacent point bar, resulting in an asymmetric cross-channel Figure 1. Idealized diagram showing general relation between meander- profile. Characteristically, pools are scoured at high flow and may ing in planimetric view (A) and meandering in third dimension (B).

Geological Society of America Bulletin, v. 89, p. 723-730, 12 figs., 4 tables, May 1978, Doc. no. 80S09.

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channel bed and bank materials are composed of unconsolidated ial deposits to a lesser or greater extent exist in all bedrock chan- materials that can be eroded and transported by the fluvial system. nels, and there is considerable variability in the quantity of alluvial Bedrock streams are those in which a conspicuous part of the chan- material along and across bedrock channels. Therefore, the effect nel bed and banks is composed of bedrock in which pools are of unconsolidated material in bedrock streams must not be ne- scoured. Study areas in bedrock and alluvial channels evaluated in glected. this paper are summarized in Table 1. A main criterion for selection The streams we have selected to evaluate (Table 1) range from of bedrock channels was that a particular stream flowed on one pure alluvial streams that do not ordinarily scour to bedrock, to particular rock type throughout the study reach. We emphasize bedrock streams that regularly scour to bedrock. Since streams that the distinction between bedrock and alluvial stream is not form a continuum with respect to bed and bank materials, some of precise. We recognize that all streams contain some alluvial mate- the streams we have evaluated fall in between, requiring a subjec- rial and that some streams are not influenced at all by bedrock. The tive decision as to whether to call the channel bedrock or alluvial. It only pure alluvial streams we investigated are Dry Creek, near is also worth mentioning that some of the streams evaluated have Winters, California; Durkee Run and Wea Creek, near Lafayette, been to a lesser or greater extent modified by human use and in- Indiana; Sims Creek, near Blowing Rock, North Carolina; and terest in the fluvial system. Boone Fork and its tributary, Sims Wildcat Creek near Dayton, Indiana. Boone Fork, near Blowing Creek, are both influenced by an upstream direct-overflow dam on Rock, North Carolina and McAlpine Creek, near Charlotte, North Boone Fork. McAlpine Creek has experienced morphologic recov- Carolina, are also listed in Figure 2 as alluvial streams even though ery following channelization about 20 yr ago, and Durkee Run has they do contain some bedrock in the channel beds and banks. These substantial single-family development within the drainage basin. decisions were based on field observations that suggest the amount The morphologic stability of these streams is remarkable consider- of bedrock present in these channels is small compared to the alluv- ing the variety of human pressure. The significance of this stability ial material. On the other hand, bedrock in the channel and stream has environmental consequences that are beyond the scope of this banks of Big Pine Creek, near Carbondale, Indiana; Little Bear paper (Keller, 1978). Creek and Ramsey Creek, both near Albemarle, North Carolina; In comparing large streams with small streams, it is advantage- and the Middle River near Churchville, Virginia, is very abundant, ous to measure pool-to-pool spacing in channel widths. This is ac- and detailed field work suggests that many of the pools are scoured complished by wading and merely locating the lowest point in ad- in bedrock. However, even in these streams the role of transported jacent pools. The distance between the pools is then divided by the alluvium in scouring the channel is significant. Furthermore, alluv- channel width in that reach. In general, channel width is measured

TABLE 1. SUMMARY OF CHANNEL CHARACTERISTICS

Type of Bed and bank Sinuosity Channel Channel Average pool-to- N* stream material width slope pool spacing (m) (channel widths)

Big Pine Creek, Perennial Sandstone 1.18 29.28 0.0014 6.84 22 near Carbondale, (little alluvium) Indiana Boone Fork, near Perennial Alluvial 1.25 9.46 0.0045 4.90 14 Blowing Rock, (little bedrock) North Carolina Dry Creek, near Intermittent Alluvial 2.40 10.07 0.0025 5.92 38 Winters, California (some partial consolidation) Durkee Run, Intermittent Alluvial 1.13 4.27 0.0023 5.56 33 Lafayette, Indiana Little Bear Creek, Perennial Metavolcanic 1.13 7.63 0.0036 6.28 22 near Albermarle, (litde alluvium) North Carolina McAlpine Creek, near Perennial Alluvial 1.01 6.03 0.0010 6.74 18 Charlotte, North (little bedrock) Carolina Middle River, near Perennial Limestone 2.05 14.23 0.0067 6.73 20 Churchville, Virginia (little alluvium) Ramsey Creek, near Perennial Metavolcanic 1.08 4.58 0.0089 7.00 18 Albermarle, North Carolina Sims Creek, near Perennial Alluvial 1.31 3.66 0.0049 5.52 20 Blowing Rock, North Carolina Wea Creek, near Perennial Alluvial 1.38 20.44 0.0015 5.25 16 Lafayette, Indiana Wildcat Creek, near Perennial Alluvial 1.42 25.01 0.0014 5.01 30 Dayton, Indiana * Number of pool-riffle sequences sampled.

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at a point on the riffle between pools where the cross-channel channel widths are normally distributed. Results from the one-way profile is nearly symmetrical and the banks well defined. In prac- analysis of variance for pool-to-pool spacing is shown in Table 4. tice, the channel width used in this paper is delineated by the width The hypothesis that the data from bedrock and alluvial channels of bed material or distance between major breaks in slope from the are from the same population cannot be rejected at the 0.05 level of bottom of the channel to the banks of the channel. significance, and therefore the null hypothesis of no significant dif- Field data on pool-to-pool spacing for the eleven streams studied ference between the mean spacing of pools in the eleven streams is were gathered from 1969 to 1976. More than 250 pool-to-pool accepted. This strongly suggests that there is no apparent difference spacings were recorded (Table 2). Frequency distributions for the between the spacing of pools in bedrock and alluvial streams and individual streams (Fig. 2) clearly suggests that the spacing of pools supports our hypothesis that the tendency to develop pools and is on the order of several channel widths. The average spacing is six riffles is a fundamental aspect of stream-channel morphology that times the channel width, strongly supporting the conclusion of is independent of material type. Leopold and others (1964) that pools are spaced approximately five to seven times the channel width. DISCUSSION

DATA ANALYSIS The development of pools is thought to be very significant in the origin of meandering (Leopold and others, 1964; Dury, 1969; Kel- The primary objective of the data analysis is to test the ler, 1972). Figure 1 illustrates that the planimetric straight-line hypothesis that the development and spacing of pools in alluvial wavelength of an ideal meander is equal to two wavelengths along and bedrock streams is independent of material types and thus rep- the channel bottom as delineated by pools and riffles. Thus, as resents a fundamental aspect of stream-channel morphology. The suggested by Leopold and others (1964), the pool-to-pool spacing research design is to examine statistically the variance of the spac- as measured along the channel is roughly one-half the meander ing of pools for eleven streams, incised in alluvium and different wavelength. Field measurements of more than 250 pools in a vari- rock types, to determine if a significant difference exists. However, ety of channel materials show a significant relationship defined by analysis of variance assumes that each sample to be evaluated is in the equation Y, = 5.42x101, where Y, is the pool-to-pool spacing, itself a normal distribution. Therefore, the Kolmogorov-Smirnov measured along the channel, and x is the channel width (Fig. 3). goodness of fit test for the pool-to-pool spacing data was used to test for normality. The hypothesis (null hypothesis) tested is that TABLE 2. POOL-TO-POOL DATA there is no difference between the observed distribution spacing of pools and the theoretical (expected) normal distribution. Results of Stream Spacing the analysis are shown in Table 3. In all cases the null hypothesis is (in channel widths) accepted, suggesting that pool-to-pool spacing data measured in Big Pine Creek, (1.6, 2.7) (3.5, 3.8, 4.3, 4.8) (5.2, 5.2, 5.5, 6.1, Indiana 6.1, 6.5, 6.6, 6.6, 6.7) (8.1) (9.3, 10.1, 10.7) (11.1, 11.5) (14.4) (A) Alluvial streams Boone Fork, (2.7, 2.8) (3.3) (4.1, 4.1, 4.2, 4.2, 4.5, 4.6) (5.6) BOONE DRY DURKEE McAlpine North Carolina (6.3) (7.3, 7.4, 7.5) . FORK CREEK RUN CREEK Dry Creek, (2.2, 2.8, 2.8) (3.1, 3.2, 3.2, 3.6,3.7,4.0,4.0,4.3, California 4.3, 4.4, 4.6, 4.6, 4.9) (5.0, 5.1, 5.2, 5.3, 5.4, 5.9, 6.0, 6.4, 6.6, 6.9) (7.1, 7.3, 7.6, 7.6, 7.8, 7.8, 8.4, 8.7, 8.9) (9.1,10.6) (n.d.) (n.d.) (16.7) Durkee Run, (2.5, 2.7) (3.1, 3.3, 3.8, 4.0,4.4,4.7,4.7, 4.7,4.9) Indiana (5.0, 5.1, 5.1, 5.3, 5.3, 5.5, 5.5, 5.6, 5.7, 5.8, R F 6.0, 6.2, 6.3, 6.3, 6.4) (7.0, 7.1, 7.2, 7.3, 7.8, 13 5 7 9 I 3 5 7 911 15 17 I 3 5 7I 9 II I 3 5 7 9 13 15 17 8.5) (10.7) SIMS WEA WILDCAT Little Bear Creek, (2.6) (3.3, 3.7, 4.0, 4.1, 4.4, 4.6, 4.6, 4.7) (5.1, Uj CREEK CREEK CREEK North Carolina 5.2, 5.2, 5.3, 5.4, 5.5, 5.7, 6.5) (7.2, 8.3) (9.1,

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The strength of this relationship is such that nearly 70% of the var- spacing of pools tends in some cases to be independent of channel iability of the spacing of pools can be explained by the variability in pattern (Keller, 1972). This is further substantiated by the data in channel width. Observe that the coefficient of x is very close to Table 1 which suggest there is no relationship between channel one-half the coefficient ofx in Leopold and others' (1964) relation- sinuosity and pool-to-pool spacing. However, this sinuosity—pool- im ship Y2 = 10.9 x , where Y2 is the straight-line meander spacing conclusion is at best tentative in that the range of wavelength and x is, again, the channel width. Also note (Fig. 4) sinuosities of the studied streams is not large. that if the average pool-to-pool spacing for each stream is doubled,

the data plot very close to the line relating meander wavelength and 500 01 channel width. These data strongly confirm the proposition that the y = 5.42 x' general tendency is for the pool-riffle spacing to equal one-half the r = 0.83 straight-line meander wavelength. However, it is emphasized that t = 56 the relationship between meander wavelength and pool spacing is £ d only a general tendency. Many exceptions exist, such as where sev- 200 eral pools are found on a large meander bend (Keller and Melhorn, ' V/ 1973). Moreover, straight stream reaches have well-developed pools and riffles (Leopold and others, 1964). Therefore, the regular 100 • • a/ • I • • • %%«• y • •

N cr X Dm Dc (0.05 LIS) I • > Big Pine Creek, 22 3.19 6.84 0.16 0.27 Indiana 20 Boone Fork, 14 1.65 4.90 0.12 0.35 yK:« % North Carolina I Dry Creek, 38 2.74 5.92 0.05 0.22 . r• ' California 10 L _lLl 1.1 I 0.04 Durkee Run, 33 1.69 5.56 0.23 2 5 10 20 50 Indiana Little Bear Creek, 22 4.23 6.28 0.21 0.29 CHANNEL WIDTH (METERS) North Carolina Figure 3. Relation between pool-to-pool spacing and channel width, McAlpine Creek 18 4.15 6.74 0.20 0.31 North Carolina Middle River, 20 2.83 6.73 0.06 0.29 400 Big Pine Cr. • Virginia Ramsey Creek, 18 3.29 7.00 0.11 0.31 300 Wildcat Cr North Carolina Sims Creek, 20 1.30 5.52 0.04 0.29 200 Middle River Wea Cr. North Carolina 150 Wea Creek, 16 1.88 5.25 0.12 0.33 Dry Cr. Indiana I Little Bear Cr. 100 Wildcat Creek, 30 2.31 5.01 0.03 0.24 McAlpine Cr. Boone Fork Indiana Ì * ' ^ Ramsey Cr. • 5 Note: H0 (null hypothesis) accepted for all examples: There is no differ- 8 Durkee Run ence between the observed distribution of spacing of pools and the theoreti- ÌP Sims Cr. cal (expected) normal distribution. _ N = sample size; cr = standard deviation; x = mean; Dm = maximum -C: deviation (by class intervals) between sample distribution and normal dis- 5M tribution; Dc = critical deviation for a significant difference. Y= I0.9X101

TABLE 4. ANALYSIS OF VARIANCE FOR POOL-TO-POOL SPACING 5 10 15 Source of d.f. Sum of Mean F Decision Channel width in meters variation squares square

Between groups 10 122.8 12.28 1.58 Accept

H0* Figure 4. Relation between Y*I0.9X10' Within groups 240 1865.1 7.77 two times die average pool Total about x 250 1987.9 spacing and channel width. Graph (at left) for meander Note: F (0.05; 10, 240) = 1.83. c length compared to channel 4 H (null hypothesis): There is no significant difference in the mean 0 width is from Leopold and spacing of pools for our 11 sample streams. I 10 100 1000 Channel width, m Wolman (1960).

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The statistical analysis suggests that there is no significant differ- developed on flat-lying Pennsylvanian sandstone. Nevertheless, the ence between the mean spacing of pools in the stream channels cross-channel profiles are similar to those found in corresponding studied. However, there are several minor morphologic and mor- alluvial stream channels. A thalweg profile including the upstream phometric differences between pools and riffles that form in alluvial and downstream pool from section A—A' in Figure 6 is shown in channels compared to pools and riffles in bedrock channels. Figure Figure 7. The rather abrupt change in bottom topography at the 5 illustrates the entire spectrum of variability (251 observations) of downstream end of the pool is due to a bedrock outcrop but is spacing of pools. morphologically similar to topographic changes at the downstream The morphology of the pool-riffle sequence in bedrock streams is end of many pools in alluvial stream channels. Furthermore, the quite similar to that of alluvial stream channels. Figure 6 shows a low-water surface, which is steep over the riffle and flat over the morphologic map for a reach of Big Pine Creek in Indiana. Detailed pool, is also analogous to hydrologic behavior in alluvial streams. field observation and mapping suggest that the pools and riffles are Remarkably, in this example the pool-riffle-pool sequence is exca-

21 • = Alluvial stream + = Bedrock stream A = Data for Middle River, Virginia « 19 from Leopold and Wolman, I957 S — 17 V c TO 15 -C o \ 13 O) •o- 11 + * (O a co 9 + + + . ö ° 77 a. Îtir."î"— ft2-^^ «T+-+ ,+r ++ A + — 5 + - o o + 3

10 16 20 25 30 Channel width (m.) Figure 5. Relation between pool-to-pool spacing (in channel widths) and channel width.

A A' B' "» * A c c1 t\ Nr* *

Figure 6. Morphologic map showing pools, riffles, and characteristic cross-channel profiles for reach in Big Pine Creek, Indiana. Held observations and mapping established that channel Explanation morphology is almost entirely formed in Penn- sylvanian sandstone. ^Pool 77"r- Prominent Sandstone Outcrop A—A1 Section

0°<£> Riffle ^ Sandstone Point Bar A A Alluvium

(j | 490 | 8p0ft. 0 20ft.

0 100 200 m i ' km MAP SECTIONS

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100 150 200 250 300 Distance in meters along channel centerline

vated entirely in bedrock; the only unconsolidated material in the rock bench (Hack, 1957). These bedrock benches may be found on vicinity is a thin veneer on the bottom of the pool (Fig. 8) and the the edges of pools or between pools and thus be analogous to riffles top of the riffle (Fig. 9). in alluvial stream channels. Some pools in bedrock channels are as- A difference in the channel morphology of bedrock streams and sociated with well-developed point bars of depositional origin, and alluvial streams is that the pools in bedrock streams often contain others are not. Bedrock riffles are usually veneered with alluvial very large blocks of bedrock. This has been observed by Hack material. Morphology of pools may also be affected by discon- (1957) in his study of the Middle River in the Shenandoah Valley. tinuities in bedrock. For example, the scour in one pool in Big Pine We made similar observations in Big Pine Creek and other bedrock Creek migrated down cross-bedding planes in the sandstone. In channels. The tendency for large blocks of bedrock to lie in the bot- addition, Dury (1970) commented on irregularities in pools result- tom of pools can be explained by examining the process of bank ing from joint faces in the bedrock of the channel bed and banks. calving. In alluvial stream channels, when large blocks of alluvial The effect of bedrock control is such that the distinction between material slough off the banks on the outside of a meander bend, the pools and riffles in bedrock streams is often more difficult to de- unconsolidated material is quickly added to the bed load and sus- lineate, and this is a problem because the recognition of pools and pended load of the stream channel and is quickly dissipated. How- riffles may become somewhat subjective. However, when field ever, for streams with bedrock banks, when large blocks slump into work is carried out at low-flow conditions, more than 90% of the the stream channel, they may remain there a long time until they pools and riffles in bedrock streams are readily discernible by the are broken into particles small enough for the stream to transport. criterion that pools are recognized by relatively deep, slow-moving Thus, in bedrock streams it is not uncommon to find very large water with a nearly flat water surface, and riffles are recognized by blocks of bedrock that have slumped down into the bottom of a shallow, fast-moving water with a steeper gradient. Furthermore, pool and remained there for considerable time. Figure 8 shows sev- both pools and riffles are large-scale bed forms measured in channel eral large blocks of sandstone in a pool on Big Pine Creek that have widths, and applying this criterion excludes small scour areas and been derived by this process. obstructions to flow that might be superimposed on pools and Bedrock streams also may have subtle morphology not found in riffles. Therefore, one may conclude that the nature and effect of alluvial stream channels. For example, there may be rather long bedrock control on channel morphology may be more significant areas of shallow water over what might best be described as a bed- locally than effects of general processes that tend to produce

Figure 9. Riffle morphology (downstream view) Big Pine Creek, In- Figure 8. Pool morphology (upstream view), Big Pine Creek, Indiana. diana. Shallow water in central part of photograph is location of section Location is first pool upstream from section line A-A' in Figure 6. Note A-A' in Figure 6. Parts of adjacent upstream and downstream pools are large rock blocks in pool. Field observations and mapping established that also shown. Field observation established that this riffle is entirely on bed- this pool is scoured in bedrock. rock with very thin veneer oi: rock fragments.

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EXPLANATION Figure 10. Morphologic map of bedrock reach in Sweetgrass Creek, Montana. CZ> Pool

Asymmetric Shool (Point Bar) 0 20 60 100 Ft. I—*—H 4—'—I ?»V Riffle 0 10 20 SON XXX Igneous Bed Rock (Shallow Intrusive)

rhythmic channel forms such as pools and riffles. However, these rhythmic thalweg morphology has been observed in supraglacial local controls tend to mask rather than destroy the effects of more streams (Fig. 12) with a channel slope of approximately 0.2 general processes. (Dozier, 1974, 1976). These streams form by melting (thermal ero- Recognition that pools can develop in bedrock stream channels sion), and there is no deposition, because bed and bank erosion is analogous to those in alluvial stream channels is strong if not con- transformed into discharge (Dozier, 1974). However, their mean- clusive evidence that pools in both types of channels are produced dering habit in the third dimension may be more analogous to bed- by scour at relatively high flow. This results because it is obvious rock streams than generally recognized. Thus, our observations of that pools in bedrock must be produced by differential scour and the development of pools and riffles (meandering in the third, or erosion. There is a growing body of evidence (Keller, 1972; Richards, 1976a; Andrews, 1976) which suggests that the hydraulic geometry of pools and riffles is such that with increasing discharge the velocity in pools increases faster than that in riffles. Furthermore, the convergence of velocity in pools and riffles with increasing discharge may eventually produce velocities in pools that exceed those of riffles (Keller, 1971; Church, 1972; Andrews, 1976; Richards, 1976b). Thus, the observed sequence of scour and fill in pools and riffles as well as the observed areal sorting of bed material in alluvial stream channels that produces coarser material on riffles than found in pools may be explained partly by the hydraulic geometry. Moreover, rates of change in shear stress in streams characterized by variations in bed material size rather than well-developed pools and riffles have been attributed to hydraulic geometry similar to that of the pool-riffle sequence (Dozier, 1973). In addition, it is es- sential to recognize that the observed hydraulic geometry in pools and riffles is not the only significant process operating. The kinematic wave theory (Langbein and Leopold, 1968) is important in explaining how material moves through pools and riffles, as well as how they are formed and maintained. In fact, kinematic wave theory is consistent with the observation that pools at high channel-forming discharge may have areas of faster water velocity than adjacent riffles. The apparent development of rhythmic thalweg morphology on channels with slopes a magnitude or two greater than that characteristic of most meandering streams is of considerable interest because it may suggest that the third-dimension meanders represent a more general form produced when one material flows over another. Figure 10 shows the development of pools and riffles in Sweetgrass Creek, Crazy Mountains, Montana, on a channel slope of approximately. 0.021. The stream is deeply incised in syenite bedrock, and the bed forms are eroded both in the bedrock and recent flood de- Figure 11. Upstream view of Sweetgrass Creek, Montana. Bedrock is posits. The bars (point bars?) are composed of very coarse alluvium syenite. Large steep bars composed of very coarse bed-load material are dis- at the angle of repose on the channel side (Fig. 11). Similar sected flood deposits.

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Pools in alluvial and bedrock stream channels are produced, in part, by scour at high flow. This results from the hydraulic geometry of pools and riffles in which the velocity of water in pools increases with increasing discharge faster than that of adjacent riffles. At high flow, the velocity in pools may exceed that of adjacent riffles. This conclusion is not inconsistent with kinematic wave theory, which remains an important process in pools and riffles.

ACKNOWLEDGMENTS

Critical reading and suggestions for improvement by J. Dozier, J. T. Hack, and R. M. Norris are gratefully acknowledged, as is as- sistance with statistical analysis by N. R. Nunnally. Financial sup- port, in part, was provided by the Water Resources Research Pur- due University Project A-021-IND and University of North Carolina Project B-089-NC.

REFERENCES CITED

Andrews, E. D., 1976, River channel scour and fill: Geol. Soc. America Abs. with Programs, v. 8, p. 755. Cherkauer, D. S., 1973, Minimization of power expenditure in a riffle-pool alluvial channel: Water Resources Research, v. 9, p. 1613-1628. Church, M., 1972, Baffin Island sandurs: A study of Arctic fluvial processes: Canada Geol. Survey Bull., v. 216, p. 89-93. Dolling, R. K., 1968, Occurrence of pools and riffles: An element in the quasi-equilibrium state of river channels: Ontario Geography, no. 2, p. 3-11. Dozier, J., 1973, An evaluation of the variance minimization principle in river channel adjustment [Ph.D. dissert.]: Ann Arbor, Univ. Michigan, 117 p. 1974, Channel adjustments in supraglacial streams, in Icefield ranges research project, scientific results, Vol. 4: Am. Geog. Soc., p. 189- 205. Figure 12. Meanders and stepped water surface on supraglacial stream 1976, An examination of the variance minimization tendencies of a reflecting third-dimension meanders. Photograph courtesy of Jeff Dozier. supraglacial stream: Jour. Hydrology, v. 31, p. 359-380. Dury, G. H., 1969, Relation of morphometry to runoff frequency, in Chor- ley, R. J., ed., Water, earth and man: London, Methuen, p. 419—430. vertical, dimension) may be manifestations of a more general phe- 1970, A re-survey of pait of the Hawkesbury River, New South Wales, nomenon that is present whenever one material flows differentially after one hundred years: Australian Geog. Studies, v. 8, p. 121-132. over another. Moreover, it may well be true that development of Hack, J. T., 1957, Studies of longitudinal stream profiles in Virginia and pools and riffles, undulating bottom topography on supraglacial Maryland: U.S. Geol. Survey Prof. Paper 294-B, p. 45-97. streams, and perhaps even the development of stepped topography Keller, E. A., 1971, Areal sorting of bed-load material: The hypothesis of velocity reversal: Geol. Soc. America Bull., v. 82, p. 753 — 756. in glacial valleys and third-dimension meandering of oceanic cur- 1972, Development of alluvial stream channels: A five-stage model: rents might be, in part, diverse examples of a common principle. Geol. Soc. America Bull., v. 83, p. 1531-1536. 1978, Pools riffles and channelization: Environmental Geology (in CONCLUSIONS press). Keller, E. A., and Melhorn, W. N., 1973, Bedforms and fluvial processes in alluvial stream channels: Selected observations, in Morisawa, M.,ed., There is no significant difference between the mean spacing of Fluvial geomorphology: New York State Univ. Publ. in Geomorphol- pools in bedrock and alluvial stream channels. Therefore, the ten- ogy, p. 253-283. dency for the development of pools and riffles is a fundamental Langbein, W. B., and Leopold, L B., 1968, River channel bars and dunes — Theory of kinematic waves: U.S. Geol. Survey Prof. Paper 422-L, 20 p. characteristic of many streams, largely independent of the type of Leopold, L. B., and Wolman, M. G., 1960, River meanders: Geol. Soc. material in channel banks and beds. America Bull., v. 71, p. 769-794. The spacing of pools in bedrock and alluvial stream channels is Leopold, L. B., Wolman, G. M., and Miller, J. P., 1964, Fluvial processes in normally distributed. geomorphology: San Francisco, Freeman, 522 p. In general (but with notable exceptions), one straight-line mean- Richards, K. S., 1976a, The morphology of riffle-pool sequences: Earth Sur- face Processes, v. 1, p. 71-88. der wavelength in a planimetric view is equivalent to two pool-riffle 1976b, Channel width and the riffle-pool sequence: Geol. Soc. America meander wavelengths along the bottom (thalweg) of a stream Bull., v. 87, p. 883-890. channel. Yang, C. T., 1971, Formation of riffles and pools: Water Resources Re- The tendency for large blocks of rock to occur in bedrock pools search, v. 7, p. 1567-1574. is explained by bank-calving processes and differs from processes MANUSCRIPT RECEIVED BY THE SOCIETY NOVEMBER 29, 1976 operating in alluvial stream channels in that these bedrock blocks REVISED MANUSCRIPT RECEIVED MAY 16, 1977 are more persistent than blocks of alluvium that slump into pools. MANUSCRIPT ACCEPTED JUNE 13,1977

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