<<

DEVELOPING HYDRAULIC RELATIONSHIPS AT THE CREST

THALWEG IN GRAVEL BED

By

Gabriel Jacob Rossi

A Thesis Presented to The Faculty of Humboldt State University In Partial Fulfillment of the Requirements for the Degree Master of Science in Environmental Systems: Environmental Resource

Committee Membership Dr. Margaret Lang, Committee Chair Dr. William Trush, Committee Member Dr. Eileen Cashman, Committee Member Dr. Andre Lehre, Committee Member Dr. Christopher Dugaw, Graduate Coordinator

December 2012

ABSTRACT

Developing Hydraulic Relationships At The Riffle Crest In Gravel Bed Streams

Gabriel Jacob Rossi

The alluvial riffle crest is a recurring, geomorphic feature of gravel bed that has a strong influence on low flow and ecology in streams. Riffle crest depth has been used to quantify availability in the upstream pool. Recently, a quantitative relationship between streamflow (Q) and median riffle crest thalweg depth

(mRCT) has been observed by researchers in gravel bed streams throughout Northern

California. The mRCT is the median from a data set of riffle crest thalweg (RCT) depths measured along a reach of known streamflow. This thesis was undertaken to: (1) determine the strength of correlation between mRCT and streamflow in gravel bed streams, and (2) if possible, to refine the RCT depth-Q relationship into a useful tool for ecological management and restoration.

A field method was developed to reproducibly locate the RCT. Riffle crests were sampled in nineteen reaches from thirteen streams across Northern California. While

RCT depth was moderately correlated to Q (R2 = 0.55), mRCT was strongly correlated to Q (R2 = 0.84). The regression equation from the mRCT-Q relationship was used to predict streamflows between 1 - 155 cfs, with the best prediction (5.1 cfs median error) in

ii

the 12-30 cfs range and the worst prediction (12.1 cfs median error) in the 55 - 155 cfs range.

Median size (D50) and wetted width of the channel (WWC) had an appreciable effect on RCT depth at a given flow. In addition, an inflection in the RCT depth-Q relationship was shown to occur when streamflow reached the active channel stage. The RCT depth-Q relationship appears not to be scaled to drainage area which stands in contrast of commonly used hydraulic geometry relationships. A dimensionless

variable was developed to scale the RCT depth-Q relationship to local channel

morphology. The -RCT relationship produced a streamflow prediction error for

individual riffle crests of 5.3 cfs based on a sample of 38 riffle crests.

This thesis shows that both RCT and mRCT are correlated to Q, although the mRCT-Q correlation is much stronger. In addition, scatter in the RCT depth-Q and mRCT-Q relationships appear to be caused by variability in sediment size and wetted width of flow between riffle crests. The relationships developed in this thesis: RCT

depth-Q, mRCT-Q and -RCT, have potential to become tools in ecological

management applications in which depth of flow at the riffle crest is an ecological control. Such applications include fish passage through natural and developing streamflow-habitat relationships.

iii

ACKNOWLEDGEMENTS

I am grateful and fortunate to have been guided, supported, inspired and encouraged by many people throughout this project. First and foremost I am grateful to my wife Maya, for spending hours in leaky waders, more hours editing and advising, and countless hours listening to nerdy blather about rivers. Dr. Bill Trush provided the genesis of, and continued inspiration for, this project as well as my career in restoration. Dr. Margaret Lang read, re-read and re-re-read my thesis, offering valuable direction and guidance. Drs. Eileen Cashman and Andre Lehre also read, commented on, and helped me to refine this . Kyle Garmany spent many hours in the field, not only helping me with data collection but also providing valuable dialogue on river hydraulics

(all for the price of a few tri-tip sandwiches). Lucas Walton P.E., Randy Klein, Brian

Powell and Jason Bone all volunteered to provide independent testing of my field methods. Scott McBain provided time off from work, and encouragement for me to cross the finish line. Besides introducing me to the world of aquatic ecology, Dr. Robert

Gearheart advised me not to “get married, get a job, or become a father…” if I wanted to get my thesis finished. Having done all three, I see now the wisdom in his words. In addition to all those mentioned by name, many professionals and academics accepted my phone calls, emails, and in some cases personal intrusions into their busy lives to answer my questions and inform the writing of this thesis. Finally I give thanks and praise to the

Great Artist, and the source of all rivers.

iv

DEDICATION

This thesis is dedicated to Luna Leopold, whose thinking was primarily responsible for the foundation of the work presented here; and to my infant son Maximo

Benjamin, whom I hope to fill with the wonder of rivers.

v

TABLE OF CONTENTS

1 Introduction ...... 2

2 Background ...... 4

2.1 Fluvial Geomorphic Setting ...... 4

2.2 The Active Channel ...... 8

2.3 Hydraulic Geometry ...... 11

2.4 Equations to Predict Flow over Riffles ...... 14

2.5 The Ecological Significance of the Riffle Crest...... 15

2.6 Objectives and Tasks ...... 16

3 Methods...... 18

3.1 RCT Data Collection Methods ...... 18

3.1.1 Step 1—Visually identify the RPL ...... 19

3.1.2 Step 2—Identify the thalweg within the RPL region...... 20

3.1.3 Step 3 – Locate the RCT ...... 20

3.2 Streamflow Data ...... 23

3.3 Sample Size Analysis ...... 24

3.4 Statistical Analysis of RCT Depth-Q Data ...... 26

3.5 Independent Testing of RCT Depth-Q Relationship ...... 29

vi

3.6 Other Hydraulic and Geomorphic Controls on RCT Depth ...... 29

3.6.1 Wetted Width Data Collection and Analysis ...... 30

3.6.2 Drainage Area Data Collection and Analysis ...... 31

3.6.3 Sediment Size Data Collection and Analysis...... 32

3.6.4 Active Channel Stage Data Collection and Analysis ...... 33

3.7 Analysis of Multiple Variables ...... 33

4 Results ...... 36

4.1 Statistical Correlation between mRCT and Streamflow ...... 36

4.2 Statistics for the RCT –Q Relationship ...... 37

4.3 Statistics for the mRCT-Q Relationship ...... 37

4.3.1 Variance in RCT Depths Within a Sample Reach ...... 39

4.4 Cross Validation of the mRCT Data Set ...... 40

4.5 Independent Testing of RCT Depth-Q Relationship ...... 41

4.6 The Effect of Non-Hydraulic Controls on the mRCT-Q Relationship ...... 43

4.6.1 Wetted Width of Channel ...... 43

4.6.2 Drainage Area ...... 45

4.6.3 Sediment Size...... 46

4.7 Analysis of Multiple Variables ...... 47

4.8 Comparing Predictive Capabilities of Three Regression Models ...... 53

vii

4.9 Active Channel Boundary ...... 54

4.10 Sample Size Analysis Results ...... 57

5 Discussion ...... 60

5.1 The strength and significance of the correlation between mRCT and Q ...... 61

5.2 Refining the mRCT-Q relationship into a tool for ecological restoration ...... 65

5.3 Future Applications of the mRCT-Q Relationship ...... 71

6 Conclusion ...... 73

7 Works Cited ...... 75

8 Appendix ...... 80

viii

LIST OF TABLES

Table 1: Reaches sampled to assess the mRCT-Q relationship...... 27

Table 2. Variance in the RCT data sets...... 39

Table 3. Cross validation of predicted vs. observed streamflows by quartile...... 41

Table 4. Comparing measurement error between operators...... 42

Table 5. Multiple linear regression of the untransformed RCT, WWC and D50 ...... 50

Table 6. Multiple linear regression of the LN transformed RCT, WWC and D50 ...... 50

Table 7. Results of random two-fold cross validation analysis...... 54

Table 8. Parameter estimates from Shapiro-Wilkes Test for normality...... 58

Table 9. Confidence intervals for sampled RCT data sets...... 59

ix

LIST OF FIGURES

Figure 1. An idealized alternating sequence of an ...... 5

Figure 2. Active channel vs. bankfull stage (Flosi et al, 1998)...... 9

Figure 3. Exceedence probability of active channel streamflow ...... 10

Figure 4. Hydraulic Geometries from Leopold and Maddock (1953)...... 12

Figure 5. A typical alluvial riffle crest observed below active channel flow...... 19

Figure 6. Riffle crest in small confined ...... 21

Figure 7. Riffle crest in a medium-sized stream ...... 21

Figure 8. Change in state of flow in a gravel/cobble dominated stream...... 22

Figure 9. Cchange in state of flow in a bedcrock/boulder dominated stream ...... 23

Figure 10. Location of wetted width measurement for a typical riffle crest...... 31

Figure 11. Riffle crest depths plotted against streamflow...... 37

Figure 12. Median riffle crest depths plotted against streamflow ...... 38

Figure 13. An example of the variance in RCT ...... 39

Figure 14. Random subsets of the mRCT-Q data from cross validation ...... 40

Figure 15. Streamflows predicted vs observed from cross validation ...... 41

Figure 16. mRCT depths from independent test for operator bias ...... 43

Figure 17. The relationship between mRCT and mWWC ...... 44

Figure 18. The relationship between mRCT and mWWC per unit streamflow...... 44

Figure 19. The relationship between drainage area and mRCT...... 45

Figure 20. The relationship between drainage area per unit Q and mRCT...... 45

Figure 21. The relationship between median sediment size and RCT depth...... 46

x

Figure 22. Median Sediment size compared with RCT/Q...... 47

Figure 23. The relationship between RCT depth, WWC, and D50 ranked by ascending

RCT depths. Data from Lost Man Creek (DA = 12mi2) ...... 48

Figure 24. The relationship between RCT depth, WWC, and D50 ranked by ascending

RCT depths. Data from the South Fork Eel River ...... 48

Figure 25. The relationship between RCT depth, WWC and D50 ranked by ascending

RCT depths. Data from the Redwood Creek near Blue Lake (DA = 67.7mi2) ...... 49

Figure 26. The relationship between RCT depth, WWC and D50 ranked by ascending

RCT depths. Data from Redwood Creek near Orick (DA = 277mi2)...... 49

Figure 27. The relationship between D50/WWC and Q per foot of RCT depth...... 52

Figure 28.The relationship between D50/WWC and RCT depth...... 52

Figure 29. RCT depth-Q and active channel stage for RCT #1 on Jacoby Creek ...... 55

Figure 30. RCT depth-Q and active channel stage for RCT #2 on Jacoby Creek ...... 55

Figure 31. RCT depth-Q and active channel stage for RCT #3 on Jacoby Creek...... 56

Figure 32. Hydraulic controls above and below Qactive on Little Lost Man Creek...... 57

Figure 33. Histogram and P-value test results from Shapiro Wilkes test...... 58

Figure 34. A schematic of the effect of D50 and WWC on mRCT vs Q ...... 68

xi

LIST OF ACRONYMS

AHG…………………..……………….……………….At-A-Station Hydraulic Geometry

ARC…………………………………………………………………..Alluvial Riffle Crest cfs…………………………………………………………………..Cubic Feet per Second

D50.………………………………....Median Grain Size (measured across the riffle crest)

DA………………...………………………………………………………...Drainage Area

DHG………………………………………….………...Downstream Hydraulic Geometry mRCT…………………….………………...... median Riffle Crest Thalweg Depth

PRS………………………………………………..…………………Pool-Riffle Sequence

Q………………………………………….…………………………………….Streamflow

Qactive………………………………..……………...... Streamflow at Active Channel Stage

RCT …………………..…………...... Riffle Crest Thalweg

RPL……………..……………………………………………………..Residual Pool Limit

WWC…………..……………..Wetted Width of the Channel (measured at the riffle crest)

xii

1

FIRST PRINCIPLES

The river...is the carpenter of its own edifice — Luna Leopold.

1. The shape and composition of a river bed are formed by the interaction between

hydraulic driving forces, sediment supply, and geomorphic resisting forces. This

interaction is defined by the minimization of energy expenditure. Life forms in a

river depend on the physical structure and composition of the channel at different

streamflows; therefore, the minimization of stream is also a driver of lotic

ecology.

We must begin thinking like a river if we are to leave a legacy of beauty and life

for future generations — David Brower.

2. To preserve the inherent ecological processes of rivers while making use of the

services they provide (water, power, and gravel), we must try to understand the

physical and hydraulic indicators of a healthy riverine community. The very best

indicators of the health of a river system are found where physical and biological

processes meet.

2

1 INTRODUCTION

The alluvial riffle crest is a recurring, geomorphic feature of gravel bed rivers that has a strong influence on low flow hydraulics and ecology in streams. Observations of riffle crests in northern California coastal streams indicate that a quantitative relationship exists between volumetric streamflow (Q) and the depth of flow, where the thalweg

(deepest continuous line of flow) crosses the riffle crest (WJ Trush, personal communication 2008). The location in a channel where the thalweg crosses a riffle crest is termed the riffle crest thalweg (RCT). Initial observations suggested that relating streamflow to the median RCT (mRCT) depth for a reach would reveal the underlying relationship, which might be obscured by variance between individual RCT depths.

Among other uses, a quantitative relationship between Q and RCT depth has the potential to inform us about interactions between streamflow and depth-dependent ecological variables such as fish passage and aquatic habitat. This thesis is undertaken to describe and document the relationship between Q and RCT depth.

There are two primary objectives of this thesis: to determine the strength of correlation between mRCT and streamflow in gravel bed streams, and if possible, to refine the mRCT -Q relationship into a useful tool for ecological management and restoration. To accomplish the first objective, the statistical correlation between RCT depth and Q (and mRCT -Q) is established by direct measurement. A wide range of channels and streamflows are sampled to evaluate the consistency and limitations of the relationship.

3

However, the strength of correlation alone does not imply that the mRCT-Q relationship will be a useful tool for ecological management. For the mRCT to serve as an indicator of function, specific relationships must be developed between

RCT hydraulics and the life history needs of aquatic organisms. In addition the effect of channel morphology on RCT depth must be defined so that the RCT depth-Q relationship can be used in specific management applications.

This thesis investigates the physical parameters of the RCT depth-Q relationship and the effect of channel structure on the RCT depth-Q relationship. Some fundamental geomorphic variables that influence channel structure (sediment size and wetted width of flow) are related to RCT depth. The ecological significance of riffle crests is not directly studied; however, the literature of stream ecology widely recognizes the influence of riffle crest controls on low flow habitat conditions (See Section 2.4). Drainage area is also related to RCT depth per unit streamflow to determine if the RCT depth-Q relationship is scaled to drainage area (see discussion of hydraulic geometry, Section

2.3). The effect of changing stage is also investigated as a possible control on the RCT depth-Q relationship. Finally, various geomorphic variables are combined with RCT depth in the attempt to develop an empirical relationship that improves flow prediction capability. Beyond improving flow prediction capacity, describing the interaction between multiple hydraulic and geomorphic variables is used to discuss the macro-scale channel processes which maintain the relationship between mRCT and streamflow.

4

2 BACKGROUND

To establish the background for this study, the fluvial geomorphic setting in which riffle crests persist is presented (Section 2.1 and Section 2.2). Next, a review of traditional hydraulic relationships and their applications is included (Section 2.3), along with a summary of past research on the riffle crest depth—flow relationship (Section 2.4)

A brief discussion about the influence of riffle crests on lotic ecology is also included

(Section 2.5). The specific tasks necessary to meet the thesis objectives are outlined in

Section 2.6.

2.1 Fluvial Geomorphic Setting

The form of a river channel is continuously adjusted to minimize stream power or energy dissipation as water flows downstream (Langbein and Leopold 1964; Leopold and

Langbein 1962; Chang 1979; Yang and Song 1986). Gradient and streamflow negotiate a dynamic equilibrium with the resisting forces of and grain roughness, in which the least possible energy is used by the river system to transport water and sediment to the ocean (Wohl 1993). This dynamic equilibrium results in the and of into characteristic that define the shape of different river systems. In gravel bed rivers, the minimization of stream power is expressed as a meandering channel, flowing between and over alternating depositional bars and scoured pools,

Figure 1 (Knighton 1998; Richards 1976a; Trush et al. 2000). Gravel deposition and scour in alluvial rivers creates the geomorphic and hydraulic conditions that underpin the alluvial . During low flow conditions only the longitudinal extremities of

5

gravel bars are submerged, forming shallow reaches of tumbling flow characterized by small hydraulic drops and jumps known as riffles. The pool-riffle sequence (PRS),

Figure 1, is described as alternating areas of deeper, slow moving water with low surface gradient and shallower, fast moving water with high surface gradient. Pools generally occur on the outside of bends at the apices of bars, while riffles occur at bar extremities.

Figure 1. An idealized alternating bar sequence of an alluvial river (adapted from Trush et al. 2000). The red line shows the path of . Riffles tend to occur at the submerged extremity of the gravel bars where the path of sediment transport crosses from an upstream to a downstream .

6

The PRS is ubiquitous in streams with heterogeneous bed material from 2 mm to 256 mm and gradients less than 2% (Knighton 1998; Montgomery and Buffington 1997). Riffle spacing is correlated to stream width; the distance between riffles is generally between 5 to 7 bankfull widths (Leopold et al. 1964).

The natural PRS is considered a self-regulating structure of energy dissipation

(Keller 1971; Wohl 1993; de Almeida and Rodriguez 2010). The foremost theory on the maintenance of the pool-riffle sequence is the ‘reversal hypothesis’ (Lane and Borland

1954; Leopold et al. 1964; Keller 1971; Lisle 1979). The reversal hypothesis states that during low flow, sediment transport capacity (measured by velocity or sometimes shear stress) is maximized at riffle crests, and minimized in pools. As flow increases, the distribution of sediment transport capacity is reversed and pools become areas of maximum sediment transport capacity while riffles become depositional. Not all researchers agree with the reversal hypothesis, and several models have failed to find evidence of reversal (Carling 1991).

The mechanisms by which pool-riffle morphology is maintained are still being debated (Keller and Melhorn 1973; Richards 1982; Wilkinson et al. 2004). Wilkinson et al. (2004) recently hypothesized that instead of being reversed, maxima and minima in shear stress are -shifted with respect to the pool–riffle sequence bedform profile, so that maximum shear stress occurs upstream of riffle crests at high flow, and downstream at low flow. Wilkinson’s model predicts that these phase shifts produce gradients of shear stress that explain riffle deposition and pool scour at high flow, in accord with sediment

7

continuity (Wilkinson et al. 2004). Regardless of how the PRS is maintained during high flow in gravel bed rivers, once flows recede the resulting low flow channel bed is an undulating sequence of topographic highs (riffles) and lows (pools). While the channel bed is constantly adjusting to hydraulic forces during high flow, during low flow, the bed becomes a stable, independent control, to which flow geometry adjusts (Richards 1976b).

The riffle crest is defined as the geomorphic downstream limit of a residual pool

(RPL) – the line of zero residual depth spanning the width of the channel (Lisle 1987).

As flow recedes to zero and connectivity is lost between two consecutive pools, the riffle bed is exposed and the residual pools remain like standing cups of water. The line formed by the downstream edge of the residual pool sketches the riffle crest. Riffle crests are visible as prevalent hydraulic features, associated with the extremities of bars in gravel bed streams exhibiting pool-riffle sequences (Knighton 1998; Richards 1982). During low flows, riffle crests act as natural , where the depth of flow passing over the riffle crest establishes the upstream water surface elevation, and a change in state of flow occurs as water flows over the riffle crest. Riffle crests are perhaps the most stable low- flow characteristic of gravel bed streams, because over time they tend to occur in the same longitudinal location (Dury 1970; Wilkinson et al. 2004), and, providing the stream is in relative sediment equilibrium, tend to maintain the same elevation ( Wilkinson et al.

2004).

Alluvial riffle crests (ARCs) are riffle crests that are built out of material which is entrained during bankfull events and deposited by the receding limb of the .

8

Therefore, ARCs are a physical expression of the dynamic equilibrium of forces in gravel bed rivers. ARCs are differentiated from RCs which may be forced by large boulders, bedrock, channel constrictions, or woody debris. Forced riffles are not as intimately related to the dynamic equilibrium of alluvial rivers as ARCs, and are not necessarily associated with the extremities of gravel bars. ARCs only act as hydraulic controls during a portion of the low flow hydrograph. As flow increases ARCs begin to drown out and non-alluvial controls such as channel constrictions or bedrock protrusions begin to dominate (Leopold and Langbein 1962; Lisle 1982).

2.2 The Active Channel

During high flow events when a stream fills its bed and banks, the alluvial riffle crest is in a state of ; coarse sediment is scoured and transported from upstream riffles and deposited downstream, and the cross-sectional shape of the channel is continuously changing. As flow and coarse sediment transport recede, the morphology of the low flow channel is established, and the alluvial riffle crest begins to control water surface elevation in the upstream pool. This transition, which marks the highest flow at which

RCT depth can be functionally related to streamflow, occurs when flow recedes into the active channel.

Osterkamp and Hedman (1977) define the active channel as the portion of the that is “actively if not totally, sculptured by the normal process of water and sediment .” Wallerstien et al. (2006) refine the definition of active channel as

“the portion of the channel within which excess stream power acts to perform significant

9

geomorphic work through transporting sediment.” Active channel stage (Qacive) is the highest streamflow that can be confined within the active channel.

Active channel stage is clearly differentiated from bankfull stage, although the two are frequently confused, Figure 2. Bankfull stage is associated with the maximum streamflow a channel can hold without spilling onto its , with the tops of alluvial bars (in non-aggrading reaches), and with a flow recurrence interval of 1.5 to 2 years. Active channel stage is normal high water level, being inundated 5% to 20% of the time (Osterkamp and Hupp 1984; Flosi et. al. 1998).

Figure 2. Active channel vs. bankfull stage (Flosi et al, 1998).

The extent (width) of the active channel is commonly identified by a variety of indicators including: the boundary between cleanly scoured sediments and vegetation, the first break in slope above freshly scoured sediment and breaks in rooted vegetation (Flosi et. al. 1998). Active channel stage is considered more relevant than bankfull stage the RCT because once flow reaches bankfull stage, alluvial riffle crests have drowned out.

10

The shape and structure of the active channel define the RCT depth-Q relationship.

In channels with wide active channels, the riffle crest can control streamflow over a wider range of flows than in channels with narrow, confined active channels. An inflection occurs in most hydraulic relationships at active channel stage (flow-depth; flow-velocity; flow-width), which indicates an abrupt change in physical and possibly ecological processes at that streamflow. When the depth of streamflow exceeds active channel stage, water inundating the active channel shelf establishes new habitat and introduces new nutrient sources into the stream ecosystem. Therefore, influence of active channel stage on the RCT depth-Q relationship is of interest both physically and ecologically. As with bankfull stage, regional relationships between active channel streamflow and drainage area can be empirically derived (Figure 3).

Figure 3. Exceedence probability of active channel streamflow for northern California coastal streams as a function of DA (adapted from McBain & Trush & Trout Unlimited, 2008).

11

2.3 Hydraulic Geometry

Empirically derived hydraulic relationships have long been used in channel design, channel assessment, and ecological restoration of gravel bed rivers (Singh 2003). The most common type of empirical hydraulic relationships in streams compare hydraulic variables such as width, depth, and velocity (w,d,v) to streamflow (Q). The variation in hydraulic characteristics of a stream, with respect to streamflow, was termed hydraulic geometry by Leopold and Maddock in their seminal paper from 1953. The mRCT-Q relationship under investigation warrants a review of existing open channel hydraulic relationships, especially the mathematical behavior and scaling of hydraulic geometry.

Leopold and Maddock (1953) show that most hydraulic characteristics can be related to streamflow with simple power functions: w = aQb , d = cQf , and v = kQm

Figure 4). The coefficients and exponents that define these power functions are empirically derived, and they change based on the shape and roughness of the stream channel. As described above, channel shape is a response to the equilibrium between driving and resisting forces, and therefore hydraulic geometry equations can be seen as mathematical expressions of the equilibrium between stream power, sediment supply, and channel roughness. Differences in hydraulic geometries ( w = aQb , d = cQf , v = kQm ) between two streams numerically express their differences in stream power, sediment supply, channel roughness and resistance.

Hydraulic geometry is commonly applied in two ways: downstream and at-a- station hydraulic geometry. Downstream hydraulic geometry is the study of variation in

12

channel form and process at a specific return interval (often the 1.5 year–bankfull flow) along a stream network (Dunne and Leopold 1978). Many parameters used in downstream hydraulic geometry (depth, velocity, width) increase systematically with drainage area when compared at the same average recurrence intervals (Stall and Yang

1970).

Figure 4. Hydraulic Geometries from Leopold and Maddock (1953).

Variation of hydraulic parameters at a single cross-section, over a range of streamflows, is termed at-a-station hydraulic geometry (Leopold and Maddock 1953;

13

Rhodes 1991). At-a-station hydraulic geometry can be used to quantify how a specific cross-section adjusts to changes in sediment supply or streamflow. In low flow conditions, at-a-station geometries quantify how flow fills an essentially non-deforming channel, which is useful for instream flow studies, fish passage analysis, and quantifying habitat availability.

At-a-station hydraulic geometries (AHGs) are often used as tools in ecological restoration. Generally in restoration work, AHG’s are studied on the ‘limiting’ cross- section with respect to a specific species or life stage (Gipple and Stewardson 1998;

Nehring 1979; Reid et al. 2010). This approach is based on the assumption that achieving desired hydraulics at critical or limiting cross-sections will guarantee success throughout the rest of the hydraulic system. A limitation of this method, however, is that at-a-station hydraulic geometries have been shown to be highly variable, even between similar channel units such as riffles (Richards 1976a; Knighton 1975; Wohl 2007; Reid et al.

2010). Therefore, data from one or two AHG cross-sections may not represent data from similar cross-sections throughout a reach. There are also weak relationships between channel shape and hydraulic geometry. Particularly in small streams, local constraints such as bedrock outcroppings may exert a significant impact on width, average depth, and velocity.

RCT hydraulic relationships differ from traditional hydraulic geometry in that the

RCT is a single ‘point’ in the channel. RCT depth and velocity are specific measurements, not averages. Unlike downstream hydraulic geometry, the relationship

14

between RCT hydraulics and streamflows does not have to be compared at similar recurrence intervals. However, like at-a-station (AHG) geometry, the RCT is expected to adjust to changes in sediment supply, because the riffle crest is a depositional feature.

2.4 Weir Equations to Predict Flow over Riffles

The similarity between a natural riffle and a man-made weir was observed as early as 1900 by Seddon (from Richards 1976b). Noting this similarity, Richards applied a standard weir equation to compute depth of flow over a riffle based on .

Equation 1 h = (Q/CB)2/3 where h is the depth of flow (m), Q is the volumetric flow rate (m3/s), B is the width of the weir or riffle (m), and C is an average streamflow coefficient. Using a streamflow coefficient of 3.2, Richards states that Equation 1 produces a depth of flow that “accords well” with measured data from a gravel bed reach of the River Fowey in Cornwall,

England (Richards 1976b). However, no specific riffle depth data were presented.

Equation 1 can also be rearranged to predict streamflow:

Equation 2 Q = CBh3/2

Equation 2 is similar to the relationship between RCT depth and streamflow in that Q is related to depth (or height in this case) using a power function. However, the weir

15

equation assumes uniform depth over the riffle crest (e.g. a rectangular channel) while the

RCT is related to a specific location in the stream channel.

2.5 The Ecological Significance of the Riffle Crest

Pool-riffle hydraulics, morphology, and substrate are important drivers in most gravel bed stream . The characteristics of flow (depth, velocity, turbulence, temperature etc.), and the morphology and substrate of the channel bed, create the environment in which aquatic organisms move, feed, and reproduce. As an hydraulic control, the shape of the riffle crest influences characteristics of flow, and therefore, influences the aquatic in both the upstream pool and the downstream riffle. But, as discussed in section 2.1, riffle crest shape and substrate, which impose a hydraulic control, are themselves defined by hydraulic driving and geomorphic resisting forces of the channel. Therefore, the riffle crest is found at the nexus between physical and ecological processes in the lotic environment.

A quantitative relationship between streamflow and riffle crest thalweg depth is relevant to ecological assessment and management in streams. Several ecological relationships which depend on riffle crest hydraulics have been identified:

 Depth of flow over the riffle crest is used to quantify pool depth upstream,

independently of streamflow. This is known as height above residual pool depth

(Lisle 1987). Residual pool depth is commonly used as a tool to quantify habitat

availability in the upstream pool (Pleus et al. 1999).

16

 Depth and velocity of flow over the riffle crest are important indicators of

instream flow requirements for fish passage (Bjornn and Reiser 1991; Reinfelds

and Williams 2009; McBain & Trush and Trout Unlimited 2008). The riffle crest

generally represents the shallowest cross-section that migrating fish will have to

pass. Streamflows that produce passable riffle crest depths could be used as one

indicator of instream flow needs.

 Complex hydraulics such as near bed turbulence and free flow turbulence, are

considered to impact the distribution and quality of habitat for benthic

invertebrates, as well as for fish and other lotic organisms (Statzner et. al 1988;

Quinn and Hickey 1994; Gorman and Karr 1978). These complex elements of

flow can be estimated for the downstream riffle from simple flow characteristics

(such as velocity, depth, and bed roughness) measured at the riffle crest.

Therefore, characteristics of substrate and flow at the riffle crest might be

valuable indicators of downstream benthic and aquatic habitats.

2.6 Objectives and Tasks

There are four objectives needed to achieve the goals this thesis:

I. Calculate the statistical correlation between mRCT and Q over a wide range of

alluvial channels and streamflows, and develop an empirical equation to predict Q

as a function of RCT and mRCT.

17

II. Investigate other controls on RCT depth besides streamflow (e.g. sediment size

and width of flow) and determine if/how they affect the mRCT-Q relationship.

III. Develop empirical relationships to adjust the RCT depth-Q regression, according

to the physical conditions of a local channel.

IV. Discuss useful applications for RCT hydraulic relationships.

In order to meet these objectives, the following tasks were necessary:

1. Develop and test a method to consistently locate and measure RCT depth.

2. Determine how many RCT depth measurements are needed to calculate a

representative median.

3. Determine which fluvial and geomorphic variables to test as possible controls of

RCT depth.

4. Collect a large body of mRCT and associated stream data from a range of alluvial

streams to develop a mRCT-Q relationship and to identify possible correlations

between mRCT and other geomorphic variables.

5. Decide which statistical methods would best address objectives I-III,

perform the necessary logical and statistical analysis and interpret the results.

6. Based on the strength and limitations of the mRCT-Q relationship, use existing

case studies and literature to suggest useful applications for RCT hydraulic

relationships.

18

3 METHODS

To establish a statistical correlation between mRCT and flow (Objective I), a reproducible method was developed to accurately locate the RCT in any channel (Section

3.1). In addition, a consistent protocol for streamflow measurement was developed

(Section 3.2) and an analysis was completed to identify appropriate RCT sample sizes

(Section 3.3). The strength of the RCT depth-Q and mRCT-Q correlations was statistically evaluated (Section 3.4), and the RCT depth-Q relationship was sampled by four independent volunteers to test for operator bias (Section 3.5). To accomplish

Objective II, methods were developed for data collection and analysis of other controls on RCT depth (besides streamflow) (Section 3.6). To address Objective III, two multivariate relationships were developed to improve the prediction capacity of the RCT depth-Q relationship and to adjust the relationship based on the physical constraints of each local channel (Section 3.7). Potential applications (Objective IV) of the mRCT-Q relationship and other multivariate RCT depth-Q relationships are discussed in Section

5.3.

3.1 RCT Data Collection Methods

The riffle crest was defined as the downstream limit of the residual pool (RPL).

RCT depth was measured by locating the point where the thalweg intersects a riffle crest, then measuring the depth of flow at that location. Locating the point where the thalweg intersects a riffle crest can be considered a three-step process: visually identify the

19

channel region containing the RPL, locate the thalweg within this region, and use inflection in thalweg depth to identify where the thalweg crosses the riffle crest.

3.1.1 Step 1—Visually identify the RPL

In low flow conditions, a region of the channel that includes the RPL can be visually identified. Downstream of this region, high water velocity, steeper water surface slope, and the presence of hydraulic jumps and drops clearly indicate a riffle. Upstream of this region, low water velocity, low water-surface slope, and a smooth water surface clearly indicate a pool. Often the riffle crest will produce a V-shaped inflection (velocity tongue) in the water surface (Figure 5).

Figure 5. A typical alluvial riffle crest observed below active channel flow. The V-shaped inflection in the water surface generally indicates the presence of the thalweg. Here, the white arrow points at the RCT location.

20

If a region bound by an upstream pool and a downstream riffle cannot be visually identified, then the immediate reach does not display pool-riffle morphology or high flow has drowned out the riffle crest.

3.1.2 Step 2—Identify the thalweg within the RPL region

Once the general location of the riffle crest was visually located, the path of deepest flow (thalweg) through the pool-riffle unit was identified. Here the thalweg, which is the continuous line of greatest depth longitudinally down a channel, must be differentiated from any isolated areas of scour. Relatively immobile features such as large boulders, instream wood, or even a bridge pier, will form eddies in the flow around them which scour the channel bed. Scour holes associated with these features may be deeper than the thalweg at some locations, but they are not part of the continuous line of deepest flow. They therefore should be differentiated from the thalweg.

3.1.3 Step 3 – Locate the RCT

Starting downstream of the riffle crest region, the surveyor walks upstream, measuring thalweg depths every foot. The riffle crest is located near the point where thalweg depth begins to increase. This increase in thalweg depth is generally concurrent with an increase in velocity produced at the riffle crest. This can also be visualized by observing the acceleration of a floating object as it passes the riffle crest. Figure 6 and

Figure 7 show the components of an RCT measurement overlain on photographs of two riffle crest.

21

Figure 6. Riffle crest in small confined stream where the RCT is easy to locate.

Figure 7. Riffle crest in a medium-sized stream where the RCT is less obvious. Although depth is greater in the scour hole on the right side of the channel, RCT should still be measured along the thalweg.

22

The inflection or increase in thalweg depth, observed upstream of the RPL, is a more consistent indicator of the location of the RCT than change in velocity or water surface slope. At riffle crests where the upstream pool ramp is gradual and approaches an alluvial RPL (Figure 8), the RCT depth measured at the change in velocity and water surface slope is nearly equal to the RCT measured at the RPL; however, for riffle crests where the pool tail ramp terminates suddenly and the RPL is created by larger boulders or bedrock (Figure 9), the RCT depth measured at the change in velocity and water surface slope is often significantly different from the RCT measured at the RPL. For this reason, all RCT depths are measured at the RPL to reduce the measurement error.

4 Riffle Crest Schematic for Small Confined Stream with Heterogeneous Sediment

3.5 Thalweg Cross-Section

3

2.5

2 100 cfs RCT at ∆ Depth/Vel= 0.65 ft. 1.5 RCT at RPL = 0.6 ft. 1 15 cfs

Elevation(ft) 0.5 0 cfs 0 ResidualPool -0.5

-1 Distance between ∆ Depth/Vel and RPL = 4 ft. -1.5

-2 0 10 20 30 40 50 60 70 Distance (ft) Figure 8. Although the change in state of flow here occurs four feet upstream of the RPL at 15 cfs, the respective RCT depths are within 5 hundredths of a foot. This is often the case with gravel and cobble type riffle crests.

23

4 Riffle Crest Schematic for Small Confined Stream with Boulder Control

3.5 Thalweg Cross-Section

3

2.5 RCT at ∆ Depth/Vel= 1.0 ft. 2

1.5 100 cfs RCT at RPL = 0.6 ft.

1 15 cfs 0.5

Elevation(ft) 0 0

-0.5

-1 Distance between ∆ -1.5 Depth/Vel and RPL = 3 ft.

-2

-2.5 0 10 20 30 40 50 60 70 Distance (ft) Figure 9. In many boulder and bedrock control riffle crests, the change in state of flow occurs relatively close to the RPL, however the RCT depths are significantly different. In these cases it is especially important to measure the RCT depth at the RPL.

3.2 Streamflow Data

Streamflow was determined during each RCT sampling either from an existing

USGS gage or by direct measurement. Ten of the nineteen reaches sampled in this project were gaged by the USGS during the period of sampling. On gaged reaches, stage height was recorded at the beginning and end of sampling and streamflow was accessed from the USGS website. On all ungaged reaches, streamflow was measured directly before or after RCT data collection. Streamflow was measured using a standard USGS 4ft topset rod and USGS model 6205 Pygmy Meter. Pygmy meter range of operation was

0.1 to 4.9 feet per second (0.03 to 1.5 meters per second) which was adequate for all

24

velocities sampled during this project. Streamflow measurements were made according to the guidelines from Harrelson et al. (1994).

3.3 Sample Size Analysis

Initially, a sample size of ten RCT depths measured in each sample reach, was estimated as a quantity that would produce a representative median RCT depth for a given survey reach. Once some RCT depth-Q data had been collected, the ten RCT sample size assumption was tested, using confidence intervals for normally distributed data. The term “representative median” was defined as the derived median (mRCT) which an observer could be 95% confident was within ten percent of the true median

RCT depth for the reach. For a population with an unknown standard deviation, a confidence interval for the population median, based on a simple random sample of size N, is:

Equation 3

̃ √

Where, ̃ is the sample median, t* is the upper critical value for the t distribution, is the sample standard deviation, and is the sample size. Equation 3 assumes normally distributed data and an unknown standard deviation.

The confidence interval for a population mean will have a specified margin of error m when the sample size is:

25

Equation 4

= [ ]

The margin of error (m) for a derived mRCT to be within 10% of the true median RCT depth is equal to 0.10 ̃, where ̃ is the derived mRCT. For the 95% confidence interval of normally distributed data, t* is 1.96. Therefore, the sample size is defined as:

Equation 5 [ ̃ ]

Where s is the sample standard deviation, ̅ is the sample median, is the desired accuracy percent and is the sample size required to achieve a representative median as defined above.

Equation 5 assumes a normally distributed data set; therefore, before doing any sample size calculations using Equation 5, it was necessary to determine if the RCT data sets were normally distributed. The Shapiro-Wilkes test for normality was chosen for its generalized application and because it is not significantly affected by ties (which occur frequently in the RCT data sets). The Anderson-Darling test was not used because it is influenced by ties in the data. The Shapiro-Wilkes test rejects the hypothesis of normality when the test p-value is less than or equal to 0.05. Failing the normality test provides

95% confidence that the data do not fit the normal distribution. Passing the normality test only provides that no significant departure from normality was found. Due to the small

26

sample size of the RCT data sets, only the largest two sample sets were tested, and normality (in the remainder of the samples) was inferred from the tested data sets.

3.4 Statistical Analysis of RCT Depth-Q Data

The first objective of this project was to calculate the statistical correlation between mRCT and Q over a wide range of channels and streamflows. Forty three RCT depth-Q data sets were collected through direct measurement. Five hundred fifty two RCT depths were measured during the data collection for this thesis. Table 1 shows the range of drainage areas and flows in which RCT depths were sampled. Nine RCT depth data sets from Rush Creek ( to Mono Lake) were collected by McBain & Trush staff as part of separate instream flow analyses. All other RCT depth data sets were collected by the author between fall of 2009 and of 2012.

27

Table 1: Reaches sampled to assess the correlation between mRCT and streamflow.

Drainage Data Stream Area (mi2) Sets Flows (cfs) Alameda Creek at Welch Creek 145 1 32

Alameda Creek in Niles 633 4 27; 38; 72; 105;

Alameda Creek in Ohlone Park 135 1 32

Alameda Creek in Upper Sunol 150 4 30; 25; 65; 18

Bull Creek (lower) 27 1 15

South Fork Eel River 537 3 46; 24; 48

Jacoby Creek 14 4 12; 54; 20; 17

Little Lost Man Creek (lower) 3.5 1 39

Little Lost Man Creek (upper) 3 2 3.3; 24

Little River near USGS gage 40.5 3 138; 3; 77

Lost Man Creek 12 1 10.6

Mill Creek west of Healdsburg 6.7 1 10.4

Morrison 0.99 3 3.4; 0.8; 7.5

Redwood Creek at Hwy 299 67.7 3 29; 3.7; 36

Redwood Creek near Orick 277 1 43.0

Rush Creek (Ford Bottom Lands)* ~22 5 14; 28; 45.6; 57; 77

Rush Creek (Upper)* ~10 4 17; 33; 50; 90

Sonoma Creek 54 1 30 Total 43 Max 138cfs, Min 0.8cfs *McBain & Trush unpublished data (2010)

28

Both the collective raw RCT data and the derived mRCT data from each sample set were analyzed for statistical correlation with streamflow. The following process was used to evaluate the statistical correlation between mRCT and Q:

1. Scatter plots were created with RCT (or mRCT) on the X axis and streamflow on

the Y axis.

2. Linear and power functions were fit to the data using Micosoft Excel trendline

regressions.

3. The following regression statistics were compiled: R2 and adjusted R2, root mean

squared error, intercept coefficient and variable (RCT or mRCT) coefficient.

4. Predictive equations (prediction streamflow with RCT or mRCT) were developed

from the regression coefficients.

5. Variance and standard deviation were calculated for each RCT data set.

6. A cross-validation process was performed in which a random subset of half the

mRCT-Q data was used to generate a regression equation which was then used to

predict the other half of the mRCTs.

Linear functions and power functions were used to describe the RCT depth-Q relationship because visually, RCT depth-Q data generally appears to fit either function quite well. Power functions have been used to describe hydraulic geometry relationships since the 1950s (Leopold and Maddock 1953). Like hydraulic geometry relationships,

RCT depth is an hydraulic parameter, empirically related to streamflow (although it is a specific parameter, not a channel average). Although the R2 values are similar between

29

linear and power models for RCT depth-Q data, a power function is a more realistic way to describe RCT depth-Q relationships than a linear function because power functions always pass through the point 0,0. At zero flow, the riffle crest depth will necessarily be zero. While the linear model may fit the body of the RCT data reasonably well, it would also generally show some RCT depth at zero flow, which is unrealistic.

3.5 Independent Testing of RCT Depth-Q Relationship

Four volunteers completed RCT surveys to test for operator bias in the RCT depth-

Q data set. The volunteers were given no prior information about the RCT depth-Q relationship, but where given a ‘primer’ on how to identify RCTs in the field. A survey sheet (Appendix) was developed that contained detailed instructions for locating the

RCT, using the methods described in section 3.1. Each surveyor was asked to collect ten

RCT depths on a reach with known streamflow. Median RCTs were computed from the four test data sets and plotted against measured streamflow. Streamflow was also predicted for each sampled data set, using the sample mRCT and the power function developed from the author’s mRCT-Q regression (Figure 12). The difference between predicted and observed streamflow was called “error.” Error from the volunteer’s sample test was compared with error from the author’s RCT data sets.

3.6 Other Hydraulic and Geomorphic Controls on RCT Depth

The statistical correlation between mRCT and streamflow indicates the presence and strength of the relationship. However, variation in the mRCT-Q relationship suggests that a broader understanding of the mechanisms which influence RCT depth at a given

30

flow would be useful when applying mRCT as an ecological indicator. Addressing multiple controls on RCT depth is especially important if mRCT is to serve as an ecological tool, because each potential control (e.g. sediment size) has specific ecological implications (e.g. substrate for benthic macro invertebrates). To investigate the influence of fluvial-geomorphic controls besides streamflow on the mRCT, four variables were chosen: wetted width of channel at the riffle crest (WWC), median (D50) sediment size, drainage area and active channel stage.

Wetted width data were collected at thirteen of the nineteen reaches and at twenty four discrete streamflows. Drainage area was determined for 15 reaches and related to

RCT depth per unit of streamflow at 36 discrete streamflows. Sediment size data were collected in four reaches each at a different streamflow, for a total of 38 individual riffle crests. The relationship between the RCT depth-Q curve and the active channel stage was studied at three riffle crests over a range of descending streamflows after a high flow event.

3.6.1 Wetted Width Data Collection and Analysis

Wetted width of the channel was measured perpendicular to flow at the riffle crest thalweg (Figure 10), using a Kesontm 100 ft fiberglass field tape graduated in 10ths of feet.

Wetted width was measured on thirteen reaches over a range of streamflows—310 total measurements were completed.

31

To analyze the influence of wetted width on the mRCT-Q relationship, individual wetted width data (WWC) and median wetted width (mWWC) data were regressed against RCT and mRCT, respectively, and fit to both linear and power functions (see

Section 4.6.1). Wetted width was also normalized by streamflow to determine if the streamflow per foot of width was related to mRCT. Wetted width data is also included in the analyses of multiple variables (See 4.7).

Figure 10. Location of wetted width measurement for a typical riffle crest. The measurement is perpendicular to the direction of flow and intersects the RCT point.

3.6.2 Drainage Area Data Collection and Analysis

For reaches with USGS gages, drainage area was found from the annual USGS

Water Data Report sheet associated with each gaging station. Water Data Report sheets are available at the local USGS field office and online at http://waterdata.usgs.gov.

Drainage areas for all other reaches were established by reports from California State

32

Parks, Alameda County Water District, and USFS Stream Systems Technology Center.

Drainage area was estimated all of the 19 sampled reaches. To determine if the mRCT-Q relationship is scaled by drainage area, drainage area and streamflow per unit drainage area were regressed against RCT and mRCT data (See 4.6.2). Linear and power functions were fit to the RCT—drainage area regressions.

3.6.3 Sediment Size Data Collection and Analysis

Pebble counts were performed to establish sediment size at 38 riffle crests on four reaches. On each riffle crest, a transect was established, perpendicular to flow, within the active channel, and at the immediate vicinity of the riffle crest. The purpose of the pebble counts was to differentiate the sediment size distributions of riffle crests. Pebbles and cobble were collected at intervals with a maximum length of two feet across a given transect. A minimum of 20 pebbles were collected at each riffle crest, and the average sample size was 33. Other than sample size, the sampling protocol established by

Wolman (1954) and Leopold (1970) was used: a transect was paced in increments of every two feet and, with eyes averted, the first particle touched by the finger at the tip of the boot was selected. The particle b-axis (second longest axis) length was measured to the nearest millimeter, and then translated to units of feet. Median (D50) particle size was computed for each riffle crest sampled (38 riffle crests), and regressed against RCT depth

(See 4.6.3). Regressions from four streams were compared. Sediment size data was also used in the analysis of multiple variables (See 4.7).

33

3.6.4 Active Channel Stage Data Collection and Analysis

Active channel stage (Qactive) was defined as the stage at which streamflow has completely filled the active channel. Streamflows greater than Qactive are generally confined by the vegetated bankfull shelf and not by the scoured and deposited sediment of the active channel. Active channel stage was estimated in the field using the indicators outlined in California Salmonid Manual part four, (Flosi et al, 1998).

Active channel stage was estimated in feet above the RCT elevation.

To investigate the relationship between the RCT depth-Q curve and active channel stage, a reach of Jacoby Creek (DA 14 mi2) was selected. Active channel stage and streamflow (Qactive), were identified using channel indicators, and corroborated using the active channel flow rating curve from McBain & Trush and Trout Unlimited (2008),

Figure 3. Three RCT locations were identified within the reach. During the descending limb of a spring freshet, RCT depth was measured systematically as streamflow decreased. RCT depths were plotted against streamflow, including RCTs above and below the active channel stage (See 4.9). Inflections in RCT depth were observed at active channel stage. A regional RCT depth-Q curve was used as a datum to evaluate inflections in the specific RCT depth-Q data points from Jacoby Creek.

3.7 Analysis of Multiple Variables

Bivariate regression was useful to establish the strength of correlation between

RCT depth or mRCT and streamflow. However, correlation neither implies that Q is the causal mechanism of mRCT nor describes how channel geometry affects their

34

relationship. If geomorphic variables are responsible for scatter in the mRCT-Q regression, then incorporating them into a multivariate relationship can serve at least two purposes. First, the relationship can explain how change in multiple geomorphic variables affects RCT depth. This is especially important for applying the RCT or mRCT as an ecological indicator in channels with different . Second, it could lead to the development of an empirical relationship that would have a better flow prediction capacity than RCT depth or mRCT alone.

The following analyses were performed to explore the relationship between RCT depth and multiple geomorphic and hydraulic variables:

 Ranked RCT depths (smallest to largest), their corresponding wetted channel

widths (WWCs), and median sediment sizes (D50s) were plotted on the same

chart to show the trends of multiple variables.

 A bivariate RCT depth-Q regression was compared with a multivariate regression

[RCT depth∙WWC∙D50] –Q to determine if the addition of WWC and sediment

size data would improve RCT flow prediction.

Multiple correlations between geomorphic variables and the RCT can also provide insight into the causal mechanism of the mRCT-Q relationship. Knighton (1998) theorizes that in pool-riffle channels, channel development is principally driven by bed material size relative to the transport potential in a reach. Because the riffle crest is the central feature of the self-adjusting pool-riffle channel, one hypothesis is that bed

35

material size, relative to the transport potential in a reach, also is the principal driver of the mRCT-Q relationship. To test this hypothesis, a dimensionless variable was developed to express the relationship between bed material size and the transport potential. Median sediment size (D50) was chosen to represent bed material size and wetted width of flow was chosen to represent transport potential. Wetted width was chosen because channels which experience larger tractive forces will tend towards narrower wetted widths per unit flow (smaller width to depth ratio) (Wohl 1993). Wetted width and D50 were also chosen because they are relatively easy to measure in the field,

which helps in developing an empirical relationship. The dimensionless variable

( ) was also scaled per unit flow, giving to allow to be related to an RCT depth

at any flow. The scaled variable has unites of seconds/ feet3. Variable 1, scaled by

streamflow, was regressed against RCT, to determine if can reduce the scatter in

the RCT depth-Q relationship, Figure 28.

36

4 RESULTS

Data collection had two main purposes: (1) to compile an hydraulic data set to develop the correlation between mRCT and Q (Sections 4.1 to 4.5), and (2) to compile a geomorphic data set to determine the effect of non-hydraulic (geomorphic) controls on

RCT depth (Section 4.6) and analyze multiple variables to refine the mRCT-Q relationship (Section 4.7). Thirteen streams from Humboldt, Mendocino, Sonoma, and

Alameda Counties were used to collect RCT depths and supporting data (Table 1).

Nineteen reaches were selected, and 43 RCT data sets were compiled at discrete streamflows. In addition, four of the established reaches (two sites on Redwood Creek, one site on Little Lost Man Creek, and one site on the South Fork Eel River) were selected for an analysis of multiple variables to explore the effect of channel structure on

RCT depth.

4.1 Statistical Correlation between mRCT and Streamflow

The relationship between mRCT and Q was developed using direct observations.

To create a mRCT-Q data point, a series of riffle crest depths were measured along a sample reach of known streamflow. The median riffle crest depth was then computed.

RCT depth measurements were collected according to the guidelines described previously in Section 3.1.

37

4.2 Statistics for the RCT –Q Relationship

The collective (non-median) RCT depth-Q data were assessed to contrast with the calculated mRCT-Q data. RCT depth data sets were plotted against streamflow to show their relationship (Figure 11). Linear and power functions (see Methods 3.4) were both applied to the RCT depth-Q data to determine which model best describes the relationship.

Figure 11. Riffle crest depths plotted against streamflow. A linear model and a power function are both used to describe the RCT depth-Q relationship.

4.3 Statistics for the mRCT-Q Relationship

The median riffle crest depth (mRCT) from each RCT depth data set was computed. The mRCTs were also plotted against streamflow to show their relationship and explore possible descriptive models. As with the raw RCT depth-Q data, linear and

38

power functions were applied to the mRCT-Q data to determine which model best described the relationship.

Figure 12. Median riffle crest depths plotted against streamflow. A linear model and a power function are both used to define the mRCT-Q relationship. Nineteen reaches and 43 discrete streamflows are included in this relationship.

39

4.3.1 Variance in RCT Depths Within a Sample Reach

Variance of RCT depths occurred within each sampled reach. The average variance observed was 0.051 ft (Table 2). Variance of RCT depths increased in reaches with geomorphic discontinuities such as bedrock protrusions or abrupt changes in channel slope. Figure 13 shows a typical range in RCT variance over four streamflows.

Table 2. Variance in the RCT data sets.

Variance Summary For RCT Data Sets Average Variance in RCT depth data sets 0.051 (ft) Median Variance in RCT depth data sets 0.033 (ft) Maximum Variance in RCT depth data sets 0.303 (ft) Minimum Variance in RCT depth data sets 0.001 (ft) Average number of RCT depths collected per data set n = 11.9 Average number of RCT depths collected per data set n = 11 Maximum number of RCT depths collected per data set n = 26 Minimum number of RCT depths collected per data set n = 6

Figure 13. An example of the variance in RCT depth over a range in streamflows for a single reach – in this case Sullivan Gulch (DA 2mi2). Although each data set shows variance in RCT depth at a given flow, the median RCT value tends to be uniquely related to a streamflow.

40

4.4 Cross Validation of the mRCT Data Set

A cross validation was performed using the complete mRCT-Q data set to determine the predictive capabilities of mRCT over a range of streamflows.

1. The mRCT data set was split into subsets A and B, using a randomized index. A

mRCT-Q regression was developed from each subset (Figure 14).

2. The regression equation from subset B was used to predict streamflows for the

mRCTs from subset A (Figure 15). Resulting predictions were compared to the

1:1 line as a visual assessment of prediction quality.

3. The flows included in the mRCT-Q data set were split into quartiles.

4. Steps one and two were completed 20 times for each quartile. The median

prediction error (predicted streamflow – observed streamflow) and the standard

deviation of mRCT for each quartile was computed (Table 3).

Figure 14. Two random subsets of the mRCT-Q data and their respective regression equations.

41

130.00 120.00 110.00 100.00 90.00 80.00 70.00 60.00 50.00 40.00 30.00

20.00 Observed Streamflow (cfs) Observed Streamflow 10.00 1:1 Line 0.00 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Predicted Streamflow (cfs) Figure 15. Streamflows predicted using the regression equation from Subset B and the mRCTs from Subset A, versus actual streamflows from subset A.

Table 3. Analysis from mRCT cross validation of predicted vs. observed streamflows by quartile.

Standard Deviation of Median Streamflow Prediction Error Range mRCTs (Observed –Predicted) Quartile [cfs] [ft] [cfs] 1st 0-11.5 0.11 8.7

2nd 11.6-31 0.15 5.1

3rd 31.1-55.2 0.09 7.0

4th 55.3-155 0.30 12.3

4.5 Independent Testing of RCT Depth-Q Relationship

As described in Section 3.5, four volunteers completed RCT surveys to test for operator bias in the RCT depth-Q data set. The results of four independent tests for operator bias are shown in Table 4 and Figure 16. Median RCTs were computed from the four test data sets and plotted against measured streamflow. Streamflow was also

42

predicted for each test data set, using the sample mRCT and the power function developed from the author’s mRCT-Q regression (Figure 12).The differences between predicted and observed streamflow were computed for the test data and compared with the observed error in the author’s data (Table 4). Two of the volunteers had smaller error

(observed streamflow minus the streamflow predicted from the author’s regional mRCT-

Q curve, Figure 12) than the median error from the author’s mRCT-Q data set for the same flow range (Table 3), while two of the tests had larger error. One of the sampled tests (test #4) was clearly an outlier in this group, with an error six times the author’s median error for the same flow range. Figure 16 shows the median RCT depth as well as the range of RCT depths from each independent test, compared with the regional mRCT-

Q curve from Figure 12. Figure 16 also shows the author’s standard deviation of mRCT for four quartiles. Although mRCT varied from the regional curve, the range of RCT depths from each independent test bracketed the mRCT predicted from the regional curve. The implications of these results are discussed in Section 5.1.

Table 4. Comparing measurement error between operators.

Error Author’s Median (Observed – Streamflow Test mRCT Flow Predicted Flow* Predicted) Prediction Error 1 0.60 14.0 10.5 3.5 5.1 2 0.87 25.0 30.5 5.5 5.1 3 0.95 30.0 38.5 8.5 5.1 4 0.60 52.5 10.5 42 7.0

43

Figure 16. Median RCT depths computed from independent test for operator bias. Results are compared with the mRCT-Q curve developed during this project in Figure 12.

4.6 The Effect of Non-Hydraulic Controls on the mRCT-Q Relationship

To investigate the effect of non-hydraulic controls on the mRCT-Q relationship, four variables were chosen: wetted width of channel at the riffle crest (WWC), median sediment size (D50) of the riffle crest, drainage area, and active channel stage.

4.6.1 Wetted Width of Channel

To analyze the influence of wetted width of the channel on the mRCT-Q relationship, median wetted width (mWWC) data was plotted against mRCT , Figure 17.

44

Median WWC was also normalized by streamflow to determine if the streamflow per foot of wetted width was related to mRCT, Figure 18. The mRCT-(Q/WWC) regression

2 has a slightly lower R than the mRCT-Q regression (Figure 12).

80 y = 34.284x1.0692 70 R² = 0.4327

60

50

40

mWWC (ft) mWWC 30

20

10

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 mRCT (ft) Figure 17. mRCT vs. mWWC for thirteen reaches and twenty four discrete data points are included in this relationship.

Figure 18. mRCT vs. mWWC per unit streamflow. Thirteen reaches, twenty-four discrete streamflows, and 310 data points are included in this relationship.

45

4.6.2 Drainage Area

The relationship between drainage area and mRCT was analyzed to determine if the mRCT relationship is scaled by drainage area. Drainage area and drainage area normalized by streamflow are plotted against mRCT in Figure 19 and Figure 20, respectively.

Figure 19. Drainage area vs. mRCT for 19 reaches and 36 discrete mRCTs.

Figure 20. Drainage area per unit streamflow vs. mRCT for 19 reaches and 36 mRCTs.

46

4.6.3 Sediment Size

The relationship between sediment size and RCT depth was analyzed for one streamflow at four sites, for a total of 38 unique RCTs. At each riffle crest, a pebble count was performed. Median sediment diameter was plotted against RCT depth for each

RCT sampled, Figure 21.

Figure 21. Median sediment size vs. RCT depth. Four sites and 37 riffles where sampled for this analysis. RCT depth increases with sediment size at slopes between 0.25 and 0.42.

Figure 22 shows the same set of RCT depths as Figure 21, however sediment size becomes the independent variable and RCT/Q becomes the dependent variable. Figure

22 establishes the influence of sediment size on RCT depth per unit of streamflow.

47

Figure 22. Median Sediment size compared with RCT/Q. The median D50 for each reach is also included.

4.7 Analysis of Multiple Variables

As part of the sediment size analysis, WWC and RCT depth data were also collected. Figure 23 through Figure 26 show the relationship between these three parameters for four reaches, each at a different streamflow.

48

0.9 50 0.8 45 0.7 40 0.6 35 30 0.5 25 0.4 20 0.3 15 (ft) Width 0.2 10 RCT and Sed Size (ft) Size Sed and RCT 0.1 5 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Rank RCT Depth (ft) Median Sediment Size (ft) Width (ft)

Figure 23. The relationship between RCT depth, WWC, and sediment size ranked by ascending RCT depths. Data from Lost Man Creek (DA = 12mi2); streamflow 10.5 cfs.

1.2 180 160 1 140 0.8 120 100 0.6 80

0.4 60 (Ft) Width 40 0.2 RCT and Sed Size (ft) Size Sed and RCT 20 0 0 0 1 2 3 4 5 6 7 8 9 10 Rank RCT Depth (ft) Median Sediment Size (ft) Width (ft)

Figure 24. The relationship between RCT depth, WWC, and sediment size ranked by ascending RCT depths. Data from the South Fork Eel River (DA = 537mi2); streamflow 46 cfs.

49

1.4 90 1.2 80 70 1 60 0.8 50 0.6 40

30 (Ft) Width 0.4 20 0.2

RCT and Sed Size(ft) andSed RCT 10 0 0 0 1 2 3 4 5 6 7 8 9 Rank RCT Depth (ft) Median Sediment Size (ft) Width (ft)

Figure 25. The relationship between RCT depth, WWC and sediment size ranked by ascending RCT depths. Data from the Redwood Creek near Blue Lake (DA = 67.7mi2); streamflow 36 cfs.

1 100 0.9 90 0.8 80 0.7 70 0.6 60 0.5 50 0.4 40 0.3 30 (ft) Width 0.2 20 RCT and Sed Size (ft) Size Sed and RCT 0.1 10 0 0 0 1 2 3 4 5 6 7 8 9 Rank RCT Depth (ft) Median Sediment Size (ft) Width (ft)

Figure 26. The relationship between RCT depth, WWC and Sediment size ranked by ascending RCT depths. Data from Redwood Creek near Orick (DA = 277mi2); streamflow 43 cfs.

A multiple regression was performed to determine if the addition of WWC and sediment size data improve the accuracy of RCT flow prediction. Data from the four sites in the sediment size analysis was used in the regression. A bivariate regression of the

RCT depth-Q data was used as the baseline from which to compare the multiple

50

regression data. Multiple linear regression was completed for both untransformed (Table

5) and LN transformed (Table 6) RCT depth, WWC and D50 sediment size data. In both cases, the addition of WWC and D50 increased the regression coefficient by more than

0.5.

Table 5. Multiple linear regression of the untransformed RCT, WWC and sediment size data from four sites. Each site is sampled once; a total of 38 RCTs are included in this regression.

Table 6. Multiple linear regression of the LN transformed RCT, WWC and sediment size data from four sites. Each site is sampled once; a total of 38 RCTs are included in this regression

51

Results of the multiple regression suggested that wetted width and median sediment size may exert a significant effect on RCT and thereby on mRCT at a given flow. To express the influence of wetted width and median sediment size on RCT, depth

two variables were developed, and . The variable was plotted against

Q/RCT, to assess how change in the geomorphic variables influences the volumetric streamflow per foot of RCT depth, Figure 27. Another way to think of Figure 27 is that

the change in is related to the change in riffle crest depth relative to the flow rate.

A more useful way to express Figure 27 was to normalize the geomorphic variables by

streamflow and relate them directly to RCT depth. In Figure 28, the variable was

plotted against RCT depth. As sediment size increases relative to the wetted channel width at any given flow, RCT depth is shown to increase.

52

Figure 27. The relationship between and streamflow per foot of RCT depth.

0.3 Lost Man Creek South Fork Eel River 0.25 Redwood Creek (at Orick) 0.2 Redwood Creek (above Blue Lake)

0.15 D50/(WWC/Q)= 0.1731(RCT)2.3402 R² = 0.7392

0.1 D50/WWC/Q(cfs)

0.05

0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 RCT (ft)

Figure 28.The relationship between and RCT depth.

53

4.8 Comparing Predictive Capabilities of Three Regression Models

To determine the streamflow prediction capacity of the RCT - regression, the

regression equation is first arranged to isolate streamflow. The regression equation from

Figure 28 becomes:

Equation 6

A two-fold cross validation analysis was performed (separate from the mRCT cross validation in Section 4.4) to compare the predictive capacity of the three existing

regression models: RCT depth-Q (Figure 11), mRCT-Q (Figure 12), and RCT- ,

(Figure 28, Equation 6). Using the RCT depth-Q data as an example, the two-fold cross validation is described below:

 From the RCT –depth Q data set, a random subset totaling half the RCT depth-Q

data was extracted and regressed.

 The regression equation was then used to predict the dependent (RCT depth)

variables of the remaining data set given their matched independent variable (Q).

 Error, measured in ft3/s and percent error were recorded for each prediction.

 The data set was reshuffled and the process was repeated 20 times.

 The average error and average percent error from each method was recorded.

The results of the two-fold cross validation analysis are recorded in Table 7.

54

Table 7. Results of random two-fold cross validation analysis.

Average # of Data x Prediction Percentage Regression Model Points # of Flows Error (cfs) Error RCT depth - Q 546 43 14.6 47.4 % mRCT –Q 43 43 7.0 31.4 % RCT depth – D50/(WWC/Q) 38 4 5.3 22.9 %

4.9 Active Channel Boundary

Three RCT locations on Jacoby Creek were identified to investigate the relationship between the RCT depth-Q curve and the active channel stage, Figure 29 to

Figure 31. During the descending limb of a spring freshet hydrograph, RCT depth was measured systematically as streamflow decreased. Each of the RCT depth-Q relationships was plotted over a range of streamflows that included the active channel stage Figure 29 to Figure 31. A cross-section survey was completed at each riffle crest to highlight the active channel shelf.

In all three riffle crests, the RCT depth-Q relationship appears to follow the regional curve from Figure 12 (red dashed line) until streamflow reaches the active channel boundary. Once streamflow exceeds Qactive RCT depth begins to increase rapidly as water moves up the vegetated bankfull shelf. The third riffle crest (Figure 31) had a left bank scour hole, which caused Qactive to occur at a higher flow than on the other two cross sections (Figure 29 and Figure 30).

55

Figure 29. The relationship between RCT depth-Q and active channel confinement at RCT #1 on Jacoby Creek.

Figure 30. The relationship between RCT depth-Q and active channel confinement at RCT #2 on Jacoby Creek.

56

Figure 31. The relationship between RCT depth-Q and active channel confinement at RCT #3 on Jacoby Creek.

Pool-riffle morphology in confined alluvial channels is often submerged at streamflows greater than Qactive. This phenomena is highlighted in the two photographs from Little Lost Man Creek (3.4 mi2), Figure 32. In the first photo at 5 cfs, Little Lost

Man Creek displays pool-riffle morphology with obvious riffle crests. In the second photo at 38 cfs, the flow depth has submerged the riffle crests and pool-riffle morphology is no longer evident. Estimated active channel flow at the photograph location was ~20 cfs based on active channel indicators and corroborated by the exceedence curve from

Figure 3.

57

Figure 32. On Little Lost Man Creek Qactive is approximately 20 cfs. Riffle crest hydraulic controls are in evident below (left photograph) at 5 cfs, however they are submerged (right photograph) at 38 cfs.

4.10 Sample Size Analysis Results

At the onset of data collection for this thesis, a sample size of ten RCT depths was estimated as a quantity that would produce a representative median RCT depth. This assumption was tested using confidence intervals for normally distributed data. The

Shapiro-Wilkes test was chosen to determine if the RCT data sets are normally distributed. An example of the Shapiro-Wilkes test is shown in Figure 33 using data from the Alameda Creek at Niles Canyon RCT data set. JMP 9 Statistical Software was used to perform the normality test and produce the parameter estimates and test results

58

(Table 8). In Table 8, location (M) is the mean RCT depth in the data set, and dispersion

(Σ) is the variance about the mean.

P-value 0.07

Figure 33. Histogram and P-value test results from Shapiro Wilkes test for normality of RCT data set for Alameda Creek at Niles Canyon .

Table 8. Parameter estimates from Shapiro-Wilkes Test for normality.

Type Parameter Estimate Lower 95% Upper 95% Location Μ 0.84 0.79 0.89

Dispersion Σ 0.13 0.11 0.18

The p-value of 0.07 in Figure 33 shows that no significant departure from normality was found in the Alameda Creek at Niles Canyon RCT data set. Due to the small sample size of the RCT data sets, the two largest sample sets were tested with the above method and both met the normality criteria. Normality (in the rest of the samples) was inferred from the tested data sets and Equation 5 was applied.

59

The sample size required to derive a “representative median” (95% confidence interval) was calculated for each of the collected RCT data sets using Equation 5, and compared to the actual sample size collected, Table 9. Confidence intervals of 90% and 80% were also analyzed.

Table 9. Confidence intervals for sampled RCT data sets.

Confidence level Proximity to true Number of data sets Number of data sets median that met criteria. 95% (representative 10% 43 17 median) 90% 10% 43 22 80% 10% 43 36

60

5 DISCUSSION

A stream and its bed make up a constantly changing, often chaotic environment.

How this environment so often resolves into the stable (Leopold and Wolman 1957) and repeating pool-riffle sequence is a fundamental question of fluvial geomorphology

(Langbein and Leopold 1968; Richards 1982; Lisle 1979; Newbury and Gaboury 1993;

Carling and Wood 1994). The most stable feature of the pool-riffle sequence is the alluvial riffle crest. For its unique stability and centrality in the pool-riffle sequence, the riffle crest deserves attention from geomorphic and ecological perspectives.

The balance between transport capacity and sediment size in a channel dictates the position and cross-sectional shape of a riffle crest, so the riffle crest is of interest in the study of channel evolution and maintenance. However, riffle crests are also a controlling factor in the pool-riffle ecosystem. As a hydraulic control, the riffle crest affects water surface elevation in the upstream pool thereby influencing both habitat and lotic productivity. A first step in understanding the influence of riffle crest dynamics on ecological variables (such as habitat or productivity) is to develop a hydraulic relationship between streamflow and the physical characteristics of flow over the riffle crest.

In this study, a hydraulic relationship between median riffle crest thalweg depth

(mRCT) and streamflow (Q) has been described. The mRCT-Q relationship was developed from nineteen gravel bed streams in northern California (Figure 12). As with hydraulic geometry, the mRCT-Q relationship defines how change in a physical variable

61

(mRCT) is related to streamflow by a power function. The mRCT-Q relationship is different from traditional hydraulic geometry, however, because median RCT depth does not appear to be scaled to drainage area (Figure 19, Figure 20), and relates to streamflow at any recurrence interval so long as flow is confined within the active channel and the riffle crests are acting as hydraulic controls (Figure 29, Figure 30 and Figure 31). This represents a significant difference from both downstream (DHG) hydraulic geometry, which is scaled to drainage area and depends on a single recurrence interval for relevancy, and from at-a-station hydraulic geometry (AHG) which, although strongly correlated to streamflow at a single location, varies widely between AHG cross-sections

(Richards 1973; Knighton 1975; Park 1977; Wohl 2007; Reid et al. 2010).

This study was concerned first with identifying the strength and the significance of the relationship between streamflow and mRCT , and secondly with investigating the geomorphic conditions that influence RCT depth. The first objective establishes the existence and the strength of the mRCT-Q relationship, the second provides some insight into how this relationship can be applied most accurately in a range of different stream types.

5.1 The strength and significance of the correlation between mRCT and Q

The first objective of this project was to determine the strength of correlation between mRCT and streamflow in gravel bed streams. Data were collected to visually observe the relationship between mRCT and streamflow (Figure 12). A power function appears to describe the relationship between mRCT and Q well, with a regression

62

coefficient of 0.84. However, the regression coefficient alone may not be the best means to determine the strength, significance, or the usefulness of the mRCT-Q relationship because correlation does not imply causation.

Two analyses are offered to assess the significance and predictive capacity of the correlation between mRCT and Q: (1) comparing the R2 from the mRCT-Q regression with R2’s of common hydraulic geometries, and a cross-validation analyses to assess how well mRCT predicts streamflow and vice versa. These analyses and their merits are discussed below.

The regression coefficient (R2) from the mRCT-Q correlation in Figure 12 was

0.84. This regression, developed from 43 mRCT datasets, compared favorably with regression fits for hydraulic geometries. Downstream hydraulic geometry relationships had regression coefficients between 0.50 and 0.99 when compared at bankfull streamflow

(Lee and Julien 2006; Griffiths 1980). At-a-station hydraulic geometries were correlated to streamflow with regression coefficients between 0.7 and 0.99 for most hydraulic variables (Reid 2010; Stewardson 2005).

Several factors must be considered, however, when the mRCT-Q regression coefficient is compared with coefficients from hydraulic geometry (HG) regressions. At- a-station HG regressions are developed at a single cross-section whereas the mRCT-Q relationship applies to any sample of riffle crests in an alluvial channel, where flow is below the active channel stage. Downstream HG regressions are computed at discrete cross-sections within the same channel network and at specific recurrence intervals

63

whereas the mRCT-Q regression was developed from 19 streams, and at 43 different streamflow recurrence intervals. Considering hydraulic and geomorphic variation between sampled riffle crests, channel networks and recurrence intervals, the mRCT-Q relationship appears to have broader application and stronger correlation than most traditional hydraulic geometries.

However, for the mRCT-Q relationship to function as an ecological indicator its required prediction capacity or resolution is determined not by a regression coefficient, but by ecological thresholds. Therefore, rather than comparing regression coefficients, a better measure of usefulness is how accurately and reproducibly mRCT predicts streamflow over a range of flows. In many ecological applications the necessary accuracy of the mRCT-Q regression will be a function of streamflow and management objectives. For example, when predicting a mRCT that relates to passage for adult salmon in small stream (at higher streamflows) perhaps 5 cfs is an acceptable error in streamflow prediction; while when predicting passage for juvenile fish (at lower streamflows) perhaps 1 cfs error or less is required. Therefore quantifying the accuracy of mRCT flow prediction over a range of flows is an important step in refining the mRCT-Q relationship into an ecological management tool.

Table 3, shows the median flow prediction error and the standard deviation in mRCTs for all the sample flows separated into quartiles. The flow prediction error and the standard deviation in mRCTs were computed from a two-fold cross-validation analysis (Section 4.4). The first and fourth quartiles (lowest and highest flows) showed

64

the largest difference between observed and predicted streamflow with 8.7 cfs and 12.3 cfs errors, respectively. The smallest differences between observed and predicted flow occurred in the second quartile (12 cfs to 31 cfs) and the third quartile (31 to 55 cfs) with

5.1 and 7 cfs errors respectively. While the first quartile had worse flow prediction capacity then the second quartile, the standard deviation of mRCT depths was smaller in the first than the second quartile.

A proposed explanation for the larger error in low flow prediction is the influence of sediment size on riffle crest stage. Figure 21 shows that RCT depth increases with median sediment size over a range of flows. As the depth of flow decreases and approaches the D84, grain roughness becomes the dominant component of the resistance to flow (Knighton 1998) and relative roughness increases. The influence of sediment size on RCT depth (stage) was therefore assumed to increase as flow decreases. Two streams with a large difference in sediment size (regardless of drainage area) can be assumed to have a significant difference in RCT depths especially at low flows. Even though the standard deviation in mRCT was lower during low flows than high flows (meaning RCT depth measurement was accurate during low flow conditions), the high error in streamflow prediction may have been a function of variation in channel roughness between reaches. The larger error in flow prediction during high flows, however, may have been a function of RCT depth measurement error. As flow increases above 50 cfs in smaller streams, turbidity and high water velocity can make it more difficult to locate and accurately measure the RCT depth. This is corroborated by the large standard deviation in mRCTs at higher flows Table 3.

65

The error between predicted and observed streamflows from the quartile cross- validation analysis suggests that the regional mRCT-Q curve (Figure 12) may not be precise enough in general, or over a specific range of streamflows (e.g. very low flows) for some ecological applications, such as fish passage. A median error of 8 cfs for predicted streamflows between 0 and 12 cfs (Table 3) suggests that factors besides streamflow are influencing RCT depth. To reduce error in streamflow prediction, and therefore improve its management value (and ecological applicability), the mRCT-Q relationship was adjusted based on two geomorphic conditions of the local channel: sediment size, and cross-sectional shape.

5.2 Refining the mRCT-Q relationship into a tool for ecological restoration

Although grain roughness affects RCT depth especially at low flows, the influence sediment size on RCT depth suggests a broader relationship between channel structure and RCT depth at any flow. Sediment size has been shown to be a principle driver of the shape and structure of pool-riffle morphology (Milne, 1982; Dade and Friend, 1998;

Lofthouse and Robert, 2008). Knighton (1981 and 1998) concludes that sediment size and boundary erodibility are the principal drivers of the longitudinal profile. Knighton also predicts that the relationship between sediment size and transport potential defines the degree of pool-riffle development in general:

66

“The degree of pool-riffle development probably varies with bed material size relative to the transport potential in a reach since the ability of a stream to modify its bed depends on the mobility of the available material and the frequency of competent flows, which have a longitudinal dimension.” (Knighton 1998).

Pool-riffle development in this case is the magnitude of variation in the longitudinal profile of a stream between topographic high points (riffles) and topographic low points

(pools).

If sediment size and boundary composition are the dominant physical variables controlling the longitudinal and cross-sectional structure of pool-riffle morphology, then it is reasonable to assume that these variables also exert an influence on depth of flow over the riffle crest. Wohl (1993) noted that as gradient and available unit stream power decreased, the riffle–pool sequence became longer and depth of flow over riffles became shallower (and therefore wider), while the relative depth of pools increased. Unit stream power is stream power (rate on energy dissipation, see Section 2.1) per unit of channel width. The size of sediment which a stream can transport also decreases with unit stream power (Yang and Stall 1974; Leopold and Emmet 1976) and, in general, low gradient reaches are associated with finer bed material and larger width/depth ratios than high gradient reaches. From the observations of Wohl (1993), and the relationships between stream power, sediment size, and cross-section, the hypothesis was developed that RCT depth decreases with width of flow and increases with sediment size.

67

Data were collected on four reaches to test the supposition that RCT depth decreases with width of flow and increases with sediment size. The sampled reaches had significantly different drainage areas and morphologies, ranging from small, confined, high-gradient reaches (Lost Man Creek, 12 mi2) , to a medium sized coarse-grained reach

(Upper Redwood Creek 68 mi2) to larger alluvial channels with moderate sediment size

(South Fork Eel River 537 mi2 and Lower Redwood Creek 277 mi2). Data was collected at a single flow for each site and flows ranged from 12-45 cfs. Although there was some scatter about the trendlines RCT depth increased with sediment size and decreased with width of flow at all four sites, Figure 23 to Figure 26.

The strong observed correlations between sediment size, wetted width, and RCT depth, provides the basis for an explanation of the observed scatter in the mRCT-Q regression (Figure 12). The general mRCT-Q regression was constructed from multiple channels with a wide range of morphologies and sediment sizes; therefore, according to the observed correlations from Figure 23 to Figure 26, variation in D50 and width/depth ratios would have influenced mRCTs independently of streamflow. As an example,

Figure 34 shows how deviation from the mRCT-Q regression could be a function of sediment size and wetted width.

68

Figure 34. The effect of D50 and wetted width on the mRCT-Q curve from Figure 12.

Data from the general mRCT-Q relationship show that median wetted widths varied from

6 ft to over 70 ft at the riffle crest, and although sediment size data was only collected on four channels, median sediment sizes are estimated to range from 0.05 ft to 0.5 ft (15 mm to 150 mm). Considering the degree to which RCT depth increased with sediment size and decreased with width of flow, it is conceivable that most of the scatter in Figure

12 is a product of variation in sediment size and wetted width.

Given that RCT depth increases with sediment size and decreases with wetted width of flow, the variance of any single RCT depth from the defined mRCT-Q

relationship is proportional to , where D50 is the median sediment size across the

riffle crest, and WWC is the width of flow at the riffle crest. To incorporate into

69

the continuous RCT depth-Q function, WWC was normalized by streamflow,

forming . ( )

The variable was plotted against RCT depth (Figure 28). As sediment size

increased relative to the wetted channel width at any given flow, RCT depth also increased. The purpose of Figure 28 was to improve the prediction capacity of the RCT and thereby by make it a more useful ecological indicator. Therefore, the regression equation from Figure 28 was re-arranged to predict streamflow. A two-fold cross validation analysis was performed to compare the prediction capacity of the three regression models developed in this thesis: RCT depth-Q (Figure 11), mRCT-Q (Figure

12), and RCT- , (Figure 28). The results of the cross-validation analysis show that

by incorporating , the streamflow prediction error of the RCT depth-Q regression is

reduced by 9.3 cfs, from 14.6 cfs to 5.3 cfs, Table 7. Over the small range of flows on

which it is based, the RCT- relationship (when re-arranged to predict streamflow)

has about the same streamflow prediction capacity as the mRCT-Q relationship. These results suggest that if median D50 and median WWC were added to the mRCT-Q regression, it would strengthen the correlation and improve the current R2 of 0.843; however, not enough data were collected to test this conjecture.

70

Further analysis is needed to fully define the correlations between sediment size, wetted width and RCT depth. The coefficients in Equation 6 are derived from the 38 riffle crests sampled in the analysis of multiple variables (Figure 23 to Figure 26). This analysis represents only four discrete streamflows and it is likely that the coefficients in

Equation 6 will change when more data are collected.

By incorporating , the RCT depth-Q relationship can be adjusted according to

the physical constraints of a specific channel. While this mechanism does not address the effect of forcing structures such as bedrock or large buried wood, it does address variation between alluvial channels where riffle crest morphology is a result of the equilibrium of driving and resisting forces. The relationship between sediment size and wetted width can be considered an ‘equilibrium scaling factor’ because channels which experience larger tractive and roughness forces (a more intense equilibrium) will tend towards larger sediment and narrower wetted widths per unit flow (smaller width to depth ratio). Figure 28 shows that these channels will have deeper riffle crests than channels with smaller tractive and roughness forces. Once the equilibrium scale becomes sufficiently large, pool-riffle morphology is replaced by step-pool morphology

(Montgomery and Buffington, 1997) where the RCT depth-Q relationship is undefined empirically, and may not exist.

71

5.3 Future Applications of the mRCT-Q Relationship

As streamflow recedes in gravel bed rivers, the varied life history needs of aquatic organisms begin to depend on the shape and structure of the low flow channel.

Everything from primary producers to benthic invertebrates to amphibians, small game fish and salmon rely on the hydraulic geometry (width, depth, and velocity) of streamflow across the topography of the channel bed. During the receding hydrograph, and into the summer period, the shape and structure of the riffle crest controls the upstream hydraulic geometry. Relating RCT depth to the life history needs of aquatic organisms is the first step in applying the hydraulic relationships developed in this thesis toward ecological management and restoration.

Riffle crest thalweg depth was related to streamflow, both alone and in a multivariate regression. Riffle crest thalweg depth could also be related to the life history needs of aquatic organisms in one of two ways: either (1) threshold RCT depths could be identified which indicate the incipient condition of some ecological process, or (2) a continuous function between RCT depth and an ecological process could be established.

Once RCT has been related to a specific life history need, the hydraulic relationships in this study could be used in management applications.

The relationships developed in this study particularly lend themselves to instream flow needs assessments and ecological channel design. For example, threshold RCT depths could be used in conjunction with the mRCT-Q regression to identify incipient instream flows for salmonid spawning habitat, or productive benthic invertebrate habitat.

72

Since the alluvial riffle crest acts as a natural weir, threshold depths at the RCT can be confidently used to indicate equal or greater thawleg depths upstream. While the RCT-

relationship could also be used in instream flow applications, it has the added ( )

potential of informing channel designs that promote riffle crest development for specific aquatic habitat needs. For example, an empirical relationship between sediment size and wetted width (e.g. Equation 6) could inform the size sediment for gravel augmentation programs to promote specific RCT depths at a given flow. This type of application can be used in the design of dynamic channels.

73

6 CONCLUSION

The alluvial riffle crest is constructed and maintained during high flow by counteracting forces in a river system. In turn, during low flow conditions, the riffle crests acts as hydraulic control creating habitat and effecting connectivity between habitats as well as near-bed hydraulics which influence lotic productivity. As a central feature in both the geomorphic and ecological maintenance of streams, the riffle crest warrants attention.

A quantitative relationship between streamflow (Q) and median riffle crest thalweg depth (mRCT) has been described for gravel bed streams throughout Northern California.

Independent of drainage area and recurrence interval (so long as the riffle crest is not drowned out), mRCT is able to predict streamflow to within an average of 7 cfs for streamflows up to 150 cfs. The mRCT-Q relationship had the lowest streamflow prediction error (5.1 cfs median error) in the 12-30 cfs range and the highest streamflow prediction error (12.1 cfs median error) in the 55 - 155 cfs range. The mRCT-Q relationship was developed over a wide range of . Median wetted widths (at the riffle crest) varied from 6 ft to over 70 ft, and although sediment size data was only collected on four channels, median sediment sizes are estimated to range from 0.05 to 0.5 ft (15 mm to 150 mm).

Variance in thalweg depth between riffle crests at a given streamflow is largely explained by variation in sediment size and width to depth ratio. By incorporating the

74

variable, , the results suggest that a single RCT depth is able to predict streamflow to

within 5.3 cfs for a range of flows between 10 and 50 cfs.

The relationship between mRCT and streamflow may have important implications for ecological management. Many ecological processes and life histories are depth dependent. Instream flows that meet depth thresholds for specific ecological processes can be estimated using the mRCT-Q relationship, and refined using sediment size and width to depth ratio from the local channel. This relationship provides an empirical basis for instream flow assessments which often depend complex hydraulic and biological

modeling. In addition, the RCT- relationship can be used in channel design to ( )

inform the channel geometries and sediment sizes that would produce a specific RCT depth-Q relationship. To support these applications of the mRCT-Q relationship, future work should focus on identifying and describing in detail specific biological and ecological consequences of RCT depth.

75

7 WORKS CITED

Bjornn TC, and Reiser DW. 1991. Habitat requirements of salmonids in streams. In Influence of forest and range management on salmonid fishes and their habitats, Pages 83-138. American Fisheries Society Special Publication 19, Bethesda, MD. Carling PA. 1991. An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the river severn, England. Ambleside, Cumbria, LA2 0LP, U.K.: Institute of Freshwater Ecology, Windermere Laboratory. Carling PA, Wood N. 1994. Simulation of flow over pool–riffle topography: a consideration of the velocity reversal hypothesis. Earth Surface Processes and . Vol. 19, p. 319–332. Chang HH. 1979. Minimum stream power and river channel patterns. Journal of Hydrology. Vol. 41, p. 303-327. Daniels MD and McCusker MH. 2010. Operator bias characterizing stream substrates using Wolman pebble counts with a standard measurement template. Geomorphology. Vol. 115, p. 194-198. Dade WB and Friend PF. 1998. Grain-Size, Sediment-Transport Regime, and Channel Slope in Alluvial Rivers. The Journal of Geology. Vol. 106, p. 661-675. de Almeida GAM, and Rodriguez JF. 2010. Understanding pool-riffle dynamics through continous morphological simulations. Water Resources Research. Vol. 47. W01502. Dunne and Leopold. 1978. Water in Environmental Planning. W.H. Freeman and Company, New York.

Dury GH. 1970. A resurvey of part of the Hawkesbury River, New South Wales, after one hundred years. Australian Geographical Studies. Vol. 8, p. 121–132.

Flosi G, Downie S, Hopelain J, Bird M, Coey R, and Collins, B. 1998. California Salmonid Stream Habitat Restoration Manual, 3rd edition. California Department of Fish and Game, Sacramento, California. Gipple CJ, and Stewardson MJ. 1998. Use of in defining minimum environmental flows. Regulated Rivers Research and Management. Vol. 14, p. 53–67 Gorden ND. 2004. Stream Hydrology - An Introduction for Ecologists. West Sussex. John Wiley and Sons ltd.

76

Gorman OT, and Karr JR. 1978. Habitat structure and stream fish communities. Ecology. Vol. 59, p. 507-515. Griffiths GA. 1980. Hydraulic geometry relationships of some New Zealand gravel bed rivers. Journal of Hydrology (New Zealand). Vol. 19, p. 106-118. Harrelson CC, Rawlins CL, and Potyondy JP. 1994. Stream Channel Reference Sites: An Illustrated Guide to Field Technique. General Technical Report RM-245. U.S. Department of Agriculture, U.S. Forest Service, Rocky Mountain Research Station, Fort Collins, CO. Keller EA. 1971. Areal sorting of bed-load material: the hypothesis of velocity reversal. Geological Society of America Bulletin. Vol. 82, p. 753-756. Keller, EA. and Melhorn WN. 1973. Bedforms and in Alluvial Stream Channels: Selected Observations. In - Fluvial Geomorphology, M. Morisawa (Editor). State University of New York, Binghamton, New York. Pages 253 to 283 Knighton D. 1998. Fluvial forms and processes: A new perspective. Oxford University Press Inc, New York, NY. Knighton D. 1981. Asymmetry of River Channel Cross-sections: Part I Quantitative Indices. Earth Surface Processes and Landforms. Vol. 6, p. 581-588. Knighton D. 1975., Variations in at-a-station hydraulic geometry, American Journal of Science. Vol. 275, p. 186-218. Kristin Bunte JP. 2006. Path Of Gravel Movement In A Coarse Stream Channel. Proceedings from the Eighth Federal Interagency Conference. April 2-6, 2006, p. 162-170. Reno. Lane EW, and Borland WM. 1954. River-bed scour during . Transactions of the American Society of Civil Engineers, vol. 119, p. 1069-1089. Langbein WB, and Leopold LB. 1964. Quasi-Equilibrium States in Channel Morphology. American Journal of Science. Vol. 262 p.782-794. Langbein WB, and Leopold, LB. 1968. River Channel Bars and Theory of Kinematic Waves. U.S. Geological Survey Professional Paper 422-L. Lee JS, and Julien PY. 2006. Downstream Hydraulic Geometry of Alluvial Channels. Journal of Hydraulic Engineering. Vol. 132, p. 1347-1352. Leopold LB. and Maddock TJ. 1953. Hydraulic geometry of stream channels and some physiographic implications. U. S. Geological Survey Professional Paper 252.

77

Leopold LB, and Langbein WB. 1962. The Concept of in Landscape Evolution. U.S. Geological Survey Professional Paper 500-A, 20p. Leopold LB and Wolman MG. 1957. River Channel Patterns: Braided, meandering, straight. U.S. Geological Survey Professional Papers 282-B. Leopold LB, Wolman MG, and Miller JP. 1964. Fluvial Processes in Geomorphology. Freeman, San Francisco. Leopold LB. 1970. An Improved Method for Size Distribution in Stream-Bed Gravel. Water Resources Research , Vol 6, p. 1357-1366. Leopold LB, and Emmet W. 1976. Bedload measurements, East Fork River, Wyoming. Proceedings of The National Academy of Sciences, p. 1000-1004. Lisle T. 1979. A sorting mechanism for a riffle-pool sequence. Geological Society of America Bulletin 90, p. 1142-1157. Lisle TE. 1982. Effects of and degradationon riffle–pool morphology in natural gravel channels, northwestern California. Water Resources Research. Vol. 18, p. 1643–1651. Lisle TE. 1987. Using ‘‘residual depths’’ to monitor pool depths independently of discharge. U.S. Forest Service Research Note PSW-394. Lofthouse C, and Robert A. 2008. Riffle–pool sequences and meander morphology. Geomorphology , Vol. 99, p. 214-223. McBain & Trush and Trout Unlimited. 2008. Commentary on Draft A.B. 2121 Instream Flow Policy: Framework Proposal for Defining Stream Management Objectives. Joint letter to the State Water Resources Control Board. Draft April 30, 2008. Milne J. 1982. Bed-material size and the riffle-pool sequence. Sedimentology, Vol. 29, p. 267-278. Montgomery DR, Buffington JM. 1997. Channel-reach morphology in mountain drainage basins. Geological Society of America Bulletin, Vol. 109, p 596-611. Nehring, R. B. 1979. Evaluation of instream flow methods and determination of water quantity needs for streams in the State of Colorado. Fort Collins. CO Division of Wildlife. Newbury R, and Gaboury M. 1993. Stream analysis and fish habitat design -A field manual. Newbury Hydraulics Ltd. Gibsons, British Columbia.

78

Osterkamp WR, and Hedman ER. 1977. Variation of width and discharge for natural high-gradient stream channels. Water Resources Research. Vol. 13, p. 256-258. Osterkamp WR, and Hupp CR. 1984. Geomorphic and vegetative characteristics along three Northern Virginia streams. Geological Society of America Bulletin. Vol. 95, p. 1093-1101. Park CC. 1977. World-wide variations in hydraulic geometry exponents of stream channels: An analysis and some observations. Journal of Hydrology, Vol. 33, p. 133-146. Pleus A, Schuett-Hames D, Bullchild L. 1999. TFW Monitoring Program method manual for the habitat unit survey. Prepared for the Washington State Dept. of Natural Resources under the Timber, Fish, and Wildlife Agreement. TFW-AM9-99-003. DNR #105 Quinn JM, and Hickey CW. 1994. Hydraulic parameters and benthic invertebrate distributions in two gravelbed New Zealand rivers. Freshwater Biology. Vol. 32, p. 489–500. Reid D, Babakaiff S, and Hickin EJ. 2010. Hydraulic geometry of small steep mountain stream channels in southwestern British Columbia. Geomorphology. Vol. 122, p. 39-55.

Reinfelds I, Williams S. 2009. Environmental water monitoring in unregulated rivers - Assessment of fish passage and low flow habitat protection – Coopers Creek, NSW, Sydney. State of New South Wales through the Department of Water and Energy, 2009 Rhodes BL. 1991. A Continuously Varying Parameter Model of Downstream Hydraulic Geometry. Water Resources Research. Vol. 27, p. 1865-1872. Richards KS. 1982. Rivers: Forms and Processes in Alluvial Channels. London. Methuen. Richards KS. 1976a. The Morphology of Pool-Riffle Sequences. Earth Surface Processes. Vol. 1, p. 71-88. Richards KS. 1976b. Simulation of Flow Geometry in a Riffle-Pool Stream. Earth Surface Processes. Vol. 3, p. 345-354. Richards K. S. 1973. Hydraulic geometry and channel roughness – a non-linear system. American Journal of Science. Vol. 273, p 877–896 Singh VP. 2003. On The Theories of Hydraulic Geometry. International Journal of Sediment Research. Vol. 18, p. 196-218.

79

Stall JB, and Yang CT. 1970. Hydraulic geometry of 12 selected stream systems of the United States. University of Illinois Water Resources Center Research Report No. 32, Urbana. Statzner B, Gore JA, and Resh VH. 1988. Hydraulic stream ecology: observed patterns and potential applications. Journal of the North American Benthological Society. Vol. 7, p. 307–360. Stewardson MJ. 2005. Hydraulic geometry ofstream reaches. Journal of Hydrology. Vol. 306, p. 97-111. Trush WJ, McBain S. and Leopold LB. 2000. Attributes of an Alluvial River and their Relation to Water Policy and Managment. Proceedings of the National Academy of Sciences, Vol. 97, p. 1158-1163. Vannote RL, Minshall GW, Cummins KW, Sedell JR, and Cushing CE. 1980. The . Canadian Journal of Fisheries Aquatic Science. Vol. 37, p. 130-137. Wallerstein NP, Soar PJ, and Thorne CR. 2006. River Energy Auditing Scheme (REAS) for catchment management planning. In: Ferreira, R. M. L., Alves, E. C. T. L., Leal, J. G. A. B. and Cardoso, A. H. (Eds.), Proceedings of IAHR, River Flow 2006. Lisbon, Portugal, 2, 6-8 September, 2006. Taylor & Francis Group, London, 1923-1932. Wilkinson SN, Keller RJ, and Rutherfurd ID. 2004. Phase-shifts in shear stress as an explanation for the maintenance of pool–riffle sequences. Earth Surface Processes and Landforms. Vol. 29, p. 737–753. Wohl EE. 2007. Channel-unit hydraulics on a pool-riffle channel. Physical Geography. Vol. 28, p. 233-248. Wohl EE. 1993. Pool and riffle characteristics in relation to channel gradient. Geomorphology. Vol 6, p 99-110. Wolman, M. 1954. A Method of Sampling Coarse River-bed Material. American Geophysical Union. Vol. 35, p. 951-956. Yang CT, and Song CS. 1986. Theory of minimum energy and energy dissipation rate. Chapter 11 in Encyclopedia of Fluid Mechanics, Gulf Publishing Company. Yang CT, and Stall JB. 1974. Unit stream power for sediment transport in natural rivers. University of Illinois Water Resources Center Research Report No. 88, Urbana.

80

8 APPENDIX

Riffle Crest Thalweg Survey Instructions

Thank you for participating in the riffle crest survey!

This survey involves, choosing a stream reach with a known discharge and measuring 10 riffle crest thalweg depths. Please record riffle crest depths in 10ths of ft and discharge in cfs and return these data to me. Using a gauged stream is encouraged. 5 cfs is maximum acceptable discharge error.

To ensure that these surveys are performed under the hydraulic and geomorphic conditions in which the RCT-discharge relationship is relevant, the following survey guidelines are established.

Geomorphic Parameters Reaches should exhibit pool riffle morphology. Slopes should be greater than 0.5% but not exceed 2%. D50 riffle crest sediment should be in the range of fine gravel to small cobble (from 16 to 256 mm).

Hydraulic Parameters It is important to gather data when flow is not confined by channel walls. If flow is confined by the scoured channel walls and not by alluvial material it is safe to assume the low flow hydraulic control is NOT in effect, and the relationship between RCT depth and flow is now a function of channel width.

Riffles to Avoid The RCT-discharge relationship is assumed to be a function of the processes that maintain alluvial pool-riffle hydraulics. Therefore a number of riffles that “look” good may not be applicable to this survey. For the purposes of this survey please exclude any riffles that: are forced by bedrock or large woody debris. Also please indicate on the survey riffles where the channel thalweg is located along a bank. These hydraulic situations involve significant secondary flows that change riffle crest dynamics.

Guidelines for locating RCT The riffle crest is defined as the downstream limit of the residual pool (RPL), where residual water depth is zero. There are three steps to identify a riffle crest thalweg point: visually identify the region containing the RPL, locate the thalweg within this region, and use inflection in thalweg depth to identify where the thalweg crosses the riffle crest – the RCT.

Step 1-Visually dentify the RPL. In low flow conditions it is generally possible to visually identify a longitudinal region of the channel that includes the RPL. This visual identification is called the tea-cup method as it is compared to a teacup that is tipped just to point where tea is about to fall over the brim. Downstream of this region, high velocity and water surface slope along with broken water surface and the presence of hydraulic jumps and drops, clearly indicate a riffle. Upstream of this region, low velocity and water-surface slope along with a smooth water-surface clearly indicate a pool. If it is not possible to visually identify a regional bounded by an upstream pool and a downstream riffle, than the immediate reach does not display pool-riffle morphology and no RCT measurement can be taken. This is the case in plane-bed morphology.

Step 2- Identify the thalweg within the RPL region. The tea cup method defines a region that contains the riffle crest. The thalweg is then identified through this region visually and by quickly measuring depths along several cross-sections within the region.

Step 3 – Locate the RCT. Starting downstream of the riffle crest region, thalweg depths are measured as the surveyor walks upstream. Once depths begin to increase the immediate location of the riffle crest has been encountered. This increase in thalweg depth is generally concurrent with the velocity ramp produced at the riffle crest. This can also be visually identified by streamlines on the water surface or by observing the change in velocity of a floating object as it passes the riffle crest.

81

Riffle RCT Depth Notes

# (ft)

1

2

3

4

5

6

7

8

9

10

11

12