Scholarly article on topic 'Tools for gauging the capacity of salmon spawning substrates'

Tools for gauging the capacity of salmon spawning substrates Academic research paper on "Environmental engineering"

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Academic research paper on topic "Tools for gauging the capacity of salmon spawning substrates"

EARTH SURFACE PROCESSES AND LANDFORMS Earth Surf. Process. Landforms 41, 130-142 (2016)

© 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd. Published online 4 November 2015 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/esp.3831

Tools for gauging the capacity of salmon spawning substrates

Brandon T. Overstreet,1* Clifford S. Riebe,2* John K. Wooster,3 Leonard S. Sklar4 and Dino Bellugi5

1 Department of Geography, University of Wyoming, Laramie, WY, USA

2 Department of Geology and Geophysics, University of Wyoming, Laramie, WY, USA

3 NOAA - Fisheries, Habitat Conservation Division, Santa Rosa, CA, USA

4 Department of Earth and Climate Sciences, San Francisco State University, San Francisco, CA, USA

5 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Received 19 January 2015; Revised 29 July 2015; Accepted 18 August 2015

Correspondence to: Brandon T. Overstreet, Department of Geography, University of Wyoming, Laramie, WY, USA. E-mail: boverstr@uwyo.edu or Clifford S. Riebe, Department of Geology and Geophysics, University of Wyoming, Laramie, WY, USA. E-mail: criebe@uwyo.edu

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Earth Surface Processes and Landforms

ABSTRACT: We present a set of river management tools based on a recently developed method for estimating the amount of salmon spawning habitat in coarse-bedded rivers. The method, which was developed from a mechanistic model of redd building by female salmon, combines empirical relationships between fish length, redd area, and the sizes of particles moved by fish during spawning. Model inputs are the grain-size indices D50 and D84 and an estimate of female fish length, which is used to predict the size of the redd that they will build and the size of the largest particle that they can move on the bed. Outputs include predictions of the fraction of the bed that the fish can use for redd building and the number of redds that they can build within the useable area. We cast the model into easy-to-use look-up tables, charts, an Excel worksheet, a JavaScript web applet, and a MATLAB user interface. We explain how these tools can be used in a new, mechanistic approach to assessing spawning substrates and optimizing gravel augmentation projects in coarse-bedded rivers. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.

KEYWORDS: river restoration; Pacific salmon; salmon spawning habitat; fluvial geomorphology; aquatic ecology

Introduction

Salmon populations are in decline throughout much of their historical range, reflecting natural and human-induced changes in aquatic food webs and habitats, including degradation of riverbed sediments where salmon spawn (e.g. Nehlsen et al., 1991; Yoshiyama et al., 1998; Carlson and Satterthwaite, 2011). To reverse losses in salmon populations, and thus maintain the economic, cultural, and ecosystem services that salmon provide, river managers spend millions of dollars every year on restoring salmon spawning habitat (e.g. Kondolf etal., 2007). For example, in 2013 alone, the United States Bureau of Reclamation budgeted over $600,000 (USD) for improving spawning habitat as part of the Central Valley Project Improvement Act (USBR and USFWS, 2014), which covers just a few of the US rivers targeted for habitat restoration that year. Despite expenditures such as these, the benefits of restoration have remained unclear, in part because of poor communication between scientists and managers (Wohl et al., 2005; Bernhardt et al., 2007). To overcome this limitation, scientists must develop tools that address the questions that managers ask when designing and monitoring restoration projects (Bernhardt et al., 2005, 2007; Wohl et al., 2005; Beechie and Snover, 2014). Moreover, for the science to

confer benefits to restoration, the tools that are developed must be both accessible to restoration managers and practical to use in field settings (Bernhardt etal., 2007; Beechie and Snover, 2014).

In a recent study, we developed a new understanding of how the amount of salmon spawning habitat in coarse riverbeds depends on grain size and fish length (Riebe etal., 2014). These findings, which are based on empirical relationships between fish length, redd area, and the size of the largest particles that fish can move, provide a scientific basis for designing spawning substrate restoration projects and monitoring their benefits over time. However, to be useful in restoration, our findings must first be translated into practical tools and made available to the managers who might use them.

Here we present a set of tools that managers can readily use to gauge the amount of salmon spawning habitat in coarse-bedded rivers. We begin by summarizing the conceptual and mathematical basis of the approach. We then describe how we encoded the math into a series of easy-to-use look-up charts and tables. We also present computer-based applications of the approach, including an Excel worksheet, a JavaScript web applet, and a MATLAB user interface. This comprehensive set of tools, including charts and software, is publically available in the main article, in Supplementary Material, and online. We discuss

how managers can use these tools as part of a new, mechanistic approach to assessing salmon spawning substrates and to designing cost-effective spawning habitat restoration projects.

A New Approach to Assessing Salmon Spawning Substrates

Particle sizes and redd building

Grain size can limit spawning by preventing redd construction if particles are too big for female fish to move and thus use during redd building (Kondolf, 1988; Kondolf and Wolman, 1993; Ligon etal, 1995; Kondolf, 2000; Riebe et al, 2014). Female salmon construct redds by turning on their sides, swatting at the bed with their tails, and thus inducing lift forces that excavate particles from the bed surface (Burner, 1951). In coarse-bedded rivers, some particles may be too big for fish to move, depending on the magnitude of the lift forces that the fish can generate with its tail. If the bed harbours just a few of these immovable particles, they may not hinder spawning because salmon may be able to simply build their redds around them (Quinn etal., 1995). However, as immovable particles become more concentrated, the area of the bed that can accommodate redd building decreases and should be roughly equal to the total area of the bed minus the area occupied by particles that are too big to move. This relationship is illustrated conceptually with bed-surface grain-size distributions in Figure 1. For each of the two distributions in Figure 1B, the shaded area under the curve corresponds to the fraction of the total bed-surface area that is covered by particles with diameters bigger than DT, the

(a) Map view of immovable particles

Grain size

Figure 1. Relationship between grain-size distribution, threshold particle size, and area of the bed covered by particles that are too big for fish to move. (a) Immovable particles on the bed limit ability to construct redds by decreasing the amount of area useable for redd building. For each distribution in (b), the shaded area under the curve is the fractional coverage by particles bigger than DT, illustrating how usable spawning area changes with D84. As D84 increases for a given D50, the amount of usable substrate decreases, because a greater fraction of the bed is covered by particles with diameters greater than DT. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

threshold size that differentiates what fish can and cannot move. When the median particle size on the bed (D50) and DTare both constant, coverage by immovable particles increases with increasing variance in the grain-size distribution (Figure 1B), as reflected in increasing D84 (i.e. the 84th percentile of grain diameters). As coverage by immovable particles increases, less of the bed is suitable for redd building, leading to a decrease in the number of redds that salmon can build per unit area of bed. Henceforth, we use the term "spawning capacity" and the notation NREDDS to refer to the maximum number of redds per unit area that a substrate can physically accommodate for a species of interest. As we show in sections that follow, NREDDS depends on the grain-size distribution of the bed, the size of the largest particle that fish can move, and the size of the redds they build.

Predicting the fractional coverage of movable particles

If the size of the largest movable particle is known, the fractional coverage of the bed by movable particles can be estimated from the bed-surface grain-size distribution by simply integrating it from zero to DT, and thus quantifying the non-shaded area under the curve in Figure 1B (Riebe et al., 2014). Although salmonid spawning substrates have been studied for decades (Burner, 1951; Chambers etal., 1955; McNeil and Anhell, 1964; Orcutt et al., 1968; Crisp and Carling, 1989; Bjornn and Reiser, 1991; Kondolf and Wolman, 1993; Kondolf, 2000), much of the work focused on understanding how fine sediment degrades salmon spawning habitat by influencing fluvial scour (May et al., 2009), preventing delivery of life-sustaining oxygen to eggs (McNeil and Anhell, 1964; Chapman, 1988; Greig et al., 2005), and entombing fry (Phillips et al., 1975). Meanwhile, the upper particle-size limits on redd building in coarse-bedded rivers have rarely been quantified (Kondolf, 1988; Kondolf and Wolman, 1993). Moreover, the relationship between fish length and DT had not been quantified until our own recent study of redd building by Chinook, sockeye, and pink salmon (Oncorhynchus tshawytscha, O. nerka, and O. gorbuscha), three different-sized species of Pacific salmon (Riebe et al., 2014). According to data from 73 redds examined in that work, the intermediate axis diameter of the largest particle moved increased systematically with fish length (L), in a power-law relationship expressed in Equation (1).

DT = 115(L/600)0:62 (1)

Here, DTand L are both expressed in millimetres, and the constant in the denominator is a reference fish length (600 mm); when L is equal to it, DT is equal to the power-law intercept (115 mm). Equation (1) assumes that the intermediate-axis diameters of the largest particles moved in redds can be used as a proxy for DT(Riebe etal., 2014).

When applied at the reach scale (e.g. over hundreds of square metres of spawning habitat) Equation (1) can be used to divide the riverbed into the fraction of grains on the surface that fish of a particular size can move and the fraction they cannot. All that is needed is an estimate of the bed-surface grain-size distribution, which can be readily quantified in a grid-based, Wolman-style pebble count (Wolman, 1954; Bunte and Abt, 2001b). In these pebble counts, the frequency of a particular-sized particle represents its fractional coverage on the bed (Wolman, 1954; Kellerhals and Bray, 1971; Bunte and Abt, 2001b). Hence, the fractional area of the bed that the fish can move (FM) can be quantified graphically from the cumulative distribution function (CDF) of grain size by simply reading the value of the CDF that corresponds to DT (Figure 2; after Riebe et al., 2014). If the full grain-size distribution is not available, but D50 and D84 are known,

Grain size, D (mm) 10 100 1000

Grain size, D (mm)

Figure 2. A graphical approach to quantifying the suitability of spawning substrates. Cumulative distribution functions (CDFs) of grain size for two lognormal grain-size distributions with equal D50 and differing D84, illustrating how the fraction of the bed that the fish can move (FM) can be quantified graphically when DT is known (after Riebe et al., 2014); FM is equivalent to the fraction finer than DT, which can be read from the vertical axis at the intersection of DT with the CDF. This figure is available in colour online at wileyonlinelibrary.com/journal/espl.

data in many instances although grain-size measurement methods and data quality should always be carefully assessed. Moreover, the need for just three readily measured variables and the fairly simple form of Equation (4) make it easier to apply than the graphical approach. Nevertheless it is important to quantify the scale of typical errors introduced by using Equation (4) instead of the graphical approach. We did so here using grain-size distributions from the Riebe et al. (2014) calibration sites, which span a wide range of conditions; D50 ranged from 49 to 118 mm, D84 ranged from 86 to 385 mm, and mean fork length of spawning female salmon ranged from 445 to 721 mm. The agreement between predictions from Equation (4) and the graphical approach is illustrated in Figure 3. All of the data plot close to the 1:1 line of perfect correspondence between the analytical and graphical approaches. Residuals relative to the 1:1 line (Figure 3B) show that the model agrees with observations to within ~7% across a greater than four-fold range in fractional coverage by movable particles. Moreover, the Nash-Sutcliffe statistic is 0.92, indicating that the variance in the graphically measured FM values is efficiently explained by the model. Hence, although none of the grain-size distributions that we examined were strictly lognormal, our analysis indicates that errors introduced in the assumptions of Equation (4) may often be small enough to ignore.

FM can still be estimated using the analytical approximation expressed in Equations (2)-(4) (after Riebe etal., 2014).

FM = 1+e"

Here, FM is the dimensionless fractional area of the bed that fish can move (e.g. in m2/m2). The right side of Equation (2) is a one-parameter logistic function that approximates the cumulative normal distribution to within 1% (Bowling etal., 2009). Here, z is analogous to the Z statistic in the parlance of statisticians. Recognizing that grain-size distributions are often more lognormal than normal in shape (e.g. Bunte and Abt, 2001b), we calculate z using Equation (3) (after Riebe etal., 2014).

log(DT/D50)

log(D84/D50

Here log(D50) and log(D84/D50) are the mean and standard deviation of a lognormal grain-size distribution, and the grain size indices D84 and D50 are expressed in consistent units of length (e.g. millimetres). Assuming that the grain-size distribution is approximately lognormal, Equations (2) and (3) can be used together to estimate the fraction of the bed covered by grains smaller than the threshold size DT, as shown in Equation (4) (after Riebe etal., 2014).

Fm = <1 + exp

-1.702-

log\ 115(L/600)°'62/ D50

log [D84/D50]

Here we express DT in terms of Equation (1). If a site-specific estimate of DT is available then it could be used instead in the numerator of the exponential term.

Equation (4) is easy to apply when estimates of fish length and grain size are available, but it assumes that the grain-size distribution is lognormal. Hence, it will generally be more accurate to use the graphical approach (e.g. Figure 2) for estimating FM because it does not require assumptions about the shape of the grain-size distribution. However, complete grain-size distributions are not often reported in studies of rivers, whereas the indices D50 and D84 typically are. Equation (4) should be a suitable option for assessing spawning substrates from existing

Predicting the spawning capacity of riverbeds

Once FM is quantified, whether by the graphical or analytical approach, it can be recast in terms of spawning capacity, defined as the number of redds that salmon can build per unit area and denoted NREDDS (e.g. in redds/100 m2) in Equation (5).

N redds = Fm/Aredd x100

§ 0.9

™ 0.8

f 0.6 CO

III I | I I I I | I I I I | I I I I | I I I I | I I I I | I III.

I 1 1 1 1 I 1

Species • Pink O Sockeye O Chinook

1:1 line

III III I I I I I I I I I I I I I I I I I I I I I I III III

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FM predicted from equation 4

Figure 3. Comparison between Equation (4) and graphical approach to predicting FM. (top graph) Coverage by movable particles (FM) measured using graphical approach (see Figure 2) plotted against coverage by movable particles predicted from Equation (4) for Chinook salmon (grey circles; L = 721 mm), sockeye salmon (open circles; L = 569 mm), and pink salmon (black circles; L = 445 mm) based on data from Riebe etal. (2014). Residuals show that model-predicted values agree with graphical estimates to within ~7% across the three species of salmon (bottom graph).

1:702z

Here, Aredd is the area (in m2) of a typical redd constructed by the species of interest. The factor of 100 is included so that NREDDS is expressed in units of redds/100 m2, consistent with the spatial dimensions of typical spawning patches. The value of AREDD can be estimated from redd dimensions measured in the field or from Equation (6), which is an empirical relationship between redd area and female salmonid length (Riebe et al., 2014).

Aredd = 3.3[L/600]23 (6)

Here, the power-law intercept and exponent are regression parameters based on a best fit to data from redds built by salmonids spanning a wide range of sizes (after Riebe ef al., 2014, based on data from Crisp and Carling, 1989). As in Equation (1), the denominator on the right side of Equation (6) is a reference value for the regression; when L is equal to it (i.e. 600 mm), the predicted redd area is equal to the power-law intercept (i.e. 3.3 m2). Although Equation (6) provides a very good fit to Crisp and Carling's (1989) data on Atlantic salmon (Salmo salar) and trout (S. trutta and Oncorhynchus mykiss), and also to Riebe et al.'s (2014) data on Chinook, sockeye, and pink salmon (see Riebe et al., 2014), site-specific values of redd area could be used to translate values of FM into estimates of substrate spawning capacity via Equation (4).

For a wide variety of species, including both Atlantic and Pacific salmon, Equation (6) should be an acceptable predictor of redd area. When it is, Equations (4)-(6) can be combined into a single expression for estimating spawning capacity.

Nredds = 100^ 3.3(L/600)23

Like the expression in Equation (4) for FM, Equation (7) for NREDDS has just three variables: fish length and two grain-size indices that are widely reported in the literature. Hence, although Equations (4) and (7) are somewhat complicated in form, they are both computationally easy to apply to data available from the literature (Riebe et al., 2014).

Coverage by movable particles and the spawning capacity of substrates predicted from Equations (4) and (7) are both potentially useful in river management, because they constrain the maximum amount of redd building a substrate can

accommodate when fish are spawning en masse, in conditions that are not limited by other factors such as flow velocity and depth (Moir and Pasternack, 2010), and hyporheic flow through redds (Tonina and Buffington, 2009). This is demonstrated in Figure 4 for spawning by three Pacific salmon species across the 31 sites of Riebe etal. (2014). In all but a few cases, field-surveyed areal coverage by redds was less than or equal to the fractional coverage by movable particles predicted from Equation (4) (Figure 4A). Likewise, spawning use, which was estimated from the areal coverage of redds on the bed, was less than or equal to spawning capacity, which can be predicted from Equation (7) (Figure 4B). Data that plot near the 1:1 line in both Figures 4A and 4B imply instances in which fish were building redds in nearly all of the movable substrate. The fact that some of the observations in Figures 4A and 4B are close to the 1:1 line implies that FM and NREDDSare indices of the maximum amount of spawning habitat in a reach when other factors, such as flow conditions and fine sediment content, are not limiting (Riebe et al., 2014).

Assessing and Monitoring Salmon Spawning Substrates

Sensitivity to differences in grain size

Equations (4) and (7) show that FM and NREDDS can each be expressed as a function of just three variables. In applying them to the assessment of spawning substrates for a particular

run of salmon, it may be helpful to set fish length equal to the mean fish length for the run and thus reduce the number of variables to just two: D84 and D50. One can then explore the sensitivity of substrate spawning capacity to differences in grain size alone (e.g. from one reach to the next) by constructing contour plots of FM and NREDDS in a plotting space that includes D84 and D50. The most straightforward way to display grain size in a two-dimensional plotting space is to plot the standard deviation against the mean. Here, in the lognormal approximations of Equations (4) and (7), this can be done by

1 + exp

_1 702 ( log(115)+0.62log(L/600) - log(P5Q) . log(D84) - log(D50)

Figure 4. (a) Spawning use observed in field versus FM predicted from Equation (4) for three species of salmon. The fractional area used for spawning should be less than or equal to the fractional area covered by movable substrate (FM) - this is a theoretical cap on spawning use illustrated by the 1:1 line. (b) Spawning use observed in field versus spawning capacity predicted from Equation (7) for three species of salmon (after Riebe et al., 2014). Error bars show ±1 standard error propagated from measurement and model uncertainties. Points that plot close to the 1:1 lines (a and b) are cases of fish spawning en masse and building redds in nearly every patch of movable substrate. This shows that model predictions of FM and NREDDS yield realistic estimates of substrate capacity for accommodating redds in riverbeds.

plotting log(D50) (the mean) on the horizontal axis and log (D84/D50) (the standard deviation) on the vertical axis. Because D50 and D84 appear in exponential form in Equations (4) and (7), it is appropriate to plot them using log scales. This yields the patterns in FM and NREDDS shown in Figures 5A and 5B. Inspection of these panels shows that, for a given D84/D50 (i.e. for a constant spread in the grain-size distribution), FM and NREDDS are both more sensitive to D50 when D84/D50 is low than when D84/D50 is large. In addition, when D50 is less than DT, increases in D84/D50 correspond to decreases in FM (Figure 5A) and NREDDS (Figure 5B). This is consistent with concepts illustrated in Figure 1: when the spread in the distribution is bigger, more of the distribution lies above the threshold particle size, such that there is less coverage by movable particles. The converse is true when D50 is greater than DT, because increases in the spread in the distribution increase the fraction of the bed sediment with grain sizes smaller than the threshold particle size (which means there is more useable substrate for redd building). Thus, the plots shown in Figures 5A and 5B provide useful tools for understanding how changes in grain size are likely to influence the amount of spawning substrate in riverbeds.

Graphical assessment of substrate spawning capacity

The plots in Figures 5A and 5B illustrate the sensitivity of FM and Nredds to differences in grain size for a fish with a length of 600 mm. Another way to show the results in grain-size space is to simply plot D84 versus D50 (Figures 5C and 5D). This plotting space is complicated by a 'forbidden zone', (the grey space in Figures 5C and 5D), which arises because D84 can never be less

than D50. Nevertheless, plots like these are easier to use with data from pebble counts, because they obviate the intermediate step of calculating D84/D50; one can simply read the value of FM or Nredds directly from the plot at the intersection of D84 and D50 (Figures 5C and 5D). Thus a field worker can readily quantify the amount of spawning habitat in a study reach using a graphical approach that obviates the somewhat complicated calculations of Equations (4) and (7). This graphical approach can be applied to salmon of any size after generating a size-specific chart for the fish of interest. We illustrate this for salmon ranging in length from 250 to 950 mm (in 50 mm increments) for both FM in Figure 6 and NREDDS in Figure 7. The physical limitations on redd building that are encapsulated in Equations (4) and (7) should apply across all of the fish lengths represented in Figures 6 and 7, but only Figures 6e-6h lie within the tested range of the model (Riebe et al., 2014); more work is needed to verify the model's applicability to larger and smaller fish.

Applying the charts in Figures 6 and 7 to spawning habitat assessment is straightforward. For example, if the goal is to assess spawning substrate in a reach with D50 = 100 and D84 = 2 50 mm for a sockeye salmon with average length of 710 mm, FM and Nredds can be read from the intersection of D50 and D84 in Figures 6j and 7j, which correspond to contour plots of FM and Nredds of a 700 mm fish. Because the plots do not correspond exactly to the fish length of interest, the graphical estimates (i.e. FM = 0.61 and NREDDS = 12.8 redds/100 m2) are not exact. In the hypothetical case outlined here, the graphical approach underestimates FM and overestimates NREDDS by less than 1% relative to what one would calculate using Equations (4) and (7). We suggest that errors introduced by rounding fish lengths to the nearest 50 mm may often be small enough to ignore.

coverage by movable particles (FJ

30 100

D^ (mm)

300 10

500 450 400 350 "E 300 X 250 Q 200 150 100 50

III - o P « O) c 1 1 / //<"3 Tf CO <v K» O O O" O' UU

- dso<Dt

^ \\ ' 1 1 D50 cannot be greater than DM -i i i

50 100 150 200 250 300 Da, (mm)

50 100 150 200 250 300 Dg, (mm)

Figure 5. Variations in FM and NREDDS with grain size. Fractional coverage by movable particles (a) and spawning capacity, equal to the number of redds per 100 m2 (b) plotted as a function of the standard deviation and the median grain size (equal to D84/D50 and D50, respectively, for a lognormal bed-surface grain-size distribution) for a 600 mm long female salmon. Increases in the spread of the distribution lead to increases or decreases in FM depending on whether D50 is greater than or less than DT (which is denoted by the bold vertical line in each plot). (c) and (d) recast the functions shown in (a) and (b) in terms of D84 and D50. In this plotting space, there is a forbidden zone (grey space) encompassing impossible scenarios, in which D50 > D84. These plots can be used in a graphical approach to assessing spawning substrates; managers can read the predicted value of FM and Nredds directly from these plots at the intersection of D84 and D50 for the reach of interest.

D50 (mm) 100 200

D60 (mm) 100 200

Da, (mm)

J. 300

QS 200

0.2 0.4 0.6 0.8

Fractional coverage by movable particles

Figure 6. Variations in FM with grain size for 15 different sizes of fish ranging from 250 mm (a) to 950 mm (o). Grey region encompasses forbidden zone of impossible scenarios in which D84 is less than D50. These graphs are reproduced in Supplementary Material 1 in a series of full-page charts that managers can print and use in the field to estimate the fractional coverage by movable particles using the following steps: (i) measure grain-size distribution of the bed using a pebble count or other approach; (ii) select chart corresponding to fish length of interest; (iii) read FM from the intersection of D84 and D50. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Look-up charts and tables

To make the habitat assessment approach of Equations (4) and (7) accessible to river managers, we have reproduced Figures 6 and 7 in a series of larger look-up charts (sized at one per page) that could be printed and brought into the field for rapid assessment of spawning substrates. These charts are included in Supplementary Material 1 and 2, which are available online and by request from the authors. The charts show contours of FM and Nredds, similar to those shown in Figures 6 and 7, but without the colour, to conform to back-and-white printers and thus facilitate use in the field. Each chart is specific to a particular fish length ranging from 250 to 950 mm in

increments of 50 mm from one page to the next. The D50 and D84 range from 10 to 300 mm and 10 to 500 mm, respectively, in each chart, and thus cover a wide range of conditions that might be encountered in the field. Managers can use them by simply reading off FM and NREDDS at the intersection of a measured D50 and D84 for a fish of a particular length.

As an alternative to these charts, we have also encoded Equations (4) and (7) into easy-to-use look-up tables, available online as Supplementary Material 3 and 4. In the tables, D50 ranges from 20 to 300 mm in 10 mm increments, D84 ranges from 40 to 500 mm in 20 mm increments, and L ranges from 100 to 1100 mm in 100 mm increments. To use these tables, one simply finds the intersection of measured values of D50,

Dm (mm) 100 200

Dx (mm)

Dx (mm)

Number of redds /100 m2

Figure 7. Variations in NREDDS with grain size for 15 different sizes of fish ranging from 250 mm (a) to 950 mm (o). Grey region encompasses forbidden zone of impossible scenarios in which D84 is less than D50. These graphs are reproduced in Supplementary Material 2 in a series of full-page charts that managers can print and use in the field to assess the capacity of spawning habitat using the following steps: (i) measure grain-size distribution of the bed using a pebble count or other approach; (ii) select chart corresponding to fish length of interest; (iii) read NREDDS from the intersection of D84 and D50. This figure is available in colour online atwileyonlinelibrary.com/journal/espl

D84, and L, and reads of the value of FM (Supplementary Material 3) or Nredds (Supplementary Material 4). Values that lie between these increments can be approximated by interpolation. With Supplementary Material 1 and 2 or 3 and 4 in hand, the approach encapsulated in Equations (4) and (7) can be readily implemented with grain-size data from pebble counts and with fish lengths from carcass surveys and fish traps.

Computer-based tools for applying the approach

Recognizing that it may not always be convenient to use the look-up tables or charts, we have also encoded Equations (4)

and (7) into a series of computer-based tools, which are available in Supplementary Material 5-7 and on the second author's website. One of the computer-based tools (Supplementary Material 5) is an Excel workbook consisting of three worksheets. Data are entered on the sheet labelled 'Input data here.' Model outputs for the specified fish length and grain sizes are reported in the sheet labelled 'Model outputs.' A third sheet titled 'Read me' provides detailed instructions and an explanation of error messages. Up to 500 sets offish length and grain-size data can be input at a time by copying and pasting input values into the appropriate columns in the workbook.

We also generated a JavaScript web applet (Supplementary Material 6), which accepts user-provided data in an easy-to-

use graphical user interface (GUI) that can be opened in JavaScript-enabled browsers (Figure 8). Data are entered in the panel marked 'Input' (at right, under the 'Data' heading), either by typing the values for fish length, D50, and D84, or by clicking and dragging the slider bars. The input panel automatically keeps the values within a realistic range that is appropriate given the calibration data and ensures that D50 is never mistakenly given a value greater than D84. When values are changed, the button marked 'Update Model' must be clicked to generate results for the specified fish length and grain size indices in the panel marked 'Output'. This also updates the contour plots of fractional coverage by movable particles and spawning capacity, which can be viewed by clicking the tables under the 'Plots' heading in Figure 8. The bold red data point in each plot corresponds to the specified D84 and D50. Inputs can be reset to their default values (shown in Figure 8) by clicking on the button marked 'Reset Values'.

To cater to the wide audience of potential users, we have replicated much of the functionality of the JavaScript web applet in a MATLAB-based GUI. Data are entered in the panel marked 'Enter data here'. Results for the specified fish length and grain size indices are reported in the table in the middle panel. The outputs are updated after new data are entered by clicking within the GUI or pressing 'Enter' on the keyboard. The user can select and update the desired plot (e.g. FM and Nredds) using buttons in the panel labelled 'Update figure'. A contour plot of the desired output is generated in the D84 versus D50 plotting space within the GUI (at left) for the fish of interest, with a data point corresponding to the specified D84 and D50.

Discussion

The strength of Equations (4) and (7) and the associated charts, look-up tables, and computer-based applications is that they are good predictors of FM (Figure 3), which in turn appears to be a good reflector of NREDDS (Figure 4), the substrate's capacity for accommodating redds built by the fish of interest. The predictive power of the model stems from its ability to take a bed-surface grain-size distribution (represented simply by D50

and D84) together with a measure of the largest movable particle on the bed (predicted from fish length) and arrive at a realistic estimate of the area covered by movable particles. Thus, the toolkit we have derived from the model allows managers to gauge the spawning capacity of a substrate for a given species as a continuous function of substrate grain size. This is apparently because Equation (4) provides a robust approximation to the integral of the grain-size distribution from the smallest grain on the bed to largest grain that fish can move (Figure 1).

Limitations of the tools

The tools presented here are only demonstrably robust over the range of sizes represented by the calibration data — in this case, where D50 is between 39 and 118 mm, D84 is between 85 and 385 mm, and L is between 445 and 721 mm (Riebe et al., 2014). Outside these ranges, application of the relationship for calculating DT is extrapolative. However, the calibration data span a large range in all of the calibration variables. For example, the dominant grain size on the bed ranged from medium gravel to cobbles and boulders. Moreover, the 445-721 mm range in salmon length corresponds to a broad range in the ability of salmon to move sediment, spanning a 0.4-2.6 kg range in the size of the largest particle moved in redds (Riebe et al., 2014). Thus, the model should be applicable to salmon and trout in general, to the extent that it captures interspecies differences in ability to build redds using the cutting motion typical of salmonids. More research is needed to test this hypothesis.

Our tools do not account for the widely recognized effects of fine sediment on egg survival to emergence (e.g. Everest etal., 1987; Bjornn and Reiser, 1991; Greig et al., 2005, 2007). Sediment finer than 10 mm can fill interstices of sediment and trap fry in redds by blocking pathways for emergence (Bjornn, 1969; Phillips etal., 1975; McCuddin, 1977; Harshbarger and Porter, 1982; Bennett et al., 2003). When sediment is even finer - less than about 1 mm in diameter - it can impede intragravel flow of water, thus depriving incubating eggs of oxygen-rich water and preventing removal of toxic metabolic wastes

Figure 8. Screen capture of web-based JavaScript interface, which can be accessed online in Supplementary Material 6 and on the second author's website. The interface generates a plot (at left) and output data (at right) for a user-provided inputs of grain size and fish length (upper right). Users can choose to display one of three indicators of the amount of spawning habitat in the D84 versus D50 plotting space by clicking on tabs in the plot window. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

(McNeil and Anhell, 1964; Greig et al., 2005). We refer the reader to several thorough reviews of the effects of fine sediment on egg survival to emergence for details (e.g. Chapman, 1988; Bjornn and Reiser, 1991; Kondolf, 2000; Jensen et al., 2009). In summary, egg-to-fry survival for Pacific salmon has been shown to drop significantly when sediment with grain sizes less than 0.85 mm exceeds 10% of the sediment contained in the bed (Jensen etal., 2009). The tools presented here apply to upper particle size limits on redd building and we advise that they should be used in combination with methods for assessing fine sediment suitability (e.g. Kondolf, 2000; Bunte, 2004; Jensen et al., 2009).

Particles on bed surfaces that have been winnowed of fine sediment are often more difficult to move than the same sized particles on a loose bed (Parker and Klingeman 1982; Dietrich et al., 1989). On such armoured beds, estimates of DT from Equation (1) may be larger than what a spawning salmon can realistically move. For the most realistic estimates of DT, we recommend site-specific measurements of the largest particles moved in spawning redds, which could be used instead of Equation (1) if armouring is expected to be important.

Our tools do not account for the effects of superimposition (e.g. Fukushima et al., 1998), which occurs when female salmon destroy existing redds by building new redds over them. Somewhat paradoxically, superimposition can increase the spawning capacity of a substrate by decreasing the average spacing of egg pockets (van den Berghe and Gross, 1984). Thus we suggest that the estimates of spawning capacity (i.e. NREDDS in Figure 7) are minima, due to the reduction in minimum area required per redd that may be caused by superimposition. As a direction for future research, the effects of superimposition on the spawning capacity of substrates could be explored at the reach scale by coupling our substrate model (Equations (4) and (7)) with an individually based population model, and thus account for run timing, guarded area, and other factors that influence superimposition (e.g. Bartholow, 1996).

Data requirements

Our tools for gauging the capacity of spawning substrates are easy to use. Only fish length and a measurement of the grain-size distribution are needed to apply it to a site. The pebble count is a straightforward, widely used method for characterizing the grain-size distribution of a riverbed. However, care is needed to obtain accurate, repeatable measurements. Operator bias (Hey and Thorne, 1983; Marcus et al., 1995; Wohl et al., 1996), sample size (Rice and Church, 1996), particle selection methods (Bunte and Abt, 2001a, 2001b; Bunte etal., 2009), and measurement methods (Bunte et al., 2009) all influence pebble count results. Likewise, fish lengths can vary substantially both within a given reach of river in any given year and also from one year to the next (Johnson and Friesen, 2013). These factors lead to uncertainties in FM and NREDDS that can be quantified by propagating estimated errors in D50, D84, and L through Equations (4) and (7). Thus, data quality and sampling methods should always be assessed and accounted for prior to drawing conclusions about FM and Nredds from grain-size and fish length data reported in the literature. For example, more exhaustive pebble counts may be required to resolve smaller differences in D50 and D84 (Rice and Church, 1996; Larsen et al., 2004) and thus in FM and Nredds.

Pebble counts are often a poor reflector of fine particles in the grain-size distribution due to the difficulty of sampling them and measuring their dimensions (Rice, 1995). However, this has few if any implications for application of the tools

presented here; in the conditions relevant to quantifying limits on salmon spawning due to coarse sediment, D50 and D84 are typically much greater than the 2 mm cutoff for fine sediment that must be grouped into a single size class because it is difficult to sample and measure via pebble counts (Wolman, 1954; Bunte and Abt, 2001b). Because the tools presented here apply to coarse-bedded rivers, where large grains limit a salmon's ability to move sediment, our approach is well suited to integration of image-based grain-size mapping, including both ground-based (Butler et al., 2001; Sime and Ferguson, 2003; Graham et al., 2005; Graham et al., 2010; Buscombe et al., 2010) and aerial-based techniques (Carbonneau et al., 2004; Verdu etal., 2005; Black etal., 2014). However, conversion between image- and pebble count-derived grain-size distributions will be required (Graham etal., 2012).

In practice, grain size generally needs to be measured at as many representative locations as possible, because it can vary considerably, even over the confined scale of a spawning riffle. Pebble counts should be conducted within carefully defined textural facies (Buffington and Montgomery, 1999), where the bed-surface grain-size distribution appears to be spatially invariant. The spatial extent of the grain-size measurement will be determined by the variability of textural facies. For example, in the study that calibrated Equations (4) and (7), pebble counts were conducted in 100-200 m2 sampling areas, consistent with the spatial extent of distinct textural facies within the study reaches (Riebe etal., 2014). Smaller streams may have higher spatial variability of textural facies and thus may need to have smaller sampling areas. We suggest that our model can be applied to scales ranging from a few square metres to hundreds and perhaps even thousands of square metres depending on the redd size of the species of interest, the spatial variability of grain size, and the required precision of a study.

In most cases application of this method will be limited to wadeable streams - e.g. with flow less than 1.5 m/s and depth less than 1 m (Abt et al., 1989) - where surface grain-size data can be collected via pebble counts. However, image-based grain size sampling or underwater sampling methods could allow sampling in larger rivers. Sampling in larger rivers could also be possible where flow is seasonally reduced or diverted. In any case, when sampling facies before or after a spawning season, it will be vital to consider the flow stage and inundation area that typically prevail during spawning runs to avoid overestimating or underestimating available spawning habitat. In addition, sample sites in a time series of monitoring measurements would need to be located as closely in space as possible during successive measurements if the goal is to track changes in spawning habitat over time.

Estimating the reproductive potential of spawning substrates

In attempting to gauge the viability of a prospective restoration project, it may be useful to predict outcomes in terms of salmon reproduction. For example, in our previous work, we defined the reproductive potential of the substrate (NECCS) as the number of eggs per unit area that can be accommodated within the substrate (Riebe et al., 2014). This can be calculated from Equation (8) when fecundity, E, the number of eggs produced per fish (and thus per redd), is known for the species of interest.

Neggs = Nredds E/1000 (8)

Here Neggs is the number of eggs in redds within the reach in units of thousands of eggs per 100 m2. Fecundity generally increases with fish length both within and across salmonid species (Beacham and Murray, 1993; Quinn, 2005). This is

illustrated in Equation (9), a best-fit least-squares relationship between average fecundity and average fish length for a series of measurements reported in Quinn (2005) (after Riebe et al., 2014).

E = 8.1 L —1450 (9)

Thus, by combining Equations (7) and (9) in Equation (8), it is easy to translate the contour plot of NREDDS (Figure 5B) into a contour plot of NEGGS (Figure 9). Both the JavaScript and MATLAB interfaces (Supplementary Material 6 and 7) include plots and output data for NEGGS based on E calculated using Equation (9) (see for example, Figure 8).

Equation (9) explains 70% of the variance in average fecundity across 13 species of salmon, trout, and char spanning a wide range in average fish sizes. However, it is important to recognize that regional and intrapopulation differences in fecundity-length relationships can be substantial (Healey and Heard, 1984; Beacham and Murray, 1993). Hence, we stress that estimates of NEGGS that incorporate Equation (9) can at best provide a generalized understanding of how substrate reproductive potential varies in nature. We recommend using site-specific values of Ewhenever possible to translate estimates of Nredds from Equation (7) into estimates of NEGGS via Equation (8).

Equations (4), (7), and (8) yield several potentially useful indices of ecosystem function (i.e. FM, NREDDS and NEGGS). They provide the means for translating observed changes in grain size into estimates of resulting changes in the salmon spawning

10 30 100 300

an (mm)

0 50 100

Reproductive potential (1000s of eggs/100 m2)

Figure 9. Variations in NEGGS with grain size. Number of eggs (in thousands) per 100 m2 plotted as a function of the standard deviation and the mean grain size (equal to D84/D50 and D50, respectively, for a lognormal bed-surface grain-size distribution) for a 600 mm long female salmon. The value of NEGGS is the reproductive potential of the substrate; it expresses the number of eggs the substrate could physically accommodate and reflects limitations set by the size of the fish, which determines fecundity, the number of redds that can be fit into a given area, and the fractional coverage by immovable grains on bed. The Neggs reflects a space limitation and is distinct from survival to emergence (i.e. successful reproduction), which is moderated by environmental factors such as flow depth, velocity, scour, and contamination of the bed by fine sediment. This figure is available in colour online at wileyonlinelibrary.com/journal/espl

capacity and reproductive potential of substrates. Thus, the tools presented here should provide realistic estimates of how spawning habitat degradation (or enhancement) contributes to observed decreases (or increases) in salmon populations. Yet it is crucial to recognize that Equations (4), (7), and (8) are concerned with just one of the many potential limits on salmon populations - i.e. the upper grain-size limit on redd building in coarse riverbeds. Hence the tools presented here are only likely to inform management of salmon populations when otherwise confounding factors, such as the abundance of fine sediment, ocean conditions (Nickelson, 1986), stream temperature (Richter and Kolmes, 2005), disease (Krkosek and Hilborn, 2011), and predation (Peterman and Gatto, 1978; Quinn and Kinnison, 1999) are taken into account. Moreover, care should be taken in applying the tools presented here outside the Pacific Northwest and California, where they were calibrated. Although our toolkit should be widely applicable to coarse-bedded rivers where salmonids spawn, it has limitations that will need to be accounted for in some settings. For example, in steep, step-pool reaches, where salmonid species spawn in small isolated patches of movable substrate (Montgomery et al., 1999; Sear, 2010), our tools would likely need to be calibrated to apply to only the individual patches of movable substrate.

Optimizing spawning habitat restoration projects

Equation (4) and the tools derived from it show that FM decreases monotonically with increases in D50 for a given spread in the distribution (i.e. for a given D84/D50). Hence, it is apparently always better to have a finer D50 if the desire is more movable substrate (and more spawning capacity). However, other factors besides FM must be taken into account to assess spawning substrates and optimize gravel augmentation projects. For example, in addition to the previously mentioned effects on egg survival to emergence, a bed that is too fine-grained might lack occasional large 'centrum' rocks, which may be needed to stabilize redds and provide shelter for egg deposition (Hobbs, 1937; Burner, 1951; Jones and Ball, 1954). Moreover any added sediment should be coarse enough that it is stable against mobilization and rapid downstream transport in the flow of the river (e.g. Buffington and Montgomery, 1997). Hence, we suggest that FM should be used together with sediment transport modelling (e.g. Bunte et al., 2013; Heimann etal., 2014), known flow criteria for spawning and incubation (e.g. Tonina and Buffington, 2009; Moir and Pasternack, 2010), and known limits on fine sediment accumulation in redds (Jensen et al., 2009) to engineer a hydrodynamically stable substrate that accommodates as many redds as possible without being so fine that it suffocates eggs or entombs fry. Thus the physical limits on redd building that are incorporated into Equations (4) and (7) can be used together with conventional understanding of hydraulics and sediment transport to create stable channels that support good salmon spawning habitat (Wohl et al., 2015). With insight from Equations (4), (7), and (9), the cost-benefit analysis of sediment augmentation could be simplified to the cost per egg for sediment added to the bed (Riebe et al., 2014). In this way, our approach could help managers optimize selection of restoration sites for minimal cost and maximum benefit to the species of interest.

The tools presented here can also be readily used to quantify how much bed-surface area needs to be restored to meet established restoration objectives. As noted earlier, the sensitivity of FM to differences in D50 depends on the spread in the grain-size distribution (Figures 5A and 5B); when the spread is

large, bigger changes in D50 are needed for a desired change in coverage by movable particles (and thus by extension, desired changes in NREDDS and NEGGS). This suggests that initial conditions must be considered in the assessment of how much restoration is needed. The lookup charts in Figures 6 and 7 generally suggest that bigger increases in FM and NREDDS (and thus bigger increases in NEGGS) can be gained by adding movable sediment to reaches with relatively low D84/D50 (i.e. with relatively narrow grain-size distributions). Moreover Figures 6 and 7 show that habitat can be improved by reducing D84/ D50 without changing D50 when D50 < DT. This implies that habitat can be improved without gravel augmentation by removing the coarsest sediment from the bed and thus reducing D84/D50. Somewhat paradoxically, Figures 6 and 7 also suggest that it may be more economical on a cost-per-egg basis to focus restoration on reaches that already support considerable spawning. This presumes, of course, that hydraulic factors are suitable enough for fish to exploit new areas of movable sediment in the reach. Such sites may often have the added advantage of being hydrodynamically stable, which would contribute to longer residence times for added sediment. In any case, the tools presented here can help in allocating resources to the reaches that would yield the biggest and most stable increases in reproductive potential of spawning substrates.

Once augmentation projects have been initiated, our tools for gauging spawning substrates can be readily used to monitor changes in reproductive potential over time, thus enabling assessment of whether restoration projects are meeting desired goals (Riebe et al., 2014). When historical records are available, our tools can be used to quantify how measured changes in grain size may have contributed to changes in populations over time. Hence one could test hypotheses about cause-effect connections between historical declines in spawning and changes in spawning substrates, and thus build evidence for (or rule out) gravel augmentation as a viable approach to revitalizing salmon populations in a reach of interest. Quantifying historical changes in reproductive potential could also help managers understand and possibly also predict impacts of land use and climate change on the amount and quality of spawning substrates (Riebe etal., 2014).

Conclusions

Our new tools for assessing spawning habitat quality employ easy-to-measure inputs of D50, D84, and fish length to gauge a substrate's spawning capacity, defined as the number of redds per unit area that can be accommodated by the riverbed. Though the formulations of this new approach are somewhat complex, they are derived from empirical relationships that capture the mechanics of redd building and also fit data from diverse species of salmon across riverbeds with diverse grain-size distributions. Moreover, as demonstrated here, they are readily encapsulated in a series of easy-to-use charts, tables, and computer-based applications. The result is a management toolkit that accounts for interspecies differences in ability to move sediment for salmonids that build redds using a cutting motion. All that is needed to apply this toolkit is a pebble count and a carcass survey, or some other measurement of fish length. With additional measurements of fecundity, the predictions of spawning capacity can be translated to predictions of reproductive potential, defined as the maximum number of eggs that can be deposited per unit area for the fish of interest. Thus, the tools presented here can be readily applied to address a wide range of issues in the management of salmon spawning habitat. These include:

• gauging the capacity of spawning substrates across sites and salmonid species;

• optimizing selection of restoration sites for maximum benefit to the species of interest;

• quantifying how much bed-surface area needs to be restored to meet established restoration objectives;

• improving cost-benefit analysis in the allocation of river restoration budgets among prospective sites and activities;

• optimizing grain-size distributions in gravel augmentation projects to create hydrodynamically stable substrates that hold as many redds as possible;

• monitoring changes in the reproductive potential of spawning substrates over time to assess the effectiveness of restoration projects and to quantify impacts of land use and climate change;

• contributing to more realistic models of salmon population dynamics.

In summary, the tools presented here provide a multifaceted and comprehensive new approach to gauging the spawning capacity and reproductive potential of riverbed substrates used by female salmon for redd building when factors such as fine sediment content, flow depth, and velocity are within suitable ranges. Our toolkit also provides a mechanistic basis for optimizing gravel augmentation, thus contributing to more cost-effective, scientifically based restoration of salmon spawning in coarse-bedded rivers.

Notation

Aredd Map area of redd (m2).

D50, D84 50th and 84th percentiles of grain diameters on riverbed (mm).

DT Intermediate-axis diameter of largest sediment grain

that salmon of a particular size can move during redd building (mm).

E Fecundity, which is the number of eggs female salmon

produce (eggs/fish) and thus also the maximum number they can deposit within an individual redd (eggs /redd).

FM Fractional coverage of bed by particles that female

salmon can move during redd building. L Fork length of female salmon (mm).

Nredds Substrate spawning capacity, equal to the maximum number of redds that can be built per unit area in a given reach by a fish of a given size (redds/100 m2). Neggs Substrate reproductive potential, equal to the maximum number of eggs that can be deposited per unit area in a given reach by a fish of a given size (1000 eggs/100 m2). z Dimensionless exponent analogous to Z statistic in one-

parameter logistic-function approximation of the cumulative normal distribution.

Acknowledgements—This work was supported by the National Science Foundation grant EAR-0956289 to Riebe. The authors thank Frank Ligon for inspiration and Matt Sloat and Nick Brozovic for helpful discussions. The authors also thank two anonymous reviewers and the associate editor for comments and suggestions that improved the manuscript.

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