DOI: 10.7291/d1sd4d
title: Winter-run Chinook salmon resource selection function 2020

description: We use historic aerial redd surveys of Sacramento River winter-run Chinook
 salmon, coupled with 2D hydraulic modeling, and apply multivariable
 polynomial, logistic regression to calculate spawning resource selection
 functions (RSFs) based on water velocity and depth, and examine their
 interactions with water temperature. Our methods resulted in univariate
 and multivariate resource selection functions with interactions between
 both velocity and depth preference with changing temperature. Preferred
 depth increased and preferred velocity decreased with increasing
 temperature.
description: <b>1 Redd location data </b>
             The winter-run redd aerial survey takes place from
 mid-April to mid-August and averages 12 surveys annually (Appendix S1)
 (Killam et al. 2014). The survey uses a helicopter to achieve a more
 accurate count compared to a fixed wing aircraft. A trained observer
 marked spawning site locations on a map during each flight from 1990 to
 2017 (Appendix S2). When clustered near each other, multiple redds are
 represented as a single point location (hereafter site) feature on the
 survey maps. We then georeferenced these locations in ArcGIS (ESRI 2015),
 constructed a point layer by placing a point at the center of each marked
 spawning site, and assigning the relevant metadata. As the Sacramento
 River has regulated flows and the aerial surveys occur on a frequent basis
 (on average every 9.5 days), we assumed detection date conditions were
 representative of conditions when the spawner chose the site and created
 the redd. Winter-run redd observations on the Sacramento River extend from
 Keswick Dam to the C St Bridge (73 river kilometers downstream) near
 Tehama, California (Fig. 1).             To account for
 both the error in the recorded location of each redd and the procedure of
 listing multiple redds at a single site, we created 200 different data
 sets and allowed the exact locations of the redds to vary between each
 set. Each set began with the same georeferenced redd point locations. We
 then constructed a circular buffer around each point of 36.5 m. This
 estimate of the accuracy comes from errors measured in helicopter surveys
 of plants which used similar map based recordings of locations (Rebbeck et
 al. 2015). We increased the buffer radius by a distance equal to the
 radius of a circle of area equal to the area of a Chinook redd (8.4
 m<sup>2</sup>) (Newton and Brown 2004; Gallagher and Gallagher
 2005; Giovannetti and Brown 2008; Riebe et al. 2014) multiplied by the
 number of redds counted at the current site (Fig. 2). We then randomly
 distributed a number of points inside each circle equal to the redd count
 at that site. We used these randomly distributed points as the redd
 locations for the analysis. We repeated this procedure multiple times to
 construct 200 datasets.             To create points
 where redds were never present (absence points), we created a regular grid
 bounded by the wetted area of the Sacramento River at the typical flow
 during the winter-run spawning season (300 m<sup>3</sup>/s
 flow). We assumed all this area was accessible for spawning however
 substrate composition may make some areas unusable.  We place 80000
 uniformly distributed points over this domain resulting in a point spacing
 of 7.3 m. We removed any of these absence points which were inside any of
 the circular buffers constructed around any redd site. While the presence
 points have creation dates, each absence point required a creation date in
 order to assign a flow (and thus a depth and velocity) and temperature
 value. We assigned the creation month and day based on a draw from a
 normal distribution whose mean and standard deviation come from historical
 redd observation times. We assigned each absence point a year from 1990 to
 2017, weighted by the number of redds observed each year. Therefore,
 absence points were proportional to the redds observed on the river at any
 given time. This process resulted in a set of 37221 potential absence
 points. We use a unique random set of these absence points (equal to the
 number of present points) in each of the 200 datasets (see
 below). <b>2 Modeled redd depth and
 velocity</b>             To determine velocity
 and depth at each point in the data set we constructed a 2D hydraulic
 model which used 0.5 m resolution sonar derived bathymetry from the U.S.
 Bureau of Reclamation (Bradley and Greimann 2020). This bathymetry domain
 extended from Keswick Dam to 0.5 km upstream of the confluence with Cow
 Creek (Fig. 1). Because the majority of redd sightings (98.8 %) occurred
 within this domain, we ignored all redds downstream. We used this
 bathymetry along with the flow model HEC-RAS 2D (Hydrologic Engineering
 Center 2016) to create velocity and depth rasters for the Sacramento River
 within this domain. We used HEC-GeoRAS to adjust the bathymetry to account
 for Anderson-Cottonwood Irrigation District Flashboard Dam in Redding. Our
 hydraulic model domain consisted of a 20 m resolution grid over the river
 channel. In computation, HEC-RAS 2D uses both the resolution of the domain
 grid as well as the resolution of the underlying raster (0.5 m) (high
 resolution subgrid model (Casulli 2009)). As our initial Manning’s N
 values, we used values from a previously calibrated 1D HEC-RAS model of
 the Sacramento River. We ran calibration simulations by adjusting the
 Manning’s N values until the wetted area of the river matched satellite
 imagery taken at known flows.  We ran the model for values of flow from 50
 – 800 m<sup>3</sup>/s by steps of 50
 m<sup>3</sup>/s and from 800 – 2400
 m<sup>3</sup>/s by steps of 200 m<sup>3</sup>/s.
 We chose these values based on historical flow values during the
 winter-run spawning window (April – July). During this window, 97% of
 historical flow values were below 800 m<sup>3</sup>/s,
 justifying the coarser resolution above 800 m<sup>3</sup>/s.
 Each flow simulation resulted in two 0.5 m resolution rasters; one of
 water depth and one of vertically averaged water velocity. We assumed the
 minimum reasonable resolution for sampling red site depths and velocities
 was the diameter of a redd (3.26 m). Thus, for computational efficiency,
 we used cubic splines to rescale the rasters to 3.26 m resolution.
                  We used the River Assessment for
 Forecasting Temperature (RAFT) (Pike et al. 2013; Daniels et al. 2018) to
 assign flow and temperature values to redd locations based on creation
 date. RAFT is a one-dimensional model that simulates river temperature and
 flow in the longitudinal direction. For this analysis, we ran RAFT on a
 daily time step with a 2 km spatial resolution. When reconstructing
 historical river temperatures, RAFT assimilates gauge data using a version
 of the ensemble Kalman filter to improve model performance (Evensen 2009)
 with root mean square errors often below 0.5 °C (Pike et al. 2013; Daniels
 et al. 2018). Using the 2 km resolution RAFT data, we assigned each
 presence and absence point a flow and temperature based on its creation
 date and river kilometer. We then took the flow assigned to each point and
 performed a linear interpolation between the rasters created with HEC-RAS
 (both depth and velocity) to calculate the actual depth and velocity at
 that point on the creation date. This procedure resulted in a data set
 with velocity, depth, and temperature at each presence and absence point
 for their creation date. We removed the small fraction (~1%) of presence
 points in each data set which were not wetted. Having equal number of
 presence and absence points can improve model predictive accuracy (Hattab
 et al. 2013), so in each of the 200 data sets, we used random sampling
 without replacement to reduce the number of absence points from the over
 37000 available to a number equal to the number of presence
 points.  <b>3 Statistical
 models</b>             We conducted all
 statistical analysis in a frequentist framework using generalized linear
 models (GLM) in  R (R Core Team 2015). The code used the dplyr and ggplot2
 packages and was run using RStudio (RStudio Team 2015; Wickham 2016;
 Wickham et al. 2018). We conducted a quadratic logistic regression using a
 Bernoulli link function on velocity and depth separately to get RSFs for
 each. These models had the form <i>Spawn</i><sub><i>i</i></sub><i> ~ Bernoulli(</i><i>p</i><sub><i>i</i></sub><i>)</i> <i>E</i><i>Spawn</i><sub><i>i</i></sub><i>= </i><i>p</i><sub><i>i</i></sub> <i>logit(</i><i>p</i><sub><i>i</i></sub><i>)= </i><i>b</i><sub><i>0</i></sub><i>+</i><i>b</i><sub><i>1</i></sub><i>x</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>2</i></sub><i>x</i><sub><i>i</i></sub><sup><i>2</i></sup> .                                             eqn1 In this model, <i>p<sub>i</sub></i> is the probability of use or spawning, the <i>b<sub>i</sub></i>’s are fitted parameters, and <i>x<sub>i</sub></i> represents the value of the variable of interest at the i<sup>th</sup> data point (either velocity or depth). The quadratic form allowed the RSF to be both peaked and asymmetrical. This shape was important because we expected the RSF to have an optimum value about which it need not be symmetrical.       As temperature may interact with depth and velocity in site selection, we examined the effect of temperature with the following model <i>Spawn</i><sub><i>i</i></sub><i> ~ Bernoulli(</i><i>p</i><sub><i>i</i></sub><i>)</i> <i>E</i><i>Spawn</i><sub><i>i</i></sub><i>= </i><i>p</i><sub><i>i</i></sub> <i>logit</i><i>p</i><sub><i>i</i></sub><i>= </i><i>b</i><sub><i>0</i></sub><i>+</i><i>b</i><sub><i>1</i></sub><i>v</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>2</i></sub><i>v</i><sub><i>i</i></sub><sup><i>2</i></sup><i>+</i><i>b</i><sub><i>3</i></sub><i>d</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>4</i></sub><i>d</i><sub><i>i</i></sub><sup><i>2</i></sup><i>+</i><i>b</i><sub><i>5</i></sub><i>T</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>6</i></sub><i>v</i><sub><i>i</i></sub><i>d</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>7</i></sub><i>T</i><sub><i>i</i></sub><i>v</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>8</i></sub><i>d</i><sub><i>i</i></sub><i>T</i><sub><i>i</i></sub><i>  </i> eqn 2 where <i>T<sub>i</sub></i>, <i>v<sub>i</sub></i>, and <i>d<sub>i</sub></i> represent temperature, velocity, and depth values respectively for the i<sup>th </sup>data point. We then checked to see if either of the temperature interaction terms (b<sub>7</sub> and b<sub>8</sub>) were non-zero across the 200 data sets. As either velocity or depth may be correlated with temperature in this system, an apparent credible interaction between either velocity or depth and temperature on site selection could arise irrespective of winter-run behavior. To assess this potential, we fit an equation using only depth and velocity <i>Spawn</i><sub><i>i</i></sub><i> ~ Bernoulli(</i><i>p</i><sub><i>i</i></sub><i>)</i> <i>E</i><i>Spawn</i><sub><i>i</i></sub><i>= </i><i>p</i><sub><i>i</i></sub> <i>logit</i><i>p</i><sub><i>i</i></sub><i>= </i><i>b</i><sub><i>0</i></sub><i>+</i><i>b</i><sub><i>1</i></sub><i>v</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>2</i></sub><i>v</i><sub><i>i</i></sub><sup><i>2</i></sup><i>+</i><i>b</i><sub><i>3</i></sub><i>d</i><sub><i>i</i></sub><i>+</i><i>b</i><sub><i>4</i></sub><i>d</i><sub><i>i</i></sub><sup><i>2</i></sup><i>+</i><i>b</i><sub><i>5</i></sub><i>v</i><sub><i>i</i></sub><i>d</i><sub><i>i</i></sub><i>  </i> .                           eqn 3 We used this model to construct a simulated data set where selection of redd site location was only based on depth and velocity. We constructed this data set by taking all presence and absence velocity, depth, and temperature data and assigning them simulated presence or absence values probabilistically based on the velocity and depth derived RSF. We conducted the same multivariable analysis with temperature on this simulated data set, and compared the values for the interaction terms (b<sub>7 </sub>and b<sub>8</sub>) from the actual and simulated data sets. After running the models described by equation 3, we ran a version without the interaction terms. We checked the penalized AIC of these eight models to decide on a single model for use in a visualization tool of spawning habitat. To evaluate the predictive power of the selected most parsimonious model (the model with the lowest AIC) we conducted a 4-fold partitioning of each data set by dividing our data sets into four groups, using three to calibrate the model, and using the remaining fourth to test the model. This method resulted in 800 tests of the model from which we constructed receiver operator curves (ROCs) and calculated the area under the curve (AUC) for each (Murtaugh 1996; Fielding and Bell 1997; Boyce et al. 2002). To check for spatial correlation we examined a variogram of the residuals from our model. We divided up the river into segments to remove spatial correlation and ran a generalized linear mixed model using the lme4 package in R (Bates et al. 2015) with river section as a random effect to compare to our non-spatial model.   Finally, we constructed a Shiny application (Chang et al. 2019) using the mean coefficients of the lowest AIC model to show RSF values for a user selected section of the Sacramento River given a user selected flow and temperature. The flow and temperature are treated as constant over the calculation/display domain. 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