# Simulating Spawning and Juvenile Rainbow Trout (Oncorhynchus mykiss) Habitat in Colorado River Based on High-Flow Effects

^{1}

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^{3}

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^{5}

^{6}

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## Abstract

**:**

## 1. Introduction

## 2. Study Areas and Mathematical

#### 2.1. Study Areas and Mathematical Description of CFD Simulations

_{F}). The conservation equations for both mass and momentum are presented as follows:

_{k}and G

_{b}are the turbulent kinetic energy production due to shear and buoyancy. The G

_{k}and G

_{b}can be written as follows,

_{U}= 1/Re + ν

_{tur}, χ

_{T}= 1/PrRe + ν

_{tur}/σ

_{T}, χ

_{S}= 1/ScRe + ν

_{tur}/σ

_{S}

_{K}= 1/Re + ν

_{tur}/σ

_{K}, χ

_{E}= 1.0/Re + ν

_{tur}/σ

_{E}

_{tur}= C

_{μ}K

^{2}/E, was applied to measure the turbulence strength. The k − ε model constants C

_{μ}, C

_{1}, C

_{2}, C

_{3}, σ

_{K}, σ

_{E}, σ

_{T}and σ

_{S}respectively and the values were shown as following,

_{μ}= 0.09, C

_{1}= 1.44, C

_{2}= 1.92, C

_{3}= 1.00, σ

_{K}= 1.00, σ

_{E}= 1.30, σ

_{T}= 0.90, σ

_{S}= 0.70

_{T}and turbulent Schmidt number σ

_{S}actually were expressed as function forms of the ratio of eddy to diffusivities and distance to the boundary condition. As a matter of flow properties, standard values of turbulent Schmidt and Prandtl numbers could be adopted for use in the above equations [30].

_{in}), water temperature (T

_{in}) and water depth (H

_{in}) of the inlet boundary layer. The turbulent kinetic energy and its dissipation rate were calculated based on the following equations,

_{in}(Y) = 1.50 × (10% × U

_{in}(Y))

^{2}, E

_{in}(Y) = C

_{μ}

^{0.75}K

_{in}(Y)

^{1.5}/L(Y),

^{α}, which represents the length scale of the velocity components along the flow direction.

#### 2.2. Sediment Transport

_{b}[31]:

#### 2.3. Habitat Construction

#### 2.4. WUA and OSI Construction Procedure

## 3. Numerical Model Setup and Implementation

^{−9}in this model system [42]. Significance tests were conducted for the accuracy of the model system and also the dependency of solutions for grid size. More detail can be found in Yao et al. [26,44,45].

## 4. Results and Discussion

^{2}).

#### 4.1. High Flow Effects on Velocity and Temperature

#### 4.2. Hydrodynamic Simulation Results

#### 4.2.1. High Flow Effects on River Bed Elevation and Water Depth

#### 4.2.2. High Flow Effects on Spawning and Juvenile Rainbow Trout Habitat Suitability

#### 4.3. Weighted Usable Area and Overall Usable Area Analyses

^{6}m

^{2}to 2.61 × 10

^{6}m

^{2}and the OSI increased from 0.48 to 0.51 correspondingly. However, the WUA and OSI values for spawning rainbow trout are smaller than juvenile rainbow trout. With the HFE, the WUA for spawning rainbow trout were 9.46 × 10

^{5}m

^{2}and 7.91 × 10

^{5}m

^{2}and the OSI declined from 0.19 (before HFE) to 0.16 (after HFE) (Figure 10).

^{6}m

^{2}, 2.75 × 10

^{5}m

^{2}for juvenile rainbow trout and 9.46 × 10

^{5}m

^{2}, 1.03 × 10

^{3}m

^{2}for spawning rainbow trout respectively. After the HFE, the high WUA for spawning rainbow trout decreased to 7.90 × 10

^{5}m

^{2}while the middle and low WUA increased to 3.10 × 10

^{3}m

^{2}and 4.21 × 10

^{3}m

^{2}. The high, middle and low WUA values for juvenile rainbow trout are 2.19 × 10

^{6}m

^{2}, 6.51 × 10

^{5}m

^{2}and 2.16 × 10

^{6}m

^{2}respectively.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

A_{i} | The area of the mesh i |

${C}_{eq}$ | Suspended load mass concentration at reference lever under equilibrium conditions |

CFD | Computational Fluid Dynamics |

${C}_{ref}$ | Suspended load concentration at reference lever |

${\chi}_{t}$ | Turbulence diffusivity scalar |

$\theta $ | Non-dimensional skin friction number/shields number |

${\theta}_{cr}$ | Critical shields value |

${v}_{t}$ | The eddy viscosity |

C | Chezy friction coefficient |

d_{50} | Particle size parameter in 50 percent |

f_{cor} | The Coriolis parameter |

g | Gravitational acceleration |

G_{r} | Grashof number |

h | Fluid column height |

HFE | High Flow Effect |

HSI | Habitat suitability index |

M | The total number of grid mesh |

OSI | Overall suitability index |

P’ | The non-cohesive bed porosity |

Q_{bs}, Q_{bn} | Bed-load flux |

R_{e} | Reynolds number |

SI_{v}, SI_{d}, SI_{s}, SI_{t} | Suitability index for velocity, water depth, substrates and temperature |

t | Time |

T | Temperature |

U, V | Depth average velocity components in x and y directions respectively |

WUA | Weighted usable areas |

Z-Z_{0} | Water depth |

η | Water surface elevation |

τ_{b} | Bed shear stresses |

τ_{xx} τ_{xy} τ_{yx}, τ_{yy} | Depth-average Reynolds (turbulent) stresses |

ρ_{s} | Sediment density |

ρ_{w} | Water density |

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**Figure 2.**Photogrammetric base map of the study site of the Colorado River, which extends from Glen Canyon Dam to the Lees Ferry.

**Figure 3.**Daily mean discharge released from the Glen Canyon Dam during high flow effects in 2008 (

**a**) and sediment distribution in the river bed during high flow effects in 2008 (

**b**).

**Figure 5.**Spawning (

**a**) and juvenile (

**b**) rainbow trout flow velocity, water depth, temperature and substrates preference curves. (Substrates types: 1 = plant detritus/organic material, 2 = mud/soft clay, 3 = silt (particle size < 0.062 mm), 4 = sand (particle size 0.062 to 2.000 mm), 5 = gravel (particle size 2.0 to 64.0 mm), 6 = cobble/rubble (particle size 64.0 to 250.0 mm), 7 = boulder (particle size 250.0 to 4000.0 mm), 8 = bedrock (solid rock)).

**Figure 6.**Simulation output of the velocity, water depth and temperature distribution before the high flow effect (HFE) (

**a**) and after the HFE (

**b**). (VELO = velocity; H = water depth; T. = temperature; HFE = high flow effect).

**Figure 8.**Before the HFE and after the HFE habitat suitability index distribution for spawning (

**a**) and juvenile (

**b**) rainbow trout.

**Figure 9.**Before the HFE and after the HFE high, middle and low habitat suitability index distribution for spawning (

**a**) and juvenile (

**b**) rainbow trout.

**Figure 10.**Before the HFE and after the HFE weighted usable areas (WUA) and overall suitability index (OSI) for spawning rainbow trout (

**a**) and juvenile rainbow trout (

**b**).

HSI | High | 0.7–1.0 |

Middle | 0.3–0.7 | |

Low | 0–0.3 |

**Table 2.**Description of the spawning and juvenile rainbow trout weighted usable area with the habitat suitability index larger than 0.7, 0.3–0.7 and 0–0.3 (Total area is 2,550,000 m

^{2}).

Habitat Category | Spawning | Juvenile | ||
---|---|---|---|---|

WUA | Before | High | 9.46 × 10^{5} | 2.23 × 10^{6} |

Middle | 1.03 × 10^{3} | 2.75 × 10^{5} | ||

Low | 4.05 × 10^{6} | 2.49 × 10^{6} | ||

After | High | 7.90 × 10^{5} | 2.19 × 10^{6} | |

Middle | 3.10 × 10^{3} | 6.51 × 10^{5} | ||

Low | 4.21 × 10^{6} | 2.16 × 10^{6} |

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## Share and Cite

**MDPI and ACS Style**

Yao, W.; Liu, H.; Chen, Y.; Zhang, W.; Zhong, Y.; Fan, H.; Li, L.; Bamal, S.
Simulating Spawning and Juvenile Rainbow Trout (*Oncorhynchus mykiss*) Habitat in Colorado River Based on High-Flow Effects. *Water* **2017**, *9*, 150.
https://doi.org/10.3390/w9020150

**AMA Style**

Yao W, Liu H, Chen Y, Zhang W, Zhong Y, Fan H, Li L, Bamal S.
Simulating Spawning and Juvenile Rainbow Trout (*Oncorhynchus mykiss*) Habitat in Colorado River Based on High-Flow Effects. *Water*. 2017; 9(2):150.
https://doi.org/10.3390/w9020150

**Chicago/Turabian Style**

Yao, Weiwei, Huaxian Liu, Yuansheng Chen, Wenyi Zhang, Yu Zhong, Haiyan Fan, Linkai Li, and Sudeep Bamal.
2017. "Simulating Spawning and Juvenile Rainbow Trout (*Oncorhynchus mykiss*) Habitat in Colorado River Based on High-Flow Effects" *Water* 9, no. 2: 150.
https://doi.org/10.3390/w9020150