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ARTICLE
International Journal of Water Sciences

Assessment of Spring Chinook Salmon
Habitat Suitability in the San Joaquin
River Using a 2-D Depth-Averaged Model
Regular Paper

Lubo Liu1,* and Joaquin Ramirez1
1 Department of Civil and Geomatics Engineering, Lyles College of Engineering, California State University Fresno, Fresno, US
* Corresponding author E-mail: llubo@csufresno.edu
Received 9 Sep 2013; Accepted 22 Nov 2013
DOI: 10.5772/57437
© 2013 Liu and Ramirez; licensee InTech. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract The San Joaquin River Restoration Program
(SJRRP) provides adult Chinook salmon with a passage
to upstream spawning beds and a safe route for
juveniles returning to the Delta. A two-‐‑ dimensional
depth-‐‑averaged hydrodynamic model based on the
RMA10 scheme was developed to simulate the
hydraulic properties (current velocities, depth, water
surface elevation) of three proposed alternative
migration pathways to explore flow patterns and offer
useful insights into the effects of hydrodynamic
alterations of the channel, a critical capability for
determining the best passage for migration. The finite
element model reasonably described the hydrodynamic
conditions and calculated a Suitability Index (SI) for the
habitat for spring-‐‑run Chinook salmon, with a Nash-‐‑
Sutcliffe Coefficient (NSC) of 0.75 for discharge and 0.56
for water surface elevation (WSE) respectively. The
alternatives analysed were found to be characterized by
similar SI distributions under the same boundary
conditions. Alternatives 2 and 3 had higher overall
Weighted Area Habitat Suitability Index (WAHSI)
values and would thus be expected to provide better
environments for salmon migration than Alternative 1.

Normalized cross-‐‑ correlation calculations revealed fair
correlations between the WAHSI values and upstream
discharge or downstream water surface elevation. The
hydrodynamic model may also provide a reference for
similar suitability studies of salmon habitat in other
inland rivers.

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Int. j. Spring Chinook Vol. 2, 5:2013
Lubo Liu and Joaquin Ramirez: Assessment of water sci., 2013,Salmon Habitat
Suitability in the San Joaquin River Using a 2-D Depth-Averaged Model

Keywords Hydrodynamic Model, Habitat Suitability,
Salmon Migration, Correlation

1. Introduction
As the second longest river in California, the San Joaquin
River (SJR) is a vital natural resource for numerous
residents and industries. It provides an array of utilities
within the Central Valley and is home to some of
California’s most productive agricultural areas [1].
Headwaters for the river originate in the high Sierra
Nevada, mainly from snowmelt and runoff [2].
Eventually the SJR conjoins with the Sacramento River to
form the largest river delta on the west coast of North
America [3].
1

The river is crucial for the propagation and survivability
of Chinook salmon and other aquatic species and
wildlife, but over the years it has experienced
considerable hydrologic disconnection along its reaches
due to extensive water diversion. Indigenous salmon
populations have suffered as a result and their numbers
have decreased significantly due to insufficient flows
and anthropogenic activities [4]. In order to restore
salmon and other fish populations to a point of self-‐‑
sustainment, the San Joaquin River Restoration Program
(SJRRP) was established in 2006 to maintain a
continuous flow from the Friant Dam to its confluence
with the Merced River. Due to practical limitations,
routing the flow along several alternative pathways has
been considered [5]. A critical task for the SJRRP, the so-‐‑
called “Reach 4B Project”, was to modify and improve
the channel capacity of Reach 4B (which is separated
into 4B1 and 4B2, shown in Figure 1) of the SJR.
Multiple scenarios for the restoration of the river and for
modifications of existing SJR channels were designed
and studied to ensure fish passage and adequate flow
throughout the study area [6].
Natural Chinook salmon runs along the SJR (above the
Merced River Confluence) originally occurred in fall,
spring and in late autumn for some species. However, all
runs had ceased by the late 1940s due to water diversion
[7]. In a natural river system, salmonids have evolved to
exploit natural flow patterns in streams so that
migrations can take place when water characteristics are
ideal [8]. However, anthropogenic activities alter natural
settings and offset the timing of advantageous river
conditions and hence salmonid migration [9]. As part of
the effort to restore the river’s natural conditions, a great
deal of research has been devoted to the study of habitat
and flow relationships in recent years [9-‐‑11]. In relation to
California’s waterways, researchers have mainly focused
on the delta region with only limited investigations
conducted for the SJR, especially for the middle section of
the river [12]. When salmon return to their spawning
grounds, they must complete their migration within a
certain amount of time and with adequate reserves of
energy in order to complete their life cycle [13].
Hydrodynamic conditions affecting salmon passage
include the water velocity, depth and water quality, all of
which are important factors for their migration. Sustained
water velocity and water depth provide opportune
passage conditions for the successful upstream migration
of adult salmon [14, 15]. An in-‐‑depth hydrodynamic
investigation is therefore essential to support efforts to
better delineate the impact of flow characteristics on
salmon migration and habitat conditions.
Modelling methods have been very effective tools for this
type of riverine study and several hydrodynamic models
have been constructed for the SJR. However, most have

2

Int. j. water sci., 2013, Vol. 2, 5:2013

been one-‐‑dimensional [12, 16], providing a large-‐‑scale
overview of the river network. Considering the
complexity and heterogeneous properties of the SJR, a
two-‐‑dimensional model is more suitable for describing
detailed local conditions such as those critical for the
progress of salmon migration [17-‐‑20].
The goal of the SJRRP’s Reach 4B was to provide a
passage for adult Chinook salmon to spawning beds
further upstream and a safe route for juveniles to the
delta [5]. To this end, the objective of this research was
therefore to model the stream conditions, including
current velocity, depth and water surface elevation (WSE),
for each of the three alternatives proposed in Project 4B
under the same hydrologic/hydraulic boundary
conditions. A two-‐‑dimensional depth-‐‑averaged model
incorporating disconnected portions of the SJR was
developed based on the RAM10 scheme and used to
simulate these local river characteristics and conditions to
further explore the correlations between river flow and
salmon migration under the different alternatives
proposed. The model facilitates the development of a
better understanding of the effects of different boundary
conditions, both upstream and downstream, on salmon
habitat suitability, survival and migration conditions.
Model simulations allow the exploration of flow patterns
and enable users to compare alternative scenarios.
Modelling results also provides insights into the
hydrodynamic behaviour that would result from
proposed river alterations and support the prediction and
analysis of the consequent impact on the conditions for
Chinook salmon runs.
2. Description of study area
The study area lies within the Middle San Joaquin-‐‑Lower
Chowchilla watershed and extends approximately 57.6
river miles (92.2 km) from monitoring stations SJR near
Dos Palos (SDP) to SJR at the Fremont Ford Bridge (FFB)
near California Highway 140. The SJR is divided into
different river segments in this area, designated Reaches
4A, 4B1, 4B2 and 5, Eastside Bypass and Mariposa Bypass
(see Figure 1). Initially, the channel of pathway of the SJR
consisted of Reaches 4A, 4B1, 4B2 and 5. Descriptions of
each river reach are listed in Table 1. The original Eastside
Bypass and Mariposa Bypass were utilized as flood
control channels. However, the Eastside Bypass now
conveys all water from upstream as a portion of the river
and Reach 4B1 is hydraulically disconnected. The portion
of the Eastside Bypass within our scope of study begins
directly downstream of Reach 4A near SWA and extends
to Reach 5 of the SJR. Mariposa Bypass is another channel
designed to convey flood flow and connects the Eastside
Bypass to Reach 4B2. Under normal flow conditions, the
river flows from Reach 4A to the Eastside Bypass and re-‐‑
enters the SJR at Reach 5.

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37.4

FFB
Reach 5

37.3

J2
Alt1/2/3
Alt1

Reach 4B2

Eastside Bypass

37.2
N

Alt2/3

J1

EBM
Mariposa Bypass

Latitude,

o

Alt3

Alt1/3
Alt2 Reach 4B1

SWA

37.1

Alt1/2/3

Reach 4A

San Joaquin River

37.0

SDP

5 miles
North

36.9
121.0

120.8

120.6
Longitude,

o

120.4

W

Figure 1. Geographic map showing the reaches in the modelling domain of the San Joaquin River (SJR) (Alt – Alternative, 1 mile = 1.6
km). Monitoring stations (SDP, SWA, EBM and FFB) are described in Table 2.

Reach/bypass
Reach 4A

Length
(miles)
13.5

Flow capacity
(cfs)
4500

Connections
SDP** – SWA**

Usage

Current
Status
F

River flow
Runoff, receiving water from
Reach 4B1
21.3
Unknown
SWA – J1*
NF
agricultural practices and rain events
Occasional flood water received from
Reach 4B2
11.4
10000
J1 – J2
the Eastside Bypass and backflow
F
from Reach 5
River flow received from the Eastside
Reach 5
17.5
26000
J2 – FFB**
Bypass, Reach 4B2 and agricultural
F
return flows
Eastside Bypass 21.8
15700 (average)
SWA–EBM**–J2
Flood control and SJR flow
F
Mariposa
Flood flow, transporting water from
3.4
8000
EBM–J1
F
Bypass
the Eastside Bypass to the SJR
F: Functional; NF: Not Functional; *: J1 and J2 -‐‑ Junction points; **: SDP -‐‑ SJR near Dos Palos, EBM -‐‑ Eastside Bypass
below Mariposa Bypass, SWA -‐‑ SJR near Washington Rd, FFB -‐‑ SJR near Washington Rd.
Table 1. Reaches and bypasses in the middle of the San Joaquin River (SJR)
(1 mile = 1.6 km; 1 cfs = 0.028 cms)
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Lubo Liu and Joaquin Ramirez: Assessment of Spring Chinook Salmon Habitat

3

Station Description

Station ID

Station Location,
NAD83
36.9949, -‐‑120.501
37.1114, -‐‑120.591

Reach/confluence

Agency

SJR near Dos Palos
SDP
4A
SJR near Washington Rd
SWA
4A
Eastside Bypass below Mariposa
EBM
Eastside Bypass
37.2060, -‐‑120.697
Bypass
SJR at Fremont Ford Bridge
FFB
Reach 5
37.3099, -‐‑120.931
*: CADWR -‐‑ California Department of Water Resources, USGS -‐‑ U. S. Geological Survey

CADWR*
CADWR
CADWR
USGS*

Table 2. Monitoring stations in the study river reaches

The data used for the model development and
calibration, including bathymetry, channel flow rate and
WSE, were obtained from the U.S. Geological Survey
(USGS), the U.S. Bureau of Reclamation (USBR) and the
California Department of Water Resources (CADWR).
Bathymetry data were collected during 2010 and 2011 by
USBR using GPS and the Acoustic Doppler Current
Profiler (ADCP) at a spatial interval of 20 feet. Flowrate
and river stage data were collected for the year of 2011
(from January 1st to September 30th) by the four CADWR
and USGS in-‐‑situ river gauge stations located in the study
area at 15 minute intervals. Station descriptions are listed
in Table 2. The year 2011 was selected for model
calibration because adequate interim flows were released
from upstream and the data for this period are quality-‐‑
assured by reporting agencies. The geographic boundary
of the SJR was determined using coordinates from Google
Earth based on the WGS84 global reference system. The
data collected from multiple government agencies were
converted and georeferenced using the same coordinate
system and reference datum, namely the North American
Vertical Datum NAVD 88 and California State Plane,
Zone 3, North American horizontal Datum NAD 83.
3. Hydrodynamic model
A vertically-‐‑integrated hydrodynamic model was
developed using the finite element scheme RMA10 [21] to
describe the flow velocity, water depth and WSE. The
governing equations in the x and y directions are as
follows:

∂h
∂h
∂h
∂U ∂V
+U
+V
+ h(
+
) = 0 (1)
∂t
∂x
∂y
∂x ∂y
h
=
−gh (

∂U
∂U
∂U
+ hU
+ hV
− fVh =
∂t
∂x
∂y
∂
∂U
∂
∂U
(ε xxh
)+
(ε xyh
)
ρ ∂x
∂x
∂y
∂y

1

2
2
2
∂a ∂h Ugn (U + V )
)−
+
+ ζ W 2 cosψ
1/3
∂x ∂x
h

(2)

4


h
=
−gh (

∂V
∂V
∂V
+ hU
+ hV
+ fUh =
∂t
∂x
∂y
∂
∂V
∂
∂V
(ε yxh
)+
(ε yyh
)
∂x
∂y
∂y
ρ ∂x

1

2
2
2
∂a ∂h Vgn (U + V )
+
+ ζ W 2 sinψ
)−
h 1/3
∂y ∂y

(3)

U , V are the depth-‐‑averaged velocities in the
x, y directions; h is the water depth and a is the
bottom surface elevation; g is the acceleration due to
gravity; W is the wind velocity; ψ is the wind direction;
ζ is an empirical wind coefficient; and f is the Coriolis
parameter. n denotes the Manning’s roughness

Where

coefficient and ε is the depth-‐‑averaged eddy viscosity.
Horizontal mixing was described using the Smagorinsky
eddy parameterization:

∂U
ε S = 2 Am = αA
∂x

2

∂V
+
∂y

2

1 ∂U ∂V
)
+ (
+
2 ∂y ∂x
(4)

ε S is the eddy viscosity; α is a constant in the
range 0.01-‐‑0.5 ( α = 0.05 was used for this study) and

where

A is the area of the current element. The horizontal
turbulent mixing of momentum was typically ignored in
some previous hydrodynamic models of the SJR [22, 23].
Our results suggest that the model is insensitive to the
eddy viscosity within a range from 0 to 10 m2/s, so a
constant value of 1.0 m2/s was used for the minimum
eddy viscosity. Values in the different regions were varied
depending on the element size and the velocity gradients
according to Equation 4. Wind stress and Coriolis force,
both of which typically play a critical role in large water
bodies such as oceans or lakes, were neglected in this
model of a small-‐‑scale river section.
For the initial conditions for the model, it was assumed
that the river was at rest at the start and it took a
considerable time (ten days in this case) for the model to

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Element #
Node #

Alternative 1
2483
9568

Alternative 2
1841
7056

Reaches included
(Figures 1 and 2)

Reach 4A
Eastside Bypass
Reach 5

Reach 4A
Reaches 4B1 and 4B2
Reach 5

Alternative 3
2134
8209
Reach 4A
Eastside Bypass
Mariposa Bypass
Reach 4B2
Reach 5

Table 3. Finite Element Model (FEM) information

Salmon Species
Spring Salmon
Autumn Salmon

Cruising Velocity1*
0 – 3.41 (ft/s)
0 – 1.04 (m/s)
0 – 3.41 (ft/s)
0 – 1.04 (m/s)

Swimming Speed
Sustained Velocity2*
3.41 – 10.79 (ft/s)
1.04 – 3.29 (m/s)
3.41 – 10.79 (ft/s)
1.04 – 3.29 (m/s)

Minimum Depth
Darting Velocity3*
10.79 – 22.41 (ft/s)
3.29 – 6.83 (m/s)
10.79 – 22.41 (ft/s)
3.29 – 6.83 (m/s)

0.80 (ft)
0.24 (m)
0.80 (ft)
0.24 (m)

: Cruising speed is the speed at which a fish can swim for an extended period of time, usually hours.
: Sustained is a speed that can be maintained for minutes.
3*: Darting represents a single effort or burst which is not maintainable.
1*
2*

Table 4. Salmon swimming capabilities (velocity, depth) reported in the literature [9, 13, 15]

reach the actual initial conditions. The boundary
conditions for the hydrodynamic simulation included a
no leakage condition across the surface and the bottom,
no wind stress and zero pressure at the free water surface,
a drag stress condition at the bottom of the river, a
discharge condition at the upstream and a WSE condition
at the downstream.

injuries and compromise their migration [24]. In addition,
when fish are not fully submerged they partially lose the
ability to generate thrust [25]. In Thompson’s model, it
was assumed that a safe passage depth of greater than 0.8
ft must be maintained over 25% of the stream width and
must remain continuous for 10% of the cross section [14].
5. Results and discussion

In order to accurately delineate the complex physical
boundaries of the SJR, a finite-‐‑element mesh was used
(see Table 3) for this model. The sizes of the non-‐‑uniform
elements were between 1 and 100 feet (Figure 2d).
4. Hydrodynamic considerations for salmon migration
To address the hydrodynamic impact on salmon in a
river, Bell [15] divided the swimming capabilities of
salmon into three speed categories (Table 4). Fish
normally travel at a cruising speed for several hours
during migration, at a sustainable speed over a few
minutes for navigation through difficult areas and at a
darting speed for feeding or escape [15]. Based on this
behaviour, velocity can be manipulated for use as either
an artificial barrier or as a means to attract fish. Ideally,
cruising speed can be considered attractive, while
sustained speed can become a barrier over an extended
distance and darting speed an immediate barrier if the
transition is rapid [15]. The ranges of velocity values of
these three categories are listed in Table 4. A suitable
minimum depth of 0.8 ft (0.244m) has also been
recommended for the passage of adult spring Chinook
salmon (Table 4) [14]. Although salmon have been
observed travelling at depths less than those indicated in
Table 4, at depths of less than 0.8 feet fish may suffer
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The model simulated hydrodynamic flow characteristics
under the three alternative water pathways for the spring
Chinook salmon run. The two-‐‑dimensional finite meshes
for the three alternatives are shown in Figure 2. Figure 2a
shows the Alternative 1 which has flow from Reach 4A
through the Eastside Bypass (passing through stations
SWA and EBM) to Reach 5 and the RMA10 model for
Alternative 1 does not include any finite-‐‑element mesh
for Reaches 4B1 and 4B2. Alternative 2 (Fig. 2b) has flow
from Reach 4A through the original course of the SJR
(Reaches 4B1 and 4B2) to Reach 5 and the model for
Alternative 2 does not include any mesh for the Eastside
Bypass. Figure 2c includes all sections of the study
domain. The currently preferred option (Alternative 3)
consists of conveying a small amount of flow through
reach 4B1, with the remaining restoration flow continuing
down the Eastside Bypass, transferring into the Mariposa
Bypass and re-‐‑entering the SJR in Reach 4B2 [26].
Therefore, the major fish route in Alternative 3 follows
Reach 4A, Eastside Bypass, Mariposa Bypass, Reach 4B2
and Reach 5. Figure 2d shows an enlarged portion of the
two-‐‑dimensional mesh in the area around station SWA.
The model was calibrated using the 2011 data set and
deemed applicable for modelling the investigation of

5

hydrodynamic conditions affecting salmon migration in
the SJR. The discharge data were used for the upstream
boundary condition at station SDP and the WSE data
were used for the downstream boundary condition at
station FFB. These data sets were recorded at 15-‐‑minute
intervals between January 1st and September 1st 2011, by
CADWR and USGS. Figure 3 shows these boundary
conditions. In the convergence test, 0.1% and 0.05% were
set as the convergence criteria for current velocities and
WSE respectively, for each iteration within the same time
(a)

level. The data indicate that little flow (less than 100 cfs)
occurred upstream at SDP in early spring until late March
2011 (before the 80th day of the simulation period). In
2011, the most abundant flow occurred from late spring
to late summer, the period when the adult Chinook
salmon in the spring run enter the freshwater to spawn in
the autumn. The model simulated the discharge and the
WSE in this period utilizing a time step (15 minutes) that
was the same as the data collection interval for
calibration.

(b)

FFB

FFB

Eastside Bypass
EBM

EBM

SJR

SWA

SWA

SJR

SDP
(c)

SDP

(d)

FFB

Eastside Bypass
4B2

EBM

Eastside Bypass

4B1
4B1

SWA
SWA

SJR

SDP
Figure 2. Finite element meshes of three flow pathways: (a) Alternative 1; (b) Alternative 2; (c) Alternative 3; and (d) Enlarged 2-‐‑
dimensional finite element meshes in the SJR near Washington Rd (SWA) region.

6


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Upstream condition: Discharge at SDP

Discharge (cfs)

5000

(a)

4000
3000
2000
1000
0

0

20

40

60

80

100

120

140

160

180

200

160

180

200

Downstream condition: WSE at FFB

WSE (ft)

80

(b)

70
60
50

0

20

40

60

80
100
120
Julian days, 2011

140

Figure 3. Boundary conditions: (a) Upstream condition: Discharge at the SJR near Dos Palos (SDP); and (b) Downstream condition:
Water Surface Elevation (WSE) at the SJR at Fremont Ford Bridge (FFB). (1ft = 0.3048 m, 1 cfs = 0.0283 cms)

Data Stations

SWA (Discharge)

Table 5. RMSE and

SWA (WSE)

EBM (WSE)

0.47

0.017

0.014

SDP (WSE)
0.064

0.75

Minimum RMSE
NSC

0.56

0.42

0.34

NSC results

The Manning roughness coefficient of the channel was
manually adjusted to calibrate the model using the
method of minimum normalized Root Mean Squared
Error (RMSE), which is defined as follows:

RMSE =

1
N

N
t =1

i
i
( X m − X o )2

(5)

Xo

i
i
X m and X o are the modelled and observed
discharge/WSE at time ti while N is the number of

where

observations.

X o is the average of the observed values.

By varying the values of the roughness coefficient in
Equations 2 and 3, we obtained the optimum value of
0.035, which resulted in the minimum RMSE .
In addition, to quantitatively describe the accuracy of
model output, the Nash-‐‑Sutcliffe Coefficient (NSC) was
calculated as follows,
N

NSC = 1 −

i =1
N
i =1

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i
i
( X o −X m ) 2
i
( X o −X o ) 2

(6)

where, NSC is the Nash-‐‑Sutcliffe model efficiency
Coefficient. The error results including the minimum

RMSE and the corresponding NSC are reported in
Table 5.
Figure 4 compares the observed data for the discharge
(Figure 4a) and WSE (Figure 4b) at SWA with the
modelling results. Figures 5a and 5b compare observed
WSE at SDP and at EBM, respectively, with the modelling
results. The results obtained from the hydrodynamic
model were generally found to be consistent with the
observed data and found to reasonably describe both the
WSE and the discharge at the observing stations. While
the WSE values (Figures 4b, 5a and 5b) were simulated
fairly accurately, simulating the discharge was relatively
challenging due to the lack of discharge data for several
minor tributaries along the river in the study area. The
water surface elevation abruptly dropped from 93 ft
(28.35 m) to 57 ft (17.37 m) and then rose up to 117 ft
(35.66 m) between days 22 and 35 at Station EBM in
Figure 5; these results appear to represent equipment
malfunction or error. The water surface elevation (WSE)
fluctuation of more than 50 ft (15.24 m) during these days
was not reflected by the nearest functional gauge stations
(see Figure 4b for upstream at SWA and Figure 3b for
downstream at FFB).


7

SJR Discharge at SWA

Discharge (cfs)

4000

(a)

observed
modeling

2000

0

0

20

40

60

80

100

120

140

160

180

200

140

160

180

200

SJR WSE at SWA

WSE (ft)

120
observed
modeling

110
100
90

0

20

40

60

80

100

120

Julian days, 2011
Figure 4. Comparison of observed and modelling results of: (a) San Joaquin River (SJR) discharge at the SJR near Washington Rd (SWA);
and (b) SJR Water Surface Elevation (WSE) at SWA. (1ft = 0.3048 m, 1 cfs = 0.0283 cms)

SJR WSE at SDP

WSE (ft)

130
120
110
100

observed
modeling

(a)

90
120

130

140

150

160

170

180

190

200

SJR WSE at EBM

WSE (ft)

120
100
80
60

observed
modeling

(b)
0

20

40

60

80

100

120

140

160

180

200

Julian days, 2011
Figure 5. Comparison of observed and modelling results for: (a) San Joaquin River (SJR) Water Surface Elevation (WSE) at the SJR near
Dos Palos (SDP); and (b) SJR WSE at Eastside Bypass below Mariposa Bypass (EBM). (1ft = 0.3048 m)

The output from the validated and calibrated model was
used to assess the habitat suitability of the river channel
for the spring Chinook salmon run. Historically, there
were four distinct salmon runs in the Sacramento-‐‑San
Joaquin River system, designated according to the season
in which the majority of the run entered the freshwater as
adults [27]. The spring-‐‑run Chinook salmon entered the
water system from late March through September, with
adults staying in cool water habitats through the summer
8


and then spawning in the autumn from mid-‐‑August
through early October. For this run, therefore, the
hydrodynamic scenario in the summer season is
especially critical for the salmon migrating from the
ocean to upstream spawning grounds. In this research,
the hydrodynamic model simulated water depth and
velocity between late March and late June (between day
90 and day 181 of the simulation period) of 2011 and the
corresponding habitat suitability for salmon was
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quantified using the habitat Suitability Index (SI) [27].
Figures 6a and 6b were developed by the California
Department of Fish and Wildlife (CADFW) [28, 29] and
show the standard habitat SI for Chinook salmon for
velocity (Velocity SI) and depth (Depth SI), respectively.
The range of the dimensionless SI at any location in a river
is between 1 and 0, representing the best and the worst
habitat quality, respectively. To align with the standard

convention in the literature, metric units were used for the
SI calculations, so velocities between 12.2 cm/s and 21.3
cm/s and depths between 30.5 cm and 61 cm constitute the
best ranges for Chinook salmon (Figure 6). The best
velocities in this method all support cruising velocity,
which is consistent with the literature (Table 4). Figures 6a
and 6b show that the best velocity ranges of velocity and
depth are 12 – 22 cm/s and 35 – 60 cm, respectively.

1.2

(a)

1.0

SI

0.8
0.6
0.4
0.2
0.0

0

10

20

30

40

50

60

70

80

90

100

Velocity (cm/s)
1.2

(b)

1.0

SI

0.8
0.6
0.4
0.2
0.0

0

20

40

60

80

100

120

140

160

180

200

Depth (cm)

Velocity WAHSI

Figure 6. Suitability Index (SI) curves for Chinook salmon: (a) Velocity; and (b) Depth suitability (By California Department of Fish and
Wildlife (CADFW) [28]).

1.0
0.8
0.6

(a)

Alternative 1
Alternative 2
Alternavite 3

0.4
0.2
0.0
80

100

120

140

160

180

Depth WAHSI

1.0
0.8
0.6

(b)

Alternative 1
Alternative 2
Alternavite 3

0.4
0.2
0.0
80

Overall WAHSI

200

100

120

140

160

180

2.0
1.6
1.2

200
(c)

Alternative 1
Alternative 2
Alternavite 3

0.8
0.4
0.0
80

100

120

140

160

180

200

Julian days, 2011

Figure 7. Model Weighted Area Habitat Suitability Index (WAHSI) for three alternatives for: (a) Velocity suitability; (b) Depth suitability;
and (c) Overall suitability.
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9

The representative values of velocity and depth for each
element were the values at its centre, which were calculated
by interpolating the values at all nodes of the element to the
centre using Inverse Distance Weighted method (IDW). The
calculated velocity and depth for each element were used for
determining its SIs at different times using Figures 6a and
6b. The values of velocity SI, depth SI and the overall SI
(velocity SI +depth SI) for the entire domain under
investigation can be calculated using the following weighted
average habitat suitability index ( WAHSI ),
M

WAHSI j =

i =1

( SI i , j ⋅ ∆Ai )
M
i =1

∆Ai

(7)

j =1 for velocity, 2 for depth and 3 for the
combined WAHSI for velocity and depth; M is the
where

total number of wetted finite elements; and A is the area
of element.

Figures 7a, 7b and 7c show the time variation of WAHSI
values derived from the velocity SI, depth SI and the overall
SI, respectively, for all three of the proposed alternatives. In
the late spring (day 90) and early summer (day 181), neither
velocity (with WAHSI around 0.3) nor depth (with WAHSI
around 0.1) was deemed suitable for salmon migration.
Under the conditions obtaining in the summer of 2011, the
SIs of all the proposed alternatives increased from Day 90 to
Day 145, then maintained these peak values for about 30
days. After this point, the hydrodynamic conditions for
salmon fluctuate and deteriorate, so the period between
mid-‐‑May and mid-‐‑June of that year would have been the
best period for Chinook salmon migration. Generally, the
impact of velocity is more stable than that of depth. Among
the three proposed alternatives, the WAHSI values of
Alternatives 2 and 3 were generally equal to or higher than
those of Alternative 1, which incorporates the Eastside
Bypass. The similar shapes of the depth (Figure 7b) and
overall (Figure 7c) WAHSIs indicate that the overall WAHSI
in this case is controlled by water depth, which was thus
more critical for aquatic life than the velocity under the
insufficient discharge conditions experienced during the
modelling period.

Eastside Bypass

Eastside Bypass
4B1

SWA

SWA

1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

Eastside Bypass

Eastside Bypass
SWA

(d) Depth SI for Alternative 1

1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

(c) Velocity SI for Alternative 3

(b) Velocity SI for Alternative 2

(a) Velocity SI for Alternative 1

SWA

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

4B1

SWA

(e) Depth SI for Alternative 2

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

SWA

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

(f) Depth SI for Alternative 3

Figure 8. Spatial distribution of Suitability Index (SI) in the region at the SJR near Washington Rd (SWA) at day 130 for: (a) Velocity SI
for Alternative 1; (b) Velocity SI for Alternative 2; (c) Velocity SI for Alternative 3; (d) Depth SI for Alternative 1; (e) Depth SI for
Alternative 2; and (f) Depth SI for Alternative 3.
10 Int. j. water sci., 2013, Vol. 2, 5:2013

www.intechopen.com

Eastside Bypass
SWA

Eastside Bypass
4B1
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

SWA

1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

Eastside Bypass

Eastside Bypass
SWA

(d) Depth SI for Alternative 1

1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30

(c) Velocity SI for Alternative 3

(b) Velocity SI for Alternative 2

(a) Velocity SI for Alternative 1

SWA

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

4B1

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

SWA

(e) Depth SI for Alternative 2

SWA

0.20
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

(f) Depth SI for Alternative 3

Figure 9. Spatial distribution of Suitability Index (SI) in the region at the SJR near Washington Rd (SWA) at day 170 for: (a) Velocity SI
for Alternative 1; (b) Velocity SI for Alternative 2; (c) Velocity SI for Alternative 3; (d) Depth SI for Alternative 1; (e) Depth SI for
Alternative 2; and (f) Depth SI for Alternative 3.

Since the SWA confluence region (Figure 2) is common to
all three alternative flow paths, it was used to compare
the spatial distributions of the SIs at specific times. Figure
8 (a through f) shows the distribution of SI in the SWA
confluence region on Day 130, when SI started to rise, for
velocity SI (Figures 8a, 8c and 8e for Alternatives 1, 2 and
3 respectively) and for depth SI (Figures 8b, 8d and 8f for
Alternatives 1, 2 and 3 respectively). Figure 9 shows the
corresponding distributions on day 170, when the SIs
started to fall near the end of the most suitable period. All
SIs generally increased over the period from Day 130 to
Day 170. Figure 10 shows the corresponding velocity
vectors and depth distributions at day 130. Figures 8 and
9 show the significant improvement of the SIs for all three
alternatives during the period. The areas with higher SIs
increased in both velocity SIs and depth SIs. Most
locations in the river reach on day 170 have higher

velocity SIs (greater than 0.6) than those on day 130. The
improvement of the depth SI was not as significant as that
of the velocity SI. Figures 8 and 9 show an improvement
of 0.12 -‐‑ 0.2 for depth SI and 0.2 – 0.4 for velocity SI in
many regions during this period. These observations
were consistent with Figure 7.

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Interestingly, there is some similarity between the time
variation trend for the boundary conditions (Figure 3)
and that of the WAHSIs (Figure 7) during the salmon
migration period between Day 90 and Day 180, with an
expected lag time. For example, the peak values of the
discharge at SDP and the WSE at FFB occurred at around
Day 100 and Day 87, respectively. To better understand
how the boundary conditions impact salmon migration
and thus predict the suitability for salmon migration
(WAHSI) based on the upstream incoming flow or

11

downstream WSE, it is necessary to identify any cross-‐‑
correlations. The normalized cross-‐‑correlation between
discharge or WSE and WAHSI was defined as follows [30]:
N −k

NCC =

meanwhile w(i ) and

u (i ) are the WAHSI and discharge
or WSE at the time step, respectively; i is the number of
model data points; and n is the number of lag time steps

u (n + k ) w(n)

n =1
N
i =1

[w(i)]2 ⋅

N
i =1

where NCC is the normalized cross-‐‑correlation
function and has a value between -‐‑1 and 1, with 0 being
completely unrelated and 1 or -‐‑1 highly correlated;

[u (i)]2

(8)

between two correlated parameters.

Eastside Bypass

Eastside Bypass
4B1

SWA
5.00 m
4.50 m
4.00 m
3.50 m
3.00 m
2.50 m
2.00 m
1.50 m
1.00 m
0.50 m

SWA

SWA

5.00 m
4.00 m
3.50 m
3.00 m
2.50 m
2.00 m
1.50 m
1.00 m
0.50 m

5.00 m
4.50 m
4.00 m
3.50 m
3.00 m
2.50 m
2.00 m
1.50 m
1.00 m
0.50 m

(b) Depth for Alternative 2

(a) Depth for Alternative 1

(c) Depth for Alternative 3
Eastside Bypass

Eastside Bypass
4B1

SWA

SWA

SWA

100 cm/s

(d) Velocity vector for Alternative 1

100 cm/s

100 cm/s

(f) Velocity vector for Alternative 3

(e) Velocity vector for Alternative 2

Figure 10. Spatial distribution of depth and velocity vector in the region at the SJR near Washington Rd (SWA) at day 130 for: (a) Depth
for Alternative 1; (b) Depth for Alternative 2; (c) Depth for Alternative 3; (d) Velocity vector for Alternative 1; (e) Velocity vector for
Alternative 2; and (f) Velocity vector for Alternative 3.

Parameter

Upstream Discharge (SDP)
Velocity
Depth
Overall

Downstream WSE (FFB)
Velocity
Depth
Overall

NCC

0.834

0.895

0.855

0.926

0.765

0.895

Lag Time (days)

-‐‑50.7

-‐‑47.6

-‐‑47.8(53)

0.0

0.0

0.0

Table 6. Maximum and corresponding lag time for three alternatives


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NNC (Velocity)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(a)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

NNC (Depth)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(b)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

NNC (Overall)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(c)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

Lag time (Hours)
Figure 11. Correlations between upstream discharge and Model Weighted Area Habitat Suitability Index (WAHSI) for the three
alternatives for: (a) Velocity WAHSI; (b) Depth WAHSI; and (c) Overall WAHSI

NNC (Velocity)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(a)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

NNC (Depth)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(b)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

NNC (Overall)

1
Alternative 1
Alternative 2
Alternative 3

0.8
0.6
0.4
0.2
(c)
0
−2500 −2000

−1500

−1000

−500

0

500

1000

1500

2000

2500

Lag time (Hours)
Figure 12. Correlations between downstream Water Surface Elevation (WSE) and Weighted Area Habitat Suitability Index (WAHSI) of
three alternatives for: (a) Velocity WAHSI; (b) Depth WAHSI; and (c) Overall WAHSI.

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13

Figure 11 shows the correlations represented by the
different lag times between WAHSIs (Figures 11a, 11b,
11c for velocity, depth and the overall WAHSI,
respectively) and the discharge boundary condition
(incoming flow). The figures demonstrate fairly similar
correlations for each of the three alternatives. The values
for the best correlations and their corresponding lag times
are listed in Table 6. All the best values are greater than
0.8, indicating reasonably good correlations between the
upstream flow condition at SDP and the salmon habitat
suitability expressed by the WAHSI values. However, the
best correlations occur at a time lag of about 50 days (1200
hours) between these two parameters. For example, the
salmon habitat suitability based on velocity
considerations (represented by the velocity WAHSI) fully
responds to upstream discharges in about 50 days. The
second peak values (all less than 0.5) occurring near a
zero time lag represent only the local best values and are
not optimized correlations on a global scale.
Figure 12 shows the correlations represented by the

NCC between the WAHSI and the downstream WSE
values at FFB for different lag times. The velocity WAHSI
(Figure 12a) correlates better with downstream WSE,
exhibiting a higher value (0.926) than either the depth
WAHSI (= 0.765, Figure 12b) or the overall WAHSI (=
0.895, Figure 12c). All the best correlations are observed at
a zero lag time for each of the three alternatives. This
indicates almost synchronized responses between the
downstream WSE and the WAHSI values.
6. Conclusions
The two-‐‑dimensional hydrodynamic model using a finite
element scheme developed in this study reasonably
described the hydrodynamic conditions in the middle
reaches of the San Joaquin River (SJR). It can be used to
calculate the habitat suitability in terms of Suitability
Index (SI) for the spring Chinook salmon run within the
investigation domain of the SJR. Three proposed
alternatives for the San Joaquin River Restoration
Program (SJRRP) were compared based on both their
hydrodynamic and SI aspects. All three alternatives
showed similar SI distributions under the same boundary
conditions. Alternatives 2 and 3 produced higher overall
Weighted Area Habitat Suitability Index (WAHSI) values
than Alternative 1, indicating that these alternatives could
lead to a better environment for salmon migration. There
exist fair correlations between the WAHSI values and the
boundary conditions. The lag time that produced the best
correlation between salmon habitat suitability and
upstream discharge was around 50 days based on the
cross-‐‑correlation calculations. The WAHSI and the
downstream Water Surface Elevation (WSE) values
change synchronically. This study demonstrates that the
boundary conditions may help predict habitat suitability

for salmon by using the hydrodynamic model for the SJR.
The modelling method, together with the correlation
results reported here, may provide a reference for similar
suitability studies of salmon habitat in other inland rivers.
7. Acknowledgements
The observed data, including the discharge, water surface
elevation and bathymetry data, used in this paper for
model validation and calibration were provided by the
California Department of Water Resources, the U.S.
Geological Survey (USGS) and the U.S. Bureau of
Reclamation (USBR), respectively. Special thanks go to
our colleague, Dr John Suen of the Department of Earth
and Environmental Sciences of California State
University, Fresno, whose help in reviewing the
manuscript and the many stimulating exchanges we have
enjoyed during the course of this project have greatly
improved the outcome.
8. References
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Management (2009) San Joaquin River Hydrological
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