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Susitna-Watana Hydroelectric Project Document
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Title:
Fluvial geomorphology modeling
SuWa 112
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Briefing and Technical Documents
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Susitna-Watana Hydroelectric Project document number 112
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[Anchorage, Alaska : Alaska Energy Authority, 2012]
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May 18, 2012
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Technical memorandum
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ii, 18 p.
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are posted online at http://www.arlis.org/resources/susitna-watana/
Fluvial Geomorphology Modeling
Susitna-Watana Hydroelectric Project
FERC No. 14241
Alaska Energy Authority
[Draft: 5/18/12]
Technical Memorandum
May 18, 2012
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page i AEA Review Draft: 5/18/12
TABLE OF CONTENTS
1. Introduction ........................................................................................................................1
2. Issues/Questions to be Addressed .....................................................................................1
2.1. Reach-Scale Issues .............................................................................................2
2.2. Local-Scale Issues ..............................................................................................2
2.3. Synthesis of Reach-Scale and Local-Scale Analyses ........................................3
3. Overall Modeling Approach .............................................................................................3
4. Selection of Hydraulic Models ..........................................................................................4
4.1. 1D Models ..........................................................................................................5
4.1.1. HEC-RAS ....................................................................................... 5
4.1.2. SRH-1D........................................................................................... 6
4.1.3. MIKE 11 ......................................................................................... 6
4.1.4. HEC-6T ........................................................................................... 6
4.1.5. 1D Model Selection Process and Initial Evaluation ....................... 7
4.2. 2D Models ..........................................................................................................8
4.2.1. SRH-2D........................................................................................... 8
4.2.2. ADH ................................................................................................ 9
4.2.3. MD_SWMS/SToRM ...................................................................... 9
4.2.4. MIKE 21 ....................................................................................... 10
4.2.5. 2D Model Selection Process and Initial Evaluation ..................... 10
4.3. Tributary Delta Model .....................................................................................11
5. Linkage/Interaction of Fluvial Geomorphology Modeling with Other Studies .........12
5.1. Flow Routing Study .........................................................................................12
5.2. Instream Flow Study ........................................................................................12
5.3. Riparian Instream Flow Study .........................................................................13
5.4. Ice Processes Study ..........................................................................................14
5.5. Fish Study ........................................................................................................15
6. Spatial and Temporal Considerations for Model Application ....................................15
6.1. Spatial Scale .....................................................................................................15
6.2. Model Time Scale ............................................................................................15
6.2.1. 1D Model ...................................................................................... 15
6.2.2. 2D Model ...................................................................................... 16
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page ii May 18, 2012
7. Assumptions, Limitations and Uncertainties ................................................................16
7.1. Limitations .......................................................................................................16
7.2. Uncertainties ....................................................................................................17
8. References .........................................................................................................................17
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 1 May 18, 2012
1. INTRODUCTION
This technical memorandum documents the ongoing development of the procedure for modeling
the fluvial geomorphology of the Susitna River below Watana Dam. The overall goal of the
study is to model the effects of the proposed Susitna-Watana Hydroelectric Project (Project) on
the fluvial geomorphology of the Susitna River. The results of this and other geomorphology
studies will be used in combination with geomorphic principles and criteria/thresholds defining
probable channel forms to predict the potential for alterations of channel morphology. The
purpose of this technical memorandum is to explain the proposed approach to the Susitna River
fluvial geomorphology modeling and provide an opportunity for stakeholders and other study
leads to provide feedback on modeling approach development to ensure that the needs of all
parties are being met, to the extent practical.
Specific topics covered include:
Issues/questions that need to be addressed,
Overall modeling approach,
Description of the considerations and selection process for the models,
Interaction/linkage of the fluvial geomorphology modeling with other studies and
models,
Spatial and temporal considerations for model application, and
Assumptions, limitations and uncertainties of the proposed modeling approach.
2. ISSUES/QUESTIONS TO BE ADDRESSED
The purpose of the fluvial geomorphology studies is to assess the potential impact of the Project
on the dynamic behavior of the river downstream of the proposed dam, with particular focus on
potential changes in instream and riparian habitat. Whether the existing channel morphology
will remain the same or at least be in “dynamic equilibrium” under post-Project conditions is a
significant question in any instream flow study (i.e., is the channel morphology in a state of
dynamic equilibrium such that the distribution of habitat conditions will be reflected by existing
channel morphology or will changes in morphology occur that will influence the relative
distribution or characteristics of aquatic habitat over the term of the license? [Bovee 1982]).
This key issue prompts four overall questions that must be addressed by the Geomorphology
Studies:
Is the system currently in a state of dynamic equilibrium?
If the system is not currently in a state of dynamic equilibrium what is the expected
evolution over the term of the license?
Will the Project affect the morphologic evolution of the Susitna River compared to pre-
Project conditions?
If the Project will alter the morphology of the river what are the expected changes over
the term of the license?
The methods and results from the Geomorphology Study and the Fluvial Geomorphology
Modeling Study will address these questions. To develop the modeling approach, specific issues
that need to be addressed have been identified. These specific issues have been further
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 2 May 18, 2012
differentiated into reach-scale and local-scale issues since the scale influences the proposed
approach.
2.1. Reach-Scale Issues
Reach-scale issues refer to aspects of the system that involve the overall behavior and general
characteristics of the Susitna River over many miles. Each reach represents a spatial extent of the
Susitna River that has a consistent set of fluvial geomorphic characteristics. Reach-scale issues
include:
Historical changes in the system and the existing status with respect to dynamic
equilibrium.
Changes in both the bed material (sand and coarser sizes) and wash load (fine sediment)
sediment supply to the system due to trapping in Watana Reservoir.
Long-term balance between sediment supply and transport capacity and the resulting
aggradation/degradation response of the system for pre- and post-Project conditions.
Changes in bed material mobility in terms of size and frequency of substrate mobilized
due to alteration of the magnitude and duration of peak flows by the Project.
Project-induced changes in supply and transport of finer sediments that influence
turbidity.
Potential for changes in channel dimensions (i.e., width and depth) and channel pattern
(i.e., braiding versus single-thread or multiple-thread with static islands) due to the
Project and the magnitude of the potential change.
Project-induced changes in river stage due to reach-scale changes in bed profile, channel
dimensions, and potentially hydraulic roughness.
2.2. Local-Scale Issues
Local-scale issues refer to aspects of the system that involve the specific behavior and
characteristics of the Susitna River at a scale associated with specific geomorphic and habitat
features. Local-scale issues are addressed using a more detailed assessment over a smaller spatial
area; however, these analyses must draw from and build upon the understanding and
characterization of the system behavior as determined at the reach scale. Local-scale issues
include:
Processes responsible for formation and maintenance of the individual geomorphic
features and associated habitat types.
Potential changes in geomorphic features and associated aquatic habitat types that may
result from effects of Project operation on riparian vegetation and ice processes.
Effects of changes in flow regime and sediment supply on substrate characteristics in
lateral habitat units.
Changes in upstream connectivity (breaching) of lateral habitats due to alteration of flow
regime and possibly channel aggradation/degradation. These changes may induce further
changes in the morphology of lateral habitats, including:
Potential for accumulation of sediments at the mouth.
Potential for accumulation of fines supplied during backwater connection with the
main stem.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 3 May 18, 2012
Potential for changes in riparian vegetation that could alter the width of lateral
habitat units.
Project effects at representative sites on the magnitude, frequency and spatial distribution
of hydraulic conditions that control bed mobilization, sediment transport, sediment
deposition and bank erosion.
Potential for change in patterns of bed load deposits at tributary mouths that may alter
tributary access or tributary confluence habitat.
2.3. Synthesis of Reach-Scale and Local-Scale Analyses
The final step in the effort will be the synthesis of the reach-scale and local-scale analyses to
identify potential Project-induced changes in the relative occurrence of aquatic habitat types and
associated surface area versus flow relationships. In addition to the results of the hydraulic and
sediment transport modeling, this synthesis will require application of fluvial geomorphic
relationships to develop a comprehensive and defensible assessment of potential Project effects.
Examples of this type of integrated analysis that have been successfully performed by the project
team include instream flow, habitat and recreation flow assessments to support relicensing of
Slab Creek Dam in California; a broad range of integrated geomorphic assessments and
modeling to assist the Platte River Recovery Implementation Program in Central Nebraska; and
ongoing work to support the California Department of Water Resources and Bureau of
Reclamation to design restoration measures for the San Joaquin River in the Central Valley of
California downstream of Friant Dam.
3. OVERALL MODELING APPROACH
The proposed modeling approach considers the need to address both reach-scale and local-scale
assessments and the practicality of developing and applying various models based on data
collection needs, computational time, analysis effort and model limitations. Based on these
considerations, an approach that uses one-dimensional (1D) models to address reach-scale issues
and two-dimensional (2D) models to address local-scale issues is proposed. Considering the
broad physical expanse of the Susitna River system, the general hydraulic and sediment transport
characteristics of the various subreaches that make up the overall study area will be evaluated
using 1D computer models and/or established hydraulic relationships. The 2D models will be
used to evaluate the detailed hydraulic and sediment transport characteristics on smaller, more
local scales where it is necessary to consider the more complex flow patterns to understand and
quantify the issue(s). The 2D models will be applied to specific detailed study sites that are
representative of important habitat conditions and the various channel classification types. These
sites will be chosen in coordination with the Instream Flow, Riparian Instream Flow, Ice
Processes and Fish studies to facilitate maximum integration of available information between
the studies.
The proposed approach to integrating 1D modeling at the reach-scale and 2D modeling at the
local–scale will provide the following advantages:
1D modeling will allow for efficient assessment of the hydraulic conditions and sediment
transport balance over the length of the study reach downstream of Watana Dam.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 4 May 18, 2012
The 1D model uses cross-sectional data that are being obtained as part of the Flow
Routing and Instream Flow studies. (Note that some supplemental cross sections may be
required for the 1D sediment transport model.)
The 1D model will provide the boundary conditions for the 2D model, including starting
water-surface elevations and upstream sediment supply.
2D modeling applied at the detailed study sites that are also chosen for the Ice Processes
and Riparian Instream Flow studies will allow for the fullest level of integration of these
efforts, particularly as they relate to assessments of potential changes in channel with and
pattern for this study.
2D modeling at the detailed study sites will provide an understanding of the hydraulic
conditions and sediment transport processes that contribute to formation of individual
habitat types.
2D modeling provides a much more detailed and accurate representation of the complex
hydraulic interaction between the main channel and the lateral habitats than is possible
with a 1D model.
A comparison of the capabilities of 1D and 2D models is provided in Table 3.1.
Table 3.1. 1D versus 2D Model Capabilities
Consideration 1D Models 2D Models
Sediment Balance Reach-scale Local-scale
Aggradation/degradation response Reach-scale Local-scale
Changes in bed material gradation Reach-scale Local-scale
Sediment accumulation at slough mouths / localized deposition X
Bed material mobilization X X
Flushing of fines from side slough habitats X
Complex flows in floodplain and potential erosion X
Frequency and duration of overbank flooding Reach-scale Local-scale
Distribution of flow and flow patterns between channel features X
Transverse hydraulic gradients X
Bed deformation X
4. SELECTION OF HYDRAULIC MODELS
Many computer programs are available for performing movable boundary sediment transport
simulations. The choice of an appropriate model for this study depends on a number of factors,
including (1) the level of detail required to meet the overall project objective, (2) the class, type
and regime of flows that must be modeled, (3) characteristics of the bed material and wash load
and (4) data necessary for model development and calibration. In addition, because of the wide
range of sediment sizes present in the Susitna River, both the 1D and 2D models must be capable
of routing sediment by size fractions, and ideally be capable of addressing deposition of fine
sediments (wash load). A variety of candidate models will be evaluated for application on the
Susitna River. Potential candidate models for the 1D and 2D portions of the study are discussed
below.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 5 May 18, 2012
4.1. 1D Models
Most 1D movable boundary sediment transport models are designed to simulate changes in the
cross-sectional geometry and river profile due to scour and deposition over relatively long time
periods. In most cases, the flow record of interest is divided into a quasi-unsteady sequence of
steady flows of variable discharge and duration; although some models include the capability to
perform unsteady sediment transport simulations. For large rivers such as the Susitna, the
unsteady aspect for sediment transport is probably not significant because the time scale of
typical transport changes is much longer than the time scale for changes in the flows that drive
the hydraulic conditions. In quasi-unsteady modeling the water-surface profile at each cross
section is calculated for each time-step and corresponding discharge using the step-backwater
computational procedure. The associated energy slope, velocity, depth and other hydraulic
variables along with the input bed material characteristics are used to calculate the sediment
transport capacity. The aggradation or degradation volume is computed by comparing the
transport capacity with the upstream sediment supply (i.e., the supply from the next upstream
cross section for locations not identified as an upstream boundary condition). The resulting
aggradation/degradation volume is then applied over the cross-section control volume (i.e., the
sub-channel concept) and the shape of the cross section is adjusted accordingly. Because the
sediment transport calculations are performed by size fraction the models are capable of
simulating bed-material sorting and armoring. The computations then proceed to the next time-
step and the calculations are repeated using the updated cross sections and bed-material
gradations.
1D sediment transport models have limitations. They should not be applied to situations where
2D and 3-dimensional (3D) flow conditions control the sediment transport characteristics of
interest. The models do not consider secondary currents, transverse sediment movement, lateral
variations in transport rates, turbulence and lateral diffusion; thus, the models cannot simulate
such phenomena as point bar formation, pool-riffle formation, and planform changes such as
river meandering or local bank erosion. The models typically distribute the volume of
aggradation or degradation across the entire wetted portion of the channel cross section after
each time-step; thus, the effects of channel braiding are not directly considered. In spite of these
limitations, 1D models are appropriate for efficiently evaluating the general sediment-transport
characteristics and 1D channel dynamics, including the overall sediment transport balance at the
reach-scale. 1D models also provide boundary conditions for the more localized 2D models.
1D models that are being considered for this study include the widely-used U. S. Army Corps of
Engineers (USACE) HEC-RAS (version 4.1; USACE 2010a), the Bureau of Reclamations SRH-
1D (version 2.8; USBR 2011), DHIs MIKE 11 (version 2011; DHI 2011), and Mobile Boundary
Hydraulics HEC-6T (version 5.13.22_08; MBH 2008). A summary of each of these models
including potential benefits and limitations is provided in Table 4.1 and the following sections.
4.1.1. HEC-RAS
HEC-RAS, version 4.1.0 (USACE 2010a) is a publicly available and widely-used software
package developed by USACE to perform steady-flow water-surface profile computations,
unsteady flow simulations, movable boundary sediment-transport computations and water
quality analysis. HEC-RAS includes a Windows-based graphical user interface that provides
functionality for file management, data entry and editing, river analyses, tabulation and graphical
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 6 May 18, 2012
displays of input/output data, and reporting facilities. The sediment transport module is capable
of performing sediment-transport and movable boundary calculations resulting from scour and
deposition over moderate time periods and uses the same general computational procedures that
were the basis of the HEC-6 (USACE 1993) and HEC-6T models (Mobile Boundary Hydraulics
2008). In HEC-RAS, the sediment-transport potential is calculated by grain size fraction which
allows for simulation of hydraulic sorting and armoring. This model is designed to simulate
long-term trends of scour and deposition in stream and river channels that could result from
modifications to the frequency and duration of the water discharge and stage, upstream and
tributary sediment supply and channel geometry. Benefits of the HEC-RAS software include
widespread industry acceptance, public availability and ease of use. Potential limitations of the
program for sediment-transport simulations include excessive computer run-times, file-size
output limitation, and the inherent problems associated with 1D modeling of aggradation and
degradation that results from the algorithm used to distribute the changes in sediment volume
across the cross section (in this case, the assumption of equal adjustment at all points along the
wetted portion of the bed).
4.1.2. SRH-1D
SRH-1D (Huang and Greimann 2011) is a mobile boundary hydraulic and sediment transport
computer model for open channels that is capable of simulating steady or unsteady flow
conditions, internal boundary conditions, looped river networks, cohesive and non-cohesive
sediment transport (Ruark et al. 2011), and lateral inflows. The hydraulic and sediment transport
algorithms in SRH-1D are similar to those in HEC-RAS 4.1 and HEC-6T except that it also
includes the capability to perform fully-unsteady sediment transport simulations. Advantages of
SRH-1D include robust algorithms for hydraulic conditions and sediment routing, including
sediment sorting. Potential disadvantages include limited testing under a broad range of
conditions outside the Bureau of Reclamation and the lack of graphical user interface that
complicates data input and manipulation and display of output.
4.1.3. MIKE 11
Danish Hydraulic Institute’s (DHI) MIKE 11 is a proprietary software package developed for 1D
dynamic modeling of rivers, watersheds, morphology and water quality. The model has the
ability to solve the complete non-linear St. Venant equations (in only the streamwise direction)
for open channel flow, so the model can be applied to any flow regime. MIKE 11 provides the
choice of diffusive and kinematic wave approximation and performs simplified channel routing
using either the Muskingum or Muskingum-Cunge methods. The program includes a module for
simulating erosion and deposition of non-cohesive sediments. Advantages of MIKE 11 include
its robust hydrodynamic capabilities (though not necessarily better than HEC-RAS), the user-
friendly graphical interface and the reporting and presentation capabilities. Disadvantages
primarily stem from the proprietary nature of this model and high cost of the software license.
4.1.4. HEC-6T
HEC-6T was written by William A. Thomas, former Chief of the Research Branch at the
USACE Hydrologic Engineering Center (HEC). Mr. Thomas planned, designed, wrote and
applied the publically available version of HEC-6; HEC-6T is a proprietary enhancement of the
original version. HEC-6T is a DOS-based program that includes a Windows-based graphical
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 7 May 18, 2012
user interface for input data manipulation and post-processing of simulation results. Limitations
of this program include reduced capabilities for modeling numerous ineffective flow areas as
compared to HEC-RAS 4.1 and limited capabilities of the graphical user interface. This software
is relatively inexpensive: the fact that it is proprietary is not a significant limitation.
4.1.5. 1D Model Selection Process and Initial Evaluation
Based on the above information and experience the Geomorphology Study team has with these
models, the Geomorphology Study team tentatively proposes to use HEC-6T for the reach-scale
sediment transport analysis. This proposal is based on confidence gained through previous
studies that HEC-6T is capable of effectively and efficiently modeling the processes that are
important for this scale of geomorphic analysis. The selection of the 1D (as well as the 2D)
model will be coordinated with the other pertinent studies and the stakeholders. This technical
memorandum is part of the coordination process. Specific model-selection criteria are identified
in Table 4.1 along with an evaluation of each candidate model relative to the criteria.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 8 May 18, 2012
Table 4.1. Evaluation of 1D Models
Evaluation Criteria Models
HEC-RAS SRH-1D MIKE 11 HEC-6T
General
Proprietary/cost No No Currently
Investigating $3000
Full or quasi unsteady for sediment
transport simulation Quasi Both Currently
Investigating Quasi
Ice for fixed bed Yes No Currently
Investigating No
Ice for moveable bed Currently
Investigating No Currently
Investigating No
Number of transport equations supported 7 13 10 18
Supports user defined transport equation No No Currently
Investigating Yes
Closed loop capability Not Currently Yes Yes Yes
Experience with model High Limited Limited High
Model Size Limitations
# of cross sections No limit No limit No limit 5000
# of hydrograph ordinates 40000 Not indicated Currently
Investigating No Limit
# of sediment sizes 20 Not indicated Currently
Investigating 20
Sediment Sizes Supported
Wash load (silts, clays) Yes Yes Yes Yes
Considers settling and resuspension Yes Yes Yes Yes
Sand Yes Yes Yes Yes
Gravel and cobble Yes Yes Yes Yes
4.2. 2D Models
Potential 2D models that are being considered for this study include the Bureau of Reclamation’s
SRH2-D (version 3 [Lai 2008; Greimann and Lai 2008]), USACE’s Adaptive Hydraulics (ADH
version 3.3 [USACE 2010b]), the U.S. Geological Survey’s (USGS’s) MD_SWMS (McDonald
et al. 2005), and DHIs MIKE 21 (version 2011 [DHI 2011]).
4.2.1. SRH-2D
The Bureau of Reclamation’s SRH-2D (Lai 2008) is a finite-volume, hydrodynamic model that
computes water-surface elevations and horizontal velocity components by solving the depth-
averaged St. Venant equations for free-surface flows in 2D flow fields. SRH-2D is a well-tested
2D model that can effectively simulate steady or unsteady flows and is capable of modeling
subcritical, transcritical and supercritical flow conditions. The model uses an unstructured
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 9 May 18, 2012
arbitrarily shaped mesh composed of a combination of triangular and quadrilateral elements.
SRH-2D incorporates very robust and stable numerical schemes with a seamless wetting-drying
algorithm that results in minimal requirements by the user to adjust input parameters during the
solution process. A potential limitation of this software is that the mobile bed sediment transport
module is currently not publically available; however, Tetra Tech has gained permission to use
the sediment transport module on a number of other projects. Preliminary contact with the
model developers indicates that permission would be granted for use in this study. This version
of the model (Greimann and Lai 2008) includes a “Morphology” module that calculates bed load
transport capacities at each model node based on user defined bed material sediment gradations
but does not simulate routing of that sediment and related adjustments to the channel bed. SRH-
2D also includes a second module that uses the capacities from the Morphology module to
perform sediment-routing calculations and associated bed adjustments. Based on guidance from
the model developers and confirmed by Tetra Tech’s use of the model for other studies, the
maximum practical model size is about 16,000 elements, which could be a potential limitation in
applying the model to larger-scale areas.
4.2.2. ADH
The USACE ADH program was developed by the Coastal and Hydraulics Laboratory (Engineer
Research Development Center) to model saturated and unsaturated groundwater, overland flow,
3D Navier-Stokes flow, and 2D or 3D shallow-water, open-channel flow conditions. ADH is a
depth-averaged, finite-element hydrodynamic model that has the ability to compute water-
surface elevations, horizontal velocity components and sediment transport characteristics
(including simulations to predict aggradation and degradation) for subcritical and supercritical
free-surface flows in 2D flow fields. The ADH mesh is composed of triangular elements with
corner nodes that represent the geometry of the modeled reach with the channel topography
represented by bed elevations assigned to each node in the mesh. A particular advantage of the
ADH mesh is the ability to increase the resolution of the mesh—and thereby the model
accuracy—by decreasing the size of the elements during a simulation in order to better predict
the hydraulic conditions in areas of high hydraulic variability. However, use of the adaptive
mesh option often results in excessively long simulation run times (several days per run) that
could be impractical for this study. Additionally, the wetting and drying algorithm in this model
has significant numerical stability limitations when applied to shallow, near-shore flows that
occur in rivers like the Susitna River. The model is publically available.
4.2.3. MD_SWMS/SToRM
The USGS Multi-Dimensional Surface-Water Modeling System (MD_SWMS; McDonald et al.
2005) is a pre- and post-processing application for computational models of surface-water
hydraulics. The system provides a graphical user interface (GUI) that allows the modeler to
build and edit data sets. MD_SWMS also provides a framework that links the GUI with the
modeling applications. The GUI is an interactive 1D, 2D and 3D tool that can be used to build
and visualize all aspects of computational surface-water applications, including grid building,
development of boundary conditions, simulation execution and post-processing of the simulation
results. The package includes a number of different modeling applications including SToRM
(System for Transport and River Modeling). SToRM uses an unstructured triangular mesh and
provides both steady-flow and unsteady-flow capability. The model blends some of the features
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 10 May 18, 2012
of finite volumes and finite elements, and uses multi-dimensional streamline upwinding methods
and a dynamic wetting and drying algorithm that allows for the computation of flooding.
Subcritical, supercritical and transcritical flow regimes (including hydraulic jumps) can be
simulated. The program includes advanced turbulence models, sediment transport algorithms for
cohesive and non-cohesive sediment mixtures, transport of suspended and dissolved substances
and an automatic mesh refinement tool to better predict the h ydraulic conditions in areas of high
hydraulic variability.
MD_SWMS has been successfully applied to a number of rivers in Alaska, including the Tanana
River near Tok (Conaway and Moran 2004) and the Copper River near Cordova (Brabets 1997);
some of the modules are currently being validated using high-resolution scour data from the
Knik River near Palmer.
4.2.4. MIKE 21
Developed by DHI, MIKE 21 is a proprietary modeling system for 2D free-surface flows that
can be applied in rivers, lakes, coastal and ocean environments. It has the ability to simulate
sediment transport and associated erosion and deposition patterns. The software includes a
Windows-based GUI as well as pre- and post-processing modules for use in data preparation,
analysis of simulation results and reporting modules that have graphical presentation capabilities.
MIKE 21 has the ability to model a range of 2D mesh types that include Single Grid, Multiple
Grid, Flexible Mesh, and Curvilinear Grid. The primary limitation to MIKE-21 is that is
proprietary software and is relatively expensive as compared to other available software.
4.2.5. 2D Model Selection Process and Initial Evaluation
The selection of the 2D will be coordinated with the other pertinent studies and the stakeholders.
This technical memorandum is part of the coordination process. Specific model selection criteria
are identified in Table 4.2 along with an evaluation of each candidate model relative to the
criteria.
Table 4.2. Evaluation of 2D models
Evaluation Criteria Models
SRH-2D ADH MD_SWMS/SToRM MIKE 21
General
Proprietary/cost No No No Currently
Investigating
Unsteady flow capability Yes Yes Yes Yes
Ice for fixed bed No No No No
Ice for moveable bed No No No No
Number of transport equations supported 13 2 Currently Investigating 10
Supports user defined transport equation No Yes Currently Investigating Currently
Investigating
Relative execution speed Fast Slow Currently Investigating Fast
Model stability High Moderate Currently Investigating Currently
Investigating
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 11 May 18, 2012
Experience with model High High Limited Limited
Moveable boundary simulation Yes Yes Yes Yes
Grid Structure/Model Formulation
Finite element (FE)/Finite Volume (FV) FV FE FV/FE FV/FE
Grid structure Flexible mesh Flexible Mesh Flexible Mesh Currently
Investigating
Model Size Limitations
# of grid elements 16000 Unlimited Currently Investigating Unlimited
Sediment Sizes Supported
Wash load (silts, clays) No Yes Yes Yes
Considers settling No Yes Yes Yes
Sand Yes Yes Yes Yes
Gravel and cobble Yes Yes Yes Yes
4.3. Tributary Delta Model
Tributary confluences are areas of interest for determining the potential Project effects on
sediment transport and morphology. Alternation of mainstem flow regime has the potential to
change the elevation at which tributary sediments are initially deposited since the main stem may
be at a different stage when the tributaries are at peak flow. Additionally, the ability to mobilize
and transport bed load delivered by tributaries may also be altered. Changes in the configuration
of sediments deposited at the tributary confluences can affect the ability of fish to access the
tributaries and the extent of clear water habitat associated with some tributary confluences.
Modeling sediment transport and deposition processes at select tributary mouths will therefore be
necessary.
The tributaries to be modeled will be determined in conjunction with AEA, the Instream Flow
and Fish studies and the stakeholders based on fish use and the potential for Project effects. The
Geomorphology Study team tentatively proposed modeling a subset of tributary confluences
with the Susitna River that represent the range of conditions among all of the tributaries.
Modeling of the larger tributary confluences, such as the Talkeetna, Chulitna and the Yentna is
not anticipated because it would require relatively large-scale 2D modeling and a large
commitment of resources that would detract from the studies in more critical areas. If issues are
ultimately identified that require modeling of these areas a plan will be developed at that time.
It is currently proposed that a model will be created for the tributary deltas that uses estimated
bed load transport from the tributary, the topography and the bathymetry of the confluence,
measurements of the characteristics of the tributary deposits, and the ability of the main stem in
the area of the confluence to mobilize and transport those deposits. The approach will include
field observations to characterize the sediment transport regime that will be used to identify
appropriate methods of estimating bed load transport. Surveys of tributary channel geometry and
sampling of bed material gradations will be coupled with an appropriate bed material transport
function to calculate sediment yield rating curves. Hydrology synthesized for ungaged
tributaries will be needed from other studies for each of the selected tributaries for this purpose.
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Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 12 May 18, 2012
The yield and topography in the area of the expected delta along with the ability of the main stem
to mobilize and transport the bed material will provide a basis for characterizing how Project
operations would affect the formation of tributary deposits. At this time, it is envisioned that a
relatively detailed 1D hydraulic model of the main stem in the vicinity of each tributary will
provide sufficient hydraulic information to evaluate the potential for, and likely extent of,
additional growth of the tributary deposits into the mainstem. For complex tributary
confluences that are of particular interest to the instream flow studies, local-scale 2D models can
be developed and applied to support the analysis.
5. LINKAGE/INTERACTION OF FLUVIAL GEOMORPHOLOGY
MODELING WITH OTHER STUDIES
The Fluvial Geomorphology Modeling Study team will interact extensively with the Flow
Routing, Instream Flow, Riparian Instream Flow, Ice Processes and Fish stud y teams. The types
of interaction will vary depending on the specific study, but a considerable amount of physical
data describing the system, including transects, topography/bathymetry, substrate
characterization, aerial photography, and pre- and post-Project flows generally will be shared.
Selection of joint sites for detailed studies will be an important aspect of the collaboration. By
selecting commons sites, the potential for exchange of information between the study teams will
be maximized and ensure that the most effective and extensive use of detailed study site data will
be used.
5.1. Flow Routing Study
It is anticipated that the Flow Routing Study will provide the pre- and post-Project hydrology
information for all studies, including the Fluvial Geomorphology Modeling Study. This
hydrology information will include mainstem pre- and post-Project flows at various points along
the study area and inflows for gaged and ungaged tributaries. This information is expected to be
provided for the 50 year, extended flow record.
For the Fluvial Geomorphology Modeling effort the upstream boundary condition at RM 184
will be the existing condition or pre-Project daily flows from the extended flow record. For the
post-Project condition, the upstream boundary condition will be the average daily releases from
Watana Dam unless load-following scenarios are evaluated. In the latter case, the Project
outflows will need to be on an hourly or possibly finer time increment. Estimated daily inflows
from tributaries provided by the Flow Routing Study will be input along the length of the 1D
sediment transport model and may be inputs to the localized 2D models depending on the
location and specific issues to be addressed.
5.2. Instream Flow Study
For the Instream Flow Study, an assessment of whether the current channel geometry and
substrate characterization used in evaluation of habitats will remain relatively unchanged over
the period of the license under both the pre- and post-Project conditions will be important. The
Geomorphology Studies will determine whether the channel morphology is in a state of dynamic
equilibrium such that the distribution of habitat conditions over the timeframe of the license
(assumed to be 50 years, corresponding to the maximum FERC licensing period) will be
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 13 May 18, 2012
adequately reflected by existing channel morphology. If it is determined that the river is not in a
state of dynamic equilibrium, the Geomorphology Studies will provide projections of the
direction and magnitude of the changes. Changes in the relative occurrence of aquatic habitat
types and the associated surface area versus flow relationships that may occur as a result of the
Project will be an important outcome of these studies. As part of this evaluation, pre- and post-
Project changes in channel dimensions (width and depth) and the proportion and distribution of
geomorphic features and habitat types will be estimated for each of the reach types delineated
using the channel classification system to be developed for the Susitna River. This will provide
the Instream Flow Study with an important part of the information required to evaluate the post-
Project effects on aquatic habitat. Other important information to be provided by the Fluvial
Geomorphology Modeling and the Geomorphology studies for the Instream Flow Study
includes:
Characterization of channel/habitat changes between 1980s and 2012.
Evaluation of stability of islands, side channels and floodplain surfaces over the period of
aerial photographic record (1951, 1983, current photos).
Identification of zones of substrate mobilization, deposition and scour at the reach scale
for pre- and post-Project flow regimes.
Potential changes in lateral habitat connectivity due to aggradation and degradation
Pre- and post-Project changes in spatial and seasonal patterns of the fine sediment (wash
load) transport and the associated Project effects on turbidity.
Changes in substrate composition in both the main channel and lateral habitats.
Pre- and post-Project large woody debris (LWD) recruitment and transport.
The velocity and depth measurements collected by the Instream Flow Study to characterize
habitat will be used to assist in calibrating the hydraulic model(s). Data collected on the
distribution of flow between the main channel and lateral habitat will also be important
information to help calibrate the hydraulic portion of the 2D model.
5.3. Riparian Instream Flow Study
Riparian vegetation plays a large role in the development of islands and lateral habitats,
primarily by protecting surfaces from erosion and promoting sediment deposition. Vegetation
can also contribute to channel narrowing by encroaching onto bars and islands and riverward
growth of banks through trapping of sediments. Conversely, changes in the flow regime and/or
ice processes can alter riparian vegetation patterns, including the extent, species composition and
age-classes; thus, there is a feedback mechanism between the two processes. As a result, the
influence of riparian vegetation on the morphology of the Susitna River is an important
consideration in these studies. The Riparian Instream Flow and Geomorphology studies need to
be closely coordinated because of the interaction described above. The collaboration will begin
with coordinated the selection of the detailed study sites among the Riparian Instream Flow, Ice
Processes and Geomorphology study teams. By working on the detailed study sites together the
teams will develop an understanding of the interaction between the processes that are responsible
for creation and maintenance of the islands and lateral habitats. Estimates of the ages of island
and floodplain surfaces from the Riparian Instream Flow Study based on dendrochronology
combined with the inundation results from the 2D modeling will greatly facilitate this effort by
helping to identify rates of sediment deposition and reworking of these surfaces. Similarly,
profiling of deposited sediments in the riparian corridor to identify the types of sediments that
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 14 May 18, 2012
make up the floodplain will also contribute to the understanding of the physical processes and
development of the functional model for linkage of the geomorphology, riparian vegetation and
ice processes.
The results of the fluvial geomorphology model along with applicable geomorphic principles
will be applied to interpret model results. Understanding of the geomorphology of the system
will also be used to provide a reality check on the extent of changes indicated by the modeling.
Examples of the linkage between the Riparian Instream Flow Study and the fluvial
geomorphology model include:
Altering Manning’s n-values to represent establishment (increased n) or removal
(decreased n) of vegetation.
Application of shear stress parameter to determine the erodibility of banks and potential
influence of vegetation.
Interpretation of flow and sediment transport patterns to determine areas of sediment
deposition within and adjacent to vegetation.
More accurate water surface elevations from the local-scale 2D model than is provided
by the 1D models for periods when the flows only partially inundate the riparian corridor.
Use of geomorphic threshold relationships to understand the potential for removal of
vegetation by the flows and the potential for additional channel narrowing due to changes
in the vegetation patterns.
5.4. Ice Processes Study
Ice processes influence both the channel morphology and riparian vegetation. For example, ice
can prevent vegetation from establishing on bars by annually shearing off or uprooting young
vegetation. Similarly, ice can scour vegetation from the banks, increasing their susceptibility to
erosion. In both examples these influences affect channel morphology. Ice jams can also directly
influence the channel morphology by diverting flows onto floodplain where new channels can
form, particularly when the downstream water surface elevations are low, allowing the return
flows to headcut back into the floodplain. Ice can also move bed material that would normally
not be mobilized by rafting large cobbles and boulders.
There will be close collaboration between the Geomorphology and Ice Process studies to identify
the key physical processes that interact between the two. Working together to analyze the
conditions at the detailed study sites will be a key part of this collaboration. A significant portion
of the influences of ice processes on morphology are directly related to their effects on riparian
vegetation, as discussed in Section 5.3. Additionally, influences of ice processes beyond the
riparian vegetation issues that may be incorporated directly into the fluvial geomorphology
modeling may include:
Simulating the effects of surges from ice jam breakup on hydraulics, sediment transport
and erosive forces using unsteady-flow 2D modeling with estimates of breach
hydrographs.
Simulating the effect of channel blockage by ice on the hydraulic and erosion conditions
resulting from diversion of flow onto islands and the floodplain.
Use of the detailed 2D model output to assess shear stress magnitudes and patterns in
vegetated areas, and the likelihood of removal or scouring.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 15 May 18, 2012
Use of the detailed 2D model output to assess shear stress magnitudes and patterns in
unvegetated areas, and the likelihood of direct scour of the boundary materials.
5.5. Fish Study
The primary interaction with the Fish Study will be in the selection of the sites for detailed study.
Part of the selection process will consider the use of the specific sites as well as the types of
habitat present at the site by target fish species. The local-scale 2D models can be used to
evaluate instream habitat quality on a spatially-distributed basis rather than the cross-sectionally-
based approach used in traditional Instream Flow Incremental Methodology (IFIM) studies.
6. SPATIAL AND TEMPORAL CONSIDERATIONS FOR MODEL
APPLICATION
6.1. Spatial Scale
The spatial extent of the Lower River modeling effort has not been determined. The 1D
modeling will be continued downstream into the Lower River to at least Sunshine Station (RM
84). The decision whether to continue the 1D modeling further downstream in the Lower River
and whether detailed 2D modeling sites will be included in the Lower River will be made based
on an assessment of the potential for the Project to affect channel morphology in this area. The
assessment of potential Project effects in the Lower River is being conducted in 2012 as part of
the Geomorphology Study. Results of this effort will be presented to and reviewed by the
stakeholders, AEA and key members of other study teams (Instream Flow, Riparian Instream
Flow, Ice Processes and Fish studies). This assessment will include a determination of the
downstream limit for the 1D modeling and identification of any 2D modeling sites in the Lower
River.
6.2. Model Time Scale
The time scale for the sediment transport model simulations is also an item that must be
determined in collaboration with the other studies and stakeholders. The time scale includes the
length of simulation period and the time-step of the simulation. Model execution times are often
a limitation, particularly for the 2D model. In fact, this is a key consideration for developing a
proposed modeling approach that combines 1D and 2D modeling. It will most likely be practical
to execute the 1D model for a continuous period of several decades representing the potential
length of a FERC license. On the other hand, the computational requirements for the 2D model
will likely limit simulation times to no longer than individual seasonal hydrograph.
6.2.1. 1D Model
For the 1D modeling, it is currently proposed that the simulation be conducted over a continuous
period that represents the potential length of a FERC license, assumed to be 50 years for
purposes of developing this work plan. The use of average daily flows should provide sufficient
temporal resolution unless the Project is operated in a mode that results in considerable flow
fluctuations within a day; this would be the case if load-following scenarios are included. If such
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 16 May 18, 2012
fluctuations are included in potential operational scenarios then portions of the hydrographs with
these flow fluctuations will need to be run at a time step on the order of 1 hour or less.
In addition to simulating a long-term continuous period of flows it will also be possible to
include rare flood events associated with unusual climatic conditions or ice-jam breakup to
understand conditions that form or maintain the habitats and how those conditions may be altered
by the Project. For these conditions, an appropriate time step will need to be determined on a
case-by-case basis. For example, a time step ranging from several hours to 1 day may be
appropriate for a flood event. However, for breaking of an ice jam the time step may need to be
on the order of minutes.
6.2.2. 2D Model
Because of the nature of the 2D model formulation the time increment for the simulations is
typically on the order of seconds to insure model stability; however, results are reported at longer
time intervals to limit output file size. Due to the intensive computational requirements of 2D
sediment transport modeling and the potentially long execution times it is currently proposed that
the 2D model will be executed for individual flow seasons representing typical years (low,
medium and high) when flows are expected to be sufficiently high to mobilize the bed material
(most likely late spring through the summer).
Similar to the 1D model, the 2D model may be used to perform simulations of floods of given
return periods or individual events caused by breaking of an ice jam to understand conditions
that form or maintain the habitats and how those conditions may be altered by the Project.
7. ASSUMPTIONS, LIMITATIONS AND UNCERTAINTIES
Although the hydraulic, hydrodynamic, and sediment-transport modeling discussed in the
previous sections has been successfully used for a wide variety of projects, it is important to
understand the limitations and uncertainties associated with the modeling. These considerations
are especially important when interpreting the model results because of the primary assumption
that long term channel response of the system to the Project (i.e., changes in the flow and
sediment transport regimes) can be interpreted from a combination of long term 1D modeling;
short term, site specific 2D modeling; and geomorphic principles. These limitations and
uncertainties are applicable to the suite of model platforms that are being considered for this
study, and are itemized in the following sections.
7.1. Limitations
Limitations of the fluvial geomorphology modeling include:
It will not be possible to run the 2D model for a 50-year or other long-term time frame.
Model runs for specific flows or specific season/years will likely be the time frame for
the 2D model.
The 2D model will not model the entire length of the study area; rather, specific detailed
study sites will be modeled that are representative of the range of important geomorphic
and aquatic habitat conditions.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 17 May 18, 2012
The modeling effort will not produce a 3D surface of the channel and floodplain that can
be used as a basis for cross sections in the Instream Flow Study.
Lateral migration and bank erosion are not modeled directly.
For both the 1D and 2D modeling, the predicted results at the up- and downstream
boundary conditions, and at any tributary or distributary boundary conditions, are
influenced by the user-prescribed model input.
Calibration of the 1D hydraulic model will be limited to measured water-surface
elevations and discharges, as well as aerial photography for defining inundated area,
under existing and historical conditions.
Calibration of the 1D sediment-transport model will be limited to comparative (repeat)
cross section surveys, historical gage measurements and ratings (i.e., specific gage
analyses) and available sediment-transport measurements.
Calibration of the 2D modeling will be limited to hydraulic conditions (i.e., calibration to
measured water-surface elevations, velocity and discharge measurements, and aerial
photography to determine inundated area).
7.2. Uncertainties
Inherent uncertainties for the fluvial geomorphology modeling stem from data gaps. These
uncertainties include:
Sediment transport from most of the tributaries has not been measured and will have to
be estimated using sediment transport relationships and mass balance considerations
using locations with available sediment transport measurements.
The vast majority of the tributaries are not gaged for flow so hydrology will have to be
estimate using watershed characteristics and mass balance considerations using locations
with available hydrologic records.
Only a few stream gages have records approaching 50 years which will require missing
data to be developed using correlation with other gages.
Although the calibrated 1D hydraulic and sediment-transport model will be capable of
accurately predicting the general conditions along the project reach, the ability of the
model to accurately predict conditions at a specific location that is not in the vicinity of a
calibration measurement is unknown.
Because calibration of the 2D hydraulic modeling will only involve calibration to
measured hydraulic conditions, only the hydraulic output is verifiable and the degree to
which the 2D sediment-transport modeling is representative of actual conditions is not
known.
8. REFERENCES
Bovee, K.B., 1982. A guide to stream habitat analysis using the instream flow incremental methodology.
Instream Flow Information Paper No. 12. FWS/OBS-82/26. U.S. Fish and Wildlife Service, Office
of Biological Services, Fort Collins, Colorado.
Brabets, T.P, 1997, Geomorphology of the Lower Copper River, Alaska: U.S. Geological Survey
Professional Paper 1581, 89 p.
TECHNICAL MEMORANDUM – FLUVIAL GEOMORPHOLOGY MODELING
Susitna-Watana Hydroelectric Project Alaska Energy Authority
FERC Project No. 14241 Page 18 May 18, 2012
Conaway, J.S., and Moran, E.H., 2004, Development and calibration of two-dimensional hydrodynamic
model of the Tanana River near Tok, Alaska: U.S. Geological Survey Open-File Report 2004-
1225, 22 p.
Danish Hydraulic Institute (DHI), 2007a. Mike 21 Flow Model, User’s Manual, Hydrodynamic
Module, Danish Hydraulics Institute, 90 p.
DHI, 2007b. Mike 21 ST, Non-Cohesive Sediment Transport Module, User’s Manual,
Hydrodynamic Module, Danish Hydraulics Institute, 56 p.
DHI Water and Environment, 2011. MIKE 11.
DHI Water and Environment, 2011. MIKE 21 Flow Model, Hydrodynamic Module User Guide, 90p.
Greimann, B. and Y. Lai, 2008. Two-Dimensional Total Sediment Load Model Equations, ASCE Journal
of the Hydraulics Division, 134(8): 1142–1146.
Huang, J.V. and Greimann, B.P., 2011. SRH-1D 2.8 User’s Manual, Sedimentation and River Hydraulics
– One Dimension, Version 2.8, U.S. Department of Interior, Bureau of Reclamation, Technical
Service Center, Sedimentation and River Hydraulics Group. 227p.
Lai, Y.G., 2008. SRH-2D version 2: Theory and User’s Manual, Sedimentation and River Hydraulics –
Two-Dimensional River Flow Modeling, U.S. Department of Interior, Bureau of Reclamation,
November, 113 p.
McDonald, R.R., Nelson, J.M., and Bennett, J.P., 2005, Multi-dimensional surface-water modeling
system user’s guide: U.S. Geological Survey Techniques and Methods, 6-B2, 136 p.
Mobile Boundary Hydraulics, 2008.
Ruark, M., Niemann, J., Greimann, B., and Arabi, 2011. Method for Assessing Impacts of Parameter
Uncertainty in Sediment Transport Modeling Applications, Journal of Hydraulic Engineering,
137(6): 623–636.
U.S. Army Corps of Engineers (USACE), 1993. HEC-6, Scour and Deposition in Rivers and Reservoirs,
User’s Manual, Hydrologic Engineering Center, Davis, California.
USACE, 2010a. HEC-RAS, River Analysis System, User’s Manual, Version 4.1.0, Hydrologic
Engineering Center, Davis, California.
USACE, 2010b. Adaptive Hydraulics User Manual Version 3.3. U.S. Army Corps of Engineers
Waterways Experiment Station, Vicksburg, Mississippi.