A Discontinuous Galerkin-based Forecasting Tool for the Ohio River
A Thesis
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Mariah B. Yaufman, B.S.
Graduate Program in Civil Engineering
The Ohio State University
2016
Master’s Examination Committee:
Ethan J. Kubatko, Advisor Gil Bohrer Gajan Sivandran © Copyright by
Mariah B. Yaufman
2016 ABSTRACT
This thesis presents the development and application of a multidimensional (2-
D & 1-D) river flow model in the discontinuous Galerkin framework for simulating overland flow and runoff due to rain events within the Ohio River watershed. The purpose of this work is to improve on the forecasting of stage height and discharge on the Ohio River — the largest tributary, by volume, of the Mississippi River in the
United States. This forecasting tool makes use of the 2-D kinematic wave equations for overland flow caused by the rainfall events occurring over the Ohio River watershed and the 1-D kinematic wave equation for approximating stage height and discharge in the Ohio River. We highlight some of the challenges involved in modeling the various rainfall-runoff processes. Furthermore, we discuss the various data sets incorporated into the model, such as detailed cross-sectional data for the Ohio River obtained from the US Army Corps of Engineers, topographic data generated from NASA’s
Shuttle Radar Topography Mission (SRTM), and land use/land cover data from the
US Geologic Survey. The model is verified against a set of analytic test cases and validated in a series of hindcasts that make use of historical rainfall and river gauge data.
ii To my family for their love and support, and to Stephen for making ice cream runs
with me and filling my life with laughter.
iii ACKNOWLEDGMENTS
I would like to thank my advisor, Ethan Kubatko, for captaining this river project and never giving up on it, or me. Thank you to the two C.H.I.L. members who helped us repair this sinking ship...while other members never fully got on board, fell off the boat, or jumped ship, you two hopped aboard and helped save the day. You two are awesome and I am forever grateful for the help you’ve provided me.
iv VITA
2010 ...... Bellbrook High School, Bellbrook, OH
2014 ...... B.S. Civil Engineering, Cum Laude, The Ohio State University
2014 − 2016 ...... Graduate Teaching Associate, Civil, Environmental, and Geodetic Engineering, The Ohio State University 2015 to Present ...... Graduate Research Associate, Civil, Environmental, and Geodetic Engineering, The Ohio State University FIELDS OF STUDY
Major Field: Civil Engineering Area of Specialization: Environmental Engineering and Water Resources
v TABLE OF CONTENTS
Page
Abstract ...... ii
Dedication ...... iii
Acknowledgments ...... iv
Vita...... v
List of Tables ...... viii
List of Figures ...... ix
1. Introduction ...... 1
1.1 Background ...... 1 1.2 Motivation and Objectives ...... 5 1.3 Thesis Organization ...... 6
2. Model Background ...... 8
2.1 Governing equations ...... 8 2.1.1 Overland flow ...... 8 2.1.2 Open-channel flow ...... 9 2.1.3 The kinematic wave approximation ...... 10 2.2 Domain discretization ...... 12 2.2.1 The discontinuous Galerkin spatial discretizations ...... 13 2.2.2 Multidimensional Coupling ...... 17 2.3 Mesh Generation ...... 18 2.3.1 Admesh+: Generating a constrained mesh and the accom- panying data structure ...... 19
vi 3. Data Inputs ...... 25
3.1 DEMs and Cross Sections ...... 25 3.1.1 Cross section modifications ...... 26 3.1.2 DEM modifications ...... 29 3.1.3 Combination ...... 30 3.2 U.S. Geological Survey Inputs ...... 30 3.2.1 River Inputs ...... 33
4. Forecasting ...... 35
4.1 Forecast data ...... 35 4.2 Unit hydrographs ...... 40 4.2.1 Historic Rainfall Data ...... 42 4.2.2 Historic discharge and baseflow separation ...... 43 4.2.3 Unit hydrograph implementation with forecast data . . . . . 45
5. Testing and Validation ...... 51
5.1 Graphical User Interface ...... 51 5.2 Model initialization ...... 56 5.2.1 Tributary initialization ...... 56 5.2.2 Ohio River pool initialization ...... 60 5.2.3 Running the Model ...... 61 5.3 Results ...... 64
6. Conclusions and Future Work ...... 68
6.1 Findings and Conclusions ...... 68 6.2 Future Work ...... 68
Appendices
A. Model Inputs ...... 70
Bibliography ...... 91
vii LIST OF TABLES
Table Page
1.1 Ohio River Navigational Dams...... 2
1.2 The hydroelectric dams that are owned by AMP with their production specifications...... 5
3.1 Land-use/ Land-cover description, Manning’s n coefficient, and inter- ception depth provided by the USGS...... 32
3.2 Soil infiltration parameters provided by the USGS...... 32
A.1 List of the tributary rivers in the Pittsburgh USACE Engineering dis- trict being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS...... 70
A.2 List of the tributary rivers in the Huntington USACE Engineering district being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS...... 71
A.3 List of the tributary rivers in the Louisville USACE Engineering dis- trict being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS...... 72
A.4 Stage height gauges along the Ohio River used to initialize the model. 73
viii LIST OF FIGURES
Figure Page
1.1 A map of the U.S. Army Corps of Engineers operated locks and dams along the Ohio River courtesy of the U.S. Army Corps of Engineers. . 3
2.1 Simple schematic of a watershed of horizontal extent Ω, with boundary ∂Ω indicated by the thick black line. In hydrologic modeling, the watershed’s drainage network (the set of dashed blue lines denoted by ω) is typically represented as a set of connected line segments ωi. The inset (right) shows a simple example of how junctions are handled in the numerical model; see discussion in Section 2.2.1...... 12
2.2 An illustration of the multidimensional coupling that is accomplished by simply setting qL = q · n at the common 1D and 2D (edge) Gauss– Lobatto integration points...... 17 b 2.3 The channel network (blue lines) and watershed boundary (black lines) extracted from a sample DEM using TopoToolbox...... 19
2.4 Insets showing the original representations of the channel network (left, blue line) and watershed boundary (right, black line) obtained from the DEM and the spline approximations (red lines) used in Admesh+. . 21
2.5 Example of a finite element mesh generated automatically by Admesh+, where the red lines indicate the constrained channel network...... 22
2.6 A three-dimensional profile view of a finite element mesh produced by Admesh+ for a sample watershed, where blue lines indicate edges that are part of the original constrained channel network, red lines indicate one-dimensional overland flow routing edges and large open arrows indicate flow direction over each element face. The sketch to the right illustrates a converging edge...... 24
ix 3.1 A typical UTM map projection around the world...... 28
3.2 An example of a Digital Elevation Model (green line) being combined with the raw cross section (blue line) to produce a complete river cross section...... 31
3.3 The stage height interpolation from a known tailwater to a known headwater...... 34
4.1 A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.25 inches [4]...... 39
4.2 A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.5 inches [4]...... 40
4.3 A typical unit hydrograph with an instantaneous precipitation event at time t = 0...... 41
4.4 An example of the average hydrographs that are produced as depicted by the red asterisk line on top of the rainfall-runoff events in a given volume theshold...... 45
4.5 The rainfall that falls within the watershed of USGS tributary station # 03159540 Shade River near Chester, Ohio are depicted as black circles. The tributary boundary is the black surrounding polygon and the outlet is the orange dot...... 47
4.6 A hydrograph created for input to the USGS tributary station # 03159540 Shade River near Chester, Ohio. This hydrograph depicts a single storm event...... 49
4.7 A hydrograph created for input to the USGS tributary station # 03612000 Cache River at Froman, Illinois. This hydrograph depicts two combined storm events separated by about one full day of no rain- fall...... 50
5.1 The Graphical User Interface that will be provided to AMP, on Eleva- tion view...... 52
x 5.2 The mesh from the GUI on Land-Cover view...... 53
5.3 The mesh from the GUI on Soil Data view...... 54
5.4 The complete Ohio River watershed boundary is represented by the bold red line. The stream networks are displayed as well, with the streamline magnitudes defined on the left. The boundary and stream- lines were provided by the USGS Elevation Derivatives for National Applications (EDNA)...... 55
5.5 Example of the rectangular channel cross section geometry...... 57
5.6 A sample dQ vs. Qin correction fit...... 63
5.7 The headwater and tailwater results at Montgomery Island Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data...... 65
5.8 The headwater and tailwater results at New Cumberland Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data...... 66
5.9 The headwater and tailwater results at Pike Island Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data...... 67
A.1 Pool 1 begins at the tailwaters of Dashields Lock and Dam and ends at the headwaters of Montgomery Lock and Dam. It has 2 tributaries feeding into this section of the river: Beaver River and Raccoon Creek. 74
A.2 Pool 2 begins at the tailwaters of Montgomery Lock and Dam and ends at the headwaters of New Cumberland Lock and Dam. This pool has 2 tributary river feeding into this section of the river: Little Beaver Creek and Yellow Creek...... 75
xi A.3 Pool 3 begins at the tailwaters of New Cumberland Lock and Dam and ends at the headwaters of Pike Island Lock and Dam. This pool has 2 tributaries feeding into the section: Dunkle Run and Short Creek. . . 76
A.4 Pool 4 begins at the tailwaters of Pike Island Lock and Dam and ends at the headwaters of Hannibal Lock and Dam. This pool has 3 tribu- taries feeding into this section: Wheeling Creek, Wheeling Creek, and Captina Creek...... 77
A.5 Pool 5 begins at the tailwaters of Hannibal Lock and Dam and ends at the headwaters of Willow Island Lock and Dam. This pool has a single tributary: Middle Island Creek...... 78
A.6 Pool 6 begins at the tailwaters of Willow Island Lock and Dam and ends at the headwaters of Belleville Lock and Dam. This pool has 6 tributaries...... 79
A.7 Pool 7 begins at the tailwaters of Belleville Lock and Dam and ends at the headwaters of Racine Lock and Dam. This pool has a single tributary: Shade River...... 80
A.8 Pool 8 begins at the tailwaters of Racine Lock and Dam and ends at the headwaters of R.C. Byrd Lock and Dam. This pool has 3 tributaries: Kanawha River, Coal River, and Raccoon Creek...... 81
A.9 Pool 9 begins at the tailwaters of R.C. Byrd Lock and Dam and ends at the headwaters of Greenup Lock and Dam. This pool has 7 tributaries. 82
A.10 Pool 10 begins at the tailwaters of Greenup Lock and Dam and ends at the headwaters of Meldahl Lock and Dam. This pool has 4 tributaries. 83
A.11 Pool 11 begins at the tailwaters of Meldahl Lock and Dam and ends at the headwaters of Markland Lock and Dam. This pool has 8 tributaries. 84
A.12 Pool 12 begins at the tailwaters of Markland Lock and Dam and ends at the headwaters of McAlpine Lock and Dam. This pool has 4 tributaries. 85
A.13 Pool 13 begins at the tailwaters of McAlpine Lock and Dam and ends at the headwaters of Cannelton Lock and Dam. This pool has 5 tributaries. 86
xii A.14 Pool 14 begins at the tailwaters of Cannelton Lock and Dam and ends at the headwaters of Newburgh Lock and Dam. This pool has a single tributary: Middle Fork...... 87
A.15 Pool 15 begins at the tailwaters of Newburgh Lock and Dam and ends at J.T Myers/Uniontown Lock and Dam. This pool has 2 tributaries: Green River and Pigeon Creek...... 88
A.16 Pool 16 begins at the tailwaters of J.T Myers/Uniontown Lock and Dam and ends at the headwaters of Smithland Lock and Dam. This pool has 5 tributaries...... 89
A.17 Pool 17 begins at the tailwater of Smithland Lock and Dam and end at the headwaters of Olmsted Lock and Dam. This pool has 8 tributaries. 90
xiii CHAPTER 1
INTRODUCTION
1.1 Background
There has been a long-standing need to be able to accurately predict river stage heights for a variety of reasons. For example, throughout the 1990’s, it became urgent to develop models to predict flooding of rivers in the Midwest and Plain states after devastating floods impacted those areas [21]. Within the past year, flooding was responsible for the most weather-related deaths in the United States. Creating timely river forecasts is essential to prevent that loss of life and to protect against economic damages caused by increased river depth. Forecasting major rivers will also benefit the hydroelectric industry by enabling companies to make better operational decisions and optimizing the management of water resources at specific locations, oftentimes at a dam location.
The Ohio River is the largest tributary, by volume, to the Mississippi River in the United States — contributing nearly half of the outflow for the Mississippi River.
The river begins at the confluence of the Allegheny and the Monongahela Rivers at
Pittsburgh, Pennsylvania and flows south west for 981 miles to Cairo, Illinois until it meets the Mississippi River. At its end point, the Ohio River basin covers 189,422
1 square miles and drains sections of 15 states. Naturally a shallow river, the Ohio River has a series of 20 Locks and Dams that raise the river height to navigable levels.
Table 1.1: Ohio River Navigational Dams. Lock and Dam Miles downstream Normal Pool Elevation Name: of Pittsburgh, PA (ft above NGVD29) Emsworth 6.2 710.0 Dashields 13.2 692.0 Montgomery 31.7 682.0 New Cumberland 54.4 664.5 Pike Island 84.2 644.0 Hannibal 126.4 623.0 Willow Island 161.7 602.0 Belleville 203.9 582.0 Racine 237.5 560.0 Robert C. Byrd 279.2 538.0 Greenup 341.0 515.0 Captain Anthony Meldahl 436.2 485.0 Markland 531.5 455.0 McAlpine 606.8 420.0 Cannelton 720.7 383.0 Newburgh 776.1 358.0 Uniontown 846.0 342.0 Smithland 918.5 324.0 Lock and Dam 52 938.9 302.0 Lock and Dam 53 962.6 290.0 Olmsted 964.4 TBD
The fundamental purpose of the dams along the Ohio River is for navigational purposes, not flood control — although flood prevention benefits do not go unnoticed.
A complete listing of the dams along the Ohio River can be found in Table 1.1 along with the dam’s river mile mark and vertical datum. Visually, Figure 1.1 displays all of the currently built dams as yellow ‘T’s’. Olmsted Dam is currently under construction (denoted as the red ‘T’ in the figure) and will be replacing Lock & Dam
52 and Lock & Dam 53 by 2020. All of the dams seen in Table 1.1 and Figure 1.1 are
2 Figure 1.1: A map of the U.S. Army Corps of Engineers operated locks and dams along the Ohio River courtesy of the U.S. Army Corps of Engineers.
carefully monitored by the U.S. Army Corps of Engineers (USACE). The USACE has the ability to control the stage height levels – the approximate height of the water surface in reference to an arbitrary zero altitude close to the river bottom – at the headwaters of dams. This ensures that the pool levels are deep enough for boats to travel along the river.
Until recently, the Ohio River was not considered for hydroelectric power pro- duction because its lack of large drops in head (dropping only about 6 inches per
3 mile). Typically when there is a large difference in headwater and tailwater levels, the upstream river height and downstream height of a dam, respectively, hydroelec- tric dams bring more water through the turbines that in turn produce more power.
A new turbine design has allowed existing dams along the Ohio river to be converted into hydroelectric dams. There are currently six dams along the Ohio River that are producing hydroelectricity. These are Hannibal, Belleville, Racine, Greenup, Mark- land, and McAlpine Lock and Dam. Construction is active at Willow Island, Meldahl,
Cannelton, and Smithland Lock and Dam to allow hydroelectricity to be produced at these dams. Willow Island, Meldahl, Cannelton, and Smithland Lock and Dam will be able to provide an additional 313 megawatt capacity to the American Municipal
Power, Inc (providing 44, 105, 88, and 76 megawatt capacity respectively).
American Municipal Power, Inc. (AMP) is a non-profit organization that supplies wholesale power to Ohio, Pennsylvania, Michigan, Virginia, Kentucky, West Virginia,
Indiana, Maryland, and Delaware. They produce this power through various ways such as solar, wind, fossil fuels, and land fill gases. This thesis will be focused on their dams which produce hydroelectric power — further information on these dams can be found in Table 1.2. AMP currently owns Willow Island, Belleville, Meldahl,
Greenup, Cannelton, and Smithland Lock and Dam. The first four dams lay within the Huntington USACE Engineering District and the last two are in the Louisville
District, which is important to note for subsequent chapters.
4 Table 1.2: The hydroelectric dams that are owned by AMP with their production specifications. Lock and Dam Rated Capacity Approx. Annual Output # of Turbines Name: (MW )(millionkW h) & Type Willow Island 44 239 2 bulb-turbines Belleville 42 221 2 bulb-turbines Greenup 70 282 3 bulb-turbines Captain Anthony Meldahl 105 558 3 bulb-turbines Cannelton 88 458 3 bulb-turbines Smithland 76 379 3 bulb-turbines
1.2 Motivation and Objectives
This thesis will focus on the continued development of a computational hydrody- namic model for forecasting river stage heights at the headwaters and tailwaters of dams using a multi-physics/ multidimensional modeling framework.
AMP has requested this model to forecast the headwater and tailwater heights at the dams they own with lead-times out to 3 days. Knowing the stage height allows
AMP to predict the amount of power they will be able to generate at their hydro- electric dams. AMP desires that the stage height be accurate to the nearest foot and that the model simulation time takes less than 15 minutes. The hydrodynamic model will be able to accomplish this by generating a mesh that is discretized in the discontinuous Galerkin framework, using a multi-physics/ multidimensional modeling approach, and utilizing current datasets that are available through numerous govern- ment operated websites, discussed in Chapter 3.
The model must first capture all of the topographic features within the domain boundary on a high-quality unstructured triangular mesh. The mesh generation pro- cess will be discussed in section 2.3. The elements created by this mesh will then
5 be classified as either Overland flow elements (either 2D or 1D) or Channel elements
(1D). These distinctions need to be made for the model to determine which govern- ing equation(s) need to be utilized over each element. Overland flow elements will initially be modeling dry regions and further classify if the element has a ridge edge,
flow edge, or channel edge. The multidimensional aspect of the model was developed and tested using the kinematic wave equations with the DG formulation by [26]. This aspect of the model is called DG-SAKE, which stands for Discontinuous Galerkin -
Section Averaged Kinematic Equations.
Further inputs are required to accurately model present and future conditions of the Ohio River. Inputs such as tributary discharge or Ohio River stage height will enable initial conditions to be made as accurately as possible. The use of quantitative forecast data in combination with unit hydrographs, developed specifically for each tributary watershed, will enable the model to forecast out to the desired 3-day lead- time period.
1.3 Thesis Organization
This thesis is organized as follows. Chapter 2 will provide background on the gov- erning equations, domain discretization, and mesh generation used for the creation of the AMP Hydro model, created in the C.H.I.L at The Ohio State University. Chapter
3 provides details on the input data for the model and the necessary modifications that were done on the data to make it usable within the modeling framework. We will follow this chapter with Chapter 4, which will discuss the coupling of forecast rainfall data and unit hydrographs in detail. This allows the model to predict the stage height at AMP’s dam locations along the river. In Chapter 5 we will examine
6 specific locations along the Ohio River that were used as test cases to validate the model. We will conclude with final remarks on the model along with a discussion on the potential of coupling the river model with a transport model in the future.
7 CHAPTER 2
MODEL BACKGROUND
This chapter will detail the governing equations solved in the model, the dis-
cretization of the domain, and the mesh generation.
2.1 Governing equations
2.1.1 Overland flow
Using a Cartesian coordinate system (x, y, z), consider a land surface z = f(x, y)
that describes the topography of a given watershed. When this land surface is sub-
jected to a rainfall rate r(x, y, t), which (in general) will be a function of both the horizontal (x, y) coordinates and time t, that exceeds its infiltration rate i(x, y, t), flow over the land surface — known as surface runoff or overland flow (the latter term will be used here) — can occur. This type of flow can be described by the two-dimensional shallow water equations, which consist of (i) a depth-integrated continuity equation
∂H + ∇ · HU = r − i, ∂t where H(x, y, t) is the depth of water and U = (u(x, y, t), v(x, y, t)) is the depth- averaged, horizontal velocity vector, r is the rainfall rate, i is the infiltration rate; and (ii) momentum balance equations in the horizontal directions, which can be
8 written in the form ∂ (HU) + ∇ · F = g H (S − S ) , ∂t 0 f where
Hu2 + 1 gh2 Huv ∂z S F = 2 , S = ∂x , S = fx , Huv Hv2 + 1 gH2 0 ∂z f S 2 ∂y fy
with g being gravitational acceleration and the vectors S0 and Sf being the bed (land) slope and friction slope terms, respectively. The latter is typically computed using a
Manning-type resistance law, n2 kUk S = U, f H4/3 where n is the Manning resistance coefficient, which is dependent on the land surface roughness, and can be obtained from standard references, see, for example, [6]. (Note: units for n are typically left off, however it is not dimensionless, and the form of the
equation presented here assumes all quantities are in SI base units; see, for example,
[6].)
2.1.2 Open-channel flow
Overland flow often collects into natural and man-made channels that act to route
the water within a given watershed to a single converging point. The resulting flow is
typically referred to as open-channel flow and can be described using one-dimensional,
section-averaged versions of the equations given above (also known as the Saint Venant
equations). These equations can be written in the form
∂A ∂Q + = q (2.1) ∂t ∂s L ∂Q ∂ Q2 + + gI = gA (S − S ) + g I , ∂t ∂s A 1 0 f 2
9 where s is a curvilinear coordinate along the river or channel centerline, A denotes the
area of the cross-sectional area of flow, Q =uA ¯ is the mean cross-sectional volumetric discharge (note:u ¯ is the section-averaged velocity), qL is a lateral inflow rate per unit length of channel, and I1 and I2 are integral terms accounting for pressure forces
(hydrostatic and wall pressure terms, respectively). Relatively simple expressions are obtained for these pressure terms when considering standard channel cross-sections, such as trapezoidal or rectangular sections.
In the case of open-channel flow, a Manning formulation for the friction slope Sf takes the form n u¯2 Sf = 2/3 , Rh
where Rh = A/P is the hydraulic radius, which is a ratio of the cross-sectional area
of flow A and the wetted perimeter P . It should be noted that, in addition to the
bed surface roughness, the value of n in this case can be dependent on a number of other factors such as, for example, the degree of “irregularity” and “meandering” of the channel; see, for example, [6].
2.1.3 The kinematic wave approximation
In many cases of both open-channel and overland flow, the friction and bed slope terms are dominant in the momentum equations (i.e., the remaining terms are negli- gibly small), leading to, for example, an approximate relationship of the form
n u¯2 ≈ S0 Sf = 2/3 Rh in the case of open-channel flow. Solving this expression foru ¯ gives an (approximate) relationship for the velocity of the form
β u¯ ≈ α S0 Rh , (2.2)
10p where α = 1/n and β = 2/3. (Note: setting α = C, the Chezy coefficient, and
β = 1/2 in (2.2) gives the well-known Chezy formula).
Substitution of (2.2) into (2.1) results in the so-called kinematic wave approxima- tion for open-channel flow, which reduces the problem to a single equation in terms of a single unknown A; that is,
Kinematic wave approximation: 1D open-channel flow
∂A ∂ + α S R β A = q . (2.3) ∂t ∂s 0 h L p = Q | {z }
Similar considerations in the case of overland flow result in the following kinematic wave approximation (when using a Manning-type resistance law)
Kinematic wave approximation: 2D overland flow
∂H + ∇ · q = r − i, (2.4) ∂t
where q = (qx, qy) with
S0x 5/3 S0y 5/3 qx = √ H , qy = √ H ; n S0 n S0
see, for example, [15] for a more detailed exposition on this equation.
11 ∂Ω: Watershed boundary
ω
Ω ωb ωa
Qb,j− Qa,j− j
(in) Outlet point P Qj = Qa,j− + Qb,j−
Junctionb of channel network
Figure 2.1: Simple schematic of a watershed of horizontal extent Ω, with boundary ∂Ω indicated by the thick black line. In hydrologic modeling, the watershed’s drainage network (the set of dashed blue lines denoted by ω) is typically represented as a set of connected line segments ωi. The inset (right) shows a simple example of how junctions are handled in the numerical model; see discussion in Section 2.2.1.
2.2 Domain discretization
Consider a watershed, or drainage basin, with horizontal extent Ω as illustrated in
Figure 2.1. By definition (of a watershed), all surface water flow within Ω will converge to a single outlet point P . The outlet point is the terminus of the watershed’s drainage network — a tree-like structure of “concentrated” (open-channel) flow pathways that collect the “unconfined” overland flow of neighboring hillslopes. This description gives rise to the conceptual model of a drainage basin presented in [11] — one that is particularly useful here — that consists of “two geomorphological components: a
12 set of hillslopes dominated by unconfined overland flow and a branching network of
channels conveying concentrated flow.”
Given the relative scales of these two components, in hydrologic modeling the
latter component (the channel network) is typically represented simply as a set of
connected line segments, which we denote by ωi; see inset of Figure 2.1. This indicates
that the set of hillslopes that constitute (what we will refer to as) the overland flow
component completely covers the watershed. Therefore, in our modeling approach,
the kinematic wave approximation for overland flow, i.e., Eq. (2.4), is solved over the
entire domain Ω, while the kinematic wave approximation for open-channel flow, i.e.,
Eq. (2.3), is solved over the (one-dimensional) domain ω.
Discretization of the watershed, of course, needs to take into account the coupled nature of the two geomorphological components. This is accomplished in the present modeling approach through the use of a finite element partition, or mesh, Th of Ω, consisting of elements Ωj with edges aligned along ω; see, as an example, Figure
2.5. The collection of edges aligned along ω form a one-dimensional finite element partition Eh of ω, consisting of channel elements ωi. The construction of such a mesh, starting from a given digital elevation model (DEM), is described in detail in Section
2.3.
2.2.1 The discontinuous Galerkin spatial discretizations
Given finite element partitions as described above, we obtain weak forms of (2.3) and (2.4) by multiplying the equations by suitably smooth test functions v(s) and w(x, y) and integrating over each 1D (ωi ∈ Eh) and 2D (Ωj ∈ Th) element, respectively,
13 where the flux terms are integrated by parts. This yields
At v ds − Q vs ds + Q v = qL v ds ω ω ∂ωi ω Z i Z i Z i
Ht w − q · ∇w + q · n w ds = (r − i) w , ZΩj ZΩj Z∂Ωj ZΩj where = dx dy, ∂ωi and ∂Ωj indicate the boundaries of ωi and Ωj, respectively, and n is the outward unit normal to the element boundary ∂Ωj.
Next, we seek approximate (trial) solutions (Ah,Hh) to (A, H) that belong to the
finite-dimensional spaces
(ω) = v : v| ∈ (ω ), ∀ω ∈ E , Vhp ωi Pp i i h (Ω) = w : w| ∈ (Ω ), ∀Ω ∈ T , Whp Ωj Qp j j h n o respectively, where Pp denotes the space of polynomials of degree (at most) p and Qp denotes the space of bipolynomials complete up to (at most) degree p.
Note that the spaces defined above do not enforce global continuity of the func- tions. Therefore, the trial solutions may be discontinuous at element boundaries.
Consider, for example, a discontinuity in Ah at a (non-junction) point sj with values
− + A = lim Ah(sj, t) and A = lim Ah(sj, t) j j + sj →sj− sj →sj as sj is approached from the upstream and downstream element, respectively. This
− − discontinuity in Ah, in turn, introduces, dual values of the flux Qj = Q(Aj ) and
+ + Qj = Q(Aj ) at point sj. In the DG formulation, we replace these (possibly) dual- valued fluxes (again, at non-junction points) with single-valued numerical fluxes Qj.
Given that kinematic waves propagate downstream only, we can simply employb an
− upstream numerical flux, that is, Qj ≡ Qj . Similarly, along a given flow edge Γi in
b 14 the two-dimensional formulation, we replace q| by q = q(H−), where H− is the Γi i i upstream trace of H along edge Γ . h i b In the one-dimensional formulation, note that there may be multiple upstream
− elements at junction points sj, leading to multiple flux values Qi,j at point sj from the multiple upstream elements ωi. Thus, in the downstream element, we take the incoming numerical flux to be
(in) − Qj = Qi,j (In downstream elements of junctions), i X b where the sum is over all upstream elements ωi connected at point j. (Note, however, that the outgoing numerical flux used in a given upstream element ωi is simply Qj =
− Qi,j as before.) The inset of Figure 2.1 presents a simple example of this approachb for a junction with two upstream elements.
Replacing (A, H) by their trial solutions (Ah,Hh), using the numerical fluxes
(Q, q) for (Q, q) at the element boundaries as defined above, and taking the test functions (v, w) = (v , w ), we arrive at the following discrete weak form of the b b h h problem: find Ah ∈ Vhp and Hh ∈ Whp such that for all test functions vh ∈ Vhp and
wh ∈ Whp
(in) Aht vh ds − Q(Ah) vhs ds + Q vh = qL vh ds ω ω ∂ωi ω Z i Z i Z i b (int) Hht wh − q(Hh) · ∇wh + q · n wh ds = (r − f) wh , ZΩj ZΩj Z∂Ωj ZΩj (int) (int) over each ωi ∈ Eh and each Ωj ∈ Th. (Note: vh b and wh denote the interior traces of the test functions.)
Upon choosing bases for the finite element spaces Vhp and Whp, the above dis- crete weak forms reduce to systems of time-dependent ordinary differential equations
15 (ODEs) of the form
dA dH = R(1D)(A), = R(2D)(H), (2.5) dt hp dt hp where A and H are vectors of time-dependent degrees of freedom associated with Ah
(nD) and Hh, respectively, and Rhp is the n-dimensional DG spatial operator. As an example, in the one-dimensional case, given a set of basis functions Φ =
T [ φ0, φ1, . . . , φp ] for the space Vhp, the trial solution Ah over ωi can be expressed as
T Ah|ωi = Φ Ai
where Ai is a (column) vector of the time-dependent degrees of freedom of the DG solution over ωi. The discrete weak form for each ωi can then be written as a system of ODEs in the form dA M i = F , i dt i where the components, Mkl, of the element mass matrix Mi are given by Mkl =
φkφl dx and ωj T R Fi = Fi(φ0),Fj(φ1),...,Fj(φp) h i with
dφk (int) Fi(φk) = Q ds + Q φk Ω ds ∂ωi Z i
We note that Mj is a local (element) matrix andb that the elements are coupled through the numerical flux terms appearing in Fj.
Inverting the element mass matrices, the full set of one-dimensional semidiscrete equations over a set of N elements can be written compactly as
dA = R(1D)(A) dt hp
16 where −1 A1 M1 F1 −1 A2 M2 F2 A = . , R(1D)(A) = . . . hp . −1 AN M FN N A similar set of equations is obtained in the two-dimensional case.
In our implementation, we use the set of Legendre polynomials of degree p as our basis for Vhp and either a tensor product of Legendre polynomials, in the case of quadrilateral elements, or the so-called Dubiner basis, in the case of triangular elements, for Whp; see [13] for more details. All integrals of the DG spatial operators are computed using Gauss quadrature of sufficient degree.
2.2.2 Multidimensional Coupling
p = 1 (linear element)
1-D Gauss–Lobatto rule
1D channel elements
CL
A(x, t)
Cross-section A-A
Figure 2.2: An illustration of the multidimensional coupling that is accomplished by simply setting qL = q ·n at the common 1D and 2D (edge) Gauss–Lobatto integration points. b
17 The one- and two-dimensional DG equations are coupled through the lateral flux terms qL. Specifically, for a given two-dimensional element Ωj with an edge Γl that is coincident with channel element ωi, we must have
qL ds = q · n ds. Zωi ZΓl This condition is enforced numerically by usingb the same set of Gauss quadrature points for numerically integrating the one-dimensional channel elements ωi and the edge integrals of the the two-dimensional overland flow elements. Then, we simply set qL = q · n at a given Gauss point. Here, we make use of Gauss–Lobatto rules, which include the endpoints of the interval, of degree 2p + 1 for a DG spatial discretization b of degree p, as suggested in [7]; see Figure for an illustration of this idea for p = 1
(linear) elements.
2.3 Mesh Generation
Starting from a DEM of a given geographical area, the generation of computational meshes for the numerical approach outlined above is carried out in two main steps:
1. A DEM data-extraction step that makes use of a set of open-source Matlab
functions called TopoToolbox [19] to pre-process (e.g., pit-fill, smooth, etc)
the DEM data and automatically extract watershed boundaries and channel
networks. Figure 2.3, for example, shows the extracted watershed boundary and
channel network obtained from a sample DEM. Various options are available for
identifying the extent of the channel network in TopoToolbox; e.g., selection can
be made based on the Strahler stream order or calculated flow accumulation;
see [19] for details.
18 2. A mesh-generation step that makes use of the extracted DEM data and a pro-
gram developed in the C.H.I.L called Admesh+ [9], which has been further
developed under this work. This step ultimately provides the underlying mesh
data structure that is required by the outlined numerical approach and that is
described in detail below.
Figure 2.3: The channel network (blue lines) and watershed boundary (black lines) extracted from a sample DEM using TopoToolbox.
2.3.1 Admesh+: Generating a constrained mesh and the ac- companying data structure
A full description of the Admesh+ methodology can be found in [9], which in- corporates and builds on the ideas and methodology of Persson’s DistMesh program
— a simple, open-source mesh generator implemented in Matlab []. Briefly, a mesh-
19 or element-size function, h(x), is first constructed that is used to prescribe element sizes h throughout the domain. These sizes are based on a number of geometric fac- tors, such as shoreline/boundary curvature and bathymetric/topographic gradients, as well as user-defined inputs, such as target maximum/minimum element sizes and mesh-grading specifications (i.e., the ratio of neighboring elements should not exceed some specified factor). Given the element-size function, a Delaunay triangulation of an initial set of mesh nodes with a density proportional to 1/h(x)2 is then generated and the nodes of this initial mesh are re-positioned by solving for force equilibrium
(iteratively) around each node, making use of a spring mechanics analogy; see [9] for details.
The main extension of the Admesh+ methodology for this work is to allow for interior constraints when generating the mesh. That is, we wish to compute a tri- angulation in which element edges are constrained along the specified channel net- work and watershed boundaries. Given that DEM data is typically recorded on a structured grid, the extracted channel networks and watershed boundaries will often exhibit a stair-case like appearance on the scale of the original DEM. Rather than constraining element edges to conform exactly to this representation, which can lead to low-quality elements on a scale smaller than desired in the neighborhood of the constraints, we compute and work with a smooth (Hobby) spline approximation [12] of the constraints, as illustrated in Figure 2.4.
The spline approximation allows for a simple calculation of the “curvature” of the constraints, which can then be taken into account in sizing elements along them.
Specifically, the user can specify the number of elements desired per radian of cur- vature, which acts to place smaller element edge lengths in areas of high curvature,
20 Original Network Spline Approximation Original Boundary Spline Approximation
Figure 2.4: Insets showing the original representations of the channel network (left, blue line) and watershed boundary (right, black line) obtained from the DEM and the spline approximations (red lines) used in Admesh+.
in order to capture the relevant geometry, but allows larger element edges to be used in straighter segments. A specific (uniform) element edge size along the con- straints can also be specified by the user. Given these specified constraints, the
Admesh+ methodology described above was modified to first create a constrained
Delaunay triangulation and then perform the force equilibrium calculations, where all nodes along the constraints are held fixed. Figure 2.5 shows an example of a con- strained triangulation created by Admesh+. The mesh contains 34,411 elements that range in size from approximately 50 to 400 meters and was generated automatically in
2.46 minutes. The element quality of the mesh, on a 0–1 scale where 0 is a completely
21 degenerate triangle and 1 is an equilateral triangle, averaged 0.98 with a minimum element quality of 0.70; see [9] for more details on the mesh-quality measure.
No. Elements: 34,411 hmax = 405 m hmin = 50 m qave = 0.98 qmin = 0.70 Run Time: 2.46 minutes
Figure 2.5: Example of a finite element mesh generated automatically by Admesh+, where the red lines indicate the constrained channel network.
In addition to accommodating interior constraints, Admesh+ was also further developed to provide the underlying mesh data structure required by the described numerical approach. A “standard” mesh data structure consists of a list of nodal
22 point coordinates, each associated with a unique identifier (ID), and an element con- nectivity list that contains the nodal point IDs defining a given element. This type of mesh data structure is part of the standard output of Admesh+ (and all mesh gen- erators). For the numerical approach considered here, the data structure needs to be enriched to include a list identifying all converging edges of the mesh, i.e., those edges whose attached elements both have topographic gradients (slope vectors S0) pointing towards the edge; see sketch of Figure 2.6. As flow propagates only in the direction of the slope vector for the kinematic wave approximation (that is, downhill), this list serves as the indication that flow into these edges will not be allowed to propagate through into the neighboring elements. Instead, the flow into the converging edges will act as lateral inflow, qL, into a one-dimensional kinematic wave approximation that is solved along that edge.
All edges along the original channel network will be converging edges. In addi- tion to these, the (interpolated) topography of the triangulation may also produce converging edges that are not part of the defined channel network (see red lines of
Figure 2.6). For these types of converging edges, the collected overland flow is routed to a node on the defined channel network via the steepest path. A one-dimensional kinematic wave approximation is solved over all edges along this path; Figure 2.6 illustrates an example of these concepts, where all converging edges and flow paths are highlighted.
23 z
x y
Figure 2.6: A three-dimensional profile view of a finite element mesh produced by Admesh+ for a sample watershed, where blue lines indicate edges that are part of the original constrained channel network, red lines indicate one-dimensional overland flow routing edges and large open arrows indicate flow direction over each element face. The sketch to the right illustrates a converging edge. 24 CHAPTER 3
DATA INPUTS
This chapter gives an overview of the necessary data inputs to the hydrodynamic model to accurately model current conditions within the Ohio River watershed. Mod- ifications on the data must be done to allow various data sets to be incorporated into the model, which will also be covered in this chapter.
3.1 DEMs and Cross Sections
The hydrodynamic model must be able to represent the complexities of the Ohio
River watershed topology and floodplain features; identifying the basin boundaries and channel networks is instrumental to the development of the numerical model.
Digital Elevation Models (DEMs) are flexible in terms of watershed selection and are easily accessed through open source toolboxes such as Open Topography [18].
This toolbox utilizes NASA’s Shuttle Radar Topography Mission (SRTM) to generate the DEMs for the hydrodynamic model. These DEMs were then analyzed by the
TopoToolbox [19] to develop topographic data, grid objects, and flow objects to input into Admesh+ [9], as detailed in Section 2.3. The DEMs provided by SRTM data can either have 30 or 90-meter spacing. For this model, 90-meter data was used for the entire basin and 30-meter data was used directly adjacent to the Ohio River to
25 give the best resolution to our area of interest. Due to the data being large, 48 DEM sections were made between each major tributary confluence along the Ohio River.
The DEMs were initially projected horizontally on the World Geodetic System 1984
(WGS84) datum and vertically on the Earth Gravitational Model 1996 (EGM96) datum. The radar used to measure elevation does not penetrate the surface of bodies of water, and for this reason the DEMs must be combined with the cross sectional data of the river to get a complete surface for the model.
3.1.1 Cross section modifications
The USACE provided the cross-sectional data for the Ohio River. Because the
Ohio River spans 3 separate USACE districts, the cross sections provided were on
3 different horizontal and vertical datums with 3 different data resolutions as well.
The Ohio River begins in the Pittsburgh district, which provided cross sectional data that was developed through hydrographic soundings (also referred to as hydrographic surveys), which provide the most detail of the three districts. For more information on how the Army Corps uses and gathers the information for hydrographic surveys see chapter 2 of [23]. The Pittsburgh cross-sectional data covers miles 0 to 126 of the Ohio River. The cross sections were all on the 1983 North American Datum
(NAD83) horizontally and the North American Vertical Datum of 1988 (NAVD88).
These datums are advantageous for the following reasons:
1. The unit of measurement for both the horizontal and vertical datums is U.S.
survey feet. This allows easy distance calculations to be done, as well as calcu-
lating elevation changes for channel slopes.
26 2. These datums are not local datums and can be used throughout the contiguous
United States.
3. Using the NAD83 and the NAVD88 datum together is the standard for the
Universal Transverse Mercator (UTM) coordinate system.
The UTM coordinate system has become the most widely accepted coordinate system for all scales of mapping. UTM utilizes a rectangular grid system (each grid being 6° longitude in width by 8° latitude in height) that starts at the international dateline and continues east, creating 60 UTM zones around the world, see Figure
3.1 courtesy of [17]. The Ohio River falls within zones 16N and 17N, where the “N” denotes that the coordinates are in the northern hemisphere. UTM coordinates use distances from the east (easting) and to the north (northing) to reference a point. Any point on Earth can be uniquely located knowing the zone number, the hemisphere, and the easting and northing coordinate values [16]. For these reasons, and the aforementioned reasons above, all the cross-sectional data will be projected as UTM coordinates to create a seamless river bathymetry.
The Louisville district cross sections were on two different local horizontal datums, the North Kentucky State Plane and the South Kentucky State Plane coordinate sys- tems, and vertically on the North American Vertical Datum of 1927 (NAVD27). The
North Kentucky State Plane cross sections cover miles 437 to 607 and the South
Kentucky State Plane cross sections were miles 607 to 919 of the Ohio River. The
Kentucky State Plane coordinate systems and the vertical datum for the Louisville cross sections needed to be shifted to the UTM datum to match the Pittsburgh district cross sections. This was done using the free software tool VDatum [24], developed by
27 Figure 3.1: A typical UTM map projection around the world.
NOAA’s National Geodetic Survey (NGS), Office of Coast Survey (OCS), and Cen- ter for Operational Oceanographic Products and Services (CO-OPS). This program allows the user to input the current horizontal and vertical datums of the data and project the data to new datums.
The final USACE district, the Huntington district, provided cross sections that were on horizontal Ohio South State Plane Coordinates, but had no vertical datum associated with the data. This data was recorded on particular days (instead of by river mile) and measured elevations from the bottom of the boat using a plumb bob method. The cross sections were placed in order from upstream to downstream through plotting. During the plotting process it was examined if a U.S. Geological
Survey (USGS) river gauge fell within a given cross sectional group of data. The
USGS records the datums of all of their river gauges, which allowed the cross section
28 segments to be assigned a vertical datum. For example, cross sections taken on April
17, 2012 contain the river gauge at Marietta, Ohio (mile 172.2 of the Ohio River).
This gauge has a datum of 566.06 feet above NAVD88. Combining the datum with the bottom of the boat elevations, the Huntington district cross sections were all placed on the NAVD88 vertical datum. The horizontal Ohio South State Plane Coor- dinates were then projected using the VDatum software previously mentioned. The
Huntington district is where the UTM zone changes from 17N to 16N, but VDatum automatically takes that into account with its projected coordinates.
3.1.2 DEM modifications
To enable the DEMs and the cross sections to be combined, the DEMs also had to be projected onto the UTM coordinate system. The data associated with the DEMs could not be run through NOAA’s VDatum because the vertical reference datum
(EGM96) is a geopotential model of Earth, measuring the gravity potential of points.
A geoid, or reference surface for vertical coordinates, is obtained by these gravity measurements [16]. VDatum currently does not have the ability to project surface data sets, therefore ESRI’s ArcGIS [2] was utilized to project the DEM points. The following procedure was completed for each of the 48 DEMs:
1. The text file of DEM X, Y, and Z data was imported into ArcGIS.
2. The original projection of the data was defined. In this case, the horizontal data
projection was defined as WGS84 and the vertical data projection was defined
as EGM96.
3. The new projection was then defined. For our data we wanted NAD83 UTM in
US feet horizontally and NAVD88 in US feet vertically. The UTM zone number
29 needed to be known for this step. Only one DEM fell in both UTM zone 16N
and zone 17N, but it was easy to determine what sections of data belonged in
each zone.
4. Geometry calculations were done to project the original X, Y, and Z data from
the original projection onto the new projection and the data was saved.
3.1.3 Combination
With the cross sections and DEMs on the same datum, a process for combining them to create a complete cross section at each node along the Ohio River was developed. This required the DEM and cross sections to be matched up in easting and northing coordinates, then visually inspected and combined in the Z-direction.
An example of this combination process can be seen in Figure 3.2. This process allows accurate area and wetted perimeter calculations to be done if provided either a stage height or discharge reading.
3.2 U.S. Geological Survey Inputs
The United States Geological Survey (USGS) provided land-use and land-cover data for the hydrodynamic model. Land-use/land-cover data allows the Manning’s roughness coefficient for overland flow to be determined for each element of the mesh.
Each element within the mesh is assigned one of the land cover descriptions seen in Table 3.1. The majority of the land in the Ohio River watershed is covered by deciduous forest and cultivated crops. The USGS soil maps were utilized to determine effective porosity, initial moisture content, section head, and the saturated hydraulic conductivity for each element. One of the soil classes found in Table 3.2 is assigned
30 Figure 3.2: An example of a Digital Elevation Model (green line) being combined with the raw cross section (blue line) to produce a complete river cross section.
to each element. Silt loam and silty clay loam are the two most prevalent soil types in the Ohio River watershed. The USGS also provides current river gauge information which is crucial for initializing the hydrodynamic model, explained further in section
3.2.1.
31 Table 3.1: Land-use/ Land-cover description, Manning’s n coefficient, and intercep- tion depth provided by the USGS. Manning’s n Land cover type: (s/m1/3) Open Water 0.01 Perennial Snow/Ice 0.01 Developed: Open Space 0.35 Developed: Low Intensity 0.35 Developed: Medium Intensity 0.35 Developed: High Intensity 0.35 Barren Land 0.0678 Deciduous Forest 0.36 Evergreen Forest 0.32 Mixed Forest 0.4 Dwarf Scrub 0.4 Shrub/Scrub 0.4 Grassland/Herbaceous 0.368 Sedge/Herbaceous 0.35 Linchens 0.35 Moss 0.35 Hay/Pasture 0.325 Cultivated Crops 0.325 Woody Wetlands 0.086 Emergent Herbaceous Wetlands 0.1825
Table 3.2: Soil infiltration parameters provided by the USGS. Effective Initial Suction Hydraulic Porosity Moisture Head Conductivity Soil class: (cm3/cm3)(cm3/cm3)(cm)(cm/h) Sand 0.417 0.2 4.95 11.78 Loamy Sand 0.401 0.2 6.13 2.99 Sandy Loam 0.412 0.2 11.01 1.09 Loam 0.434 0.2 8.89 0.66 Silt Loam 0.29 0 17 0.34 Sandy Clay Loam 0.33 0.2 21.85 0.15 Clay Loam 0.309 0.2 20.88 0.1 Silty Clay Loam 0.432 0.2 27.3 0.1 Sandy Clay 0.321 0.2 23.9 0.06 Silty Clay 0.423 0.2 29.22 0.05 Clay 0.385 0.2 31.63 0.03
32 3.2.1 River Inputs
The USGS automatically measures data such as stage height, discharge, stream velocity, pH of water, water temperature, and more. The hydrodynamic model is initialized by retrieving current stage height readings along the Ohio River and dis- charge readings from the tributary rivers. The National weather service also provides additional stage data at select locations. It is important to note that all of the current data is considered provisional and is subject to revision. There are 45 river gauges that measure the stage height of the Ohio River, with some of these gauges being lo- cated at dams that provide headwater and tailwater stage readings, see Table A.4 for complete information. The 1-D mesh element that the gauge falls within is assigned the current stage height of the river (constant over the entire element). Many ele- ments may pass before another stage height reading is available. These elements are appointed a stage height value by linearly interpolating between known stage height values, as seen in Figure 3.3. The Ohio River will start out at these prescribed stage heights and be checked periodically as the model runs.
The hydrodynamic model has 65 tributary river inputs feeding current discharge data into the Ohio River, see Tables A.1, A.2, and A.3 of Appendix A. Every tributary river is prescribed an initial stage height based on the flow rate (with known area)
6 days prior to present day. The tributaries then have a 2 day ramp-up period in which discharge data is fed through the river and time of concentrations are noted to accurately feed the Ohio River with time dependent data throughout the model simulation. Chapter 4 will discuss in detail how forecast flow rates were developed for these tributary locations to provide the model with continuous discharge data from
6 days in the past to 3 days in the future.
33 Upstream Gauge Ω Downstream Gauge j−3 Ωj+3 Ωj−2 Ωj−1 Ωj Ωj+1 Known TW Ωj+2
Known HW
H
H (stage height) values interpolated
Figure 3.3: The stage height interpolation from a known tailwater to a known head- water.
All of the gauges used to initialize stage height on the Ohio River and discharge at each tributary can be seen in Figures A.1 to A.17 in Appendix A. Note: the bold blue line indicates the Ohio River, while purple lines represent tributaries. An orange dot with a black outline indicates a dam with stage height readings, while a plain black dot represents a dam without readings for that particular pool — some dams may only have headwater or tailwater readings, not both. An orange dot without an outline represents a river gauge that reads in stage height. Finally, red dots represent the head of a tributary where discharge data is read in.
34 CHAPTER 4
FORECASTING
AMP desires the hydrodynamic model to forecast the stage height of the river at their dam locations out 3 days. To make this possible, forecast precipitation and discharge data must be available within the Ohio River watershed and at all of the tributaries to the Ohio River, respectively. This chapter describes how this was done for the hydrodynamic model.
4.1 Forecast data
There are several approaches that can be taken to forecast rainfall-runoff within a watershed such as autoregressive models, artificial neural network models, and loss modules and unit hydrographs [10, 25, 14]. Autoregressive models and artificial neu- ral network models have the ability to forecast rainfall-runoff with only observed
flow data or observed flow data and observed rainfall data. These models perform well, however, the study done by [10] discovered that forecast flow models could be enhanced by using quality quantitative precipitation forecasting data. The exten- sive pre-processing and post-processing of data as well as the “black-box” approach, as described in [25], also made the artificial neural network method undesirable for our specific modeling approach. [14] found that unit hydrograph-based approaches
35 perform well considering the low number of inputs these models require (rainfall, streamflow, and air temperature data) provided that the quantitative precipitation forecast data being used is accurate. To make the hydrodynamic model as accurate as possible, while still keeping it computationally inexpensive, a quantitative precip- itation forecast/unit hydrograph coupled procedure was taken for the hydrodynamic model.
Quantitative Precipitation Forecasts (QPFs) are used to quantify the amount of liquid precipitation that is expected to fall within a given period of time for a given area (note, frozen forms of water are typically not included in the accumulated total).
There are currently four widely used QPF products available over the continental
United States. These are:
The North American Mesoscale (NAM) Model: This model is run by
the National Centers for Environmental Prediction. It runs four times a day
out to 84 hours (3.5 days) and can provide 3-hour temporal resolution. The
model currently uses 12-kilometer horizontal spatial resolution over all of North
America.
The Global Forecast System (GFS): This model is also produced by the
National Centers for Environmental Prediction. Similar to NAM, the GFS runs
four times a day, but can forecast out to 193 hours (8 days) on a 3-hour temporal
resolution. The model uses a 28-kilometer spatial resolution globally.
36 The European Centre for Medium-Range Weather Forecasts (ECMWF):
Known for their accurate medium-range forecasts, the ECMWF model is capa-
ble of forecasting precipitation out to 168 hours (7 days) on a 6-hour temporal
resolution. This model has global spatial coverage.
The Weather Prediction Center: Run by NOAA’s National Weather Ser-
vice, the WPC provides quantitative precipitation forecast data out to 168
hours (7 days). For the first 72 hours, the QPFs have a 6-hour temporal resolu-
tion. These forecasts are on a 5-kilometer spatial resolution that covers most of
North America, the Western Atlantic and Eastern Pacific oceans, and the Gulf
of Mexico
QPFs are verified through statistical scores, such as a bias (Equation 4.1) and threat score (Equation 4.2), to aid in the selection of the best QPF for the model.
A bias (B) compares forecast and observed precipitation amounts to measure the accuracy of the forecast volume; specifically, it is computed as
F B = (4.1) O where the bias, B, is defined as the forecast coverage area (F ) for a particular threshold divided by the observed area of that threshold (O).
A perfect forecast would be represented by a 1, meaning the forecast amount is equal to the observed precipitation amount. A bias less than 1 means the forecast was a fraction of what was observed and a bias greater than 1 means the forecast over estimated the amount of precipitation that would fall. A threat score (TS) spatially
37 compares the amount of forecast precipitation that falls within an observed area of precipitation, and is given by
C TS = (4.2) F + O − C where TS is the threat score, F is the forecast for a given area, O is the observed precipitation in the area, and C is the “correct” precipitation (where the forecast area overlaps with the observed area).
The maximum threat score is a 1 which means the forecast precipitation falls completely within the observed area and is considered correct data. When half of the forecast precipitation falls within the observed precipitation area, the threat score will equal 0.33. Furthermore, if none of the forecast data falls within the observed area of precipitation and the threat score equals 0.
Because it is more important for our model to accurately identify the area in which rain is falling as opposed to keeping the bias at 1, we focused on choosing a QPF method with the highest threat score. In 2008 there was a study done comparing the previously mentioned forecast models [3]. The GFS and ECMWF outperformed the
NAM model, whose threat score dropped quickly within the 6 day test case period on select hurricanes and tropical cyclone hindcasting [3]. The QPFs provided by the the WPC (then the Hydrometeorological Prediction Center) performed just as well, if not better than the GFS and ECMWF models. Since that analysis, the WPC has improved its QPFs to have threat scores that surpass all of the aforementioned models for the first 54 hours on a 6-hour temporal resolution for different rainfall volumes, see Figures 4.1 and 4.2. The WPC QPFs also have the best spatial resolution of the four available datasets. Spatial resolution is influential to the accuracy of forecasting
38 flow models as displayed in [8]. QPFs using the same temporal resolution, but higher spatial resolution provide better flow approximations than lower spatial resolution data. For those reasons the hydrodynamic model will be using QPFs provided by the
Weather Prediction Center, which have the highest threat scores and the best spatial resolution, for input into the unit hydrographs used for forecast flow. This will be discussed in depth in Section 4.2.
Figure 4.1: A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.25 inches [4].
39 Figure 4.2: A comparison of threat scores of the leading forecasting products over the last year using 6-hour temporal resolution for volumes of rainfall of 0.5 inches [4].
4.2 Unit hydrographs
The unit hydrograph method is one of the most widely used methods for esti- mating excess rainfall runoff. A unit hydrograph displays the delayed response time distribution of runoff resulting from a unit depth of precipitation for a given storm event duration. This storm duration is distributed uniformly in time and space over the watershed area [5]. A typical hydrograph displays the surface-runoff response caused by rainfall events and form a simple bell-curve that has a rising limb reaching a peak discharge, then wanes back to the baseflow of the stream, as seen in Figure
40 4.3. A unit hydrograph only takes into account the discharge due to surface-runoff, although the total discharge in a stream is the sum of the surface-runoff and baseflow
(defined as the amount of discharge from ground water contributions to the stream-
flow). The time from the precipitation event to the peak discharge is commonly referred to as the lag time, which can notably vary based on antecedent conditions, land cover, and the size of the rainfall event. To create the hydrographs for the 65 tributaries leading into the Ohio River, historic rainfall data and discharge data, as well as the drainage basin area, need to be known. For a list of the tributaries feeding into the Ohio River model, see Tables A.1, A.2, and A.3 of Appendix A.
P=∆t Rainfall
∆t Peak Discharge Lag
Runoff, Q(t)
Rising Limb Receding Limb
Time, t
Figure 4.3: A typical unit hydrograph with an instantaneous precipitation event at time t = 0.
41 4.2.1 Historic Rainfall Data
Historic average daily rainfall data was gathered from a single rain gauge as close to
center of the watershed for each of the 65 tributary watersheds from October 1st, 2007 to March, 2016 (when [1] collected the data) from NOAA’s National Climatic Data
Center. This covers a total of 8 hydrological years, which are defined by the USGS as starting October 1st of a given year and ending on September 30th of the following year. It is important for the hydrograph input data to have multiple hydrological years to compare precipitation from one year to the next and to define periods of examination for the model. These periods need to be defined for modeling purposes because precipitation and evapotranspiration can vary significantly seasonally. For instance, looking at a simple water balance equation 4.3 and assuming zero change in storage over a short period of time, the discharge changes based solely on the season’s precipitation and evapotranspiration.
∆S = P − ET − Q, (4.3) ∆t where ∆S/∆t is the change in storage over time, P is the total precipitation volume,
ET is the total evapotranspiration, and Q is the total streamflow or discharge.
In the Ohio River watershed, plants during spring and summer would be taking large amounts of water out of the system through transpiration. Summer is also when evaporation would be at its highest further reducing the amount of water in the water balance for discharge. The amount of evapotranspiration decreases in autumn due to cooler temperatures and deciduous plants becoming dormant for the coming winter.
For the model, spring is defined as March, April, and May; summer is defined as June,
July, and August; and autumn is defined as September, October, and November.
42 Due to uncertainties caused by snow-melt, ice, and ground freezing and thawing, hydrographs were not created for the winter months.
The collected precipitation data was categorized into one of the above seasons.
Further processing on the rain data had to be done to separate storm events and prevent compound hydrographs from forming (see Figure 4.7 for example). Com- pound hydrographs form when there are multiple storm events occurring within a couple of days of one another. Since baseflow is normally restored after 3 days of no rainfall the rain data was separated within the seasonal groups to reflect a gap of 3 days between rainfall events at a minimum. To increase the quality of the historic hydrographs being created, rainfall events were then grouped further into different categories of total rainfall volumes to capture low, medium, high, and in some cases extreme rainfall volume events.
4.2.2 Historic discharge and baseflow separation
Historic discharge data was gathered during the same 8 hydrological year period as the rainfall data from the USGS National Water Information System. The dis- charge data must first be separated into baseflow and surface-runoff components as hydrographs only consider the surface-runoff component when rainfall events arise.
The baseflow separation was done using the local-minimum method over an interval of 5 days for all of the collected discharge data, see [22] for more detail.
The discharge data is then sorted to match each of the previously identified rainfall events. Flow from one day before the rainfall event and 4 days after the event are grouped with that event to ensure we are capturing the entire rising and receding limb of the hydrograph. The minimum discharge from the day leading up to the
43 event was found, as well as the peak discharge, and the minimum discharge in the following four days. The baseflow was subtracted from all of the discharge data and the rainfall was divided out from all of the events. A smooth curve was then fit to this data to smooth out any combined storm events that may have been missed by the initial rainfall processing. The pink lines in Figure 4.4 display the smoothed lines that are created for each rainfall-runoff event in autumn for the group of rainfall events that are from 100 to 500 hundredths of inches in volume at USGS gauge number
03114500: Middle Island Creek at Little, WV. This process was carried out for each rainfall volume for each gauge. An average hydrograph with interpolated values every
3 hours was then determined based on all of the rainfall-runoff events in each category, as seen in Figure 4.4 depicted by the red asterick line.
328 hydrographs were able to be produced for 61 of the 65 tributaries to the
Ohio River once this process was completed for all of the historic data. Certain tributaries were not represented because of the data processing involved. For instance, to avoid a single hydrograph representing an entire sample group, if there was a single hydrograph in a given sample group that hydrograph was not considered. There were also certain tributaries that did not capture all of the rainfall thresholds (low, medium, and high rainfall events) or all of the seasons. The rainfall volume thresholds for the hydrographs created were as follow:
Spring: less than 200 hundredths of an inch, 200 to 500 hundredths of an inch,
and 500 to 1000 hundredths of an inch.
Summer: less than 200 hundredths of an inch, 200 to 600 hundredths of an
inch, and 500 to 1000 hundredths of an inch.
44 Figure 4.4: An example of the average hydrographs that are produced as depicted by the red asterisk line on top of the rainfall-runoff events in a given volume theshold.
Autumn: less than 100 hundredths of an inch, 100 to 500 hundredths of an
inch, and 500 to 1000 hundredths of an inch.
For complete information on the number of samples per threshold, computed average baseflow, and average root mean square value see [1].
4.2.3 Unit hydrograph implementation with forecast data
The hydrodynamic model utilizes forecast discharge values provided by the Na- tional Weather Service’s Advanced Hydrologic Prediction Service (AHPS) whenever
45 that data is available as it will be more accurate than the approximate unit hydro- graphs that were produced [21]. Tributaries that do have this data available are indicated in Tables A.1, A.2, and A.3 of Appendix A. Before examining the unit hydrographs for a given forecast rainfall event, the tributary gauges are checked for seasonal restrictions. If a tributary gauge does not have a unit hydrograph for a given season or if the model is being run for winter time periods, the model takes the average of the preceding 6 days of discharge and uses that constant discharge value as input for the forecast period. The remainder of the gauges will then utilize the unit hydrographs in combination with the forecast data to predict the streamflow.
The forecast rainfall data is automatically collected at 00 Zulu time (also known as
Greenwich Mean Time or Coordinated Universal Time) for each day that a simulation is initiated. This means the forecast data actually begins being read into the model at 8:00 pm local Eastern Daylight Time (EDT). Rainfall events are defined from the data. A rainfall event ends when 6 hours pass with no additional precipitation.
Rain events were easy to identify using QPFs from the WPC because the accumulated precipitation is on a 6-hour temporal resolution. The rainfall event would end as soon as a zero appeared in the data. The identified rainfall events are then summed over the length of the event. At this time, the rainfall events that fall within the same tributary basin are summed. The rainfall gridded points that fall within a given watershed can be seen in Figure 4.5 for example. The rainfall gridded points are denoted by black circles, while the tributary boundary is the polygon encompassing these points. The tributary outlet is represented by the orange dot.
The unit hydrographs created are categorized by rainfall volume and by season.
Each rainfall event described above can now be placed into a category to identify the
46 Figure 4.5: The rainfall that falls within the watershed of USGS tributary station # 03159540 Shade River near Chester, Ohio are depicted as black circles. The tributary boundary is the black surrounding polygon and the outlet is the orange dot.
unit hydrograph to use. The surface-runoff discharge component can be calculated by scaling the unit hydrograph to the rainfall event by finding the product of the unit hydrograph and the precipitation event, see Equation 4.4. Each event is treated as an instantaneous pulse in precipitation at the beginning hour of the event. For example, if an event began at the 12 hour forecast, the unit hydrograph would use hour 12 as its starting hour and be scaled by the summation of the precipitation event. A time series for all of the surface-runoff events was created to ensure that, when applicable, the principal of superposition was applied correctly to the unit hydrographs. The
final step is to add the calculated average baseflow to the surface runoff created by the hydrographs to get a total forecast streamflow.
47 Q(t) = P × UH(t), (4.4) X where Q is the surface-runoff at a given time in ft3/sec, P is the summation of precipitation over the entire watershed in thousandths of an inch per second, and UH is the 3-hour interpolated unit hydrograph data at a given time in ft3/(1/1000in).
Figures 4.6 and 4.7 are examples of the total forecast streamflow created by the
QPFs and unit hydrographs. Figure 4.6 observes a single storm event that began 12 hours after 00Z. Figure 4.7 on the other hand displays two separate rainfall events.
The first event started at 06Z and did not complete its receding limb before the second rainfall event began at 42Z. This figure is a good example of the superposition principal in that the surface runoff components are added to one another. Recognizing that the forecast streamflow will be able to handle multiple events allows us to begin using them in the hydrodynamic model with confidence.
48 Figure 4.6: A hydrograph created for input to the USGS tributary station # 03159540 Shade River near Chester, Ohio. This hydrograph depicts a single storm event.
49 Figure 4.7: A hydrograph created for input to the USGS tributary station # 03612000 Cache River at Froman, Illinois. This hydrograph depicts two combined storm events separated by about one full day of no rainfall.
50 CHAPTER 5
TESTING AND VALIDATION
This chapter will provide insight on the initialization steps for the model and then discuss the hindcasting test cases that were done to verify our model.
5.1 Graphical User Interface
The final product provided to AMP will be the AMP Hydro application in the form of an easy to use Graphical User Interface (GUI), as seen in Figure 5.1. The user will simply be required to enter a run description before starting the simulation.
All of the channel networks utilized in the model are represented by bold red lines.
The Input Station Locations (all of the tributaries with discharge data being read into the model) are listed and indicated on the mesh as the green dots. The Output
Station Locations (AMP’s hydroelectric dams) are listed and represented by yellow dots. Once the simulation comes to completion, these dots will turn red and the user will be able to right click any of the output station dots, and either view the stage height results or export the results to Excel. The Land-Cover and Soil Data tables are also included on the GUI for the user’s reference. The user has the option of viewing the mesh’s elevation (as seen in Figure 5.1), Land-Cover (Figure 5.2), or Soil data (Figure 5.3).
51 52
Figure 5.1: The Graphical User Interface that will be provided to AMP, on Elevation view. 53
Figure 5.2: The mesh from the GUI on Land-Cover view. 54
Figure 5.3: The mesh from the GUI on Soil Data view. The AMP Hyrdo Application user my notice the mesh only represents the area directly adjacent to the Ohio River – and not the full Ohio river watershed (see
Figure 5.4 for the full Ohio River Watershed). The model assumes that all of the water balance variables from Equation 4.3 are taken into account when the tributary provides a discharge reading. Thus, the tributary watersheds are removed from the
final mesh.
Figure 5.4: The complete Ohio River watershed boundary is represented by the bold red line. The stream networks are displayed as well, with the streamline magnitudes defined on the left. The boundary and streamlines were provided by the USGS Elevation Derivatives for National Applications (EDNA).
55 5.2 Model initialization
The initialization steps for the model are now outlined to get a better understand- ing of the processes occurring in the background of the GUI.
5.2.1 Tributary initialization
To begin, the model identifies all of the tributary inputs with discharge readings at their starting points of the 1D channel mesh, refer to Tables A.1 to A.3 of Ap- pendix A — referred to as source tributaries for the remainder of this chapter. The discharge data at the starting points of all of the source tributaries is read in from the USGS National Water Information System website. The majority of these source tributaries have readings every 15 minutes, but some have readings every 5 minutes, every 30 minutes, or every hour. To standardize all of the source tributary readings, a prescribed timestep of 5 minutes is selected and discharge readings are linearly interpolated if need be to fill each 5 minute timestep.
Next, approximate rectangular cross sections are constructed for each tributary based on an approximate constant channel width. Cross-sectional data was not pro- vided by the USACE for the tributary rivers as it was for the Ohio River. Figure
5.5 displays a typical rectangular cross section where B is the approximated channel width and H is the height of the channel. The height for each channel is set to 100 meters for each tributary to ensure that the cross section will never overflow.
The first discharge reading from each source tributary is then assigned throughout the length of the source tributary. This stabilizes the warm-up period of the model and prevents numerical instabilities from propagating. If two or more source tributaries feed into one another before reaching the Ohio river they create what we’re calling
56 H
B
Figure 5.5: Example of the rectangular channel cross section geometry.
a junction tributary, see inset from Figure 2.1. Junction tributaries are assigned a
discharge value equal to the sum of the discharge from all of the source tributaries
feeding into it.
Finally, the lengths of each tributary element are calculated based on the X and
Y coordinates at the beginning and end node for each element. Once each element
has a length associated with it, the bed slope for each tributary is calculated. This
can be calculated simply as,
(z − z ) S = i+1 i , 0 L where S0 is the bed slope, zi+1 is the elevation at the end of the element, zi is the
elevation at the beginning of the element, and L is the length of the element.
The elevation of the end node of each element should be lower than the elevation at
the beginning node, creating negative bed slopes. If the bed slopes become positive, a
prescribed minimum bed slope of -0.0001 is assigned to the element because kinematic
waves must propagate downstream. A constant Manning’s n value is assigned for all
elements within each tributary, as the make-up of the channel is unknown.
57 From the steps above, the only unknowns in Manning’s equation will be the cross-
sectional area (A) and the wetted perimeter (P). The Manning’s equation is calculated
as,
1 A 2/3 Q = S A, (5.1) n P 0 p where Q is the discharge of the channel, n is the Manning’s roughness coefficient, A
is the cross-sectional area, P is the wetted perimeter, and S0 is the channel bed slope.
Rearranging Equation 5.1, we can place all of the known variables on the left-hand
side of the equation and the unknowns on the right-hand side of the the equation,
such that a ratio between area and wetted perimeter is established as:
Q × n A 2/3 √ = A. S0 P An initial stage height (h*) is estimated as halfway between the maximum allowable height in the cross section and the lowest allowable height in the cross section. Using a trapezoidal Riemann sum approach, an approximate area (A*) can be found based on the initial stage height guess. An approximate wetted perimeter (P*) is also calculated from the initial stage height estimate. An approximate ratio of the area
(A*) and perimeter (P*) is then compared to the area (A) and perimeter (P) ratio calculated from the known values; such that,
A 2/3 A* 2/3 A ≈ A*. (5.2) P P * If the A*/P* ratio is larger than the known A/P ratio, a new stage height guess is
approximated by bisecting between the previous stage height guess and the minimum
allowable stage height. Similarly, if the A*/P* ratio is smaller than the known A/P
58 ratio, a new stage height guess is approximated by bisecting between the previous
stage height guess and the maximum allowable stage height. The bisection process
continues until a tolerance of 1 × 10−8 is met between the two area/perimeter ratios.
This process initializes the stage height throughout every element in every tributary
river.
Using the 0th order DG method (p=0), the formula for calculating the change in
area for each timestep becomes,
1 (in) (out) ∆Ai = (Qi − Qi ), Li
where Li is the tributary element length. Expressing this equation as a vector equa-
tion, for every tributary with N elements we would have,
(in) ∆A1 1 1 Q1 , − , 0, ··· 0 (out) ∆A L1 L1 2 1 1 Q1 . 0, , − , ··· 0 out . = L2 L2 Q ( ) (5.3) ...... 2 . ...... . 1 1 . 0, 0, ··· , − ∆A LN LN (out) N QN−1 = DG Matrix = Change in Area Vector = Flux Vector | {z } For a| warm-up{z period} of 0.5 days, the inflow at each source| tributary{z } is updated and the ∆A vector from Equation 5.3 is calculated. The model uses Euler’s method of timestepping through the flow areas, i.e.,
Ai(tn+1) = Ai(tn) + ∆Ai∆t,
where tn+1 = tn + ∆t. A new stage height value is calculated from the area, as well as a new wetted perimeter from the Riemann sum approach discussed previously.
59 5.2.2 Ohio River pool initialization
The AMP Hydro model is made up of 17 different pools – sections of accumulated water – between 18 dams; see Figures A.1 to A.17. These pools are initialized in a similar fashion to the tributaries, except the Ohio River reads in stage height data from the USGS and NWS instead of discharge data. A timestep of 5 minutes is selected, again, to be consistent with the tributary discharge readings. Stage height readings are linearly interpolated to achieve 5 minute timesteps if the data has a larger gap in time between readings. The lengths of each element of a pool are calculated as well as the bed slopes (similar to the process for tributary elements), which again, are prescribed a minimum bed slope if the river is not flowing downstream. A constant
Manning’s n is empirically assigned to each element in a given pool.
The very first element in the first pool of the Ohio River channel has a discharge reading, as well as a stage height reading. Each element following this element is assigned this constant discharge value until a confluence of a tributary occurs. At this point, the discharge from the tributary is added to the constant river discharge and this sum becomes the new constant discharge for the Ohio River until another confluence occurs. Additionally, select gauges along the Ohio River have discharge readings. This reading is then prescribed as the constant flow rate until a tributary confluence is encountered.
Because most of the elements along the Ohio River do not have stage height readings, flow area and wetted perimeter are calculated using the assigned discharge value, Manning’s n, bed slopes, Equation 5.2, and the bisection method detailed previously at elements with corresponding cross-sectional data. Stage height may then be calculated from the area and the cross section. Manning’s n is calculated
60 at locations with stage height readings to add accuracy to our model by rearraging
Equation 5.1 to solve for n. Occasionally, there will be elements with missing cross-
sectional data due to dams or other structure restrictions. At these elements, the
areas, wetted perimeters, and stage heights are linearly interpolated or extrapolated
from the data available.
5.2.3 Running the Model
The change in area vector, DG matrix, and flux matrix for each pool element and
tributary feeding into that pool is constructed after each element is initialized along
the Ohio River. Equation 5.4 is an example of what the change in area equation
might look like along the Ohio River with a single tributary feeding into it. Note, the
calculations from elements along the Ohio River are on the main diagonal of the DG
matrix, while the off diagonal terms represent the tributary.
(in) Q1 1 , − 1 , 0, 0, 0, 0, 0 Q (out) ∆A1 L1 L1 1 0, 1 , − 1 , 0, 0, 0, 0 Q (out) ∆A2 L2 L2 2 1 1 1 (out) ∆A = 0, 0, , − , 0, 0, (5.4) 3 L3 L3 L3 Q3 1 1 (in) ∆A4 0, 0, 0, 0, , − , 0 L4 L4 Q4 1 1 ∆A5 0, 0, 0, 0, 0, , − (out) L5 L5 Q4 (out) = DG Matrix Q 5 | {z } = Flux Vector The inflow at the first element in the first pool is updated by reading| {z in discharge} data for each 5 minute timestep. The first element in every other pool is updated on this same timestep with the total outflow from the previous pool. For each stage height reading being read in, an area at that time is computed by,
61 δt A(t ) = A(t ) + × (Q (t ) − Q (t )), n+1 n L in n out n
where both Qin(tn) and Qout(tn) are computed using Manning’s formula. Next, using
the stage height reading at the next timestep (tn+1), we calculate what the area should be, A*(tn+1), and using the formula,
δt A*(t ) = A(t ) + × (Q (t ) − Q* (t )), n+1 n L in n out n
we solve for Q*out(tn).
A “correction” factor (dQ) — that correlates with Qin — can then be established at
the dams for the flux such that,
dQout = Q*out − Qout,
which can be rearranged to solve for the correct Q*out.
Throughout a warm-up phase of 3 days, all of the Qin values and their correspond-
ing correction factors (dQ) are saved off. After this 3 day period, we go into model
prediction mode where Qin and Qout are computed using Manning’s formula. Qout is
then “corrected” using the previously established correction factors by interpolation
and/or extrapolation by curve fitting. An example of these correction factors and
corresponding Qin values can be seen in Figure 5.6. The fit of these plots are made
empirically for each pool. The area, stage height, and wetted perimeter are updated
at every timestep while the current data is being read in, and once the model goes
into prediction mode.
62 63
Figure 5.6: A sample dQ vs. Qin correction fit. 5.3 Results
A hindcast study was done for the first 3 dams along the Ohio River model. These dams are Montgomery Island, New Cumberland, and Pike Island Lock and Dam. This study used the period of July 5th to July 8th as the initialization and warm-up period, and then predicted July 8th through the 11th. In Figures 5.7 to 5.9, each dam has its headwater and tailwater predicted as the blue line. The observed data is represented by the orange line which is then enveloped by a half foot error on each side.
The AMP Hydro model captures the headwater and tailwater depths well for about the first day and a half of prediction. The model also follows the peaks and minimas in the tailwater of Montgomery Island Lock and Dam extremely well for the first day and a half. Even after that period of time, the model typically stays within 0.5 feet of the observed data. Further calibration could be done to find better dQ vs. Qin correctional fit lines. Manning’s roughness coefficients could also be further explored and adjusted if need be. These results prove to be encouraging as we continue to model the remainder of the pools in the Ohio River.
64 65
Figure 5.7: The headwater and tailwater results at Montgomery Island Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data. 66
Figure 5.8: The headwater and tailwater results at New Cumberland Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data. 67
Figure 5.9: The headwater and tailwater results at Pike Island Lock and Dam. Observed stage height is represented by the orange line, the DG model results by the blue line, and the gray shaded region is a ±0.5 foot envelope around the observed data. CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1 Findings and Conclusions
A discontinuous Galerkin-based forecasting tool for the Ohio River has been de- veloped. This tool utilizes high-quality meshes through the use of Admesh+, with a
multi-physics/multidimensional modeling approach, and multiple data sets to make
the most accurate forecast model. The AMP Hydro model has shown to be accurate
within a foot of the observed data at the first 3 dams in the Ohio River model. This
was proven in the hindcast test case done for the model for the July 8th to 11th period.
Similar results in the remainder of the pools are expected to follow before providing
the GUI to AMP. Continuing calibration on the model could provide more accurate
results, however, the AMP Hydro model will provide AMP with valuable information
at their dam locations.
6.2 Future Work
In the future, this river model could extend to rivers in areas that experience
frequent droughts or rivers with contamination problems to allow those communities
to manage their water resources better. A model similar to AMP Hydro could be
68 made for the Maumee River to be incorporated with DG-WAVE’s new transport model capabilities [20]. This would be advantageous for examining the relationship between runoff from agricultural areas to the algal bloom development in Lake Erie.
The Maumee River flows into the section of Lake Erie that appears to have the most algal bloom overgrowth. It has been estimated that the Maumee watershed is made up of roughly two-thirds farmland, with the major crops being corn and soybeans.
It has been observed by [27] that an increase in row crop cultivation, such as corn and soybeans, increases streamflow and surface runoff due to these crops requiring less water than perennial vegetation. This runoff will carry excess phosphorus and other agricultural herbicides used on crops to Lake Erie, which could potentially be contributing to the algal bloom overgrowth.
69 APPENDIX A
MODEL INPUTS
Table A.1: List of the tributary rivers in the Pittsburgh USACE Engineering district being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. USGS Description Basin Area Number: (mi2) 03086000 Ohio River at Sewickley, PA* 19,500 03107500 Beaver River at Beaver Falls, PA* 3,106 03108000 Raccoon Creek at Moffatts Mill, PA 178 03109500 Little Beaver Creek Near East Liverpool, OH 496 03110000 Yellow Creek Near Hammondsville, OH 147 03111200 Dunkle Run Near Claysville, PA 7.69 03111500 Short Creek Near Dillonvale, OH 123 03111955 Wheeling Creek Near Majorsville, WV 152 03111548 Wheeling Creek Below Blaine, OH 97.7 03113990 Captina Creek at S.R. 148 at Armstrongs Mills, OH 127
70 Table A.2: List of the tributary rivers in the Huntington USACE Engineering district being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. USGS Description Basin Area Number: (mi2) 03114500 Middle Island Creek at Little, WV 458 03115400 Little Muskingum River at Bloomfield, OH 210 03115786 Duck Creek Below Whipple, OH 260 03150500 Muskingum River at Beverly, OH* 7,947 03155220 South Fork Hughes River Below Macfarlan, WV 229 03155000 Little Kanawha River at Palestine, WV* 1,516 03159500 Hocking River at Athens, OH* 943 03159540 Shade River Near Chester, OH 156 03198000 Kanawha River at Charleston, WV* 10,448 03200500 Coal River at Tornado, WV* 862 03202000 Raccoon Creek at Adamsville, OH 585 03203600 Guyandotte River at Logan, WV* 833 03205470 Symmes Creek at Aid, OH 302 03206600 East Fork Twelvepole Creek Near Dunlow, WV 37.9 03214500 Tug Fork at Kermit, WV 1,280 03212500 Levisa Fork at Paintsville, KY* 2,144 03215410 Blaine Creek Near Blaine, KY 79.23 03216500 Little Sandy River at Grayson, KY* 400 03217000 Tygarts Creek Near Greenup, KY 242 03237020 Scioto River at Piketon, OH* 5,836 03237500 Ohio Brush Creek Near West Union, OH 387 03238495 White Oak Creek Above Georgetown, OH 207.9
71 Table A.3: List of the tributary rivers in the Louisville USACE Engineering district being fed into the Ohio River model. Tributaries with an * next to the description have forecast discharge data provided by the National Weather Service AHPS. USGS Description Basin Area Number: (mi2) 03247500 East Fork Little Miami River at Perintown, OH 476 03245500 Little Miami River at Milford, OH* 1,203 03254520 Licking River at Hwy 536 Near Alexandria, KY 3,593 03254550 Banklick Creek at Highway 1829 Near Erlanger, KY 30 03259000 Mill Creek at Carthage, OH 115 03274000 Great Miami River at Hamilton, OH* 3,630 03276500 Whitewater River at Brookville, IN* 1,224 03277075 Gunpowder Creek at Camp Ernst Rd Near Union, KY 36.6 03291500 Eagle Creek at Glencoe, KY 437 03290500 Kentucky River at Lock 2 at Lockport, KY* 5,984 03291780 Indian-Kentuck Creek Near Canaan, IN 27.5 03294000 Silver Creek Near Sellersburg, IN 189 03298000 Floyds Fork Near Mt Washington, KY 138 03295400 Salt River at Glensboro, KY 172 03301500 Rolling Fork Near Boston, KY 1,299 03302220 Buck Creek Near New Middletown, IN 37.1 03303000 Blue River Near White Cloud, IN 284 03303300 Middle Fork Anderson River at Bristow, IN 39.8 03321500 Green River at Lock 1 at Spottsville, KY* 9,181 03322011 Pigeon Creek Near Fort Branch, IN 35.4 03378500 Wabash River at New Harmony, IN* 29,234 03381500 Little Wabash River at Carmi, IL* 3,102 03382100 South Fork Saline River Near Carrier Mills, IL 147 03384100 Tradewater River Near Providence, KY 605 03612000 Cache River at Forman, IL 244 03438000 Little River Near Cadiz, KY 244 03436100 Red River at Port Royal, TN 496 03431800 Sycamore Creek Near Ashland City, TN 97.2 03431790 Cumberland River at Ashland City, TN 13,117 03434500 Harpeth River Near Kingston Springs, TN 683 03436690 Yellow Creek at Ellis Mills, TN 103 03610200 Clarks River at Almo, KY 134 03611260 Massac Creek Near Paducah, KY 14.6
72 Table A.4: Stage height gauges along the Ohio River used to initialize the model. Associated ID Frequency of Agency Number Description: data (minutes) USGS 03086001 Sewickley-PA (TW) 15 USGS 03108490 Montgomery Dam & Locks at Ohioview-PA (HW) 15 USGS 03108500 Montgomery Lock & Dam-PA (TW) 15 USGS 03110685 New Cumberland Lock & Dam-OH (HW) 15 USGS 03110690 New Cumberland Lock & Dam-OH (TW) 15 USGS 03111515 Pike Island Dam Near Wheeling-WV (HW) 15 USGS 03111520 Pike Island Lock & Dam-WV (TW) 15 USGS 03112500 Wheeling-WV (Gauge) 15 USGS 03114275 Hannibal Lock and Dam-OH (HW) 15 USGS 03114280 Hannibal Lock and Dam-OH (TW) 15 USGS 03114306 Above Sardis-OH (Gauge) 15 NWS rnoo1 Willow Island Lock-OH (TW) 60 USGS 03150700 Marieeta-OH (Gauge) 15 USGS 03151000 Parkersburg-WV (Gauge) 15 NWS bevw2 Belleville Lock-WV (TW) 30 NWS racw2 Racine Lock-WV (TW) 30 USGS 03201500 Point Pleasant-WV (Gauge) 15 NWS galw2 R C Byrd Lock-WV (TW) 30 USGS 03206000 Huntington-WV (Gauge) 15 USGS 03216000 Ashland-KY (Gauge) 30 USGS 03216070 Ironton(River Gauge)-OH 15 USGS 03216600 Greenup Dam Near Greenup-KY (HW&TW) 15 USGS 03217200 Portsmouth(River Gauge)-OH 30 USGS 03238000 Maysville(River Gauge)-KY 30 NWS melo1 Meldahl Dam(lower)-OH 30 USGS 03255000 Cincinnati(River Gauge)-OH 15 USGS 03277200 Markland Dam Near Warsaw(upper)-KY 15 NWS mklk2 Markland (lower)-KY 15 USGS 03292494 Water Tower at Lousiville(River Gauge)-KY 15 USGS 03293551 McAlpine Dam at RRB at Louisville(upper)-KY 15 USGS 03294500 Louisville(lower)-KY 15 USGS 03294600 Kosmosdale(river gauge)-KY 15 USGS 03303280 Cannelton Dam at Cannelton(TW)-IN 15 USGS 03304300 Newburgh Lock and Dam-IN(TW) 15 USGS 03322000 Evansville (river Gauge)-IN 15 USGS 03322190 Henderson(river gauge)-KY 15 USGS 03322420 Uniontown Dam(TW)-KY 15 USGS 03381700 Old Shawneetown-IL-KY 15 USGS 03384500 Dam 51 at Golconda-IL 15 USGS 03399800 Smithland Dam-KY (HW&TW) 15 NWS pahk2 Paducah-KY 15 NWS brki2 Brookport Lock and Dam(pool)-IL 60 NWS gcti2 Grand Chain Lock and Dam(pool)-IL 60 USGS 03612600 Olmsted-IL 15 NWS ciri2 Cairo-IL (Gauge) 60
73 40.80 POOL 1
Tributary: Beaver River USGS # 03107500 40.75 Discharge data (Q) read in every 15 minutes
Montgomery L&D USGS # 03108490 40.70 Stage height (H) read in every 15 minutes
40.65
Dashields L&D Tributary: Raccoon Creek /Sewickley USGS # 03108000 USGS # 03086001 40.60 Discharge data (Q) read Stage height (H) in every 15 minutes read in every 15 minutes
40.55
-80.40 -80.35 -80.30 -80.25 -80.20 -80.15
Figure A.1: Pool 1 begins at the tailwaters of Dashields Lock and Dam and ends at the headwaters of Montgomery Lock and Dam. It has 2 tributaries feeding into this section of the river: Beaver River and Raccoon Creek.
74 POOL 2 Tributary: Little Beaver Creek 40.70 USGS # 03109500 Discharge data (Q) read in every hour Tributary: Yellow Creek USGS # 03110000 40.65 Discharge data (Q) read in every 15 minutes
Montgomery L&D 40.60 USGS # 03108500 Stage height (H) read
75 in every 15 minutes
40.55
New Cumberland L&D USGS # 03110685 Stage height (H) read 40.50 in every 15 minutes
-80.75 -80.70 -80.65 -80.60 -80.55 -80.50 -80.45 -80.40 -80.35
Figure A.2: Pool 2 begins at the tailwaters of Montgomery Lock and Dam and ends at the headwaters of New Cumberland Lock and Dam. This pool has 2 tributary river feeding into this section of the river: Little Beaver Creek and Yellow Creek. 40.55 POOL 3
New Cumberland L&D 40.50 USGS # 03110690 Stage height (H) read in every 15 minutes 40.45
40.40
40.35 Tributary: Short Creek USGS # 03111500 Discharge data (Q) read in every 40.30 Tributary: Dunkle Run 15 minutes USGS # 03111200 Discharge data (Q) read 40.25 in every 5 minutes
40.20
40.15 Pike Island L&D USGS # 03111515 Stage height (H) read in every 15 minutes 40.10
-80.80 -80.75 -80.70 -80.65 -80.60 -80.55 -80.50 -80.45 -80.40
Figure A.3: Pool 3 begins at the tailwaters of New Cumberland Lock and Dam and ends at the headwaters of Pike Island Lock and Dam. This pool has 2 tributaries feeding into the section: Dunkle Run and Short Creek.
76 40.20 POOL 4 Pike Island L&D USGS # 03111520 Tributary: Wheeling Creek Stage height (H) read USGS # 03111548 in every 15 minutes 40.10 Discharge data (Q) read in every 15 minutes
River Gauge USGS #03112500 40.00 Stage height (H) read in every 15 minutes
Tributary: Wheeling Creek 39.90 USGS # 03111955 Discharge data (Q) read in every 15 minutes Tributary: Captina Creek USGS # 03113990 39.80 Discharge data (Q) read in every 15 minutes
39.70 Hannibal L&D USGS # 03114275 Stage height (H) read in every 15 minutes
39.60
-81.00 -80.95 -80.90 -80.85 -80.80 -80.75 -80.70 -80.65 -80.60 -80.55 -80.50
Figure A.4: Pool 4 begins at the tailwaters of Pike Island Lock and Dam and ends at the headwaters of Hannibal Lock and Dam. This pool has 3 tributaries feeding into this section: Wheeling Creek, Wheeling Creek, and Captina Creek.
77 39.70 POOL 5 39.65 River Gauge USGS # 03114306 Stage height (H) read 39.60 in every 15 minutes
39.55 Hannibal L&D USGS # 03114280 Stage height (H) read 39.50 in every 15 minutes
39.45
Tributary: Middle Island Creek Willow Island L & D USGS # 03114500 39.40 Discharge data (Q) read in every 15 minutes
39.35
-81.30 -81.20 -81.10 -81.00 -80.90 -80.80
Figure A.5: Pool 5 begins at the tailwaters of Hannibal Lock and Dam and ends at the headwaters of Willow Island Lock and Dam. This pool has a single tributary: Middle Island Creek.
78 39.60 Tributaries: POOL 6 1 Discharge data (Q) read in every 30 minutes 1) Little Muskingum River USGS # 03115400 2 6) Hocking River USGS # 03159500 3 39.50 Discharge data (Q) read in every 15 minutes 2) Duck Creek USGS # 03115786 3) Muskingum River USGS # 03150500 39.40 4) South Fork Hughes USGS # 03155220 5) Little Kanawha River USGS # 03155000 a
39.30 6 Willow Island L & D NWS ID 'rnoo1' Stage height (H) read in every hour
79 b 39.20 River Gauges USGS #03150700 (a) 39.10 USGS #03151000 (b) Stage height (H) read Belleville L & D in every 15 minutes 4 5 39.00
-82.20 -82.00 -81.80 -81.60 -81.40 -81.20
Figure A.6: Pool 6 begins at the tailwaters of Willow Island Lock and Dam and ends at the headwaters of Belleville Lock and Dam. This pool has 6 tributaries. POOL 7 39.15
39.10
Belleville L&D NWS ID 'bevw2' 39.05 Tributary: Shade River Stage height (H) read USGS # 03159540 in every 30 minutes Discharge data (Q) read in every 30 minutes 39.00
38.95
Racine L&D
38.90
38.85
-81.95 -81.90 -81.85 -81.80 -81.75 -81.70
Figure A.7: Pool 7 begins at the tailwaters of Belleville Lock and Dam and ends at the headwaters of Racine Lock and Dam. This pool has a single tributary: Shade River.
80 39.10 POOL 8
River Gauge USGS # 03201500 39.00 Stage height (H) read in every 15 minutes
38.90 Racine L&D NWS ID 'racw2' 38.80 Stage height (H) read in every 30 minutes
38.70
Tributary: 38.60 Kanawha River USGS # 03198000 Tributary: Raccoon Creek Discharge 38.50 USGS # 03202000 data (Q) Discharge data (Q) read read in every in every 30 minutes 15 minutes
38.40 Tributary: Coal River USGS # 03200500 Discharge data (Q) read 38.30 in every 15 minutes
-82.40 -82.30 -82.20 -82.10 -82.00 -81.90 -81.80 -81.70 -81.60
Figure A.8: Pool 8 begins at the tailwaters of Racine Lock and Dam and ends at the headwaters of R.C. Byrd Lock and Dam. This pool has 3 tributaries: Kanawha River, Coal River, and Raccoon Creek.
81 38.80 Greenup L&D USGS # 03216600 POOL 9 R. C. Byrd L&D NWS ID 'galw2' Stage height (H) read Stage height (H) read in every 15 minutes in every 30 minutes 2 38.60 c
b
7 a
38.40 1 3
River Gauges 38.20 USGS # 03206000 (a) USGS # 03216000 (b) USGS # 03216070 (c) Stage height (H) read in every 15 (a & c) or 30 (b) minutes
38.00 6 Tributaries: Discharge data (Q) read in every 15 minutes 1) Guyandotte River USGS # 03203600 2) Symmes Creek USGS # 03205470 3) East Fork Twelvepole USGS # 03206600 5 4) Tug Fork USGS # 03214500 4 37.80 Discharge data (Q) read in every 30 minutes 5) Levisa Fork USGS # 03212500 6) Blaine Creek USGS # 03215410 7) Little Sandy Creek USGS # 03216500
-83.00 -82.80 -82.60 -82.40 -82.20 -82.00 -81.80
Figure A.9: Pool 9 begins at the tailwaters of R.C. Byrd Lock and Dam and ends at the headwaters of Greenup Lock and Dam. This pool has 7 tributaries.
82 39.20
Greenup L & D Tributaries: 39.10 Discharge data (Q) read in every 15 minutes POOL 10 USGS # 03216600 1) Tygarts Creek USGS # 03217000 Stage height (H) 2) Scioto River USGS # 03237020 read in 15 minutes 39.00 4) Ohio Brush Creek USGS # 03237500 2 4) White Oak Creek USGS # 03238495 4 38.90
Meldahl L & D 38.80 3
38.70 River Gauges b USGS # 03217200 (a) USGS # 03238000 (b) 38.60 Stage height (H) read a in every 30 minutes 1
38.50
-84.20 -84.00 -83.80 -83.60 -83.40 -83.20 -82.80 83 -83.00
Figure A.10: Pool 10 begins at the tailwaters of Greenup Lock and Dam and ends at the headwaters of Meldahl Lock and Dam. This pool has 4 tributaries. 39.60
Tributaries: Discharge data (Q) read in every 15 minutes POOL 11 39.50 1) East Fork USGS # 03247500 2) Little Miami River USGS # 03245500 3) Licking River USGS # 03254520 4) Banklick Creek USGS # 03254550 39.40 5) Mill Creek USGS # 03259000 River Gauge 6) Great Miami River # 03274000 USGS # 03255000 7) Whitewater River USGS # 03276500 8) Gunpowder Creek USGS # 03277075 Stage height (H) read 39.30 in every 15 minutes
7 6 39.20 5 2
1 39.10
39.00 8
4 38.90 3 Markland L & D USGS # 03277200 Stage height (H) read Meldahl L & D 38.80 in every 15 minutes NWS ID 'melo1' Stage height (H) read in every 30 minutes
38.70 -85.20 -85.00 -84.80 -84.60 -84.40 -84.20
Figure A.11: Pool 11 begins at the tailwaters of Meldahl Lock and Dam and ends at the headwaters of Markland Lock and Dam. This pool has 8 tributaries.
84 38.90 3 Markland L&D POOL 12 NWS ID 'mklk2' Stage height (H) read 38.80 in every 15 minutes McAlpine L&D USGS # 03293551 38.70 Stage height (H) read 1 in every 15 minutes
River Gauge 38.60 USGS # 03292494 Stage height (H) read in every 15 minutes 38.50 85
2 38.40 4 Tributaries: Discharge data (Q) read in every 15 minutes 1) Eagle Creek USGS # 03291500 2) Kentucky River USGS # 03290500 38.30 3) Indian-Kentuck Creek USGS # 03291780 4) Silver Creek USGS # 03294000
38.20 -85.80 -85.60 -85.40 -85.20 -85.00 -84.80
Figure A.12: Pool 12 begins at the tailwaters of Markland Lock and Dam and ends at the headwaters of McAlpine Lock and Dam. This pool has 4 tributaries. 38.50
38.40 McAlpine L & D POOL 13 USGS # 03294500 Stage height (H) read 38.30 in every 15 minutes 5
38.20 River Gauge 4 USGS # 03294600 38.10 1 Stage height (H) read in every 15 minutes 38.00 Cannelton L & D 2 37.90 Tributaries: 3 Discharge data (Q) read in every 15 minutes 37.80 Tributaries: 2) Salt River USGS # 03295400 Discharge data (Q) read in every 5 minutes 3) Rolling Fork USGS # 03301500 37.70 1) Floyd Fork USGS # 03298000 4) Buck Creek USGS # 03302220 5) Blue River USGS # 03303000
37.60 86 -86.80 -86.60 -86.40 -86.20 -86.00 -85.80 -85.60 -85.40 -85.20 -85.00
Figure A.13: Pool 13 begins at the tailwaters of McAlpine Lock and Dam and ends at the headwaters of Cannelton Lock and Dam. This pool has 5 tributaries. 38.20
Tributary: Middle Fork 38.15 POOL 14 USGS # 03303300 Discharge data (Q) not 38.10 currently available
38.05
38.00
37.95 Newburgh L & D 87 37.90 Cannelton L&D 37.85 USGS # 03303280 Stage height (H) read in every 15 minutes 37.80
37.75
-87.40 -87.30 -87.20 -87.10 -87.00 -86.90 -86.80 -86.70
Figure A.14: Pool 14 begins at the tailwaters of Cannelton Lock and Dam and ends at the headwaters of Newburgh Lock and Dam. This pool has a single tributary: Middle Fork. 38.30 POOL 15 2
38.20 Tributaries: Discharge data (Q) read in every 15 minutes 1) Green River USGS # 03321500 2) Pigeon Creek USGS # 03322011 38.10 River Gauges USGS # 03322000 (a) USGS # 03322190 (b) Stage height (H) read 38.00 in every 15 minutes a
37.90 1 b
Newburgh L&D 37.80 USGS # 03304300 Stage height (H) read in every 15 minutes Myers/Uniontown L&D
37.70 -88.10 -88.00 -87.90 -87.80 -87.70 -87.60 -87.50 -87.40 -87.30
Figure A.15: Pool 15 begins at the tailwaters of Newburgh Lock and Dam and ends at J.T Myers/Uniontown Lock and Dam. This pool has 2 tributaries: Green River and Pigeon Creek.
88 38.20 Tributaries: POOL 16 Discharge data (Q) not currently available 1) Wabash River USGS # 03378500 Discharge data (Q) read in every 15 minutes 1 2) Little Wabash River USGS # 03381500 3) South Fork River USGS # 03382100 2 38.00 4) Tradewater River USGS # 03384100 5) Cache River USGS # 03612000
River Gauges USGS # 03381700 (a) USGS # 03384500 (b) 37.80 Stage height (H) read in every 15 minutes a
37.60 3
4 37.40 5 b Myers/Uniontown L&D USGS # 03322420 Stage height (H) read 37.20 Smithland L&D in every 15 minutes USGS # 03399800 Stage height (H) read in every 15 minutes
37.00 -89.00 -88.80 -88.60 -88.40 -88.20 -88.00 -87.80
Figure A.16: Pool 16 begins at the tailwaters of J.T Myers/Uniontown Lock and Dam and ends at the headwaters of Smithland Lock and Dam. This pool has 5 tributaries.
89 37.50
POOL 17 Smithland L&D USGS # 03399800 Stage height (H) read in every 15 minutes
8 37.00
Olmsted L&D USGS # 03612600 River Gauges Stage height (H) read NWS ID 'pahk2' (15 minutes) in every 15 minutes 1 NWS ID 'brki2' (1hour) 7 NWS ID 'gcti2' (1 hour) Tributaries: Discharge data (Q) read in every 15 minutes
90 4) Cumberland River USGS # 03431790 36.50 2 7) Clarks River USGS # 03610200 8) Massac Creek USGS # 03611260 Discharge data (Q) read in every 30 minutes 3 1) Little River USGS # 03438000 6 2) Red River USGS # 03436100 4 3) Sycamore Creek USGS # 03431800 5) Harpeth River USGS # 03434500 5 6) Yellow Creek USGS # 03436690 36.00 -89.50 -89.00 -88.50 -88.00 -87.50 -87.00
Figure A.17: Pool 17 begins at the tailwater of Smithland Lock and Dam and end at the headwaters of Olmsted Lock and Dam. This pool has 8 tributaries. BIBLIOGRAPHY
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