United States
Environmental Protection
Agency
Office of Water
4305
May 8, 2007
<&EPA BASINS Technical Note 2
Two Automated Methods for Creating
Hydraulic Function Tables (FTABLES)
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Technical Note 2
Two Automated Methods for Creating Hydraulic Function Tables (FTABLES)
By Keara Moore, with assistance from Yusuf Mohamoud
May 8, 2007
INTRODUCTION
The HSPF model (Bicknell, et al, 1996) uses a hydraulic function table, called an
FTABLE, to represent the geometric and hydraulic properties of water bodies, including
both stream reaches and fully mixed reservoirs. The accuracy of the FTABLE is
particularly important for the model's simulation of flow velocity and sediment transport.
For HSPF projects originated through BASINS, FTABLEs are initially created by
WinHSPF as part of the project's .uci file. WinHSPF constructs FTABLEs based on
reach information included in the input files from BASINS along with a set of standard
assumptions about channel geometry and hydraulics. As described in this technical
memo, the WinHSPF interface now provides a tool to facilitate creation of a new
FTABLE that is based on alternative inputs and geometric assumptions and may lead to
improved accuracy. Additionally, a hydraulic calibration procedure has been introduced
as an option to evaluate and improve FTABLE accuracy.
The FTABLE in HSPF
An FTABLE is a piecewise linear function table - a table used to document, in discrete
numerical form, a functional relationship between two or more variables. In HSPF, the
FTABLE describes the hydraulics of a river reach or reservoir (RCHRES) segment by
defining the functional relationship between water depth, surface area, volume, and
outflow in the segment (see Figure 1). The relationship described in the FTABLE is
independent of the shape of the water body; water bodies with different shapes could
have identical FTABLEs. In other words, in order to apply the functional relationship
described in the FTABLE, it is not necessary for HSPF to have any assumptions
regarding the shape of a stream channel. In projects with multiple reaches, each will
have its own FTABLE.
The FTABLE has columns for depth, surface area, volume, and outflow with each row
containing values corresponding to a specified water depth (Figure 1). The system
obtains intermediate values by interpolation. The number of rows in the FTABLE
depends on the range of depth to be covered and the desired resolution. The FTABLEs
described in this document contain only a single outflow column, although there can be
up to five columns for outflow. Consult the HSPF manual (Bicknell et al, 1996) for
information on ways to use these extra columns to specify more complex outflow
situations such as time-dependent releases. For information on developing FTABLEs for
reservoirs see Technical Note 1, http://www.epa.gov/waterscience/BASINS/tecnotel.pdf.
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|n1|ow
— — — —
y i 3 n r- n n «
QZ a v> > U.U.U.U.
4 53 13D250D12 3C 2C 20
2 1,5 1 3 12 6 IP 0
3 1Q 15 BD 12 16 10 0
u a o a ~ u a
A) Typical reach.
B) FTABLE specifying geometry and hydraulic
properties of a reach.
Figure 1. Typical reach configuration and the FTABLE method used to represent
geometric and hydraidic properties.
FTABLE DEVELOPMENT USING WinHSPF
WinHSPF (2.3.8), the version associated with BASINS 4.0, offers two options for
automatic FTABLE development: the Standard Method, used as the default when the
initial FTABLE is created, and the Alternative Method, which is new to this WinHSPF
version and uses different estimations of hydraulic geometry properties. It is also
possible for users to create FTABLEs manually in WinHSPF, but this option will not be
discussed in the current technical memo. Both automatic methods follow a similar
process:
1) Estimate primary hydraulic geometry parameters (mean flow depth, mean flow
width, Manning's n, and longitudinal slope of the channel) based on available
data about the reach;
2) Derive the channel cross-section using the mean flow depth and width along with
a pre-defined channel and flood plain geometry;
3) At a variety of depth intervals, estimate surface area and volume based on the
channel cross-section and estimate outflow using Manning's equation; and
4) Format the results as an FTABLE that is compatible to the UCI format.
As described below, the methods differ in the assumptions and algorithms used at each
step of the process. Figure 2 demonstrates an example of how FTABLES created by
these different methods can differ for the same reach. Once the automatic FTABLE has
been created, it can be manually edited by the user or refined through hydraulic
calibration. Accuracy of the FTABLE is particularly important for accuracy in modeling
flow velocity and sediment transport; it has less effect on results for discharge.
2
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Standard Method FT ABLE
Depth
Area
Volume
Outflow
(ft)
(acres)
(acre-ft)
(ft3/s)
0
111.85
0
0
0.31
112.76
34.25
11.36
3.05
120.96
355.04
524.40
3.81
123.24
448.14
760.07
4.77
370.86
798.89
970.59
5.72
376.56
1155.08
1774.37
98.17
929.19
61516.11
704771
190.63
1481.82
172970.4
2864918
Alternative Method FTABLE
Depth
Area
Volume
Outflow
(ft)
(acres)
(acre-ft)
(ft3/s)
0
0
0
0
0.02
65.93
1.32
0.11
0.06
66.11
3.96
0.7
0.1
66.29
6.61
1.63
0.2
66.74
13.26
5.19
0.6
68.53
40.31
32.43
1
70.33
68.09
76.11
1.2
71.22
82.24
103.24
1.6
73.02
111.09
167.1
2
74.81
140.65
242.95
3
79.29
217.71
480.87
4
83.78
299.24
783.17
5
88.26
385.26
1146.63
5.71
91.43
448.78
1439.6
8.56
246.15
930.42
3537.62
11.41
258.94
1651.06
7727.39
14.27
271.74
2408.2
13178.74
17.12
284.53
3201.86
19804.82
57.07
463.65
18146.3
228802.6
a) FTABLEs created for the same reach using the Standard Method and the Alternative Method (Ridge &
Valley physiographic province).
O Standard Method
- - Alternative Method
Depth (ft)
Alternate FTABLE Methods
-VOLUME
b) Depth vs. Volume from FTABLEs created for the same watershed using both automatic methods. Inset
zooms to the bankfull depth.
Figure 2. Comparison of FTABLES createdfor the same reach using the Standard
Method and the Alternative Method.
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A. Standard Method
When an HSPF watershed model is originated through BASINS, WinHSPF by default
automatically creates FTABLEs using the Standard Method. For the first step, WinHSPF
extracts the primary geometric parameters - mean flow depth, mean flow width, and
longitudinal slope of the channel - from the BASINS stream GIS layer, defined by the
user when initiating HSPF from BASINS. The roughness coefficient, Manning's n, is set
to a default value of 0.05.
WinHSPF then derives the channel cross-section by assuming a compound trapezoidal
geometry that has one channel section with a side slope of 1:1 and two floodplain
sections, each with side slopes of 0.5:1 (see Figure 3). Additional geometric parameters
are estimated based on the mean flow depth and width using assumptions presented in
Table 1. All of these estimated geometric parameters can be adjusted by the user to
refine the model's operation, as described below.
The Standard Method FTABLE consists of area-volume-flow relationships at 8 depths,
including the zero, mean, bankfull, and maximum floodplain depths. Surface area and
volume are calculated based on the estimated channel geometry; outflow is calculated
using Manning's equation. The standard equations used in these calculations are
provided for reference in Appendix A.
How to Edit Inputs to Standard Method FTABLEs
Standard Method FTABLEs are created automatically for projects originated in BASINS.
WinHSPF provides an interface (see Figure 4) so users can adjust the default input
parameters in order to generate updated FTABLEs, as follows:
Select the reach to be edited and access its FTABLE. (Go to Reach Editor screen
and click "FTables" button.)
Click "Import from Cross Section" button.
Open project's trapezoidal {.ptf) file. (In its project folder in BASINS/modelout/.)
Edit the channel geometry and hydraulic parameters as needed; save file.
Click "OK" and a new FTABLE will be generated. Click "Apply" on the
FTABLE screen so that the new FTABLE will be included in the next HSPF run.
B. Alternative Method
A new tool available in WinHSPF facilitates replacement of the default Standard Method
FTABLE with one developed using the Alternative Method. This Method was designed
for reaches in the Mid-Atlantic Region with drainage areas greater than 3 square miles
and less than 400 square miles (Mohamoud and Parmar, 2006). The Alternative Method
can be applied in areas outside the Mid-Atlantic Region, but its suitability for such areas
has not been fully evaluated.
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Figure 3. Channel cross-section geometry assumed by WinHSPF in creation ofFT ABLE
using the Standard Method. For the Alternative Method., the channel geometry is the
same except there is a single floodplain section instead of two, and the slope represented
by "m " is the reciprocal of the slope in this figure.
Standard
Alternative
Method
Method
Source of Primary Parameters
Mean flow depth
Ym
Reach dataset
Regional regression3
Mean flow width
wm
Reach dataset
Regional regression3
Manning's n
n
0.05
Regional regression3
Longitudinal slope
S
Reach dataset
Reach dataset
Channel Geometry Assumptions
Channel side Slopeb
mi 1,12-
1.0
0.67
Floodplain side Slope b
mr M
m31.32
0.5
0.67
Floodplain width
W
11,12
wm
wm
Bankfull depth
Yc
1.25 • Ym
5 ' Ym
Max floodplain depth
Yt2
33.33 • Ytl
(= 62.5 ¦ Ym)
10 Yc
(= 50 ¦ Ym)
Floodplain split depth
Y«
1,3 -Ys
n/a - floodplain is
not split
3 Mohamoud and Parmar (2006)
b These values represent "m" as depicted in Figure 3. This is the same as the value entered as "in"
in the Standard Method but is the reciprocal of the value entered as "m" in the Alternative Method.
See figure in Appendix A. section ID for graphic representation of Alternative "m."
Table 1. Sources and assumptions used in estimating FT ABLE parameters with the
Standard Method or the Alternative Method.
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The HSPF model's hydraulic representation depends on the accuracy of the FTABLE
which, in turn, depends on the accuracy of the hydraulic geometry data. The primary
hydraulic geometry parameters selected by automatic FTABLE development methods are
generally inaccurate but provide functional initial inputs when measured data are not
available. The Alternative Method was developed to enhance HSPF's channel hydraulic
representation and principally differs from the Standard Method in how it estimates these
initial hydraulic geometry parameters. Rather than extracting the initial hydraulic
geometry parameters from the reach file, the Alternative Method is based on a set of
regional regression equations developed by Mohamoud and Parmar (2006), presented in
Appendix A. These equations use power functions to relate a reach's mean flow width
and depth to its mean annual streamflow, which is in turn related to the reach's measured
drainage area. After estimating these primary geometric parameters, the tool calculates
the roughness coefficient by applying Manning's equation using those estimated values.
This difference in estimating Manning's roughness coefficient is particularly important.
In the Standard Method, Manning's n is set at the same default value for all reaches while
in the Alternative Method, each reach has a Manning's n that is tied to its individually
measured properties.
The power functions used in the Alternative Method were developed by regression of
observed data from streams in physiographic provinces assumed to have similar
landscape characteristics. The provinces represented by these regional regression
equations are the Appalachian Plateau, the Ridge and Valley, and the Piedmont provinces
of the Mid-Atlantic Region of the United States. These equations, based on localized
data, are specific to the areas for which they were developed. They can be applied in
other areas with similar topographies, but the uncertainty this extrapolation may lead to
has not been quantified.
As with the Standard Method, once the primary hydraulic geometry parameters are set,
the Alternative Method derives the channel cross-section by assuming a compound
trapezoidal geometry (Figure 3). The default assumptions about the channel and
floodplain geometry, however, are somewhat different than in the Standard Method.
Both the channel section and the single floodplain section have side slopes of 1.5:1 with
additional geometric assumptions as presented in Table 1. The difference in geometric
assumptions leads to maximum depths in the Alternative Method that are much lower
than in the Standard Method. In some situations such as reservoirs, these depths may not
be sufficient and would need to be manually edited. It should also be noted that the
parameters entered as "side slopes" in the Alternative Method do not represent the same
parameters as in the Standard Method and as represented in Figure 3. The parameters
represented in the Alternative Method as the "side slope" are actually the reciprocals of
the "side slope" parameters in the Standard Method.
The Alternative Method also includes the option for channel and floodplain sections to
have different Manning's n values. Additionally, FTABLEs created by the Alternative
Method are of a higher resolution than those created in the Standard Method, with area-
volume-flow relationships calculated at smaller depth intervals. Channel surface area,
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Z. Edit Ftable
FT able:
1-1
3]
Depth (ft)|
Area (acres) |
Volume (acre-ft)l
Outflowl (ft3/s)
-I
0
0
0
0
J
0.02
65.93
1.32
0.11
0.06
66.11
3.96
0.7
0.1
66.23
6.61
1.63
0.2
66.74
13.26
5.19
o.e
66.53
40.31
32.43
1
70.33
68.09
76.11
1.2
71.22
82.24
103.24
1.6
73.02
111.09
167.1
2
74.31
140.65
242.35
3
A
79.23
CO 70
217.71
'JOG
480.87
700 1 7
N Flows:
NCols:
19
ImpbrtTrom
Cross Section
Compute New
F-Curve
OK
Cancel
Apply
Help
a) "Edit Ftable" screen; accessed from Reach Editor by clicking "FTables." Click "Import
from Cross-Section" to reach screen in (b) or "Compute New" to reach screen in (c).
Z Import From Cross-Section
Z. Compute New FTable - RCHRES 1
Cross-Section Files
Open
Save
FTABLE 1
Variable
Description
Value
L
Length (ft)
65033
Ym
Mean Depth (ft)
3.05005
Wrn
Mean Width (ft)
0.94657
n
Mannings Roughness Coefficient
0.05
6
Longitudinal Slope
0.00136
rm32
Side Slope of Upper Flood Plain Left
0.5
m22
Side Slope of Lower Flood Plain Left
0.5
W12
Zero Slope Flood Plain Width Left (ft)
80.347
ml 2
Side Slope of Channel Left
1
ml 1
Side Slope of Channel Right
1
W11
Zero Slope Flood Plain Width Right (ft)
80.347
m21
Side Slope Lower Flood Plain Right
0.5
m31
Side Slope Upper Flood Plain Right
0.5
Yc
Channel Depth (ft)
3.8126
Yt1
Flood Side Slope Change at Depth (ft)
5.7188
Yt2
Maximum Depth (ft)
130.628
OK | Cancel | Help
Average Channel Slope
Channel Length, ft
0.00373
r
65102.4
Channel Characteristics Estimator
Drainage Area (Sq. Miles) ( 52.83
Physiographic Province | Select Physiographic Province -
Estimate
Mean Channel Width (ft)
Mean Channel Depth (ft)
Manning N For Channel
Manning N For Floodplain
Bank full Depth (ft)
Maximum Floodplain Depth (ft)
Left Side Floodplain Width (ft)
Right Side Floodplain Width (ft)
Channel Side Slope
Floodplain Side Slope
Compute FT able
b) Screen used to import and edit hydraulic
geometry parameters for Standard Method FTABLE
c) Screen used to estimate and edit hydraulic
geometry parameters for Alternative Method
FTABLE
Figure 4. Reach Editor screens used to import and edit FTABLES.
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volume, and outflow are calculated for at least twice as many depths as in the Standard
Method, still including the zero, mean, bankfull, and maximum floodplain depths.
How to Create and Edit Alternative Method FTABLEs
When a project is originated in BASINS, it will initially be set up with a Standard
Method FTABLE. New FTABLES can be created through the WinHSPF interface
(Figure 4a), as follows:
Select the reach to be edited and access its FTABLE. (Go to Reach Editor screen
and click "FTables" button.)
Click "Compute New" button. The "Compute New FTABLE" window opens
with the average channel slope, channel length, and drainage area populated for
the current reach (Figure 4c).
Select Physiographic Province
o Appalachian Plateau (ruggedly hilly area, mountainous in part and
containing dissected plateaus and broad ridges)
o Blue Ridge & Ridge and Valley (long linear ridges and intervening
valleys)
o Piedmont (low rolling hills and low mountains)
Click "Estimate" and the table will be populated with hydraulic geometry
parameters calculated using the regional regression power functions and the pre-
defined geometric assumptions. Edit as appropriate.
Click "Compute FTable" to generate a new FTABLE. Click "Apply" on the
FTABLEs screen so that the new FTABLE will be included in the next HSPF run.
Updated FTABLEs can be created by repeating these steps to edit the geometric
parameters after they have been estimated by the tool and before the FTABLE is
computed.
HYDRAULIC CALIBRATION
The HSPF model requires that calibration and validation procedures both be applied
before running simulations. The model has well-established calibration procedures,
beginning with hydrological calibration and followed by sediment calibration and then
water quality calibration. In the past, hydraulic calibration was not an integral part of
traditional HSPF calibration, in part due to lack of observed hydraulic parameter data and
to uncertainties associated with the model's hydraulic representation - particularly the
accuracy of its FTABLE. Along with enhancing the FTABLE, the developers of the
Alternative Method have introduced a hydraulic calibration procedure to the overall
process.
As described in Mohamoud (2007), comparison of observed and simulated flow
velocities is proposed as the new hydraulic calibration procedure. This proposal is based
on developing a relationship between an observed hydraulic variable and bed shear stress.
Bed shear stress controls the deposition, scour, and transport of silt and clay fractions and
so its accurate prediction is critical to instream sediment simulation. HSPF's calculation
8
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to determine bed shear stress includes the hydraulic radius as an input parameter, and the
hydraulic radius is also related to flow velocity through Manning's equation. By
eliminating hydraulic radius from both equations, then, flow velocity can be related
directly to bed shear stress. Comparison of observed and simulated flow velocities can
therefore be used as a measure of the model's accuracy in handling bed shear stress.
A. Hydraulic Calibration Data
Hydraulic calibration can only be performed on reaches that have observed hydraulic
parameter data. When available, these data can be downloaded from a USGS gaging
station(s) through BASINS 4.0. To download data for parameters DISCHARG,
VELOCITY, WIDTH, and XSECT:
Open the "Data Download" tool under the File menu.
Select "USGS Streamflow Measurements" and click "Next."
Click in the "Measurement Site Number" box to bring up list of gaging stations
with available data. Select stations from which to download data.
Specify WDM file in which to include these data and click "Next."
These data can be also be obtained through the USGS Surface-Water Data website at
http://waterdata.usgs.gov/nwis/sw. After reaching the appropriate page for the gaging
station of interest, hydraulic parameter data when available are included in "Available
data for this site" under the category "Surface water: Field Measurements." As well as
identifying parameters measured, this data source includes information about the dates of
data collection.
B. Performing Hydraulic Calibration
Hydraulic calibration should be performed after hydrological calibration and prior to
sediment calibration. In WinHSPF, use the Output Manager to specify that the hydraulic
parameters (e.g., AVVEL,TWID, and AVSECT) should be included in the model's
output. After running the model, WDMUtil or GenScn can be used to compare the
observed velocity measurements with the simulated results. If agreement is good, the
modeled hydraulic parameters can be accepted and the user can move on to sediment
calibration. In cases where the observed and simulated flow velocities differ
substantially, the modeler should adjust the hydraulic parameters, such as mean flow
width and depth, slope, and roughness coefficients, and generate new FTABLEs to use in
rerunning the model. Manning's n values for natural channels may vary from 0.02 for
clean and straight reaches to 0.2 for very weedy reaches. For more information about the
selection of n values, users may refer to Chow (1959).
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REFERENCES
Bicknell, B. R., J. C. Imhoff, J.L. Kittle, and A. S. Donigian, 1996. Hydrological
Simulation Program - FORTRAN: User's Manual for Release 11. US EPA.
Chow, V.T., 1959. Open Channel Hydraulics, McGraw-Hill, New York, NY.
Mohamoud, Y. M. and R. S. Parmar, 2006. Estimating Streamflow and Associated
Hydraulic Geometry, the Mid-Atlantic Region, USA. Journal of the American Water
Resources Association (JAWRA) 42(3):755:768.
Mohamoud, Y.M. 2007. Enhancing HSPF Channel Hydraulic Representation (in press).
Journal of the American Water Resources Association (JAWRA).
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APPENDIX A - Equations
This Appendix identifies the equations and assumptions used by the automated tools in
WinHSPF to populate FTABLEs. An FTABLE is a piecewise linear function table with
columns for depth, surface area, volume, and outflow; each row contains values
corresponding to a specified water depth. To create this table, both tools discussed in this
technical note start by defining values for an initial set of geometric and hydraulic
parameters. The tools then calculate surface area, volume, and discharge at various
depths using these predefined values along with basic trapezoidal geometry and
Manning's equation for flow.
1. Calculating in-channel FTABLE values
A) Initial Geometric Parameters (sources and default values):
Standard Method
Alternative Method
Ym = Mean flow depth
Reach dataset
Regional regression *
Wm = Mean flow width
Reach dataset
Regional regression *
L = Length of reach
Reach dataset
Reach dataset
S = Longitudinal slope
Reach dataset
Reach dataset
mc = Side slope of channel **
1.0
1.5
n = Manning's roughness coefficient
0.05
Regional regression *
Mohamoud and Parmar (2006). Described further in Section 3 below.
" These values represent "m" as depicted in Section ID. This is the same as the value entered as "m" in
the Alternative Method but is the reciprocal of the value entered as "m" in the Standard Method. See
Figure 3 for graphic representation of Standard "m."
B) Equations for FTABLE parameters:
SA
= L
T
Where:
SA
= Surface Area
Vol
= L
A
L
= Length of reach
Q
= V
•A
T
= Width of water surface
C) Manning's Equation:
2/3 Where:
¦S
1/2
Vol = Volume
A = Cross-sectional area
Q = Discharge
V = Velocity
V = Velocity
c = Empirical constant;
1 for metric, 1.486for English
n = Manning's roughness coefficient
A = Cross-sectional area
P = Wetted perimeter
S = Longitudinal slope
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D) Basic Trapezoidal Geometry:
T = b + 2 mcy
T
y
A
b
P = b + 2y ¦ -rjmc2 +1
b = Wm - 2mcYm
because at y = Ym, T = Wm
E) Final Calculations:
Combining the above equations leads to the following calculations for estimating
FTABLE values at in-channel depths. These equations require input of only the initially
determined parameters and the depth at which the values are estimated. These equations
do not account for unit conversion to acres and acre-feet, as required for SA and Vol to
be compatible with FTABLEs.
SA = L • (b+ 2mcy)
Vol = L • (by + mcy2)
Q = ~ ' (by + mcy2)5/3 • (b + 2y^mc2 +\)'m • S1/2
Where: b = (Wm - 2incYm)
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2. Calculating floodplain FTABLE values
The floodplain FTABLE values are calculated based on the same initial assumptions,
equations, and geometry as the in-channel values, but several additional parameters need
to be accounted for, as described below.
A) Initial Geometric Parameters (default values):
Standard Method
Yc = Bankfull depth
Yti = Floodplain split depth
Yt2 = Max floodplain depth
Wf = Floodplain width
mF = Floodplain side slope*
1.25 • Ym
1.5 Yc
33.33 • Ytl
(= 62.5 ¦ Ym)
Wm
2.0
Alternative Method
5 • Ym
n/a - floodplain is not split
10 Yc
(= 50 ¦ Ym)
Wm
1.5
These values represent "m" as depicted in Section 2B. This is the same as the value entered as "m" in the
Alternative Method but is the reciprocal of the value entered as "m" in the Standard Method. See Figure 3
for graphic representation of Standard "m."
B) Basic Trapezoidal Geometry:
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3. Alternative Method for estimating hydraulic geometry parameters
The Alternative Method calculates initial hydraulic geometry parameters using power
equations derived from regression of observed regional data. More information about
these equations, presented below, can be found in Mohamoud and Parmar (2006) and
Mohamoud (2007). Note that these values are in metric units, so unit conversion in the
automated tool is required to obtain results.
Model
Appalachian Plateau
Ridge & Vallev
Piedmont
Q = xDAy*
X
0.043
0.038
0.015
(m3/s)
y
0.850
0.830
0.989
A = uQd
u
3.26
2.53
3.53
(m2)
d
0.67
0.89
0.65
wm = a Qb
a
10.21
9.41
11.95
(m)
b
0.48
0.48
0.47
II
o
O
"-b
c
0.29
0.30
0.28
(m)
f
0.24
2.25
0.22
<
II
O
3
k
0.37
0.36
0.35
(m/s)
m
0.25
0.17
0.25
Manning's _ 0.77(uQd)(cQf)2/3(Sl/2)
coefficient ~ xDAy
* DA = Drainage Area (km2)
" Uses Manning's equation assuming a parabolic channel shape with a hydraulic radius equal to 0.67 Ym.
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