Andrew Ritchey
CEE 6440
12/3/2010
Table of Contents
SCS Dimensionless Unit Hydrograph
Design Storm Hydrograph Using Convolution
Introduction:
As a Civil Engineering graduate student with an emphasis in hydraulics, I chose to perform a hydrologic analysis of the Hyrum Reservoir Watershed using Arc GIS 10. Originally I had planned to use the hydrologic analysis to produce a probable maximum flood (PMF) inflow hydrograph. Due to the highly theoretical nature of the probable maximum precipitation (PMP) and the PMF, it was decided that for the scope of the class, it would be more constructive to use definitive data. A 6 hr – 100 yr storm was chosen instead to perform the hydrologic analysis. Using the data developed in the hydrologic analysis, an inflow hydrograph was produced for the 6 hr - 100 yr storm using the SCS Curve Number Method. The inflow hydrograph produced using the SCS Curve Number Method for the 6 hr – 100 yr storm was used as an input for a flood routing program developed in Excel. The flood routing program was used to route the 6 hr – 100 yr flood through Hyrum Reservoir to determine if the current spillway would sufficiently pass the flood. The hydrologic analysis of the Hyrum Reservoir Watershed using Arc GIS 10, SCS Curve Number Method and reservoir flood routing methods determined that the current spillway has enough capacity to sufficiently pass a 6 hr – 100 yr flood.
Data Sources
Data needed for analysis was obtained from NHDplus, USGS, and NOAA Atlas 14. The data obtained from NHDplus includes the digital elevation model (DEM), flow direction, and flow accumulation raster datasets for the Great Basin Region 16b. Figure 1 shows the NHDplus website location where the Great Basin Region 16 data can be downloaded. The National Land Cover Dataset of 2001 was obtained from USGS website using the Multi-Resolution Land Characteristics Consortium (MRLC) Viewer as seen in Figure 2 below. The National Land Cover Data can be downloaded from the MRLC Viewer for a specified area.
Figure 1: NHDplus Great Basin Region 16
Figure 2: NLCD 2001 MRLC Consortium Viewer
Precipitation frequency estimates were obtained from NOAA Atlas 14 for a 6 hr – 100 yr storm. The precipitation frequency estimate was obtained for the Hardware Ranch site. The Hardware Ranch is not within the Hyrum Reservoir watershed boundary, but is just outside the watershed and provides a representative precipitation frequency estimate for the watershed. A graph of the precipitation frequency estimates for Hardware Ranch can be seen in Figure 3. The precipitation estimate for a 6 hr – 100 yr storm at the Hardware Ranch station was determined to be 2.21 in.
Figure 3: NOAA Atlas 14 Precipitation Frequency Estimates - Hardware Ranch
Analysis Using Arc GIS 10
Once all of the data was obtained from the given sources, it was imported into Arc Map 10 and prepared for analysis. All of the datasets were projected to the North American Datum of 1983 (NAD 1983). The portion of the Analysis using Arc GIS 10 includes the watershed delineation, stream delineation, stream network analysis, and land use analysis.
Watershed Delineation
One of the first steps in the analysis was to delineate the watershed draining into Hyrum Reservoir. An outlet point was defined as a point feature at the inlet of the reservoir. Defining the outlet at this point allows us later to calculate the inflow hydrograph at the inlet of the reservoir. Once the outlet was defined, the watershed was delineated using the Spatial Analyst Hydrology Tool “Watershed” as seen in Figure 4. The watershed tool requires the outlet point feature and the flow direction raster as inputs. The result is a watershed grid raster that has a value of 1 for the entire watershed and values of no data outside the watershed.
Figure 4: Hyrum Reservoir Watershed Delineation
Stream Delineation
Once the watershed was delineated, the streams were defined based on the flow accumulation within the watershed using the Map Algebra Raster Calculator and the threshold of (“fac” > 5000) & (“wshed” > 0). The result is a raster, “str”, representing the streams over the entire watershed. From the stream raster, the stream links were defined using the Spatial Analyst Hydrology Tool, “Stream Link”. The stream link function converts the stream raster into a series of stream segments with unique identifications that link between two junctions. The result is a raster, “StrLnk”, representing stream segments in the watershed. Catchments were then delineated for each stream link using the same process as described in the watershed delineation section, but instead with “StrLnk” and “fdr” as the input raster’s. Once the stream links were defined they were converted into a vector using the Spatial Analyst Hydrology Tool “Stream to Feature”. The “Stream to Feature” tool requires the input stream raster, “StrLnk” and the input flow direction raster, “fdr”. The result as seen in Figure 5 is a vector, “streamline” representing the streams delineated for the Hyrum Reservoir watershed.
Figure 5: Stream Delineation
Stream Network Analysis
After the streams are delineated a Geometric Network was created from the stream vectors. “A Geometric Network is an Arc GIS data structure that facilitates the identification of upstream and downstream connectivity”. (Tarboton) The first step in creating the Geometric network was to identify the vertex that is the outlet to the watershed and set it as a sink so that the flow direction could be determined in the Geometric Network. The Feature Vertices to Points tool was used to do this with the “streamline” vector as the input. This tool created vertices at each end of the steam network. Once the vertices were created, the vertex at the outlet of the watershed was selected and exported as a point feature “OutletSink”. A new Geometric Network was then created in Arc Catalog using the “streamline” vector and the “OutletSink” point to build the network. In order to assign the flow direction for the Geometric Network, the Ancillary Role property in “OuletSink” attribute table was set to “Sink”. After the Ancillary Role was set, the flow direction in the Geometric Network was then set by using the Utility Network Analyst tool. The flow directions were displayed using arrows as seen in Figure 6.
Figure 6: Geometric Network w/ Flow Directions and Longest Flow Path Selected
The Utility Network Analyst “Trace” tool was then used to find the longest flow path in the network. Once the Longest flow path was selected, the length was determined to be 46192 m by using the statistics tool for the shape length column of the attribute table for the selected streamlines as seen in Figure 7. The change in elevation was determined by using the info selection tool and determining the elevation from the DEM raster at the outlet and at the beginning of the flow path and taking the difference. The average slope of the longest flow path was then calculated as 0.02148 by dividing the change in elevation of the flow path by its length.
Figure 7: Longest Flow Path Analysis
Land Cover Analysis
The National Land Cover Dataset of 2001 downloaded from the USGS website was imported into Arc Map 10 as a raster dataset. In order to perform a land cover analysis of the watershed, the National Land Cover Dataset of 2001 was cropped to within the watershed boundary as seen in Figure 8. Cropping the dataset to within the watershed boundary enabled the ability to calculate the percent of the watershed in each land classification. Each cell of the raster is assigned with a unique value and color which define its specific land classification. The land cover attribute table displays the counts (number of cells) of each land classification. The percent of the watershed in each land classification was determined by dividing the count of the land classification by the total number of cells in the catchment. The percent of the watershed in each land classification was then used to calculate the curve number (CN) of the watershed.
Figure 8: National Land Cover Dataset 2001
SCS Curve Number Method
The SCS Curve Number method was used to calculate the SCS Unit Hydrograph. The SCS Unit Hydrograph was then used to determine the storm inflow hydrograph using convolution. Once the storm inflow hydrograph was produced, it was then routed through Hyrum Reservoir with a flood routing program developed in Excel.
Curve Number CN
In order to calculate the curve number (CN) for the watershed, the SCS soil group classification needed to be determined. The soil group C was selected with AMC II conditions as seen in Figure 9.
Figure 9: SCS Soil Group Classification (Bastidas)
The National Land Cover Dataset cropped to the watershed was then used to calculate the CN. The National Land Cover Dataset land classifications shown in Figure 8 were grouped into representative SCS Land Uses used to calculate the CN. The counts of the land classifications were grouped together for each SCS Land Use category and then the percent of the watershed in each SCS Land Use was calculated. Curve numbers for each SCS Land Use were taken from the table in Figure 10. The watershed CN was determined as 77.9 from the SCS Land Use percents and curve numbers as shown in Figure 11.
Figure 10: SCS Land Use Runoff Curve Numbers (Bastidas)
Figure 11: Watershed Curve Number Calculation
SCS Design Storm
The design storm was then calculated using the watershed CN of 77.9 as calculated above and the precipitation frequency estimate of 2.21 in for the 6 hr – 100 yr design storm. The design storm essentially gives the effective precipitation, Pe, hyetograph that will be used with the unit hydrograph discussed in the next section to produce the inflow hydrograph at the inlet of Hyrum Reservoir. The precipitation for the design storm calculations was obtained from the NOAA Atlas 14 Precipitation Frequency Estimates for Hardware Ranch as seen in Figure 3. The precipitation value obtained from NOAA Atlas 14 was then distributed throughout the length of the 6 hr design storm. The precipitation was distributed using the NOAA Atlas 14 6 hr Temporal Distribution graph for the general precipitation area shown below in Figure 12.
Figure 12: Temporal Distribution for General Precipitation Area (NOAA Atlas 14)
The precipitation was distributed for 1 hr time intervals throughout the 6 hr storm. Equations 1, 2 and 3 shown below were used to estimate the infiltration. The effective precipitation, Pe, was then determined by subtracting the incremental infiltration from the incremental precipitation as shown in Table 1 below. Figure 13 shows the design storm hyetograph with the incremental precipitation and the incremental infiltration. The design storm hyetograph was then modified to only display the effective precipitation as shown in Figure 14. The effective precipitation is the amount of precipitation that remains as direct runoff after infiltration. The effective precipitation hyetograph in Figure 14 will be used for the development of the inflow hydrograph at the inlet of Hyrum Reservoir.
Equation 1: Potential Maximum Retention (Bastidads) Equation 2: Inital Abstraction (Bastidas)
Equation 3: Actual Retention (Bastidas)
Table 1: Development of the Design Storm Hyetograph using NOAA Atlas 14
Figure 13: Design Storm Hyetograph with Pinc and INFinc
Figure 14: Effective Precipitation Design Storm Hyetograph
SCS Dimensionless Unit Hydrograph
After the design storm was established, a unit hydrograph was determined for the watershed. The unit hydrograph is not the final hydrograph used for the flood routing analysis. It is a hydrograph established based on 1 in of effective precipitation over the entire watershed. The unit hydrograph is then modified using the effective precipitation and convolution as discussed in the next section. The SCS Dimensionless Unit Hydrograph procedure was used. Figure 15 shows a layout of the SCS Dimensionless Unit Hydrograph and the calculated variables.
Figure 15: SCS Dimensionless Unit Hydrograph
The following equations were used in the development of the SCS Dimensionless Unit Hydrograph:
Equation 4: tc (Bastidas)
Equation 5: D (Bastidas)
Equation 6: tp (Bastidas)
Equation 7: tb (Bastidas)
Equation 8: Qp (Bastidas)
The SCS Dimensionless Unit Hydrograph developed with the above equations is shown in the following Figure 16.
Figure 16: SCS Dimensionless Unit Hydrograph for the Hyrum Reservoir Watershed
Design Storm Hydrograph Using Convolution
After the SCS Dimensionless Unit Hydrograph was developed for the Hyrum Reservoir watershed, the Design Storm Hydrograph was developed using convolution. The Unit Hydrograph and the effective precipitation values are used in the convolution procedure. The Unit Hydrograph values are multiplied by each effective precipitation value and shifted one time step (1hr) consecutively as shown in Figure 17. The resulting products were then summed in each row to develop the Design Storm Hydrograph for the 6 hr – 100 yr storm event as shown in Figure 17. The Design Storm Hydrograph was then used as the inflow hydrograph to route the flood through Hyrum Reservoir.
Figure 17: Design Storm Hydrograph - 6hr - 100 yr storm event
Reservoir Flood Routing
The inflow hydrograph produced using the SCS Curve Number Method for the Hyrum Reservoir watershed was used for the hydraulic analysis of the existing spillway. The hydraulic analysis was performed using a flood routing program developed in Excel. The flood routing program requires the inputs of the inflow hydrograph, reservoir elevation to storage relationship, head-discharge equations, and corresponding elevations of boundary conditions and spillway crests. The reservoir elevation to storage relationship was provided by Mike Talbot with the USBR. (2010. Personal Communication) The flood routing program determines the combined outflow of the operating spillways with the low level outlets and produces an outflow hydrograph with the corresponding water surface elevations in the reservoir. In order to provide sufficient freeboard for the earth dam and to ensure the stability of the bridge spanning the existing spillway channel, it was assumed that the peak water surface elevation should not exceed 4672 ft. The top elevation of the earth dam is at an elevation of 4680 ft.
The current spillway consists of three radial gates which are 12 ft in height and 16 ft wide. There are two reinforced concrete piers separating the radial gates that support the bridge spanning over the spillway. The low level outlets have a combined outflow of 300 cfs. (Talbot, M. (USBR). (2010). Personal Communication) The change in elevation from the invert of the outlet channel to the bottom of the bridge is 20 ft. The slope of the spillway channel was measured in the field as 0.01156. The dimensions of the current spillway can be seen in Figure 18.
Figure 18: Current Spillway Dimensions
For the hydraulic analysis, it was assumed that in a flood event the gates would be full open, or the operator would open them in anticipation of the flood event. Using this assumption the discharge over the spillway could be calculated as a reservoir to steep channel. For this case the water profile will pass through critical depth over the spillway and remain supercritical in the channel. The following equations were used to calculate the critical depth in the channel. The critical depth was then used with the Manning equation to calculate the discharge over the spillway.
Equation 9: Froude Number
(Finnemore 2002)
Equation 10: Specific Energy
(Finnemore 2002)
Equation 11: Manning
(Finnemore 2002)
The head-discharge relationship developed above with the Froude Number, Specific Energy, and the Manning equation was used in the flood routing program to determine whether the existing spillway combined with the low level outlets have the capacity to pass the flood. The flood routing analysis determined that the current spillway does have the capacity to pass the 6 hr – 100 yr flood. Figure 19 shows the inflow and outflow hydrographs routed through Hyrum Reservoir. Figure 20 shows that the water surface elevation stays sufficiently lower than the maximum reservoir elevation of 4672 ft.
Figure 19: Reservoir Routing Hydrographs
Figure 20: Reservoir Water Surface Elevation
Conclusion
The hydrologic analysis of the Hyrum Reservoir watershed using Arc GIS 10, the SCS Curve Number Method and flood routing analysis determine that the current spillway could pass a 6 hr – 100 yr design storm flood. With more time it would be interesting to look at different design storms to determine what size of storm could possibly overtop the dam. It would also be interesting to compare the results I have obtained to the largest flood the reservoir has seen. Hyrum Reservoir is a “high risk” dam and would cause extensive life and property loss if it failed. It is necessary to analyze dams of this category to insure public safety.
Works Cited
Bastidas, L. (2010). “Lecture Notes” CEE 3430, <http://ceefs2.cee.usu.edu/cee3430/CEE_3430_10_Lec_08_ > (Nov 1, 2010).
Finnemore J. E. and Franzini J. B. (2002) "Fluid Mechanics with Engineering Applications". 10th ed. McGraw-Hill Companies, Inc. New York
National Hydrography Dataset plus (2010) “Great Basin Region 16 b” Horizon systems Corp.
< http://www.horizon-systems.com/nhdplus/>
NOAA’s National Weather Service (2010). “Hydrometerological Design Studies Center.” Precipitation Frequency Data Server, < <http://hdsc.nws.noaa.gov/hdsc/pfds/sa/ut_pfds.html> (Nov, 15 2010).
USGS Land Cover Institute (LCI) (2010) “National Land Cover Dataset of 2001”
< http://landcover.usgs.gov/usgslandcover.php>