The optimization/simulation model for the real-time operation of river-reservoir systems has been applied to the May 2010 flood event on Cumberland River system near Nashville, TN. The main objective of this model application is to demonstrate the applicability of the model for minimizing flood damages for an actual flood event in a real-time fashion on an actual river basin. Another objective of the model application is to compare the results of using the three unsteady flow simulation scenarios: one-dimensional, two-dimensional (diffusion-wave model), and combined one- and two-dimensional (diffusion-wave model) utilizing HEC-RAS 5.7 as the simulation model for the unsteady flow. This allowed comparison of the three unsteady flow simulation methodologies used with the optimization procedure. The 100-year stage and water surface elevation at the Nashville, Tennessee gage are 48 feet and 417.52 ft, respectively; and the 100-year discharge is 172,000 cfs.
6.1 Model Set-up
The approximate watershed area of the Cumberland River system modeled in the USACE HEC-HMS model is 14,160 mi2. The modeled watershed area included head waters of the basin starting in Lechter County, Kentucky downstream to Cheatham Dam (approximately around 30 miles downstream of Nashville). The HES-HMS input was developed by the U.S, Army Corps of Engineers (USACE) and consists of 66 reaches and 69 basins. The HEC-HMS was calibrated and validated for the May 2010 storm event by Che (2015) who compared the simulated and the observed Dale Hollow reservoir inflow hydrographs for the May 2010 storm event. The one-dimensional HEC-RAS unsteady flow model of Cumberland River system consisted of 675 cross sections, 8 inline structures, 117 lateral structures and 1 bridge. Che (2015) has also calibrated and validated the 1-D unsteady flow model for the May 2010 storm event.
The portion of the Cumberland River system modeled in the unsteady flow simulations for this application is shown in Figure 7. The purpose of this application is to illustrate how to minimize the flood damages at Nashville by keeping the flood stages (water surface elevations) under the 100-year flood stage of 48 feet at the Nashville Woodland station during the storm event. Operation of Old Hickory Dam was the major component in minimizing flood damages downstream of Old Hickory Dam.
The reservoir regulation and operation rules prepared for the U.S. Army Corps of Engineers Nashville District were used in the model to set the operation rules constraints. The HEC-RAS two-dimensional module based upon the diffusion-wave equations was selected over the full equation approach because the diffusion-wave 2-D approach is much faster and more stable. The speed of computations is very important because of the many simulations required in the optimization/simulation approach.
The optimization - simulation model was applied to a portion of the Cumberland River as shown in Figure 7. The real-time rainfall data source for the May 2010 flood event is the high resolution gridded generated by Next Generation Radar (NEXRAD) was used for the hydrologic modeling. The portion of the Cumberland River modeled in HEC-RAS using the two-dimensional approach is from Old Hickory Dam downstream through Nashville to Cheatham Dam.
6.2 Solution Process
The solution process starts with the available actual rainfall data up to time t for the area upstream from Cordell Hull and J. Percy Priest reservoirs. The MATLAB code sends the actual rainfall data to the U.S. Army Corps of Engineers HEC-HMS model to simulate the rainfall runoff process. The discharge hydrograph from the HEC-HMS model becomes the inflow for the Cordell Hull Reservoir. The inflow hydrograph enters the optimization and operation model to determine the optimal releases from the Cordell Hull dam gates. The model now calls HEC-RAS to route the releases up to Old Hickory reservoir, where it considered as the inflow to the Old Hickory reservoir. Once the inflow hydrograph for Old Hickory reservoir is determined, the operation and optimization model determine the releases for the next 4 hours from the Old Hickory Dam. The optimization model employs the genetic algorithm in MATLAB to generate the initial solution considering all the operating rules constraints described previously and, calls the unsteady flow model (HEC-RAS) to test the generated solutions which is the time series of the Old Hickory gates openings. The unsteady flow model routes through the gate openings at both reservoirs downstream to the Woodland station at Nashville. The process continues iteratively until the objective function is satisfied. Then the model steps to the next time t + Δt. The model continues to run until the last Δt of the storm.
The optimization model (GA) uses the last generation or the optimal solution at time t as the initial solution for time t + Δt to reduce the search time of the next step. This saves around 17 minutes of computation time for each iteration for this application. This computational time savings may be very valuable in real-time river-reservoir operation under flood conditions.
The most important factor that could limit this model is the simulation time for the unsteady flow calculations for each time step and for each iteration of the GA of the optimization. Shorter simulation times allows the optimization model (GA) to increase the number of objective function evaluations, which means the number of times that the simulator (HEC-RAS) is called. Producing faster simulation model taking into consideration the accuracy of the mode was a priority of this research. The most time-consuming part of the overall model application are the unsteady flow simulations. Every factor that may affect the time of simulation time, including the mesh size, computation interval, mapping output and even hydrograph interval was considered.
To obtain faster two-dimensional unsteady simulations, the diffusion wave model was utilized using the current version of HEC-RAS instead of the full two-dimensional simulation. The portion of the Cumberland River modeled in HEC-RAS using the one- and two-dimensional approaches is from Old Hickory Dam downstream through Nashville to Cheatham Dam.
6.3 Operations of Old Hickory Dam
The time series of the gate openings at Old Hickory are the decision variables of the optimization–simulation model including the constraints of reservoirs constraints such as: gates openings discharge relationships, operation rules of the gates under flooding condition, the gate height hourly rate of change and reservoirs stage storage relationship. The model determines the operation for each forecasting period Δt, which is 4 hours for the of Cumberland River.
The actual operation of the Old Hickory Dam during the event started the releases at night on May 1, 2010 despite the forecast warnings from severe rainfall several days in advance. Using the optimization/simulation model with the available forecasting information could have helped the U.S. Army Corps of Engineers make decision at Old Hickory Dam before the actual storm entered the Old Hickory Reservoir in a timely manner.
6.4 Unsteady Flow Scenarios
Three scenarios were adopted to simulate the unsteady flow for the May 2010 flood event. The first scenario uses combined one- and two-dimensional unsteady flow modeling, in which the Cumberland River, Nashville reach has been model in one dimensional, while its flood plain was modeled using two-dimensional unsteady flow simulation. The two-dimensional area was divided into four sub regions, two the for the north side of the river reach and two for the south side and as NE, NW, SE and SW a shown in Figure 8. These sub areas were gridded into 832, 1068, 235 and 1208 cells respectively. The total area of these cells that cover the two-dimensional modeling is around 106 square miles. The input spacing into the 2-D flow area editor for generation of cells is 1000 x 1000 feet.
The other components include: two reaches, cross sections, storage areas, laterals, inline structures, and one junction. The Nashville reach connects Old Hickory Dam at the upstream to Cheatham Dam at the downstream using 76 cross sections over the total length of 51 miles. The other reach is Stone River reach that links the J. Percy Priest Lake to the Nashville reach via 22 cross sections. The cross sections were extracted from the terrain model and modified with the actual cross sections surveyed by U.S.AC.E. The terrain does not accurately represent the actual bathometry of a river reach because the LIDAR technology does not have the ability to penetrate water surface elevations.
Each of the two-dimensional areas is connected to the river reach (one-dimensional area) through a lateral structure. Figure 8 shows the combined one and two-dimensional areas downstream of Old Hickory and JPP, where the blue arrow illustrates the general flow direction from NE to SW. Each iteration of combined one- and two- dimensional model takes 5 to 6 minutes to run one unsteady flow simulation for this portion of Cumberland river system shown in Figure 9 is a simulated inundation map developed using the combined one- and two-dimensional approach in HEC-RAS for the May 2010 Flood Event. Figure 10 is a simulated inundation map developed using only the two-dimensional approach in HEC-RAS for the May 2010 Flood Event.
The second scenario uses only the two-dimensional unsteady flow modeling downstream of Old Hickory dam. One of the problems in using only the two-dimensional approach is that terrain data does not often include the actual terrain underneath the water surface in the channel region (river bathometry) due to the fact that LIDAR processing is not capable of penetrating the water surface elevation (U.S. Army Corps of Engineers, 2016c). As a result, many HEC-RAS users do not prefer only the two-dimensional approach. Thus, the terrain model of the only two-dimensional of the Nashville reach has been modified through RAS Mapper by creation of a terrain model of the channel region only from the cross sections surveyed and measured in field by U.S Army Corp Engineers and the cross-section interpolation surface.
The second scenario was set up with only two-dimensional area enhanced with 2-D break lines along the river reach to enforce the mesh generation tools to align the computational cell faces along the break lies. The two-dimensional flow element connected directly to the storage areas: Old hickory Reservoir and J. Percy Priest Lake using the storage area and 2-D area connections that allow to input the data of hydraulic structures such as gates to weirs as it set in normal inline structures to control the flow between the two elements of area. The 2-D area was divided into 3211 cells, with maximum cell area of 2.2 M square foot, minimum cell area of 439 K square foot, and the average cell area of 974165 square foot. The total area of these cells that cover the two-dimensional modeling is around 112.2 square miles. The input spacing into the 2-D flow area editor for generation these cells is 1000 x 1000 feet, which is considered relatively course, the reason behind that is any finer cell size will take longer time to run the simulation and that may cause exceeding the lead time in which the decision for reservoir releases has to be made. However, the model ran well with the suggested spacing.
Due to the limited availability of the LIDAR that were used to develop the terrain model for Nashville, the area upstream of Old Hickory Dam was modeled using only 1-D unsteady flow simulation. The terrain resolution used in the model was 2.5 X 2.5 feet which is considered high enough to produce more accurate and detailed hydraulic table properties for two dimensional computational cells and cell faces.
6.5 Comparison of Simulation Scenarios
All the simulation scenarios showed close simulation results for the flood situation at Nashville during the May 2010 flooding event. The optimization and the combined one- and two- dimensional simulation as well as the one-dimensional model successfully kept the discharge at or below 171,809 cfs, after 64 iterations. This peak discharge is only a little higher than the one-dimensional result of the simulation-optimization model of (Che, 2015) with 171,076 cfs.
Each simulation run of the combined one- and two- dimensional simulation required from 6 to 8 minutes for the 4-hour time interval, for which the optimization model could perform around 23 iterations. The inundation map of the observed water surface of May 2010 for Nashville simulated using the combined one- and two-dimensional simulation approach is depicted in Figure 11.
Contrary to expectations, the two-dimensional simulation model linked with the optimization model resulted in peak discharges that did not exceed 169,694 cfs during the entire period of simulation of May 2010 storm event. This two- dimensional unsteady flow model ran faster than the combined one- and two-dimensional, so the optimization model had more time to improve the solution. The reason why the previous model is slower than this one is because of the connection between the two-dimensional and one-dimensional areas, which is modeled as very long lateral structures.
The observed water surface elevations in the form of inundation map for the May 2010 event at Nashville using the two-dimensional unsteady flow modeling approach (HEC-RAS) is depicted in Figure 12, which shows the flood inundation area resulting from application of the optimization/simulation model using the two-dimensional approach.
6.6 Comparison of Optimized Operations
A comparison is now presented of the resulting optimized operations with the actual operations by the U.S. Army Corps of Engineers during the May 2010 flooding event. Figure 13 compares the optimized discharges at Nashville for the May 2010 Flood Event for the three scenarios of unsteady flow modeling. Figure 14 compares the 100-year and optimized water surface elevations for May 2010 flood event at Nashville for the three scenarios of unsteady flow modeling. Figure 15 illustrates the differences between the optimized and actual operations (flood gate openings) of the Old Hickory. For the simulations all flood gates at Old Hickory were all opened the same distance as compared to the actual operations which were also all opened the same distance. During the actual operation of the gates in the flood event the operators waited too late to open the gates. Figure 16 illustrates the optimized and actual releases at Old Hickory Dam during May 2010 flooding event. Figure 17 compares the optimized and actual flows at Nashville during the May 2010 flooding event.