The system dynamics modeling is used to simulate overland flooding. The model is developed for the Red River basin from south of the Winnipeg floodway to Ste. Agathe (Figure 4.16). Stella (HPS, 2001) is used for the system dynamics modeling. ArcView 9.3 (ESRI, 2009) is used for processing topographic information and visualization. The SD model simulates the flood propagation and provides the spatial and temporal variation of water surface elevations. In the SD model floodplain characteristics such as topography and information on infrastructure are used as inputs from the GIS.
Figure 4.16: Topographic data of the Red River Case study
Overland flow in the floodplains is modeled in this work using a cell to cell routing approach. The cell-to-cell routing involves dividing the land surface into segments, and
routing flow from one segment to the next until it arrives at a final point. From several of the cell-to-cell routing models for overland flow, the routing method of Coe (1997) is used in the SD approach. This cell to cell routing method divides the land surface into routing cells. It is assumed that discharge occurs only when the volume of water in the cells exceeds their storage capacity. Therefore, the discharge rate is a function of the difference between the volume of water in the cell and the cell’s storage capacity (Ahmad and Simonovic, 2004). The Von Neumann neighbourhood scheme is used for cell-to-cell routing. This scheme allows water from each cell to move to one or more of its four neighbouring cells. The excess water (exceeding storage capacity) is distributed to four neighbouring cells in descending order of slope difference.
The Muskingum method (Chow et al. 1988) has been used for routing flow in the river. Overland flow and river flow is modeled in the system dynamics simulation environment Stella, where basic building blocks, i.e., stocks, flows, connectors, and converters, are used to describe the model structure. Water volume in each cell is represented by a stock. Flows are used for inflows and outflows to model changes in water over time. Converters are used to provide information to the model and operate the system using logical/mathematical functions. The Flow routing sector describes the movement of water from cell to cell. Terrain information, such as surface elevation, ground slope and storage capacity in the cell, affects the flow from one cell to another. To solve the Muskingum equations of flow numerically, the region of interest is first discretized. The discretization enables the replacement of the continuous region by an array of points. In this research these points are taken as the center points of a grid. In the next step a finite difference
method is applied to these points to convert the differential equation into a set of difference equations. In Stella the set of equations is solved by Euler’s method.
The SD model used for the simulation of overland flooding is based on the following assumptions:
(i) The topography has each cell defined as a river section or as a floodplain;
(ii) Flow of water is possible either from one cell in the river to the next cell in the river, or between cells if water level and ground slope permits;
(iii) In the cell-to-cell routing model an assumption of linearity is made. This assumption is widely used in hydrology and in many routing methods such as the Muskingum method, the unit hydrograph, and the linear solutions of the St. Venant equations. Since the Muskingum method is used in this research as a cell-to-cell routing approach the assumption of linearity is valid.
Data Requirements
The SD model requires: (i) hydrologic data, and (ii) topographic data.
(i) Hydrologic Data
Daily water surface elevation near Ste. Agathe (St. No. 05OC012), precipitation, and evaporation losses are used in this case study.
(ii) Topographic Data
modeling is also used for the SD model. This LIDAR data has a grid resolution of 5m by 5m. For simplification the topographic data is processed in GIS where grid cells are merged to obtain a coarse resolution of 2km by 2 km for the SD model. The river, dikes and floodway coverage are obtained from the Surveys and Mapping Branch at the Manitoba Department of Conservation. The study area is divided into cells with coverage representing river and flood control structures (dike, floodway, diversion, reservoir), and is shown in Figure 4.17.
Figure 4.17: Study area divided into cells.
Description of System Dynamics Model for the Red River Section
The SD model deals with flow routing in the river and floodplains to describe the movement of water from cell to cell. The flow routing sector (Figure 4.18) in the model
uses the relative surface elevation of the neighbouring cells, ground slope elevation, presence of dikes, and storage capacity in the cells, to describe the cell-to-cell movement of water. The Red River basin has a flood control structure to regulate the flow. Operational strategies of flood control structure (floodway) are incorporated in the SD model to simulate the 1997 flood event. The model uses inflow, rain and evaporation as the main hydrologic and metrological inputs. The model also uses system constraints, operating curves, and flow capacity for additional information. In the overland flow model the operating rules are captured using logical statements such as IF-THEN-ELSE. The logical statements in Equation 4.1 (Ahmad and Simonovic, 2004) state the following: (i) if the floodway gates are closed then no flow is able to pass through the floodway, (ii) if the Red River flow is less than or equal to the safe carrying capacity of the river (1,400 m3/s) then flow is not diverted through the floodway, (iii) if flow in the Red River is more than the safe carrying capacity of the river (1,400 m3/s) and if the floodway gates are open, then excess flow is diverted to the floodway up to the maximum floodway capacity (1,850 m3/s).
IF (Floodway_Diversion_Control = 0) THEN (0)
ELSE IF (Red_Floodway_up<=1400) THEN (0)
ELSE IF (Floodway_Diversion_Control = 1) AND (Red_Floodway_up >= 1400)
The control screen of the SD model for the 1997 Red River flood simulation is shown in Figure 4.19. The User can change the control parameter, for instance rain, evaporation, dike height, river depth, mannings n, etc., using different sliders. For the operational strategy in the Red River basin, the module has a slider for carrying out the operation of the gates of the Red River floodway. Output of the SD model is given in tables. The results of the SD model consist in values for the variation of water surface elevations and discharges in the river and floodplain for every location and every time step. Several model runs are performed by modifying the model parameters and by changing the floodway operating rules. These modifications are necessary in order to more accurately reflect the extent of flooding and water surface elevation.
The application of the developed SD model is suitable to understand the following:
Impacts of Dike Height
The user is able to assess impacts of the dike by changing its height, removing, adding and even extending more dikes in the Red River basin. The consequence of such actions are meant to impact the spatial and temporal variability of flood extent and water surface elevation.
Impacts of Floodway Operation
The user can control the operation of the floodway in the SD model and can assess its impacts on flooding. The SD model can test different operating rules of floodway operation.
Figure 4.19: Control screen of the Red River section simulation model.