Real-time Flood Forecasting
We’ve learned to predict typhoons. What is required to predict the floods they bring?
Flow prediction is based on the construction of two models, one that simulates the real-time flow and another that begins where the real-time simulation ends and forecasts how the flow and the river stage (water surface elevation) will change in the future. These two simulation models are illustrated in Figure 5, which shows how a forecast of the river stage over time is developed for a single reach (no branches, confluent flows or irregular geometry that could cause abrupt changes or discontinuities in flow). Our real-time simulation begins at time t = t0. Figure 5a shows the acquisition of real-time stage data for upstream and downstream boundary points of the simulation. The stage data, recorded at field stations and transmitted to the modeling center at regular intervals, are incorporated in real time in our simulation model as boundary conditions for a stream reach of length L (Figure 5b). The water surface profile between the upstream and downstream boundaries, combined with flow rate (discharge) and other information, serve as initial condition data. The initial and boundary conditions are used to compute flow for a series of time intervals. The computational method that we employ outputs results for the rectangular space in the figure bounded by three fixed boundaries, the t = t0 line and the upstream and downstream boundaries, and one moving boundary, the t = present line. The output within that region is mapped to the zones marked I, II and III. The computational results for Zone I depend entirely on initial conditions, Zone II depends on initial and boundary conditions, and Zone III depends entirely on boundary conditions—features that will be important when we switch from real-time simulation to forecast simulation.
In the real-time part of the simulation system, continuous boundary-condition data are received from field stations, allowing us to compute the unsteady flow over time and generate a relief map of the stage surface data up to the present (the purple surface in Figure 5b), after which we run out of boundary-condition data.
Figure 5c and 5d portray the principle of predictive unsteady-flow simulation. The forecast simulation begins at the present time of the real-time simulation. We want the computations of forecast stages and other unsteady flow data to proceed forward in time, but with only initial-conditions data available, the computation will be confined to the triangular area of Zone I unless additional boundary-condition data are provided. Lacking (future-time) field data, we need to supplement the boundary-condition values.
We respond with extrapolated or best-estimate values for the future boundary-condition data. Clearly, the quality of the forecast simulation depends on the accuracy with which the boundary-condition data can be projected. In Zone I of the forecast in Figure 5c, we expect high accuracy. Even though the calculated results for this region occur in future time, according to the principle of the method of characteristics, they depend only on the initial values at the current time, t = present; they are not dependent on changes that occur in the future. In the early part of the simulation, the predicted surface profile along the channel is therefore mostly made up of a non-future-affected part, with two small parts (orange triangles in Figure 5c) that are slightly affected by future uncertainty. If the extrapolated boundary values can be predicted with confidence (heavy black dashes in Figure 5d), we can add to the forecast the chevron-shaped blue region between the heavy dashes as a region of high confidence.
The forecast progresses in this manner as t continues into the future, with the levels of confidence within the mapped regions progressively falling. Using these data, we advance by time steps to solve for the unknowns (stage, depth, velocity, discharge and so on) for the entire region. The previous paragraphs give only the basic physical principles employed by this flood-forecasting model. To execute the actual task of modeling and simulation of a river basin system, the concrete numerical scheme (MMOC-II, in this case) must be applied to each channel reach and junction individually and incrementally over time.
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