User's guide of Proceessing Modflow 5.0

256 Processing Modflow
6.2.7 Simulation of a Flood in a River
Folder: \pm5\examples\basic\basic7\
Overview of the Problem
This example is the second test problem of ths STR1 package. The function of the STR1
package that computes the head in the stream as well as changes in flows to and from the aquifer
was compared to an analytical solution developed by Cooper and Rorabaugh (1963). The model
grid used in the previous example was also used in this model. The aquifer properties and
assumptions are the same as those used in the previous example, except for assumptions 8 - 10,
which are replaced with the following assumptions: (1) The recharge to the aquifer is only from
the river as river stage increases with time and (2) The discharge from the aquifer is also only to
the river as river stage decreases with time.
The analytical solution from Cooper and Rorabaugh (1963, p. 355-358) is applicable for the
case where the lateral boundary is at infinity (referred to by Cooper and Rorabaugh as semi-
infinite). The impermeable boundary assigned at 4,000 ft for this model is of sufficient distance
from the river as not to interfere with the results. A flood in the river was simulated for a 30-day
period.
The procedure used to calculate the distribution of streamflow for the 30-day period and for
60 days following the flood was first to calculate a distribution of river stage using equation 71
in Cooper and Rorabaugh (1963, p. 355), assuming a maximum flood stage of 4 ft above the
initial river stage. The streamflow distribution (Fig. 6.29) was calculated from the river stage
distribution. The river has a width of 100 ft, a roughness coefficient of 0.02377 and a slope of
0.0001. A constant C = 1.486 should be used for the simulation (see eq. 3.22).
Modeling Approach and Simulation Results
Streamflow for the first 30 days was divided into l-day periods for simulation. Fig. 6.30 shows
the computed river stage. The simulation results are the same as the manually calculated river
stage values using equation 71 of Cooper and Rorabaugh (1963, p. 355). Detailed discussion on
the analytical and numerical results can be found in Prudic (1988). Results of varying both the
number of columns and the length of stress periods used to simulate the flood wave indicate that
both the number of columns and the length of the time step are important in exactly duplicating
the analytical solution.
A groundwater flow model with the Streamflow-Routing package has an advantage over
6.2.7 Simulation of a Flood in a River