Introduction

While revisiting Fortran through the book Modern Fortran by Milan Curcic, I reached Chapter 4, which dives into solving the 1D shallow water equations numerically. The chapter wraps up with a Python script for visualizing results as static figures, but I decided that an animation would be better to bring the solution to life. In this post, I share my approach to creating that animation using Python and Jupyter Notebook.

Methods

To transform raw data into an animated plot, the Python libraries NumPy and Matplotlib are used. NumPy simplifies handling numerical data, while Matplotlib generates figures and animates them through the FuncAnimation class. To display interactive plots in Jupyter Notebooks, it’s necessary the addition of ipympl. To save animations as videos, it is recommended the installation of a comprehensive multimedia framework, like FFmpeg. The import section of the code looks like this:

%matplotlib ipympl
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation, FFMpegWriter

The raw data is a table with 5001 rows and 101 columns, where each row represents a time step in the solution of the shallow water equations. The first element of each row indicates the time step, so only the other 100 elements characterize the wave elevation h as a function of the spatial position x. The raw data is retrieved from a text file and handled as follows:

data = np.loadtxt('tsunami.txt')
h = data[:,1:]
x = np.arange(1, h.shape[1]+1)

The next step is creating the base figure for the animation, allong with initializing the graph objects waterline(the water surface) and waterfill(the filled area bellow it). The code below describes this process:

fig = plt.figure(figsize=(7, 2.5))
ax = fig.add_axes((0.12, 0.2, 0.8, 0.7))
ax.set_xlim(1, 100)
ax.set_ylim(-0.2, 1.4)
ax.set_xticks(range(25, 125, 25))
ax.set_yticks(np.arange(-0.2, 1.6, 0.2))
ax.set_xlabel('Distance [m]')
ax.set_ylabel('Water elevation [m]')
ax.grid()

# Initialization.
waterline, = ax.plot([], [])
waterfill = ax.fill_between(x, -0.2, 0, color='b', alpha=0.4)

The waterflow function handles the updates of waterline and waterfill for each time step:

def waterflow(time_step):
    #waterfill update
    xverts = np.hstack((x, x[::-1]))
    yverts = np.hstack((-0.2*np.ones(x.shape), h[time_step,::-1]))
    verts = np.vstack((xverts, yverts)).T
    waterfill.set_verts([verts])

    waterline.set_data(x, h[time_step])
    ax.set_title(r'Water elevation [m], time step ' + str(time_step))

    return waterline,

The animation is generated by the Matplotlib FuncAnimation class through the execution of the waterflow function in a chosen sequence of time steps. The following code generates a frame every 10 time steps and displays the resulting animation:

anim = FuncAnimation(fig, waterflow, frames=range(0, 5002, 10), interval=100, blit=True) 
plt.show()

Alternatively, the animated plot can be saved to a video format by:

writer = FFMpegWriter(fps=10)
anim.save('waterflow.mp4', writer=writer)

Results

1D shallow water

References

  1. Milan Curcic. 2020. tsunami. https://github.com/modern-fortran/tsunami. (2025).
  2. J. D. Hunter. 2007. Matplotlib. https://matplotlib.org/stable/. (2025).

Appendices