Visualizing statistical data#

In addition to the graphical output discussed above, ASPECT produces a statistics file that collects information produced during each time step. For the remainder of this section, let us assume that we have run ASPECT with the input file discussed in Convection in a 2d box, simulating convection in a box. After running ASPECT, you will find a file called statistics in the output directory that, at the time of writing this, looked like this:

# 1: Time step number
# 2: Time (seconds)
# 3: Number of mesh cells
# 4: Number of Stokes degrees of freedom
# 5: Number of temperature degrees of freedom
# 6: Iterations for temperature solver
# 7: Iterations for Stokes solver
# 8: Velocity iterations in Stokes preconditioner
# 9: Schur complement iterations in Stokes preconditioner
# 10: Time step size (seconds)
# 11: RMS velocity (m/s)
# 12: Max. velocity (m/s)
# 13: Minimal temperature (K)
# 14: Average temperature (K)
# 15: Maximal temperature (K)
# 16: Average nondimensional temperature (K)
# 17: Outward heat flux through boundary with indicator 0 ("left") (W)
# 18: Outward heat flux through boundary with indicator 1 ("right") (W)
# 19: Outward heat flux through boundary with indicator 2 ("bottom") (W)
# 20: Outward heat flux through boundary with indicator 3 ("top") (W)
# 21: Visualization file name
 0 0.0000e+00 256 2467 1089  0 29 30 29 1.2268e-02 1.79026783e+00 2.54322608e+00
 1 1.2268e-02 256 2467 1089 32 29 30 30 3.7388e-03 5.89844152e+00 8.35160076e+00
 2 1.6007e-02 256 2467 1089 20 28 29 29 2.0239e-03 1.09071922e+01 1.54298908e+01
 3 1.8031e-02 256 2467 1089 15 27 28 28 1.3644e-03 1.61759153e+01 2.28931189e+01
 4 1.9395e-02 256 2467 1089 13 26 27 27 1.0284e-03 2.14465789e+01 3.03731397e+01
 5 2.0424e-02 256 2467 1089 11 25 26 26 8.2812e-04 2.66110761e+01 3.77180480e+01

In other words, it first lists what the individual columns mean with a hash mark at the beginning of the line and then has one line for each time step in which the individual columns list what has been explained above.1

This file is easy to visualize. For example, one can import it as a whitespace separated file into a spreadsheet such as Microsoft Excel or OpenOffice/LibreOffice Calc and then generate graphs of one column against another. Or, maybe simpler, there is a multitude of simple graphing programs that do not need the overhead of a full fledged spreadsheet engine and simply plot graphs. One that is particularly simple to use and available on every major platform is Gnuplot. It is extensively documented at

Gnuplot is a command line program in which you enter commands that plot data or modify the way data is plotted. When you call it, you will first get a screen that looks like this:

/home/user/aspect/output gnuplot

        G N U P L O T
        Version 4.6 patchlevel 0    last modified 2012-03-04
        Build System: Linux x86_64

        Copyright (C) 1986-1993, 1998, 2004, 2007-2012
        Thomas Williams, Colin Kelley and many others

        gnuplot home:
        faq, bugs, etc:   type "help FAQ"
        immediate help:   type "help"  (plot window: hit 'h')

Terminal type set to 'qt'

At the prompt on the last line, you can then enter commands. Given the description of the individual columns given above, let us first try to plot the heat flux through boundary 2 (the bottom boundary of the box), i.e., column 19, as a function of time (column 2). This can be achieved using the following command:

plot "statistics" using 2:19

The left panel of Fig. 16 shows what Gnuplot will display in its output window. There are many things one can configure in these plots (see the Gnuplot manual referenced above). For example, let us assume that we want to add labels to the \(x\)- and \(y\)-axes, use not just points but lines and points for the curves, restrict the time axis to the range \([0,0.2]\) and the heat flux axis to \([-10:10]\), plot not only the flux through the bottom but also through the top boundary (column 20) and finally add a key to the figure, then the following commands achieve this:

set xlabel "Time"
  set ylabel "Heat flux"
  set style data linespoints
  plot [0:0.2][-10:10] "statistics" using 2:19 title "Bottom boundary", \
                       "statistics" using 2:20 title "Top boundary"

If a line gets too long, you can continue it by ending it in a backslash as above. This is rarely used on the command line but useful when writing the commands above into a script file, see below. We have done it here to get the entire command into the width of the page.


Fig. 16 Visualizing the statistics file obtained from the example in Convection in a 2d box using Gnuplot: Output using simple commands.#

For those who are lazy, Gnuplot allows to abbreviate things in many different ways. For example, one can abbreviate most commands. Furthermore, one does not need to repeat the name of an input file if it is the same as the previous one in a plot command. Thus, instead of the commands above, the following abbreviated form would have achieved the same effect:

se xl "Time"
  se yl "Heat flux"
  se sty da lp
  pl [:0.2][-10:10] "statistics" us 2:19 t "Bottom boundary", "" us 2:20 t "Top boundary"

This is of course unreadable at first but becomes useful once you become more familiar with the commands offered by this program.

Once you have gotten the commands that create the plot you want right, you probably want to save it into a file. Gnuplot can write output in many different formats. For inclusion in publications, either eps or png are the most common. In the latter case, the commands to achieve this are

set terminal png
  set output "heatflux.png"

The last command will simply generate the same plot again but this time into the given file. The result is a graphics file similar to the one shown in Fig. 19.


After setting output to a file, all following plot commands will want to write to this file. Thus, if you want to create more plots after the one just created, you need to reset output back to the screen. On Linux, this is done using the command set terminal X11. You can then continue experimenting with plots and when you have the next plot ready, switch back to output to a file.

What makes Gnuplot so useful is that it doesn’t just allow entering all these commands at the prompt. Rather, one can write them all into a file, say plot-heatflux.gnuplot, and then, on the command line, call

gnuplot plot-heatflux.gnuplot

to generate the heatflux.png file. This comes in handy if one wants to create the same plot for multiple simulations while playing with parameters of the physical setup. It is also a very useful tool if one wants to generate the same kind of plot again later with a different data set, for example when a reviewer requested additional computations to be made for a paper or if one realizes that one has forgotten or misspelled an axis label in a plot.2

Gnuplot has many many more features we have not even touched upon. For example, it is equally happy to produce three-dimensional graphics, and it also has statistics modules that can do things like curve fits, statistical regression, and many more operations on the data you provide in the columns of an input file. We will not try to cover them here but instead refer to the manual at You can also get a good amount of information by typing help at the prompt, or a command like help plot to get help on the plot command.


With input files that ask for initial adaptive refinement, the first time step may appear twice because we solve on a mesh that is globally refined and we then start the entire computation over again on a once adaptively refined mesh (see the parameters in Mesh refinement for how to do that).


In my own work, I usually save the ASPECT input file, the statistics output file and the Gnuplot script along with the actual figure I want to include in a paper. This way, it is easy to either re-run an entire simulation, or just tweak the graphic at a later time. Speaking from experience, you will not believe how often one wants to tweak a figure long after it was first created. In such situations it is outstandingly helpful if one still has both the actual data as well as the script that generated the graphic.