Quantifying probabilities from ballistic models

Here is presented an extended version of the Matlab post-processing function developed for the Great Balls of Fire model for the probabilistic hazard assessment of ballistic impact.

Table of content

• tags: gbf
  • Table of content
  • Requirements
  • Source material
  • Dependencies
  • Access the code
• 1. From ballistic modelling to probabilistic hazard assessment
  • 1.1 The need of a reference area
  • 1.2 What probabilities?
• 2 Using the function
  • 2.1 Input arguments
    • 2.1.1 Using the GUI
    • 2.1.2 Using arguments
    • 2.1.3 Using an input structure
  • 2.2 Output argument
• 3 Outputs and results
  • 3.1 ASCII grid format
  • 3.2 Matlab format
    • .bal
    • .pixel
    • .concentric
    • .radial
• 4 Displaying results

Requirements

The initial function provided with the Great Balls of Fire model has been modified so output files of virtually any model can be loaded and processed through methods described here. Requirements are:

1. Impact coordinates must be defined in UTM WGS84
2. Files must be ascii and tab delimited
3. Columns in the output file should be organised as indicated in the table below. Note that adding extra columns is acceptable

Source material

Source material includes:

1. Our JVGR paper
2. The GBF user manual
3. This 2017 IAVCEI presentation

Dependencies

The post-processing functions rely on two files published on the Matlab File Exchange:

1. utm2ll by François Beauducel
2. plot_google_map by Zohar Bar-Yehuda

Access the code

The post-processing function can be obtained here

1. From ballistic modelling to probabilistic hazard assessment

1.1 The need of a reference area

Unlike for tephra deposits, the discrete nature of ballistic impacts requires to average single ballistic impacts on a grid. Grids can fall in two main categories that are polar and cartesian. However, averaging impacts on a grid creates a dependancy of the final result to the spatial resolution. In other words:

1. Is it acceptable for a grid to have pixels areas that vary with distance from the vent (e.g., polar grids)?
2. Since increasing the pixel area increases the probability of impact, is there a threshold of grid resolution that provides stable results?
3. How does the grid shape/resolution interacts with the number of simulated ballistics and affect the stability of results?

Probabilistic hazard assessment for ballistic impacts should therefore address these issues, one possible way to do so being through sensitivity analysis. This new post-processing function can be accessed either through a GUI or programatically, which facilitates sensitivity analyses. Refer to our JVGR paper for more information.

In this post-processing function, a true polar grid is not implemented. Instead, probabilities of impact are calculated using both a given distance from the vent (i.e., concentric rings) and at a given radial sector around the vent. The union probability of both approaches will result in a polar grid.

1.2 What probabilities?

In frequentist analyses, probabilities must represent a ratio between a number of ballistic impacts satisfying a given characteristics (e.g., a kinetic energy at impact that exceeds a threshold) and a total number of ballistics. Depending on our definition of the second term, let’s call it B_TOT, probabilities are going to express a different message.

If B_TOT is the total number of simulated ballistics, the probability expresses P(Z, E_T), that is:

If B_TOT is the total number of ballistics impacting a given zone, the probability expresses P(E_T|Z), that is:

These probabilities are significantly different, and both are considered in the post-processing approach presented here. For simplicity, we will refer to B_TOT as absolute probabilities and B_TOT as relative probabilities.

2 Using the function

2.1 Input arguments

Table 2 summarises the input parameters required by the processGBF function. Functions can be called using a GUI, arguments or a structure. The following steps assume that you are in the root of the folder containing the functions.

2.1.1 Using the GUI

In the Matlab command, type:

processGBF

This approach will open two consecutive GUIs that will prompt you to i) locate the input file and ii) define the additional variables described above.

2.1.2 Using arguments

This approach allows the user to enter all input argument separately from the command line:

processGBF(pth, name, gridRes, subset, eT, pT, dI, rI, vE, vN, vZ)

All variables refer to Table 1.

2.1.3 Using an input structure

The structure approach combines the arguments 2-9 of the argument approach into a structure. It is useful to use to output of a GBF post-processing run.

processGBF(pth, run)

where run is a Matlab structure named as the arguments 2-9 of the argument approach.

2.2 Output argument

Calling:

project = processGBF(...)

returns a Matlab structure containing all the output data… but stick around until the next section!

3 Outputs and results

Upon completion of the processGBF function, a folder named after the name variable is created, which contains results in a Matlab format (i.e., name.mat) and in a ESRI ASCII grid format. All probabilities are expressed in % and all energies are expressed in Joules.

3.1 ASCII grid format

Three main categories of ASCII files are written:

1. pixel, which use a cartesian grid
2. concentric, which use concentric zones around the vent
3. radial, which use radial sectors around the vent

Each of these categories have sub-categories defined by:

1. prob, which contain the exceedence probabilities (%) for ballistic impacts to exceed a given threshold of kinetic energy
2. en, which contain the typical kinetic energy (J) at impact for a given exceedance probabillity

The probability files are themselves differentiated between:

1. abs, which contain absolute probabilities and
2. rel, which contain relative probabilities

3.2 Matlab format

The Matlab output file, i.e. name.mat, contains the most comprehensive output. It is compiled as a Matlab structure containing:

1. inBal, which is a duplicate of the input arguments shown in Table 1
2. bal, which contains the data of all simulated particles
3. pixel, which contains the result of the processing performed using a cartesian grid
4. concentric, which contains the result of the processing performed using concentric zones around the vent
5. radial, which contains the result of the processing performed using radial sectors around the vent

.bal

.pixel

.concentric

Note that binM, NtM, NM, EM, PabsM and PrelM contain the same data as bin, Nt, N, E, Pabs and Prel gridded on a matrix, which can be used along east/north or lon/lat for plotting on a map.

.radial

Here again, binM, NtM, NM, EM, PabsM and PrelM contain the same data as bin, Nt, N, E, Pabs and Prel gridded on a matrix, which can be used along east/north or lon/lat for plotting on a map.

4 Displaying results

The displayGBF function offers an interactive GUI to plot the results of the processGBF function. Start it by typing

displayGBF

in the Matlab command. Then select the name*.mat file output of the processGBF function and you are good to go!