# ana5Utils

## distanceTimeAnalysis: Visualizing the temporal evolution of flow variables

With the functions gathered in this module, flow variables of avalanche simulation results can be
visualized in a distance versus time diagram, the so called **thalweg-time diagram**.
The **tt-diagram** provides a way to identify main features of the temporal evolution of
flow variables along the avalanche path.
This is based on the ideas presented in [FFGS13] and [RK20], where
avalanche simulation results have been transformed into the radar coordinate system to facilitate
direct comparison, combined with the attempt to analyze simulation results in an avalanche path
dependent coordinate system ([Fis13]).
In addition to the **tt-diagram**, `ana5Utils.distanceTimeAnalysis`

also offers the possibility to
produce simulated **range-time diagrams** of the flow variables with respect to a radar field
of view. With this, simulation results can be directly compared to radar measurements (for
example moving-target-identification (MTI) images from [KMS18]) in terms
of front position and inferred approach velocity. The colorcoding of the simulated
**range-time** diagrams show the average values of the chosen flow parameter
(e.g. flow thickness (FT), flow velocity (FV)) at specified range gates. This colorcoding is not directly
comparable to the MTI intensity given in the range-time diagram from radar measurements.

Note

The data processing for the **tt-diagram** and the **range-time diagram** can be done
*during run time* of `com1DFA`

, or as a postprocessing step. However, the second option
requires first saving and then reading all the required time steps of the flow variable fields,
which is much more computationally expensive compared to the first option.

### To run

During run-time of `com1DFA`

:

in your local copy of

`com1DFA/com1DFACfg.ini`

in [VISUALISATION] set createRangeTimeDiagram to True and choose if you want a*TTdiagram*by setting this flag to True or in the case of a simulated range-time diagram to Falsein your local copy of

`ana5Utils/distanceTimeAnalysisCfg.ini`

you can adjust the default settings for the generation of the diagramsrun

`runCom1DFA.py`

to calculate mtiInfo dictionary (saved as pickle in`avalancheDir/Outputs/com1DFA/distanceTimeAnalysis/mtiInfo_simHash.p`

) that contains the required data for producing the**tt-diagram**or**range-time diagram**run

`runScripts.runThalwegTimeDiagram.py`

or`runScripts.runRangeTimeDiagram.py`

and set the preProcessedData flag to True

As a postprocessing step:

first you need to run

`com1DFA`

to produce fields of the desired flow variable (e.g. FT, FV) of sufficient temporal resolution (every second), for this in your local copy of com1DFACfg.ini add e.g. FT to the resType and change the tSteps to 0:1have a look at

`runScripts.runThalwegTimeDiagram.py`

and`runScripts.runRangeTimeDiagram.py`

in your local copy of

`ana5Utils/distanceTimeAnalysisCfg.ini`

you can adjust the default settings for the generation of the diagrams

The resulting figures are saved to `avalancheDirectory/Outputs/ana5Utils`

.

Note

The **tt-diagram** requires info on an avalanche path (see ana3AIMEC: Aimec).
The simulated **range-time diagram** requires info on the coordinates of the radar location
(x0, y0), a point in the direction of the field of view (x1, y1), the aperture angle and the width of
the range gates. The maximum approach velocity is indicated in the distance-time diagrams with a
red star and is computed as the ratio of the distance traveled by the front and the respective
time needed for a time step difference of at least minVelTimeStep which is set to 2 seconds as
default. The approach velocity is a projection on the horizontal plane since the distance traveled
by the front is also measured in this same plane.

### Theory

### Thalweg-time diagram

First, the flow variable result field is transformed into a path-following coordinate system, of
which the centerline is the avalanche path.
For this step, functions from `ana3AIMEC`

are used.
The distance of the avalanche front to the *start of runout area point* is determined using a user
defined threshold of the flow variable. The front positions defined with this
method for all the time steps are shown as black dots in the **tt-diagram**.
The mean values of the flow variable are computed at cross profiles along the avalanche path for
each time step and included in the **tt-diagram** as colored field. When computing the mean values,
all the area where the flow variable is bigger than zero is taken into account.
For this analysis, all available flow variables can be chosen, but the interpretation of the
tt-diagram structures and the corresponding meaning of avalanche front may be different for
flow thickness or flow velocity.

### Simulated Range-Time diagram

The radar’s field of view is determined using its location, a point in the direction of the field of view and the horizontal (azimuth) aperture angle of the antenna. The elevation or vertical aperture angle is not yet included. The line-of-sight distance of every grid point in the simulation results to the radar location is computed. The simulation results which lie outside the radar’s field of view are masked. The distance of the avalanche front with respect to the radar location is determined for a user defined threshold in the flow variable and the average values of the result field for each range gate along the radar’s line of sight are computed. This data is plotted in a range-time diagram, where the black dots indicate the avalanche front, and the colored field indicates the mean values of the flow variable for the range gates at each time step.

## Automated path generation

Computational modules like \(\alpha\beta\) (com2AB: Alpha Beta Model) or analysis modules like the Thalweg-time diagram (ana5Utils) or Aimec (ana3AIMEC: Aimec) require an avalanche path and split point as input. This avalanche path and split point are usually created manually based on an expert opinion. The objective of this module is to automatically generate an avalanche path from a dense flow avalanche (DFA) simulation and placing a split point. The path is generated from the center of mass position of the dense material, so it is called the mass averaged path. It is extended towards the top of the release area and at the bottom. Therefore it covers the entire length of the avalanche with some buffer in the runout area. The split point is extracted from the parabola that is fitted on to the avalanche path profile.

### Input

The automatic path generation needs dense flow simulation results as input. These can be flow mass and flow thickness or particles for multiple time steps. com1DFA provides these already in the correct way.

We provide `runComputeDFAPath`

, in which two options exist:

DFA simulation results already exist: in this case, you want to provide these as inputs to the path generation function. The flag

`runDFAModule`

in`runComputeDFAPath`

is set to`False`

. You need to provide the avalanche directory in your`local_avaframeCfg.ini`

file. This avalanche directory should already have`Outputs/com1DFA`

with one or multiple simulation results. The simulation DEM is also required.No DFA simulation results exist: use com1DFA to generate the simulation results before generating a path. Change the

`runDFAModule`

flag in`runComputeDFAPath`

to True. The default configuration for com1DFA is read.`tSteps`

are adjusted,`resType`

and`simTypeList`

are modified before running com1DFA.

### Outputs

A mass averaged path is produced for each com1DFA simulation. The path is/are saved in
`avalancheDir/Outputs/DFAPath`

### To run automated path

go to

`AvaFrame/avaframe`

copy

`ana5Utils/DFAPathGenerationCfg.ini`

to`ana5Utils/local_DFAPathGenerationCfg.ini`

and edit (if not, default values are used)run:

python3 runScripts/runComputeDFAPath.py

### Theory automated path

#### Mass average path

Any DFA simulation should be able to produce information about mass distribution for different time steps of the simulation (either flow thickness, mass, velocities… rasters or particles). This information is used to compute time dependent mass average quantities such as position (center of mass), velocity… For a flow quantity \(\mathbf{a}(\mathbf{x}, t)\), the associated mass averaged quantity is defined by:

where \(m_k\) respectively \(\mathbf{a}_k(t)\) defines the mass respectively flow quantity of particle or raster cell \(k\). Applying the mass averaging to \((x, y, z)\) gives the mass average path profile.

Note

The mass average path profiles does not necessarily lie on the topography

It is also possible to compute the mass averaged velocity squared \(\overline{\mathbf{u^2}}(t)\), kinetic energy \(\overline{\frac{1}{2}m\mathbf{u^2}}(t)\) or travel distance \(s\) (which are used in the Energy line test).

The path is resampled at `nCellsResample`

x cellsize and is extended towards the release area top
to produce meaningful results when used in the com2AB module.
Since results from the \(\alpha\beta\) analysis depend on the path profile start,
moving the starting point of the profile will shift the \(\alpha\) upwards or downwards and
affect the runout value.

#### Extending path towards the top (release)

There are two options available to extend the mass averaged path profile in the release area
(`extTopOption`

in the configuration file):

Extend the path up to the highest point in the release (highest particle or highest cell depending on which particles or rasters are available).

Extend the path towards the point that will lead to the longest runout. This point does not necessarily coincide with the highest point in the release area and corresponds to the point for which \((\Delta z - \Delta s \tan{\alpha})\) is maximum. \(\alpha\) corresponds to the angle of the runout line going from first to last point of the mass averaged line. \(\Delta z\) and \(\Delta s\) represent the vertical and horizontal distance between a point in the release and the first point of the mass averaged path profile.

#### Extending path towards the bottom (runout)

It is also necessary to extend the profile in the runout area. This is done by finding the
direction of the path given by the few last points in the path in (x,y) (all points at a distance
`nCellsMinExtend`

x cellSize < distance < `nCellsMaxExtend`

x cellSize)) and extending in
this direction for a given percentage (`factBottomExt`

) of the total length of the path \(s\).

#### Split point generation

A parabolic curve is fitted to the avalanche path profile extracted from the DFA simulation (non-extended profile),
where the first and last point of the parabolic profile match the avalanche path profile. To find the
best fitting parabolic profile, an additional constraint is needed. Two options are available:
the default one (```
fitOption``= 0) minimises the distance between the parabolic profile and the avalanche path
profile. The second option (``fitOption``= 1) matches the end slope of the parabola to the profile.
This parabolic fit determines the split point location. It is the first point for which the slope is
lower than the ``slopeSplitPoint
```

angle. This point is then projected on the avalanche path profile.

#### Resampling

If the center of mass positions are derived in an equal time interval from the simulations,
derived points will not be spaced equally due to variations in flow velocity.
Especially in the release and runout area, lower velocites result in a denser spacing of extracted centers of mass,
which can cause a crossing of grid lines that are drawn perpendicularly to the thalweg over the width of the domain.
In order to reduce these overlaps, a the resampling function `in3Utils.geoTrans.prepareLine()`

can be used,
where the thalweg is generated based on a spline of degree k scipy splprep and a user defined approximate distance between points along the spline.