# Fixed grid monitoring¶

Warning

This feature has been modified and this documentation describes the version introduced in 5.2.1.

See also:

fgmax_tools_module - Tools for working with fgmax files

Fixed grid maximum monitoring / arrival times - For adding fgmax data to setrun.py

GeoClaw has the capability to monitor certain quantities on a specified “fixed grid” by interpolating from the AMR grids active at each time step, or at specified time increments. This is useful in particular to record the maximum flow depth observed at each point over the course of a computation, or the maximum flow velocity, momentum, or momentum flux. These quantities are often of interest in hazard modeling.

It is also possible to record the *arrival time* of a flow or wave at each
point on the grid.

The “grids” do not have to be rectangular grids aligned with the coordinate directions, but can consist of an arbitrary list of points that could also be points along a one-dimensional transect or points following a coastline, for example. It is also possible to specify logically rectangular grids of points covering an arbitrary quadrilateral.

Each grid is specified by an input file in a specified form described below. The list of file names for desired grids is specified in the setrun function, see Fixed grid maximum monitoring / arrival times.

This is an improved version of the algorithms used in earlier versions of GeoClaw, and now correctly interpolates when a grid point lies near the junction of two grid patches, which was not always handled properly before. The earlier version can still be used for outputing results at intermediate times on a fixed grid (see Fixed grid output), but is not recommended for the purpose of monitoring maxima or arrival times.

## Input file specification¶

(changed in Clawpack 5.2.0.)

The GeoClaw Fortran code reads in one or more files that specify grid(s) for monitoring values during the computation.

The input file(s) are specified to GeoClaw by a list of file names set in setrun.py by setting rundata.fgmax_data.fgmax_files. The order the files appear in this list determines the number assigned to this grid (starting with 1) that may be needed for processing or plotting the results.

Currently at most 5 fgmax grids are allowed by default. If you need more, you can adjust the parameter FG_MAXNUM_FGRIDS in $CLAW/geoclaw/src/2d/shallow/fgmax_module.f90 and the do make new to recomile everything that depends on this module.

Each input file describing a grid of points has the following form:

```
tstart_max
tend_max
dt_check
min_level_check
arrival_tol
point_style
```

followed by additional lines that depend on the value of point_style.

If point_style == 0, an arbitrary collection of (x,y) points is allowed and all must be listed, preceeded by the number of points:

```
npts # number of points
x1 y1 # first point
x2 y2 # second point
... # etc.
```

These points need not lie on a regular grid and can be specified in any order.

If point_style == 1, a 1-dimensional transect of points is specified by the next three lines of the file, in the form:

```
npts # number of points to generate
x1, y1 # first point
x2, y2 # last point
```

If point_style == 2, a 2-dimensional cartesian of points is specified by the next three lines of the file, in the form:

```
nx, ny # number of points in x and y (nx by ny grid)
x1, y1 # lower left corner of cartesian grid
x2, y2 # upper right corner of cartesian grid
```

If point_style == 3, a 2-dimensional logically rectangular array of points is specified by the next five lines of the file, in the form:

```
n12, n23 # number of points along adjacent edges (see below)
x1, y1 # first corner of grid
x2, y2 # second corner of grid
x3, y3 # third corner of grid
x4, y4 # fourth corner of grid
```

The corners should define a convex quadrilateral (ordered clockwise around the perimeter). An array of points will be defined as the intersection points of two sets of lines. The first set is obtained by connecting n12 equally spaced points on the side from (x1,y1) to (x2,y2) with the same number of points equally spaced on the side from (x3,y3) to (x4,y4). The second set of lines is obtained by connecting n23 equally spaced points on the side from (x2,y2) to (x3,y3) with the same number of points equally spaced on the side from (x4,y4) to (x1,y1)

The other paramters in the input file are:

tstart_max : float

starting time to monitor maximum

tend_max : float

ending time to monitor maximum

dt_check : float

time increment for monitoring maximum and arrivals. Interpolate to fixed grid and update values only if the time since the last updating exceeds this time increment. Set to 0 to monitor every time step.

min_level_check : integer

Minimum AMR level to check for updating the maximum value observed and the arrival time. Care must be taken in selecting this value since the maximum observed when interpolating to a point from a coarse AMR level may be much larger than the value that would be seen on a fine grid that better resolves the topography at this point. Often AMR “regions” are used to specify that a fine grid at some level L should always be used in the region of interest over the time period from start_max to tend_max, and then it is natural to set min_level_check to L.

arrival_tol : float

The time reported as the “arrival time” is the first time the value of the surface elevation is greater than sea_level + arrival_tol.

## Tools to create a input file¶

See class FGmaxGrid in the fgmax_tools_module. The function FGmaxGrid.write_input_data can be used to create an input file of the form described above, and may be useful if you want to use Python to assist in setting the parameters or defining a set of points to list with point_style == 0.

## Values to monitor¶

The values to be monitored are specified by the subroutine fgmax_values. The default subroutine found in the library $CLAW/geoclaw/src/2d/shallow/fgmax_values.f90 is now set up to monitor the depth h (rather than the value eta_tilde used in Version 5.1) and optionally will also monitor the speed \(s = \sqrt{u^2 + v^2}\) and three other quantities (the momentum \(hs\), the momentum flux \(hs^2\), and \(-h\), which is useful to monitor the minimum depth at each point, e.g. in a harbor where ships may be grounded).

The values monitored by the default routine described above is determined by the value of the fgmax_module variable FG_NUM_VAL, which can be set to 1, 2, or 5. This value is now read in from the data file fgmax.data and can be set by specifying the value of rundata.fgmax_data.num_fgmax_val in setrun.py.

## Choice of interpolation procedure¶

The library routine geoclaw/src/2d/shallow/fgmax_interpolate.f90 has been improved in 5.2.0 to fix some bugs. This routine does bilinear interpolation the finite volume grid centers to the fixed grid in order to update the maximum of values such as depth or velocity.

An alternative version of this routine has been added in 5.2.0 that does piecewise constant interpolation instead. This simply uses the value in the finite volume grid cell that contains the fixed grid point (0 order extrapolation) and avoids problems sometimes seen when doing linear interpolation near the margins of the flow.

This routine is in fgmax_interpolate0.f90 and is now recommended. To use this routine, modify the Makefile in an application directory to replace the line

```
$(GEOLIB)/fgmax_interpolate.f90 \
```

by

```
$(GEOLIB)/fgmax_interpolate0.f90 \
```

## Processing and plotting fgmax output¶

After GeoClaw has run, the output directory should contain the following files:

fort.FG1.valuemax containing values at each fgmax grid point,

fort.FG1.aux1 containing the bathymetry at each fgmax grid point.

If more than one fgmax grid was specified by rundata.fgmax_data.fgmax_files then there will be similar files fort.FG2.*, etc. They will be numbered in the order they appear in the list of input files.

These files are most easily dealt with using fgmax_tools_module by defining an object of class fgmax_tools.FGmaxGrid and using the class function read_output to read the output.

For some examples, see apps/tsunami/chile2010_fgmax and apps/tsunami/bowl_radial_fgmax in the Clawpack Applications repository. Sample results appear in the gallery_geoclaw.

TODO: Add a simple example here?

## Format of the output files¶

The paragraphs below describe in more detail the structure of the output files for users who need to process them differently.

If point_style == 0 for a grid then the points will be listed in the same order as specified in the input file. For other values of point_style (1-dimensional transects or 2-dimensional arrays) the values will be output in a natural order. In all cases the first two columns of each output file are the longitude and latitude of the point.

The remaining columns of fort.FG1.aux1 contain the bathymetry (the first component of the aux array in GeoClaw) interpolated to this fgmax grid point. There will be one column for each level of AMR (up to the number specified in setrun.py by the parameter amr_levels_max). These values are initialize to -0.99999000E+99 and only updated if interpolation at this level is used to update a value at this particular grid point. Values at different levels may be needed to interpret the output stored fort.FG1.valuemax, e.g. to determine if a point is onshore or off-shore, and to compute the maximum surface elevation at a point \(\eta = h + B\) from the maximum depth recorded at this point.

The file fort.FG1.valuemax contains the longitude and latitude of each point in columns 1 and 2. Column 3 contains the AMR level at which the maximum that is recorded was observed. (This is used to index into the array of bathymetry values from fort.FG1.aux1 when doing computations as described in the previous paragraph).

The **last** column of fort.FG1.valuemax contains the arrival time of the wave
at this grid point, as determined by the tolerance arrival_tol specified in
the input file. The time reported as the “arrival time” is the first time the
value of the surface elevation is greater than sea_level + arrival_tol.
Points where this value is -0.99999000E+99 never met this criterion, perhaps
because the point was never inundated.

The intermediate columns of fort.FG1.valuemax contain the maximum observed value of a quantity such as the flow depth along with the time at which the maximum was observed. How many values are recorded depends on the setting of rundata.fgmax_data.num_fgmax_val in setrun.py:

- If rundata.fgmax_data.num_fgmax_val == 1:

Column 4 contains maximum value of depth h,

Column 5 contains time of maximum h.

- If rundata.fgmax_data.num_fgmax_val == 2:

Column 4 contains maximum value of depth h,

Column 5 contains maximum value of speed,

Column 6 contains time of maximum h,

Column 7 contains time of maximum speed.

- If rundata.fgmax_data.num_fgmax_val == 5:

Columns 4,5,6,7,8 contain maximum value depth, speed, momentum, momentum flux, and hmin, respectively,

Columns 9,10,11,12,13 contain times the maximum was recorded, for each value above.