# Fixed grid monitoring (fgmax)¶

Warning

This feature has been modified and this documentation describes the version introduced in 5.7.0.

See also:

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

fgmax examples - Links to some examples

GeoClaw has the capability to monitor the maximum value of certain quantities on a specified fixed “fgmax 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.

**New in v5.7.0:** One can also specify a set of fgmax point by providing a
data file in the style of a topography DEM file with topo_type==3, but in
which the values provided are either 0 or 1 instead of topography values, with
1 indicating that a point should be used as an fgmax point, 0 indicating it
should not be used. This is particularly convenient if you want to select
fgmax points that are a subset of points on a DEM. This option is described
more below under point_style==4.

**New in v5.7.0:** Most fgmax information is now most easily set
in setrun.py and is written out to the file fgmax_grids.data
when this script is executed, e.g. by “make data”. The information
required is described below. See also Fixed grid maximum monitoring / arrival times.

This is an improved version of the algorithms used in much 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 (fgout)), but is not recommended for the purpose of monitoring maxima or arrival times.

## Input file specification¶

**(Changed in Clawpack 5.7.0.)**

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

The fgmax grid(s) are specified to GeoClaw in setrun.py by setting rundata.fgmax_data.fgmax_grids to be a list of objects of class fgmax_tools.FGmaxGrid. 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. The output appears in files such as _output/fgmax0001.txt.

**New in v5.7.0:** You can now assign numbers to each fgmax gauge
using the fgno attribute, described below, rather than being numbered
sequentially by order specified in the setrun.py file.

Currently at most 50 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 fgmax_tools.FGmaxGrid object (fg, for example) describing a grid of points has the following attributes:

```
fg.fgno
fg.tstart_max
fg.tend_max
fg.dt_check
fg.min_level_check
fg.arrival_tol
fg.interp_method
fg.point_style
```

These are explained further below.

Additional attributes depend on the value of fg.point_style.

### Different point styles¶

**If `fg.point_style == 0`,** an arbitrary collection of (x,y) points is allowed.
In this case you can either set

fg.npts

to the number of points and

fg.X fg.Y

to lists (or numpy arrays) of the coordinates, or you can set

fg.npts = 0

and set

fg.xy_file

to a string with the path to a file of the form:

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 attributes:

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

**If `point_style == 2`,** a 2-dimensional cartesian of points is specified by
the attributes:

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

**If `point_style == 3`,** a 2-dimensional logically rectangular array
of points is specified by the attributes:

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

**If `point_style == 4`,** a file is expected that has the form of a
topofile with topo_type == 3 as described in Topography data.
This file has a header that describes a uniform 2d grid of points, followed
by one line for each row of the grid (moving from north to south).
Unlike a standard topofile, the values are not topography elevations,
however, but are either 1 or 0, with the value 1 indicating that this point
should be used as an fgmax point.

Other tools are available to construct such a file by preprocessing a topography DEM and selecting only the points that satisfy certain criteria. For example, if we only want to capture onshore inundation depths and it is known that regions above a certain elevation will always stay dry, then we may want to select only points that are onshore and below this elevation. See Marching Front algorithm for more details and examples.

### Other attributes¶

The standard required attributes for any fgmax_tools.FGmaxGrid object are:

fgno : int

The number of this fgmax grid, should be a positive integer with at most 4 digits since the output file will then have the form fgmax0001.txt, for example, if fgno = 1. If these are not specified then they will be numbered sequentially based on the order they are specified in the fgmax_grids list.

tstart_max : float

Starting time to monitor maximum. Often we only want to monitor on the finest grids around the location of interest, and only after waves arrive, and this can be chosen correspondingly.

tend_max : float

Ending time to monitor maximum. Set to e.g. 1e9 to monitor until end of simulation

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.

But also note that if we monitor over multiple levels then we also keep track of what level the current maximum was computed on. If the level at this point is greater than the level used for the current maximum (because new finer grids were introduced since the last monitor time) then the old maximum is discarded and the current value as used as to reinitialize the maximum at this point.

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.

Note that this captures the first positive wave but doesn’t capture the time of arrival of the first wave if it is a leading depression rather than a positive wave.

interp_method : int

The method to be used to interpolate from finite volume cell averages in GeoClaw to pointwise values at the fgmax points.

The default is 0, meaning we take the value directly from the cell average in the grid cell containing the fgmax point (zero-order piecewise constant interpolation).

Setting to 1 will instead use bilinear interpolation between 4 cell centers. This is not recommended since it can give spurious results near the margins of the flow. See below, Choice of interpolation procedure.

## 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 read in from the data file fgmax_grids.data and can be set by specifying the value of rundata.fgmax_data.num_fgmax_val in setrun.py.

## Choice of interpolation procedure¶

Before v5.7.0, the choice of interpolation procedure was governed by use of the library routine geoclaw/src/2d/shallow/fgmax_interpolate.f90 (for bilinear interpolation) or geoclaw/src/2d/shallow/fgmax_interpolate0.f90 (for constant interpolation).

**Starting in v5.7.0,** there is a single library routine
geoclaw/src/2d/shallow/fgmax_interp.f90 and the choice is controlled by
the fg.interp_method parameter described above.

Setting fg.interp_method = 0 is recommended since interpolating the fluid depth and the topography separately and then computing the surface elevation by adding these may give unrealistic high values. See Nearshore interpolation.

## A simple example¶

This is taken from $CLAW/geoclaw/examples/tsunami/radial-ocean-island-fgmax/setrun.py, where other point styles are also illustrated:

```
from clawpack.geoclaw import fgmax_tools
# Points on a uniform 2d grid:
fg = fgmax_tools.FGmaxGrid()
fg.point_style = 2 # uniform rectangular x-y grid
fg.x1 = 14.25
fg.x2 = 14.65
fg.y1 = 50.10
fg.y2 = 50.35
fg.dx = 15/ 3600. # desired resolution of fgmax grid
fg.min_level_check = amrdata.amr_levels_max # which levels to monitor max on
fg.tstart_max = 8000. # just before wave arrives
fg.tend_max = 1.e10 # when to stop monitoring max values
fg.dt_check = 20. # how often to update max values
fg.interp_method = 0 # 0 ==> pw const in cells, recommended
rundata.fgmax_data.fgmax_grids.append(fg) # written to fgmax_grids.data
```

## Processing and plotting fgmax output¶

After GeoClaw has run, the output directory should contain files of this form for each fgmax grid:

fgmax0001.txt

**Note:** This file format is new in Version 5.7.0. Previously two files
such as fort.FG1.valuemax and fort.FG1.aux1 were created to each
fgmax grid. Now the topo value at each grid point is included along with
the max values in the single file.

If more than one fgmax grid was specified by rundata.fgmax_data.fgmax_grids then there will be similar files fgmax0002.txt, etc. They will be numbered in the order they appear in the list of input files in setrun.py unless you explicitly set fg.fgno in which case these numbers will be used.

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

For examples, see fgmax examples.

## 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 columns of fgmax0001.txt contain the following values, where N refers to the number of quantities of interest being monitored, as specified by rundata.fgmax_data.num_fgmax_val and described further below:

Column 1: longitude

Column 2: latitude

Column 3: AMR level

Column 4: topo value B

Columns 5 to 5+N: maximum value recorded of each QoI

Columns 6+N to 5+2N: time max value was recorded

Column 6+2N: arrival time

The AMR level is the level of finest level grids covering this fgmax point at the time the maximum was recorded.

The “topo value B” is the value of the GeoClaw topography B interpolated to the fgmax point on this AMR level (with the method of interpolation being specified by fg.interp_method, as for the values).

The value of N above is assumed to be 1, 2, or 5 in the default routines, as specified in setrun.py by the value of rundata.fgmax_data.num_fgmax_val. The quantities monitored are:

- If rundata.fgmax_data.num_fgmax_val == 1:

Column 5 contains maximum value of depth h,

Column 6 contains time of maximum h.

- If rundata.fgmax_data.num_fgmax_val == 2:

Column 5 contains maximum value of depth h,

Column 6 contains maximum value of speed,

Column 7 contains time of maximum h,

Column 8 contains time of maximum speed.

- If rundata.fgmax_data.num_fgmax_val == 5:

Columns 5,6,7,8,9 contain maximum value depth, speed, momentum, momentum flux, and hmin, respectively,

Columns 10,11,12,13,14 contain times the maximum was recorded, for each value above.

The **last** column of fgmax0001.txt 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.

## fgmax examples¶

For an example of how to process and plot the fgmax results, see the notebook make_input_files.ipynb in the directory $CLAW/geoclaw/examples/tsunami/radial-ocean-island-fgmax or the rendered version linked from the README in the GeoClaw Gallery

For another examples, see $CLAW/geoclaw/examples/tsunami/chile2010_fgmax-fgout and its README.